Subgroups — C₇⋊#17984456 #44525908

Order 30940.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₁₀₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×C₁₃×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇⋊#11725130	—	5	1	no	maximal, Hall
4	#17984456	—	7	1	no	maximal, Hall
5	C₇×D₂₂₁	—	5	1	no	—
6	C₇⋊#66775	—	13	1	no	maximal, Hall
7	D₁₁₀₅	D₇	1	1	yes	characteristic
8	C₇⋊#63122	—	17	1	no	maximal, Hall
9	C₇×C₁₃×C₁₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
10	C₇×D₈₅	—	13	1	no	—
11	C₅×C₁₃×C₁₇	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₇×D₆₅	—	17	1	no	—
13	#11725130	—	35	1	no	Hall
14	C₅×C₇×C₁₇	#261	1	1	yes	characteristic, complemented, Hall
15	C₇⋊#595	—	65	1	no	Hall
16	C₅×C₇×C₁₃	#595	1	1	yes	characteristic, complemented, Hall
17	D₂₂₁	—	5	1	no	—
18	C₇⋊#261	—	85	1	no	Hall
19	#66775	—	91	1	no	Hall
20	#63122	—	119	1	no	Hall
21	C₇×D₁₇	—	65	1	no	—
22	C₁₃×C₁₇	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
23	C₇×D₁₃	—	85	1	no	—
24	D₈₅	—	13	1	no	—
25	C₇⋊AGL(1,𝔽₅)	—	221	1	no	Hall
26	D₆₅	—	17	1	no	—
27	C₇×C₁₇	#63122	1	1	yes	characteristic, complemented, Hall
28	C₇×C₁₃	#66775	1	1	yes	characteristic, complemented, Hall
29	C₅×C₁₇	C₇⋊#261	1	1	yes	characteristic, complemented, Hall
30	C₇×D₅	—	221	1	no	—
31	#595	—	455	1	no	Hall
32	C₅×C₁₃	C₇⋊#595	1	1	yes	characteristic, complemented, Hall
33	#261	—	595	1	no	Hall
34	C₅×C₇	#11725130	1	1	yes	characteristic, complemented, Hall
35	D₁₇	—	65	1	no	—
36	Dic₇	—	1105	1	no	Hall
37	D₁₃	—	85	1	no	—
38	AGL(1,𝔽₅)	—	1547	1	no	Hall
39	C₁₇	C₇⋊#63122	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₇	—	1105	1	no	—
41	C₁₃	C₇⋊#66775	1	1	yes	characteristic, complemented, Sylow
42	D₅	—	221	1	no	—
43	C₇	#17984456	1	1	yes	characteristic, complemented, Sylow
44	C₅	C₇⋊#11725130	1	1	yes	characteristic, complemented, Sylow
45	C₄	—	7735	1	no	Sylow
46	C₂	—	1105	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₇×C₁₃×C₁₇	C₄
prime radical, cosocle	C₇×D₁₁₀₅	C₂
LCS	G ▷ C₅×C₇×C₁₃×C₁₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₅×C₇×C₁₃×C₁₇	C₄	semidirect
9. C₇×C₁₃×C₁₇	AGL(1,𝔽₅)	semidirect
11. C₅×C₁₃×C₁₇	Dic₇	semidirect
14. C₅×C₇×C₁₇	#261	semidirect
16. C₅×C₇×C₁₃	#595	semidirect
22. C₁₃×C₁₇	C₇⋊AGL(1,𝔽₅)	semidirect
27. C₇×C₁₇	#63122	semidirect
28. C₇×C₁₃	#66775	semidirect
29. C₅×C₁₇	C₇⋊#261	semidirect
32. C₅×C₁₃	C₇⋊#595	semidirect
34. C₅×C₇	#11725130	semidirect
39. C₁₇	C₇⋊#63122	semidirect
41. C₁₃	C₇⋊#66775	semidirect
43. C₇	#17984456	semidirect
44. C₅	C₇⋊#11725130	semidirect

Maximal subgroups

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

subgroup	index
C₇×D₁₁₀₅	2
C₇⋊#11725130	5
#17984456	7
C₇⋊#66775	13
C₇⋊#63122	17

Subgroups — C7⋊#17984456 #44525908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇⋊#17984456 #44525908