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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 157 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
15116544.df.1.a1 $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ ✓ ✓ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $C_1$ $1$ ✓
15116544.df.2.A $C_3^9.C_2^6.C_6$ $2^{7} \cdot 3^{10}$ ✓ ✓ ✓ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $C_2$ $2$ ✓
15116544.df.2.B $C_3^9.C_2^6.S_3$ $2^{7} \cdot 3^{10}$ ✓ ✓ ✓ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $C_2$ $2$ ✓
15116544.df.2.C $C_3^9.C_2^6.S_3$ $2^{7} \cdot 3^{10}$ ✓ ✓ ✓ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $C_2$ $2$ ✓
15116544.df.3.a1 $C_3^9.C_2^4.C_2^4$ $2^{8} \cdot 3^{9}$ ✓ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $3$ $-$
15116544.df.4.A $C_3^9.C_2^6.C_3$ $2^{6} \cdot 3^{10}$ ✓ ✓ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $C_2^2$ $2^{2}$ ✓
15116544.df.4.B $C_3^6.C_6^3:S_4$ $2^{6} \cdot 3^{10}$ ✓ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{2}$ $-$
15116544.df.4.C $C_3^8.C_2^4:S_3^2$ $2^{6} \cdot 3^{10}$ ✓ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{2}$ $-$
15116544.df.4.D $C_3^9.C_2^4.D_6$ $2^{6} \cdot 3^{10}$ ✓ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{2}$ $-$
15116544.df.6.A $C_3^9.C_2^5.C_2^2$ $2^{7} \cdot 3^{9}$ ✓ ✓ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $S_3$ $2 \cdot 3$
15116544.df.6.B $C_3^9.C_2^3.C_2^4$ $2^{7} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2 \cdot 3$ $-$
15116544.df.6.C $C_3^9.C_2^4.C_2^3$ $2^{7} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2 \cdot 3$ $-$
15116544.df.6.D $C_3^9.C_2^4.C_2^3$ $2^{7} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2 \cdot 3$ $-$
15116544.df.6.E $C_3^9.C_2^4.C_2^3$ $2^{7} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2 \cdot 3$ $-$
15116544.df.6.F $C_3^9.C_2^3.C_2^4$ $2^{7} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2 \cdot 3$ $-$
15116544.df.6.G $C_3^9.C_2^4.C_2^3$ $2^{7} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2 \cdot 3$ $-$
15116544.df.6.H $C_3^8.C_2^4.C_6.C_2^2$ $2^{7} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2 \cdot 3$ $-$
15116544.df.6.I $C_3^9.C_2^4.C_2^3$ $2^{7} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2 \cdot 3$ $-$
15116544.df.6.J $C_3^9.C_2^5.C_2^2$ $2^{7} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2 \cdot 3$ $-$
15116544.df.6.K $C_3^9.C_2^4.C_2^3$ $2^{7} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2 \cdot 3$ $-$
15116544.df.6.L $C_3^9.C_2^5.C_2^2$ $2^{7} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2 \cdot 3$ $-$
15116544.df.6.M $C_3^9.C_2^5.C_2^2$ $2^{7} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2 \cdot 3$ $-$
15116544.df.6.N $C_3^9.C_2^5.C_2^2$ $2^{7} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2 \cdot 3$ $-$
15116544.df.6.O $C_3^9.C_2^5.C_2^2$ $2^{7} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2 \cdot 3$ $-$
15116544.df.8.A $C_3^7.C_6^2:S_4$ $2^{5} \cdot 3^{10}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{3}$ $-$
15116544.df.8.B $C_3^6.C_6^3:A_4$ $2^{5} \cdot 3^{10}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{3}$ $-$
15116544.df.8.C $C_3^9.C_2^4.S_3$ $2^{5} \cdot 3^{10}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{3}$ $-$
15116544.df.8.D $C_3^9.C_2^4.S_3$ $2^{5} \cdot 3^{10}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{3}$ $-$
15116544.df.8.E $C_3^9.C_2^4.S_3$ $2^{5} \cdot 3^{10}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{3}$ $-$
15116544.df.8.F $C_3^9.C_2^4.S_3$ $2^{5} \cdot 3^{10}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{3}$ $-$
15116544.df.8.G $C_3^7.C_6^2:S_4$ $2^{5} \cdot 3^{10}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{3}$ $-$
15116544.df.8.H $C_3^9.C_2^4.C_6$ $2^{5} \cdot 3^{10}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{3}$ $-$
15116544.df.8.I $C_3^7.C_6^2:S_4$ $2^{5} \cdot 3^{10}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{3}$ $-$
15116544.df.8.J $C_3^9.C_2^4.S_3$ $2^{5} \cdot 3^{10}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{3}$ $-$
15116544.df.8.K $C_3^9.C_2^4.C_6$ $2^{5} \cdot 3^{10}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{3}$ $-$
15116544.df.8.L $C_3^9.C_2^4.S_3$ $2^{5} \cdot 3^{10}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{3}$ $-$
15116544.df.8.M $C_3^9.C_2^4.C_6$ $2^{5} \cdot 3^{10}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{3}$ $-$
15116544.df.8.N $C_3^9.C_2^4.S_3$ $2^{5} \cdot 3^{10}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{3}$ $-$
15116544.df.9.a1 $C_3^8.C_2^4.C_2^4$ $2^{8} \cdot 3^{8}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $3^{2}$ $-$
15116544.df.12.A $C_3^9.C_2^6$ $2^{6} \cdot 3^{9}$ ✓ ✓ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $D_6$ $2^{2} \cdot 3$
15116544.df.12.B $C_3^9.C_2^4.C_2^2$ $2^{6} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
15116544.df.12.C $C_3^9.C_2^4.C_2^2$ $2^{6} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
15116544.df.12.D $C_3^9.D_4^2$ $2^{6} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
15116544.df.12.E $C_3^9.C_2^4.C_2^2$ $2^{6} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
15116544.df.12.F $C_3^9.C_2^4.C_2^2$ $2^{6} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
15116544.df.12.G $C_3^9.C_2^4.C_2^2$ $2^{6} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
15116544.df.12.H $C_3^8.D_6.C_2^4$ $2^{6} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
15116544.df.12.I $C_3^9.C_2^4.C_2^2$ $2^{6} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
15116544.df.12.J $C_3^9.C_2^3.C_2^3$ $2^{6} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
15116544.df.12.K $C_3^9.C_2^3.C_2^3$ $2^{6} \cdot 3^{9}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $2^{2} \cdot 3$ $-$
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