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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 292 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1728.1701.1.a1.a1 $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_1$ $1$ ✓
1728.1701.2.a1.a1 $C_{12}^2.C_6$ $2^{5} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.1701.2.b1.a1 $C_{12}^2.C_6$ $2^{5} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.1701.2.c1.a1 $C_{12}^2.C_6$ $2^{5} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.1701.3.a1.a1 $C_{12}^2.C_2^2$ $2^{6} \cdot 3^{2}$ ✓ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_3$ $3$ ✓
1728.1701.3.b1.a1 $C_{12}^2.C_2^2$ $2^{6} \cdot 3^{2}$ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $3$ $-$
1728.1701.4.a1.a1 $C_4^2\times \He_3$ $2^{4} \cdot 3^{3}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.1701.4.b1.a1 $C_4:C_4\times \He_3$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_4$ $2^{2}$ ✓
1728.1701.4.b1.b1 $C_4:C_4\times \He_3$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_4$ $2^{2}$ ✓
1728.1701.4.c1.a1 $C_{12}.C_6^2$ $2^{4} \cdot 3^{3}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2}$ $-$
1728.1701.4.d1.a1 $C_6^2.C_{12}$ $2^{4} \cdot 3^{3}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2}$ $-$
1728.1701.4.e1.a1 $C_4:C_4\times \He_3$ $2^{4} \cdot 3^{3}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2}$ $-$
1728.1701.4.f1.a1 $C_6^2.C_{12}$ $2^{4} \cdot 3^{3}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2}$ $-$
1728.1701.6.a1.a1 $C_{12}^2.C_2$ $2^{5} \cdot 3^{2}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $S_3$ $2 \cdot 3$
1728.1701.6.b1.a1 $C_{12}^2.C_2$ $2^{5} \cdot 3^{2}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.1701.6.c1.a1 $C_{12}.D_{12}$ $2^{5} \cdot 3^{2}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.1701.6.d1.a1 $C_{12}.D_{12}$ $2^{5} \cdot 3^{2}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.1701.6.e1.a1 $C_{12}:C_{24}$ $2^{5} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.1701.6.f1.a1 $C_{12}:C_{24}$ $2^{5} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.1701.6.g1.a1 $C_{12}^2.C_2$ $2^{5} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.1701.8.a1.a1 $C_6.C_6^2$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $D_4$ $2^{3}$
1728.1701.8.b1.a1 $C_6.C_6^2$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $D_4$ $2^{3}$
1728.1701.8.c1.a1 $C_6.C_6^2$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2\times C_4$ $2^{3}$ ✓
1728.1701.8.d1.a1 $C_6.C_6^2$ $2^{3} \cdot 3^{3}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{3}$ $-$
1728.1701.8.d1.b1 $C_6.C_6^2$ $2^{3} \cdot 3^{3}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{3}$ $-$
1728.1701.8.e1.a1 $Q_8\times \He_3$ $2^{3} \cdot 3^{3}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{3}$ $-$
1728.1701.8.f1.a1 $C_3^2:C_{24}$ $2^{3} \cdot 3^{3}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{3}$ $-$
1728.1701.8.g1.a1 $Q_8\times \He_3$ $2^{3} \cdot 3^{3}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{3}$ $-$
1728.1701.8.h1.a1 $C_3^2:C_{24}$ $2^{3} \cdot 3^{3}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{3}$ $-$
1728.1701.9.a1.a1 $C_{12}.D_8$ $2^{6} \cdot 3$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $3^{2}$ $-$
1728.1701.9.b1.a1 $C_{12}.D_8$ $2^{6} \cdot 3$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $3^{2}$ $-$
1728.1701.9.c1.a1 $C_{12}.D_8$ $2^{6} \cdot 3$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $3^{2}$ $-$
1728.1701.12.a1.a1 $C_{12}^2$ $2^{4} \cdot 3^{2}$ ✓ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $D_6$ $2^{2} \cdot 3$
1728.1701.12.b1.a1 $C_{12}:C_{12}$ $2^{4} \cdot 3^{2}$ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_3:C_4$ $2^{2} \cdot 3$
1728.1701.12.b1.b1 $C_{12}:C_{12}$ $2^{4} \cdot 3^{2}$ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_3:C_4$ $2^{2} \cdot 3$
1728.1701.12.c1.a1 $C_{12}^2$ $2^{4} \cdot 3^{2}$ ✓ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
1728.1701.12.d1.a1 $C_{12}:C_{12}$ $2^{4} \cdot 3^{2}$ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_{12}$ $2^{2} \cdot 3$ ✓
1728.1701.12.d1.b1 $C_{12}:C_{12}$ $2^{4} \cdot 3^{2}$ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_{12}$ $2^{2} \cdot 3$ ✓
1728.1701.12.e1.a1 $C_4.C_6^2$ $2^{4} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.1701.12.f1.a1 $C_6:C_{24}$ $2^{4} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.1701.12.g1.a1 $C_{12}:C_{12}$ $2^{4} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.1701.12.h1.a1 $C_6:C_{24}$ $2^{4} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.1701.12.i1.a1 $C_4.C_6^2$ $2^{4} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.1701.12.j1.a1 $C_{12}.D_6$ $2^{4} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.1701.12.k1.a1 $C_{12}:C_{12}$ $2^{4} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.1701.12.l1.a1 $C_{12}.D_6$ $2^{4} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.1701.12.m1.a1 $C_{12}^2$ $2^{4} \cdot 3^{2}$ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.1701.12.n1.a1 $C_4.C_6^2$ $2^{4} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.1701.12.n1.b1 $C_4.C_6^2$ $2^{4} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.1701.12.o1.a1 $C_{12}:C_{12}$ $2^{4} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
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