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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 96 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1296.2891.1.a1.a1 $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ ✓ ✓ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $C_1$ $1$ ✓
1296.2891.2.a1.a1 $\Unitary(3,2)$ $2^{3} \cdot 3^{4}$ ✓ ✓ ✓ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $C_2$ $2$ ✓
1296.2891.3.a1.a1 $\He_3:\SD_{16}$ $2^{4} \cdot 3^{3}$ ✓ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $3$ $-$
1296.2891.4.a1.a1 $C_3^3:D_6$ $2^{2} \cdot 3^{4}$ ✓ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{2}$ $-$
1296.2891.6.a1.a1 $\SU(3,2)$ $2^{3} \cdot 3^{3}$ ✓ ✓ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
1296.2891.6.b1.a1 $\He_3:D_4$ $2^{3} \cdot 3^{3}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.2891.6.c1.a1 $\He_3:C_8$ $2^{3} \cdot 3^{3}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.2891.8.a1.a1 $C_3\wr S_3$ $2 \cdot 3^{4}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{3}$ $-$
1296.2891.8.b1.a1 $C_3^3:C_6$ $2 \cdot 3^{4}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{3}$ $-$
1296.2891.8.b2.a1 $C_3^3:S_3$ $2 \cdot 3^{4}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{3}$ $-$
1296.2891.9.a1.a1 $C_3:\GL(2,3)$ $2^{4} \cdot 3^{2}$ ✓ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $3^{2}$ $-$
1296.2891.12.a1.a1 $C_3:S_3^2$ $2^{2} \cdot 3^{3}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
1296.2891.12.b1.a1 $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
1296.2891.12.c1.a1 $\He_3:C_4$ $2^{2} \cdot 3^{3}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
1296.2891.16.a1.a1 $C_3\wr C_3$ $3^{4}$ $3$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{4}$ $-$
1296.2891.18.a1.a1 $C_3\times \SL(2,3)$ $2^{3} \cdot 3^{2}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
1296.2891.24.a1.a1 $C_3^2:S_3$ $2 \cdot 3^{3}$ ✓ ✓ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $S_4$ $2^{3} \cdot 3$
1296.2891.24.b1.a1 $S_3\times C_3^2$ $2 \cdot 3^{3}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1296.2891.24.c1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1296.2891.24.d1.a1 $C_9:C_6$ $2 \cdot 3^{3}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1296.2891.24.e1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1296.2891.24.f1.a1 $C_3^2:S_3$ $2 \cdot 3^{3}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1296.2891.27.a1.a1 $Q_8:S_3$ $2^{4} \cdot 3$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $3^{3}$ $-$
1296.2891.27.b1.a1 $\GL(2,3)$ $2^{4} \cdot 3$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $3^{3}$ $-$
1296.2891.27.b1.b1 $\GL(2,3)$ $2^{4} \cdot 3$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $3^{3}$ $-$
1296.2891.27.b1.c1 $\GL(2,3)$ $2^{4} \cdot 3$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $3^{3}$ $-$
1296.2891.36.a1.a1 $C_6:S_3$ $2^{2} \cdot 3^{2}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
1296.2891.36.b1.a1 $S_3^2$ $2^{2} \cdot 3^{2}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
1296.2891.36.c1.a1 $S_3^2$ $2^{2} \cdot 3^{2}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
1296.2891.36.c1.b1 $S_3^2$ $2^{2} \cdot 3^{2}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
1296.2891.36.c1.c1 $S_3^2$ $2^{2} \cdot 3^{2}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
1296.2891.48.a1.a1 $\He_3$ $3^{3}$ ✓ ✓ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $\GL(2,3)$ $2^{4} \cdot 3$
1296.2891.48.b1.a1 $C_3^3$ $3^{3}$ ✓ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{4} \cdot 3$ $-$
1296.2891.48.c1.a1 $C_9:C_3$ $3^{3}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{4} \cdot 3$ $-$
1296.2891.54.a1.a1 $D_{12}$ $2^{3} \cdot 3$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2 \cdot 3^{3}$ $-$
1296.2891.54.b1.a1 $C_3:C_8$ $2^{3} \cdot 3$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2 \cdot 3^{3}$ $-$
1296.2891.54.c1.a1 $C_3\times Q_8$ $2^{3} \cdot 3$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2 \cdot 3^{3}$ $-$
1296.2891.54.d1.a1 $\SL(2,3)$ $2^{3} \cdot 3$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2 \cdot 3^{3}$ $-$
1296.2891.54.d1.b1 $\SL(2,3)$ $2^{3} \cdot 3$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2 \cdot 3^{3}$ $-$
1296.2891.54.d1.c1 $\SL(2,3)$ $2^{3} \cdot 3$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2 \cdot 3^{3}$ $-$
1296.2891.72.a1.a1 $C_3\times C_6$ $2 \cdot 3^{2}$ ✓ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{3} \cdot 3^{2}$ $-$
1296.2891.72.b1.a1 $C_3\times S_3$ $2 \cdot 3^{2}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{3} \cdot 3^{2}$ $-$
1296.2891.72.c1.a1 $C_3\times S_3$ $2 \cdot 3^{2}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{3} \cdot 3^{2}$ $-$
1296.2891.72.c1.b1 $C_3\times S_3$ $2 \cdot 3^{2}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{3} \cdot 3^{2}$ $-$
1296.2891.72.c1.c1 $C_3\times S_3$ $2 \cdot 3^{2}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{3} \cdot 3^{2}$ $-$
1296.2891.72.d1.a1 $C_3\times S_3$ $2 \cdot 3^{2}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{3} \cdot 3^{2}$ $-$
1296.2891.72.e1.a1 $C_3\times S_3$ $2 \cdot 3^{2}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{3} \cdot 3^{2}$ $-$
1296.2891.72.e1.b1 $C_3\times S_3$ $2 \cdot 3^{2}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{3} \cdot 3^{2}$ $-$
1296.2891.72.e1.c1 $C_3\times S_3$ $2 \cdot 3^{2}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{3} \cdot 3^{2}$ $-$
1296.2891.72.f1.a1 $C_3:S_3$ $2 \cdot 3^{2}$ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $2^{3} \cdot 3^{2}$ $-$
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