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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 958 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
5376.bl.1.a1 $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ ✓ ✓ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $C_1$ $1$ ✓
5376.bl.2.a1 $C_2^3:F_8:C_6$ $2^{7} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
5376.bl.2.b1 $C_2^3:F_8:C_6$ $2^{7} \cdot 3 \cdot 7$ ✓ ✓ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
5376.bl.3.a1 $C_2^5:F_8$ $2^{8} \cdot 7$ ✓ ✓ ✓ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $C_3$ $3$ ✓
5376.bl.4.a1 $C_2^3:F_8:C_3$ $2^{6} \cdot 3 \cdot 7$ ✓ ✓ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
5376.bl.6.a1 $C_2^4:F_8$ $2^{7} \cdot 7$ ✓ ✓ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $C_6$ $2 \cdot 3$ ✓
5376.bl.6.b1 $C_2^4:F_8$ $2^{7} \cdot 7$ ✓ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $C_6$ $2 \cdot 3$ ✓
5376.bl.7.a1 $C_2^7:C_6$ $2^{8} \cdot 3$ ✓ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $7$ $-$
5376.bl.8.a1 $C_2\times F_8:C_6$ $2^{5} \cdot 3 \cdot 7$ ✓ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{3}$ $-$
5376.bl.12.a1 $C_2^3:F_8$ $2^{6} \cdot 7$ ✓ ✓ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
5376.bl.14.a1 $C_2^5:A_4$ $2^{7} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2 \cdot 7$ $-$
5376.bl.14.b1 $C_2^5:C_{12}$ $2^{7} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2 \cdot 7$ $-$
5376.bl.14.c1 $C_2^5:A_4$ $2^{7} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2 \cdot 7$ $-$
5376.bl.14.d1 $C_2\wr C_6$ $2^{7} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2 \cdot 7$ $-$
5376.bl.14.e1 $C_2\wr C_6$ $2^{7} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2 \cdot 7$ $-$
5376.bl.16.a1 $F_8:C_6$ $2^{4} \cdot 3 \cdot 7$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{4}$ $-$
5376.bl.16.b1 $F_8:C_6$ $2^{4} \cdot 3 \cdot 7$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{4}$ $-$
5376.bl.16.c1 $F_8:C_6$ $2^{4} \cdot 3 \cdot 7$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{4}$ $-$
5376.bl.21.a1 $C_2^5:D_4$ $2^{8}$ $2$ ✓ ✓ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $C_7:C_3$ $3 \cdot 7$
5376.bl.24.a1 $C_2^2\times F_8$ $2^{5} \cdot 7$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{3} \cdot 3$ $-$
5376.bl.28.a1 $C_2^4:A_4$ $2^{6} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{2} \cdot 7$ $-$
5376.bl.28.b1 $C_2^2\wr C_3$ $2^{6} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{2} \cdot 7$ $-$
5376.bl.28.c1 $C_2^5:C_6$ $2^{6} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{2} \cdot 7$ $-$
5376.bl.28.d1 $C_2^2\wr C_3$ $2^{6} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{2} \cdot 7$ $-$
5376.bl.28.e1 $C_2^4:A_4$ $2^{6} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{2} \cdot 7$ $-$
5376.bl.28.f1 $C_2^2\wr C_3$ $2^{6} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{2} \cdot 7$ $-$
5376.bl.28.g1 $C_2^4:A_4$ $2^{6} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{2} \cdot 7$ $-$
5376.bl.28.h1 $C_2^2\wr C_3$ $2^{6} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{2} \cdot 7$ $-$
5376.bl.28.i1 $C_2^4:C_{12}$ $2^{6} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{2} \cdot 7$ $-$
5376.bl.28.j1 $C_2^2\wr C_3$ $2^{6} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{2} \cdot 7$ $-$
5376.bl.32.a1 $F_8:C_3$ $2^{3} \cdot 3 \cdot 7$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{5}$ $-$
5376.bl.32.b1 $F_8:C_3$ $2^{3} \cdot 3 \cdot 7$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{5}$ $-$
5376.bl.42.a1 $C_2^7$ $2^{7}$ ✓ ✓ ✓ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $C_7:C_6$ $2 \cdot 3 \cdot 7$
5376.bl.42.b1 $C_2^3\wr C_2$ $2^{7}$ ✓ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $C_7:C_6$ $2 \cdot 3 \cdot 7$
5376.bl.42.c1 $C_2^4:D_4$ $2^{7}$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2 \cdot 3 \cdot 7$ $-$
5376.bl.42.d1 $C_2^5:C_4$ $2^{7}$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2 \cdot 3 \cdot 7$ $-$
5376.bl.42.e1 $C_2^3\wr C_2$ $2^{7}$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2 \cdot 3 \cdot 7$ $-$
5376.bl.48.a1 $C_2\times F_8$ $2^{4} \cdot 7$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{4} \cdot 3$ $-$
5376.bl.48.b1 $C_2\times F_8$ $2^{4} \cdot 7$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{4} \cdot 3$ $-$
5376.bl.48.c1 $C_2\times F_8$ $2^{4} \cdot 7$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{4} \cdot 3$ $-$
5376.bl.48.d1 $C_2\times F_8$ $2^{4} \cdot 7$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{4} \cdot 3$ $-$
5376.bl.56.a1 $C_2^3\times A_4$ $2^{5} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{3} \cdot 7$ $-$
5376.bl.56.b1 $C_2^3\times A_4$ $2^{5} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{3} \cdot 7$ $-$
5376.bl.56.c1 $C_2^3:A_4$ $2^{5} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{3} \cdot 7$ $-$
5376.bl.56.d1 $C_2^3\times A_4$ $2^{5} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{3} \cdot 7$ $-$
5376.bl.56.e1 $C_2^3\times A_4$ $2^{5} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{3} \cdot 7$ $-$
5376.bl.56.f1 $C_2^3:C_{12}$ $2^{5} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{3} \cdot 7$ $-$
5376.bl.56.g1 $C_2^3:A_4$ $2^{5} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{3} \cdot 7$ $-$
5376.bl.56.h1 $C_2^3:A_4$ $2^{5} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{3} \cdot 7$ $-$
5376.bl.56.i1 $C_2^3:A_4$ $2^{5} \cdot 3$ $C_2^4:F_8:C_6$ $2^{8} \cdot 3 \cdot 7$ $2^{3} \cdot 7$ $-$
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