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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 169 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
26873856.sw.1.a1 $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_1$ $1$ ✓
26873856.sw.2.A $C_3^8:(C_2\times \OD_{16}).D_4^2$ $2^{11} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2$ $2$ ✓
26873856.sw.2.B $C_3^8.C_4^3.C_2^3.C_2^2$ $2^{11} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2$ $2$ ✓
26873856.sw.2.C $C_3^8:C_2^3.D_4^2:C_2^2$ $2^{11} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2$ $2$ ✓
26873856.sw.2.D $C_3^8:C_2^3.D_4^2:C_4$ $2^{11} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2$ $2$ ✓
26873856.sw.2.E $C_3^8.C_2^3.C_2^4.C_2^4$ $2^{11} \cdot 3^{8}$ ✓ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2$ $2$ ✓
26873856.sw.2.F $C_3^8:C_2^3.D_4^2:C_2^2$ $2^{11} \cdot 3^{8}$ ✓ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2$ $2$ ✓
26873856.sw.2.G $C_3^8.C_2.C_4:D_4.C_4.C_2^3$ $2^{11} \cdot 3^{8}$ ✓ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2$ $2$ ✓
26873856.sw.2.H $C_3^8:(C_2^2\times C_8).D_4^2$ $2^{11} \cdot 3^{8}$ ✓ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2$ $2$ ✓
26873856.sw.2.I $C_3^8.C_4^3.C_2^4.C_2$ $2^{11} \cdot 3^{8}$ ✓ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2$ $2$ ✓
26873856.sw.2.J $C_3^8:C_4^2.C_4^2.C_2^3$ $2^{11} \cdot 3^{8}$ ✓ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2$ $2$ ✓
26873856.sw.2.K $C_3^8.C_4^3.C_2^3.C_2^2$ $2^{11} \cdot 3^{8}$ ✓ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2$ $2$ ✓
26873856.sw.4.A $C_3^8.C_4^3.C_2^4$ $2^{10} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.B $C_3^8.C_2^3.D_4^2.C_2$ $2^{10} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.C $C_3^8:(D_4^2:Q_8).C_2$ $2^{10} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.D $C_3^8:(D_4^2:C_8).C_2$ $2^{10} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.E $C_3^8:C_8.(C_4^2.D_4)$ $2^{10} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.F $C_3^8:C_8.(C_4^2.D_4)$ $2^{10} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.G $C_3^8.C_4^3.C_2^4$ $2^{10} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.H $C_3^8.C_2^3.C_2^4.C_2^3$ $2^{10} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.I $C_3^8:(C_2^2\times C_8).C_2^5$ $2^{10} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.J $C_3^8:C_8.D_4:\SD_{16}$ $2^{10} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.K $C_3^8:C_4^2.(C_2^3.D_4)$ $2^{10} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.L $C_3^8.C_4^3.C_2^4$ $2^{10} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.M $C_3^8:C_8.D_8:Q_8$ $2^{10} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.N $C_3^8:C_8.(C_8\times D_8)$ $2^{10} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.O $C_3^8:C_4^2.(C_2^3.C_2^3)$ $2^{10} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.P $C_3^8:C_4^2.(\OD_{16}.C_2^2)$ $2^{10} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.Q $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.R $C_3^8.C_4:\OD_{16}.C_4.C_2^2$ $2^{10} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.S $C_3^8:C_8.(C_4^2.D_4)$ $2^{10} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.T $C_3^8.C_4:\OD_{16}.C_2^3.C_2$ $2^{10} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.U $C_3^8.C_4^3.C_2^4$ $2^{10} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.V $C_3^8:C_4^2.C_4^2:C_2^2$ $2^{10} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.4.W $C_3^8:C_8.C_8:D_8$ $2^{10} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26873856.sw.8.A $C_3^8.C_2.C_2^3.C_2^5$ $2^{9} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $D_4$ $2^{3}$
26873856.sw.8.B $C_3^8.C_2^3.D_4^2$ $2^{9} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $D_4$ $2^{3}$
26873856.sw.8.C $C_3^8.C_4^3.C_2^3$ $2^{9} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $D_4$ $2^{3}$
26873856.sw.8.D $C_3^8.C_2^3.C_2^3.C_2^3$ $2^{9} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $D_4$ $2^{3}$
26873856.sw.8.E $C_3^8.C_4^3.C_2^3$ $2^{9} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^3$ $2^{3}$ ✓
26873856.sw.8.F $C_3^8.C_4^2.C_4.C_2^3$ $2^{9} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $D_4$ $2^{3}$
26873856.sw.8.G $C_3^8.C_4^2.C_2^5$ $2^{9} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $D_4$ $2^{3}$
26873856.sw.8.H $C_3^8.C_2^3.C_2^3.C_2^3$ $2^{9} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $D_4$ $2^{3}$
26873856.sw.8.I $C_3^8.C_2^3.C_2.C_2^5$ $2^{9} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^3$ $2^{3}$ ✓
26873856.sw.8.J $C_3^8.C_2.C_2^4.C_2^4$ $2^{9} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $D_4$ $2^{3}$
26873856.sw.8.K $C_3^8.C_4^3.C_2^3$ $2^{9} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $D_4$ $2^{3}$
26873856.sw.8.L $C_3^8.C_4^3.C_2^3$ $2^{9} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $D_4$ $2^{3}$
26873856.sw.8.M $C_3^8.C_2^3.C_4:D_4.C_2$ $2^{9} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $D_4$ $2^{3}$
26873856.sw.8.N $C_3^8.C_2^3.C_2^4.C_2^2$ $2^{9} \cdot 3^{8}$ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $D_4$ $2^{3}$
26873856.sw.8.O $C_3^8.C_4^3.C_2^3$ $2^{9} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_2^3.D_4^2:D_4$ $2^{12} \cdot 3^{8}$ $C_2^3$ $2^{3}$ ✓
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