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 (1-50 of 62 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
11664.kk.1.a1 $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ ✓ ✓ $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_1$ $1$ ✓
23328.jf.2.b1 $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ ✓ ✓ ✓ $(S_3\times D_9)\wr C_2$ $2^{5} \cdot 3^{6}$ $C_2$ $2$ ✓
34992.me.3.b1 $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ ✓ $(C_3^3\times S_3^2).S_3^2$ $2^{4} \cdot 3^{7}$ $3$ $-$
69984.io.6.e1 $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_3^3.S_3^2\wr C_2$ $2^{5} \cdot 3^{7}$ $2 \cdot 3$ $-$
104976.nt.9.A $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ ✓ $C_3^4.D_{18}:D_{18}$ $2^{4} \cdot 3^{8}$ $3^{2}$ $-$
104976.qc.9._.A $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ ✓ $D_9^2.D_9^2$ $2^{4} \cdot 3^{8}$ $3^{2}$ $-$
209952.kf.18._.J $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_3^4.D_{18}\wr C_2$ $2^{5} \cdot 3^{8}$ $2 \cdot 3^{2}$ $-$
209952.kg.18._.C $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9^2.C_3\wr D_4$ $2^{5} \cdot 3^{8}$ $2 \cdot 3^{2}$ $-$
209952.lf.18._.C $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9^2\wr C_2$ $2^{5} \cdot 3^{8}$ $2 \cdot 3^{2}$ $-$
209952.lf.18._.L $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9^2\wr C_2$ $2^{5} \cdot 3^{8}$ $2 \cdot 3^{2}$ $-$
314928.nj.27.A $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_3^4.C_{18}^2:D_6$ $2^{4} \cdot 3^{9}$ $3^{3}$ $-$
314928.nn.27.B $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_3^7.D_6:D_6$ $2^{4} \cdot 3^{9}$ $3^{3}$ $-$
314928.nv.27.S $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_3^7.D_6:D_6$ $2^{4} \cdot 3^{9}$ $3^{3}$ $-$
314928.qn.27._.A $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_9^4.(C_6\times D_4)$ $2^{4} \cdot 3^{9}$ $3^{3}$ $-$
314928.qo.27._.B $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_9^4.C_6:D_4$ $2^{4} \cdot 3^{9}$ $3^{3}$ $-$
314928.qp.27._.B $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_9^4.(C_2\times S_4)$ $2^{4} \cdot 3^{9}$ $3^{3}$ $-$
419904.ln.36._.C $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9\wr C_2^2$ $2^{6} \cdot 3^{8}$ $2^{2} \cdot 3^{2}$ $-$
419904.ln.36._.G $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9\wr C_2^2$ $2^{6} \cdot 3^{8}$ $2^{2} \cdot 3^{2}$ $-$
419904.ln.36._.K $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9\wr C_2^2$ $2^{6} \cdot 3^{8}$ $2^{2} \cdot 3^{2}$ $-$
629856.iq.54.F $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $2 \cdot 3^{3}$ $-$
629856.ir.54._.I $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $2 \cdot 3^{3}$ $-$
629856.ka.54._.I $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $2 \cdot 3^{3}$ $-$
629856.ka.54._.R $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $2 \cdot 3^{3}$ $-$
629856.kb.54._.D $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9^2\wr C_2.C_3$ $2^{5} \cdot 3^{9}$ $2 \cdot 3^{3}$ $-$
629856.kb.54._.K $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9^2\wr C_2.C_3$ $2^{5} \cdot 3^{9}$ $2 \cdot 3^{3}$ $-$
839808.mj.72._.J $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9\wr D_4$ $2^{7} \cdot 3^{8}$ $2^{3} \cdot 3^{2}$ $-$
839808.mj.72._.Q $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9\wr D_4$ $2^{7} \cdot 3^{8}$ $2^{3} \cdot 3^{2}$ $-$
839808.mj.72._.BE $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9\wr D_4$ $2^{7} \cdot 3^{8}$ $2^{3} \cdot 3^{2}$ $-$
839808.mj.72._.BI $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9\wr D_4$ $2^{7} \cdot 3^{8}$ $2^{3} \cdot 3^{2}$ $-$
839808.mj.72._.CJ $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9\wr D_4$ $2^{7} \cdot 3^{8}$ $2^{3} \cdot 3^{2}$ $-$
839808.mj.72._.CM $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9\wr D_4$ $2^{7} \cdot 3^{8}$ $2^{3} \cdot 3^{2}$ $-$
944784.rx.81.A $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_3^6.S_3^2:S_3^2$ $2^{4} \cdot 3^{10}$ $3^{4}$ $-$
944784.sc.81._.C $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_9^4.(C_6\times S_4)$ $2^{4} \cdot 3^{10}$ $3^{4}$ $-$
1259712.jh.108._.C $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9^2\wr C_2.S_3$ $2^{6} \cdot 3^{9}$ $2^{2} \cdot 3^{3}$ $-$
1259712.jh.108._.N $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9^2\wr C_2.S_3$ $2^{6} \cdot 3^{9}$ $2^{2} \cdot 3^{3}$ $-$
1259712.jh.108._.W $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9^2\wr C_2.S_3$ $2^{6} \cdot 3^{9}$ $2^{2} \cdot 3^{3}$ $-$
1259712.ji.108._.D $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9^2\wr C_2.C_6$ $2^{6} \cdot 3^{9}$ $2^{2} \cdot 3^{3}$ $-$
1259712.ji.108._.I $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9^2\wr C_2.C_6$ $2^{6} \cdot 3^{9}$ $2^{2} \cdot 3^{3}$ $-$
1259712.ji.108._.P $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9^2\wr C_2.C_6$ $2^{6} \cdot 3^{9}$ $2^{2} \cdot 3^{3}$ $-$
1259712.jj.108._.D $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9\wr C_4.C_3$ $2^{6} \cdot 3^{9}$ $2^{2} \cdot 3^{3}$ $-$
1259712.jk.108._.E $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9^2\wr C_2.S_3$ $2^{6} \cdot 3^{9}$ $2^{2} \cdot 3^{3}$ $-$
1259712.jp.108._.E $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9\wr A_4$ $2^{6} \cdot 3^{9}$ $2^{2} \cdot 3^{3}$ $-$
1259712.jq.108._.G $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9\wr C_2^2.C_3$ $2^{6} \cdot 3^{9}$ $2^{2} \cdot 3^{3}$ $-$
1259712.js.108._.E $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_9:D_9^3.S_4$ $2^{6} \cdot 3^{9}$ $2^{2} \cdot 3^{3}$ $-$
1259712.js.108._.J $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_9:D_9^3.S_4$ $2^{6} \cdot 3^{9}$ $2^{2} \cdot 3^{3}$ $-$
1259712.js.108._.T $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_9:D_9^3.S_4$ $2^{6} \cdot 3^{9}$ $2^{2} \cdot 3^{3}$ $-$
1574640.x.135.A $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_9^4:(C_2\times S_5)$ $2^{4} \cdot 3^{9} \cdot 5$ $3^{3} \cdot 5$ $-$
1889568.ou.162.A $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $C_3^4.C_3^4:D_6\wr C_2$ $2^{5} \cdot 3^{10}$ $2 \cdot 3^{4}$ $-$
2519424.jy.216.I $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9\wr C_4.C_6$ $2^{7} \cdot 3^{9}$ $2^{3} \cdot 3^{3}$ $-$
2519424.jy.216.J $S_3^2:D_9^2$ $2^{4} \cdot 3^{6}$ $D_9\wr C_4.C_6$ $2^{7} \cdot 3^{9}$ $2^{3} \cdot 3^{3}$ $-$
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