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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 358 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
9216.kh.1.a1 $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ ✓ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_1$ $1$ ✓
9216.kh.2.A $C_2^5.D_6^2$ $2^{9} \cdot 3^{2}$ ✓ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2$ $2$ ✓
9216.kh.2.B $C_2^5.D_6^2$ $2^{9} \cdot 3^{2}$ ✓ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2$ $2$ ✓
9216.kh.2.C $C_2^6:(C_6\times D_6)$ $2^{9} \cdot 3^{2}$ ✓ ✓ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2$ $2$ ✓
9216.kh.2.D $C_2^5.D_6^2$ $2^{9} \cdot 3^{2}$ ✓ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2$ $2$ ✓
9216.kh.2.E $C_2^5.D_6^2$ $2^{9} \cdot 3^{2}$ ✓ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2$ $2$ ✓
9216.kh.2.F $(C_6\times S_4).C_2^5$ $2^{9} \cdot 3^{2}$ ✓ ✓ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2$ $2$ ✓
9216.kh.2.G $C_2^5.D_6^2$ $2^{9} \cdot 3^{2}$ ✓ ✓ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2$ $2$ ✓
9216.kh.2.H $C_2^5.D_6^2$ $2^{9} \cdot 3^{2}$ ✓ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2$ $2$ ✓
9216.kh.2.I $C_2^5.D_6^2$ $2^{9} \cdot 3^{2}$ ✓ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2$ $2$ ✓
9216.kh.2.J $(C_6\times \GL(2,\mathbb{Z}/4)):D_4$ $2^{9} \cdot 3^{2}$ ✓ ✓ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2$ $2$ ✓
9216.kh.2.K $C_6:\GL(2,\mathbb{Z}/4):D_4$ $2^{9} \cdot 3^{2}$ ✓ ✓ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2$ $2$ ✓
9216.kh.2.L $C_2^5.D_6^2$ $2^{9} \cdot 3^{2}$ ✓ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2$ $2$ ✓
9216.kh.2.M $C_2^5.D_6^2$ $2^{9} \cdot 3^{2}$ ✓ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2$ $2$ ✓
9216.kh.2.N $C_2^5.D_6^2$ $2^{9} \cdot 3^{2}$ ✓ ✓ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2$ $2$ ✓
9216.kh.2.O $C_2^5.D_6^2$ $2^{9} \cdot 3^{2}$ ✓ ✓ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2$ $2$ ✓
9216.kh.4.A $A_4\times C_2^4:D_6$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.B $C_2^4:D_6^2$ $2^{8} \cdot 3^{2}$ ✓ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.C $C_2^6:S_3^2$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.D $C_2^4:D_6^2$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.E $C_2^4.D_6^2$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.F $C_2^4.D_6^2$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.G $(C_2^3\times D_{12}).C_{12}$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.H $S_3\times C_2^2.\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.I $(C_6\times A_4).C_2^5$ $2^{8} \cdot 3^{2}$ ✓ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.J $C_2^4.D_6^2$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.K $C_2^4.D_6^2$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.L $(C_2^2\times C_6\times A_4).C_2^3$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.M $C_2^4:C_6\times S_4$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.N $A_4\times C_2^4:D_6$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.O $(A_4\times C_2^4):D_6$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.P $C_3\times C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.Q $(C_2\times C_{12}):\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.R $C_2^6:C_6^2$ $2^{8} \cdot 3^{2}$ ✓ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.S $C_2^6:S_3^2$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.T $C_2^6:S_3^2$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.U $C_2^6:S_3^2$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.V $C_2^4.D_6^2$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.W $C_2^4.D_6^2$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.X $C_2^3:C_{12}\times S_4$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.Y $(C_6\times \GL(2,\mathbb{Z}/4)):C_4$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.Z $A_4\times C_2^3:D_{12}$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.BA $C_2^4.D_6^2$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.BB $(C_2\times C_{12}):\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.BC $(C_2\times C_{12}):\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.BD $C_2^4.D_6^2$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.BE $(C_2\times C_{12}):\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.BF $(C_2\times C_{12}):\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.BG $C_6:\GL(2,\mathbb{Z}/4):C_4$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
9216.kh.4.BH $C_2^3.(D_6\times S_4)$ $2^{8} \cdot 3^{2}$ ✓ $C_2^6.D_6^2$ $2^{10} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
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