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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 780 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1728.47319.1.a1 $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ ✓ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_1$ $1$ ✓
1728.47319.2.a1 $D_6^2:S_3$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47319.2.b1 $D_6^2:C_6$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47319.2.c1 $C_6.D_6^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47319.2.d1 $S_3\times D_6^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47319.2.e1 $C_6.D_6^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47319.2.f1 $C_6.D_6^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47319.2.g1 $C_6.D_6^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47319.2.h1 $C_6.D_6^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47319.2.i1 $D_{12}\times S_3^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47319.3.a1 $C_4:D_6^2$ $2^{6} \cdot 3^{2}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $3$ $-$
1728.47319.3.b1 $C_4:D_6^2$ $2^{6} \cdot 3^{2}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $3$ $-$
1728.47319.4.a1 $C_3\times D_6^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.b1 $C_3:D_6^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.c1 $C_{12}:C_6^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.d1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.e1 $C_3\times D_6^2$ $2^{4} \cdot 3^{3}$ ✓ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.f1 $C_3:D_6^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.g1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.h1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.i1 $C_{12}:C_6^2$ $2^{4} \cdot 3^{3}$ ✓ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.j1 $C_3:D_6^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.k1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.l1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.m1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.n1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.o1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.p1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.q1 $D_6:S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.r1 $C_{12}:S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.s1 $C_{12}:S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.t1 $C_2\times S_3^3$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.u1 $C_{12}\times S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.v1 $D_6:S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.w1 $C_{12}:S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.x1 $C_{12}:S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47319.4.y1 $C_2\times S_3^3$ $2^{4} \cdot 3^{3}$ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $2^{2}$ $-$
1728.47319.6.a1 $D_6\times D_{12}$ $2^{5} \cdot 3^{2}$ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $S_3$ $2 \cdot 3$
1728.47319.6.b1 $C_2.D_6^2$ $2^{5} \cdot 3^{2}$ ✓ ✓ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $S_3$ $2 \cdot 3$
1728.47319.6.c1 $C_6^2:D_4$ $2^{5} \cdot 3^{2}$ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47319.6.d1 $C_6^2:D_4$ $2^{5} \cdot 3^{2}$ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47319.6.e1 $C_6^2:D_4$ $2^{5} \cdot 3^{2}$ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47319.6.f1 $D_6^2:C_2$ $2^{5} \cdot 3^{2}$ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47319.6.g1 $C_6^2:C_2^3$ $2^{5} \cdot 3^{2}$ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47319.6.h1 $D_6\times D_{12}$ $2^{5} \cdot 3^{2}$ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47319.6.i1 $D_6\times D_{12}$ $2^{5} \cdot 3^{2}$ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47319.6.j1 $D_6\times D_{12}$ $2^{5} \cdot 3^{2}$ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47319.6.k1 $D_6\times D_{12}$ $2^{5} \cdot 3^{2}$ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47319.6.l1 $C_2\times D_6^2$ $2^{5} \cdot 3^{2}$ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47319.6.m1 $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_{12}:D_6^2$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
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