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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 59 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1327104.d.1327104.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
5308416.bx.1327104.A $C_2^2$ $2^{2}$ ✓ ✓ ✓ $A_4^2.S_4^2:C_2^3.D_4$ $2^{16} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
5308416.by.1327104.A $C_2^2$ $2^{2}$ ✓ ✓ ✓ $A_4^2.S_4^2:C_2^3.D_4$ $2^{16} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
5308416.bz.1327104.A $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^{10}.C_3^4:D_4:D_4$ $2^{16} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
10616832.r.1327104.A $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_2^{10}.(C_6:S_3^3.D_4)$ $2^{17} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
10616832.s.1327104.A $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_2^{10}.(C_6:S_3^3.D_4)$ $2^{17} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
21233664.f.1327104.A $C_2^4$ $2^{4}$ ✓ ✓ ✓ $C_2^8.(C_6^4.D_4:D_4)$ $2^{18} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
339738624.gt.1327104._.A $C_2^8$ $2^{8}$ ✓ ✓ $C_2^{16}.C_3^4.D_4:D_4$ $2^{22} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$ ✓
339738624.gt.1327104._.B $C_2^8$ $2^{8}$ ✓ ✓ $C_2^{16}.C_3^4.D_4:D_4$ $2^{22} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$ ✓
679477248.ck.1327104._.A $C_2^9$ $2^{9}$ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3$ $2^{23} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
679477248.ck.1327104._.B $C_2^9$ $2^{9}$ ✓ ✓ $C_2^{16}.C_3^4.C_4^2.C_2^3$ $2^{23} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
679477248.cl.1327104._.A $C_2^9$ $2^{9}$ ✓ ✓ $C_2^9.(A_4^2\wr C_2.C_2^2.D_4)$ $2^{23} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
679477248.cl.1327104._.B $C_2^9$ $2^{9}$ ✓ ✓ $C_2^9.(A_4^2\wr C_2.C_2^2.D_4)$ $2^{23} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
679477248.cm.1327104._.A $C_2^9$ $2^{9}$ ✓ ✓ $C_2^{16}.C_3^4.\OD_{16}.D_4$ $2^{23} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
679477248.cm.1327104._.B $C_2^9$ $2^{9}$ ✓ ✓ $C_2^{16}.C_3^4.\OD_{16}.D_4$ $2^{23} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
1358954496.l.1327104._.A $C_2^{10}$ $2^{10}$ ✓ ✓ $C_2^{16}.C_6^2.\PSU(3,2).D_4$ $2^{24} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
1358954496.l.1327104._.B $C_2^{10}$ $2^{10}$ ✓ ✓ $C_2^{16}.C_6^2.\PSU(3,2).D_4$ $2^{24} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
43486543872.be.1327104._.A $C_2^{15}$ $2^{15}$ ✓ ✓ ✓ $C_2^{12}.(C_2^{10}.(C_6:S_3^3.D_4))$ $2^{29} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
43486543872.bf.1327104._.A $C_2^{15}$ $2^{15}$ ✓ ✓ ✓ $C_2^{12}.(C_2^{10}.C_3^4:\OD_{16}.D_4)$ $2^{29} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
43486543872.bh.1327104._.A $C_2^{15}$ $2^{15}$ ✓ ✓ ✓ $C_2^{12}.(C_2^{10}.C_3^4:\OD_{16}.D_4)$ $2^{29} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
43486543872.bi.1327104._.A $C_2^{15}$ $2^{15}$ ✓ ✓ ✓ $C_2^{12}.(C_2^{10}.(C_6:S_3^3.D_4))$ $2^{29} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
43486543872.bj.1327104._.A $C_2^{15}$ $2^{15}$ ✓ ✓ ✓ $C_2^{12}.(C_2^{10}.(C_6:S_3^3.D_4))$ $2^{29} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
86973087744.l.1327104._.A $C_2^{16}$ $2^{16}$ ✓ ✓ ✓ $C_2^{12}.(C_2^8.(C_6^4.D_4:D_4))$ $2^{30} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
139314069504.i.1327104._.A $C_3^8.C_2^4$ $2^{4} \cdot 3^{8}$ ✓ ✓ $C_3^8.C_2^4.C_2^8.C_3^4.D_4:D_4$ $2^{18} \cdot 3^{12}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
705277476864.ia.1327104._.A $C_3^{12}$ $3^{12}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$ ✓
705277476864.ib.1327104._.A $C_3^{12}$ $3^{12}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$ ✓
705277476864.ic.1327104._.A $C_3^{12}$ $3^{12}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$ ✓
705277476864.id.1327104._.A $C_3^{12}$ $3^{12}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$ ✓
705277476864.ie.1327104._.A $C_3^{12}$ $3^{12}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$ ✓
705277476864.if.1327104._.A $C_3^{12}$ $3^{12}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$ ✓
705277476864.ig.1327104._.A $C_3^{12}$ $3^{12}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$ ✓
705277476864.ih.1327104._.A $C_3^{12}$ $3^{12}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$ ✓
1410554953728.ft.1327104._.A $C_3^{12}.C_2$ $2 \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.\OD_{16}.D_4$ $2^{15} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
1410554953728.fu.1327104._.A $C_3^{12}.C_2$ $2 \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
1410554953728.fv.1327104._.A $C_3^{12}.C_2$ $2 \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.\OD_{16}.C_2^3$ $2^{15} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
1410554953728.fw.1327104._.A $C_3^{12}.C_2$ $2 \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2.C_2\wr C_2^2$ $2^{15} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
1410554953728.fx.1327104._.A $C_3^{12}.C_2$ $2 \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2.C_2\wr C_2^2$ $2^{15} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
1410554953728.fy.1327104._.A $C_3^{12}.C_2$ $2 \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2.C_2\wr C_2^2$ $2^{15} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
1410554953728.fz.1327104._.A $C_3^{12}.C_2$ $2 \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.\OD_{16}.C_2^3$ $2^{15} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
1410554953728.ga.1327104._.A $C_3^{12}.C_2$ $2 \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.\OD_{16}.D_4$ $2^{15} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
1410554953728.gb.1327104._.A $C_3^{12}.C_2$ $2 \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_4:C_4.D_4$ $2^{15} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
1410554953728.gc.1327104._.A $C_3^{12}.C_2$ $2 \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2.C_2\wr C_2^2$ $2^{15} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
1410554953728.gd.1327104._.A $C_3^{12}.C_2$ $2 \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2.C_2\wr C_2^2$ $2^{15} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
1410554953728.ge.1327104._.A $C_3^{12}.C_2$ $2 \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2.C_2\wr C_2^2$ $2^{15} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
2821109907456.cx.1327104._.A $C_3^{11}.D_6$ $2^{2} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
2821109907456.cy.1327104._.A $C_3^{11}.D_6$ $2^{2} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
2821109907456.cz.1327104._.A $C_3^{11}.D_6$ $2^{2} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
2821109907456.da.1327104._.A $C_3^{11}.D_6$ $2^{2} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
2821109907456.db.1327104._.A $C_3^{11}.D_6$ $2^{2} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
2821109907456.dc.1327104._.A $C_3^{11}.D_6$ $2^{2} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.C_2^2:D_4.D_4$ $2^{16} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$
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