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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 51 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
38263752.dc.1.a1 $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ ✓ ✓ $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_1$ $1$ ✓
76527504.ei.2.a1.a1 $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ ✓ ✓ ✓ $C_3^8.C_3^5:(C_2\times \SL(2,3))$ $2^{4} \cdot 3^{14}$ $C_2$ $2$ ✓
76527504.eu.2.a1.a1 $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ ✓ ✓ ✓ $C_3^8.C_3^5:\GL(2,3)$ $2^{4} \cdot 3^{14}$ $C_2$ $2$ ✓
76527504.ev.2.a1.a1 $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ ✓ ✓ ✓ $C_3^8.C_3^5:\GL(2,3)$ $2^{4} \cdot 3^{14}$ $C_2$ $2$ ✓
114791256.ba.3._.D $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ ✓ ✓ ✓ $C_3^8.C_3^6:\SL(2,3)$ $2^{3} \cdot 3^{15}$ $C_3$ $3$ ✓
153055008.eu.4._.A $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ ✓ ✓ $C_3^8.C_3^5:(C_2\times \GL(2,3))$ $2^{5} \cdot 3^{14}$ $C_2^2$ $2^{2}$ ✓
229582512.bo.6._.B $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ ✓ ✓ $C_3^8.C_3^5:(S_3\times \SL(2,3))$ $2^{4} \cdot 3^{15}$ $S_3$ $2 \cdot 3$
229582512.bu.6._.A $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ ✓ ✓ $C_3^8.C_3^6:\GL(2,3)$ $2^{4} \cdot 3^{15}$ $C_6$ $2 \cdot 3$ ✓
229582512.bv.6._.A $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ ✓ ✓ $C_3^8.C_3^6:\GL(2,3)$ $2^{4} \cdot 3^{15}$ $S_3$ $2 \cdot 3$
344373768.bn.9._.B $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ ✓ $C_3^8.(C_3^7.\SL(2,3))$ $2^{3} \cdot 3^{16}$ $3^{2}$ $-$
459165024.bp.12._.B $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ ✓ ✓ $C_3^8.C_3^5:(S_3\times \GL(2,3))$ $2^{5} \cdot 3^{15}$ $D_6$ $2^{2} \cdot 3$
688747536.dh.18._.G $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.(C_3^7.(C_2\times \SL(2,3)))$ $2^{4} \cdot 3^{16}$ $2 \cdot 3^{2}$ $-$
688747536.dq.18._.B $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.(C_3^7.\GL(2,3))$ $2^{4} \cdot 3^{16}$ $2 \cdot 3^{2}$ $-$
688747536.dr.18._.B $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.(C_3^7.\GL(2,3))$ $2^{4} \cdot 3^{16}$ $2 \cdot 3^{2}$ $-$
918330048.bc.24._.P $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.C_3^6:(C_2^3:\SL(2,3))$ $2^{6} \cdot 3^{15}$ $2^{3} \cdot 3$ $-$
918330048.bc.24._.Q $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.C_3^6:(C_2^3:\SL(2,3))$ $2^{6} \cdot 3^{15}$ $2^{3} \cdot 3$ $-$
1033121304.f.27._.E $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.(C_3^8.\SL(2,3))$ $2^{3} \cdot 3^{17}$ $3^{3}$ $-$
1377495072.fs.36._.G $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.(C_3^7.(C_2\times \GL(2,3)))$ $2^{5} \cdot 3^{16}$ $2^{2} \cdot 3^{2}$ $-$
1377495072.ft.36._.CM $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.C_3^7:C_2^3.A_4$ $2^{5} \cdot 3^{16}$ $2^{2} \cdot 3^{2}$ $-$
1377495072.ft.36._.CN $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.C_3^7:C_2^3.A_4$ $2^{5} \cdot 3^{16}$ $2^{2} \cdot 3^{2}$ $-$
1836660096.g.48._.BG $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.(S_3^4.\PU(3,2))$ $2^{7} \cdot 3^{15}$ $2^{4} \cdot 3$ $-$
1836660096.p.48._.L $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^{12}.C_3^2.C_2^4.S_4$ $2^{7} \cdot 3^{15}$ $2^{4} \cdot 3$ $-$
1836660096.p.48._.M $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^{12}.C_3^2.C_2^4.S_4$ $2^{7} \cdot 3^{15}$ $2^{4} \cdot 3$ $-$
1836660096.q.48._.Z $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^{12}.C_3^2.C_2^4.S_4$ $2^{7} \cdot 3^{15}$ $2^{4} \cdot 3$ $-$
2066242608.d.54._.C $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.(C_3^7.(S_3\times \SL(2,3)))$ $2^{4} \cdot 3^{17}$ $2 \cdot 3^{3}$ $-$
2066242608.o.54._.B $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.(C_3^8.\GL(2,3))$ $2^{4} \cdot 3^{17}$ $2 \cdot 3^{3}$ $-$
2066242608.p.54._.D $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.(C_3^8.\GL(2,3))$ $2^{4} \cdot 3^{17}$ $2 \cdot 3^{3}$ $-$
2754990144.ir.72._.LA $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.C_3^7:C_2^4.A_4$ $2^{6} \cdot 3^{16}$ $2^{3} \cdot 3^{2}$ $-$
2754990144.ir.72._.LB $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.C_3^7:C_2^4.A_4$ $2^{6} \cdot 3^{16}$ $2^{3} \cdot 3^{2}$ $-$
2754990144.is.72._.GD $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^4.(C_3^7.S_3\wr A_4)$ $2^{6} \cdot 3^{16}$ $2^{3} \cdot 3^{2}$ $-$
2754990144.iu.72._.ER $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^4.(C_3^7.S_3\wr A_4)$ $2^{6} \cdot 3^{16}$ $2^{3} \cdot 3^{2}$ $-$
2754990144.iv.72._.GL $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.C_3^7:C_2^3.S_4$ $2^{6} \cdot 3^{16}$ $2^{3} \cdot 3^{2}$ $-$
2754990144.ix.72._.FC $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.C_3^7:C_2^3.S_4$ $2^{6} \cdot 3^{16}$ $2^{3} \cdot 3^{2}$ $-$
2754990144.iy.72._.DP $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.C_3^4.C_6^3.S_4$ $2^{6} \cdot 3^{16}$ $2^{3} \cdot 3^{2}$ $-$
2754990144.iy.72._.DR $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.C_3^4.C_6^3.S_4$ $2^{6} \cdot 3^{16}$ $2^{3} \cdot 3^{2}$ $-$
2754990144.ja.72._.DT $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.(C_3^7.Q_8:S_4)$ $2^{6} \cdot 3^{16}$ $2^{3} \cdot 3^{2}$ $-$
2754990144.ja.72._.EA $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.(C_3^7.Q_8:S_4)$ $2^{6} \cdot 3^{16}$ $2^{3} \cdot 3^{2}$ $-$
2984572656.a.78._.A $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^{12}.\SL(3,3)$ $2^{4} \cdot 3^{15} \cdot 13$ $2 \cdot 3 \cdot 13$ $-$
3673320192.b.96._.BR $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^4.(C_3^6.S_3^4:\GL(2,3))$ $2^{8} \cdot 3^{15}$ $2^{5} \cdot 3$ $-$
5969145312.a.156._.A $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^{12}.C_2.\SL(3,3)$ $2^{5} \cdot 3^{15} \cdot 13$ $2^{2} \cdot 3 \cdot 13$ $-$
8264970432.i.216._.P $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.C_3^8:C_2^4.A_4$ $2^{6} \cdot 3^{17}$ $2^{3} \cdot 3^{3}$ $-$
8264970432.m.216._.N $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.(C_3^8.C_2^3:\SL(2,3))$ $2^{6} \cdot 3^{17}$ $2^{3} \cdot 3^{3}$ $-$
8264970432.m.216._.CB $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^8.(C_3^8.C_2^3:\SL(2,3))$ $2^{6} \cdot 3^{17}$ $2^{3} \cdot 3^{3}$ $-$
8953717968.b.234._.B $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^{13}.\SL(3,3)$ $2^{4} \cdot 3^{16} \cdot 13$ $2 \cdot 3^{2} \cdot 13$ $-$
8953717968.b.234._.Q $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^{13}.\SL(3,3)$ $2^{4} \cdot 3^{16} \cdot 13$ $2 \cdot 3^{2} \cdot 13$ $-$
16836050880.a.440._.A $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^{11}.M_{12}$ $2^{6} \cdot 3^{14} \cdot 5 \cdot 11$ $2^{3} \cdot 5 \cdot 11$ $-$
17907435936.b.468._.B $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^{12}.\SL(3,3).S_3$ $2^{5} \cdot 3^{16} \cdot 13$ $2^{2} \cdot 3^{2} \cdot 13$ $-$
17907435936.b.468._.O $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^{12}.\SL(3,3).S_3$ $2^{5} \cdot 3^{16} \cdot 13$ $2^{2} \cdot 3^{2} \cdot 13$ $-$
33672101760.a.880._.A $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^{11}.C_2.M_{12}$ $2^{7} \cdot 3^{14} \cdot 5 \cdot 11$ $2^{4} \cdot 5 \cdot 11$ $-$
50508152640.a.1320._.A $C_3^8.C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{14}$ $C_3^{12}.M_{12}$ $2^{6} \cdot 3^{15} \cdot 5 \cdot 11$ $2^{3} \cdot 3 \cdot 5 \cdot 11$ $-$
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