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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 61 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
384.20164.1.a1 $C_2^4:S_4$ $2^{7} \cdot 3$ ✓ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $C_1$ $1$ ✓
384.20164.2.a1 $C_2^4:A_4$ $2^{6} \cdot 3$ ✓ ✓ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $C_2$ $2$ ✓
384.20164.3.a1 $C_2^3\wr C_2$ $2^{7}$ $2$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $3$ $-$
384.20164.4.a1 $C_2^2:S_4$ $2^{5} \cdot 3$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{2}$ $-$
384.20164.6.a1 $C_2^6$ $2^{6}$ ✓ ✓ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $S_3$ $2 \cdot 3$
384.20164.6.b1 $C_2^3:D_4$ $2^{6}$ $C_2^4:S_4$ $2^{7} \cdot 3$ $2 \cdot 3$ $-$
384.20164.6.c1 $C_2^4:C_4$ $2^{6}$ $C_2^4:S_4$ $2^{7} \cdot 3$ $2 \cdot 3$ $-$
384.20164.8.a1 $C_2^2:A_4$ $2^{4} \cdot 3$ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{3}$ $-$
384.20164.8.b1 $C_2^2:A_4$ $2^{4} \cdot 3$ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{3}$ $-$
384.20164.12.a1 $C_2^2\wr C_2$ $2^{5}$ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{2} \cdot 3$ $-$
384.20164.12.b1 $C_2^2\wr C_2$ $2^{5}$ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{2} \cdot 3$ $-$
384.20164.12.c1 $C_2^2\times D_4$ $2^{5}$ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{2} \cdot 3$ $-$
384.20164.12.d1 $C_2^3:C_4$ $2^{5}$ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{2} \cdot 3$ $-$
384.20164.12.e1 $C_2^5$ $2^{5}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{2} \cdot 3$ $-$
384.20164.12.f1 $C_2^5$ $2^{5}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{2} \cdot 3$ $-$
384.20164.16.a1 $S_4$ $2^{3} \cdot 3$ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{4}$ $-$
384.20164.24.a1 $C_2^4$ $2^{4}$ ✓ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $S_4$ $2^{3} \cdot 3$
384.20164.24.b1 $C_2\times D_4$ $2^{4}$ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{3} \cdot 3$ $-$
384.20164.24.c1 $C_2^2:C_4$ $2^{4}$ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{3} \cdot 3$ $-$
384.20164.24.d1 $C_2^4$ $2^{4}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{3} \cdot 3$ $-$
384.20164.24.d2 $C_2^4$ $2^{4}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{3} \cdot 3$ $-$
384.20164.24.e1 $C_2\times D_4$ $2^{4}$ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{3} \cdot 3$ $-$
384.20164.24.f1 $C_2^2:C_4$ $2^{4}$ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{3} \cdot 3$ $-$
384.20164.24.g1 $C_2^4$ $2^{4}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{3} \cdot 3$ $-$
384.20164.24.g2 $C_2^4$ $2^{4}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{3} \cdot 3$ $-$
384.20164.24.h1 $C_2^4$ $2^{4}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{3} \cdot 3$ $-$
384.20164.24.i1 $C_2^4$ $2^{4}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{3} \cdot 3$ $-$
384.20164.24.j1 $C_2^2\times C_4$ $2^{4}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{3} \cdot 3$ $-$
384.20164.24.k1 $C_2^4$ $2^{4}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{3} \cdot 3$ $-$
384.20164.32.a1 $A_4$ $2^{2} \cdot 3$ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{5}$ $-$
384.20164.32.b1 $A_4$ $2^{2} \cdot 3$ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{5}$ $-$
384.20164.48.a1 $D_4$ $2^{3}$ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{4} \cdot 3$ $-$
384.20164.48.b1 $C_2^3$ $2^{3}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{4} \cdot 3$ $-$
384.20164.48.b2 $C_2^3$ $2^{3}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{4} \cdot 3$ $-$
384.20164.48.c1 $C_2^3$ $2^{3}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{4} \cdot 3$ $-$
384.20164.48.d1 $C_2^3$ $2^{3}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{4} \cdot 3$ $-$
384.20164.48.d2 $C_2^3$ $2^{3}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{4} \cdot 3$ $-$
384.20164.48.d3 $C_2^3$ $2^{3}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{4} \cdot 3$ $-$
384.20164.48.d4 $C_2^3$ $2^{3}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{4} \cdot 3$ $-$
384.20164.48.e1 $D_4$ $2^{3}$ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{4} \cdot 3$ $-$
384.20164.48.f1 $C_2^3$ $2^{3}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{4} \cdot 3$ $-$
384.20164.48.g1 $C_2\times C_4$ $2^{3}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{4} \cdot 3$ $-$
384.20164.48.h1 $C_2^3$ $2^{3}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{4} \cdot 3$ $-$
384.20164.48.i1 $C_2^3$ $2^{3}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{4} \cdot 3$ $-$
384.20164.48.j1 $C_2^3$ $2^{3}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{4} \cdot 3$ $-$
384.20164.48.k1 $C_2^3$ $2^{3}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{4} \cdot 3$ $-$
384.20164.64.a1 $S_3$ $2 \cdot 3$ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{6}$ $-$
384.20164.96.a1 $C_2^2$ $2^{2}$ ✓ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $C_2^2:S_4$ $2^{5} \cdot 3$ ✓
384.20164.96.b1 $C_2^2$ $2^{2}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{5} \cdot 3$ $-$
384.20164.96.b2 $C_2^2$ $2^{2}$ ✓ $C_2^4:S_4$ $2^{7} \cdot 3$ $2^{5} \cdot 3$ $-$
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