Note: Search results may be incomplete due to uncomputed quantities: Subgroup label (103813812 objects)

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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 (41 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
3888.em.1.a1.a1 $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ ✓ ✓ $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_1$ $1$ ✓
7776.cw.2._.E $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ ✓ ✓ ✓ $C_3^4:(S_3\times \SD_{16})$ $2^{5} \cdot 3^{5}$ $C_2$ $2$ ✓
15552.lb.4.c1.a1 $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ ✓ $C_3^3:S_3.\GL(2,\mathbb{Z}/4)$ $2^{6} \cdot 3^{5}$ $2^{2}$ $-$
23328.dt.6.f1.a1 $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^4:(S_3\times \GL(2,3))$ $2^{5} \cdot 3^{6}$ $2 \cdot 3$ $-$
23328.jz.6.g1.a1 $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^4:C_{24}:D_6$ $2^{5} \cdot 3^{6}$ $2 \cdot 3$ $-$
23328.jz.6.g1.b1 $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^4:C_{24}:D_6$ $2^{5} \cdot 3^{6}$ $2 \cdot 3$ $-$
31104.mg.8._.G $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^4:\GL(2,3):D_4$ $2^{7} \cdot 3^{5}$ $2^{3}$ $-$
69984.cm.18.E $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^6:(S_3\times \SD_{16})$ $2^{5} \cdot 3^{7}$ $2 \cdot 3^{2}$ $-$
69984.jh.18.j1 $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^4.F_9:D_6$ $2^{5} \cdot 3^{7}$ $2 \cdot 3^{2}$ $-$
93312.jq.24.c1.a1 $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^4:\GL(2,3):S_4$ $2^{7} \cdot 3^{6}$ $2^{3} \cdot 3$ $-$
93312.jq.24.c1.b1 $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^4:\GL(2,3):S_4$ $2^{7} \cdot 3^{6}$ $2^{3} \cdot 3$ $-$
93312.jr.24.bi1 $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^4:(S_4\times \GL(2,3))$ $2^{7} \cdot 3^{6}$ $2^{3} \cdot 3$ $-$
139968.ci.36.b1 $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^5:S_3.\GL(2,\mathbb{Z}/4)$ $2^{6} \cdot 3^{7}$ $2^{2} \cdot 3^{2}$ $-$
209952.dj.54.G $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^6:(S_3\times \GL(2,3))$ $2^{5} \cdot 3^{8}$ $2 \cdot 3^{3}$ $-$
209952.ml.54.O $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^6.C_{24}:D_6$ $2^{5} \cdot 3^{8}$ $2 \cdot 3^{3}$ $-$
209952.mm.54.BI $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^6:(S_3\times \GL(2,3))$ $2^{5} \cdot 3^{8}$ $2 \cdot 3^{3}$ $-$
279936.bv.72.V $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^6.(\SD_{16}\times S_4)$ $2^{7} \cdot 3^{7}$ $2^{3} \cdot 3^{2}$ $-$
303264.a.78.e1.a1 $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^3:\GL(3,3)$ $2^{5} \cdot 3^{6} \cdot 13$ $2 \cdot 3 \cdot 13$ $-$
311040.j.80.f1.a1 $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^3:S_3.C_2^4:S_5$ $2^{8} \cdot 3^{5} \cdot 5$ $2^{4} \cdot 5$ $-$
419904.hu.108._.BN $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^6.C_6^2:\SD_{16}$ $2^{6} \cdot 3^{8}$ $2^{2} \cdot 3^{3}$ $-$
559872.l.144.BV $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $(C_3:S_3)^3.\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{7}$ $2^{4} \cdot 3^{2}$ $-$
559872.r.144.CO $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $(C_3:S_3)^3.\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{7}$ $2^{4} \cdot 3^{2}$ $-$
629856.bv.162._.H $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^8:D_4.D_6$ $2^{5} \cdot 3^{9}$ $2 \cdot 3^{4}$ $-$
629856.bv.162._.I $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^8:D_4.D_6$ $2^{5} \cdot 3^{9}$ $2 \cdot 3^{4}$ $-$
629856.bv.162._.J $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^8:D_4.D_6$ $2^{5} \cdot 3^{9}$ $2 \cdot 3^{4}$ $-$
629856.bv.162._.L $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^8:D_4.D_6$ $2^{5} \cdot 3^{9}$ $2 \cdot 3^{4}$ $-$
629856.bv.162._.M $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^8:D_4.D_6$ $2^{5} \cdot 3^{9}$ $2 \cdot 3^{4}$ $-$
629856.bv.162._.N $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^8:D_4.D_6$ $2^{5} \cdot 3^{9}$ $2 \cdot 3^{4}$ $-$
629856.le.162._.V $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^5.(S_3\times C_3^2:\GL(2,3))$ $2^{5} \cdot 3^{9}$ $2 \cdot 3^{4}$ $-$
629856.le.162._.BA $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^5.(S_3\times C_3^2:\GL(2,3))$ $2^{5} \cdot 3^{9}$ $2 \cdot 3^{4}$ $-$
629856.lg.162.BB $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^6.C_{24}:S_3^2$ $2^{5} \cdot 3^{9}$ $2 \cdot 3^{4}$ $-$
629856.lh.162.U $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^6.C_{24}:S_3^2$ $2^{5} \cdot 3^{9}$ $2 \cdot 3^{4}$ $-$
699840.c.180.f1 $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^6:(C_8:S_5)$ $2^{6} \cdot 3^{7} \cdot 5$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
839808.hi.216.CP $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^6.(S_4\times \GL(2,3))$ $2^{7} \cdot 3^{8}$ $2^{3} \cdot 3^{3}$ $-$
933120.a.240.k1 $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $\AGammaL(2,9)$ $2^{8} \cdot 3^{6} \cdot 5$ $2^{4} \cdot 3 \cdot 5$ $-$
933120.a.240.s1 $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $\AGammaL(2,9)$ $2^{8} \cdot 3^{6} \cdot 5$ $2^{4} \cdot 3 \cdot 5$ $-$
1259712.lp.324.C $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^8:D_4.S_4$ $2^{6} \cdot 3^{9}$ $2^{2} \cdot 3^{4}$ $-$
1259712.lp.324.D $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^8:D_4.S_4$ $2^{6} \cdot 3^{9}$ $2^{2} \cdot 3^{4}$ $-$
1259712.lp.324.E $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^8:D_4.S_4$ $2^{6} \cdot 3^{9}$ $2^{2} \cdot 3^{4}$ $-$
4199040.a.1080.j1 $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^4:\Sp(4,3)$ $2^{7} \cdot 3^{8} \cdot 5$ $2^{3} \cdot 3^{3} \cdot 5$ $-$
8398080.j.2160._.U $C_3^3:F_9:C_2$ $2^{4} \cdot 3^{5}$ $C_3^3:S_3.\SO(5,3)$ $2^{8} \cdot 3^{8} \cdot 5$ $2^{4} \cdot 3^{3} \cdot 5$ $-$
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