Subgroups — C₃²×D₇×D₂₉ #20300644

Order 7308.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₂₀₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×D₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₇×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₇×D₂₉	C₃	1	4	yes	maximal, direct product factor
5	C₃²×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₂₀₃	C₂×C₃	1	4	yes	complemented
7	C₃×D₇×C₂₉	C₂×C₃	1	4	yes	complemented
8	C₃×C₇×D₂₉	C₂×C₃	1	4	yes	complemented
9	C₂×C₃²×D₂₉	—	7	1	no	maximal, Hall
10	D₇×D₂₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₇×C₂₉	C₂²×C₃	1	4	yes	complemented
12	C₂×C₃²×C₂₉	—	7	1	no	—
13	C₃²×D₂₉	—	7	1	no	—
14	C₃²×D₂₉	D₇	1	1	yes	characteristic, direct product factor
15	D₂₀₃	C₂×C₃²	1	1	yes	characteristic, complemented
16	C₇×D₂₉	C₂×C₃²	1	1	yes	characteristic, complemented
17	D₇×C₂₉	C₂×C₃²	1	1	yes	characteristic, complemented
18	C₂×C₃×D₂₉	—	7	4	no	—
19	C₃²×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃²×D₇	—	29	1	no	maximal, Hall
21	C₇×C₂₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₂₉	—	7	4	no	—
23	C₃×D₂₉	—	7	4	no	—
24	C₃×D₂₉	C₃×D₇	1	4	yes	direct product factor
25	C₂×C₃²×C₇	—	29	1	no	—
26	C₃²×D₇	—	29	1	no	—
27	C₃²×D₇	D₂₉	1	1	yes	characteristic, direct product factor
28	C₂×D₂₉	—	7	1	no	Hall
29	C₃×C₂₉	C₂×C₃×D₇	1	4	yes	complemented
30	C₂×C₃×D₇	—	29	4	no	—
31	C₃²×C₇	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
32	C₂×C₂₉	—	7	1	no	—
33	D₂₉	—	7	1	no	—
34	D₂₉	C₃²×D₇	1	1	yes	characteristic, direct product factor
35	C₂×C₃×C₇	—	29	4	no	—
36	C₃×D₇	—	29	4	no	—
37	C₃×D₇	C₃×D₂₉	1	4	yes	direct product factor
38	C₂²×C₃²	—	203	1	no	Hall
39	C₂₉	C₂×C₃²×D₇	1	1	yes	characteristic, complemented, Sylow
40	C₂×D₇	—	29	1	no	Hall
41	C₃×C₇	C₂×C₃×D₂₉	1	4	yes	complemented
42	C₂×C₃²	—	7	1	no	—
43	C₂×C₃²	—	29	1	no	—
44	C₂×C₃²	—	203	1	no	—
45	C₂×C₇	—	29	1	no	—
46	D₇	—	29	1	no	—
47	D₇	C₃²×D₂₉	1	1	yes	characteristic, direct product factor
48	C₂²×C₃	—	203	4	no	—
49	C₃²	D₇×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
50	C₇	C₂×C₃²×D₂₉	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	7	4	no	—
52	C₂×C₃	—	29	4	no	—
53	C₂×C₃	—	203	4	no	—
54	C₂²	—	203	1	no	Sylow
55	C₃	C₃×D₇×D₂₉	1	4	yes	direct product factor
56	C₂	—	7	1	no	—
57	C₂	—	29	1	no	—
58	C₂	—	203	1	no	—

	subgroup	G/H
center, hypercenter	C₃²	D₇×D₂₉
commutator, hypocenter	C₇×C₂₉	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₂₉	C₂²
LCS	G ▷ C₇×C₂₉
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×D₂₀₃	C₂	semidirect
2. C₃²×D₇×C₂₉	C₂	semidirect
3. C₃²×C₇×D₂₉	C₂	semidirect
4. C₃×D₇×D₂₉	C₃	direct (N × H)
5. C₃²×C₇×C₂₉	C₂²	semidirect
6. C₃×D₂₀₃	C₂×C₃	semidirect
7. C₃×D₇×C₂₉	C₂×C₃	semidirect
8. C₃×C₇×D₂₉	C₂×C₃	semidirect
10. D₇×D₂₉	C₃²	direct (N × H)
11. C₃×C₇×C₂₉	C₂²×C₃	semidirect
14. C₃²×D₂₉	D₇	direct (N × H)
15. D₂₀₃	C₂×C₃²	semidirect
16. C₇×D₂₉	C₂×C₃²	semidirect
17. D₇×C₂₉	C₂×C₃²	semidirect
19. C₃²×C₂₉	C₂×D₇	semidirect
21. C₇×C₂₉	C₂²×C₃²	semidirect
24. C₃×D₂₉	C₃×D₇	direct (N × H)
27. C₃²×D₇	D₂₉	direct (N × H)
29. C₃×C₂₉	C₂×C₃×D₇	semidirect
31. C₃²×C₇	C₂×D₂₉	semidirect
34. D₂₉	C₃²×D₇	direct (N × H)
37. C₃×D₇	C₃×D₂₉	direct (N × H)
39. C₂₉	C₂×C₃²×D₇	semidirect
41. C₃×C₇	C₂×C₃×D₂₉	semidirect
47. D₇	C₃²×D₂₉	direct (N × H)
49. C₃²	D₇×D₂₉	direct (N × H)
50. C₇	C₂×C₃²×D₂₉	semidirect
55. C₃	C₃×D₇×D₂₉	direct (N × H)

Subgroups — C32×D7×D29 #20300644

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×D₇×D₂₉ #20300644