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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 58 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._.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._.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._.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.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._.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._.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._.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.8._.A $C_3^8.C_4^3.C_2$ $2^{7} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^3$ $2^{3}$ ✓
6718464.bbw.8._.B $C_3^8.C_4^2.C_2^3$ $2^{7} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^3$ $2^{3}$ ✓
6718464.bbw.8._.C $C_3^8.C_4^2.C_2^3$ $2^{7} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^3$ $2^{3}$ ✓
6718464.bbw.8._.D $C_3^8.C_2^3.C_4^2$ $2^{7} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^3$ $2^{3}$ ✓
6718464.bbw.8._.I $C_3^8.C_2^3.C_4^2$ $2^{7} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^3$ $2^{3}$ ✓
6718464.bbw.8._.J $C_3^8.C_4^2.C_2^3$ $2^{7} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^3$ $2^{3}$ ✓
6718464.bbw.8._.M $C_3^8.C_2.C_2^3.C_2^3$ $2^{7} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^3$ $2^{3}$ ✓
6718464.bbw.8._.X $C_3^8.C_4^3.C_2$ $2^{7} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $D_4$ $2^{3}$
6718464.bbw.8._.Y $C_3^8.C_4^2.C_2^3$ $2^{7} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $D_4$ $2^{3}$
6718464.bbw.8._.Z $C_3^8.C_4^3.C_2$ $2^{7} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $D_4$ $2^{3}$
6718464.bbw.8._.BA $C_3^8.C_4^2.C_2^3$ $2^{7} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $D_4$ $2^{3}$
6718464.bbw.16._.A $C_3^8.C_4:\SD_{16}$ $2^{6} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $\SD_{16}$ $2^{4}$
6718464.bbw.16._.B $C_3^8.C_4^3$ $2^{6} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2\times D_4$ $2^{4}$
6718464.bbw.16._.C $C_3^8.C_2^2.C_2^4$ $2^{6} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2\times D_4$ $2^{4}$
6718464.bbw.16._.D $C_3^8.C_4^2.C_2^2$ $2^{6} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2\times D_4$ $2^{4}$
6718464.bbw.16._.E $C_3^8.C_2^2.C_2^4$ $2^{6} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2\times D_4$ $2^{4}$
6718464.bbw.16._.R $C_3^8.C_4^2.C_2^2$ $2^{6} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2\times D_4$ $2^{4}$
6718464.bbw.16._.S $C_3^8.C_4:\OD_{16}$ $2^{6} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2\times D_4$ $2^{4}$
6718464.bbw.16._.T $C_3^8.C_4:\OD_{16}$ $2^{6} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^4$ $2^{4}$ ✓
6718464.bbw.16._.U $C_3^8.C_2.C_4:D_4$ $2^{6} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $\SD_{16}$ $2^{4}$
6718464.bbw.16._.V $C_3^8.C_2.C_4:D_4$ $2^{6} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $\SD_{16}$ $2^{4}$
6718464.bbw.16._.W $C_3^8.C_4:\SD_{16}$ $2^{6} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $\SD_{16}$ $2^{4}$
6718464.bbw.32._.C $C_3^8.C_4:Q_8$ $2^{5} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2\times \SD_{16}$ $2^{5}$
6718464.bbw.32._.D $C_3^8.C_4:D_4$ $2^{5} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2\times \SD_{16}$ $2^{5}$
6718464.bbw.32._.F $C_3^8.C_2^2.C_2^3$ $2^{5} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2\times D_4$ $2^{5}$
6718464.bbw.32._.G $C_3^8.C_4^2.C_2$ $2^{5} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2\times \SD_{16}$ $2^{5}$
6718464.bbw.32._.I $C_3^8.C_4^2.C_2$ $2^{5} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2\times \SD_{16}$ $2^{5}$
6718464.bbw.32._.J $C_3^8.C_4:Q_8$ $2^{5} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2\times \SD_{16}$ $2^{5}$
6718464.bbw.32._.K $C_3^8:(C_2^2\times C_8)$ $2^{5} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2\wr C_2$ $2^{5}$
6718464.bbw.32._.L $C_3^8.C_4.C_2^3$ $2^{5} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2\wr C_2$ $2^{5}$
6718464.bbw.32._.M $C_3^8.C_4:D_4$ $2^{5} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2\times \SD_{16}$ $2^{5}$
6718464.bbw.64._.A $C_3^8:C_4^2$ $2^{4} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $Q_{16}:C_2^2$ $2^{6}$
6718464.bbw.64._.E $C_3^8.C_4.C_2^2$ $2^{4} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2\wr C_2^2$ $2^{6}$
6718464.bbw.64._.F $C_3^8.C_4^2$ $2^{4} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^2\times \SD_{16}$ $2^{6}$
6718464.bbw.64._.G $C_3^8:(C_2^2\times C_4)$ $2^{4} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^3:D_4$ $2^{6}$
6718464.bbw.64._.H $C_3^8:(C_2\times C_8)$ $2^{4} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2\wr C_2^2$ $2^{6}$
6718464.bbw.128._.A $C_3^8.C_8$ $2^{3} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_4^2.D_4$ $2^{7}$
6718464.bbw.128._.B $C_3^8:C_8$ $2^{3} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_4^2.D_4$ $2^{7}$
6718464.bbw.128._.C $C_3^8:(C_2\times C_4)$ $2^{3} \cdot 3^{8}$ ✓ ✓ $C_3^8:C_4^2.Q_{16}:C_2^2$ $2^{10} \cdot 3^{8}$ $C_2^3:\SD_{16}$ $2^{7}$
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