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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 224 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
113246208.d.1.a1.a1 $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_1$ $1$ ✓
113246208.d.2._.A $C_2^{10}.(S_4^2.\GL(2,\mathbb{Z}/4))$ $2^{21} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2$ $2$ ✓
113246208.d.2._.B $C_2^{12}.C_2^6:S_3^3$ $2^{21} \cdot 3^{3}$ ✓ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2$ $2$ ✓
113246208.d.2._.C $C_2^{10}.(S_4^3.C_2^2)$ $2^{21} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2$ $2$ ✓
113246208.d.2._.D $C_2^{12}.A_4^3:D_4$ $2^{21} \cdot 3^{3}$ ✓ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2$ $2$ ✓
113246208.d.2._.E $C_2^{10}.(S_4^3.C_4)$ $2^{21} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2$ $2$ ✓
113246208.d.2._.F $C_2^{12}.A_4^3:D_4$ $2^{21} \cdot 3^{3}$ ✓ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2$ $2$ ✓
113246208.d.2._.G $C_2^{12}.S_4^2:D_{12}$ $2^{21} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2$ $2$ ✓
113246208.d.2._.H $C_2^{16}.C_3^3.C_2^5$ $2^{21} \cdot 3^{3}$ ✓ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2$ $2$ ✓
113246208.d.2._.I $C_2^{12}.S_4^2:D_{12}$ $2^{21} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2$ $2$ ✓
113246208.d.2._.J $C_2^{12}.(A_4^2:C_4\times S_4)$ $2^{21} \cdot 3^{3}$ ✓ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2$ $2$ ✓
113246208.d.2._.K $C_2^{10}.(S_4^3.C_4)$ $2^{21} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2$ $2$ ✓
113246208.d.2._.L $C_2^{12}.S_4^2:S_4$ $2^{21} \cdot 3^{3}$ ✓ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2$ $2$ ✓
113246208.d.2._.M $C_2^{10}.(S_4^3.C_2^2)$ $2^{21} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2$ $2$ ✓
113246208.d.2._.N $C_2^{12}.A_4^2:\GL(2,\mathbb{Z}/4)$ $2^{21} \cdot 3^{3}$ ✓ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2$ $2$ ✓
113246208.d.2._.O $C_2^{10}.(S_4^2.\GL(2,\mathbb{Z}/4))$ $2^{21} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2$ $2$ ✓
113246208.d.4._.A $C_2^{12}.C_6^2.A_4.C_2^4$ $2^{20} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.B $C_2^{16}.C_3.D_6^2$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.C $C_2^{12}.S_4^2:D_6$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.D $C_2^{12}.S_4^2:C_{12}$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.E $C_2^{16}.C_3.D_6^2$ $2^{20} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.F $C_2^{16}.C_3.D_6^2$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.G $C_2^{12}.(D_6\times A_4^2):C_4$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.H $C_2.(C_2^{16}.S_3^3)$ $2^{20} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.I $C_2^{12}.A_4^3:C_2^2$ $2^{20} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.J $C_2^{10}.((C_2\times A_4^3).D_4)$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.K $C_2^{10}.(A_4\times S_4^2):C_4$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.L $C_2.(C_2^{16}.S_3^3)$ $2^{20} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.M $C_2^{12}.A_4^3:C_4$ $2^{20} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.N $C_2^{10}.(C_2\times A_4^3:D_4)$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.O $C_2^{12}.(A_4^2:C_4\times D_6)$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.P $C_2^{12}.S_4^2:C_{12}$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.Q $C_2^{16}.C_3.D_6^2$ $2^{20} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.R $C_2^{16}.C_3.D_6^2$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.S $C_2^{10}.((C_2\times A_4^2).\GL(2,\mathbb{Z}/4))$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.T $C_2^{10}.(C_2\times A_4^3:D_4)$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.U $C_2^{12}.A_4^3:C_2^2$ $2^{20} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.V $C_2^{12}.(C_6\times S_4\wr C_2)$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.W $C_2^{10}.(C_2\times A_4^2:\GL(2,\mathbb{Z}/4))$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.X $C_2^{12}.C_2^5:S_3^3$ $2^{20} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.Y $C_2^{12}.A_4^3:C_4$ $2^{20} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.Z $C_2^{12}.S_4^2:D_6$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.BA $C_2^{10}.((C_2\times A_4^2).\GL(2,\mathbb{Z}/4))$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.BB $C_2^{12}.(A_4^2:C_4\times D_6)$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.BC $C_2^{16}.C_3.D_6^2$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.BD $C_2^{10}.((C_2\times A_4^3).D_4)$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.BE $C_2^{12}.(C_6\times S_4\wr C_2)$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.BF $C_2.(C_2^{16}.S_3^3)$ $2^{20} \cdot 3^{3}$ ✓ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.BG $C_2^{10}.(A_4\times S_4^2):C_4$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
113246208.d.4._.BH $C_2^{12}.(D_6\times A_4^2):C_4$ $2^{20} \cdot 3^{3}$ ✓ $C_2^{12}.S_4^3:C_2$ $2^{22} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
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