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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 815 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
16128.bb.1.a1.a1 $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ ✓ ✓ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $C_1$ $1$ ✓
16128.bb.2.a1.a1 $C_3\times D_8.\PSL(2,7)$ $2^{7} \cdot 3^{2} \cdot 7$ ✓ ✓ ✓ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $C_2$ $2$ ✓
16128.bb.2.b1.a1 $(C_3\times \SL(2,7)):D_4$ $2^{7} \cdot 3^{2} \cdot 7$ ✓ ✓ ✓ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $C_2$ $2$ ✓
16128.bb.2.c1.a1 $C_{48}.\PSL(2,7)$ $2^{7} \cdot 3^{2} \cdot 7$ ✓ ✓ ✓ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $C_2$ $2$ ✓
16128.bb.3.a1.a1 $\SL(2,7).D_8$ $2^{8} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $C_3$ $3$ ✓
16128.bb.4.a1.a1 $\SL(2,7):C_{12}$ $2^{6} \cdot 3^{2} \cdot 7$ ✓ ✓ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $C_2^2$ $2^{2}$ ✓
16128.bb.4.b1.a1 $(C_2\times \SL(2,7)):C_6$ $2^{6} \cdot 3^{2} \cdot 7$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2^{2}$ $-$
16128.bb.4.c1.a1 $C_3\times \SL(2,7):C_2^2$ $2^{6} \cdot 3^{2} \cdot 7$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2^{2}$ $-$
16128.bb.6.a1.a1 $D_8.\PSL(2,7)$ $2^{7} \cdot 3 \cdot 7$ ✓ ✓ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $C_6$ $2 \cdot 3$ ✓
16128.bb.6.b1.a1 $Q_{16}.\PSL(2,7)$ $2^{7} \cdot 3 \cdot 7$ ✓ ✓ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $C_6$ $2 \cdot 3$ ✓
16128.bb.6.c1.a1 $C_{16}.\PSL(2,7)$ $2^{7} \cdot 3 \cdot 7$ ✓ ✓ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $C_6$ $2 \cdot 3$ ✓
16128.bb.7.a1.a1 $C_3\times \GL(2,3).D_8$ $2^{8} \cdot 3^{2}$ ✓ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $7$ $-$
16128.bb.7.a1.a2 $C_3\times \GL(2,3).D_8$ $2^{8} \cdot 3^{2}$ ✓ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $7$ $-$
16128.bb.8.a1.a1 $\SL(2,7):C_6$ $2^{5} \cdot 3^{2} \cdot 7$ ✓ ✓ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $D_4$ $2^{3}$
16128.bb.8.b1.a1 $C_6\times \SL(2,7)$ $2^{5} \cdot 3^{2} \cdot 7$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2^{3}$ $-$
16128.bb.8.c1.a1 $C_{336}:C_6$ $2^{5} \cdot 3^{2} \cdot 7$ ✓ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2^{3}$ $-$
16128.bb.8.d1.a1 $\SL(2,7):C_6$ $2^{5} \cdot 3^{2} \cdot 7$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2^{3}$ $-$
16128.bb.12.a1.a1 $\SL(2,7):C_4$ $2^{6} \cdot 3 \cdot 7$ ✓ ✓ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
16128.bb.12.b1.a1 $D_4.\PSL(2,7)$ $2^{6} \cdot 3 \cdot 7$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2^{2} \cdot 3$ $-$
16128.bb.12.c1.a1 $\SL(2,7):C_2^2$ $2^{6} \cdot 3 \cdot 7$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2^{2} \cdot 3$ $-$
16128.bb.14.a1.a1 $C_3\times \SL(2,3).D_8$ $2^{7} \cdot 3^{2}$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2 \cdot 7$ $-$
16128.bb.14.a1.a2 $C_3\times \SL(2,3).D_8$ $2^{7} \cdot 3^{2}$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2 \cdot 7$ $-$
16128.bb.14.b1.a1 $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2 \cdot 7$ $-$
16128.bb.14.b1.a2 $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2 \cdot 7$ $-$
16128.bb.14.c1.a1 $C_3\times D_8.S_4$ $2^{7} \cdot 3^{2}$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2 \cdot 7$ $-$
16128.bb.14.c1.a2 $C_3\times D_8.S_4$ $2^{7} \cdot 3^{2}$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2 \cdot 7$ $-$
16128.bb.14.d1.a1 $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2 \cdot 7$ $-$
16128.bb.14.d1.a2 $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2 \cdot 7$ $-$
16128.bb.14.e1.a1 $C_{48}.S_4$ $2^{7} \cdot 3^{2}$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2 \cdot 7$ $-$
16128.bb.14.e1.a2 $C_{48}.S_4$ $2^{7} \cdot 3^{2}$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2 \cdot 7$ $-$
16128.bb.14.f1.a1 $C_3\times \GL(2,3):D_4$ $2^{7} \cdot 3^{2}$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2 \cdot 7$ $-$
16128.bb.14.f1.a2 $C_3\times \GL(2,3):D_4$ $2^{7} \cdot 3^{2}$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2 \cdot 7$ $-$
16128.bb.14.g1.a1 $C_{48}.S_4$ $2^{7} \cdot 3^{2}$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2 \cdot 7$ $-$
16128.bb.14.g1.a2 $C_{48}.S_4$ $2^{7} \cdot 3^{2}$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2 \cdot 7$ $-$
16128.bb.16.a1.a1 $C_3\times \SL(2,7)$ $2^{4} \cdot 3^{2} \cdot 7$ ✓ ✓ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $D_8$ $2^{4}$
16128.bb.16.b1.a1 $C_{168}:C_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2^{4}$ $-$
16128.bb.16.c1.a1 $C_{168}.C_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2^{4}$ $-$
16128.bb.16.d1.a1 $C_{21}:C_{48}$ $2^{4} \cdot 3^{2} \cdot 7$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2^{4}$ $-$
16128.bb.21.a1.a1 $C_{12}.D_4^2$ $2^{8} \cdot 3$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $3 \cdot 7$ $-$
16128.bb.21.b1.a1 $\GL(2,3).D_8$ $2^{8} \cdot 3$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $3 \cdot 7$ $-$
16128.bb.21.b1.a2 $\GL(2,3).D_8$ $2^{8} \cdot 3$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $3 \cdot 7$ $-$
16128.bb.24.a1.a1 $\SL(2,7):C_2$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $C_3\times D_4$ $2^{3} \cdot 3$
16128.bb.24.b1.a1 $C_2\times \SL(2,7)$ $2^{5} \cdot 3 \cdot 7$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2^{3} \cdot 3$ $-$
16128.bb.24.c1.a1 $C_{21}\times \SD_{32}$ $2^{5} \cdot 3 \cdot 7$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2^{3} \cdot 3$ $-$
16128.bb.24.d1.a1 $C_{112}:C_6$ $2^{5} \cdot 3 \cdot 7$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2^{3} \cdot 3$ $-$
16128.bb.24.e1.a1 $C_{112}:C_6$ $2^{5} \cdot 3 \cdot 7$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2^{3} \cdot 3$ $-$
16128.bb.24.e1.a2 $C_{112}:C_6$ $2^{5} \cdot 3 \cdot 7$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2^{3} \cdot 3$ $-$
16128.bb.24.f1.a1 $\SL(2,7):C_2$ $2^{5} \cdot 3 \cdot 7$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2^{3} \cdot 3$ $-$
16128.bb.28.a1.a1 $C_6.\GL(2,\mathbb{Z}/4)$ $2^{6} \cdot 3^{2}$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2^{2} \cdot 7$ $-$
16128.bb.28.a1.a2 $C_6.\GL(2,\mathbb{Z}/4)$ $2^{6} \cdot 3^{2}$ $C_3\times \SL(2,7).D_8$ $2^{8} \cdot 3^{2} \cdot 7$ $2^{2} \cdot 7$ $-$
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