Subgroups — #92150⋊(C₇⋊C₉) #44478929

Order 30492.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₁₁⋊D₁₁)⋊(C₇⋊C₉)	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×#92150	C₃	1	1	yes	maximal, characteristic
3	C₇⋊(C₁₁²⋊C₉)	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×C₁₁⋊D₁₁	C₂×C₃	1	1	yes	characteristic
5	#92150⋊C₉	—	7	1	no	maximal, Hall
6	C₇×#92150	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇×C₁₁²	C₃×C₄	1	1	yes	characteristic
8	(C₁₁⋊D₁₁)⋊C₉	—	7	1	no	—
9	C₇×C₁₁⋊D₁₁	C₂×C₉	1	1	yes	characteristic
10	C₃×#92150	ΓL(1,𝔽₈)	1	1	yes	characteristic
11	C₁₁²⋊C₉	—	7	1	no	Hall
12	C₇×C₁₁²	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₁⋊D₁₁	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
14	#92150	C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
15	C₃×C₇×D₁₁	—	66	2	no	—
16	C₃×C₁₁²	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
17	C₄×C₇⋊C₉	—	121	1	no	maximal, Hall
18	C₁₁⋊D₁₁	C₂×C₇⋊C₉	1	1	yes	characteristic
19	C₃×C₇×C₁₁	—	6	2	no	—
20	C₇×D₁₁	—	66	2	no	—
21	C₂×C₇⋊C₉	—	121	1	no	—
22	C₁₁²	C₄×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
23	C₃×C₄×C₇	—	363	1	no	—
24	C₇×C₁₁	—	6	2	no	—
25	C₃×D₁₁	—	66	2	no	—
26	C₇⋊C₉	—	121	1	no	Hall
27	C₂×C₃×C₇	—	363	1	no	—
28	C₄×C₉	—	847	1	no	Hall
29	C₃×C₁₁	—	6	2	no	—
30	C₄×C₇	—	363	1	no	Hall
31	D₁₁	—	66	2	no	—
32	C₃×C₇	#92150⋊C₃	1	1	yes	characteristic
33	C₂×C₉	—	847	1	no	—
34	C₂×C₇	—	363	1	no	—
35	C₃×C₄	—	363	1	no	—
36	C₁₁	—	6	2	no	—
37	C₉	—	847	1	no	Sylow
38	C₇	#92150⋊C₉	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₃	—	363	1	no	—
40	C₄	—	363	1	no	Sylow
41	C₃	#92150⋊ΓL(1,𝔽₈)	1	1	yes	characteristic
42	C₂	—	363	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	#92150⋊ΓL(1,𝔽₈)
commutator, hypocenter	C₇×C₁₁²	C₄×C₉
Fitting, socle	C₃×C₇×C₁₁²	C₃×C₄
prime radical, cosocle	C₃×C₇×C₁₁⋊D₁₁	C₂×C₃
LCS	G ▷ C₇×C₁₁²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
3. C₇⋊(C₁₁²⋊C₉)	C₄	semidirect
6. C₇×#92150	C₉	semidirect
12. C₇×C₁₁²	C₄×C₉	semidirect
14. #92150	C₇⋊C₉	semidirect
22. C₁₁²	C₄×C₇⋊C₉	semidirect
38. C₇	#92150⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
(C₁₁⋊D₁₁)⋊(C₇⋊C₉)	2
C₃×C₇×#92150	3
#92150⋊C₉	7
C₄×C₇⋊C₉	121

Subgroups — #92150⋊(C7⋊C9) #44478929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #92150⋊(C₇⋊C₉) #44478929