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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 638 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
512.7572924.1.a1 $C_2^3:D_4^2$ $2^{9}$ $2$ ✓ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_1$ $1$ ✓
512.7572924.2.a1 $C_2^2.D_4^2$ $2^{8}$ ✓ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2$ $2$ ✓
512.7572924.2.b1 $C_2^2.D_4^2$ $2^{8}$ ✓ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2$ $2$ ✓
512.7572924.2.c1 $C_2^5:D_4$ $2^{8}$ ✓ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2$ $2$ ✓
512.7572924.2.d1 $C_2^5:D_4$ $2^{8}$ ✓ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2$ $2$ ✓
512.7572924.2.e1 $C_2^2.D_4^2$ $2^{8}$ ✓ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2$ $2$ ✓
512.7572924.2.f1 $C_2^2\times D_4^2$ $2^{8}$ ✓ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2$ $2$ ✓
512.7572924.2.g1 $C_2^5:D_4$ $2^{8}$ ✓ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2$ $2$ ✓
512.7572924.2.h1 $C_2^2.D_4^2$ $2^{8}$ ✓ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2$ $2$ ✓
512.7572924.2.i1 $C_2^5:C_2^3$ $2^{8}$ ✓ ✓ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2$ $2$ ✓
512.7572924.2.j1 $C_2^2:D_4^2$ $2^{8}$ ✓ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2$ $2$ ✓
512.7572924.4.a1 $D_4\times C_2^4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.b1 $C_2^4:D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.c1 $C_2^4:D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.d1 $C_2^5:C_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.e1 $C_2^4:D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.f1 $C_2^5:C_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.g1 $C_2^4:D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.h1 $C_2^4.D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.i1 $C_4^2:C_2^3$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.j1 $D_4\times C_2^4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.k1 $C_2^4.D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.l1 $C_2^4:D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.m1 $C_2^4.D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.n1 $C_2^3:C_4^2$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.o1 $D_4\times C_2^4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.p1 $C_2^4:D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.q1 $C_2^4:D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.r1 $C_2^5:C_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.s1 $C_2^7$ $2^{7}$ ✓ ✓ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.t1 $C_2^4:D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.u1 $C_2^4:D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.v1 $C_4^2:C_2^3$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.w1 $C_2^4.D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.x1 $C_2^4.D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.y1 $C_2^3.C_2^4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.z1 $C_2^4:D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.ba1 $C_2^4.D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.bb1 $C_2^4:D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.bc1 $C_2^3.C_2^4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.bd1 $C_2^4:D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.be1 $C_2^4:D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.bf1 $C_2^4:D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.bg1 $C_2^4.D_4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.bh1 $C_2^4:D_4$ $2^{7}$ ✓ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.bi1 $C_2^3.C_2^4$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.bj1 $C_4^2:C_2^3$ $2^{7}$ ✓ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.bk1 $C_2^4.Q_8$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.bl1 $C_2.D_4^2$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
512.7572924.4.bm1 $C_2.D_4^2$ $2^{7}$ ✓ $C_2^3:D_4^2$ $2^{9}$ $C_2^2$ $2^{2}$ ✓
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