Subgroups — (C₇⋊C₉)⋊#92150 #44478927

Order 30492.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊C₉×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇⋊#92150	C₃	1	1	yes	maximal, characteristic
3	C₁₁²×C₇⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×C₁₁⋊D₁₁	C₂×C₃	1	1	yes	characteristic
5	C₉×#92150	—	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	C₉×C₁₁⋊D₁₁	—	7	1	no	—
9	C₇×C₁₁⋊D₁₁	C₂×C₉	1	1	yes	characteristic
10	C₃×#92150	—	21	1	no	—
11	D₁₁×C₇⋊C₉	—	22	6	no	—
12	C₉×C₁₁²	—	7	1	no	Hall
13	C₇×C₁₁²	C₄×C₉	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₁⋊D₁₁	AGL(1,𝔽₇)	1	1	yes	characteristic
15	C₁₁×C₇⋊C₉	—	2	6	no	—
16	#92150	—	21	1	no	Hall
17	C₃×C₇×D₁₁	—	22	6	no	—
18	C₃×C₁₁²	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
19	Dic₇⋊C₉	—	121	1	no	maximal, Hall
20	C₁₁⋊D₁₁	D₇⋊C₉	1	1	yes	characteristic
21	C₃×C₇×C₁₁	—	2	6	no	—
22	C₉×D₁₁	—	154	6	no	—
23	C₇×D₁₁	—	22	6	no	—
24	C₂×C₇⋊C₉	—	121	1	no	—
25	C₁₁²	Dic₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
26	C₉×C₁₁	—	14	6	no	—
27	C₃×Dic₇	—	121	1	no	—
28	C₇×C₁₁	—	2	6	no	—
29	C₃×D₁₁	—	22	6	no	—
30	C₇⋊C₉	#92150	1	1	yes	characteristic, complemented, Hall
31	C₂×C₃×C₇	—	121	1	no	—
32	C₄×C₉	—	847	1	no	Hall
33	C₃×C₁₁	—	2	6	no	—
34	Dic₇	—	121	1	no	Hall
35	D₁₁	—	22	6	no	—
36	C₃×C₇	C₃×#92150	1	1	yes	characteristic
37	C₂×C₉	—	847	1	no	—
38	C₂×C₇	—	121	1	no	—
39	C₃×C₄	—	2541	1	no	—
40	C₁₁	—	2	6	no	—
41	C₉	—	7	1	no	Sylow
42	C₇	C₉×#92150	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	121	1	no	—
44	C₄	—	2541	1	no	Sylow
45	C₃	ΓL(1,𝔽₈)⋊#92150	1	1	yes	characteristic
46	C₂	—	121	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	ΓL(1,𝔽₈)⋊#92150
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. C₁₁²×C₇⋊C₉	C₄	semidirect
6. C₇⋊#92150	C₉	semidirect
13. C₇×C₁₁²	C₄×C₉	semidirect
25. C₁₁²	Dic₇⋊C₉	semidirect
30. C₇⋊C₉	#92150	semidirect
42. C₇	C₉×#92150	semidirect

Maximal subgroups

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

subgroup	index
C₇⋊C₉×C₁₁⋊D₁₁	2
C₃×C₇⋊#92150	3
C₉×#92150	7
Dic₇⋊C₉	121

Subgroups — (C7⋊C9)⋊#92150 #44478927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₇⋊C₉)⋊#92150 #44478927