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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 590 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1728.23380.1.a1.a1 $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_1$ $1$ ✓
1728.23380.2.a1.a1 $C_{12}^2.C_6$ $2^{5} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.23380.2.b1.a1 $C_{12}^2.C_6$ $2^{5} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.23380.2.c1.a1 $C_{12}^2.C_6$ $2^{5} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.23380.2.d1.a1 $C_6^2.D_{12}$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.23380.2.d1.b1 $C_6^2.D_{12}$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.23380.2.e1.a1 $C_6^2.D_{12}$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.23380.2.e1.b1 $C_6^2.D_{12}$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.23380.3.a1.a1 $C_4^2.S_3^2$ $2^{6} \cdot 3^{2}$ ✓ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_3$ $3$ ✓
1728.23380.3.b1.a1 $C_{12}^2.C_2^2$ $2^{6} \cdot 3^{2}$ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $3$ $-$
1728.23380.3.c1.a1 $C_{12}^2.C_2^2$ $2^{6} \cdot 3^{2}$ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $3$ $-$
1728.23380.4.a1.a1 $C_3\times C_{12}^2$ $2^{4} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.23380.4.b1.a1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.23380.4.b1.b1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.23380.4.c1.a1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.23380.4.d1.a1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.23380.4.e1.a1 $C_{12}.C_6^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.23380.4.e1.b1 $C_{12}.C_6^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.23380.4.f1.a1 $C_{12}.C_6^2$ $2^{4} \cdot 3^{3}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2}$ $-$
1728.23380.4.g1.a1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2}$ $-$
1728.23380.4.h1.a1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2}$ $-$
1728.23380.4.i1.a1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2^{2}$ $-$
1728.23380.6.a1.a1 $C_{12}.D_{12}$ $2^{5} \cdot 3^{2}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $S_3$ $2 \cdot 3$
1728.23380.6.b1.a1 $C_{12}:C_{24}$ $2^{5} \cdot 3^{2}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $S_3$ $2 \cdot 3$
1728.23380.6.c1.a1 $C_{12}.D_{12}$ $2^{5} \cdot 3^{2}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.23380.6.d1.a1 $C_{12}^2.C_2$ $2^{5} \cdot 3^{2}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.23380.6.e1.a1 $C_{12}:C_{24}$ $2^{5} \cdot 3^{2}$ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.23380.6.f1.a1 $C_{12}.D_{12}$ $2^{5} \cdot 3^{2}$ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.23380.6.f1.b1 $C_{12}.D_{12}$ $2^{5} \cdot 3^{2}$ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.23380.6.g1.a1 $C_6^2.D_4$ $2^{5} \cdot 3^{2}$ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.23380.6.g1.b1 $C_6^2.D_4$ $2^{5} \cdot 3^{2}$ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
1728.23380.6.h1.a1 $C_{12}^2.C_2$ $2^{5} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.23380.6.i1.a1 $C_{12}:C_{24}$ $2^{5} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.23380.6.j1.a1 $C_6^2.D_4$ $2^{5} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.23380.6.j1.b1 $C_6^2.D_4$ $2^{5} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.23380.6.k1.a1 $C_{24}:C_{12}$ $2^{5} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.23380.6.k1.b1 $C_{24}:C_{12}$ $2^{5} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.23380.6.l1.a1 $C_{12}^2.C_2$ $2^{5} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.23380.6.m1.a1 $C_{12}^2.C_2$ $2^{5} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.23380.6.n1.a1 $C_{12}.D_{12}$ $2^{5} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.23380.6.n1.b1 $C_{12}.D_{12}$ $2^{5} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.23380.6.o1.a1 $C_6^2.D_4$ $2^{5} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.23380.6.o1.b1 $C_6^2.D_4$ $2^{5} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.23380.6.p1.a1 $C_{12}^2.C_2$ $2^{5} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.23380.6.q1.a1 $C_{12}.D_{12}$ $2^{5} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.23380.6.r1.a1 $C_{12}:C_{24}$ $2^{5} \cdot 3^{2}$ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.23380.8.a1.a1 $C_3\times C_6\times C_{12}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $C_2^3$ $2^{3}$ ✓
1728.23380.8.b1.a1 $C_3\times C_6\times C_{12}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $D_4$ $2^{3}$
1728.23380.8.c1.a1 $C_3\times C_6\times C_{12}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $D_4$ $2^{3}$
1728.23380.8.d1.a1 $C_3^3:Q_8$ $2^{3} \cdot 3^{3}$ ✓ $C_{12}^2.D_6$ $2^{6} \cdot 3^{3}$ $Q_8$ $2^{3}$
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