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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 146 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
6144.ej.6144.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
12288.bao.6144._.A $C_2$ $2$ ✓ ✓ ✓ $C_2^7.\GL(2,\mathbb{Z}/4)$ $2^{12} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$ ✓
12288.bao.6144._.B $C_2$ $2$ ✓ ✓ ✓ $C_2^7.\GL(2,\mathbb{Z}/4)$ $2^{12} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$ ✓
12288.bck.6144._.B $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^7.\GL(2,\mathbb{Z}/4)$ $2^{12} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$ ✓
24576.bs.6144._.B $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^8.\GL(2,\mathbb{Z}/4)$ $2^{13} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
24576.bt.6144._.B $C_2^2$ $2^{2}$ ✓ ✓ $C_2^8.\GL(2,\mathbb{Z}/4)$ $2^{13} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
24576.bt.6144._.D $C_2^2$ $2^{2}$ ✓ ✓ $C_2^8.\GL(2,\mathbb{Z}/4)$ $2^{13} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
24576.zk.6144._.A $C_2^2$ $2^{2}$ ✓ ✓ $C_2^8.\GL(2,\mathbb{Z}/4)$ $2^{13} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
24576.zk.6144._.F $C_2^2$ $2^{2}$ ✓ ✓ $C_2^8.\GL(2,\mathbb{Z}/4)$ $2^{13} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
49152.kw.6144.A $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_2^7.C_2\wr S_3$ $2^{14} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
49152.ky.6144.A $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_2^7.C_2\wr S_3$ $2^{14} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
49152.lc.6144.A $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_2^7.C_2\wr S_3$ $2^{14} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
49152.ld.6144.A $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_2^7.C_2\wr S_3$ $2^{14} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
49152.pn.6144.A $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_2^5.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{14} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
49152.qf.6144.A $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_2^5.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{14} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
49152.yg.6144.A $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_4^3.C_2^5:S_4$ $2^{14} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
49152.yh.6144.A $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_4^3.C_2^5:S_4$ $2^{14} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
98304.fk.6144.B $C_2^4$ $2^{4}$ ✓ ✓ $C_2^8.C_2\wr S_3$ $2^{15} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
98304.jp.6144.B $C_2^4$ $2^{4}$ ✓ ✓ ✓ $C_2^8.C_2\wr S_3$ $2^{15} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
98304.re.6144.A $C_2^4$ $2^{4}$ ✓ ✓ ✓ $C_4^3.C_2^6:D_{12}$ $2^{15} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
98304.rm.6144._.A $C_2^2\times C_4$ $2^{4}$ ✓ ✓ ✓ $C_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
98304.rm.6144._.B $C_2^4$ $2^{4}$ ✓ ✓ ✓ $C_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
98304.rv.6144.B $C_2^2\times C_4$ $2^{4}$ ✓ ✓ ✓ $C_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
98304.sb.6144.B $C_2^2\times C_4$ $2^{4}$ ✓ ✓ $C_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
98304.tm.6144._.A $C_2^2\times C_4$ $2^{4}$ ✓ ✓ ✓ $C_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
196608.fe.6144._.A $C_2^3\times C_4$ $2^{5}$ ✓ ✓ ✓ $C_2^7.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{16} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
196608.fe.6144._.B $C_2^5$ $2^{5}$ ✓ ✓ ✓ $C_2^7.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{16} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
196608.fh.6144.B $C_2^5$ $2^{5}$ ✓ ✓ ✓ $C_2^8.C_2\wr D_6$ $2^{16} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
196608.fh.6144.C $C_2^3\times C_4$ $2^{5}$ ✓ ✓ ✓ $C_2^8.C_2\wr D_6$ $2^{16} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
196608.jc.6144.A $C_2^5$ $2^{5}$ ✓ ✓ $C_2^7.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{16} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
196608.je.6144.A $C_2^5$ $2^{5}$ ✓ ✓ $C_2^7.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{16} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
196608.jn.6144.B $C_2^5$ $2^{5}$ ✓ ✓ ✓ $C_2^9.C_2\wr S_3$ $2^{16} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
196608.js.6144._.B $C_2^5$ $2^{5}$ ✓ ✓ ✓ $C_2^9.C_2\wr S_3$ $2^{16} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
196608.kf.6144.C $C_2^3\times C_4$ $2^{5}$ ✓ ✓ ✓ $C_2^9.C_2^4:D_{12}$ $2^{16} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
196608.ll.6144.C $C_2^2\times D_4$ $2^{5}$ ✓ ✓ $C_2^8.C_2\wr D_6$ $2^{16} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
196608.ll.6144.D $C_2^2\times Q_8$ $2^{5}$ ✓ ✓ $C_2^8.C_2\wr D_6$ $2^{16} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
393216.dg.6144.A $C_2^6$ $2^{6}$ ✓ ✓ ✓ $C_2^8.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{17} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
393216.dk.6144.A $C_2^6$ $2^{6}$ ✓ ✓ ✓ $C_2^8.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{17} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
393216.es.6144.A $C_2^6$ $2^{6}$ ✓ ✓ ✓ $C_2^8.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{17} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
393216.et.6144.A $C_2^6$ $2^{6}$ ✓ ✓ ✓ $C_2^8.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{17} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
786432.bi.6144.B $C_2^7$ $2^{7}$ ✓ ✓ ✓ $C_2^9.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{18} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
786432.bi.6144.C $C_2^5\times C_4$ $2^{7}$ ✓ ✓ ✓ $C_2^9.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{18} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
786432.cx.6144.A $C_2^7$ $2^{7}$ ✓ ✓ $C_2^9.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{18} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
786432.cy.6144.A $C_2^7$ $2^{7}$ ✓ ✓ ✓ $C_2^9.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{18} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
786432.cz.6144.B $C_2^7$ $2^{7}$ ✓ ✓ ✓ $C_2^9.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{18} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
786432.eg.6144.C $C_2^5\times C_4$ $2^{7}$ ✓ ✓ ✓ $C_2^9.C_2^6:D_{12}$ $2^{18} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
1572864.l.6144.A $C_2^8$ $2^{8}$ ✓ ✓ ✓ $C_2^{10}.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{19} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
1572864.l.6144.E $C_2^6:C_4$ $2^{8}$ ✓ ✓ $C_2^{10}.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{19} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
1572864.bw.6144.C $D_4\times C_2^5$ $2^{8}$ ✓ ✓ $C_2^6.(C_2^8.\GL(2,\mathbb{Z}/4))$ $2^{19} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
1572864.bw.6144.D $C_2^4\times C_4^2$ $2^{8}$ ✓ ✓ ✓ $C_2^6.(C_2^8.\GL(2,\mathbb{Z}/4))$ $2^{19} \cdot 3$ $C_2^6.\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3$
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