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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 114 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
15840.q.1.a1.a1 $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ ✓ ✓ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $C_1$ $1$ ✓
15840.q.2.a1.a1 $M_{11}$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 11$ ✓ ✓ ✓ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $C_2$ $2$ ✓ ✓
15840.q.11.a1.a1 $A_6.C_2^2$ $2^{5} \cdot 3^{2} \cdot 5$ ✓ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $11$ $-$
15840.q.12.a1.a1 $C_2\times \PSL(2,11)$ $2^{3} \cdot 3 \cdot 5 \cdot 11$ ✓ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{2} \cdot 3$ $-$
15840.q.22.a1.a1 $C_2\times A_6$ $2^{4} \cdot 3^{2} \cdot 5$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2 \cdot 11$ $-$
15840.q.22.b1.a1 $A_6.C_2$ $2^{4} \cdot 3^{2} \cdot 5$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2 \cdot 11$ $-$
15840.q.22.c1.a1 $A_6.C_2$ $2^{4} \cdot 3^{2} \cdot 5$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2 \cdot 11$ $-$
15840.q.24.a1.a1 $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{3} \cdot 3$ $-$
15840.q.44.a1.a1 $A_6$ $2^{3} \cdot 3^{2} \cdot 5$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{2} \cdot 11$ $-$
15840.q.55.a1.a1 $F_9:C_2^2$ $2^{5} \cdot 3^{2}$ ✓ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $5 \cdot 11$ $-$
15840.q.66.a1.a1 $C_2\times S_5$ $2^{4} \cdot 3 \cdot 5$ ✓ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2 \cdot 3 \cdot 11$ $-$
15840.q.110.a1.a1 $C_2\times F_9$ $2^{4} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2 \cdot 5 \cdot 11$ $-$
15840.q.110.b1.a1 $C_2\times \PSU(3,2)$ $2^{4} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2 \cdot 5 \cdot 11$ $-$
15840.q.110.c1.a1 $S_3^2:C_2^2$ $2^{4} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2 \cdot 5 \cdot 11$ $-$
15840.q.110.d1.a1 $F_9:C_2$ $2^{4} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2 \cdot 5 \cdot 11$ $-$
15840.q.110.e1.a1 $F_9:C_2$ $2^{4} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2 \cdot 5 \cdot 11$ $-$
15840.q.110.f1.a1 $F_9:C_2$ $2^{4} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2 \cdot 5 \cdot 11$ $-$
15840.q.110.g1.a1 $F_9:C_2$ $2^{4} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2 \cdot 5 \cdot 11$ $-$
15840.q.132.a1.a1 $C_2\times A_5$ $2^{3} \cdot 3 \cdot 5$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ $-$
15840.q.132.a2.a1 $C_2\times A_5$ $2^{3} \cdot 3 \cdot 5$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ $-$
15840.q.132.b1.a1 $S_5$ $2^{3} \cdot 3 \cdot 5$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ $-$
15840.q.132.c1.a1 $S_5$ $2^{3} \cdot 3 \cdot 5$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ $-$
15840.q.144.a1.a1 $C_{11}:C_{10}$ $2 \cdot 5 \cdot 11$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{4} \cdot 3^{2}$ $-$
15840.q.165.a1.a1 $C_2\times \GL(2,3)$ $2^{5} \cdot 3$ ✓ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $3 \cdot 5 \cdot 11$ $-$
15840.q.220.a1.a1 $C_2\times C_3^2:C_4$ $2^{3} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{2} \cdot 5 \cdot 11$ $-$
15840.q.220.a2.a1 $C_2\times C_3^2:C_4$ $2^{3} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{2} \cdot 5 \cdot 11$ $-$
15840.q.220.b1.a1 $S_3\times D_6$ $2^{3} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{2} \cdot 5 \cdot 11$ $-$
15840.q.220.c1.a1 $\SOPlus(4,2)$ $2^{3} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{2} \cdot 5 \cdot 11$ $-$
15840.q.220.d1.a1 $\PSU(3,2)$ $2^{3} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{2} \cdot 5 \cdot 11$ $-$
15840.q.220.d2.a1 $\PSU(3,2)$ $2^{3} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{2} \cdot 5 \cdot 11$ $-$
15840.q.220.e1.a1 $F_9$ $2^{3} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{2} \cdot 5 \cdot 11$ $-$
15840.q.220.f1.a1 $F_9$ $2^{3} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{2} \cdot 5 \cdot 11$ $-$
15840.q.220.g1.a1 $\PSU(3,2)$ $2^{3} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{2} \cdot 5 \cdot 11$ $-$
15840.q.220.h1.a1 $\SOPlus(4,2)$ $2^{3} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{2} \cdot 5 \cdot 11$ $-$
15840.q.220.i1.a1 $\SOPlus(4,2)$ $2^{3} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{2} \cdot 5 \cdot 11$ $-$
15840.q.264.a1.a1 $A_5$ $2^{2} \cdot 3 \cdot 5$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{3} \cdot 3 \cdot 11$ $-$
15840.q.264.a2.a1 $A_5$ $2^{2} \cdot 3 \cdot 5$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{3} \cdot 3 \cdot 11$ $-$
15840.q.288.a1.a1 $C_{11}:C_5$ $5 \cdot 11$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{5} \cdot 3^{2}$ $-$
15840.q.330.a1.a1 $C_2\times \SL(2,3)$ $2^{4} \cdot 3$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2 \cdot 3 \cdot 5 \cdot 11$ $-$
15840.q.330.b1.a1 $C_2\times S_4$ $2^{4} \cdot 3$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2 \cdot 3 \cdot 5 \cdot 11$ $-$
15840.q.330.c1.a1 $\GL(2,3)$ $2^{4} \cdot 3$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2 \cdot 3 \cdot 5 \cdot 11$ $-$
15840.q.330.d1.a1 $\GL(2,3)$ $2^{4} \cdot 3$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2 \cdot 3 \cdot 5 \cdot 11$ $-$
15840.q.396.a1.a1 $C_2\times F_5$ $2^{3} \cdot 5$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{2} \cdot 3^{2} \cdot 11$ $-$
15840.q.440.a1.a1 $C_6\times S_3$ $2^{2} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{3} \cdot 5 \cdot 11$ $-$
15840.q.440.b1.a1 $C_6:S_3$ $2^{2} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{3} \cdot 5 \cdot 11$ $-$
15840.q.440.c1.a1 $S_3^2$ $2^{2} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{3} \cdot 5 \cdot 11$ $-$
15840.q.440.d1.a1 $S_3^2$ $2^{2} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{3} \cdot 5 \cdot 11$ $-$
15840.q.440.e1.a1 $C_3^2:C_4$ $2^{2} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{3} \cdot 5 \cdot 11$ $-$
15840.q.440.e2.a1 $C_3^2:C_4$ $2^{2} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{3} \cdot 5 \cdot 11$ $-$
15840.q.440.f1.a1 $C_3^2:C_4$ $2^{2} \cdot 3^{2}$ $C_2\times M_{11}$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{3} \cdot 5 \cdot 11$ $-$
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