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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 67 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
16.14.1.a1.a1 $C_2^4$ $2^{4}$ $2$ ✓ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_1$ $1$ ✓
16.14.2.a1.a1 $C_2^3$ $2^{3}$ ✓ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2$ $2$ ✓
16.14.2.a1.b1 $C_2^3$ $2^{3}$ ✓ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2$ $2$ ✓
16.14.2.a1.c1 $C_2^3$ $2^{3}$ ✓ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2$ $2$ ✓
16.14.2.a1.d1 $C_2^3$ $2^{3}$ ✓ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2$ $2$ ✓
16.14.2.a1.e1 $C_2^3$ $2^{3}$ ✓ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2$ $2$ ✓
16.14.2.a1.f1 $C_2^3$ $2^{3}$ ✓ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2$ $2$ ✓
16.14.2.a1.g1 $C_2^3$ $2^{3}$ ✓ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2$ $2$ ✓
16.14.2.a1.h1 $C_2^3$ $2^{3}$ ✓ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2$ $2$ ✓
16.14.2.a1.i1 $C_2^3$ $2^{3}$ ✓ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2$ $2$ ✓
16.14.2.a1.j1 $C_2^3$ $2^{3}$ ✓ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2$ $2$ ✓
16.14.2.a1.k1 $C_2^3$ $2^{3}$ ✓ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2$ $2$ ✓
16.14.2.a1.l1 $C_2^3$ $2^{3}$ ✓ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2$ $2$ ✓
16.14.2.a1.m1 $C_2^3$ $2^{3}$ ✓ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2$ $2$ ✓
16.14.2.a1.n1 $C_2^3$ $2^{3}$ ✓ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2$ $2$ ✓
16.14.2.a1.o1 $C_2^3$ $2^{3}$ ✓ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2$ $2$ ✓
16.14.4.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.b1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.c1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.d1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.e1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.f1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.g1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.h1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.i1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.j1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.k1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.l1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.m1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.n1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.o1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.p1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.q1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.r1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.s1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.t1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.u1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.v1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.w1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.x1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.y1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.z1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.ba1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.bb1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.bc1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.bd1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.be1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.bf1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.bg1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
16.14.4.a1.bh1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^4$ $2^{4}$ $C_2^2$ $2^{2}$ ✓
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