Subgroups — C₇×#19103988 #49089856

Order 35868.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×D₆₁⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₇×C₇⋊#6923	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₆₁⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇²×D₆₁	C₂×C₃	1	1	yes	characteristic
5	#19103988	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₇×#6923⋊C₃	—	7	1	no	maximal
7	C₇²×C₆₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₇×D₆₁⋊C₃	—	2	3	no	—
9	C₇×D₆₁⋊C₃	D₇	1	1	yes	characteristic
10	C₇×D₆₁⋊C₃	C₂×C₇	1	1	yes	characteristic
11	C₇⋊#6923	C₃×C₇	1	1	yes	characteristic, complemented
12	C₇×#6923	—	7	1	no	—
13	C₇×C₆₁⋊C₃	—	2	3	no	—
14	C₇×C₆₁⋊C₃	Dic₇	1	1	yes	characteristic, complemented
15	C₇×C₆₁⋊C₃	C₄×C₇	1	1	yes	characteristic, complemented
16	C₇×D₆₁	—	2	3	no	—
17	C₇×D₆₁	C₃×D₇	1	1	yes	characteristic
18	C₇×D₆₁	C₂×C₃×C₇	1	1	yes	characteristic
19	#6923⋊C₃	—	7	1	no	Hall
20	C₃×C₇×Dic₇	—	61	1	no	maximal, Hall
21	C₇×C₆₁	—	2	3	no	—
22	C₇×C₆₁	C₃×Dic₇	1	1	yes	characteristic, complemented
23	C₇×C₆₁	C₃×C₄×C₇	1	1	yes	characteristic, complemented
24	D₆₁⋊C₃	C₇×D₇	1	1	yes	characteristic
25	C₂×C₃×C₇²	—	61	1	no	—
26	#6923	—	7	1	no	Hall
27	C₇×Dic₇	—	61	1	no	Hall
28	C₆₁⋊C₃	C₇×Dic₇	1	1	yes	characteristic, complemented, Hall
29	C₃×C₇²	—	61	1	no	Hall
30	D₆₁	C₃×C₇×D₇	1	1	yes	characteristic
31	C₂×C₇²	—	61	1	no	—
32	C₃×C₄×C₇	—	427	1	no	—
33	C₃×Dic₇	—	61	1	no	—
34	C₆₁	C₃×C₇×Dic₇	1	1	yes	characteristic, complemented, Sylow
35	C₇²	#6923⋊C₃	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₇	—	61	1	no	—
37	C₂×C₃×C₇	—	61	1	no	—
38	C₂×C₃×C₇	—	122	3	no	—
39	C₄×C₇	—	427	1	no	—
40	Dic₇	—	61	1	no	—
41	C₃×C₇	—	61	1	no	—
42	C₃×C₇	—	61	1	no	—
43	C₃×C₇	—	122	3	no	—
44	C₂×C₇	—	61	1	no	—
45	C₂×C₇	—	61	1	no	—
46	C₂×C₇	—	122	3	no	—
47	C₃×C₄	—	427	1	no	Hall
48	C₇	—	2	3	no	—
49	C₇	C₇×#6923⋊C₃	1	1	yes	characteristic, complemented
50	C₇	#19103988	1	1	yes	characteristic, direct product factor
51	C₂×C₃	—	61	1	no	—
52	C₄	—	427	1	no	Sylow
53	C₃	—	61	1	no	Sylow
54	C₂	—	61	1	no	—

	subgroup	G/H
center, hypercenter	C₇	#19103988
commutator, hypocenter	C₇×C₆₁	C₃×C₄×C₇
Frattini	C₁	G
Fitting, socle	C₇²×C₆₁	C₃×C₄
prime radical	C₇²×D₆₁⋊C₃	C₂
cosocle	C₇×D₆₁	C₂×C₃×C₇
LCS	G ▷ C₇×C₆₁
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
2. C₇×C₇⋊#6923	C₃	semidirect
3. C₇²×C₆₁⋊C₃	C₄	semidirect
5. #19103988	C₇	direct (N × H)
7. C₇²×C₆₁	C₃×C₄	semidirect
11. C₇⋊#6923	C₃×C₇	semidirect
14. C₇×C₆₁⋊C₃	Dic₇	semidirect
15. C₇×C₆₁⋊C₃	C₄×C₇	semidirect
22. C₇×C₆₁	C₃×Dic₇	semidirect
23. C₇×C₆₁	C₃×C₄×C₇	semidirect
28. C₆₁⋊C₃	C₇×Dic₇	semidirect
34. C₆₁	C₃×C₇×Dic₇	semidirect
35. C₇²	#6923⋊C₃	semidirect
49. C₇	C₇×#6923⋊C₃	semidirect
50. C₇	#19103988	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇²×D₆₁⋊C₃	2
C₇×C₇⋊#6923	3
#19103988	7
C₇×#6923⋊C₃	7
C₃×C₇×Dic₇	61

Subgroups — C7×#19103988 #49089856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19103988 #49089856