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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 873 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
186624.dy.1.a1 $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ ✓ ✓ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $C_1$ $1$ ✓
186624.dy.2.A $C_2^4.C_3^4:C_3.D_6.C_2$ $2^{7} \cdot 3^{6}$ ✓ ✓ ✓ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $C_2$ $2$ ✓
186624.dy.2.B $C_6^4:(C_6.D_6)$ $2^{7} \cdot 3^{6}$ ✓ ✓ ✓ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $C_2$ $2$ ✓
186624.dy.2.C $C_3^4:(C_2\times A_4^2:C_4)$ $2^{7} \cdot 3^{6}$ ✓ ✓ ✓ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $C_2$ $2$ ✓
186624.dy.4.A $C_2^4.C_3^4.C_6^2$ $2^{6} \cdot 3^{6}$ ✓ ✓ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $C_4$ $2^{2}$ ✓
186624.dy.4.B $C_6^4.C_3.D_6$ $2^{6} \cdot 3^{6}$ ✓ ✓ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
186624.dy.4.C $C_2^4.C_3^4:C_3.D_6$ $2^{6} \cdot 3^{6}$ ✓ ✓ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $C_4$ $2^{2}$ ✓
186624.dy.4.D $C_6^2.C_3^3.A_4.C_2^2$ $2^{6} \cdot 3^{6}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2}$ $-$
186624.dy.4.E $C_2^4.C_3^4:C_3.D_6$ $2^{6} \cdot 3^{6}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2}$ $-$
186624.dy.4.F $C_6^4:(C_3:C_{12})$ $2^{6} \cdot 3^{6}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2}$ $-$
186624.dy.4.G $C_3^4:(A_4^2:C_4)$ $2^{6} \cdot 3^{6}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2}$ $-$
186624.dy.6.A $C_6^2:C_3.D_6^2.C_2$ $2^{7} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2 \cdot 3$ $-$
186624.dy.6.B $C_2^4.C_3^4.D_6.C_2$ $2^{7} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2 \cdot 3$ $-$
186624.dy.6.C $(C_2^2\times C_6^2).S_3^3$ $2^{7} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2 \cdot 3$ $-$
186624.dy.6.D $C_6^4:(C_4\times S_3)$ $2^{7} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2 \cdot 3$ $-$
186624.dy.8.A $C_6^4.C_3.C_6$ $2^{5} \cdot 3^{6}$ ✓ ✓ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $D_4$ $2^{3}$
186624.dy.8.B $C_2^4.C_3^4.C_3.C_6$ $2^{5} \cdot 3^{6}$ ✓ ✓ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $C_2\times C_4$ $2^{3}$ ✓
186624.dy.8.C $C_2^4.C_3^4:C_3.S_3$ $2^{5} \cdot 3^{6}$ ✓ ✓ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $D_4$ $2^{3}$
186624.dy.8.D $C_6^2.C_3^4.C_2^3$ $2^{5} \cdot 3^{6}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{3}$ $-$
186624.dy.8.E $(C_6^2\times A_4).C_3^3.C_2$ $2^{5} \cdot 3^{6}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{3}$ $-$
186624.dy.8.F $C_6^2.C_3^3.A_4.C_2$ $2^{5} \cdot 3^{6}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{3}$ $-$
186624.dy.9.A $C_6^2.D_6^2:C_4$ $2^{8} \cdot 3^{4}$ ✓ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $3^{2}$ $-$
186624.dy.9.B $C_3^2:S_4^2:C_4$ $2^{8} \cdot 3^{4}$ ✓ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $3^{2}$ $-$
186624.dy.12.A $C_6^2:C_3.D_6:D_6$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.B $C_6^2.C_3^3:C_2:D_4$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.C $C_6^2.C_3^3.C_2^3.C_2$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.D $C_6^2.C_3^3.C_2^3.C_2$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.E $C_6^2.C_3^3.C_2^4$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.F $(C_3^2\times A_4).C_6^2.C_2^2$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.G $C_6^2.(C_3:S_3\times D_{12})$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.H $C_6^2.(C_6\times S_3):D_6$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.I $C_3^4.(C_2\times D_4\times A_4)$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.J $C_6^2.C_3^3.C_2^3.C_2$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.K $(C_3\times A_4).C_6^2.C_6.C_2$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.L $(C_3^3\times A_4).A_4.C_2^2$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.M $(C_3\times A_4).C_6^2.C_6.C_2$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.N $C_2\times C_6^2.C_3^3.C_2^3$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.O $C_3\times (C_3\times A_4):A_4.D_6$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.P $(C_2\times C_6^3).S_3^2$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.Q $C_3\times (C_3\times A_4^2).D_6$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.R $C_2^4.(C_3\times \He_3).D_6$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.S $C_3\times C_6^2:C_3.C_6.C_2^3$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.T $C_2^4.C_3^4:C_6.C_2$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.U $C_2^4.C_3^4:C_6.C_2$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.V $(C_3\times C_6\times A_4).C_6^2.C_2$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.W $C_2^4.C_3^4.C_6.C_2$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.X $C_2^4.C_3^4.C_6.C_2$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.Y $C_2^4:\He_3.S_3^2$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.Z $C_2^4.(C_3\times \He_3).D_6$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
186624.dy.12.BA $C_6^2:C_3.D_6:D_6$ $2^{6} \cdot 3^{5}$ $C_3^4.S_4^2:C_4$ $2^{8} \cdot 3^{6}$ $2^{2} \cdot 3$ $-$
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