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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 80 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
279936000.c.1.a1.a1 $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ ✓ ✓ $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $C_1$ $1$ ✓
559872000.a.2._.A $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ ✓ ✓ ✓ $A_6^3.D_6$ $2^{11} \cdot 3^{7} \cdot 5^{3}$ $C_2$ $2$ ✓
559872000.f.2._.A $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ ✓ ✓ ✓ $A_6^3.D_6$ $2^{11} \cdot 3^{7} \cdot 5^{3}$ $C_2$ $2$ ✓
559872000.g.2._.A $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ ✓ ✓ ✓ $A_6^3.D_6$ $2^{11} \cdot 3^{7} \cdot 5^{3}$ $C_2$ $2$ ✓
559872000.o.2._.B $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ ✓ ✓ $C_2\times A_6\wr S_3$ $2^{11} \cdot 3^{7} \cdot 5^{3}$ $C_2$ $2$ ✓
559872000.o.2._.C $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ ✓ ✓ $C_2\times A_6\wr S_3$ $2^{11} \cdot 3^{7} \cdot 5^{3}$ $C_2$ $2$ ✓
1119744000.c.4.a1.a1 $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ ✓ $A_6^3.S_4$ $2^{12} \cdot 3^{7} \cdot 5^{3}$ $2^{2}$ $-$
1119744000.i.4._.A $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ ✓ ✓ $A_6\wr C_3.C_2^3$ $2^{12} \cdot 3^{7} \cdot 5^{3}$ $C_2^2$ $2^{2}$ ✓
1119744000.s.4.a1.a1 $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ ✓ $A_6^3.S_4$ $2^{12} \cdot 3^{7} \cdot 5^{3}$ $2^{2}$ $-$
1119744000.y.4.a1.a1 $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ ✓ $A_6^3.S_4$ $2^{12} \cdot 3^{7} \cdot 5^{3}$ $2^{2}$ $-$
1119744000.bc.4.a1.a1 $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ ✓ $C_2^2.A_6\wr S_3$ $2^{12} \cdot 3^{7} \cdot 5^{3}$ $2^{2}$ $-$
1119744000.bd.4._.A $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ ✓ $A_6\wr C_3.C_2^3$ $2^{12} \cdot 3^{7} \cdot 5^{3}$ $C_2^2$ $2^{2}$ ✓
1119744000.bd.4._.B $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ ✓ $A_6\wr C_3.C_2^3$ $2^{12} \cdot 3^{7} \cdot 5^{3}$ $C_2^2$ $2^{2}$ ✓
2239488000.a.8._.C $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $S_6\wr C_3.C_2$ $2^{13} \cdot 3^{7} \cdot 5^{3}$ $2^{3}$ $-$
2239488000.f.8._.A $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $A_6^3.S_4.C_2$ $2^{13} \cdot 3^{7} \cdot 5^{3}$ $2^{3}$ $-$
2239488000.h.8._.A $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $A_6^3.S_4.C_2$ $2^{13} \cdot 3^{7} \cdot 5^{3}$ $2^{3}$ $-$
2239488000.k.8._.A $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $A_6^3.S_4.C_2$ $2^{13} \cdot 3^{7} \cdot 5^{3}$ $2^{3}$ $-$
2239488000.n.8._.C $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $A_6^3.S_4.C_2$ $2^{13} \cdot 3^{7} \cdot 5^{3}$ $2^{3}$ $-$
2239488000.p.8._.A $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $A_6^3.S_4.C_2$ $2^{13} \cdot 3^{7} \cdot 5^{3}$ $2^{3}$ $-$
2239488000.r.8._.B $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $A_6^3.S_4.C_2$ $2^{13} \cdot 3^{7} \cdot 5^{3}$ $2^{3}$ $-$
2239488000.t.8._.A $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $A_6^3.S_4.C_2$ $2^{13} \cdot 3^{7} \cdot 5^{3}$ $2^{3}$ $-$
2239488000.u.8._.A $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $A_6^3.S_4.C_2$ $2^{13} \cdot 3^{7} \cdot 5^{3}$ $2^{3}$ $-$
2239488000.z.8._.B $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $C_2^3.A_6\wr S_3$ $2^{13} \cdot 3^{7} \cdot 5^{3}$ $2^{3}$ $-$
2239488000.z.8._.C $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $C_2^3.A_6\wr S_3$ $2^{13} \cdot 3^{7} \cdot 5^{3}$ $2^{3}$ $-$
2239488000.ba.8._.A $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $C_2^2.A_6^3.D_6$ $2^{13} \cdot 3^{7} \cdot 5^{3}$ $2^{3}$ $-$
2239488000.be.8._.A $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $C_2.A_6^3.S_4$ $2^{13} \cdot 3^{7} \cdot 5^{3}$ $2^{3}$ $-$
2239488000.be.8._.B $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $C_2.A_6^3.S_4$ $2^{13} \cdot 3^{7} \cdot 5^{3}$ $2^{3}$ $-$
4478976000.b.16._.B $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $A_6^3.S_4.C_2^2$ $2^{14} \cdot 3^{7} \cdot 5^{3}$ $2^{4}$ $-$
4478976000.g.16._.C $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $A_6^3.S_4.C_2^2$ $2^{14} \cdot 3^{7} \cdot 5^{3}$ $2^{4}$ $-$
4478976000.h.16._.B $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $S_6\wr C_3.C_2^2$ $2^{14} \cdot 3^{7} \cdot 5^{3}$ $2^{4}$ $-$
4478976000.i.16.a1.a1 $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $A_6^3.C_2^4.S_3$ $2^{14} \cdot 3^{7} \cdot 5^{3}$ $2^{4}$ $-$
4478976000.k.16._.A $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $C_2^3.A_6^3.D_6$ $2^{14} \cdot 3^{7} \cdot 5^{3}$ $2^{4}$ $-$
4478976000.k.16._.B $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $C_2^3.A_6^3.D_6$ $2^{14} \cdot 3^{7} \cdot 5^{3}$ $2^{4}$ $-$
4478976000.o.16.a1.a1 $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $C_2^2.A_6^3.S_4$ $2^{14} \cdot 3^{7} \cdot 5^{3}$ $2^{4}$ $-$
4478976000.p.16._.C $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $S_6\wr C_3.C_2^2$ $2^{14} \cdot 3^{7} \cdot 5^{3}$ $2^{4}$ $-$
4478976000.p.16._.D $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $S_6\wr C_3.C_2^2$ $2^{14} \cdot 3^{7} \cdot 5^{3}$ $2^{4}$ $-$
8957952000.d.32._.B $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $A_6^3.C_2^4.D_6$ $2^{15} \cdot 3^{7} \cdot 5^{3}$ $2^{5}$ $-$
8957952000.e.32._.B $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $A_6^3.C_2^4.D_6$ $2^{15} \cdot 3^{7} \cdot 5^{3}$ $2^{5}$ $-$
8957952000.g.32._.C $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $A_6^3.C_2^4.D_6$ $2^{15} \cdot 3^{7} \cdot 5^{3}$ $2^{5}$ $-$
8957952000.j.32._.A $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $C_2^3.A_6^3.S_4$ $2^{15} \cdot 3^{7} \cdot 5^{3}$ $2^{5}$ $-$
8957952000.j.32._.B $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $C_2^3.A_6^3.S_4$ $2^{15} \cdot 3^{7} \cdot 5^{3}$ $2^{5}$ $-$
8957952000.k.32._.C $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $C_2^2.S_6\wr C_3.C_2$ $2^{15} \cdot 3^{7} \cdot 5^{3}$ $2^{5}$ $-$
96018048000.c.343.a1.a1 $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ ✓ $A_7\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3} \cdot 7^{3}$ $7^{3}$ $-$
192036096000.a.686._.A $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $A_7^3.D_6$ $2^{11} \cdot 3^{7} \cdot 5^{3} \cdot 7^{3}$ $2 \cdot 7^{3}$ $-$
192036096000.f.686._.A $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $C_2.A_7\wr S_3$ $2^{11} \cdot 3^{7} \cdot 5^{3} \cdot 7^{3}$ $2 \cdot 7^{3}$ $-$
192036096000.f.686._.B $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $C_2.A_7\wr S_3$ $2^{11} \cdot 3^{7} \cdot 5^{3} \cdot 7^{3}$ $2 \cdot 7^{3}$ $-$
384072192000.b.1372.a1.a1 $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $A_7^3.S_4$ $2^{12} \cdot 3^{7} \cdot 5^{3} \cdot 7^{3}$ $2^{2} \cdot 7^{3}$ $-$
384072192000.g.1372.a1.a1 $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $C_2^2.A_7\wr S_3$ $2^{12} \cdot 3^{7} \cdot 5^{3} \cdot 7^{3}$ $2^{2} \cdot 7^{3}$ $-$
384072192000.h.1372._.A $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $A_7\wr C_3.C_2^3$ $2^{12} \cdot 3^{7} \cdot 5^{3} \cdot 7^{3}$ $2^{2} \cdot 7^{3}$ $-$
384072192000.h.1372._.B $A_6\wr S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $A_7\wr C_3.C_2^3$ $2^{12} \cdot 3^{7} \cdot 5^{3} \cdot 7^{3}$ $2^{2} \cdot 7^{3}$ $-$
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