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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 99 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
84934656.br.1.a1.a1 $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_1$ $1$ ✓
169869312.x.2._.F $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^{10}.A_4^2\wr C_2.C_4$ $2^{21} \cdot 3^{4}$ $C_2$ $2$ ✓
169869312.y.2._.B $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^{12}.A_4^2.(D_4\times S_3^2)$ $2^{21} \cdot 3^{4}$ $C_2$ $2$ ✓
169869312.y.2._.J $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^{12}.A_4^2.(D_4\times S_3^2)$ $2^{21} \cdot 3^{4}$ $C_2$ $2$ ✓
169869312.bs.2._.F $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^{12}.C_6^2:S_4\wr C_2$ $2^{21} \cdot 3^{4}$ $C_2$ $2$ ✓
169869312.bt.2._.B $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_6^2.\SOPlus(4,2)$ $2^{21} \cdot 3^{4}$ $C_2$ $2$ ✓
169869312.bt.2._.F $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_6^2.\SOPlus(4,2)$ $2^{21} \cdot 3^{4}$ $C_2$ $2$ ✓
169869312.bv.2._.F $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^{12}.C_6^2:S_4\wr C_2$ $2^{21} \cdot 3^{4}$ $C_2$ $2$ ✓
254803968.e.3._.A $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^{12}.(C_2^3\times C_6^3):S_3^2$ $2^{20} \cdot 3^{5}$ $C_3$ $3$ ✓
254803968.w.3._.A $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{12}.(C_2^3\times C_6^3):S_3^2$ $2^{20} \cdot 3^{5}$ $3$ $-$
339738624.k.4._.H $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^{10}.A_4^2\wr C_2.C_8$ $2^{22} \cdot 3^{4}$ $C_4$ $2^{2}$ ✓
339738624.q.4._.M $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{10}.(A_4^2\wr C_2.D_4)$ $2^{22} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
339738624.q.4._.Y $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{10}.(A_4^2\wr C_2.D_4)$ $2^{22} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
339738624.s.4._.CB $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^9.A_4\wr C_4.C_2^3$ $2^{22} \cdot 3^{4}$ $2^{2}$ $-$
339738624.t.4._.Y $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_6^2.S_3^2.C_2^2$ $2^{22} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
339738624.u.4._.U $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_6^2.S_3^2.C_2^2$ $2^{22} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
339738624.u.4._.Y $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_6^2.S_3^2.C_2^2$ $2^{22} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
339738624.v.4._.M $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.D_4^2$ $2^{22} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
339738624.v.4._.U $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_3^4.D_4^2$ $2^{22} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
339738624.v.4._.Y $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_3^4.D_4^2$ $2^{22} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
339738624.w.4._.Z $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^{10}.A_4^2\wr C_2.Q_8$ $2^{22} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
339738624.x.4._.R $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_6^2.S_3^2.C_2^2$ $2^{22} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
339738624.x.4._.Z $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_6^2.S_3^2.C_2^2$ $2^{22} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
339738624.x.4._.BH $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_6^2.S_3^2.C_2^2$ $2^{22} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
339738624.ba.4._.F $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_6^2.F_9.C_2$ $2^{22} \cdot 3^{4}$ $C_4$ $2^{2}$ ✓
339738624.bb.4._.H $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^{16}.C_3^4.C_2^2:D_8$ $2^{22} \cdot 3^{4}$ $2^{2}$ $-$
339738624.bb.4._.J $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^{16}.C_3^4.C_2^2:D_8$ $2^{22} \cdot 3^{4}$ $2^{2}$ $-$
339738624.bf.4._.J $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^{12}.A_4^2.F_9:D_4$ $2^{22} \cdot 3^{4}$ $2^{2}$ $-$
339738624.bh.4._.N $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^{16}.C_6^2.F_9.C_2$ $2^{22} \cdot 3^{4}$ $2^{2}$ $-$
339738624.bv.4._.J $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^{16}.C_6^2.F_9:C_2$ $2^{22} \cdot 3^{4}$ $2^{2}$ $-$
509607936.k.6._.B $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^6.A_4^3.S_4^2:D_4$ $2^{21} \cdot 3^{5}$ $C_6$ $2 \cdot 3$ ✓
509607936.n.6._.A $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^{10}.A_4^2\wr C_2.D_6$ $2^{21} \cdot 3^{5}$ $S_3$ $2 \cdot 3$
509607936.n.6._.BF $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^{10}.A_4^2\wr C_2.D_6$ $2^{21} \cdot 3^{5}$ $2 \cdot 3$ $-$
509607936.z.6._.F $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^6.A_4^3.S_4^2:D_4$ $2^{21} \cdot 3^{5}$ $2 \cdot 3$ $-$
509607936.ba.6._.A $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^6.A_4^3.S_4^2:D_4$ $2^{21} \cdot 3^{5}$ $S_3$ $2 \cdot 3$
509607936.bb.6._.F $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^6.A_4^3.S_4^2:D_4$ $2^{21} \cdot 3^{5}$ $2 \cdot 3$ $-$
679477248.k.8._.BG $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{12}.A_4^2:D_6^2.C_2^3$ $2^{23} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
679477248.k.8._.BW $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{12}.A_4^2:D_6^2.C_2^3$ $2^{23} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
679477248.k.8._.CE $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{12}.A_4^2:D_6^2.C_2^3$ $2^{23} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
679477248.k.8._.DC $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{12}.A_4^2:D_6^2.C_2^3$ $2^{23} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
679477248.l.8._.L $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_6^2.S_3^2.C_2^3$ $2^{23} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
679477248.l.8._.P $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_6^2.S_3^2.C_2^3$ $2^{23} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
679477248.l.8._.BV $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_6^2.S_3^2.C_2^3$ $2^{23} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
679477248.l.8._.DF $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_6^2.S_3^2.C_2^3$ $2^{23} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
679477248.m.8._.Z $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_6^2.F_9.C_2^2$ $2^{23} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
679477248.m.8._.BJ $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ $C_2^{16}.C_6^2.F_9.C_2^2$ $2^{23} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
679477248.n.8._.Y $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^{16}.C_6^2.\PSU(3,2).C_2^2$ $2^{23} \cdot 3^{4}$ $2^{3}$ $-$
679477248.n.8._.BW $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^{16}.C_6^2.\PSU(3,2).C_2^2$ $2^{23} \cdot 3^{4}$ $2^{3}$ $-$
679477248.o.8._.F $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ ✓ ✓ $C_2^{16}.C_6^2.S_3^2.D_4$ $2^{23} \cdot 3^{4}$ $D_4$ $2^{3}$
679477248.o.8._.BF $C_2^{16}.C_6^2.S_3^2$ $2^{20} \cdot 3^{4}$ $C_2^{16}.C_6^2.S_3^2.D_4$ $2^{23} \cdot 3^{4}$ $2^{3}$ $-$
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