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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 70 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 $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_1$ $1$ ✓
10871635968.b.2._.D $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.\OD_{16}.C_2^4.C_2^3$ $2^{27} \cdot 3^{4}$ $C_2$ $2$ ✓
10871635968.b.2._.F $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.\OD_{16}.C_2^4.C_2^3$ $2^{27} \cdot 3^{4}$ $C_2$ $2$ ✓
10871635968.b.2._.H $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.\OD_{16}.C_2^4.C_2^3$ $2^{27} \cdot 3^{4}$ $C_2$ $2$ ✓
10871635968.b.2._.J $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.\OD_{16}.C_2^4.C_2^3$ $2^{27} \cdot 3^{4}$ $C_2$ $2$ ✓
48922361856.c.9.a1.a1 $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.Q_8^2.S_3^2.C_2^2$ $2^{26} \cdot 3^{6}$ $3^{2}$ $-$
97844723712.a.18._.A $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{16}.C_3^4.Q_8^2.D_6\wr C_2$ $2^{27} \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
97844723712.a.18._.F $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{16}.C_3^4.Q_8^2.D_6\wr C_2$ $2^{27} \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
97844723712.a.18._.J $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{16}.C_3^4.Q_8^2.D_6\wr C_2$ $2^{27} \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
97844723712.a.18._.L $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{16}.C_3^4.Q_8^2.D_6\wr C_2$ $2^{27} \cdot 3^{6}$ $2 \cdot 3^{2}$ $-$
1087163596800.bo.200._.A $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bo.200._.B $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bo.200._.D $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bo.200._.F $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bq.200._.A $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bq.200._.D $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bq.200._.J $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bq.200._.N $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.br.200._.B $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.br.200._.F $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.br.200._.H $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.br.200._.L $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bs.200._.A $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bs.200._.F $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bs.200._.J $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bs.200._.L $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bt.200._.K $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bt.200._.L $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bt.200._.M $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bt.200._.N $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bu.200._.K $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bu.200._.L $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bu.200._.M $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bu.200._.N $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bv.200._.E $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bv.200._.F $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bv.200._.K $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bv.200._.L $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bw.200._.A $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bw.200._.F $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bw.200._.J $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bw.200._.L $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bx.200._.A $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bx.200._.D $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bx.200._.J $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.bx.200._.N $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.by.200._.B $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.by.200._.C $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.by.200._.M $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
1087163596800.by.200._.N $C_2^{16}.C_3^4.C_2.D_4^2.C_2^3$ $2^{26} \cdot 3^{4}$ $C_2^{18}.A_6^2.C_2^4.C_2$ $2^{29} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 5^{2}$ $-$
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