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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 413 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
2821109907456.cx.1.a1.a1 $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_1$ $1$ ✓
2821109907456.cx.2._.A $C_3^{12}.C_2^8.C_3^4.\OD_{16}.D_4$ $2^{15} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2$ $2$ ✓
2821109907456.cx.2._.B $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2$ $2$ ✓
2821109907456.cx.2._.C $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.C_4$ $2^{15} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2$ $2$ ✓
2821109907456.cx.2._.D $C_3^{12}.C_2^8.C_3^4.\OD_{16}.D_4$ $2^{15} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2$ $2$ ✓
2821109907456.cx.2._.E $C_3^{12}.C_2^8.C_3^4.C_4:C_4.C_2^3$ $2^{15} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2$ $2$ ✓
2821109907456.cx.2._.F $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2$ $2$ ✓
2821109907456.cx.2._.G $C_3^{12}.C_2^8.C_3^4.C_2^5.C_2^2$ $2^{15} \cdot 3^{16}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2$ $2$ ✓
2821109907456.cx.2._.H $C_3^{12}.C_2^8.C_3^4.\OD_{16}.D_4$ $2^{15} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2$ $2$ ✓
2821109907456.cx.2._.I $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.C_4$ $2^{15} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2$ $2$ ✓
2821109907456.cx.2._.J $C_3^{12}.C_2^8.C_3^4.\OD_{16}.C_2^3$ $2^{15} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2$ $2$ ✓
2821109907456.cx.2._.K $C_3^{12}.C_2^8.C_3^4.C_2^2:\OD_{16}.C_2$ $2^{15} \cdot 3^{16}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2$ $2$ ✓
2821109907456.cx.2._.L $C_3^{12}.C_2^8.C_3^4.\OD_{16}.D_4$ $2^{15} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2$ $2$ ✓
2821109907456.cx.2._.M $C_3^{12}.C_2^8.C_3^4.C_4:C_4.C_2^3$ $2^{15} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2$ $2$ ✓
2821109907456.cx.2._.N $C_3^{12}.C_2^8.C_3^4.\OD_{16}.C_2^3$ $2^{15} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2$ $2$ ✓
2821109907456.cx.2._.O $C_3^{12}.C_2^4.A_4^2.C_3^2.C_2^5.C_2^2$ $2^{15} \cdot 3^{16}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2$ $2$ ✓
2821109907456.cx.4._.A $C_3^{12}.C_2^8.C_3^4.C_4.C_4^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.B $C_3^{12}.C_2^8.C_3^4.C_4:C_4.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.C $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.D $C_3^{12}.C_2^8.C_3^4.\OD_{16}.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.E $C_3^{12}.C_2^8.C_3^4.\OD_{16}.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.F $C_3^{12}.C_2^8.C_3^4.C_8.C_2^3$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.G $C_3^{12}.C_2^4.A_4^2.D_6^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.H $C_3^{12}.C_2^8.C_3^4.C_4:C_4.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.I $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.J $C_3^{12}.C_2^8.C_3^4.C_4.C_4^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.K $C_3^{12}.C_2^8.C_3^4.\OD_{16}.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.L $C_3^{12}.C_2^8.C_3^4.C_4:C_4.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.M $C_3^{12}.C_2^4.A_4^2.D_6^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.N $C_3^{12}.C_2^8.C_3^4.C_4.C_4^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.O $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.P $C_3^{12}.C_2^8.C_3^4.\OD_{16}.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.Q $C_3^{12}.C_2^8.C_3^4.C_2^2:\OD_{16}$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.R $C_3^{12}.C_2^8.C_3^4.\OD_{16}.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.S $C_3^{12}.C_2^4.A_4^2.C_3:S_3.C_2^4.C_2$ $2^{14} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.T $C_3^{12}.C_2^8.C_3^4.\OD_{16}.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.U $C_3^{12}.C_2^8.C_3^4.\OD_{16}.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.V $C_3^{12}.C_2^8.C_3^4.C_8.C_2^3$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.W $C_3^{12}.C_2^4.C_2^4.C_3^4.C_2^4.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.X $C_3^{12}.C_2^8.C_3^4.C_8.C_2^3$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.Y $C_3^{12}.C_2^8.C_3^4.C_2^2:\OD_{16}$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.Z $C_3^{12}.C_2^8.C_3^4.C_8.C_2^3$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.BA $C_3^{12}.C_2^4.A_4^2.C_3:S_3.C_2^5$ $2^{14} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.BB $C_3^{12}.C_2^8.C_3^4.C_4.C_4^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.BC $C_3^{12}.C_2^8.C_3^4.\OD_{16}.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.BD $C_3^{12}.C_2^8.C_3^4.C_4:C_4.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.BE $C_3^{12}.C_2^4.C_2^4.C_3^4.C_2^4.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.BF $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.BG $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.cx.4._.BH $C_3^{12}.C_2^8.C_3.S_3^3.C_2^3$ $2^{14} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
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