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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 426 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
20160.l.1.a1 $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $C_1$ $1$ ✓
20160.l.2.a1 $C_2\times S_7$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2$ $2$ ✓
20160.l.2.b1 $C_2^2\times A_7$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2$ $2$ ✓
20160.l.4.a1 $C_2\times A_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2^2$ $2^{2}$ ✓
20160.l.4.b1 $S_7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2^2$ $2^{2}$ ✓
20160.l.7.a1 $C_2^2\times S_6$ $2^{6} \cdot 3^{2} \cdot 5$ ✓ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $7$ $-$
20160.l.8.a1 $A_7$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ ✓ ✓ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $C_2^3$ $2^{3}$ ✓ ✓
20160.l.14.a1 $C_2\times S_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2 \cdot 7$ $-$
20160.l.14.b1 $C_2^2\times A_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2 \cdot 7$ $-$
20160.l.21.a1 $C_2^3\times S_5$ $2^{6} \cdot 3 \cdot 5$ ✓ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $3 \cdot 7$ $-$
20160.l.28.a1 $C_2\times A_6$ $2^{4} \cdot 3^{2} \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 7$ $-$
20160.l.28.b1 $S_6$ $2^{4} \cdot 3^{2} \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 7$ $-$
20160.l.30.a1 $C_2^2\times \GL(3,2)$ $2^{5} \cdot 3 \cdot 7$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2 \cdot 3 \cdot 5$ $-$
20160.l.35.a1 $C_2^2:D_6^2$ $2^{6} \cdot 3^{2}$ ✓ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $5 \cdot 7$ $-$
20160.l.42.a1 $C_2^2\times S_5$ $2^{5} \cdot 3 \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2 \cdot 3 \cdot 7$ $-$
20160.l.42.b1 $C_2^2\times S_5$ $2^{5} \cdot 3 \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2 \cdot 3 \cdot 7$ $-$
20160.l.42.c1 $C_2^3\times A_5$ $2^{5} \cdot 3 \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2 \cdot 3 \cdot 7$ $-$
20160.l.42.d1 $C_2^2\times S_5$ $2^{5} \cdot 3 \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2 \cdot 3 \cdot 7$ $-$
20160.l.42.e1 $C_2^2\times S_5$ $2^{5} \cdot 3 \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2 \cdot 3 \cdot 7$ $-$
20160.l.42.f1 $C_2^2\times S_5$ $2^{5} \cdot 3 \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2 \cdot 3 \cdot 7$ $-$
20160.l.56.a1 $A_6$ $2^{3} \cdot 3^{2} \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{3} \cdot 7$ $-$
20160.l.60.a1 $C_2\times \GL(3,2)$ $2^{4} \cdot 3 \cdot 7$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 3 \cdot 5$ $-$
20160.l.70.a1 $D_6\times S_4$ $2^{5} \cdot 3^{2}$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2 \cdot 5 \cdot 7$ $-$
20160.l.70.b1 $D_6\times S_4$ $2^{5} \cdot 3^{2}$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2 \cdot 5 \cdot 7$ $-$
20160.l.70.c1 $C_2\times A_4\times D_6$ $2^{5} \cdot 3^{2}$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2 \cdot 5 \cdot 7$ $-$
20160.l.70.d1 $C_2\times C_6\times S_4$ $2^{5} \cdot 3^{2}$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2 \cdot 5 \cdot 7$ $-$
20160.l.70.e1 $C_6^2:D_4$ $2^{5} \cdot 3^{2}$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2 \cdot 5 \cdot 7$ $-$
20160.l.70.f1 $C_2\times C_6:S_4$ $2^{5} \cdot 3^{2}$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2 \cdot 5 \cdot 7$ $-$
20160.l.84.a1 $C_2^2\times A_5$ $2^{4} \cdot 3 \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 3 \cdot 7$ $-$
20160.l.84.b1 $C_2\times S_5$ $2^{4} \cdot 3 \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 3 \cdot 7$ $-$
20160.l.84.c1 $C_2\times S_5$ $2^{4} \cdot 3 \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 3 \cdot 7$ $-$
20160.l.84.d1 $C_2\times S_5$ $2^{4} \cdot 3 \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 3 \cdot 7$ $-$
20160.l.84.e1 $C_2\times S_5$ $2^{4} \cdot 3 \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 3 \cdot 7$ $-$
20160.l.84.f1 $C_2^2\times A_5$ $2^{4} \cdot 3 \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 3 \cdot 7$ $-$
20160.l.84.g1 $C_2^2\times A_5$ $2^{4} \cdot 3 \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 3 \cdot 7$ $-$
20160.l.84.h1 $C_2\times S_5$ $2^{4} \cdot 3 \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 3 \cdot 7$ $-$
20160.l.84.i1 $C_2\times S_5$ $2^{4} \cdot 3 \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 3 \cdot 7$ $-$
20160.l.105.a1 $C_2^3\times S_4$ $2^{6} \cdot 3$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $3 \cdot 5 \cdot 7$ $-$
20160.l.105.b1 $C_{12}:C_2^4$ $2^{6} \cdot 3$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $3 \cdot 5 \cdot 7$ $-$
20160.l.105.c1 $C_2^3\times S_4$ $2^{6} \cdot 3$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $3 \cdot 5 \cdot 7$ $-$
20160.l.120.a1 $C_2^2\times F_7$ $2^{3} \cdot 3 \cdot 7$ ✓ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{3} \cdot 3 \cdot 5$ $-$
20160.l.120.b1 $\PSL(2,7)$ $2^{3} \cdot 3 \cdot 7$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{3} \cdot 3 \cdot 5$ $-$
20160.l.126.a1 $C_2^3\times F_5$ $2^{5} \cdot 5$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2 \cdot 3^{2} \cdot 7$ $-$
20160.l.140.a1 $A_4\times D_6$ $2^{4} \cdot 3^{2}$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 5 \cdot 7$ $-$
20160.l.140.b1 $C_6\times S_4$ $2^{4} \cdot 3^{2}$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 5 \cdot 7$ $-$
20160.l.140.c1 $S_3^2:C_2^2$ $2^{4} \cdot 3^{2}$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 5 \cdot 7$ $-$
20160.l.140.d1 $S_3^2:C_2^2$ $2^{4} \cdot 3^{2}$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 5 \cdot 7$ $-$
20160.l.140.e1 $C_6:S_4$ $2^{4} \cdot 3^{2}$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 5 \cdot 7$ $-$
20160.l.140.f1 $C_6:S_4$ $2^{4} \cdot 3^{2}$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 5 \cdot 7$ $-$
20160.l.140.g1 $D_6^2$ $2^{4} \cdot 3^{2}$ $C_2^2\times S_7$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 5 \cdot 7$ $-$
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