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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 873 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
256.53973.1.a1.a1 $C_4^2.C_2^4$ $2^{8}$ $2$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_1$ $1$ ✓
256.53973.2.a1.a1 $C_2^4.D_4$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.b1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.c1.a1 $C_2^4.D_4$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.d1.a1 $C_2^4.D_4$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.e1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.f1.a1 $C_2^4.D_4$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.g1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.h1.a1 $C_4^2.D_4$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.i1.a1 $C_4^2.D_4$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.j1.a1 $C_4^2.D_4$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.k1.a1 $C_4^2.D_4$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.l1.a1 $C_4^2.D_4$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.m1.a1 $C_4^2.D_4$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.n1.a1 $C_4^2.D_4$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.o1.a1 $C_4^2.D_4$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.p1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.q1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.r1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.s1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.t1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.u1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.v1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.w1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.x1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.y1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.z1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.ba1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.bb1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.bc1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.bd1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.2.be1.a1 $C_4^2.C_2^3$ $2^{7}$ ✓ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2$ $2$ ✓
256.53973.4.a1.a1 $C_4^2:C_2^2$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.53973.4.b1.a1 $C_2^3:D_4$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.53973.4.c1.a1 $C_4^2:C_2^2$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.53973.4.d1.a1 $C_4^2:C_2^2$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.53973.4.e1.a1 $C_4^2:C_2^2$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.53973.4.f1.a1 $C_2^3:C_8$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.53973.4.g1.a1 $C_2^2:\OD_{16}$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.53973.4.h1.a1 $D_4:D_4$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.53973.4.i1.a1 $C_4^2.C_2^2$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.53973.4.j1.a1 $D_4:D_4$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.53973.4.k1.a1 $D_4:D_4$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.53973.4.l1.a1 $C_4^2.C_2^2$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.53973.4.m1.a1 $D_4.D_4$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.53973.4.n1.a1 $D_4:D_4$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.53973.4.o1.a1 $C_4^2.C_2^2$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.53973.4.p1.a1 $C_4^2.C_2^2$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.53973.4.q1.a1 $C_2^3.D_4$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
256.53973.4.r1.a1 $C_2^3.D_4$ $2^{6}$ ✓ ✓ $C_4^2.C_2^4$ $2^{8}$ $C_2^2$ $2^{2}$ ✓
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