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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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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
4608.dl.1.a1 $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ ✓ ✓ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $C_1$ $1$ ✓
4608.dl.2.A $C_2^4:D_6^2$ $2^{8} \cdot 3^{2}$ ✓ ✓ ✓ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $C_2$ $2$ ✓
4608.dl.2.B $\GL(2,\mathbb{Z}/4):S_4$ $2^{8} \cdot 3^{2}$ ✓ ✓ ✓ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $C_2$ $2$ ✓
4608.dl.2.C $(C_2^2\times A_4^2):C_4$ $2^{8} \cdot 3^{2}$ ✓ ✓ ✓ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $C_2$ $2$ ✓
4608.dl.2.D $S_4^2:C_2^2$ $2^{8} \cdot 3^{2}$ ✓ ✓ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $C_2$ $2$ ✓
4608.dl.2.E $\POPlus(4,3):C_4$ $2^{8} \cdot 3^{2}$ ✓ ✓ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $C_2$ $2$ ✓
4608.dl.4.A $A_4^2:C_2^3$ $2^{7} \cdot 3^{2}$ ✓ ✓ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
4608.dl.4.B $A_4^2:C_2^3$ $2^{7} \cdot 3^{2}$ ✓ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
4608.dl.4.C $C_2\times S_4^2$ $2^{7} \cdot 3^{2}$ ✓ ✓ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
4608.dl.4.D $C_2.S_4^2$ $2^{7} \cdot 3^{2}$ ✓ ✓ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
4608.dl.4.E $C_2\times A_4^2:C_4$ $2^{7} \cdot 3^{2}$ ✓ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
4608.dl.4.F $A_4^2:C_2^3$ $2^{7} \cdot 3^{2}$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2}$ $-$
4608.dl.4.G $A_4\times \GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2}$ $-$
4608.dl.4.H $A_4^2:C_2^3$ $2^{7} \cdot 3^{2}$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2}$ $-$
4608.dl.4.I $A_4:\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2}$ $-$
4608.dl.4.J $A_4^2:C_2^3$ $2^{7} \cdot 3^{2}$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2}$ $-$
4608.dl.4.K $S_4\wr C_2$ $2^{7} \cdot 3^{2}$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2}$ $-$
4608.dl.6.A $C_2^5:S_4$ $2^{8} \cdot 3$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
4608.dl.6.B $A_4:D_4^2$ $2^{8} \cdot 3$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
4608.dl.8.A $C_2^2\times A_4^2$ $2^{6} \cdot 3^{2}$ ✓ ✓ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $D_4$ $2^{3}$
4608.dl.8.B $A_4^2:C_2^2$ $2^{6} \cdot 3^{2}$ ✓ ✓ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $C_2^3$ $2^{3}$ ✓
4608.dl.8.C $A_4^2:C_2^2$ $2^{6} \cdot 3^{2}$ ✓ ✓ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $D_4$ $2^{3}$
4608.dl.8.D $\POPlus(4,3)$ $2^{6} \cdot 3^{2}$ ✓ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $D_4$ $2^{3}$
4608.dl.8.E $\GL(2,\mathbb{Z}/4):S_3$ $2^{6} \cdot 3^{2}$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{3}$ $-$
4608.dl.8.F $A_4^2:C_2^2$ $2^{6} \cdot 3^{2}$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{3}$ $-$
4608.dl.8.G $A_4^2:C_2^2$ $2^{6} \cdot 3^{2}$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{3}$ $-$
4608.dl.8.H $A_4^2:C_4$ $2^{6} \cdot 3^{2}$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{3}$ $-$
4608.dl.8.I $A_4^2:C_2^2$ $2^{6} \cdot 3^{2}$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{3}$ $-$
4608.dl.8.J $A_4^2:C_2^2$ $2^{6} \cdot 3^{2}$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{3}$ $-$
4608.dl.8.K $\POPlus(4,3)$ $2^{6} \cdot 3^{2}$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{3}$ $-$
4608.dl.8.L $\POPlus(4,3)$ $2^{6} \cdot 3^{2}$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{3}$ $-$
4608.dl.8.M $S_4^2$ $2^{6} \cdot 3^{2}$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{3}$ $-$
4608.dl.8.N $A_4^2:C_4$ $2^{6} \cdot 3^{2}$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{3}$ $-$
4608.dl.9.a1 $C_2^6:D_4$ $2^{9}$ $2$ ✓ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $3^{2}$ $-$
4608.dl.12.A $C_2^2:\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.dl.12.B $\GL(2,\mathbb{Z}/4):C_4$ $2^{7} \cdot 3$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.dl.12.C $\GL(2,\mathbb{Z}/4):C_2^2$ $2^{7} \cdot 3$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.dl.12.D $C_2^4:D_{12}$ $2^{7} \cdot 3$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.dl.12.E $C_2^5:A_4$ $2^{7} \cdot 3$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.dl.12.F $C_2^2\wr S_3$ $2^{7} \cdot 3$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.dl.12.G $C_2^6:C_6$ $2^{7} \cdot 3$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.dl.12.H $C_2^2\times \GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.dl.12.I $C_2^2\times \GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.dl.12.J $C_2^2\wr S_3$ $2^{7} \cdot 3$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.dl.12.K $C_4:\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.dl.12.L $C_2^5.D_6$ $2^{7} \cdot 3$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.dl.12.M $C_2^2:\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.dl.12.N $C_2^5.D_6$ $2^{7} \cdot 3$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.dl.12.O $C_2^4:S_4$ $2^{7} \cdot 3$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.dl.12.P $C_2^4:S_4$ $2^{7} \cdot 3$ $C_2^6:\SOPlus(4,2)$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
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