Subgroups — ΓL(1,𝔽₈)×C₇⋊#595 #23756198

Order 9996.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×ΓL(1,𝔽₈)×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₇×C₇⋊#595	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₇×ΓL(1,𝔽₈)	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇²×D₁₇	C₂×C₃	1	1	yes	characteristic
5	C₃×C₇⋊#595	—	7	1	no	maximal
6	ΓL(1,𝔽₈)×#595	—	7	1	no	maximal
7	C₇²×C₁₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇×D₁₇	—	7	1	no	—
9	ΓL(1,𝔽₈)×D₁₇	D₇	1	1	yes	characteristic
10	ΓL(1,𝔽₈)×Dic₇	—	17	1	no	maximal, Hall
11	C₇⋊#595	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
12	C₇×#595	—	7	1	no	—
13	C₃×C₇×C₁₇	—	7	1	no	—
14	C₁₇×ΓL(1,𝔽₈)	Dic₇	1	1	yes	characteristic, complemented
15	C₂×C₇×ΓL(1,𝔽₈)	—	17	1	no	—
16	C₇×D₁₇	—	6	1	no	—
17	C₇×D₁₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
18	C₇×D₁₇	C₃×D₇	1	1	yes	characteristic
19	C₃×#595	—	49	1	no	Hall
20	C₇×Dic₇	—	17	1	no	Hall
21	C₇×ΓL(1,𝔽₈)	#595	1	1	yes	characteristic, complemented, Hall
22	C₇×C₁₇	—	6	1	no	—
23	C₇×C₁₇	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
24	C₇×C₁₇	C₃×Dic₇	1	1	yes	characteristic, complemented
25	C₃×D₁₇	—	7	1	no	—
26	C₂×C₇²	—	17	1	no	—
27	C₃×Dic₇	—	119	1	no	—
28	C₄×ΓL(1,𝔽₈)	—	119	1	no	—
29	#595	—	7	1	no	Hall
30	C₃×C₁₇	—	7	1	no	Hall
31	C₇²	C₃×#595	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃×C₇	—	119	1	no	—
33	C₂×ΓL(1,𝔽₈)	—	17	1	no	—
34	D₁₇	D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
35	C₄×C₇	—	119	1	no	—
36	Dic₇	—	17	1	no	—
37	C₃×C₇	—	7	1	no	—
38	ΓL(1,𝔽₈)	C₇⋊#595	1	1	yes	characteristic, direct product factor
39	C₁₇	ΓL(1,𝔽₈)×Dic₇	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₇	—	17	1	no	—
41	C₂×C₇	—	17	1	no	—
42	C₂×C₇	—	102	1	no	—
43	C₃×C₄	—	833	1	no	Hall
44	C₇	—	6	1	no	—
45	C₇	ΓL(1,𝔽₈)×#595	1	1	yes	characteristic, complemented
46	C₇	C₃×C₇⋊#595	1	1	yes	characteristic, complemented
47	C₂×C₃	—	119	1	no	—
48	C₄	—	119	1	no	Sylow
49	C₃	—	7	1	no	Sylow
50	C₂	—	17	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₁₇	C₃×C₄
prime radical	C₇×ΓL(1,𝔽₈)×D₁₇	C₂
cosocle	C₇²×D₁₇	C₂×C₃
LCS	G ▷ C₇²×C₁₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₇×C₇⋊#595	C₃	semidirect
3. C₇×C₁₇×ΓL(1,𝔽₈)	C₄	semidirect
7. C₇²×C₁₇	C₃×C₄	semidirect
11. C₇⋊#595	ΓL(1,𝔽₈)	direct (N × H)
14. C₁₇×ΓL(1,𝔽₈)	Dic₇	semidirect
21. C₇×ΓL(1,𝔽₈)	#595	semidirect
23. C₇×C₁₇	C₄×ΓL(1,𝔽₈)	semidirect
24. C₇×C₁₇	C₃×Dic₇	semidirect
31. C₇²	C₃×#595	semidirect
38. ΓL(1,𝔽₈)	C₇⋊#595	direct (N × H)
39. C₁₇	ΓL(1,𝔽₈)×Dic₇	semidirect
45. C₇	ΓL(1,𝔽₈)×#595	semidirect
46. C₇	C₃×C₇⋊#595	semidirect

Subgroups — ΓL(1,𝔽8)×C7⋊#595 #23756198

Conjugacy classes of subgroups

Complements

Subgroups — ΓL(1,𝔽₈)×C₇⋊#595 #23756198