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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 97 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
46656.hu.1.a1 $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_1$ $1$ ✓
46656.hu.2.A $C_2\times C_3^4.C_3^2.C_2^4$ $2^{5} \cdot 3^{6}$ ✓ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2$ $2$ ✓
46656.hu.2.B $C_3^4.C_6^2.C_2^3$ $2^{5} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2$ $2$ ✓
46656.hu.2.C $(C_3\times C_6^2).S_3^3$ $2^{5} \cdot 3^{6}$ ✓ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2$ $2$ ✓
46656.hu.2.D $C_3^4:C_2^3.S_3^2$ $2^{5} \cdot 3^{6}$ ✓ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2$ $2$ ✓
46656.hu.2.E $C_3^4:D_6\wr C_2$ $2^{5} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2$ $2$ ✓
46656.hu.2.F $\He_3^2:(C_2^2\times D_4)$ $2^{5} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2$ $2$ ✓
46656.hu.2.G $\He_3^2:C_2^3:C_4$ $2^{5} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2$ $2$ ✓
46656.hu.2.H $C_3^4:D_6\wr C_2$ $2^{5} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2$ $2$ ✓
46656.hu.4.A $C_2\times C_3^4.C_6^2.C_2$ $2^{4} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
46656.hu.4.B $C_2\times C_3^4.C_3^2.C_2^3$ $2^{4} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
46656.hu.4.C $(C_3^2\times C_6^2):S_3^2$ $2^{4} \cdot 3^{6}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
46656.hu.4.D $C_2\times C_3^4.S_3^2.C_2$ $2^{4} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
46656.hu.4.E $C_6^2.C_3\wr C_4$ $2^{4} \cdot 3^{6}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
46656.hu.4.F $(C_3\times \He_3).D_6^2$ $2^{4} \cdot 3^{6}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
46656.hu.4.G $C_2\times \He_3^2:D_4$ $2^{4} \cdot 3^{6}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
46656.hu.4.H $C_3^4.C_3^2.C_2^4$ $2^{4} \cdot 3^{6}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
46656.hu.4.I $(C_2\times \He_3^2).D_4$ $2^{4} \cdot 3^{6}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
46656.hu.4.J $C_3^4:D_6^2$ $2^{4} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
46656.hu.4.K $\He_3^2:(C_2^2\times C_4)$ $2^{4} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
46656.hu.4.L $\He_3^2:(C_2^2\times C_4)$ $2^{4} \cdot 3^{6}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
46656.hu.4.M $C_2\times \He_3^2:D_4$ $2^{4} \cdot 3^{6}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
46656.hu.4.N $\He_3^2:(C_2\times D_4)$ $2^{4} \cdot 3^{6}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
46656.hu.4.O $(C_2\times \He_3^2).D_4$ $2^{4} \cdot 3^{6}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
46656.hu.4.P $C_3^4:C_6.D_{12}$ $2^{4} \cdot 3^{6}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
46656.hu.6.A $C_3^3:D_6\wr C_2$ $2^{5} \cdot 3^{5}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $S_3$ $2 \cdot 3$
46656.hu.8.A $C_2\times C_3^4.C_6^2$ $2^{3} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $D_4$ $2^{3}$
46656.hu.8.B $C_2\times C_3^4.C_6^2$ $2^{3} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^3$ $2^{3}$ ✓
46656.hu.8.C $C_2\times C_3^4.C_3:S_3.C_2$ $2^{3} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $D_4$ $2^{3}$
46656.hu.8.D $C_3^4.C_6^2.C_2$ $2^{3} \cdot 3^{6}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^3$ $2^{3}$ ✓
46656.hu.8.E $C_3^4.C_3^2.C_2^3$ $2^{3} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^3$ $2^{3}$ ✓
46656.hu.8.F $C_3^4.S_3^2.C_2$ $2^{3} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $D_4$ $2^{3}$
46656.hu.8.G $\He_3^2:C_2^3$ $2^{3} \cdot 3^{6}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^3$ $2^{3}$ ✓
46656.hu.8.H $C_3^3.C_3^3.C_2^3$ $2^{3} \cdot 3^{6}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^3$ $2^{3}$ ✓
46656.hu.8.I $C_3^4.C_3^2.C_2^3$ $2^{3} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^3$ $2^{3}$ ✓
46656.hu.8.J $\He_3^2:(C_2\times C_4)$ $2^{3} \cdot 3^{6}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^3$ $2^{3}$ ✓
46656.hu.8.K $C_2\times \He_3^2:C_4$ $2^{3} \cdot 3^{6}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^3$ $2^{3}$ ✓
46656.hu.8.L $C_3^4.C_3^2.C_2^3$ $2^{3} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $D_4$ $2^{3}$
46656.hu.8.M $\He_3^2:C_2^3$ $2^{3} \cdot 3^{6}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $D_4$ $2^{3}$
46656.hu.12.A $C_2\times C_3^4:C_6.C_2^2$ $2^{4} \cdot 3^{5}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $D_6$ $2^{2} \cdot 3$
46656.hu.12.B $(C_3\times C_6^2):S_3^2$ $2^{4} \cdot 3^{5}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $D_6$ $2^{2} \cdot 3$
46656.hu.12.C $C_3^3:C_6^2:C_4$ $2^{4} \cdot 3^{5}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $D_6$ $2^{2} \cdot 3$
46656.hu.12.D $C_3^4:C_6:D_4$ $2^{4} \cdot 3^{5}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $D_6$ $2^{2} \cdot 3$
46656.hu.12.E $C_3^3:S_3^2:C_4$ $2^{4} \cdot 3^{5}$ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $D_6$ $2^{2} \cdot 3$
46656.hu.16.A $C_2\times C_2:(C_3^3.C_3^3)$ $2^{2} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2\times D_4$ $2^{4}$
46656.hu.16.B $C_3^4.C_6^2$ $2^{2} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2\times D_4$ $2^{4}$
46656.hu.16.C $C_3^4.C_6^2$ $2^{2} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2^4$ $2^{4}$ ✓
46656.hu.16.D $C_3^4.C_3:S_3.C_2$ $2^{2} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2\times D_4$ $2^{4}$
46656.hu.16.E $C_3^4.C_6^2$ $2^{2} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2\times D_4$ $2^{4}$
46656.hu.16.F $C_3^4.C_3:S_3.C_2$ $2^{2} \cdot 3^{6}$ ✓ ✓ $C_6^2:S_3^2:S_3^2$ $2^{6} \cdot 3^{6}$ $C_2\times D_4$ $2^{4}$
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