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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 75 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1358954496.by.1.a1.a1 $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_1$ $1$ ✓
1358954496.by.2._.A $C_2^{16}.C_3^4.C_4:\SD_{16}.C_2$ $2^{23} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2$ $2$ ✓
1358954496.by.2._.B $C_2^{16}.C_3^4.C_4:\SD_{16}.C_2$ $2^{23} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2$ $2$ ✓
1358954496.by.2._.C $C_2^{16}.C_3^4.\OD_{32}.C_2^2$ $2^{23} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2$ $2$ ✓
1358954496.by.2._.D $C_2^{16}.C_3^4.C_4:\SD_{16}.C_2$ $2^{23} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2$ $2$ ✓
1358954496.by.2._.E $C_2^{16}.C_3^4.\OD_{32}.C_2^2$ $2^{23} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2$ $2$ ✓
1358954496.by.2._.F $C_2^{16}.C_3^4.C_4:\SD_{16}.C_2$ $2^{23} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2$ $2$ ✓
1358954496.by.2._.G $C_2^{16}.C_3^4.C_2^2.C_2^4.C_2$ $2^{23} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2$ $2$ ✓
1358954496.by.4._.A $C_2^{16}.C_3^4.(C_8.C_8)$ $2^{22} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1358954496.by.4._.B $C_2^{16}.C_3^4.(C_8.C_8)$ $2^{22} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1358954496.by.4._.C $C_2^{16}.C_3^4.C_4:\SD_{16}$ $2^{22} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1358954496.by.4._.D $C_2^{16}.C_3^4.(C_8.C_8)$ $2^{22} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1358954496.by.4._.E $C_2^{16}.C_3^4.C_4:\SD_{16}$ $2^{22} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1358954496.by.4._.F $C_2^{16}.C_3^4.(C_8.C_8)$ $2^{22} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1358954496.by.4._.G $C_2^{16}.C_3^4.(C_2\times C_4\times C_8)$ $2^{22} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1358954496.by.4._.H $C_2^{16}.C_3^4.C_2^4.C_2^2$ $2^{22} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_4$ $2^{2}$ ✓
1358954496.by.4._.I $C_2^{16}.C_3^4.C_4:\SD_{16}$ $2^{22} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_4$ $2^{2}$ ✓
1358954496.by.4._.J $C_2^{16}.C_3^4.C_2^3.C_2^3$ $2^{22} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_4$ $2^{2}$ ✓
1358954496.by.4._.K $C_2^{16}.C_3^4.C_4:\SD_{16}$ $2^{22} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_4$ $2^{2}$ ✓
1358954496.by.8._.A $C_2^{16}.C_3^4.C_2^3.C_2^2$ $2^{21} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
1358954496.by.8._.B $C_2^{16}.C_3^4.C_4.C_2^3$ $2^{21} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $D_4$ $2^{3}$
1358954496.by.8._.C $C_2^{16}.C_3^4.C_4^2.C_2$ $2^{21} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $D_4$ $2^{3}$
1358954496.by.8._.D $C_2^{16}.C_3^4.C_4^2.C_2$ $2^{21} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
1358954496.by.8._.E $C_2^{16}.C_3^4.C_4:Q_8$ $2^{21} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
1358954496.by.8._.F $C_2^{16}.C_3^4.C_4:D_4$ $2^{21} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
1358954496.by.8._.G $C_2^{16}.C_3^4.C_4:Q_8$ $2^{21} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
1358954496.by.8._.H $C_2^{16}.C_3^4.C_4^2.C_2$ $2^{21} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $D_4$ $2^{3}$
1358954496.by.8._.I $C_2^{16}.C_3^4.C_4^2.C_2$ $2^{21} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
1358954496.by.8._.J $C_2^{16}.C_3^4.C_4:D_4$ $2^{21} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
1358954496.by.8._.K $C_2^{16}.C_3^4.C_4.C_2^3$ $2^{21} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $D_4$ $2^{3}$
1358954496.by.16._.A $C_2^{16}.C_3^4.C_4^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2^2\times C_4$ $2^{4}$ ✓
1358954496.by.16._.B $C_2^{16}.C_3^4.C_4.C_2^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $\SD_{16}$ $2^{4}$
1358954496.by.16._.C $C_2^{16}.C_3^4.C_4.C_2^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $\SD_{16}$ $2^{4}$
1358954496.by.16._.D $C_2^{16}.C_3^4.C_4.C_2^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $D_8$ $2^{4}$
1358954496.by.16._.E $C_2^{16}.C_3^4.C_4.C_2^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $D_8$ $2^{4}$
1358954496.by.16._.F $C_2^{16}.C_3^4.C_4.C_2^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $\SD_{16}$ $2^{4}$
1358954496.by.16._.G $C_2^{16}.C_3^4.C_4.C_2^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $D_8$ $2^{4}$
1358954496.by.16._.H $C_2^{16}.C_3^4.C_4.C_2^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $\SD_{16}$ $2^{4}$
1358954496.by.16._.I $C_2^{16}.C_3^4.C_4.C_2^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $D_8$ $2^{4}$
1358954496.by.16._.J $C_2^{16}.C_3^4.C_4.C_2^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2\times D_4$ $2^{4}$
1358954496.by.16._.K $C_2^{16}.C_3^4.C_4.C_2^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2^2:C_4$ $2^{4}$
1358954496.by.16._.L $C_2^{16}.C_3^4.C_2^3.C_2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2^2:C_4$ $2^{4}$
1358954496.by.16._.M $C_2^{16}.C_3^4.C_4.C_2^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2^2:C_4$ $2^{4}$
1358954496.by.16._.N $C_2^{16}.C_3^4.C_4.C_2^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2\times D_4$ $2^{4}$
1358954496.by.16._.O $C_2^{16}.C_3^4.C_4^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2^2:C_4$ $2^{4}$
1358954496.by.32._.A $C_2^{16}.C_3^4.C_2^2.C_2$ $2^{19} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2^3:C_4$ $2^{5}$
1358954496.by.32._.B $C_2^{16}.C_3^4.C_8$ $2^{19} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2\times \SD_{16}$ $2^{5}$
1358954496.by.32._.C $C_2^{16}.C_3^4.C_8$ $2^{19} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $C_2\times D_8$ $2^{5}$
1358954496.by.32._.D $C_2^{16}.C_3^4.C_8$ $2^{19} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $D_4:C_4$ $2^{5}$
1358954496.by.32._.E $C_2^{16}.C_3^4.C_8$ $2^{19} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3.C_2$ $2^{24} \cdot 3^{4}$ $D_4:C_4$ $2^{5}$
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