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Subgroup label Subgroup order Cyclic Abelian Solvable
Normal Characteristic Perfect Maximal Central
Ambient label Ambient order Direct product Semidirect product
Quotient label Subgroup index Cyclic quotient Abelian quotient Solvable quotient
Maximal quotient Non-trivial proper Hall subgroup Sylow subgroup
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Results (1-50 of 734 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1152.156064.1.a1.a1 $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_1$ $1$ ✓
1152.156064.2.a1.a1 $S_3\times D_4\times A_4$ $2^{6} \cdot 3^{2}$ ✓ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.156064.2.b1.a1 $S_3\times A_4:Q_8$ $2^{6} \cdot 3^{2}$ ✓ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.156064.2.c1.a1 $S_3\times A_4:C_8$ $2^{6} \cdot 3^{2}$ ✓ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.156064.2.d1.a1 $C_6.\GL(2,\mathbb{Z}/4)$ $2^{6} \cdot 3^{2}$ ✓ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.156064.2.e1.a1 $C_6.\GL(2,\mathbb{Z}/4)$ $2^{6} \cdot 3^{2}$ ✓ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.156064.2.f1.a1 $C_6.\GL(2,\mathbb{Z}/4)$ $2^{6} \cdot 3^{2}$ ✓ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.156064.2.g1.a1 $C_6.\GL(2,\mathbb{Z}/4)$ $2^{6} \cdot 3^{2}$ ✓ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.156064.3.a1.a1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $3$ $-$
1152.156064.3.b1.a1 $S_3\times C_2^2:\SD_{16}$ $2^{7} \cdot 3$ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $3$ $-$
1152.156064.4.a1.a1 $C_4\times S_3\times A_4$ $2^{5} \cdot 3^{2}$ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.156064.4.b1.a1 $C_2^3.C_6^2$ $2^{5} \cdot 3^{2}$ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.156064.4.c1.a1 $A_4\times D_{12}$ $2^{5} \cdot 3^{2}$ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.156064.4.d1.a1 $C_{12}.S_4$ $2^{5} \cdot 3^{2}$ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.156064.4.e1.a1 $C_{12}.S_4$ $2^{5} \cdot 3^{2}$ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.156064.4.f1.a1 $A_4:C_{24}$ $2^{5} \cdot 3^{2}$ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.156064.4.g1.a1 $C_{12}.S_4$ $2^{5} \cdot 3^{2}$ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.156064.4.h1.a1 $C_2\times A_4\times D_6$ $2^{5} \cdot 3^{2}$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.156064.4.i1.a1 $D_6.S_4$ $2^{5} \cdot 3^{2}$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.156064.4.j1.a1 $A_4\times C_3:D_4$ $2^{5} \cdot 3^{2}$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.156064.4.k1.a1 $C_2^3.S_3^2$ $2^{5} \cdot 3^{2}$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.156064.4.l1.a1 $D_{12}.D_6$ $2^{5} \cdot 3^{2}$ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.156064.6.a1.a1 $C_{12}:C_2^4$ $2^{6} \cdot 3$ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $S_3$ $2 \cdot 3$
1152.156064.6.b1.a1 $A_4:\SD_{16}$ $2^{6} \cdot 3$ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $S_3$ $2 \cdot 3$
1152.156064.6.c1.a1 $D_6.D_8$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.d1.a1 $D_6\times \SD_{16}$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.e1.a1 $D_6.D_8$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.f1.a1 $D_6\times \SD_{16}$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.g1.a1 $D_6:\SD_{16}$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.h1.a1 $D_6:\SD_{16}$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.i1.a1 $D_6:\SD_{16}$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.j1.a1 $D_6:\SD_{16}$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.k1.a1 $C_2^5:C_6$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.l1.a1 $C_2^4.D_6$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.m1.a1 $C_2\times A_4:C_8$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.n1.a1 $S_3\times C_2^2:Q_8$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.o1.a1 $D_6.\OD_{16}$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.p1.a1 $C_3\times C_2^2:\SD_{16}$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.q1.a1 $(C_2\times C_6):\SD_{16}$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.r1.a1 $A_4:\SD_{16}$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.s1.a1 $A_4:\SD_{16}$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.t1.a1 $A_4:\SD_{16}$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.u1.a1 $A_4:\SD_{16}$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.v1.a1 $D_{12}.D_4$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.6.w1.a1 $D_{12}.D_4$ $2^{6} \cdot 3$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.156064.8.a1.a1 $A_4\times D_6$ $2^{4} \cdot 3^{2}$ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $D_4$ $2^{3}$
1152.156064.8.b1.a1 $C_{12}\times A_4$ $2^{4} \cdot 3^{2}$ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2^3$ $2^{3}$ ✓
1152.156064.8.c1.a1 $A_4\times C_3:C_4$ $2^{4} \cdot 3^{2}$ ✓ ✓ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $D_4$ $2^{3}$
1152.156064.8.d1.a1 $C_2^2:C_6^2$ $2^{4} \cdot 3^{2}$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{3}$ $-$
1152.156064.8.e1.a1 $A_4\times D_6$ $2^{4} \cdot 3^{2}$ $D_6.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{3}$ $-$
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