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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 187 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1728.47846.1.a1.a1 $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ ✓ ✓ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $C_1$ $1$ ✓
1728.47846.2.a1.a1 $C_6^2:\SL(2,3)$ $2^{5} \cdot 3^{3}$ ✓ ✓ ✓ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47846.3.a1.a1 $C_6^2:\SD_{16}$ $2^{6} \cdot 3^{2}$ ✓ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $3$ $-$
1728.47846.4.a1.a1 $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{2}$ $-$
1728.47846.4.b1.a1 $C_3^2:\GL(2,3)$ $2^{4} \cdot 3^{3}$ ✓ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{2}$ $-$
1728.47846.4.b1.b1 $C_3^2:\GL(2,3)$ $2^{4} \cdot 3^{3}$ ✓ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{2}$ $-$
1728.47846.6.a1.a1 $C_6^2:Q_8$ $2^{5} \cdot 3^{2}$ ✓ ✓ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $S_3$ $2 \cdot 3$
1728.47846.6.b1.a1 $F_9:C_2^2$ $2^{5} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47846.6.b1.b1 $F_9:C_2^2$ $2^{5} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47846.6.c1.a1 $\PSU(3,2):C_4$ $2^{5} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47846.6.c1.b1 $\PSU(3,2):C_4$ $2^{5} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47846.6.d1.a1 $C_6^2:D_4$ $2^{5} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47846.6.e1.a1 $C_6^2:C_8$ $2^{5} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2 \cdot 3$ $-$
1728.47846.8.a1.a1 $C_6^2:C_6$ $2^{3} \cdot 3^{3}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{3}$ $-$
1728.47846.8.b1.a1 $C_3^2:S_4$ $2^{3} \cdot 3^{3}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{3}$ $-$
1728.47846.8.b2.a1 $C_3^2:S_4$ $2^{3} \cdot 3^{3}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{3}$ $-$
1728.47846.8.c1.a1 $\PU(3,2)$ $2^{3} \cdot 3^{3}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{3}$ $-$
1728.47846.8.c1.b1 $\PU(3,2)$ $2^{3} \cdot 3^{3}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{3}$ $-$
1728.47846.8.d1.a1 $\PU(3,2)$ $2^{3} \cdot 3^{3}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{3}$ $-$
1728.47846.9.a1.a1 $Q_8:S_4$ $2^{6} \cdot 3$ ✓ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $3^{2}$ $-$
1728.47846.12.a1.a1 $S_3^2:C_4$ $2^{4} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.47846.12.b1.a1 $S_3^2:C_2^2$ $2^{4} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.47846.12.c1.a1 $C_2.\SOPlus(4,2)$ $2^{4} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.47846.12.d1.a1 $C_2\times \PSU(3,2)$ $2^{4} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.47846.12.e1.a1 $C_2\times F_9$ $2^{4} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.47846.12.e1.b1 $C_2\times F_9$ $2^{4} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.47846.12.f1.a1 $C_2\times \PSU(3,2)$ $2^{4} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.47846.12.f1.b1 $C_2\times \PSU(3,2)$ $2^{4} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.47846.12.g1.a1 $S_3\times S_4$ $2^{4} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.47846.12.h1.a1 $D_6:D_6$ $2^{4} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.47846.12.i1.a1 $C_6^2:C_4$ $2^{4} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.47846.12.j1.a1 $F_9:C_2$ $2^{4} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.47846.12.j1.b1 $F_9:C_2$ $2^{4} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.47846.12.k1.a1 $F_9:C_2$ $2^{4} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.47846.12.k1.b1 $F_9:C_2$ $2^{4} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{2} \cdot 3$ $-$
1728.47846.16.a1.a1 $C_3^2:A_4$ $2^{2} \cdot 3^{3}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{4}$ $-$
1728.47846.16.b1.a1 $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{4}$ $-$
1728.47846.18.a1.a1 $Q_8:A_4$ $2^{5} \cdot 3$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2 \cdot 3^{2}$ $-$
1728.47846.24.a1.a1 $C_6:D_6$ $2^{3} \cdot 3^{2}$ ✓ ✓ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $S_4$ $2^{3} \cdot 3$
1728.47846.24.b1.a1 $\PSU(3,2)$ $2^{3} \cdot 3^{2}$ ✓ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $S_4$ $2^{3} \cdot 3$
1728.47846.24.b1.b1 $\PSU(3,2)$ $2^{3} \cdot 3^{2}$ ✓ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $S_4$ $2^{3} \cdot 3$
1728.47846.24.c1.a1 $S_3\times D_6$ $2^{3} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{3} \cdot 3$ $-$
1728.47846.24.d1.a1 $C_2\times C_3^2:C_4$ $2^{3} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{3} \cdot 3$ $-$
1728.47846.24.d1.b1 $C_2\times C_3^2:C_4$ $2^{3} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{3} \cdot 3$ $-$
1728.47846.24.e1.a1 $C_2\times C_3^2:C_4$ $2^{3} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{3} \cdot 3$ $-$
1728.47846.24.f1.a1 $C_6.D_6$ $2^{3} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{3} \cdot 3$ $-$
1728.47846.24.g1.a1 $C_2\times C_3^2:C_4$ $2^{3} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{3} \cdot 3$ $-$
1728.47846.24.h1.a1 $C_3:D_{12}$ $2^{3} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{3} \cdot 3$ $-$
1728.47846.24.i1.a1 $S_3\times A_4$ $2^{3} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{3} \cdot 3$ $-$
1728.47846.24.j1.a1 $C_3\times S_4$ $2^{3} \cdot 3^{2}$ $C_6^2:\GL(2,3)$ $2^{6} \cdot 3^{3}$ $2^{3} \cdot 3$ $-$
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