Subgroups — C₃⋊(#92150⋊ΓL(1,𝔽₈)) #44479114

Order 30492.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×(C₁₁⋊D₁₁)⋊ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic
2	C₇×C₃⋊#92150	C₃	1	1	yes	maximal, characteristic, complemented
3	#92150⋊ΓL(1,𝔽₈)	—	3	1	no	maximal
4	C₃×C₇⋊(C₁₁²⋊C₃)	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×C₁₁⋊D₁₁	C₂×C₃	1	1	yes	characteristic
6	(C₁₁⋊D₁₁)⋊ΓL(1,𝔽₈)	—	2	1	no	—
7	(C₁₁⋊D₁₁)⋊ΓL(1,𝔽₈)	D₃	1	1	yes	characteristic
8	C₃⋊(#92150⋊C₃)	—	7	1	no	maximal, Hall
9	C₇×#92150	—	3	1	no	Hall
10	C₇⋊(C₁₁²⋊C₃)	—	2	1	no	—
11	C₇⋊(C₁₁²⋊C₃)	Dic₃	1	1	yes	characteristic, complemented
12	C₃×C₇×C₁₁²	C₃×C₄	1	1	yes	characteristic, complemented
13	C₃×(C₁₁⋊D₁₁)⋊C₃	—	7	1	no	—
14	C₇×C₁₁⋊D₁₁	C₃×D₃	1	1	yes	characteristic
15	C₃⋊#92150	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
16	#92150⋊C₃	—	21	1	no	—
17	C₃×C₁₁²⋊C₃	—	7	1	no	Hall
18	C₇×C₁₁²	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
19	C₃×C₁₁⋊D₁₁	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
20	(C₁₁⋊D₁₁)⋊C₃	—	7	1	no	—
21	(C₁₁⋊D₁₁)⋊C₃	—	14	1	no	—
22	#92150	—	3	1	no	Hall
23	C₃×C₇×D₁₁	—	66	2	no	—
24	C₃×C₁₁²	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
25	C₁₁²⋊C₃	—	7	1	no	—
26	C₁₁²⋊C₃	—	14	1	no	—
27	Dic₃×ΓL(1,𝔽₈)	—	121	1	no	maximal, Hall
28	C₁₁⋊D₁₁	D₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
29	C₃×C₇×C₁₁	—	6	2	no	—
30	C₇×D₁₁	—	66	2	no	—
31	C₂×C₃×ΓL(1,𝔽₈)	—	121	1	no	—
32	C₁₁²	Dic₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
33	C₇×Dic₃	—	121	1	no	—
34	C₄×ΓL(1,𝔽₈)	—	363	1	no	—
35	C₇×C₁₁	—	6	2	no	—
36	C₃×D₁₁	—	66	2	no	—
37	C₃×ΓL(1,𝔽₈)	—	484	1	no	Hall
38	C₂×C₃×C₇	—	121	1	no	—
39	C₂×ΓL(1,𝔽₈)	—	121	1	no	—
40	C₂×ΓL(1,𝔽₈)	—	242	1	no	—
41	C₃×Dic₃	—	847	1	no	Hall
42	C₃×C₁₁	—	6	2	no	—
43	C₄×C₇	—	363	1	no	Hall
44	D₁₁	—	66	2	no	—
45	C₃×C₇	#92150⋊C₃	1	1	yes	characteristic, complemented
46	ΓL(1,𝔽₈)	—	484	1	no	—
47	ΓL(1,𝔽₈)	—	484	1	no	—
48	C₂×C₃²	—	847	1	no	—
49	C₂×C₇	—	121	1	no	—
50	C₃×C₄	—	2541	1	no	—
51	Dic₃	—	121	1	no	—
52	C₁₁	—	6	2	no	—
53	C₃²	—	3388	1	no	Sylow
54	C₇	C₃⋊(#92150⋊C₃)	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₃	—	847	1	no	—
56	C₂×C₃	—	121	1	no	—
57	C₂×C₃	—	1694	1	no	—
58	C₄	—	363	1	no	Sylow
59	C₃	—	3388	1	no	—
60	C₃	—	3388	1	no	—
61	C₃	#92150⋊ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
62	C₂	—	121	1	no	—

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

Complements

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

N	H ≅ G/N	type
2. C₇×C₃⋊#92150	C₃	semidirect
4. C₃×C₇⋊(C₁₁²⋊C₃)	C₄	semidirect
11. C₇⋊(C₁₁²⋊C₃)	Dic₃	semidirect
12. C₃×C₇×C₁₁²	C₃×C₄	semidirect
15. C₃⋊#92150	ΓL(1,𝔽₈)	semidirect
18. C₇×C₁₁²	C₃×Dic₃	semidirect
24. C₃×C₁₁²	C₄×ΓL(1,𝔽₈)	semidirect
32. C₁₁²	Dic₃×ΓL(1,𝔽₈)	semidirect
45. C₃×C₇	#92150⋊C₃	semidirect
54. C₇	C₃⋊(#92150⋊C₃)	semidirect
61. C₃	#92150⋊ΓL(1,𝔽₈)	semidirect

Maximal subgroups

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

subgroup	index
C₃×(C₁₁⋊D₁₁)⋊ΓL(1,𝔽₈)	2
C₇×C₃⋊#92150	3
#92150⋊ΓL(1,𝔽₈)	3
C₃⋊(#92150⋊C₃)	7
Dic₃×ΓL(1,𝔽₈)	121

Subgroups — C3⋊(#92150⋊ΓL(1,𝔽8)) #44479114

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(#92150⋊ΓL(1,𝔽₈)) #44479114