Subgroups — C₇×C₉×D₇×C₂₉ #38784635

Order 25578.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₉×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₇×C₂₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₂₉	C₂×C₃	1	1	yes	characteristic
4	C₉×D₇×C₂₉	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₇×C₉×C₂₉	—	7	1	no	maximal
6	C₇×D₇×C₂₉	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₇×C₉×C₂₉	—	2	3	no	—
8	C₇×C₉×C₂₉	D₇	1	1	yes	characteristic, direct product factor
9	C₇×C₉×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
10	C₇²×C₂₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₇×C₂₉	—	7	1	no	—
12	C₃×D₇×C₂₉	C₃×C₇	1	1	yes	characteristic
13	C₇×C₉×D₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃×C₇×C₂₉	—	2	3	no	—
15	C₃×C₇×C₂₉	C₃×D₇	1	1	yes	characteristic
16	C₃×C₇×C₂₉	C₂×C₃×C₇	1	1	yes	characteristic
17	C₂×C₉×C₂₉	—	7	1	no	Hall
18	C₇²×C₉	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
19	C₂×C₇×C₂₉	—	7	1	no	—
20	D₇×C₂₉	C₇×C₉	1	1	yes	characteristic, direct product factor
21	C₃×C₇×D₇	C₃×C₂₉	1	1	yes	characteristic
22	C₉×C₂₉	C₇×D₇	1	1	yes	characteristic, direct product factor, Hall
23	C₇×C₂₉	—	2	3	no	—
24	C₇×C₂₉	C₉×D₇	1	1	yes	characteristic, direct product factor
25	C₇×C₂₉	C₂×C₇×C₉	1	1	yes	characteristic, complemented
26	C₂×C₃×C₂₉	—	7	1	no	—
27	C₃×C₇²	C₂×C₃×C₂₉	1	1	yes	characteristic
28	C₂×C₇×C₉	—	7	1	no	—
29	C₉×D₇	C₇×C₂₉	1	1	yes	characteristic, direct product factor
30	C₇×D₇	C₉×C₂₉	1	1	yes	characteristic, direct product factor, Hall
31	C₃×C₂₉	C₃×C₇×D₇	1	1	yes	characteristic
32	C₇×C₉	—	2	3	no	—
33	C₇×C₉	D₇×C₂₉	1	1	yes	characteristic, direct product factor
34	C₇×C₉	C₂×C₇×C₂₉	1	1	yes	characteristic, complemented
35	C₂×C₂₉	—	7	1	no	Hall
36	C₇²	C₂×C₉×C₂₉	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃×C₇	—	7	1	no	—
38	C₃×D₇	C₃×C₇×C₂₉	1	1	yes	characteristic
39	C₂₉	C₇×C₉×D₇	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×C₇	—	2	3	no	—
41	C₃×C₇	C₃×D₇×C₂₉	1	1	yes	characteristic
42	C₃×C₇	C₂×C₃×C₇×C₂₉	1	1	yes	characteristic
43	C₂×C₉	—	7	1	no	Hall
44	C₂×C₇	—	7	1	no	—
45	D₇	C₇×C₉×C₂₉	1	1	yes	characteristic, direct product factor
46	C₉	C₇×D₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
47	C₇	—	2	3	no	—
48	C₇	C₂×C₇×C₉×C₂₉	1	1	yes	characteristic, complemented
49	C₇	C₉×D₇×C₂₉	1	1	yes	characteristic, direct product factor
50	C₂×C₃	—	7	1	no	—
51	C₃	C₃×C₇×D₇×C₂₉	1	1	yes	characteristic
52	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₉×C₂₉	D₇
commutator, hypocenter	C₇	C₂×C₇×C₉×C₂₉
Frattini	C₃	C₃×C₇×D₇×C₂₉
Fitting	C₇²×C₉×C₂₉	C₂
socle	C₃×C₇²×C₂₉	C₂×C₃
prime radical	C₃×C₇×D₇×C₂₉	C₃
cosocle	C₃×C₇	C₂×C₃×C₇×C₂₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₇×C₉×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₇²×C₉×C₂₉	C₂	semidirect
4. C₉×D₇×C₂₉	C₇	direct (N × H)
6. C₇×D₇×C₂₉	C₉	direct (N × H)
8. C₇×C₉×C₂₉	D₇	direct (N × H)
9. C₇×C₉×C₂₉	C₂×C₇	semidirect
10. C₇²×C₂₉	C₂×C₉	semidirect
13. C₇×C₉×D₇	C₂₉	direct (N × H)
18. C₇²×C₉	C₂×C₂₉	semidirect
20. D₇×C₂₉	C₇×C₉	direct (N × H)
22. C₉×C₂₉	C₇×D₇	direct (N × H)
24. C₇×C₂₉	C₉×D₇	direct (N × H)
25. C₇×C₂₉	C₂×C₇×C₉	semidirect
29. C₉×D₇	C₇×C₂₉	direct (N × H)
30. C₇×D₇	C₉×C₂₉	direct (N × H)
33. C₇×C₉	D₇×C₂₉	direct (N × H)
34. C₇×C₉	C₂×C₇×C₂₉	semidirect
36. C₇²	C₂×C₉×C₂₉	semidirect
39. C₂₉	C₇×C₉×D₇	direct (N × H)
45. D₇	C₇×C₉×C₂₉	direct (N × H)
46. C₉	C₇×D₇×C₂₉	direct (N × H)
48. C₇	C₂×C₇×C₉×C₂₉	semidirect
49. C₇	C₉×D₇×C₂₉	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×C₉×C₂₉	2
C₃×C₇×D₇×C₂₉	3
C₉×D₇×C₂₉	7
C₂×C₇×C₉×C₂₉	7
C₇×C₉×D₇	29

Subgroups — C7×C9×D7×C29 #38784635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₉×D₇×C₂₉ #38784635