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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 74 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
559872.lw.559872.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
1119744.jy.559872.A $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3^6.C_2^6:S_4$ $2^{9} \cdot 3^{7}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
1119744.nc.559872.A $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3^6.(C_2^7.D_6)$ $2^{9} \cdot 3^{7}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
1119744.nd.559872.A $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3^6.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{9} \cdot 3^{7}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
1119744.ne.559872.A $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3^6.C_2^6:D_{12}$ $2^{9} \cdot 3^{7}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
2239488.ge.559872.A $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_3^6.C_2^8:D_6$ $2^{10} \cdot 3^{7}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
2239488.gf.559872.A $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_3^5\times C_6).C_2^6:S_4$ $2^{10} \cdot 3^{7}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
4478976.dt.559872.A $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_3^6.(C_2^9.D_6)$ $2^{11} \cdot 3^{7}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
4478976.du.559872.A $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_3^6.(C_2^9.D_6)$ $2^{11} \cdot 3^{7}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
4478976.dv.559872.A $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_3^6.(C_2^8.D_{12})$ $2^{11} \cdot 3^{7}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
4478976.dw.559872.A $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_3^6.(C_2^6.\GL(2,\mathbb{Z}/4))$ $2^{11} \cdot 3^{7}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
8957952.v.559872.A $C_2^4$ $2^{4}$ ✓ ✓ ✓ $C_3^6.(C_2^9.S_4)$ $2^{12} \cdot 3^{7}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
8957952.bk.559872.A $C_2^4$ $2^{4}$ ✓ ✓ ✓ $C_3^6.(C_2^{10}.D_6)$ $2^{12} \cdot 3^{7}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
15116544.da.559872.A $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
15116544.db.559872.A $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
15116544.de.559872.A $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
15116544.df.559872.A $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
30233088.bg.559872.A $C_3^2:S_3$ $2 \cdot 3^{3}$ ✓ ✓ $C_3^5:D_6.D_6\wr S_3$ $2^{9} \cdot 3^{10}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
408146688.is.559872._.A $C_3^6$ $3^{6}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
408146688.is.559872._.B $C_3^6$ $3^{6}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
408146688.jb.559872._.A $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
408146688.sl.559872._.A $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
408146688.sr.559872._.A $C_3^6$ $3^{6}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
408146688.sr.559872._.B $C_3^6$ $3^{6}$ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
408146688.wq.559872._.B $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
408146688.wu.559872._.A $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
408146688.xh.559872._.A $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
408146688.xi.559872._.B $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
408146688.xl.559872._.B $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
408146688.xo.559872._.B $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
408146688.xt.559872._.B $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
408146688.xv.559872._.B $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
816293376.qr.559872._.A $C_3^5:S_3$ $2 \cdot 3^{6}$ ✓ ✓ $C_3^6.(C_3^6.C_2^6:S_4)$ $2^{9} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
816293376.se.559872._.A $C_3^5:S_3$ $2 \cdot 3^{6}$ ✓ ✓ $C_3^6.(C_3^6.C_2^4:\GL(2,\mathbb{Z}/4))$ $2^{9} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
816293376.sk.559872._.A $C_3^5:S_3$ $2 \cdot 3^{6}$ ✓ ✓ $C_3^{12}.C_2^6.C_{12}.C_2$ $2^{9} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
816293376.sr.559872._.A $C_3^5:S_3$ $2 \cdot 3^{6}$ ✓ ✓ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
816293376.bcu.559872._.A $C_3^5:S_3$ $2 \cdot 3^{6}$ ✓ ✓ $C_3^6.(C_3^6.C_2^6:S_4)$ $2^{9} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
816293376.bjz.559872._.A $C_3^5:S_3$ $2 \cdot 3^{6}$ ✓ ✓ $C_3^6.(C_3^6.C_2^6:S_4)$ $2^{9} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
816293376.bkf.559872._.A $C_3^5:S_3$ $2 \cdot 3^{6}$ ✓ ✓ $C_3^6.(C_6^3.S_3^3:S_4)$ $2^{9} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
816293376.bki.559872._.A $C_3^5:S_3$ $2 \cdot 3^{6}$ ✓ ✓ $C_3^6.(C_3^6.C_2^6:S_4)$ $2^{9} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
816293376.bmp.559872._.A $C_3^5:S_3$ $2 \cdot 3^{6}$ ✓ ✓ $C_3^6.(C_3^6.C_2^4:\GL(2,\mathbb{Z}/4))$ $2^{9} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
816293376.bnz.559872._.A $C_3^5:S_3$ $2 \cdot 3^{6}$ ✓ ✓ $C_3^{12}.C_2^6.D_{12}$ $2^{9} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
816293376.boe.559872._.A $C_3^5:S_3$ $2 \cdot 3^{6}$ ✓ ✓ $C_3^{12}.C_2^6.C_{12}.C_2$ $2^{9} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
1632586752.vt.559872._.C $C_3^5.D_6$ $2^{2} \cdot 3^{6}$ ✓ ✓ $C_3^{12}.C_2^6.S_3.D_4$ $2^{10} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
1632586752.bas.559872._.B $C_3^5:D_6$ $2^{2} \cdot 3^{6}$ ✓ ✓ $C_3^{12}.C_2^6.S_4.C_2$ $2^{10} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
1632586752.bay.559872._.A $C_3^5:D_6$ $2^{2} \cdot 3^{6}$ ✓ $C_3^{12}.C_2^6.S_4.C_2$ $2^{10} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
1632586752.bay.559872._.B $C_3^5:D_6$ $2^{2} \cdot 3^{6}$ ✓ $C_3^{12}.C_2^6.S_4.C_2$ $2^{10} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
1632586752.bom.559872._.C $C_3^5.D_6$ $2^{2} \cdot 3^{6}$ ✓ ✓ $C_3^{12}.C_2^6.D_{12}.C_2$ $2^{10} \cdot 3^{13}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$
2293235712.lm.559872._.A $C_2^{12}$ $2^{12}$ ✓ ✓ ✓ $C_2^{12}.(C_3^6.C_2^5:S_4)$ $2^{20} \cdot 3^{7}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
2293235712.ms.559872._.A $C_2^{12}$ $2^{12}$ ✓ ✓ ✓ $C_2^{12}.(C_3^6.C_2^5:S_4)$ $2^{20} \cdot 3^{7}$ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ ✓
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