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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 136 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
6718464.bbw.1.a1.a1 $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_1$ $1$ ✓
6718464.bbw.2._.A $C_3^8.C_4:\OD_{16}.C_2^3$ $2^{9} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2$ $2$ ✓
6718464.bbw.2._.B $C_3^8:C_4^2.Q_{16}:C_2$ $2^{9} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2$ $2$ ✓
6718464.bbw.2._.C $C_3^8:C_4^2.(C_2\times Q_{16})$ $2^{9} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2$ $2$ ✓
6718464.bbw.2._.D $C_3^8:(C_4^3.D_4)$ $2^{9} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2$ $2$ ✓
6718464.bbw.2._.E $C_3^8.C_4:\OD_{16}.C_2^3$ $2^{9} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2$ $2$ ✓
6718464.bbw.2._.F $C_3^8.C_4^3.C_2^3$ $2^{9} \cdot 3^{8}$ ✓ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2$ $2$ ✓
6718464.bbw.2._.G $C_3^8:C_4^2.Q_{16}:C_2$ $2^{9} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2$ $2$ ✓
6718464.bbw.2._.H $C_3^8.C_4^3.C_2^3$ $2^{9} \cdot 3^{8}$ ✓ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2$ $2$ ✓
6718464.bbw.2._.I $C_3^8.C_4:\OD_{16}.C_2^3$ $2^{9} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2$ $2$ ✓
6718464.bbw.2._.J $C_3^8:C_4^2.Q_{16}:C_2$ $2^{9} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2$ $2$ ✓
6718464.bbw.2._.K $C_3^8:C_4^2.(C_2\times Q_{16})$ $2^{9} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2$ $2$ ✓
6718464.bbw.2._.L $C_3^8:(C_4^3.D_4)$ $2^{9} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2$ $2$ ✓
6718464.bbw.2._.M $C_3^8.C_4:\OD_{16}.C_2^3$ $2^{9} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2$ $2$ ✓
6718464.bbw.2._.N $C_3^8.C_4^2.C_4.C_2^3$ $2^{9} \cdot 3^{8}$ ✓ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2$ $2$ ✓
6718464.bbw.2._.O $C_3^8:C_4^2.Q_{16}:C_2$ $2^{9} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2$ $2$ ✓
6718464.bbw.4._.A $C_3^8.C_4^3.C_2^2$ $2^{8} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.B $C_3^8.C_4:\OD_{16}.C_2^2$ $2^{8} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.C $C_3^8.C_4:\OD_{16}.C_2^2$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.D $C_3^8.C_4:\OD_{16}.C_2^2$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.E $C_3^8.C_4^3.C_2^2$ $2^{8} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.F $C_3^8.C_4^2.C_2^4$ $2^{8} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.G $C_3^8:C_4^2.\SD_{16}$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.H $C_3^8:C_4^2.\SD_{16}$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.I $C_3^8.C_4^3.C_2^2$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.J $C_3^8:C_4^2.(C_2\times Q_8)$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.K $C_3^8:C_4^2.\SD_{16}$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.L $C_3^8.C_4:\OD_{16}.C_2^2$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.M $C_3^8.C_4^3.C_2^2$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.N $C_3^8:C_4^2.(C_2\times Q_8)$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.O $C_3^8.C_4:\OD_{16}.C_2^2$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.P $C_3^8:C_4^2.\SD_{16}$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.Q $C_3^8.C_4^3.C_2^2$ $2^{8} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.R $C_3^8.C_2.C_2^3.D_4.C_2$ $2^{8} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.S $C_3^8.C_4^2.C_4.C_2^2$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.T $C_3^8:(C_4\times C_8).Q_8$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.U $C_3^8.C_4^2.C_4.C_2^2$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.V $C_3^8:C_4^2.\SD_{16}$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.W $C_3^8:C_4^2.(C_2\times C_8)$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.X $C_3^8.C_4:\OD_{16}.C_2^2$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.Y $C_3^8.C_4^2.C_4.C_2^2$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.Z $C_3^8:C_4^2.\SD_{16}$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.BA $C_3^8:C_4^2.(C_2\times C_8)$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.BB $C_3^8.C_4:\OD_{16}.C_2^2$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.BC $C_3^8.C_4:\OD_{16}.C_2^2$ $2^{8} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.BD $C_3^8:(C_4\times C_8).Q_8$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.BE $C_3^8.C_4:\OD_{16}.C_2^2$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.BF $C_3^8:C_4^2.\SD_{16}$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.BG $C_3^8.C_4:\OD_{16}.C_2^2$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
6718464.bbw.4._.BH $C_3^8:C_4^2.\SD_{16}$ $2^{8} \cdot 3^{8}$ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
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