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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 418 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1728.47367.1.a1 $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ ✓ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_1$ $1$ ✓
1728.47367.2.a1 $C_6.D_6^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47367.2.b1 $C_4\times S_3^3$ $2^{5} \cdot 3^{3}$ ✓ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47367.2.c1 $D_{12}:S_3^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47367.2.d1 $D_{12}:S_3^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47367.2.e1 $C_6.D_6^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47367.2.f1 $C_4:S_3^3$ $2^{5} \cdot 3^{3}$ ✓ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47367.2.g1 $C_6.D_6^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47367.3.a1 $C_4.D_6^2$ $2^{6} \cdot 3^{2}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $3$ $-$
1728.47367.4.a1 $C_{12}:S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47367.4.b1 $C_2.S_3^3$ $2^{4} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47367.4.c1 $C_{12}.S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47367.4.d1 $C_{12}:S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47367.4.e1 $C_{12}\times S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47367.4.f1 $C_2.S_3^3$ $2^{4} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47367.4.g1 $C_{12}.S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47367.4.h1 $C_2.S_3^3$ $2^{4} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47367.4.i1 $D_6:S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47367.4.j1 $C_2\times S_3^3$ $2^{4} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47367.4.k1 $C_{12}.S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47367.4.l1 $C_{12}.C_6^2$ $2^{4} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47367.4.m1 $C_2.S_3^3$ $2^{4} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47367.4.n1 $C_{12}:S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47367.4.o1 $C_{12}.S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47367.4.p1 $C_3^2:C_6\times Q_8$ $2^{4} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47367.4.q1 $C_{12}:S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47367.4.r1 $C_2.S_3^3$ $2^{4} \cdot 3^{3}$ ✓ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47367.4.s1 $(Q_8\times C_3^2):S_3$ $2^{4} \cdot 3^{3}$ ✓ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47367.6.a1 $D_{12}:D_6$ $2^{5} \cdot 3^{2}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $S_3$ $2 \cdot 3$
1728.47367.6.b1 $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47367.6.c1 $C_2.D_6^2$ $2^{5} \cdot 3^{2}$ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47367.6.d1 $D_4:S_3^2$ $2^{5} \cdot 3^{2}$ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47367.6.e1 $D_{12}:D_6$ $2^{5} \cdot 3^{2}$ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47367.6.f1 $D_{12}:D_6$ $2^{5} \cdot 3^{2}$ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47367.6.g1 $D_{12}:D_6$ $2^{5} \cdot 3^{2}$ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47367.6.h1 $D_{12}:D_6$ $2^{5} \cdot 3^{2}$ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47367.6.i1 $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47367.6.j1 $D_{12}:D_6$ $2^{5} \cdot 3^{2}$ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47367.6.k1 $D_4\times S_3^2$ $2^{5} \cdot 3^{2}$ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47367.6.l1 $Q_8\times S_3^2$ $2^{5} \cdot 3^{2}$ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47367.8.a1 $C_6:S_3^2$ $2^{3} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^3$ $2^{3}$ ✓
1728.47367.8.b1 $C_3^2:D_{12}$ $2^{3} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^3$ $2^{3}$ ✓
1728.47367.8.c1 $C_6.C_6^2$ $2^{3} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^3$ $2^{3}$ ✓
1728.47367.8.d1 $C_6.S_3^2$ $2^{3} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^3$ $2^{3}$ ✓
1728.47367.8.e1 $C_6.S_3^2$ $2^{3} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^3$ $2^{3}$ ✓
1728.47367.8.f1 $C_6\times S_3^2$ $2^{3} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^3$ $2^{3}$ ✓
1728.47367.8.g1 $C_3^2\times D_{12}$ $2^{3} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^3$ $2^{3}$ ✓
1728.47367.8.h1 $C_3^3:D_4$ $2^{3} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^3$ $2^{3}$ ✓
1728.47367.8.i1 $C_3:S_3\times C_{12}$ $2^{3} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^3$ $2^{3}$ ✓
1728.47367.8.j1 $C_6.S_3^2$ $2^{3} \cdot 3^{3}$ ✓ $Q_8:S_3^3$ $2^{6} \cdot 3^{3}$ $C_2^3$ $2^{3}$ ✓
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