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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 146 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
384.1698.1.a1.a1 $\OD_{32}.D_6$ $2^{7} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_1$ $1$ ✓
384.1698.2.a1.a1 $C_{24}.D_4$ $2^{6} \cdot 3$ ✓ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2$ $2$ ✓
384.1698.2.b1.a1 $\OD_{32}:C_6$ $2^{6} \cdot 3$ ✓ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2$ $2$ ✓
384.1698.2.c1.a1 $C_{24}.C_2^3$ $2^{6} \cdot 3$ ✓ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2$ $2$ ✓
384.1698.2.d1.a1 $C_8.D_{12}$ $2^{6} \cdot 3$ ✓ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2$ $2$ ✓
384.1698.2.e1.a1 $\OD_{32}:S_3$ $2^{6} \cdot 3$ ✓ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2$ $2$ ✓
384.1698.2.f1.a1 $C_{48}:C_4$ $2^{6} \cdot 3$ ✓ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2$ $2$ ✓
384.1698.2.g1.a1 $C_{24}.D_4$ $2^{6} \cdot 3$ ✓ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2$ $2$ ✓
384.1698.3.a1.a1 $C_{16}.D_4$ $2^{7}$ $2$ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $3$ $-$
384.1698.4.a1.a1 $C_{12}.D_4$ $2^{5} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_4$ $2^{2}$ ✓
384.1698.4.b1.a1 $C_{12}.D_4$ $2^{5} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_4$ $2^{2}$ ✓
384.1698.4.c1.a1 $\OD_{16}:C_6$ $2^{5} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2^2$ $2^{2}$ ✓
384.1698.4.d1.a1 $D_{12}:C_4$ $2^{5} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_4$ $2^{2}$ ✓
384.1698.4.e1.a1 $C_8.D_6$ $2^{5} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2^2$ $2^{2}$ ✓
384.1698.4.f1.a1 $C_{24}:C_4$ $2^{5} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2^2$ $2^{2}$ ✓
384.1698.4.g1.a1 $C_2\times C_{48}$ $2^{5} \cdot 3$ ✓ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2^2$ $2^{2}$ ✓
384.1698.4.h1.a1 $C_6:C_{16}$ $2^{5} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2^2$ $2^{2}$ ✓
384.1698.4.i1.a1 $C_3\times \OD_{32}$ $2^{5} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2^2$ $2^{2}$ ✓
384.1698.4.j1.a1 $C_3:\OD_{32}$ $2^{5} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2^2$ $2^{2}$ ✓
384.1698.4.k1.a1 $C_{12}.D_4$ $2^{5} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_4$ $2^{2}$ ✓
384.1698.4.l1.a1 $C_6:C_{16}$ $2^{5} \cdot 3$ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $2^{2}$ $-$
384.1698.4.m1.a1 $C_3:\OD_{32}$ $2^{5} \cdot 3$ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $2^{2}$ $-$
384.1698.4.n1.a1 $S_3\times C_{16}$ $2^{5} \cdot 3$ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $2^{2}$ $-$
384.1698.4.o1.a1 $C_{48}:C_2$ $2^{5} \cdot 3$ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $2^{2}$ $-$
384.1698.6.a1.a1 $\OD_{32}:C_2$ $2^{6}$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $S_3$ $2 \cdot 3$
384.1698.6.b1.a1 $D_8:C_4$ $2^{6}$ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $2 \cdot 3$ $-$
384.1698.6.c1.a1 $\OD_{32}:C_2$ $2^{6}$ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $2 \cdot 3$ $-$
384.1698.6.d1.a1 $\OD_{32}:C_2$ $2^{6}$ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $2 \cdot 3$ $-$
384.1698.6.e1.a1 $\OD_{32}:C_2$ $2^{6}$ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $2 \cdot 3$ $-$
384.1698.6.f1.a1 $C_4\times C_{16}$ $2^{6}$ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $2 \cdot 3$ $-$
384.1698.6.g1.a1 $C_8.C_8$ $2^{6}$ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $2 \cdot 3$ $-$
384.1698.8.a1.a1 $D_4:C_6$ $2^{4} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2\times C_4$ $2^{3}$ ✓
384.1698.8.b1.a1 $D_{12}:C_2$ $2^{4} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2\times C_4$ $2^{3}$ ✓
384.1698.8.c1.a1 $C_{12}:C_4$ $2^{4} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2\times C_4$ $2^{3}$ ✓
384.1698.8.d1.a1 $C_2\times C_{24}$ $2^{4} \cdot 3$ ✓ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2^3$ $2^{3}$ ✓
384.1698.8.e1.a1 $C_3\times \OD_{16}$ $2^{4} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2\times C_4$ $2^{3}$ ✓
384.1698.8.f1.a1 $C_6:C_8$ $2^{4} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2\times C_4$ $2^{3}$ ✓
384.1698.8.g1.a1 $C_3:\OD_{16}$ $2^{4} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_2\times C_4$ $2^{3}$ ✓
384.1698.8.h1.a1 $C_3:D_8$ $2^{4} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_8$ $2^{3}$ ✓
384.1698.8.i1.a1 $C_3:\SD_{16}$ $2^{4} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_8$ $2^{3}$ ✓
384.1698.8.j1.a1 $Q_8:S_3$ $2^{4} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_8$ $2^{3}$ ✓
384.1698.8.k1.a1 $C_3:C_{16}$ $2^{4} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $D_4$ $2^{3}$
384.1698.8.l1.a1 $C_3:C_{16}$ $2^{4} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $D_4$ $2^{3}$
384.1698.8.m1.a1 $C_3:Q_{16}$ $2^{4} \cdot 3$ ✓ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $C_8$ $2^{3}$ ✓
384.1698.8.n1.a1 $C_2\times C_{24}$ $2^{4} \cdot 3$ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $2^{3}$ $-$
384.1698.8.o1.a1 $C_3\times \OD_{16}$ $2^{4} \cdot 3$ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $2^{3}$ $-$
384.1698.8.p1.a1 $S_3\times C_8$ $2^{4} \cdot 3$ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $2^{3}$ $-$
384.1698.8.q1.a1 $C_{24}:C_2$ $2^{4} \cdot 3$ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $2^{3}$ $-$
384.1698.8.r1.a1 $C_{48}$ $2^{4} \cdot 3$ ✓ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $2^{3}$ $-$
384.1698.8.s1.a1 $C_3:C_{16}$ $2^{4} \cdot 3$ $\OD_{32}.D_6$ $2^{7} \cdot 3$ $2^{3}$ $-$
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