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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 135 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
472392.sf.1.a1 $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ ✓ ✓ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $C_1$ $1$ ✓
472392.sf.2.A $C_3^6.C_3\wr C_2^2$ $2^{2} \cdot 3^{10}$ ✓ ✓ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $C_2$ $2$ ✓
472392.sf.2.B $C_3^6.C_3^3.D_6$ $2^{2} \cdot 3^{10}$ ✓ ✓ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $C_2$ $2$ ✓
472392.sf.2.C $C_3^6.C_3^3.D_6$ $2^{2} \cdot 3^{10}$ ✓ ✓ ✓ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $C_2$ $2$ ✓
472392.sf.3.a1 $C_3^6.S_3^3$ $2^{3} \cdot 3^{9}$ ✓ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $3$ $-$
472392.sf.4.A $C_3^6.C_3^4.C_2$ $2 \cdot 3^{10}$ ✓ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $C_2^2$ $2^{2}$ ✓
472392.sf.4.B $C_3^6.C_3^4.C_2$ $2 \cdot 3^{10}$ ✓ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $C_2^2$ $2^{2}$ ✓
472392.sf.4.C $C_3^6.C_3^4.C_2$ $2 \cdot 3^{10}$ ✓ ✓ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $C_2^2$ $2^{2}$ ✓
472392.sf.6.A $C_3^6.C_3^2.D_6$ $2^{2} \cdot 3^{9}$ ✓ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $S_3$ $2 \cdot 3$
472392.sf.6.B $C_3^5.C_3^3.C_6.C_2$ $2^{2} \cdot 3^{9}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3$ $-$
472392.sf.6.C $C_3^6.C_3^3.C_2^2$ $2^{2} \cdot 3^{9}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3$ $-$
472392.sf.6.D $C_3^6.C_3^2.D_6$ $2^{2} \cdot 3^{9}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3$ $-$
472392.sf.6.E $C_3^5.\He_3.D_6$ $2^{2} \cdot 3^{9}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3$ $-$
472392.sf.6.F $C_3^5.C_3^3.D_6$ $2^{2} \cdot 3^{9}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3$ $-$
472392.sf.6.G $C_3^5.\He_3.D_6$ $2^{2} \cdot 3^{9}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3$ $-$
472392.sf.8.a1 $C_3^6.C_3^4$ $3^{10}$ $3$ ✓ ✓ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $C_2^3$ $2^{3}$ ✓
472392.sf.9.A $C_3^4.C_3^4.C_2^3$ $2^{3} \cdot 3^{8}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $3^{2}$ $-$
472392.sf.9.B $C_3^5.S_3^3$ $2^{3} \cdot 3^{8}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $3^{2}$ $-$
472392.sf.12.A $C_3^6.C_3^3.C_2$ $2 \cdot 3^{9}$ ✓ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $D_6$ $2^{2} \cdot 3$
472392.sf.12.B $C_3^6.C_3^3.C_2$ $2 \cdot 3^{9}$ ✓ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $D_6$ $2^{2} \cdot 3$
472392.sf.12.C $C_3^4.C_3^4.C_6$ $2 \cdot 3^{9}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
472392.sf.12.D $C_3^6.C_3^3.C_2$ $2 \cdot 3^{9}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
472392.sf.12.E $C_3^5.C_3^3.C_6$ $2 \cdot 3^{9}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
472392.sf.12.F $C_3^5.C_3^3.C_6$ $2 \cdot 3^{9}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
472392.sf.12.G $C_3^6.C_3^3.C_2$ $2 \cdot 3^{9}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
472392.sf.12.H $C_3^5.C_3^3.C_6$ $2 \cdot 3^{9}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
472392.sf.12.I $C_3^5.\He_3:S_3$ $2 \cdot 3^{9}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
472392.sf.12.J $C_3^5.\He_3.S_3$ $2 \cdot 3^{9}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
472392.sf.12.K $C_3^5.C_3^4.C_2$ $2 \cdot 3^{9}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
472392.sf.12.L $C_3^3.C_3^5.C_6$ $2 \cdot 3^{9}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
472392.sf.12.M $C_3^5.\He_3:S_3$ $2 \cdot 3^{9}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
472392.sf.12.N $C_3^5.\He_3.S_3$ $2 \cdot 3^{9}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
472392.sf.18.A $C_3^6.(C_6\times S_3)$ $2^{2} \cdot 3^{8}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3^{2}$ $-$
472392.sf.18.B $C_3^5.(C_{18}\times S_3)$ $2^{2} \cdot 3^{8}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3^{2}$ $-$
472392.sf.18.C $C_3^4:D_9^2$ $2^{2} \cdot 3^{8}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3^{2}$ $-$
472392.sf.18.D $C_3^5.C_3^3.C_2^2$ $2^{2} \cdot 3^{8}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3^{2}$ $-$
472392.sf.18.E $C_3^5.C_3^3.C_2^2$ $2^{2} \cdot 3^{8}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3^{2}$ $-$
472392.sf.18.F $C_3^4.C_3^3.C_6.C_2$ $2^{2} \cdot 3^{8}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3^{2}$ $-$
472392.sf.18.G $C_3^5.C_3^3.C_2^2$ $2^{2} \cdot 3^{8}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3^{2}$ $-$
472392.sf.18.H $C_3^4.C_3^4.C_2^2$ $2^{2} \cdot 3^{8}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3^{2}$ $-$
472392.sf.18.I $C_3^6.C_3.D_6$ $2^{2} \cdot 3^{8}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3^{2}$ $-$
472392.sf.18.J $C_3^6.S_3^2$ $2^{2} \cdot 3^{8}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3^{2}$ $-$
472392.sf.18.K $C_3^4.C_3^3.D_6$ $2^{2} \cdot 3^{8}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3^{2}$ $-$
472392.sf.18.L $C_3^3.C_3^4.D_6$ $2^{2} \cdot 3^{8}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3^{2}$ $-$
472392.sf.18.M $C_3^5.C_3^2.D_6$ $2^{2} \cdot 3^{8}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3^{2}$ $-$
472392.sf.18.N $C_3^6.S_3^2$ $2^{2} \cdot 3^{8}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3^{2}$ $-$
472392.sf.18.O $C_3^4.C_3^3.D_6$ $2^{2} \cdot 3^{8}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3^{2}$ $-$
472392.sf.18.P $C_3^4.C_3^3.D_6$ $2^{2} \cdot 3^{8}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2 \cdot 3^{2}$ $-$
472392.sf.24.A $C_3^6.C_3^3$ $3^{9}$ ✓ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $C_2\times D_6$ $2^{3} \cdot 3$
472392.sf.24.B $C_3^6.C_3^3$ $3^{9}$ $C_3^6.C_3:S_3^3$ $2^{3} \cdot 3^{10}$ $2^{3} \cdot 3$ $-$
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