Subgroups — D₇×C₂₉×D₂₉ #37555463

Order 23548.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×D₂₀₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₇×C₂₉²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₂₉×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₂₉²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₂₉×D₂₉	—	7	1	no	maximal, Hall
6	C₂×C₂₉²	—	7	1	no	—
7	C₂₉×D₂₉	—	7	1	no	—
8	C₂₉×D₂₉	D₇	1	1	yes	characteristic, direct product factor
9	C₂₉²	C₂×D₇	1	1	yes	characteristic, complemented, Sylow
10	C₂×D₇×C₂₉	—	29	1	no	maximal
11	D₇×D₂₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor
12	C₂×C₇×C₂₉	—	29	1	no	—
13	D₂₀₃	C₂×C₂₉	1	1	yes	characteristic, complemented
14	C₇×D₂₉	C₂×C₂₉	1	1	yes	characteristic, complemented
15	D₇×C₂₉	—	2	14	no	—
16	D₇×C₂₉	—	29	1	no	—
17	D₇×C₂₉	D₂₉	1	1	yes	characteristic, direct product factor
18	D₇×C₂₉	C₂×C₂₉	1	1	yes	characteristic, complemented
19	C₇×C₂₉	—	2	14	no	—
20	C₇×C₂₉	C₂×D₂₉	1	1	yes	characteristic, complemented
21	C₇×C₂₉	C₂²×C₂₉	1	1	yes	characteristic, complemented
22	C₂²×C₂₉	—	203	1	no	—
23	C₂×D₂₉	—	7	1	no	—
24	C₂×C₂₉	—	7	1	no	—
25	C₂×C₂₉	—	7	1	no	—
26	C₂×C₂₉	—	14	14	no	—
27	C₂×C₂₉	—	29	1	no	—
28	C₂×C₂₉	—	203	1	no	—
29	D₂₉	—	7	1	no	—
30	D₂₉	D₇×C₂₉	1	1	yes	characteristic, direct product factor
31	C₂₉	—	2	14	no	—
32	C₂₉	D₇×D₂₉	1	1	yes	characteristic, direct product factor
33	C₂₉	C₂×D₇×C₂₉	1	1	yes	characteristic, complemented
34	C₂×D₇	—	29	1	no	Hall
35	C₂×C₇	—	29	1	no	—
36	D₇	—	29	1	no	—
37	D₇	C₂₉×D₂₉	1	1	yes	characteristic, direct product factor
38	C₇	C₂×C₂₉×D₂₉	1	1	yes	characteristic, complemented, Sylow
39	C₂²	—	203	1	no	Sylow
40	C₂	—	7	1	no	—
41	C₂	—	29	1	no	—
42	C₂	—	203	1	no	—

	subgroup	G/H
center, hypercenter	C₂₉	D₇×D₂₉
commutator, cosocle, hypocenter	C₇×C₂₉	C₂²×C₂₉
Frattini	C₁	G
Fitting, socle	C₇×C₂₉²	C₂²
LCS	G ▷ C₇×C₂₉
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂₉×D₂₀₃	C₂	semidirect
2. D₇×C₂₉²	C₂	semidirect
3. C₇×C₂₉×D₂₉	C₂	semidirect
4. C₇×C₂₉²	C₂²	semidirect
8. C₂₉×D₂₉	D₇	direct (N × H)
9. C₂₉²	C₂×D₇	semidirect
11. D₇×D₂₉	C₂₉	direct (N × H)
13. D₂₀₃	C₂×C₂₉	semidirect
14. C₇×D₂₉	C₂×C₂₉	semidirect
17. D₇×C₂₉	D₂₉	direct (N × H)
18. D₇×C₂₉	C₂×C₂₉	semidirect
20. C₇×C₂₉	C₂×D₂₉	semidirect
21. C₇×C₂₉	C₂²×C₂₉	semidirect
30. D₂₉	D₇×C₂₉	direct (N × H)
32. C₂₉	D₇×D₂₉	direct (N × H)
33. C₂₉	C₂×D₇×C₂₉	semidirect
37. D₇	C₂₉×D₂₉	direct (N × H)
38. C₇	C₂×C₂₉×D₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×D₂₀₃	2
D₇×C₂₉²	2
C₇×C₂₉×D₂₉	2
C₂×C₂₉×D₂₉	7
C₂×D₇×C₂₉	29
D₇×D₂₉	29

Subgroups — D7×C29×D29 #37555463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×C₂₉×D₂₉ #37555463