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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 248 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
6144.hg.6144.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_2^8.S_4$ $2^{11} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
49152.bm.6144.A $C_2^3$ $2^{3}$ ✓ ✓ $C_2^{10}.(C_2\times S_4)$ $2^{14} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
49152.nz.6144.B $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_2^8.C_2^3:S_4$ $2^{14} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
49152.zv.6144.B $C_2^3$ $2^{3}$ ✓ ✓ $C_2^5.C_2\wr S_4$ $2^{14} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
49152.bax.6144.A $C_2^3$ $2^{3}$ ✓ ✓ $C_2^5.C_2\wr S_4$ $2^{14} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
49152.bax.6144.D $C_2^3$ $2^{3}$ ✓ ✓ $C_2^5.C_2\wr S_4$ $2^{14} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
98304.xu.6144.A $C_2^4$ $2^{4}$ ✓ ✓ $C_2^{12}.S_4$ $2^{15} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.cn.6144.B $C_2^6$ $2^{6}$ ✓ ✓ $C_2^7.C_2^7:S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.cp.6144.B $C_2^6$ $2^{6}$ ✓ ✓ $C_2^7.C_2^7:S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.cq.6144.B $C_2^6$ $2^{6}$ ✓ ✓ $C_2^8.C_2\wr S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.cs.6144.B $C_2^6$ $2^{6}$ ✓ ✓ $C_2^8.C_2\wr S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.cs.6144.E $C_2^6$ $2^{6}$ ✓ ✓ $C_2^8.C_2\wr S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.cy.6144.C $C_2^6$ $2^{6}$ ✓ ✓ $C_2^8.C_2\wr S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.cy.6144.D $C_2^6$ $2^{6}$ ✓ ✓ $C_2^8.C_2\wr S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.gr.6144.B $C_2^2\times C_4^2$ $2^{6}$ ✓ ✓ $C_2^7.C_2^7:S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.gt.6144.B $C_2^2\times C_4^2$ $2^{6}$ ✓ ✓ $C_2^7.C_2^7:S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.gt.6144.F $C_4^3$ $2^{6}$ ✓ ✓ $C_2^7.C_2^7:S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.ig.6144.B $C_2^2\times C_4^2$ $2^{6}$ ✓ ✓ $C_2^7.C_2^7:S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.ii.6144.B $C_2^2\times C_4^2$ $2^{6}$ ✓ ✓ $C_2^7.C_2^7:S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.ii.6144.F $C_4^3$ $2^{6}$ ✓ ✓ $C_2^7.C_2^7:S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.jf.6144.D $C_2^4\times C_4$ $2^{6}$ ✓ ✓ ✓ $C_2^8.C_2\wr S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.jf.6144.H $C_4^3$ $2^{6}$ ✓ ✓ ✓ $C_2^8.C_2\wr S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.jj.6144.C $C_2^2\times C_4^2$ $2^{6}$ ✓ ✓ ✓ $C_2^8.C_2\wr S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.jj.6144.D $C_2^4\times C_4$ $2^{6}$ ✓ ✓ ✓ $C_2^8.C_2\wr S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.jj.6144.E $C_2^4\times C_4$ $2^{6}$ ✓ ✓ ✓ $C_2^8.C_2\wr S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.jj.6144.J $C_4^3$ $2^{6}$ ✓ ✓ ✓ $C_2^8.C_2\wr S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.jq.6144.B $C_2^2\times C_4^2$ $2^{6}$ ✓ ✓ ✓ $C_2^8.C_2\wr S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.jq.6144.D $C_2^4\times C_4$ $2^{6}$ ✓ ✓ ✓ $C_2^8.C_2\wr S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.jq.6144.E $C_2^4\times C_4$ $2^{6}$ ✓ ✓ ✓ $C_2^8.C_2\wr S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
393216.jq.6144.J $C_4^3$ $2^{6}$ ✓ ✓ ✓ $C_2^8.C_2\wr S_4$ $2^{17} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
786432.cc.6144.D $D_4\times C_2^4$ $2^{7}$ ✓ $C_2^9.C_2\wr S_4$ $2^{18} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
786432.hb.6144.C $C_4^2:D_4$ $2^{7}$ ✓ $D_4^3.C_2\wr S_4$ $2^{18} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
786432.hb.6144.E $D_4\times C_2^4$ $2^{7}$ ✓ $D_4^3.C_2\wr S_4$ $2^{18} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
786432.hb.6144.G $C_4^3:C_2$ $2^{7}$ ✓ $D_4^3.C_2\wr S_4$ $2^{18} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
786432.ic.6144.E $C_2^7$ $2^{7}$ ✓ ✓ ✓ $C_2^{12}.C_2^3:S_4$ $2^{18} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
786432.ic.6144.F $C_2^7$ $2^{7}$ ✓ ✓ ✓ $C_2^{12}.C_2^3:S_4$ $2^{18} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
3145728.a.6144.D $C_2^6:D_4$ $2^{9}$ ✓ ✓ $C_2^{10}.C_2^7:S_4$ $2^{20} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
3145728.a.6144.E $C_4^2.C_2^5$ $2^{9}$ ✓ ✓ $C_2^{10}.C_2^7:S_4$ $2^{20} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
3145728.a.6144.I $C_2^8.C_2$ $2^{9}$ ✓ ✓ $C_2^{10}.C_2^7:S_4$ $2^{20} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
3145728.a.6144.J $C_4^2.C_2^5$ $2^{9}$ ✓ ✓ $C_2^{10}.C_2^7:S_4$ $2^{20} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
3145728.g.6144.G $C_2^6:D_4$ $2^{9}$ ✓ ✓ $C_2^{10}.C_2^7:S_4$ $2^{20} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
3145728.g.6144.H $C_2^8.C_2$ $2^{9}$ ✓ ✓ $C_2^{10}.C_2^7:S_4$ $2^{20} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
3145728.g.6144.I $C_4^2.C_2^5$ $2^{9}$ ✓ ✓ $C_2^{10}.C_2^7:S_4$ $2^{20} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
3145728.g.6144.J $C_4^2.C_2^5$ $2^{9}$ ✓ ✓ $C_2^{10}.C_2^7:S_4$ $2^{20} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
3145728.h.6144.C $C_2^6:D_4$ $2^{9}$ ✓ ✓ $C_2^{10}.C_2^7:S_4$ $2^{20} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
3145728.h.6144.D $C_4^2.C_2^5$ $2^{9}$ ✓ ✓ $C_2^{10}.C_2^7:S_4$ $2^{20} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
3145728.u.6144.C $C_2^8.C_2$ $2^{9}$ ✓ $C_2^9.(C_2^8.S_4)$ $2^{20} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
3145728.y.6144.B $C_2^6:D_4$ $2^{9}$ ✓ $C_2^9.(C_2^8.S_4)$ $2^{20} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
3145728.y.6144.C $C_2^8.C_2$ $2^{9}$ ✓ $C_2^9.(C_2^8.S_4)$ $2^{20} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
3145728.z.6144.B $C_2^6:D_4$ $2^{9}$ ✓ $C_2^9.(C_2^8.S_4)$ $2^{20} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$
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