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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 179 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
18432.bx.1.a1.a1 $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ ✓ ✓ $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $C_1$ $1$ ✓
36864.dh.2.B $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ ✓ ✓ $D_4^2.A_4^2:C_4$ $2^{12} \cdot 3^{2}$ $C_2$ $2$ ✓
36864.dl.2.C $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ ✓ ✓ ✓ $(C_2^3\times S_4^2).D_4$ $2^{12} \cdot 3^{2}$ $C_2$ $2$ ✓
36864.dm.2.C $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ ✓ ✓ ✓ $(C_2^3\times S_4^2).D_4$ $2^{12} \cdot 3^{2}$ $C_2$ $2$ ✓
73728.ea.4.F $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ ✓ $S_4^2.C_2\wr D_4$ $2^{13} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
165888.bl.9.a1 $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ ✓ $A_4^2.(C_2\times A_4^2:C_4)$ $2^{11} \cdot 3^{4}$ $3^{2}$ $-$
294912.i.16.A $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ ✓ $C_2^8.(C_2\times A_4^2:C_4)$ $2^{15} \cdot 3^{2}$ $2^{4}$ $-$
294912.bp.16.Q $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ ✓ $C_2^8.(C_2\times A_4^2:C_4)$ $2^{15} \cdot 3^{2}$ $2^{4}$ $-$
294912.db.16.T $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ ✓ $C_2^8.(C_2\times A_4^2:C_4)$ $2^{15} \cdot 3^{2}$ $2^{4}$ $-$
331776.a.18.A $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $C_2^8.C_3^4:\OD_{16}$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.b.18.C $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2:\POPlus(4,3).C_2^2$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.cf.18.F $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $S_4^2.A_4^2:C_4$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.cf.18.N $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $S_4^2.A_4^2:C_4$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.cf.18.P $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $S_4^2.A_4^2:C_4$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.cg.18.J $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2.S_4^2:C_2^2$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.dp.18._.C $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2.(A_4^2:C_4\times C_2^2)$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.dp.18._.D $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2.(A_4^2:C_4\times C_2^2)$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.dp.18._.E $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2.(A_4^2:C_4\times C_2^2)$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.dp.18._.F $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2.(A_4^2:C_4\times C_2^2)$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.dp.18._.I $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2.(A_4^2:C_4\times C_2^2)$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.dp.18._.J $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2.(A_4^2:C_4\times C_2^2)$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.dp.18._.M $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2.(A_4^2:C_4\times C_2^2)$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.dp.18._.N $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2.(A_4^2:C_4\times C_2^2)$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.dp.18._.P $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2.(A_4^2:C_4\times C_2^2)$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.dp.18._.R $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2.(A_4^2:C_4\times C_2^2)$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.dp.18._.S $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2.(A_4^2:C_4\times C_2^2)$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.dp.18._.U $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2.(A_4^2:C_4\times C_2^2)$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.dp.18._.X $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2.(A_4^2:C_4\times C_2^2)$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.dp.18._.Z $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2.(A_4^2:C_4\times C_2^2)$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.dp.18._.BA $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2.(A_4^2:C_4\times C_2^2)$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
331776.dp.18._.BC $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2.(A_4^2:C_4\times C_2^2)$ $2^{12} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
460800.b.25.a1 $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ ✓ $A_5^2.C_2^5:C_4$ $2^{11} \cdot 3^{2} \cdot 5^{2}$ $5^{2}$ $-$
663552.a.36.J $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2:\POPlus(4,3).C_2^3$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
663552.b.36.I $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $C_2^8.C_3^4.C_4\wr C_2$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
663552.d.36.L $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2:(A_4^2:C_4).D_4$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
663552.e.36.J $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2\wr C_2.C_2^2.C_4$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
663552.f.36.J $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2:\POPlus(4,3).D_4$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
663552.g.36.R $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2\wr C_2.C_2^2.C_4$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
663552.cn.36.BV $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2\wr C_2.C_2^2.C_2^2$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
663552.cn.36.BY $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2\wr C_2.C_2^2.C_2^2$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
663552.cp.36.BV $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2.S_4\wr C_2.C_4$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
663552.cp.36.BY $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2.S_4\wr C_2.C_4$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
663552.cq.36.BC $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $C_2^8.C_3^4:C_4^2:C_2$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
663552.cq.36.BD $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $C_2^8.C_3^4:C_4^2:C_2$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
663552.ct.36.BD $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2:\POPlus(4,3).C_2^3$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
663552.ct.36.BG $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $A_4^2:\POPlus(4,3).C_2^3$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
663552.cu.36._.F $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $C_2^9.C_3^4:\OD_{16}$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
663552.cu.36._.G $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $C_2^9.C_3^4:\OD_{16}$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
663552.cu.36._.H $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $C_2^9.C_3^4:\OD_{16}$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
663552.cu.36._.I $A_4^2.C_2^5:C_4$ $2^{11} \cdot 3^{2}$ $C_2^9.C_3^4:\OD_{16}$ $2^{13} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
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