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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 528 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
768.1090131.1.a1.a1 $C_2^5:S_4$ $2^{8} \cdot 3$ ✓ ✓ $C_2^5:S_4$ $2^{8} \cdot 3$ $C_1$ $1$ ✓
768.1090131.2.a1.a1 $C_2^5:A_4$ $2^{7} \cdot 3$ ✓ ✓ ✓ $C_2^5:S_4$ $2^{8} \cdot 3$ $C_2$ $2$ ✓
768.1090131.2.b1.a1 $C_4^2:S_4$ $2^{7} \cdot 3$ ✓ ✓ $C_2^5:S_4$ $2^{8} \cdot 3$ $C_2$ $2$ ✓
768.1090131.2.b1.b1 $C_4^2:S_4$ $2^{7} \cdot 3$ ✓ ✓ $C_2^5:S_4$ $2^{8} \cdot 3$ $C_2$ $2$ ✓
768.1090131.3.a1.a1 $C_2^5:D_4$ $2^{8}$ $2$ ✓ $C_2^5:S_4$ $2^{8} \cdot 3$ $3$ $-$
768.1090131.4.a1.a1 $C_4^2:A_4$ $2^{6} \cdot 3$ ✓ ✓ $C_2^5:S_4$ $2^{8} \cdot 3$ $C_2^2$ $2^{2}$ ✓
768.1090131.4.b1.a1 $C_2^3:S_4$ $2^{6} \cdot 3$ ✓ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{2}$ $-$
768.1090131.4.b1.b1 $C_2^3:S_4$ $2^{6} \cdot 3$ ✓ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{2}$ $-$
768.1090131.4.c1.a1 $C_4^2:D_6$ $2^{6} \cdot 3$ ✓ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{2}$ $-$
768.1090131.6.a1.a1 $C_4^2:C_2^3$ $2^{7}$ ✓ ✓ $C_2^5:S_4$ $2^{8} \cdot 3$ $S_3$ $2 \cdot 3$
768.1090131.6.b1.a1 $C_4^2:C_2^3$ $2^{7}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2 \cdot 3$ $-$
768.1090131.6.c1.a1 $C_2^4.D_4$ $2^{7}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2 \cdot 3$ $-$
768.1090131.6.d1.a1 $C_2^4:D_4$ $2^{7}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2 \cdot 3$ $-$
768.1090131.6.d1.b1 $C_2^4:D_4$ $2^{7}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2 \cdot 3$ $-$
768.1090131.6.e1.a1 $C_2^5:C_4$ $2^{7}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2 \cdot 3$ $-$
768.1090131.6.e1.b1 $C_2^5:C_4$ $2^{7}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2 \cdot 3$ $-$
768.1090131.6.f1.a1 $C_4^2:D_4$ $2^{7}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2 \cdot 3$ $-$
768.1090131.6.f1.b1 $C_4^2:D_4$ $2^{7}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2 \cdot 3$ $-$
768.1090131.6.f1.c1 $C_4^2:D_4$ $2^{7}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2 \cdot 3$ $-$
768.1090131.6.f1.d1 $C_4^2:D_4$ $2^{7}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2 \cdot 3$ $-$
768.1090131.6.g1.a1 $C_4^2:D_4$ $2^{7}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2 \cdot 3$ $-$
768.1090131.6.g1.b1 $C_4^2:D_4$ $2^{7}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2 \cdot 3$ $-$
768.1090131.6.h1.a1 $C_4^2:D_4$ $2^{7}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2 \cdot 3$ $-$
768.1090131.6.h1.b1 $C_4^2:D_4$ $2^{7}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2 \cdot 3$ $-$
768.1090131.8.a1.a1 $C_2^3:A_4$ $2^{5} \cdot 3$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{3}$ $-$
768.1090131.8.a1.b1 $C_2^3:A_4$ $2^{5} \cdot 3$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{3}$ $-$
768.1090131.8.b1.a1 $C_4^2:C_6$ $2^{5} \cdot 3$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{3}$ $-$
768.1090131.8.c1.a1 $C_4^2:C_6$ $2^{5} \cdot 3$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{3}$ $-$
768.1090131.8.d1.a1 $C_2^2:S_4$ $2^{5} \cdot 3$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{3}$ $-$
768.1090131.8.d1.b1 $C_2^2:S_4$ $2^{5} \cdot 3$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{3}$ $-$
768.1090131.8.d1.c1 $C_2^2:S_4$ $2^{5} \cdot 3$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{3}$ $-$
768.1090131.8.d1.d1 $C_2^2:S_4$ $2^{5} \cdot 3$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{3}$ $-$
768.1090131.8.e1.a1 $C_4^2:S_3$ $2^{5} \cdot 3$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{3}$ $-$
768.1090131.8.e1.b1 $C_4^2:S_3$ $2^{5} \cdot 3$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{3}$ $-$
768.1090131.12.a1.a1 $C_4^2:C_2^2$ $2^{6}$ ✓ ✓ $C_2^5:S_4$ $2^{8} \cdot 3$ $D_6$ $2^{2} \cdot 3$
768.1090131.12.b1.a1 $C_2^4:C_4$ $2^{6}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{2} \cdot 3$ $-$
768.1090131.12.b1.b1 $C_2^4:C_4$ $2^{6}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{2} \cdot 3$ $-$
768.1090131.12.c1.a1 $D_4:C_2^3$ $2^{6}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{2} \cdot 3$ $-$
768.1090131.12.d1.a1 $C_4^2:C_2^2$ $2^{6}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{2} \cdot 3$ $-$
768.1090131.12.e1.a1 $C_2^4:C_4$ $2^{6}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{2} \cdot 3$ $-$
768.1090131.12.e1.b1 $C_2^4:C_4$ $2^{6}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{2} \cdot 3$ $-$
768.1090131.12.f1.a1 $\OD_{16}:C_2^2$ $2^{6}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{2} \cdot 3$ $-$
768.1090131.12.g1.a1 $C_4^2:C_2^2$ $2^{6}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{2} \cdot 3$ $-$
768.1090131.12.h1.a1 $C_2^3:D_4$ $2^{6}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{2} \cdot 3$ $-$
768.1090131.12.h1.b1 $C_2^3:D_4$ $2^{6}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{2} \cdot 3$ $-$
768.1090131.12.i1.a1 $C_2^3:D_4$ $2^{6}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{2} \cdot 3$ $-$
768.1090131.12.i1.b1 $C_2^3:D_4$ $2^{6}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{2} \cdot 3$ $-$
768.1090131.12.j1.a1 $Q_{16}:C_2^2$ $2^{6}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{2} \cdot 3$ $-$
768.1090131.12.k1.a1 $C_4^2:C_2^2$ $2^{6}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{2} \cdot 3$ $-$
768.1090131.12.l1.a1 $C_2\wr C_2^2$ $2^{6}$ $C_2^5:S_4$ $2^{8} \cdot 3$ $2^{2} \cdot 3$ $-$
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