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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
384.4310.1.a1 $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_1$ $1$
384.4310.2.a1 $C_2\times C_{12}.Q_8$ $2^{6} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_2$ $2$
384.4310.2.b1 $C_{12}.C_4^2$ $2^{6} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_2$ $2$
384.4310.2.c1 $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_2$ $2$
384.4310.3.a1 $C_4^2.D_4$ $2^{7}$ $2$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $3$ $-$
384.4310.4.a1 $C_2\times C_4\times C_{12}$ $2^{5} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_2^2$ $2^{2}$
384.4310.4.b1 $C_2\times C_4:C_{12}$ $2^{5} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_4$ $2^{2}$
384.4310.4.c1 $C_{12}.Q_8$ $2^{5} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_2^2$ $2^{2}$
384.4310.4.d1 $C_6.C_4^2$ $2^{5} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_2^2$ $2^{2}$
384.4310.4.e1 $C_{12}.Q_8$ $2^{5} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_4$ $2^{2}$
384.4310.4.f1 $C_2\times C_4:C_{12}$ $2^{5} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{2}$ $-$
384.4310.4.g1 $C_{12}.C_2^3$ $2^{5} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{2}$ $-$
384.4310.4.h1 $C_{12}.Q_8$ $2^{5} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{2}$ $-$
384.4310.4.i1 $C_6.C_4^2$ $2^{5} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{2}$ $-$
384.4310.6.a1 $C_4^2.C_2^2$ $2^{6}$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $S_3$ $2 \cdot 3$
384.4310.6.b1 $C_4.C_4^2$ $2^{6}$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2 \cdot 3$ $-$
384.4310.6.c1 $C_4^2.C_2^2$ $2^{6}$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2 \cdot 3$ $-$
384.4310.8.a1 $C_2^2\times C_{12}$ $2^{4} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $D_4$ $2^{3}$
384.4310.8.b1 $C_2^2\times C_{12}$ $2^{4} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_2\times C_4$ $2^{3}$
384.4310.8.c1 $C_4\times C_{12}$ $2^{4} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $D_4$ $2^{3}$
384.4310.8.d1 $C_4\times C_{12}$ $2^{4} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_2^3$ $2^{3}$
384.4310.8.e1 $C_4\times C_{12}$ $2^{4} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_2\times C_4$ $2^{3}$
384.4310.8.f1 $C_4:C_{12}$ $2^{4} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_2\times C_4$ $2^{3}$
384.4310.8.g1 $C_6:C_8$ $2^{4} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{3}$ $-$
384.4310.8.h1 $C_2^2\times C_{12}$ $2^{4} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{3}$ $-$
384.4310.8.i1 $C_4:C_{12}$ $2^{4} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{3}$ $-$
384.4310.8.j1 $C_6:C_8$ $2^{4} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{3}$ $-$
384.4310.8.k1 $C_4:C_{12}$ $2^{4} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{3}$ $-$
384.4310.8.l1 $C_4:C_{12}$ $2^{4} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{3}$ $-$
384.4310.12.a1 $C_2\times C_4^2$ $2^{5}$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $D_6$ $2^{2} \cdot 3$
384.4310.12.b1 $C_2^2.D_4$ $2^{5}$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_3:C_4$ $2^{2} \cdot 3$
384.4310.12.c1 $C_4.Q_8$ $2^{5}$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $D_6$ $2^{2} \cdot 3$
384.4310.12.d1 $C_4.Q_8$ $2^{5}$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_3:C_4$ $2^{2} \cdot 3$
384.4310.12.e1 $C_2^2.D_4$ $2^{5}$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{2} \cdot 3$ $-$
384.4310.12.f1 $C_2^2\times C_8$ $2^{5}$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{2} \cdot 3$ $-$
384.4310.12.g1 $C_4.Q_8$ $2^{5}$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{2} \cdot 3$ $-$
384.4310.12.h1 $C_8:C_4$ $2^{5}$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{2} \cdot 3$ $-$
384.4310.12.i1 $C_8:C_4$ $2^{5}$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{2} \cdot 3$ $-$
384.4310.16.a1 $C_2^2\times C_6$ $2^{3} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_2^2:C_4$ $2^{4}$
384.4310.16.b1 $C_2\times C_{12}$ $2^{3} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_2\times D_4$ $2^{4}$
384.4310.16.c1 $C_2\times C_{12}$ $2^{3} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_2^2:C_4$ $2^{4}$
384.4310.16.d1 $C_2\times C_{12}$ $2^{3} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_2^2\times C_4$ $2^{4}$
384.4310.16.e1 $C_2\times C_{12}$ $2^{3} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_2^2:C_4$ $2^{4}$
384.4310.16.f1 $C_2\times C_{12}$ $2^{3} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{4}$ $-$
384.4310.16.g1 $C_2\times C_{12}$ $2^{3} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{4}$ $-$
384.4310.16.h1 $C_2\times C_{12}$ $2^{3} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{4}$ $-$
384.4310.16.i1 $C_3:C_8$ $2^{3} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{4}$ $-$
384.4310.16.j1 $C_2\times C_{12}$ $2^{3} \cdot 3$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $2^{4}$ $-$
384.4310.24.a1 $C_2^2\times C_4$ $2^{4}$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_3:D_4$ $2^{3} \cdot 3$
384.4310.24.b1 $C_2^2\times C_4$ $2^{4}$ $C_2\times C_4^2.D_6$ $2^{7} \cdot 3$ $C_6:C_4$ $2^{3} \cdot 3$
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