$BQ^4_{1}\quad U=\iota\quad D=\iota\quad \hbox{order 2} \quad S, DPQ, c_1 = 8, c_2 = 0$\hfil\break $BQ^4_{2}\quad U=(\iota , \iota , (3 4) , (3 4))\quad D=(\iota , \iota , (3 4) , (3 4))\quad \hbox{order 2} \quad S, c_1 = 4, c_2 = 0$\hfil\break $BQ^4_{3}\quad U=(\iota , \iota , (3 4) , (3 4))\quad D=(\iota , (3 4) , (3 4) , (3 4))\quad \hbox{order 4} \quad c_1 = 4, c_2 = 0$\hfil\break $BQ^4_{4}\quad U=(\iota , \iota , (2 4 3) , (2 3 4))\quad D=(\iota , (3 4) , (3 4) , (3 4))\quad \hbox{order 6} \quad c_1 = 3, c_2 = 1$\hfil\break $BQ^4_{5}\quad U=(\iota , \iota , (3 4) , (3 4))\quad D=((3 4) , (3 4) , (3 4) , (3 4))\quad \hbox{order 4} \quad PQ, c_1 = 6, c_2 = 2$\hfil\break $BQ^4_{6}\quad U=(\iota , \iota , (1 2)(3 4) , (1 2)(3 4))\quad D=(\iota , \iota , (3 4) , (3 4))\quad \hbox{order 4} \quad c_1 = 2, c_2 = 2$\hfil\break $BQ^4_{7}\quad U=(\iota , \iota , (1 2) , (1 2))\quad D=((3 4) , (3 4) , \iota , \iota)\quad \hbox{order 4} \quad c_1 = 4, c_2 = 0$\hfil\break $BQ^4_{8}\quad U=(\iota , \iota , (1 2)(3 4) , (1 2)(3 4))\quad D=((3 4) , (3 4) , (3 4) , (3 4))\quad \hbox{order 4} \quad PQ, c_1 = 4, c_2 = 4$\hfil\break $BQ^4_{9}\quad U=(\iota , \iota , \iota , (2 3))\quad D=(\iota , \iota , \iota , (2 3))\quad \hbox{order 2} \quad S, c_1 = 4, c_2 = 0$\hfil\break $BQ^4_{10}\quad U=(\iota , (3 4) , (3 4) , (3 4))\quad D=(\iota , (3 4) , (3 4) , (3 4))\quad \hbox{order 2} \quad S, c_1 = 4, c_2 = 0$\hfil\break $BQ^4_{11}\quad U=(\iota , (3 4) , \iota , \iota)\quad D=((3 4) , \iota , \iota , \iota)\quad \hbox{order 4} \quad c_1 = 4, c_2 = 0$\hfil\break $BQ^4_{12}\quad U=(\iota , (3 4) , (3 4) , (3 4))\quad D=((3 4) , \iota , (3 4) , (3 4))\quad \hbox{order 4} \quad c_1 = 4, c_2 = 0$\hfil\break $BQ^4_{13}\quad U=(\iota , (3 4) , \iota , \iota)\quad D=((3 4) , (3 4) , \iota , \iota)\quad \hbox{order 4} \quad c_1 = 4, c_2 = 0$\hfil\break $BQ^4_{14}\quad U=(\iota , (3 4) , (3 4) , (3 4))\quad D=((3 4) , (3 4) , (3 4) , (3 4))\quad \hbox{order 4} \quad PQ, c_1 = 6, c_2 = 2$\hfil\break $BQ^4_{15}\quad U=(\iota , (3 4) , (1 4 3) , (1 3 4))\quad D=((3 4) , (3 4) , (3 4) , (3 4))\quad \hbox{order 6} \quad PQ, c_1 = 5, c_2 = 3$\hfil\break $BQ^4_{16}\quad U=(\iota , (2 3) , (3 4) , (2 4))\quad D=(\iota , (2 3 4) , (2 3 4) , (2 3 4))\quad \hbox{order 6} \quad c_1 = 2, c_2 = 0$\hfil\break $BQ^4_{17}\quad U=(\iota , (2 3 4) , (2 3 4) , (2 3 4))\quad D=(\iota , (2 4 3) , (2 4 3) , (2 4 3))\quad \hbox{order 2} \quad c_1 = 2, c_2 = 0$\hfil\break $BQ^4_{18}\quad U=(\iota , (2 3 4) , (2 3 4) , (2 3 4))\quad D=((2 3 4) , (2 4 3) , (2 4 3) , (2 4 3))\quad \hbox{order 6} \quad c_1 = 2, c_2 = 0$\hfil\break $BQ^4_{19}\quad U=(\iota , (2 4 3) , (2 4 3) , (2 4 3))\quad D=((2 3 4) , (2 3 4) , (2 3 4) , (2 3 4))\quad \hbox{order 6} \quad PQ, c_1 = 5, c_2 = 3$\hfil\break $BQ^4_{20}\quad U=(\iota , (1 3)(2 4) , (1 4)(2 3) , (1 2)(3 4))\quad D=((2 4 3) , (2 4 3) , (2 4 3) , (2 4 3))\quad \hbox{order 3} \quad PQ, c_1 = 4, c_2 = 4$\hfil\break $BQ^4_{21}\quad U=(\iota , \iota , (3 4) , (1 2)(3 4))\quad D=(\iota , \iota , (3 4) , (1 2)(3 4))\quad \hbox{order 2} \quad S, c_1 = 0, c_2 = 0$\hfil\break $BQ^4_{22}\quad U=(\iota , \iota , (1 2)(3 4) , (3 4))\quad D=(\iota , \iota , (3 4) , (1 2)(3 4))\quad \hbox{order 4} \quad c_1 = 0, c_2 = 0$\hfil\break $BQ^4_{23}\quad U=(\iota , \iota , \iota , (1 2 3))\quad D=(\iota , \iota , \iota , (1 2 3))\quad \hbox{order 6} \quad S, c_1 = 2, c_2 = 0$\hfil\break $BQ^4_{24}\quad U=(\iota , \iota , \iota , (1 3 2))\quad D=(\iota , \iota , \iota , (1 2 3))\quad \hbox{order 2} \quad c_1 = 2, c_2 = 0$\hfil\break $BQ^4_{25}\quad U=(\iota , \iota , (3 4) , (3 4))\quad D=((3 4) , (3 4) , (1 2)(3 4) , (1 2)(3 4))\quad \hbox{order 4} \quad c_1 = 4, c_2 = 0$\hfil\break $BQ^4_{26}\quad U=(\iota , \iota , (1 2) , (1 2))\quad D=(\iota , \iota , (1 2) , (1 2))\quad \hbox{order 2} \quad S, c_1 = 4, c_2 = 0$\hfil\break $BQ^4_{27}\quad U=(\iota , \iota , (1 2)(3 4) , (1 2)(3 4))\quad D=(\iota , \iota , (1 2)(3 4) , (1 2)(3 4))\quad \hbox{order 2} \quad S, c_1 = 0, c_2 = 0$\hfil\break $BQ^4_{28}\quad U=(\iota , \iota , (1 2) , (1 2))\quad D=((3 4) , (3 4) , (1 2) , (1 2))\quad \hbox{order 4} \quad c_1 = 2, c_2 = 2$\hfil\break $BQ^4_{29}\quad U=(\iota , \iota , (1 2)(3 4) , (1 2)(3 4))\quad D=((3 4) , (3 4) , (1 2)(3 4) , (1 2)(3 4))\quad \hbox{order 4} \quad c_1 = 2, c_2 = 2$\hfil\break $BQ^4_{30}\quad U=(\iota , (3 4) , \iota , \iota)\quad D=((3 4) , (3 4) , (1 4) , (1 3))\quad \hbox{order 6} \quad c_1 = 3, c_2 = 1$\hfil\break $BQ^4_{31}\quad U=((3 4) , (3 4) , (3 4) , (3 4))\quad D=((3 4) , (3 4) , (3 4) , (3 4))\quad \hbox{order 2} \quad S, DPQ, c_1 = 8, c_2 = 0$\hfil\break $BQ^4_{32}\quad U=((3 4) , (3 4) , (1 2)(3 4) , (1 2)(3 4))\quad D=((3 4) , (3 4) , (3 4) , (3 4))\quad \hbox{order 4} \quad PQ, c_1 = 6, c_2 = 2$\hfil\break $BQ^4_{33}\quad U=((3 4) , (3 4) , (1 2) , (1 2))\quad D=((3 4) , (3 4) , (1 2) , (1 2))\quad \hbox{order 2} \quad S, c_1 = 0, c_2 = 0$\hfil\break $BQ^4_{34}\quad U=((3 4) , (3 4) , (1 2)(3 4) , (1 2)(3 4))\quad D=((3 4) , (3 4) , (1 2)(3 4) , (1 2)(3 4))\quad \hbox{order 2} \quad S, c_1 = 4, c_2 = 0$\hfil\break $BQ^4_{35}\quad U=(\iota , \iota , \iota , (1 3 2))\quad D=((2 3) , (1 3) , (1 2) , (1 2 3))\quad \hbox{order 6} \quad c_1 = 2, c_2 = 0$\hfil\break $BQ^4_{36}\quad U=((3 4) , (1 4 2 3) , (1 2) , (1 3 2 4))\quad D=((2 3) , (1 3 4 2) , (1 4) , (1 2 4 3))\quad \hbox{order 2} \quad c_1 = 0, c_2 = 0$\hfil\break $BQ^4_{37}\quad U=((2 3 4) , (2 3 4) , (2 3 4) , (2 3 4))\quad D=((2 3 4) , (2 4 3) , (2 4 3) , (2 4 3))\quad \hbox{order 6} \quad PQ, c_1 = 5, c_2 = 3$\hfil\break $BQ^4_{38}\quad U=((2 3 4) , (2 3) , (3 4) , (2 4))\quad D=((2 4 3) , (2 3 4) , (2 3 4) , (2 3 4))\quad \hbox{order 6} \quad c_1 = 2, c_2 = 0$\hfil\break $BQ^4_{39}\quad U=((2 3 4) , (2 3 4) , (2 3 4) , (2 3 4))\quad D=((2 4 3) , (2 3) , (3 4) , (2 4))\quad \hbox{order 6} \quad PQ, c_1 = 5, c_2 = 3$\hfil\break $BQ^4_{40}\quad U=((2 3 4) , (2 3 4) , (2 3 4) , (2 3 4))\quad D=((2 4 3) , (2 4 3) , (2 4 3) , (2 4 3))\quad \hbox{order 2} \quad DPQ, c_1 = 8, c_2 = 0$\hfil\break $BQ^4_{41}\quad U=((2 3 4) , (2 4 3) , (2 4 3) , (2 4 3))\quad D=((2 4 3) , (2 3 4) , (2 3 4) , (2 3 4))\quad \hbox{order 2} \quad c_1 = 2, c_2 = 0$\hfil\break $BQ^4_{42}\quad U=((2 3 4) , (1 3 2) , (1 4 3) , (1 2 4))\quad D=((2 3 4) , (2 3 4) , (2 3 4) , (2 3 4))\quad \hbox{order 3} \quad PQ, c_1 = 4, c_2 = 4$\hfil\break $BQ^4_{43}\quad U=((2 4 3) , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 6} \quad PQ, c_1 = 5, c_2 = 3$\hfil\break $BQ^4_{44}\quad U=((2 4 3) , (1 3 4) , (1 4 2) , (1 2 3))\quad D=\iota\quad \hbox{order 3} \quad PQ, c_1 = 4, c_2 = 4$\hfil\break $BQ^4_{45}\quad U=((2 4) , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 4} \quad PQ, c_1 = 6, c_2 = 2$\hfil\break $BQ^4_{46}\quad U=((2 4) , \iota , (2 4) , \iota)\quad D=\iota\quad \hbox{order 4} \quad PQ, c_1 = 6, c_2 = 2$\hfil\break $BQ^4_{47}\quad U=((2 4) , (1 3) , (2 4) , (1 3))\quad D=\iota\quad \hbox{order 4} \quad PQ, c_1 = 4, c_2 = 4$\hfil\break $BQ^4_{48}\quad U=((2 4) , (1 4) , \iota , (1 2))\quad D=\iota\quad \hbox{order 6} \quad PQ, c_1 = 5, c_2 = 3$\hfil\break $BQ^4_{49}\quad U=((1 2) , (1 2) , (3 4) , (3 4))\quad D=((1 2) , (1 2) , (3 4) , (3 4))\quad \hbox{order 2} \quad S, c_1 = 0, c_2 = 0$\hfil\break $BQ^4_{50}\quad U=((1 2) , (1 2) , (3 4) , (3 4))\quad D=((1 2)(3 4) , (1 2)(3 4) , (3 4) , (3 4))\quad \hbox{order 4} \quad c_1 = 2, c_2 = 2$\hfil\break $BQ^4_{51}\quad U=((1 2) , (1 2) , (1 2)(3 4) , (1 2)(3 4))\quad D=((1 2)(3 4) , (1 2)(3 4) , (3 4) , (3 4))\quad \hbox{order 4} \quad c_1 = 4, c_2 = 0$\hfil\break $BQ^4_{52}\quad U=((1 2) , (1 2)(3 4) , (3 4) , (3 4))\quad D=((1 2) , (1 2)(3 4) , (3 4) , (3 4))\quad \hbox{order 2} \quad S, c_1 = 0, c_2 = 0$\hfil\break $BQ^4_{53}\quad U=((1 2) , (1 2)(3 4) , (3 4) , (3 4))\quad D=((1 2)(3 4) , (1 2) , (3 4) , (3 4))\quad \hbox{order 4} \quad c_1 = 0, c_2 = 0$\hfil\break $BQ^4_{54}\quad U=((1 2) , (1 2) , (3 4) , (3 4))\quad D=((1 2)(3 4) , (1 2)(3 4) , (1 2)(3 4) , (1 2)(3 4))\quad \hbox{order 4} \quad PQ, c_1 = 4, c_2 = 4$\hfil\break $BQ^4_{55}\quad U=((1 2) , (1 2) , (1 2)(3 4) , (1 2)(3 4))\quad D=((1 2) , (1 2) , (1 2)(3 4) , (1 2)(3 4))\quad \hbox{order 2} \quad S, c_1 = 4, c_2 = 0$\hfil\break $BQ^4_{56}\quad U=((1 2) , (1 2) , (1 2)(3 4) , (1 2)(3 4))\quad D=((1 2)(3 4) , (1 2)(3 4) , (1 2)(3 4) , (1 2)(3 4))\quad \hbox{order 4} \quad PQ, c_1 = 6, c_2 = 2$\hfil\break $BQ^4_{57}\quad U=((1 2)(3 4) , (1 2)(3 4) , (1 2)(3 4) , (1 2)(3 4))\quad D=((1 2)(3 4) , (1 2)(3 4) , (1 2)(3 4) , (1 2)(3 4))\quad \hbox{order 2} \quad S, DPQ, c_1 = 8, c_2 = 0$\hfil\break $BQ^4_{58}\quad U=((1 2)(3 4) , (1 3)(2 4) , (1 3)(2 4) , (1 2)(3 4))\quad D=((1 2 4 3) , (1 2 4 3) , (1 2 4 3) , (1 2 4 3))\quad \hbox{order 4} \quad PQ, c_1 = 4, c_2 = 4$\hfil\break $BQ^4_{59}\quad U=((1 2 3 4) , (1 4 3 2) , (1 3) , (2 4))\quad D=((1 2 4 3) , (1 3 4 2) , (2 3) , (1 4))\quad \hbox{order 2} \quad c_1 = 0, c_2 = 0$\hfil\break $BQ^4_{60}\quad U=((1 2 3 4) , (1 4 3 2) , (1 2 3 4) , (1 4 3 2))\quad D=((1 2 3 4) , (1 4 3 2) , (1 2 3 4) , (1 4 3 2))\quad \hbox{order 2} \quad S, c_1 = 0, c_2 = 0$\hfil\break $BQ^4_{61}\quad U=((1 2)(3 4) , (1 2)(3 4) , (1 2)(3 4) , (1 2)(3 4))\quad D=((1 3 4 2) , (1 2 4 3) , (1 2 4 3) , (1 3 4 2))\quad \hbox{order 4} \quad PQ, c_1 = 4, c_2 = 4$\hfil\break $BQ^4_{62}\quad U=((1 2)(3 4) , (1 3)(2 4) , (1 3)(2 4) , (1 2)(3 4))\quad D=((1 3)(2 4) , (1 2)(3 4) , (1 2)(3 4) , (1 3)(2 4))\quad \hbox{order 2} \quad c_1 = 0, c_2 = 0$\hfil\break $BQ^4_{63}\quad U=((1 2)(3 4) , (1 2)(3 4) , (1 2)(3 4) , (1 2)(3 4))\quad D=((1 3 2) , (1 2 4) , (1 4 3) , (2 3 4))\quad \hbox{order 3} \quad PQ, c_1 = 4, c_2 = 4$\hfil\break $BQ^4_{64}\quad U=((1 2 4 3) , (1 2 4 3) , (1 2 4 3) , (1 2 4 3))\quad D=((1 3 4 2) , (1 3 4 2) , (1 3 4 2) , (1 3 4 2))\quad \hbox{order 2} \quad DPQ, c_1 = 8, c_2 = 0$\hfil\break