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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 109 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
256.26539.1.a1.a1 $D_4^2:C_2^2$ $2^{8}$ $2$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_1$ $1$ ✓
256.26539.2.a1.a1 $D_4^2:C_2$ $2^{7}$ ✓ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2$ $2$ ✓
256.26539.2.b1.a1 $C_2^4:D_4$ $2^{7}$ ✓ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2$ $2$ ✓
256.26539.2.c1.a1 $C_2^5:C_4$ $2^{7}$ ✓ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2$ $2$ ✓
256.26539.2.d1.a1 $C_4^2:C_2^3$ $2^{7}$ ✓ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2$ $2$ ✓
256.26539.2.e1.a1 $C_2^4.D_4$ $2^{7}$ ✓ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2$ $2$ ✓
256.26539.2.f1.a1 $C_2^4:D_4$ $2^{7}$ ✓ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2$ $2$ ✓
256.26539.2.g1.a1 $C_2^4.D_4$ $2^{7}$ ✓ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2$ $2$ ✓
256.26539.2.h1.a1 $C_2\wr D_4$ $2^{7}$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2$ $2$ ✓
256.26539.2.h1.b1 $C_2\wr D_4$ $2^{7}$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2$ $2$ ✓
256.26539.2.i1.a1 $C_4^2:D_4$ $2^{7}$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2$ $2$ ✓
256.26539.2.i1.b1 $C_4^2:D_4$ $2^{7}$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2$ $2$ ✓
256.26539.2.j1.a1 $C_4^2:D_4$ $2^{7}$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2$ $2$ ✓
256.26539.2.j1.b1 $C_4^2:D_4$ $2^{7}$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2$ $2$ ✓
256.26539.2.k1.a1 $C_4^2:D_4$ $2^{7}$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2$ $2$ ✓
256.26539.2.k1.b1 $C_4^2:D_4$ $2^{7}$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2$ $2$ ✓
256.26539.4.a1.a1 $C_2^3:D_4$ $2^{6}$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.b1.a1 $C_4^2:C_2^2$ $2^{6}$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.c1.a1 $D_4:C_2^3$ $2^{6}$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.d1.a1 $C_2^3:D_4$ $2^{6}$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.e1.a1 $C_2^4:C_4$ $2^{6}$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.f1.a1 $C_2^4:C_4$ $2^{6}$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.g1.a1 $\OD_{16}:C_2^2$ $2^{6}$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.h1.a1 $D_4^2$ $2^{6}$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.i1.a1 $C_2\wr C_2^2$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.i1.b1 $C_2\wr C_2^2$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.j1.a1 $C_4^2:C_2^2$ $2^{6}$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.k1.a1 $C_2\wr C_4$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.k1.b1 $C_2\wr C_4$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.l1.a1 $D_4:D_4$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.l1.b1 $D_4:D_4$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.m1.a1 $C_4^2:C_2^2$ $2^{6}$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.n1.a1 $C_4^2:C_4$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.n1.b1 $C_4^2:C_4$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.o1.a1 $C_2\wr C_2^2$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.o1.b1 $C_2\wr C_2^2$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.p1.a1 $C_2\wr C_2^2$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.p1.b1 $C_2\wr C_2^2$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.q1.a1 $C_4^2:C_2^2$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.q1.b1 $C_4^2:C_2^2$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.r1.a1 $C_2^3.D_4$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.r1.b1 $C_2^3.D_4$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.s1.a1 $C_4^2:C_2^2$ $2^{6}$ ✓ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.t1.a1 $C_2\wr C_4$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.t1.b1 $C_2\wr C_4$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.u1.a1 $C_2\wr C_4$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.u1.b1 $C_2\wr C_4$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.v1.a1 $C_4^2:C_4$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.v1.b1 $C_4^2:C_4$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.26539.4.w1.a1 $C_2^3.D_4$ $2^{6}$ ✓ $D_4^2:C_2^2$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
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