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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 990 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
331776.a.1.a1 $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ ✓ ✓ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $C_1$ $1$ ✓
331776.a.2.A $A_4^2.(C_2\times A_4^2:C_4)$ $2^{11} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $C_2$ $2$ ✓
331776.a.2.B $C_2^8.C_3^2:F_9$ $2^{11} \cdot 3^{4}$ ✓ ✓ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $C_2$ $2$ ✓
331776.a.4.A $C_2^8.C_3^3.D_6$ $2^{10} \cdot 3^{4}$ ✓ ✓ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $C_4$ $2^{2}$ ✓
331776.a.4.B $A_4^2:(A_4^2:C_4)$ $2^{10} \cdot 3^{4}$ ✓ ✓ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
331776.a.4.C $A_4^2:(A_4^2:C_4)$ $2^{10} \cdot 3^{4}$ ✓ ✓ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $C_4$ $2^{2}$ ✓
331776.a.8.A $C_2^8.C_3^4.C_2$ $2^{9} \cdot 3^{4}$ ✓ ✓ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
331776.a.8.B $A_4^2.A_4^2.C_2$ $2^{9} \cdot 3^{4}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{3}$ $-$
331776.a.12.A $C_2^8.C_3^2.D_6$ $2^{10} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
331776.a.12.B $C_2^6.C_3^3.C_2^3.C_2$ $2^{10} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
331776.a.16.A $C_2^8.C_3^4$ $2^{8} \cdot 3^{4}$ ✓ ✓ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $\OD_{16}$ $2^{4}$
331776.a.16.B $A_4^3.D_6$ $2^{8} \cdot 3^{4}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{4}$ $-$
331776.a.18.A $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.a.18.B $C_2^8.F_9$ $2^{11} \cdot 3^{2}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.a.24.A $C_2^6.C_3^3.D_4$ $2^{9} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
331776.a.24.B $C_2^6.C_3^2.D_6.C_2$ $2^{9} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
331776.a.24.C $A_4^3.C_2^3$ $2^{9} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
331776.a.24.D $C_2^6.C_3^3.D_4$ $2^{9} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
331776.a.24.E $C_2^4:C_3.A_4^2.C_2$ $2^{9} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
331776.a.24.F $A_4.C_2^5.C_6^2$ $2^{9} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
331776.a.24.G $A_4^2.C_2^4.C_6$ $2^{9} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
331776.a.24.H $A_4^2.A_4.C_2^3$ $2^{9} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
331776.a.24.I $C_2^2:A_4^2.S_4$ $2^{9} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
331776.a.24.J $C_2^8.C_3^3.C_2$ $2^{9} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
331776.a.24.K $C_2^8.C_3^3.C_2$ $2^{9} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
331776.a.24.L $C_2^6.C_3^3.D_4$ $2^{9} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
331776.a.24.M $C_2^2.A_4^2:S_4$ $2^{9} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
331776.a.32.A $(C_3^2\times A_4^2):(C_2\times C_4)$ $2^{7} \cdot 3^{4}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{5}$ $-$
331776.a.32.B $A_4^3:S_3$ $2^{7} \cdot 3^{4}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{5}$ $-$
331776.a.32.C $A_4^3:C_6$ $2^{7} \cdot 3^{4}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{5}$ $-$
331776.a.32.D $A_4^3:S_3$ $2^{7} \cdot 3^{4}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{5}$ $-$
331776.a.36.A $A_4^2:C_2^4:C_4$ $2^{10} \cdot 3^{2}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
331776.a.36.B $A_4^2:\OD_{16}:C_2^2$ $2^{10} \cdot 3^{2}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
331776.a.36.C $A_4^2:C_2\wr C_4$ $2^{10} \cdot 3^{2}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
331776.a.36.D $A_4^2:C_2\wr C_4$ $2^{10} \cdot 3^{2}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
331776.a.36.E $C_2^6.(S_3\times C_3:D_4)$ $2^{10} \cdot 3^{2}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
331776.a.36.F $A_4^2.D_4^2$ $2^{10} \cdot 3^{2}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
331776.a.36.G $(C_2^2:S_4)^2$ $2^{10} \cdot 3^{2}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
331776.a.36.H $A_4^2.C_2^3.C_2^3$ $2^{10} \cdot 3^{2}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
331776.a.36.I $A_4^2:C_2\wr C_4$ $2^{10} \cdot 3^{2}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
331776.a.36.J $A_4^2:C_2\wr C_4$ $2^{10} \cdot 3^{2}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
331776.a.36.K $C_2^4.A_4^2:C_4$ $2^{10} \cdot 3^{2}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
331776.a.36.L $C_2^4.A_4^2:C_4$ $2^{10} \cdot 3^{2}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
331776.a.36.M $C_2^4.A_4^2:C_4$ $2^{10} \cdot 3^{2}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
331776.a.36.N $C_2^4.A_4^2:C_4$ $2^{10} \cdot 3^{2}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
331776.a.48.A $A_4:S_4^2$ $2^{8} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{4} \cdot 3$ $-$
331776.a.48.B $A_4:S_4^2$ $2^{8} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{4} \cdot 3$ $-$
331776.a.48.C $(C_2\times C_6):S_4^2$ $2^{8} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{4} \cdot 3$ $-$
331776.a.48.D $C_3:S_4\times \GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{4} \cdot 3$ $-$
331776.a.48.E $A_4:S_4^2$ $2^{8} \cdot 3^{3}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2^{4} \cdot 3$ $-$
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