Subgroups — C₇×#611 #92607

Order 504.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×D₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#67	—	3	1	no	maximal
5	C₂×C₇×C₉	—	2	1	no	—
6	C₂×C₇×C₉	C₂²	1	1	yes	characteristic
7	C₇×D₉	—	2	1	no	—
8	C₂²×C₃×C₇	D₃	1	1	yes	characteristic
9	C₂×D₃×C₇	—	3	1	no	—
10	C₇×Dic₃	—	3	1	no	—
11	#611	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₇×C₉	D₄	1	1	yes	characteristic, complemented, Hall
13	C₇×D₄	—	9	1	no	Hall
14	C₂×C₃×C₇	—	2	1	no	—
15	C₂×C₃×C₇	C₂×D₃	1	1	yes	characteristic
16	D₃×C₇	—	6	1	no	—
17	C₂²×C₉	C₂×C₇	1	1	yes	characteristic, complemented
18	C₂×D₉	C₂×C₇	1	1	yes	characteristic, complemented
19	Dic₉	C₂×C₇	1	1	yes	characteristic, complemented
20	C₂²×C₇	—	9	1	no	—
21	C₂²×C₇	D₉	1	1	yes	characteristic, complemented
22	C₄×C₇	—	9	1	no	—
23	#67	—	3	1	no	—
24	C₃×C₇	#67	1	1	yes	characteristic
25	C₂×C₉	—	2	1	no	—
26	C₂×C₉	C₂²×C₇	1	1	yes	characteristic
27	D₉	—	2	1	no	—
28	C₂×C₇	—	2	1	no	—
29	C₂×C₇	—	18	1	no	—
30	C₂×C₇	C₂×D₉	1	1	yes	characteristic
31	C₂²×C₃	D₃×C₇	1	1	yes	characteristic
32	C₂×D₃	—	3	1	no	—
33	Dic₃	—	3	1	no	—
34	C₉	C₇×D₄	1	1	yes	characteristic, complemented, Sylow
35	D₄	—	9	1	no	Sylow
36	C₇	#611	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₃	—	2	1	no	—
38	C₂×C₃	C₂×D₃×C₇	1	1	yes	characteristic
39	D₃	—	6	1	no	—
40	C₂²	—	9	1	no	—
41	C₂²	C₇×D₉	1	1	yes	characteristic, complemented
42	C₄	—	9	1	no	—
43	C₃	C₇×#67	1	1	yes	characteristic
44	C₂	—	2	1	no	—
45	C₂	—	18	1	no	—
46	C₂	C₂×C₇×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₇	C₂×D₉
commutator, cosocle	C₂×C₉	C₂²×C₇
Frattini	C₂×C₃	C₂×D₃×C₇
Fitting	C₂²×C₇×C₉	C₂
socle	C₂×C₃×C₇	C₂×D₃
hypercenter	C₂²×C₇	D₉
hypocenter	C₉	C₇×D₄
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₇ ◁ C₂²×C₇

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇×C₉	C₂	semidirect
2. C₂×C₇×D₉	C₂	semidirect
3. C₇×Dic₉	C₂	semidirect
11. #611	C₇	direct (N × H)
12. C₇×C₉	D₄	semidirect
17. C₂²×C₉	C₂×C₇	semidirect
18. C₂×D₉	C₂×C₇	semidirect
19. Dic₉	C₂×C₇	semidirect
21. C₂²×C₇	D₉	semidirect
34. C₉	C₇×D₄	semidirect
36. C₇	#611	direct (N × H)
41. C₂²	C₇×D₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₇×C₉	2
C₂×C₇×D₉	2
C₇×Dic₉	2
C₇×#67	3
#611	7

Subgroups — C7×#611 #92607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#611 #92607