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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 at least 1000)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1728.47288.1.a1 $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_1$ $1$ ✓
1728.47288.2.a1 $C_6.D_6^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47288.2.b1 $C_6.D_6^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47288.2.c1 $C_6.D_6^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47288.2.d1 $C_6.D_6^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47288.2.e1 $C_6.D_6^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47288.2.f1 $C_6.D_6^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47288.2.g1 $C_6.D_6^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47288.2.h1 $C_4.S_3^3$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47288.2.i1 $C_4.S_3^3$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47288.2.j1 $C_4.S_3^3$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47288.2.k1 $D_{12}:S_3^2$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47288.2.l1 $C_4.S_3^3$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47288.2.m1 $C_4.S_3^3$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47288.2.n1 $C_4.S_3^3$ $2^{5} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2$ $2$ ✓
1728.47288.3.a1 $C_4.D_6^2$ $2^{6} \cdot 3^{2}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $3$ $-$
1728.47288.3.b1 $C_4.D_6^2$ $2^{6} \cdot 3^{2}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $3$ $-$
1728.47288.4.a1 $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.b1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.c1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.d1 $C_{12}.C_6^2$ $2^{4} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.e1 $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.f1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.g1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.h1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.i1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.j1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.k1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.l1 $C_{12}.C_6^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.m1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.n1 $D_6:S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.o1 $C_{12}:S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.p1 $C_2.S_3^3$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.q1 $C_2.S_3^3$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.r1 $C_{12}.S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.s1 $C_2.S_3^3$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.t1 $C_{12}.S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.u1 $C_2.S_3^3$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.v1 $C_{12}.S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.w1 $C_2.S_3^3$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.x1 $C_{12}:S_3^2$ $2^{4} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.y1 $C_{12}.S_3^2$ $2^{4} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.z1 $C_{12}.S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.ba1 $C_{12}:S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.bb1 $C_2.S_3^3$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.bc1 $C_{12}:S_3^2$ $2^{4} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.bd1 $C_{12}.S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.be1 $C_{12}.S_3^2$ $2^{4} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.bf1 $C_{12}.S_3^2$ $2^{4} \cdot 3^{3}$ ✓ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
1728.47288.4.bg1 $C_{12}.S_3^2$ $2^{4} \cdot 3^{3}$ ✓ $C_{12}.D_6^2$ $2^{6} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
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