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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 751 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1152.32548.1.a1.a1 $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ ✓ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $C_1$ $1$ ✓
1152.32548.2.a1.a1 $C_{12}^2:C_2^2$ $2^{6} \cdot 3^{2}$ ✓ ✓ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.32548.2.b1.a1 $C_{12}^2:C_2^2$ $2^{6} \cdot 3^{2}$ ✓ ✓ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.32548.2.c1.a1 $C_{12}^2:C_4$ $2^{6} \cdot 3^{2}$ ✓ ✓ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.32548.2.d1.a1 $(C_6\times C_{12}):D_4$ $2^{6} \cdot 3^{2}$ ✓ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.32548.2.d1.b1 $(C_6\times C_{12}):D_4$ $2^{6} \cdot 3^{2}$ ✓ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.32548.2.e1.a1 $(C_6\times C_{12}).D_4$ $2^{6} \cdot 3^{2}$ ✓ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.32548.2.e1.b1 $(C_6\times C_{12}).D_4$ $2^{6} \cdot 3^{2}$ ✓ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.32548.3.a1.a1 $D_4^2:S_3$ $2^{7} \cdot 3$ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $3$ $-$
1152.32548.3.b1.a1 $(C_4\times C_{12}):D_4$ $2^{7} \cdot 3$ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $3$ $-$
1152.32548.4.a1.a1 $C_{12}^2:C_2$ $2^{5} \cdot 3^{2}$ ✓ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.32548.4.b1.a1 $C_6^2:D_4$ $2^{5} \cdot 3^{2}$ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.32548.4.b1.b1 $C_6^2:D_4$ $2^{5} \cdot 3^{2}$ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.32548.4.c1.a1 $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ ✓ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.32548.4.d1.a1 $C_6^2.D_4$ $2^{5} \cdot 3^{2}$ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.32548.4.d1.b1 $C_6^2.D_4$ $2^{5} \cdot 3^{2}$ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.32548.4.e1.a1 $C_3\times C_{12}.D_4$ $2^{5} \cdot 3^{2}$ ✓ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.32548.4.f1.a1 $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.32548.4.f1.b1 $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.32548.4.g1.a1 $C_6^2:C_2^3$ $2^{5} \cdot 3^{2}$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.32548.4.g1.b1 $C_6^2:C_2^3$ $2^{5} \cdot 3^{2}$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.32548.4.h1.a1 $C_6^2:D_4$ $2^{5} \cdot 3^{2}$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.32548.4.h1.b1 $C_6^2:D_4$ $2^{5} \cdot 3^{2}$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.32548.4.i1.a1 $C_6^2.D_4$ $2^{5} \cdot 3^{2}$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.32548.4.i1.b1 $C_6^2.D_4$ $2^{5} \cdot 3^{2}$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.32548.4.j1.a1 $C_6^2:D_4$ $2^{5} \cdot 3^{2}$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.32548.4.k1.a1 $C_6^2.D_4$ $2^{5} \cdot 3^{2}$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.32548.4.l1.a1 $C_{12}\times D_{12}$ $2^{5} \cdot 3^{2}$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.32548.4.m1.a1 $C_{12}\wr C_2$ $2^{5} \cdot 3^{2}$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.32548.6.a1.a1 $C_3:D_4^2$ $2^{6} \cdot 3$ ✓ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $S_3$ $2 \cdot 3$
1152.32548.6.b1.a1 $D_{12}:D_4$ $2^{6} \cdot 3$ ✓ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $S_3$ $2 \cdot 3$
1152.32548.6.c1.a1 $C_3\times D_4^2$ $2^{6} \cdot 3$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.32548.6.d1.a1 $C_3\times D_4:D_4$ $2^{6} \cdot 3$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.32548.6.e1.a1 $(C_4\times C_{12}):C_4$ $2^{6} \cdot 3$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.32548.6.f1.a1 $(C_4\times C_{12}):C_4$ $2^{6} \cdot 3$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.32548.6.g1.a1 $(C_4\times C_{12}):C_4$ $2^{6} \cdot 3$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.32548.6.h1.a1 $C_2^4:D_6$ $2^{6} \cdot 3$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.32548.6.h1.b1 $C_2^4:D_6$ $2^{6} \cdot 3$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.32548.6.i1.a1 $(C_2^3\times C_6):C_4$ $2^{6} \cdot 3$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.32548.6.i1.b1 $(C_2^3\times C_6):C_4$ $2^{6} \cdot 3$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.32548.6.j1.a1 $(C_2\times C_{12}):D_4$ $2^{6} \cdot 3$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.32548.6.j1.b1 $(C_2\times C_{12}):D_4$ $2^{6} \cdot 3$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.32548.6.k1.a1 $C_2^3.D_{12}$ $2^{6} \cdot 3$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.32548.6.k1.b1 $C_2^3.D_{12}$ $2^{6} \cdot 3$ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.32548.8.a1.a1 $C_6^2:C_2^2$ $2^{4} \cdot 3^{2}$ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $D_4$ $2^{3}$
1152.32548.8.a1.b1 $C_6^2:C_2^2$ $2^{4} \cdot 3^{2}$ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $D_4$ $2^{3}$
1152.32548.8.b1.a1 $C_6^2:C_4$ $2^{4} \cdot 3^{2}$ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $D_4$ $2^{3}$
1152.32548.8.b1.b1 $C_6^2:C_4$ $2^{4} \cdot 3^{2}$ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $D_4$ $2^{3}$
1152.32548.8.c1.a1 $C_4:C_6^2$ $2^{4} \cdot 3^{2}$ ✓ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $C_2^3$ $2^{3}$ ✓
1152.32548.8.d1.a1 $C_4:C_6^2$ $2^{4} \cdot 3^{2}$ ✓ ✓ $C_{12}^2:D_4$ $2^{7} \cdot 3^{2}$ $D_4$ $2^{3}$
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