↑

Learn more

Refine search

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
Sort order Select

Results (1-50 of 536 matches)

Next   displayed columns for results
Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1152.157730.1.a1 $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ ✓ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_1$ $1$ ✓
1152.157730.2.a1 $C_6:\GL(2,\mathbb{Z}/4)$ $2^{6} \cdot 3^{2}$ ✓ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.157730.2.b1 $C_2^4:C_6^2$ $2^{6} \cdot 3^{2}$ ✓ ✓ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.157730.2.c1 $(C_2\times C_{12}):S_4$ $2^{6} \cdot 3^{2}$ ✓ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.157730.2.d1 $(C_3\times D_4):S_4$ $2^{6} \cdot 3^{2}$ ✓ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.157730.2.e1 $D_4\times C_3:S_4$ $2^{6} \cdot 3^{2}$ ✓ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2$ $2$ ✓
1152.157730.3.a1 $C_2^5:D_6$ $2^{7} \cdot 3$ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $3$ $-$
1152.157730.3.b1 $\GL(2,\mathbb{Z}/4):C_2^2$ $2^{7} \cdot 3$ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $3$ $-$
1152.157730.4.a1 $C_2^3:C_6^2$ $2^{5} \cdot 3^{2}$ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.157730.4.b1 $C_3:\GL(2,\mathbb{Z}/4)$ $2^{5} \cdot 3^{2}$ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.157730.4.c1 $C_2^3.C_6^2$ $2^{5} \cdot 3^{2}$ ✓ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.157730.4.d1 $C_3:\GL(2,\mathbb{Z}/4)$ $2^{5} \cdot 3^{2}$ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.157730.4.e1 $C_2\times C_6:S_4$ $2^{5} \cdot 3^{2}$ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.157730.4.f1 $C_2\times C_6.S_4$ $2^{5} \cdot 3^{2}$ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.157730.4.g1 $C_2^3.C_6^2$ $2^{5} \cdot 3^{2}$ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.157730.4.h1 $C_{12}:S_4$ $2^{5} \cdot 3^{2}$ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.157730.4.i1 $C_{12}:S_4$ $2^{5} \cdot 3^{2}$ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.157730.4.j1 $C_{12}.S_4$ $2^{5} \cdot 3^{2}$ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
1152.157730.4.k1 $C_6^2.C_2^3$ $2^{5} \cdot 3^{2}$ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2^{2}$ $-$
1152.157730.6.a1 $C_{12}:C_2^4$ $2^{6} \cdot 3$ ✓ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $S_3$ $2 \cdot 3$
1152.157730.6.b1 $C_2^5:C_6$ $2^{6} \cdot 3$ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $S_3$ $2 \cdot 3$
1152.157730.6.c1 $C_2^4:D_6$ $2^{6} \cdot 3$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.157730.6.d1 $C_2^4:D_6$ $2^{6} \cdot 3$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.157730.6.e1 $C_2\times \GL(2,\mathbb{Z}/4)$ $2^{6} \cdot 3$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.157730.6.f1 $D_{12}:C_2^3$ $2^{6} \cdot 3$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.157730.6.g1 $C_2^4.D_6$ $2^{6} \cdot 3$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.157730.6.h1 $C_2^4.D_6$ $2^{6} \cdot 3$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.157730.6.i1 $C_2^4.D_6$ $2^{6} \cdot 3$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.157730.6.j1 $\GL(2,\mathbb{Z}/4):C_2$ $2^{6} \cdot 3$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.157730.6.k1 $C_2^4.D_6$ $2^{6} \cdot 3$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.157730.6.l1 $C_2^4:D_6$ $2^{6} \cdot 3$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.157730.6.m1 $C_2^4.D_6$ $2^{6} \cdot 3$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.157730.6.n1 $D_4:S_4$ $2^{6} \cdot 3$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.157730.6.o1 $C_2^4:D_6$ $2^{6} \cdot 3$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.157730.6.p1 $D_4\times S_4$ $2^{6} \cdot 3$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2 \cdot 3$ $-$
1152.157730.8.a1 $C_2^2:C_6^2$ $2^{4} \cdot 3^{2}$ ✓ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2^3$ $2^{3}$ ✓
1152.157730.8.b1 $C_2^2:C_6^2$ $2^{4} \cdot 3^{2}$ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2^3$ $2^{3}$ ✓
1152.157730.8.c1 $C_6:S_4$ $2^{4} \cdot 3^{2}$ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2^3$ $2^{3}$ ✓
1152.157730.8.d1 $C_{12}\times A_4$ $2^{4} \cdot 3^{2}$ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2^3$ $2^{3}$ ✓
1152.157730.8.e1 $C_6.S_4$ $2^{4} \cdot 3^{2}$ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $C_2^3$ $2^{3}$ ✓
1152.157730.8.f1 $C_6^2:C_2^2$ $2^{4} \cdot 3^{2}$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2^{3}$ $-$
1152.157730.8.g1 $C_4:C_6^2$ $2^{4} \cdot 3^{2}$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2^{3}$ $-$
1152.157730.8.h1 $C_{12}.D_6$ $2^{4} \cdot 3^{2}$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2^{3}$ $-$
1152.157730.8.i1 $C_{12}.D_6$ $2^{4} \cdot 3^{2}$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2^{3}$ $-$
1152.157730.8.j1 $C_{12}:D_6$ $2^{4} \cdot 3^{2}$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2^{3}$ $-$
1152.157730.8.k1 $C_2^2:C_6^2$ $2^{4} \cdot 3^{2}$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2^{3}$ $-$
1152.157730.8.l1 $C_6:S_4$ $2^{4} \cdot 3^{2}$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $2^{3}$ $-$
1152.157730.9.a1 $D_4^2:C_2$ $2^{7}$ $2$ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $3^{2}$ $-$
1152.157730.12.a1 $C_2^4\times C_6$ $2^{5} \cdot 3$ ✓ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $D_6$ $2^{2} \cdot 3$
1152.157730.12.b1 $C_2^3\times A_4$ $2^{5} \cdot 3$ ✓ $(C_6\times D_4):S_4$ $2^{7} \cdot 3^{2}$ $D_6$ $2^{2} \cdot 3$
Next   displayed columns for results