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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 291 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
256.12509.1.a1.a1 $C_4^2.C_2^4$ $2^{8}$ $2$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_1$ $1$ ✓
256.12509.2.a1.a1 $C_4^2.D_4$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.12509.2.b1.a1 $C_4^2.D_4$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.12509.2.c1.a1 $C_4^2.D_4$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.12509.2.d1.a1 $C_4^2.D_4$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.12509.2.e1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.12509.2.f1.a1 $C_4^2.D_4$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.12509.2.g1.a1 $C_4^2.D_4$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.12509.2.h1.a1 $C_8:\SD_{16}$ $2^{7}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.12509.2.h1.b1 $C_8:\SD_{16}$ $2^{7}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.12509.2.i1.a1 $C_8:\SD_{16}$ $2^{7}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.12509.2.i1.b1 $C_8:\SD_{16}$ $2^{7}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.12509.2.j1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.12509.2.j1.b1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.12509.2.k1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.12509.2.k1.b1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.12509.4.a1.a1 $C_4^2.C_2^2$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.b1.a1 $C_4^2.C_2^2$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.c1.a1 $C_4^2.C_2^2$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.d1.a1 $C_4^2.C_4$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.e1.a1 $C_4^2.C_4$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.f1.a1 $C_4^2.C_4$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.g1.a1 $C_4^2.C_4$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.h1.a1 $Q_8:D_4$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.h1.b1 $Q_8:D_4$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.i1.a1 $C_8:D_4$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.j1.a1 $C_8:D_4$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.k1.a1 $C_4.D_8$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.k1.b1 $C_4.D_8$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.l1.a1 $Q_8:Q_8$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.l1.b1 $Q_8:Q_8$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.m1.a1 $Q_8:Q_8$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.m1.b1 $Q_8:Q_8$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.n1.a1 $C_4:Q_{16}$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.n1.b1 $C_4:Q_{16}$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.o1.a1 $C_8\times Q_8$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.o1.b1 $C_8\times Q_8$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.p1.a1 $C_8:Q_8$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.p1.b1 $C_8:Q_8$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.q1.a1 $C_4.Q_{16}$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.r1.a1 $C_4.D_8$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.r1.b1 $C_4.D_8$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.s1.a1 $C_4.Q_{16}$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.t1.a1 $C_4.D_8$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.t1.b1 $C_4.D_8$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.u1.a1 $C_4.D_8$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.u1.b1 $C_4.D_8$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.v1.a1 $C_8:C_8$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.v1.b1 $C_8:C_8$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.12509.4.w1.a1 $C_8:C_8$ $2^{6}$ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
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