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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 100 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1296.3376.1296.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
5184.ci.1296.a1 $C_2^2$ $2^{2}$ ✓ ✓ $C_6\wr C_2^2$ $2^{6} \cdot 3^{4}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
11664.by.1296.e1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^5:(C_6\times D_4)$ $2^{4} \cdot 3^{6}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$ ✓
11664.fk.1296.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $(C_3^2\times C_6^2):S_3^2$ $2^{4} \cdot 3^{6}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
11664.fo.1296.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_{18}^2:(C_6\times S_3)$ $2^{4} \cdot 3^{6}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
20736.dv.1296.A $C_2^4$ $2^{4}$ ✓ ✓ ✓ $C_6^2:\POPlus(4,3)$ $2^{8} \cdot 3^{4}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$ ✓
20736.dw.1296.A $C_2^4$ $2^{4}$ ✓ ✓ ✓ $(C_2^2\times A_4^2):S_3^2$ $2^{8} \cdot 3^{4}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$ ✓
63504.c.1296.a1 $C_7^2$ $7^{2}$ $7$ ✓ ✓ ✓ $F_7^2:S_3^2$ $2^{4} \cdot 3^{4} \cdot 7^{2}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$ ✓
104976.u.1296.F $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^8:(C_2\times D_4)$ $2^{4} \cdot 3^{8}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
104976.cy.1296.A $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^4.C_6^2:S_3^2$ $2^{4} \cdot 3^{8}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
104976.db.1296.A $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^6.D_6:D_6$ $2^{4} \cdot 3^{8}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
104976.lk.1296.A $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^4:S_3^3.C_6$ $2^{4} \cdot 3^{8}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
104976.ll.1296.E $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^4.S_3^3:C_6$ $2^{4} \cdot 3^{8}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
104976.ms.1296.E $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^4.S_3^3:C_6$ $2^{4} \cdot 3^{8}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
104976.my.1296.E $C_9^2$ $3^{4}$ ✓ ✓ ✓ $D_9^2:C_3\wr C_2^2$ $2^{4} \cdot 3^{8}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
104976.nu.1296.A $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^6.D_6:D_6$ $2^{4} \cdot 3^{8}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
186624.u.1296.A $C_2^2\times C_6^2$ $2^{4} \cdot 3^{2}$ ✓ ✓ ✓ $C_6^4.C_6^2:C_2^2$ $2^{8} \cdot 3^{6}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
186624.y.1296.A $C_2^2\times C_6^2$ $2^{4} \cdot 3^{2}$ ✓ ✓ ✓ $C_3^4.C_2\wr S_3^2$ $2^{8} \cdot 3^{6}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
186624.z.1296.A $C_2^2\times C_6^2$ $2^{4} \cdot 3^{2}$ ✓ ✓ ✓ $C_3^4.C_2\wr S_3^2$ $2^{8} \cdot 3^{6}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
331776.n.1296.A $C_2^8$ $2^{8}$ ✓ ✓ ✓ $A_4^2\wr C_2.D_4$ $2^{12} \cdot 3^{4}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$ ✓
331776.cs.1296.A $C_2^8$ $2^{8}$ ✓ ✓ ✓ $A_4^2.C_2\wr S_3^2$ $2^{12} \cdot 3^{4}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
419904.ba.1296.A $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ ✓ $C_3^8:C_2\wr C_2^2$ $2^{6} \cdot 3^{8}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
944784.jz.1296.A $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^6.C_6^2:S_3^2$ $2^{4} \cdot 3^{10}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
944784.ka.1296.D $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^6.C_6^2:S_3^2$ $2^{4} \cdot 3^{10}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
944784.kc.1296.B $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^6.C_6^2:S_3^2$ $2^{4} \cdot 3^{10}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
944784.kv.1296.E $\He_3^2$ $3^{6}$ ✓ ✓ $C_3^6.S_3^3:C_6$ $2^{4} \cdot 3^{10}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
944784.kw.1296.E $\He_3^2$ $3^{6}$ ✓ ✓ $C_3^6.S_3^3:C_6$ $2^{4} \cdot 3^{10}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
944784.lg.1296.E $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^6.S_3^3:C_6$ $2^{4} \cdot 3^{10}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
944784.lh.1296.E $C_3^2\times C_9^2$ $3^{6}$ ✓ ✓ ✓ $C_3^6.S_3^3:C_6$ $2^{4} \cdot 3^{10}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
944784.no.1296.D $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^8.D_6:D_6$ $2^{4} \cdot 3^{10}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
944784.nq.1296.A $C_3^6$ $3^{6}$ ✓ ✓ ✓ $S_3^2.C_3\wr S_3^2$ $2^{4} \cdot 3^{10}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
944784.oa.1296.C $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^8.D_6:D_6$ $2^{4} \cdot 3^{10}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
944784.ob.1296.C $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^8.D_6:D_6$ $2^{4} \cdot 3^{10}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
944784.rz.1296.E $C_3^2\times C_9^2$ $3^{6}$ ✓ ✓ ✓ $C_9^4.C_6^2:C_2^2$ $2^{4} \cdot 3^{10}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
944784.se.1296.E $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^6.C_6^2:S_3^2$ $2^{4} \cdot 3^{10}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
1327104.g.1296.A $C_2^{10}$ $2^{10}$ ✓ ✓ $C_2^8.C_6\wr C_2^2$ $2^{14} \cdot 3^{4}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
1679616.hm.1296._.A $C_6^4$ $2^{4} \cdot 3^{4}$ ✓ ✓ ✓ $C_6^4.C_6^2:S_3^2$ $2^{8} \cdot 3^{8}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
1679616.hp.1296._.A $C_6^4$ $2^{4} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^6.C_3\wr S_3^2$ $2^{8} \cdot 3^{8}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
3111696.c.1296.a1.a1 $C_7^4$ $7^{4}$ $7$ ✓ ✓ ✓ $C_7^4:(C_6^2:S_3^2)$ $2^{4} \cdot 3^{4} \cdot 7^{4}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$ ✓
5308416.el.1296.A $C_2^{12}$ $2^{12}$ ✓ ✓ ✓ $C_2^{12}.C_6^2:S_3^2$ $2^{16} \cdot 3^{4}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
5308416.em.1296.A $C_2^{12}$ $2^{12}$ ✓ ✓ ✓ $C_2^{10}.A_4^2:S_3^2$ $2^{16} \cdot 3^{4}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
8503056.fj.1296._.A $C_3^8$ $3^{8}$ ✓ ✓ ✓ $C_3^8.C_6^2:S_3^2$ $2^{4} \cdot 3^{12}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
8503056.fk.1296._.C $C_3^8$ $3^{8}$ ✓ ✓ ✓ $C_3^8.C_6^2:S_3^2$ $2^{4} \cdot 3^{12}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
8503056.go.1296._.G $C_3^2\times C_3^4.C_3^2$ $3^{8}$ ✓ ✓ $C_3^8.S_3^3:C_6$ $2^{4} \cdot 3^{12}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
8503056.gr.1296._.D $C_3^2\times C_3^4.C_3^2$ $3^{8}$ ✓ ✓ $C_3^8.S_3^3:C_6$ $2^{4} \cdot 3^{12}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
8503056.gs.1296._.A $C_3^6.C_3^2$ $3^{8}$ ✓ ✓ $C_3^8.S_3^3:C_6$ $2^{4} \cdot 3^{12}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
8503056.hs.1296._.F $C_3^8$ $3^{8}$ ✓ ✓ ✓ $C_3^8.C_6^2:S_3^2$ $2^{4} \cdot 3^{12}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
8503056.hv.1296._.A $C_3^8$ $3^{8}$ ✓ ✓ ✓ $C_3^8.C_6^2:S_3^2$ $2^{4} \cdot 3^{12}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
8503056.hx.1296._.E $C_3^8$ $3^{8}$ ✓ ✓ ✓ $C_3^8.C_6^2:S_3^2$ $2^{4} \cdot 3^{12}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
8503056.jq.1296._.C $C_3^8$ $3^{8}$ ✓ ✓ ✓ $C_3^8.C_6^2:S_3^2$ $2^{4} \cdot 3^{12}$ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$
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