Subgroups — C₇⋊C₉×C₇⋊#595 #44472549

Order 29988.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₇×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×C₇⋊#595	C₃	1	1	yes	maximal, characteristic
3	C₇×C₁₇×C₇⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇²×D₁₇	C₂×C₃	1	1	yes	characteristic
5	C₉×C₇⋊#595	—	7	1	no	maximal
6	C₇⋊C₉×#595	—	7	1	no	maximal
7	C₇×C₇⋊#595	C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇²×C₁₇	C₃×C₄	1	1	yes	characteristic
9	C₇×C₉×D₁₇	—	7	1	no	—
10	D₁₇×C₇⋊C₉	D₇	1	1	yes	characteristic
11	Dic₇×C₇⋊C₉	—	17	1	no	maximal, Hall
12	C₇²×D₁₇	C₂×C₉	1	1	yes	characteristic
13	C₃×C₇⋊#595	ΓL(1,𝔽₈)	1	1	yes	characteristic
14	C₃×C₇×#595	—	7	1	no	—
15	C₇×C₉×C₁₇	—	7	1	no	—
16	C₁₇×C₇⋊C₉	Dic₇	1	1	yes	characteristic, complemented
17	C₂×C₇×C₇⋊C₉	—	17	1	no	—
18	C₇²×C₁₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
19	C₃×C₇×D₁₇	—	6	1	no	—
20	C₃×C₇×D₁₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
21	C₃×C₇×D₁₇	C₃×D₇	1	1	yes	characteristic
22	C₉×#595	—	49	1	no	Hall
23	C₃×C₇×Dic₇	—	17	1	no	—
24	C₇⋊#595	C₇⋊C₉	1	1	yes	characteristic, direct product factor
25	C₇×#595	—	7	1	no	—
26	C₇×C₇⋊C₉	#595	1	1	yes	characteristic, complemented, Hall
27	C₃×C₇×C₁₇	—	6	1	no	—
28	C₃×C₇×C₁₇	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
29	C₃×C₇×C₁₇	C₃×Dic₇	1	1	yes	characteristic
30	C₉×D₁₇	—	7	1	no	—
31	C₂×C₃×C₇²	—	17	1	no	—
32	C₉×Dic₇	—	119	1	no	—
33	C₄×C₇⋊C₉	—	119	1	no	—
34	C₇×D₁₇	—	6	1	no	—
35	C₇×D₁₇	C₂×C₇⋊C₉	1	1	yes	characteristic
36	C₇×D₁₇	C₉×D₇	1	1	yes	characteristic
37	C₃×#595	—	7	1	no	—
38	C₇×Dic₇	—	17	1	no	Hall
39	C₉×C₁₇	—	7	1	no	Hall
40	C₃×C₇²	C₃×#595	1	1	yes	characteristic
41	C₂×C₇×C₉	—	119	1	no	—
42	C₂×C₇⋊C₉	—	17	1	no	—
43	C₇×C₁₇	—	6	1	no	—
44	C₇×C₁₇	C₄×C₇⋊C₉	1	1	yes	characteristic, complemented
45	C₇×C₁₇	C₉×Dic₇	1	1	yes	characteristic, complemented
46	C₃×D₁₇	D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
47	C₂×C₇²	—	17	1	no	—
48	C₃×C₄×C₇	—	119	1	no	—
49	C₃×Dic₇	—	17	1	no	—
50	#595	—	7	1	no	Hall
51	C₇×C₉	—	7	1	no	—
52	C₇⋊C₉	C₇⋊#595	1	1	yes	characteristic, direct product factor
53	C₃×C₁₇	ΓL(1,𝔽₈)×Dic₇	1	1	yes	characteristic
54	C₇²	C₉×#595	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₃×C₇	—	17	1	no	—
56	C₂×C₃×C₇	—	17	1	no	—
57	C₂×C₃×C₇	—	102	1	no	—
58	C₄×C₉	—	833	1	no	Hall
59	D₁₇	D₇×C₇⋊C₉	1	1	yes	characteristic
60	C₄×C₇	—	119	1	no	—
61	Dic₇	—	17	1	no	—
62	C₃×C₇	—	6	1	no	—
63	C₃×C₇	ΓL(1,𝔽₈)×#595	1	1	yes	characteristic
64	C₃×C₇	C₃×C₇⋊#595	1	1	yes	characteristic
65	C₂×C₉	—	119	1	no	—
66	C₁₇	Dic₇×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₇	—	17	1	no	—
68	C₂×C₇	—	17	1	no	—
69	C₂×C₇	—	102	1	no	—
70	C₃×C₄	—	119	1	no	—
71	C₉	—	7	1	no	Sylow
72	C₇	—	6	1	no	—
73	C₇	C₇⋊C₉×#595	1	1	yes	characteristic, complemented
74	C₇	C₉×C₇⋊#595	1	1	yes	characteristic, complemented
75	C₂×C₃	—	17	1	no	—
76	C₄	—	119	1	no	Sylow
77	C₃	ΓL(1,𝔽₈)×C₇⋊#595	1	1	yes	characteristic
78	C₂	—	17	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	ΓL(1,𝔽₈)×C₇⋊#595
commutator, hypocenter	C₇²×C₁₇	C₄×C₉
Fitting, socle	C₃×C₇²×C₁₇	C₃×C₄
prime radical, cosocle	C₃×C₇²×D₁₇	C₂×C₃
LCS	G ▷ C₇²×C₁₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
3. C₇×C₁₇×C₇⋊C₉	C₄	semidirect
7. C₇×C₇⋊#595	C₉	semidirect
16. C₁₇×C₇⋊C₉	Dic₇	semidirect
18. C₇²×C₁₇	C₄×C₉	semidirect
24. C₇⋊#595	C₇⋊C₉	direct (N × H)
26. C₇×C₇⋊C₉	#595	semidirect
44. C₇×C₁₇	C₄×C₇⋊C₉	semidirect
45. C₇×C₁₇	C₉×Dic₇	semidirect
52. C₇⋊C₉	C₇⋊#595	direct (N × H)
54. C₇²	C₉×#595	semidirect
66. C₁₇	Dic₇×C₇⋊C₉	semidirect
73. C₇	C₇⋊C₉×#595	semidirect
74. C₇	C₉×C₇⋊#595	semidirect

Maximal subgroups

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

subgroup	index
C₇×D₁₇×C₇⋊C₉	2
C₃×C₇×C₇⋊#595	3
C₉×C₇⋊#595	7
C₇⋊C₉×#595	7
Dic₇×C₇⋊C₉	17

Subgroups — C7⋊C9×C7⋊#595 #44472549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇⋊C₉×C₇⋊#595 #44472549