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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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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
14641.15.1.a1.a1 $C_{11}^4$ $11^{4}$ $11$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_1$ $1$ ✓
14641.15.11._.A $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.B $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.C $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.D $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.E $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.F $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.G $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.H $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.I $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.J $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.K $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.L $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.M $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.N $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.O $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.P $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.Q $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.R $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.S $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.T $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.U $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.V $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.W $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.X $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.Y $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.Z $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BA $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BB $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BC $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BD $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BE $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BF $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BG $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BH $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BI $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BJ $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BK $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BL $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BM $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BN $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BO $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BP $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BQ $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BR $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BS $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BT $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BU $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BV $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
14641.15.11._.BW $C_{11}^3$ $11^{3}$ ✓ ✓ ✓ ✓ $C_{11}^4$ $11^{4}$ $C_{11}$ $11$ ✓
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