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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 137 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1944.2330.1.a1.a1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ ✓ ✓ $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_1$ $1$ ✓
3888.ec.2.b1.a1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ ✓ ✓ ✓ $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_2$ $2$ ✓
3888.ee.2.c1.a1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ ✓ ✓ ✓ $C_3^4:(S_3\times Q_8)$ $2^{4} \cdot 3^{5}$ $C_2$ $2$ ✓
3888.el.2.b1.a1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ ✓ ✓ ✓ $C_3^4:(C_3\times \SD_{16})$ $2^{4} \cdot 3^{5}$ $C_2$ $2$ ✓
5832.el.3.a1.a1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ ✓ ✓ ✓ $C_3^4:(C_3\times \SL(2,3))$ $2^{3} \cdot 3^{6}$ $C_3$ $3$ ✓
7776.cw.4._.D $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ ✓ ✓ $C_3^4:(S_3\times \SD_{16})$ $2^{5} \cdot 3^{5}$ $C_2^2$ $2^{2}$ ✓
7776.iq.4.b1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ ✓ $C_3^4:\SL(2,3):C_2^2$ $2^{5} \cdot 3^{5}$ $2^{2}$ $-$
11664.ej.6.a1.a1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ ✓ ✓ $C_3^4:(S_3\times \SL(2,3))$ $2^{4} \cdot 3^{6}$ $C_6$ $2 \cdot 3$ ✓
11664.en.6.a1.a1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ ✓ ✓ $C_3^4:(C_3\times \GL(2,3))$ $2^{4} \cdot 3^{6}$ $S_3$ $2 \cdot 3$
11664.er.6.a1.a1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ ✓ ✓ $C_3^4:C_3:\GL(2,3)$ $2^{4} \cdot 3^{6}$ $S_3$ $2 \cdot 3$
15552.kc.8.c1.a1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^4:\SL(2,3):D_4$ $2^{6} \cdot 3^{5}$ $2^{3}$ $-$
15552.kz.8.D $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^4:\GL(2,3):C_2^2$ $2^{6} \cdot 3^{5}$ $2^{3}$ $-$
15552.la.8._.C $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^4:\SL(2,3).D_4$ $2^{6} \cdot 3^{5}$ $2^{3}$ $-$
17496.ec.9.a1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ ✓ $C_3^2\wr C_3:Q_8$ $2^{3} \cdot 3^{7}$ $3^{2}$ $-$
17496.gk.9.B $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ ✓ $C_3^5.\PSU(3,2)$ $2^{3} \cdot 3^{7}$ $3^{2}$ $-$
23328.dt.12.a1.a1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ ✓ ✓ $C_3^4:(S_3\times \GL(2,3))$ $2^{5} \cdot 3^{6}$ $D_6$ $2^{2} \cdot 3$
23328.je.12.c1.a1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^4:\OmegaPlus(4,3)$ $2^{5} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
23328.je.12.c1.b1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^4:\OmegaPlus(4,3)$ $2^{5} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
23328.jz.12.k1.a1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^4:C_{24}:D_6$ $2^{5} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
23328.jz.12.k1.b1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^4:C_{24}:D_6$ $2^{5} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
31104.mg.16._.H $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^4:\GL(2,3):D_4$ $2^{7} \cdot 3^{5}$ $2^{4}$ $-$
34992.cs.18.b1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^6:(C_3\times \SD_{16})$ $2^{4} \cdot 3^{7}$ $2 \cdot 3^{2}$ $-$
34992.cu.18.b1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^2\wr C_3:\SD_{16}$ $2^{4} \cdot 3^{7}$ $2 \cdot 3^{2}$ $-$
34992.cz.18.c1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^6.(S_3\times Q_8)$ $2^{4} \cdot 3^{7}$ $2 \cdot 3^{2}$ $-$
34992.gk.18.F $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^6.(S_3\times Q_8)$ $2^{4} \cdot 3^{7}$ $2 \cdot 3^{2}$ $-$
34992.gk.18.H $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^6.(S_3\times Q_8)$ $2^{4} \cdot 3^{7}$ $2 \cdot 3^{2}$ $-$
34992.hc.18.e1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^5.F_9:C_2$ $2^{4} \cdot 3^{7}$ $2 \cdot 3^{2}$ $-$
34992.hj.18.F $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^6.(C_3\times \SD_{16})$ $2^{4} \cdot 3^{7}$ $2 \cdot 3^{2}$ $-$
34992.hj.18.H $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^6.(C_3\times \SD_{16})$ $2^{4} \cdot 3^{7}$ $2 \cdot 3^{2}$ $-$
46656.iz.24.e1.a1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^4:\SOPlus(4,3)$ $2^{6} \cdot 3^{6}$ $2^{3} \cdot 3$ $-$
46656.iz.24.e1.b1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^4:\SOPlus(4,3)$ $2^{6} \cdot 3^{6}$ $2^{3} \cdot 3$ $-$
46656.ja.24.f1.a1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^4:\OmegaPlus(4,3):C_2$ $2^{6} \cdot 3^{6}$ $2^{3} \cdot 3$ $-$
46656.js.24._.G $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^4:\GL(2,3):A_4$ $2^{6} \cdot 3^{6}$ $2^{3} \cdot 3$ $-$
46656.js.24._.I $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^4:\GL(2,3):A_4$ $2^{6} \cdot 3^{6}$ $2^{3} \cdot 3$ $-$
52488.cm.27.B $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^6:(C_3\times \SL(2,3))$ $2^{3} \cdot 3^{8}$ $3^{3}$ $-$
52488.kt.27.D $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^6.\PSU(3,2)$ $2^{3} \cdot 3^{8}$ $3^{3}$ $-$
52488.ky.27.b1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^6:(C_3\times \SL(2,3))$ $2^{3} \cdot 3^{8}$ $3^{3}$ $-$
52488.kz.27.C $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^6.(C_3\times \SL(2,3))$ $2^{3} \cdot 3^{8}$ $3^{3}$ $-$
69984.cl.36.B $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^6:(Q_8\times A_4)$ $2^{5} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
69984.cm.36.K $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^6:(S_3\times \SD_{16})$ $2^{5} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
69984.hw.36.BC $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^6.(S_3\times \SD_{16})$ $2^{5} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
69984.hw.36.BH $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^6.(S_3\times \SD_{16})$ $2^{5} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
69984.jh.36.bj1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^4.F_9:D_6$ $2^{5} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
69984.jh.36.bn1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^4.F_9:D_6$ $2^{5} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
93312.it.48.i1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^4:\GOrthPlus(4,3)$ $2^{7} \cdot 3^{6}$ $2^{4} \cdot 3$ $-$
93312.jq.48.l1.a1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^4:\GL(2,3):S_4$ $2^{7} \cdot 3^{6}$ $2^{4} \cdot 3$ $-$
93312.jq.48.l1.b1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^4:\GL(2,3):S_4$ $2^{7} \cdot 3^{6}$ $2^{4} \cdot 3$ $-$
93312.jr.48.cf1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^4:(S_4\times \GL(2,3))$ $2^{7} \cdot 3^{6}$ $2^{4} \cdot 3$ $-$
104976.cf.54.d1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^6:(C_3\times \GL(2,3))$ $2^{4} \cdot 3^{8}$ $2 \cdot 3^{3}$ $-$
104976.cu.54.c1 $C_3^3:\PSU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^2\wr C_3:\GL(2,3)$ $2^{4} \cdot 3^{8}$ $2 \cdot 3^{3}$ $-$
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