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Note: Search results may be incomplete due to uncomputed quantities: Subgroup label (103813812 objects)

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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 90 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
192.12.2.b1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ $C_{24}:C_8$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.12.2.b1.b1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ $C_{24}:C_8$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.13.2.b1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.13.2.c1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.14.2.b1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ $C_{24}:C_8$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.14.2.b1.b1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ $C_{24}:C_8$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.38.2.b1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_{12}.D_8$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.39.2.b1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.42.2.c1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $D_{12}:C_8$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.43.2.c1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_{12}.Q_{16}$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.93.2.b1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_{12}.D_8$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.94.2.b1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_{12}.Q_{16}$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.243.2.d1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $D_6.C_4^2$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.244.2.d1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.246.2.d1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_{12}:\OD_{16}$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.267.2.e1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $D_6.C_4^2$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.268.2.d1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.383.2.f1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.389.2.c1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.390.2.c1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.393.2.e1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $D_{12}:C_8$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.397.2.e1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_{12}:\OD_{16}$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.479.2.c1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ $C_{12}.C_4^2$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.481.2.c1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ $C_{12}:\OD_{16}$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.484.2.c1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.484.2.c1.b1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.556.2.d1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ $C_{12}.C_4^2$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.556.2.d1.b1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ $C_{12}.C_4^2$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.559.2.c1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.569.2.d1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.571.2.d1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_{12}:\OD_{16}$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.572.2.f1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_{12}:D_8$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.576.2.e1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_{12}:\SD_{16}$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.582.2.a1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.582.2.a1.b1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.582.2.a1.c1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.583.2.b1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.584.2.e1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_{12}:\SD_{16}$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.588.2.c1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_{12}:Q_{16}$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.615.2.d1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.618.2.f1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.624.2.c1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.627.2.d1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.629.2.d1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_{12}.D_8$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.632.2.d1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_{12}:D_8$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.635.2.d1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_{12}:\SD_{16}$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.637.2.c1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_{12}.D_8$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.638.2.c1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_{12}.Q_{16}$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.639.2.c1.a1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_4^2.D_6$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
192.644.2.d1 $C_{12}:C_8$ $2^{5} \cdot 3$ ✓ ✓ ✓ $C_{12}:\SD_{16}$ $2^{6} \cdot 3$ $C_2$ $2$ ✓
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