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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 53 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
5435817984.t.1.a1.a1 $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_1$ $1$ ✓
5435817984.t.2._.B $C_2^{12}.A_4^2:S_3^2.C_2^4.D_4$ $2^{25} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2$ $2$ ✓
5435817984.t.2._.F $C_2^{16}.C_3^4.D_8.(C_2\times \SD_{16})$ $2^{25} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2$ $2$ ✓
5435817984.t.2._.G $C_2\times C_2^{16}.C_3^4.D_4^2.C_2^2$ $2^{25} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2$ $2$ ✓
5435817984.t.2._.J $C_2^{16}.C_3^4.C_4^2.C_2^4.C_2$ $2^{25} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2$ $2$ ✓
5435817984.t.2._.K $C_2^{16}.C_3^4.C_4^2.C_2^4.C_2$ $2^{25} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2$ $2$ ✓
5435817984.t.2._.N $C_2^{16}.C_3^4.C_4^2.C_2^4.C_2$ $2^{25} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2$ $2$ ✓
5435817984.t.2._.O $C_2^{16}.C_3^4.C_4^2.C_2^5$ $2^{25} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2$ $2$ ✓
5435817984.t.4._.H $C_2^{16}.C_3^4.\OD_{16}.C_2^4$ $2^{24} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
5435817984.t.4._.J $C_2^{16}.C_3^4.C_4:Q_8.C_2^3$ $2^{24} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
5435817984.t.4._.M $C_2^{16}.C_3^4.C_4^2.C_2^4$ $2^{24} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
5435817984.t.4._.BC $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
5435817984.t.4._.BE $C_2^{16}.C_3^4.C_4^2.C_2^4$ $2^{24} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
5435817984.t.4._.BH $C_2^{16}.C_3^4.C_4:D_4.C_2^3$ $2^{24} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
5435817984.t.4._.BI $C_2^{16}.C_3^4.C_4^2.C_2^4$ $2^{24} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
5435817984.t.8._.F $C_2^{16}.C_3^4.C_2^2.C_2^4.C_2$ $2^{23} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
5435817984.t.8._.I $C_2^{16}.C_3^4.C_4^2.C_2^3$ $2^{23} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $D_4$ $2^{3}$
5435817984.t.8._.L $C_2^{16}.C_3^4.C_2^4.C_2^3$ $2^{23} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $D_4$ $2^{3}$
5435817984.t.8._.N $C_2^{16}.C_3^4.C_2^2.C_2^4.C_2$ $2^{23} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $D_4$ $2^{3}$
5435817984.t.8._.P $C_2^{16}.C_3^4.C_4^2.C_2^3$ $2^{23} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $D_4$ $2^{3}$
5435817984.t.8._.R $C_2^{16}.C_3^4.C_4^2.C_2^3$ $2^{23} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $D_4$ $2^{3}$
5435817984.t.8._.T $C_2^{16}.C_3^4.C_2^3.C_2^4$ $2^{23} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $D_4$ $2^{3}$
5435817984.t.16._.B $C_2^{16}.C_3^4.C_4:\SD_{16}$ $2^{22} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^4$ $2^{4}$ ✓
5435817984.t.16._.I $C_2^{16}.C_3^4.C_4:\SD_{16}$ $2^{22} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2\times D_4$ $2^{4}$
5435817984.t.16._.K $C_2^{16}.C_3^4.(C_2\times C_4\times C_8)$ $2^{22} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2\times D_4$ $2^{4}$
5435817984.t.16._.N $C_2^{16}.C_3^4.C_4:\SD_{16}$ $2^{22} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2\times D_4$ $2^{4}$
5435817984.t.16._.P $C_2^{16}.C_3^4.C_2^3.C_2^3$ $2^{22} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2\times D_4$ $2^{4}$
5435817984.t.16._.Q $C_2^{16}.C_3^4.C_4:\SD_{16}$ $2^{22} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2\times D_4$ $2^{4}$
5435817984.t.16._.S $C_2^{16}.C_3^4.C_2^3.C_2^3$ $2^{22} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2\times D_4$ $2^{4}$
5435817984.t.32._.A $C_2^{16}.C_3^4.C_4^2.C_2$ $2^{21} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^2\wr C_2$ $2^{5}$
5435817984.t.32._.B $C_2^{16}.C_3^4.C_4:D_4$ $2^{21} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^2\wr C_2$ $2^{5}$
5435817984.t.32._.C $C_2^{16}.C_3^4.C_2^3.C_2^2$ $2^{21} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^2\wr C_2$ $2^{5}$
5435817984.t.32._.D $C_2^{16}.C_3^4.C_4^2.C_2$ $2^{21} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^2\times D_4$ $2^{5}$
5435817984.t.32._.E $C_2^{16}.C_3^4.C_4:D_4$ $2^{21} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^2\times D_4$ $2^{5}$
5435817984.t.32._.F $C_2^{16}.C_3^4.C_4:Q_8$ $2^{21} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^2\times D_4$ $2^{5}$
5435817984.t.32._.G $C_2^{16}.C_3^4.C_4:Q_8$ $2^{21} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^2\wr C_2$ $2^{5}$
5435817984.t.64._.A $C_2^{16}.C_3^4.C_2^3.C_2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2\wr C_2^2$ $2^{6}$
5435817984.t.64._.B $C_2^{16}.C_3^4.C_4^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^3:D_4$ $2^{6}$
5435817984.t.64._.C $C_2^{16}.C_3^4.C_4^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2\wr C_2^2$ $2^{6}$
5435817984.t.128._.A $C_2^{16}.C_3^4.C_2^2.C_2$ $2^{19} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2\wr D_4$ $2^{7}$
5435817984.t.128._.B $C_2^{16}.C_3^4.C_2^2.C_2$ $2^{19} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^4:D_4$ $2^{7}$
5435817984.t.128._.C $C_2^{16}.C_3^4.C_2^3$ $2^{19} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2\wr D_4$ $2^{7}$
5435817984.t.256._.A $C_2^{16}.C_3^3.D_6$ $2^{18} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $D_4^2.C_2^2$ $2^{8}$
5435817984.t.256._.B $C_2^{16}.C_3^3.D_6$ $2^{18} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $D_4^2.C_2^2$ $2^{8}$
5435817984.t.256._.C $C_2^{16}.C_3^3.D_6$ $2^{18} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $D_4^2:C_2^2$ $2^{8}$
5435817984.t.512._.A $C_2^{16}.C_3^4.C_2$ $2^{17} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $\SD_{16}\wr C_2$ $2^{9}$
5435817984.t.512._.B $C_2^{16}.C_3^4.C_2$ $2^{17} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $\SD_{16}\wr C_2$ $2^{9}$
5435817984.t.512._.C $C_2^{16}.C_3^4.C_2$ $2^{17} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $D_4^2.C_2^3$ $2^{9}$
5435817984.t.1024._.A $C_2^{16}.C_3^4$ $2^{16} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_4:\SD_{16}.C_2^4$ $2^{10}$
5435817984.t.41472._.A $C_2^{17}$ $2^{17}$ ✓ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $\SOPlus(4,2)^2.D_4$ $2^{9} \cdot 3^{4}$
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