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Note: Search results may be incomplete due to uncomputed quantities: Subgroup label (103813812 objects)

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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 52 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
705277476864.dm.1.a1.a1 $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_1$ $1$ ✓
1410554953728.ca.2._.T $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4^2.C_2$ $2^{15} \cdot 3^{16}$ $C_2$ $2$ ✓
1410554953728.ca.2._.BB $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4^2.C_2$ $2^{15} \cdot 3^{16}$ $C_2$ $2$ ✓
1410554953728.cb.2._.T $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4^2.C_2$ $2^{15} \cdot 3^{16}$ $C_2$ $2$ ✓
1410554953728.ft.2._.E $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.\OD_{16}.D_4$ $2^{15} \cdot 3^{16}$ $C_2$ $2$ ✓
2821109907456.m.4._.DC $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ? $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.m.4._.DF $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ? $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.m.4._.DS $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ? $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.m.4._.DT $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ? $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.m.4._.FQ $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ? $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.m.4._.FS $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ? $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.m.4._.GX $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ? $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.m.4._.GZ $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ? $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.m.4._.HR $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ? $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.m.4._.HZ $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ? $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.m.4._.IV $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ? $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.m.4._.JD $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ ? $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^4$ $2^{16} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
2821109907456.bq.4._.BZ $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_2^6.C_2^2$ $2^{16} \cdot 3^{16}$ $2^{2}$ $-$
2821109907456.bu.4._.BJ $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_2^6.C_2^2$ $2^{16} \cdot 3^{16}$ $2^{2}$ $-$
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._.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.cz.4._.H $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_4$ $2^{2}$ ✓
2821109907456.cz.4._.K $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $C_4$ $2^{2}$ ✓
2821109907456.df.4._.X $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_2^5.C_2^3$ $2^{16} \cdot 3^{16}$ $2^{2}$ $-$
2821109907456.dh.4._.BR $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_2^5.C_2^3$ $2^{16} \cdot 3^{16}$ $2^{2}$ $-$
5642219814912.bd.8._.I $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^3:Q_8.D_4$ $2^{17} \cdot 3^{16}$ $D_4$ $2^{3}$
5642219814912.bd.8._.J $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^3:Q_8.D_4$ $2^{17} \cdot 3^{16}$ $D_4$ $2^{3}$
5642219814912.bd.8._.M $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^3:Q_8.D_4$ $2^{17} \cdot 3^{16}$ $D_4$ $2^{3}$
5642219814912.bd.8._.O $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^3:Q_8.D_4$ $2^{17} \cdot 3^{16}$ $D_4$ $2^{3}$
5642219814912.bq.8._.BY $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_2^4.C_4^2.C_2$ $2^{17} \cdot 3^{16}$ $2^{3}$ $-$
5642219814912.br.8._.BH $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3.S_3^3.C_2^3.D_4$ $2^{17} \cdot 3^{16}$ $2^{3}$ $-$
5642219814912.bt.8._.BG $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2.D_4$ $2^{17} \cdot 3^{16}$ $2^{3}$ $-$
8463329722368.c.12._.BS $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_2^6.A_4$ $2^{16} \cdot 3^{17}$ $2^{2} \cdot 3$ $-$
8463329722368.c.12._.CF $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_2^6.A_4$ $2^{16} \cdot 3^{17}$ $2^{2} \cdot 3$ $-$
8463329722368.c.12._.EN $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_2^6.A_4$ $2^{16} \cdot 3^{17}$ $2^{2} \cdot 3$ $-$
8463329722368.c.12._.FC $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_2^6.A_4$ $2^{16} \cdot 3^{17}$ $2^{2} \cdot 3$ $-$
16926659444736.a.24._.HM $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_6^3.C_2^2.D_6.A_4$ $2^{17} \cdot 3^{17}$ $2^{3} \cdot 3$ $-$
16926659444736.a.24._.HS $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_6^3.C_2^2.D_6.A_4$ $2^{17} \cdot 3^{17}$ $2^{3} \cdot 3$ $-$
16926659444736.b.24._.FN $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^4.C_6$ $2^{17} \cdot 3^{17}$ $2^{3} \cdot 3$ $-$
16926659444736.b.24._.FZ $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^4.C_6$ $2^{17} \cdot 3^{17}$ $2^{3} \cdot 3$ $-$
16926659444736.c.24._.HQ $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^4.C_6$ $2^{17} \cdot 3^{17}$ $2^{3} \cdot 3$ $-$
16926659444736.c.24._.HS $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^4.C_6$ $2^{17} \cdot 3^{17}$ $2^{3} \cdot 3$ $-$
16926659444736.d.24._.IA $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_2^6.S_4$ $2^{17} \cdot 3^{17}$ $2^{3} \cdot 3$ $-$
16926659444736.d.24._.IL $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_2^6.S_4$ $2^{17} \cdot 3^{17}$ $2^{3} \cdot 3$ $-$
16926659444736.e.24._.GT $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_2^6.S_4$ $2^{17} \cdot 3^{17}$ $2^{3} \cdot 3$ $-$
16926659444736.e.24._.HE $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_2^6.S_4$ $2^{17} \cdot 3^{17}$ $2^{3} \cdot 3$ $-$
16926659444736.f.24._.GN $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_2^6.S_4$ $2^{17} \cdot 3^{17}$ $2^{3} \cdot 3$ $-$
16926659444736.f.24._.GW $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_2^6.S_4$ $2^{17} \cdot 3^{17}$ $2^{3} \cdot 3$ $-$
16926659444736.g.24._.Z $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_2^6.S_4$ $2^{17} \cdot 3^{17}$ $2^{3} \cdot 3$ $-$
16926659444736.g.24._.BD $C_3^{12}.C_2^8.C_3^4.C_4^2.C_2^2$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.C_2^6.S_4$ $2^{17} \cdot 3^{17}$ $2^{3} \cdot 3$ $-$
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