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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 (34 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
408146688.wu.1.a1.a1 $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_1$ $1$ ✓
408146688.wu.2._.A $C_3^{12}.C_2^6.C_6$ $2^{7} \cdot 3^{13}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_2$ $2$ ✓
408146688.wu.2._.B $C_3^{12}.C_2^6.S_3$ $2^{7} \cdot 3^{13}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_2$ $2$ ✓
408146688.wu.2._.C $C_3^{12}.C_2^6.S_3$ $2^{7} \cdot 3^{13}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_2$ $2$ ✓
408146688.wu.4._.A $C_3^{12}.C_2^6.C_3$ $2^{6} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_2^2$ $2^{2}$ ✓
408146688.wu.6._.A $C_3^{12}.C_2^6.C_2$ $2^{7} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $S_3$ $2 \cdot 3$
408146688.wu.12._.A $C_3^{12}.C_2^6$ $2^{6} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $D_6$ $2^{2} \cdot 3$
408146688.wu.24._.A $C_3^{12}.C_2^5$ $2^{5} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $S_4$ $2^{3} \cdot 3$
408146688.wu.24._.B $C_3^9.C_6^3.C_2^2$ $2^{5} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $S_4$ $2^{3} \cdot 3$
408146688.wu.24._.C $C_3^{12}.C_2^4.C_2$ $2^{5} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $S_4$ $2^{3} \cdot 3$
408146688.wu.48._.A $C_3^{12}.C_2^4$ $2^{4} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_2\times S_4$ $2^{4} \cdot 3$
408146688.wu.48._.B $C_3^{12}.C_2^4$ $2^{4} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_2\times S_4$ $2^{4} \cdot 3$
408146688.wu.48._.C $C_3^{12}.C_2^4$ $2^{4} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_2\times S_4$ $2^{4} \cdot 3$
408146688.wu.96._.A $C_3^9.C_6^3$ $2^{3} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_2^2:S_4$ $2^{5} \cdot 3$
408146688.wu.192._.A $C_3^{11}.D_6$ $2^{2} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_2^3:S_4$ $2^{6} \cdot 3$
408146688.wu.192._.B $C_3^{12}.C_2^2$ $2^{2} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_2^3:S_4$ $2^{6} \cdot 3$
408146688.wu.192._.C $C_3^{12}.C_2^2$ $2^{2} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_2^3:S_4$ $2^{6} \cdot 3$
408146688.wu.648._.A $C_3^9.C_2^4.C_2$ $2^{5} \cdot 3^{9}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^3:S_4$ $2^{3} \cdot 3^{4}$
408146688.wu.768._.A $C_3^{12}$ $3^{12}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_2^5:S_4$ $2^{8} \cdot 3$
408146688.wu.1296._.A $C_3^9.C_2^4$ $2^{4} \cdot 3^{9}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_2\times C_3^3:S_4$ $2^{4} \cdot 3^{4}$
408146688.wu.1296._.B $C_3^9.C_2^4$ $2^{4} \cdot 3^{9}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $S_3\wr S_3$ $2^{4} \cdot 3^{4}$
408146688.wu.2592._.A $C_3^9.C_2^3$ $2^{3} \cdot 3^{9}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $(C_3\times C_6^2):S_4$ $2^{5} \cdot 3^{4}$
408146688.wu.5184._.A $C_3^9.C_2^2$ $2^{2} \cdot 3^{9}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $S_3^3:S_4$ $2^{6} \cdot 3^{4}$
408146688.wu.5184._.B $C_3^9.C_2^2$ $2^{2} \cdot 3^{9}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_6^3:S_4$ $2^{6} \cdot 3^{4}$
408146688.wu.20736._.A $C_3^9$ $3^{9}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $(S_3\times D_6^2).S_4$ $2^{8} \cdot 3^{4}$
408146688.wu.20736._.B $C_3^9$ $3^{9}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
408146688.wu.34992._.A $C_3^6.C_2^4$ $2^{4} \cdot 3^{6}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^6:(C_2\times S_4)$ $2^{4} \cdot 3^{7}$
408146688.wu.139968._.A $C_3^5:D_6$ $2^{2} \cdot 3^{6}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^6:C_2^3:S_4$ $2^{6} \cdot 3^{7}$
408146688.wu.139968._.B $C_3^5:D_6$ $2^{2} \cdot 3^{6}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^3.C_6^3:S_4$ $2^{6} \cdot 3^{7}$
408146688.wu.559872._.A $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
408146688.wu.559872._.B $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
408146688.wu.15116544._.A $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ ✓
408146688.wu.15116544._.B $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ ✓
408146688.wu.408146688.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$
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