Subgroups — C₇×D₉×C₂₉⋊C₇ #38784608

Order 25578.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₇×C₂₉⋊C₇	—	3	1	no	maximal
3	C₃×C₇×C₂₉⋊C₇	D₃	1	1	yes	characteristic
4	C₇×D₉×C₂₉	C₇	1	1	yes	maximal, characteristic, complemented
5	D₉×C₂₉⋊C₇	C₇	1	7	yes	maximal, direct product factor
6	C₂×C₇×C₂₉⋊C₇	—	9	1	no	Hall
7	C₇×C₉×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
8	C₉×C₂₉⋊C₇	C₂×C₇	1	7	yes	complemented
9	C₇×C₂₉⋊C₇	D₉	1	1	yes	characteristic, direct product factor, Hall
10	D₃×C₇×C₂₉	—	3	1	no	—
11	D₃×C₂₉⋊C₇	—	3	7	no	—
12	C₇²×D₉	—	29	1	no	maximal, Hall
13	C₃×C₇×C₂₉	D₃×C₇	1	1	yes	characteristic
14	C₃×C₂₉⋊C₇	D₃×C₇	1	7	yes	—
15	D₉×C₂₉	C₇²	1	1	yes	characteristic, complemented, Hall
16	C₇²×C₉	—	29	1	no	Hall
17	C₂×C₇×C₂₉	—	9	1	no	—
18	C₂×C₂₉⋊C₇	—	9	7	no	—
19	D₃×C₇²	—	87	1	no	—
20	C₉×C₂₉	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
21	C₇×C₂₉	C₇×D₉	1	1	yes	characteristic, complemented
22	C₂₉⋊C₇	C₇×D₉	1	7	yes	direct product factor
23	D₃×C₂₉	—	3	1	no	—
24	C₃×C₇²	—	29	1	no	—
25	C₇×D₉	—	29	7	no	—
26	C₇×D₉	C₂₉⋊C₇	1	1	yes	characteristic, direct product factor
27	C₂×C₇²	—	261	1	no	Hall
28	C₃×C₂₉	D₃×C₇²	1	1	yes	characteristic
29	C₇×C₉	—	29	7	no	—
30	C₇×C₉	C₂×C₂₉⋊C₇	1	1	yes	characteristic, complemented
31	C₂×C₂₉	—	9	1	no	Hall
32	C₇²	—	29	1	no	Sylow
33	D₃×C₇	—	3	1	no	—
34	D₃×C₇	—	87	7	no	—
35	C₂₉	C₇²×D₉	1	1	yes	characteristic, complemented, Sylow
36	C₃×C₇	—	29	7	no	—
37	C₃×C₇	D₃×C₂₉⋊C₇	1	1	yes	characteristic
38	D₉	C₇×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₇	—	261	7	no	—
40	C₂×C₇	—	9	1	no	—
41	C₉	C₂×C₇×C₂₉⋊C₇	1	1	yes	characteristic, complemented, Sylow
42	C₇	—	29	7	no	—
43	C₇	D₉×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor
44	D₃	—	3	1	no	—
45	C₃	D₃×C₇×C₂₉⋊C₇	1	1	yes	characteristic
46	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₉×C₂₉⋊C₇
commutator, cosocle, hypocenter	C₉×C₂₉	C₂×C₇²
Frattini	C₃	D₃×C₇×C₂₉⋊C₇
Fitting	C₇×C₉×C₂₉	C₂×C₇
socle	C₃×C₇×C₂₉	D₃×C₇
LCS	G ▷ C₉×C₂₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₉×C₂₉⋊C₇	C₂	semidirect
4. C₇×D₉×C₂₉	C₇	semidirect
5. D₉×C₂₉⋊C₇	C₇	direct (N × H)
7. C₇×C₉×C₂₉	C₂×C₇	semidirect
8. C₉×C₂₉⋊C₇	C₂×C₇	semidirect
9. C₇×C₂₉⋊C₇	D₉	direct (N × H)
15. D₉×C₂₉	C₇²	semidirect
20. C₉×C₂₉	C₂×C₇²	semidirect
21. C₇×C₂₉	C₇×D₉	semidirect
22. C₂₉⋊C₇	C₇×D₉	direct (N × H)
26. C₇×D₉	C₂₉⋊C₇	direct (N × H)
30. C₇×C₉	C₂×C₂₉⋊C₇	semidirect
35. C₂₉	C₇²×D₉	semidirect
38. D₉	C₇×C₂₉⋊C₇	direct (N × H)
41. C₉	C₂×C₇×C₂₉⋊C₇	semidirect
43. C₇	D₉×C₂₉⋊C₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₉×C₂₉⋊C₇	2
D₃×C₇×C₂₉⋊C₇	3
C₇×D₉×C₂₉	7
D₉×C₂₉⋊C₇	7
C₇²×D₉	29

Subgroups — C7×D9×C29⋊C7 #38784608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₉×C₂₉⋊C₇ #38784608