Subgroups — C₁₁×C₂₉×C₇⋊C₉ #34117136

Order 20097.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₁×C₂₉	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₁×C₂₉	—	7	1	no	maximal, Hall
3	C₇×C₁₁×C₂₉	C₉	1	1	yes	characteristic, complemented, Hall
4	C₂₉×C₇⋊C₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₁×C₂₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
6	C₁₁×C₇⋊C₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₇×C₂₉	C₃×C₁₁	1	1	yes	characteristic
8	C₁₁×C₂₉	C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₉×C₂₉	—	7	1	no	Hall
10	C₃×C₇×C₁₁	C₃×C₂₉	1	1	yes	characteristic
11	C₇×C₂₉	C₉×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₉×C₁₁	—	7	1	no	Hall
13	C₃×C₂₉	C₁₁×ΓL(1,𝔽₈)	1	1	yes	characteristic
14	C₇×C₁₁	C₉×C₂₉	1	1	yes	characteristic, complemented, Hall
15	C₇⋊C₉	C₁₁×C₂₉	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₁	ΓL(1,𝔽₈)×C₂₉	1	1	yes	characteristic
17	C₂₉	C₁₁×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₇	C₃×C₁₁×C₂₉	1	1	yes	characteristic
19	C₁₁	C₂₉×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₉	—	7	1	no	Sylow
21	C₇	C₉×C₁₁×C₂₉	1	1	yes	characteristic, complemented, Sylow
22	C₃	C₁₁×ΓL(1,𝔽₈)×C₂₉	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.