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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 201 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1152.154927.1.a1.a1 $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ ✓ ✓ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_1$ $1$ ✓
1152.154927.2.a1.a1 $C_3\times Q_{16}.A_4$ $2^{6} \cdot 3^{2}$ ✓ ✓ ✓ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.154927.2.b1.a1 $C_{24}.S_4$ $2^{6} \cdot 3^{2}$ ✓ ✓ ✓ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.154927.2.c1.a1 $C_{24}.S_4$ $2^{6} \cdot 3^{2}$ ✓ ✓ ✓ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.154927.3.a1.a1 $C_4.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ ✓ ✓ ✓ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_3$ $3$ ✓
1152.154927.3.b1.a1 $C_3\times D_4.D_8$ $2^{7} \cdot 3$ ✓ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $3$ $-$
1152.154927.4.a1.a1 $C_{24}.A_4$ $2^{5} \cdot 3^{2}$ ✓ ✓ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.154927.4.b1.a1 $Q_8.C_6^2$ $2^{5} \cdot 3^{2}$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.154927.4.c1.a1 $C_{12}.S_4$ $2^{5} \cdot 3^{2}$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.154927.4.d1.a1 $C_3^2:Q_{32}$ $2^{5} \cdot 3^{2}$ ✓ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.154927.6.a1.a1 $C_{12}.C_2^4$ $2^{6} \cdot 3$ ✓ ✓ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $S_3$ $2 \cdot 3$
1152.154927.6.b1.a1 $Q_{16}.A_4$ $2^{6} \cdot 3$ ✓ ✓ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_6$ $2 \cdot 3$ ✓
1152.154927.6.c1.a1 $C_8.S_4$ $2^{6} \cdot 3$ ✓ ✓ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_6$ $2 \cdot 3$ ✓
1152.154927.6.d1.a1 $C_8.S_4$ $2^{6} \cdot 3$ ✓ ✓ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_6$ $2 \cdot 3$ ✓
1152.154927.6.e1.a1 $Q_{32}:C_6$ $2^{6} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.154927.6.f1.a1 $C_{12}.D_8$ $2^{6} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.154927.6.g1.a1 $C_6\times \SD_{32}$ $2^{6} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.154927.6.h1.a1 $\OD_{32}:C_6$ $2^{6} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.154927.6.i1.a1 $Q_{16}.A_4$ $2^{6} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.154927.6.j1.a1 $C_{24}.D_4$ $2^{6} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.154927.6.k1.a1 $\OD_{32}:C_6$ $2^{6} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.154927.8.a1.a1 $\SL(2,3):C_6$ $2^{4} \cdot 3^{2}$ ✓ ✓ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $D_4$ $2^{3}$
1152.154927.8.b1.a1 $\SL(2,3):C_6$ $2^{4} \cdot 3^{2}$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{3}$ $-$
1152.154927.8.c1.a1 $C_3^2\times Q_{16}$ $2^{4} \cdot 3^{2}$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{3}$ $-$
1152.154927.8.d1.a1 $C_3^2:Q_{16}$ $2^{4} \cdot 3^{2}$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{3}$ $-$
1152.154927.8.e1.a1 $C_3:C_{48}$ $2^{4} \cdot 3^{2}$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{3}$ $-$
1152.154927.8.f1.a1 $C_6.S_4$ $2^{4} \cdot 3^{2}$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{3}$ $-$
1152.154927.9.a1.a1 $D_4.D_8$ $2^{7}$ $2$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $3^{2}$ $-$
1152.154927.12.a1.a1 $\OD_{16}:C_6$ $2^{5} \cdot 3$ ✓ ✓ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $D_6$ $2^{2} \cdot 3$
1152.154927.12.b1.a1 $C_8.A_4$ $2^{5} \cdot 3$ ✓ ✓ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
1152.154927.12.c1.a1 $D_8:C_6$ $2^{5} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
1152.154927.12.d1.a1 $D_8:C_6$ $2^{5} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
1152.154927.12.e1.a1 $C_6\times D_8$ $2^{5} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
1152.154927.12.f1.a1 $C_{12}.D_4$ $2^{5} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
1152.154927.12.g1.a1 $C_6\times Q_{16}$ $2^{5} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
1152.154927.12.h1.a1 $C_8.C_{12}$ $2^{5} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
1152.154927.12.i1.a1 $C_2\times C_{48}$ $2^{5} \cdot 3$ ✓ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
1152.154927.12.j1.a1 $C_3\times \OD_{32}$ $2^{5} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
1152.154927.12.k1.a1 $C_6.C_2^4$ $2^{5} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
1152.154927.12.l1.a1 $\SL(2,3):C_2^2$ $2^{5} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
1152.154927.12.m1.a1 $\SL(2,3):C_2^2$ $2^{5} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
1152.154927.12.m1.b1 $\SL(2,3):C_2^2$ $2^{5} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
1152.154927.12.n1.a1 $Q_{16}:C_6$ $2^{5} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
1152.154927.12.o1.a1 $C_4.S_4$ $2^{5} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
1152.154927.12.p1.a1 $C_8.A_4$ $2^{5} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
1152.154927.12.q1.a1 $C_3\times \SD_{32}$ $2^{5} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
1152.154927.12.r1.a1 $C_3\times \SD_{32}$ $2^{5} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
1152.154927.12.r1.a2 $C_3\times \SD_{32}$ $2^{5} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
1152.154927.12.s1.a1 $C_3\times Q_{32}$ $2^{5} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
1152.154927.12.t1.a1 $C_3:Q_{32}$ $2^{5} \cdot 3$ $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
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