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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 61 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1632586752.bbj.1.a1.a1 $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ ✓ ✓ $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_1$ $1$ ✓
3265173504.gs.2._.O $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6.D_4$ $2^{11} \cdot 3^{13}$ $C_2$ $2$ ✓
3265173504.gu.2._.G $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6.D_4$ $2^{11} \cdot 3^{13}$ $C_2$ $2$ ✓
3265173504.bdf.2._.D $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.C_2^4$ $2^{11} \cdot 3^{13}$ $C_2$ $2$ ✓
3265173504.bdf.2._.M $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.C_2^4$ $2^{11} \cdot 3^{13}$ $C_2$ $2$ ✓
3265173504.bdf.2._.X $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.C_2^4$ $2^{11} \cdot 3^{13}$ $C_2$ $2$ ✓
3265173504.bdf.2._.Y $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ ✓ ✓ $C_3^{12}.C_2^6.C_6.C_2^4$ $2^{11} \cdot 3^{13}$ $C_2$ $2$ ✓
6530347008.gc.4._.N $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ ✓ $C_3^{12}.C_2^6.D_6.(C_2\times D_4)$ $2^{12} \cdot 3^{13}$ $C_2^2$ $2^{2}$ ✓
6530347008.gc.4._.BB $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ ✓ $C_3^{12}.C_2^6.D_6.(C_2\times D_4)$ $2^{12} \cdot 3^{13}$ $C_2^2$ $2^{2}$ ✓
6530347008.gc.4._.BX $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_6.(C_2\times D_4)$ $2^{12} \cdot 3^{13}$ $2^{2}$ $-$
6530347008.yk.4._.I $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ ✓ $C_3^6.(C_3^6.(C_2^9.S_4))$ $2^{12} \cdot 3^{13}$ $2^{2}$ $-$
6530347008.biv.4._.BT $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_6.(C_2\times D_4)$ $2^{12} \cdot 3^{13}$ $2^{2}$ $-$
6530347008.biv.4._.BU $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_6.(C_2\times D_4)$ $2^{12} \cdot 3^{13}$ $2^{2}$ $-$
9795520512.cy.6._.O $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^6.D_6.S_4$ $2^{11} \cdot 3^{14}$ $2 \cdot 3$ $-$
13060694016.dg.8._.N $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2.C_2^6.S_4.D_4$ $2^{13} \cdot 3^{13}$ $2^{3}$ $-$
13060694016.di.8._.BD $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2.C_2^6.(D_4\times S_4)$ $2^{13} \cdot 3^{13}$ $2^{3}$ $-$
13060694016.et.8._.BV $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^6.(C_6^3.D_6\wr S_3).D_4$ $2^{13} \cdot 3^{13}$ $2^{3}$ $-$
13060694016.ex.8._.BF $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^6.(C_6^3.D_6\wr S_3).D_4$ $2^{13} \cdot 3^{13}$ $2^{3}$ $-$
13060694016.ex.8._.CG $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^6.(C_6^3.D_6\wr S_3).D_4$ $2^{13} \cdot 3^{13}$ $2^{3}$ $-$
13060694016.ff.8._.BE $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^6.S_4.C_2^2:C_4$ $2^{13} \cdot 3^{13}$ $2^{3}$ $-$
13060694016.fi.8._.BU $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^6.(D_4\times S_4).C_2$ $2^{13} \cdot 3^{13}$ $2^{3}$ $-$
13060694016.lo.8._.M $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2.C_2^6.S_4.D_4$ $2^{13} \cdot 3^{13}$ $2^{3}$ $-$
13060694016.lq.8._.O $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2.C_2^6.S_4.D_4$ $2^{13} \cdot 3^{13}$ $2^{3}$ $-$
13060694016.sl.8._.BF $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^6.(C_3^6.(C_2^{10}.S_4))$ $2^{13} \cdot 3^{13}$ $2^{3}$ $-$
13060694016.sl.8._.BI $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^6.(C_3^6.(C_2^{10}.S_4))$ $2^{13} \cdot 3^{13}$ $2^{3}$ $-$
13060694016.sl.8._.BO $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^6.(C_3^6.(C_2^{10}.S_4))$ $2^{13} \cdot 3^{13}$ $2^{3}$ $-$
13060694016.sl.8._.BX $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^6.(C_3^6.(C_2^{10}.S_4))$ $2^{13} \cdot 3^{13}$ $2^{3}$ $-$
13060694016.bbx.8._.P $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^6.(C_3^6.(C_2^{10}.S_4))$ $2^{13} \cdot 3^{13}$ $2^{3}$ $-$
13060694016.bbx.8._.DU $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^6.(C_3^6.(C_2^{10}.S_4))$ $2^{13} \cdot 3^{13}$ $2^{3}$ $-$
13060694016.bbx.8._.DV $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^6.(C_3^6.(C_2^{10}.S_4))$ $2^{13} \cdot 3^{13}$ $2^{3}$ $-$
13060694016.bbx.8._.EC $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^6.(C_3^6.(C_2^{10}.S_4))$ $2^{13} \cdot 3^{13}$ $2^{3}$ $-$
26121388032.ck.16._.IL $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^6.S_3.C_2\wr D_4$ $2^{14} \cdot 3^{13}$ $2^{4}$ $-$
26121388032.cp.16._.DX $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^6.S_4.C_2^2\wr C_2$ $2^{14} \cdot 3^{13}$ $2^{4}$ $-$
26121388032.cp.16._.EB $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^6.S_4.C_2^2\wr C_2$ $2^{14} \cdot 3^{13}$ $2^{4}$ $-$
26121388032.cp.16._.GW $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^6.S_4.C_2^2\wr C_2$ $2^{14} \cdot 3^{13}$ $2^{4}$ $-$
26121388032.kf.16._.CK $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^3.C_2^6.S_4.C_2^2$ $2^{14} \cdot 3^{13}$ $2^{4}$ $-$
26121388032.kf.16._.CO $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^3.C_2^6.S_4.C_2^2$ $2^{14} \cdot 3^{13}$ $2^{4}$ $-$
26121388032.ky.16._.Q $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^5.C_2^4.D_6.D_4$ $2^{14} \cdot 3^{13}$ $2^{4}$ $-$
26121388032.ky.16._.V $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^5.C_2^4.D_6.D_4$ $2^{14} \cdot 3^{13}$ $2^{4}$ $-$
26121388032.ky.16._.DB $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^5.C_2^4.D_6.D_4$ $2^{14} \cdot 3^{13}$ $2^{4}$ $-$
39182082048.dz.24._.KT $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^4.A_4^2.C_4.C_2^3$ $2^{13} \cdot 3^{14}$ $2^{3} \cdot 3$ $-$
39182082048.dz.24._.LY $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^4.A_4^2.C_4.C_2^3$ $2^{13} \cdot 3^{14}$ $2^{3} \cdot 3$ $-$
39182082048.eb.24._.IB $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^4.A_4^2.C_2^4.C_2$ $2^{13} \cdot 3^{14}$ $2^{3} \cdot 3$ $-$
39182082048.eb.24._.IC $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^4.A_4^2.C_2^4.C_2$ $2^{13} \cdot 3^{14}$ $2^{3} \cdot 3$ $-$
39182082048.ee.24._.IZ $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^4.A_4^2.C_2^4.C_2$ $2^{13} \cdot 3^{14}$ $2^{3} \cdot 3$ $-$
39182082048.ef.24._.IW $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^4.A_4^2.C_2^4.C_2$ $2^{13} \cdot 3^{14}$ $2^{3} \cdot 3$ $-$
39182082048.eg.24._.BJ $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^5.C_2^6.S_3^2$ $2^{13} \cdot 3^{14}$ $2^{3} \cdot 3$ $-$
39182082048.eg.24._.BV $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^5.C_2^6.S_3^2$ $2^{13} \cdot 3^{14}$ $2^{3} \cdot 3$ $-$
39182082048.el.24._.DB $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^6.A_4^2.C_2^3$ $2^{13} \cdot 3^{14}$ $2^{3} \cdot 3$ $-$
52242776064.ei.32._.CJ $C_3^6.(C_3^6.C_2^7:S_4)$ $2^{10} \cdot 3^{13}$ $C_3^{12}.C_2^6.C_4^2.S_4.C_2^2$ $2^{15} \cdot 3^{13}$ $2^{5}$ $-$
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