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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 229 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
128.1824.1.a1.a1 $C_2^4.D_4$ $2^{7}$ $2$ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_1$ $1$ ✓
128.1824.2.a1.a1 $C_4^2:C_2^2$ $2^{6}$ ✓ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.1824.2.b1.a1 $C_2^3.D_4$ $2^{6}$ ✓ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.1824.2.c1.a1 $C_2^2:\OD_{16}$ $2^{6}$ ✓ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.1824.2.d1.a1 $C_2^2.D_8$ $2^{6}$ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.1824.2.d1.b1 $C_2^2.D_8$ $2^{6}$ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.1824.2.e1.a1 $C_2^3.D_4$ $2^{6}$ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.1824.2.e1.b1 $C_2^3.D_4$ $2^{6}$ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.1824.2.f1.a1 $C_2^3.D_4$ $2^{6}$ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.1824.2.f1.b1 $C_2^3.D_4$ $2^{6}$ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.1824.2.g1.a1 $\OD_{16}:C_4$ $2^{6}$ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.1824.2.g1.b1 $\OD_{16}:C_4$ $2^{6}$ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.1824.2.h1.a1 $C_2^3.D_4$ $2^{6}$ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.1824.2.h1.b1 $C_2^3.D_4$ $2^{6}$ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.1824.2.i1.a1 $C_2^2.Q_{16}$ $2^{6}$ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.1824.2.i1.b1 $C_2^2.Q_{16}$ $2^{6}$ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2$ $2$ ✓
128.1824.4.a1.a1 $C_2^3\times C_4$ $2^{5}$ ✓ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.b1.a1 $C_4:D_4$ $2^{5}$ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.c1.a1 $C_2^2.D_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.c1.b1 $C_2^2.D_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.d1.a1 $C_2^2:Q_8$ $2^{5}$ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.e1.a1 $C_2^2:C_8$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.e1.b1 $C_2^2:C_8$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.f1.a1 $D_4:C_2^2$ $2^{5}$ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.g1.a1 $C_2^2.D_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.g1.b1 $C_2^2.D_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.h1.a1 $C_4^2:C_2$ $2^{5}$ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.i1.a1 $C_2\times \OD_{16}$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.i1.b1 $C_2\times \OD_{16}$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.j1.a1 $C_4:D_4$ $2^{5}$ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.k1.a1 $C_2^2.D_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.k1.b1 $C_2^2.D_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.l1.a1 $C_2^2:Q_8$ $2^{5}$ ✓ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.m1.a1 $C_2^2:C_8$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.m1.b1 $C_2^2:C_8$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.n1.a1 $D_4:C_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.n1.b1 $D_4:C_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.n1.c1 $D_4:C_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.n1.d1 $D_4:C_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.o1.a1 $C_8:C_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.o1.b1 $C_8:C_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.o1.c1 $C_8:C_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.o1.d1 $C_8:C_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.p1.a1 $Q_8:C_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.p1.b1 $Q_8:C_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.p1.c1 $Q_8:C_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.p1.d1 $Q_8:C_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.q1.a1 $C_8:C_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.q1.b1 $C_8:C_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
128.1824.4.q1.c1 $C_8:C_4$ $2^{5}$ ✓ $C_2^4.D_4$ $2^{7}$ $C_2^2$ $2^{2}$ ✓
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