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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 63 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1944.3473.1.a1 $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ ✓ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $C_1$ $1$ ✓
1944.3473.2.a1 $(C_3^2\times \He_3):C_4$ $2^{2} \cdot 3^{5}$ ✓ ✓ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $C_2$ $2$ ✓
1944.3473.4.a1 $C_3^4:S_3$ $2 \cdot 3^{5}$ ✓ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $C_4$ $2^{2}$ ✓
1944.3473.6.a1 $(C_3\times \He_3):C_4$ $2^{2} \cdot 3^{4}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3473.8.a1 $C_3^2\times \He_3$ $3^{5}$ $3$ ✓ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $C_8$ $2^{3}$ ✓
1944.3473.9.a1 $C_3^3:C_8$ $2^{3} \cdot 3^{3}$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $3^{2}$ $-$
1944.3473.9.b1 $\He_3:C_8$ $2^{3} \cdot 3^{3}$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $3^{2}$ $-$
1944.3473.12.a1 $S_3\times C_3^3$ $2 \cdot 3^{4}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
1944.3473.12.b1 $C_3^3:S_3$ $2 \cdot 3^{4}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
1944.3473.18.a1 $C_3^2:C_{12}$ $2^{2} \cdot 3^{3}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
1944.3473.18.b1 $\He_3:C_4$ $2^{2} \cdot 3^{3}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{2}$ $-$
1944.3473.24.a1 $C_3\times \He_3$ $3^{4}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{3} \cdot 3$ $-$
1944.3473.24.b1 $C_3\times \He_3$ $3^{4}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{3} \cdot 3$ $-$
1944.3473.24.c1 $C_3^4$ $3^{4}$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{3} \cdot 3$ $-$
1944.3473.27.a1 $C_3^2:C_8$ $2^{3} \cdot 3^{2}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $3^{3}$ $-$
1944.3473.36.a1 $C_3^2:S_3$ $2 \cdot 3^{3}$ ✓ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $C_3^2:C_4$ $2^{2} \cdot 3^{2}$
1944.3473.36.b1 $C_3^2\times C_6$ $2 \cdot 3^{3}$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3^{2}$ $-$
1944.3473.36.c1 $S_3\times C_3^2$ $2 \cdot 3^{3}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3^{2}$ $-$
1944.3473.36.d1 $S_3\times C_3^2$ $2 \cdot 3^{3}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3^{2}$ $-$
1944.3473.36.e1 $S_3\times C_3^2$ $2 \cdot 3^{3}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3^{2}$ $-$
1944.3473.54.a1 $C_3:C_{12}$ $2^{2} \cdot 3^{2}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{3}$ $-$
1944.3473.54.b1 $C_3^2:C_4$ $2^{2} \cdot 3^{2}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{3}$ $-$
1944.3473.72.a1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $F_9$ $2^{3} \cdot 3^{2}$
1944.3473.72.b1 $\He_3$ $3^{3}$ ✓ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $C_3^2:C_8$ $2^{3} \cdot 3^{2}$
1944.3473.72.c1 $C_3^3$ $3^{3}$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{3} \cdot 3^{2}$ $-$
1944.3473.72.d1 $C_3^3$ $3^{3}$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{3} \cdot 3^{2}$ $-$
1944.3473.72.e1 $\He_3$ $3^{3}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{3} \cdot 3^{2}$ $-$
1944.3473.72.f1 $\He_3$ $3^{3}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{3} \cdot 3^{2}$ $-$
1944.3473.72.f2 $\He_3$ $3^{3}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{3} \cdot 3^{2}$ $-$
1944.3473.72.f3 $\He_3$ $3^{3}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{3} \cdot 3^{2}$ $-$
1944.3473.72.g1 $C_3^3$ $3^{3}$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{3} \cdot 3^{2}$ $-$
1944.3473.72.h1 $C_3^3$ $3^{3}$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{3} \cdot 3^{2}$ $-$
1944.3473.81.a1 $C_3:C_8$ $2^{3} \cdot 3$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $3^{4}$ $-$
1944.3473.108.a1 $C_3\times C_6$ $2 \cdot 3^{2}$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3^{3}$ $-$
1944.3473.108.b1 $C_3\times C_6$ $2 \cdot 3^{2}$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3^{3}$ $-$
1944.3473.108.c1 $C_3\times C_6$ $2 \cdot 3^{2}$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3^{3}$ $-$
1944.3473.108.d1 $C_3\times S_3$ $2 \cdot 3^{2}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3^{3}$ $-$
1944.3473.108.e1 $C_3\times S_3$ $2 \cdot 3^{2}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3^{3}$ $-$
1944.3473.108.f1 $C_3\times S_3$ $2 \cdot 3^{2}$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{2} \cdot 3^{3}$ $-$
1944.3473.162.a1 $C_{12}$ $2^{2} \cdot 3$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{4}$ $-$
1944.3473.162.b1 $C_3:C_4$ $2^{2} \cdot 3$ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2 \cdot 3^{4}$ $-$
1944.3473.216.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $\He_3:C_8$ $2^{3} \cdot 3^{3}$ ✓
1944.3473.216.b1 $C_3^2$ $3^{2}$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{3} \cdot 3^{3}$ $-$
1944.3473.216.c1 $C_3^2$ $3^{2}$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{3} \cdot 3^{3}$ $-$
1944.3473.216.d1 $C_3^2$ $3^{2}$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{3} \cdot 3^{3}$ $-$
1944.3473.216.e1 $C_3^2$ $3^{2}$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{3} \cdot 3^{3}$ $-$
1944.3473.216.f1 $C_3^2$ $3^{2}$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{3} \cdot 3^{3}$ $-$
1944.3473.216.g1 $C_3^2$ $3^{2}$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{3} \cdot 3^{3}$ $-$
1944.3473.216.h1 $C_3^2$ $3^{2}$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{3} \cdot 3^{3}$ $-$
1944.3473.216.i1 $C_3^2$ $3^{2}$ ✓ $C_3^3.F_9$ $2^{3} \cdot 3^{5}$ $2^{3} \cdot 3^{3}$ $-$
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