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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 65 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
55296.de.1.a1 $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $C_1$ $1$ ✓
110592.di.2.D $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ ✓ $A_4^2.C_2^3:\GL(2,\mathbb{Z}/4)$ $2^{12} \cdot 3^{3}$ $C_2$ $2$ ✓
110592.ef.2.D $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ ✓ $C_2^9.S_3^3$ $2^{12} \cdot 3^{3}$ $C_2$ $2$ ✓
110592.ei.2.D $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ ✓ $C_2^9.S_3^3$ $2^{12} \cdot 3^{3}$ $C_2$ $2$ ✓
110592.ez.2.B $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ ✓ $(C_2^3\times S_4^2).S_4$ $2^{12} \cdot 3^{3}$ $C_2$ $2$ ✓
110592.fc.2.B $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ ✓ $A_4^2:C_2^3.\GL(2,\mathbb{Z}/4)$ $2^{12} \cdot 3^{3}$ $C_2$ $2$ ✓
165888.bz.3.A $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ ✓ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $C_3$ $3$ ✓
221184.eu.4.Q $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ $C_2^{10}.S_3^3$ $2^{13} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
221184.fd.4._.F $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ $(C_2^2\times S_4^2).\GL(2,\mathbb{Z}/4)$ $2^{13} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
221184.fe.4.D $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ $C_2^4.A_4^3:D_4$ $2^{13} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
221184.fw.4.E $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ $(C_2^2\times S_4^2).\GL(2,\mathbb{Z}/4)$ $2^{13} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
221184.fx.4.E $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ $C_2^5.S_4^2:D_6$ $2^{13} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
331776.cs.6.F $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ $A_4^2.C_2\wr S_3^2$ $2^{12} \cdot 3^{4}$ $C_6$ $2 \cdot 3$ ✓
331776.do.6.C $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ $C_2^9.C_3\wr D_4$ $2^{12} \cdot 3^{4}$ $C_6$ $2 \cdot 3$ ✓
331776.ds.6.A $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ $C_2^9.C_3:S_3^3$ $2^{12} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
331776.du.6.B $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ $A_4^2.C_2\wr S_3^2$ $2^{12} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
331776.fd.6.A $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ $A_4^2.S_4^2:C_4$ $2^{12} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
442368.fj.8.M $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ $S_4^2.C_2\wr D_6$ $2^{14} \cdot 3^{3}$ $C_2^3$ $2^{3}$ ✓
663552.br.12.D $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $A_4^2.S_4\wr C_2.C_4$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
663552.bt.12.D $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $C_2.A_4^2\wr C_2.D_4$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
663552.bv.12.D $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $C_2.A_4^2\wr C_2.D_4$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
663552.ey.12.F $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ $C_2^{10}.C_3\wr D_4$ $2^{13} \cdot 3^{4}$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
663552.fa.12.D $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ $C_2^5.A_4^2:D_6^2$ $2^{13} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
663552.fy.12.E $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ $A_4^2.S_4^2:D_4$ $2^{13} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
663552.hg.12.L $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $A_4^2.(C_2\times S_4^2:C_4)$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
663552.hj.12.B $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ $C_2^5.S_4^2:S_3^2$ $2^{13} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
663552.hj.12.BJ $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $C_2^5.S_4^2:S_3^2$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
663552.hk.12.D $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ $A_4^2.S_4^2:D_4$ $2^{13} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
1327104.bx.24.BV $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $C_2^8.C_3^4:D_4^2$ $2^{14} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1327104.by.24.BV $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $C_2^{10}.C_3^4:(C_2\times D_4)$ $2^{14} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1327104.cc.24.BI $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $C_2^{10}.C_3^4:(C_2\times D_4)$ $2^{14} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1327104.cc.24.BK $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $C_2^{10}.C_3^4:(C_2\times D_4)$ $2^{14} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1327104.df.24.V $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $A_4^2.S_4\wr C_2.D_4$ $2^{14} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1327104.dh.24.M $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1327104.di.24.J $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1327104.dj.24.K $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1327104.dk.24.Q $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1327104.dl.24.L $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1327104.dm.24.G $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $C_2^8.C_3:S_3^3:Q_8$ $2^{14} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1327104.dt.24._.A $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $C_2^8.C_3:S_3^3:C_8$ $2^{14} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1327104.eb.24.H $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $C_2^9.C_3:S_3^3:C_4$ $2^{14} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1327104.ec.24.H $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $C_2^9.C_3:S_3^3:C_4$ $2^{14} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1327104.ef.24.BT $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $C_2^9:C_3^2.D_6\wr C_2$ $2^{14} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1327104.eg.24.BT $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $C_2^9.S_3^2\wr C_2$ $2^{14} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
1327104.ik.24.D $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ $S_4^2.C_2\wr S_3^2$ $2^{14} \cdot 3^{4}$ $C_2\times D_6$ $2^{3} \cdot 3$
2654208.dg.48.CB $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $C_2^8.(C_2.S_3\wr C_4)$ $2^{15} \cdot 3^{4}$ $2^{4} \cdot 3$ $-$
2654208.di.48.BY $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $C_2^9.C_3^4:C_4^2:C_4$ $2^{15} \cdot 3^{4}$ $2^{4} \cdot 3$ $-$
2654208.dk.48.EK $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $C_2^8.S_3^4:C_8$ $2^{15} \cdot 3^{4}$ $2^{4} \cdot 3$ $-$
2654208.dl.48.BY $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $C_2^9.C_3:S_3^3.D_4$ $2^{15} \cdot 3^{4}$ $2^{4} \cdot 3$ $-$
2654208.dm.48.BY $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ $C_2^8.C_3:S_3^3:D_8$ $2^{15} \cdot 3^{4}$ $2^{4} \cdot 3$ $-$
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