Subgroups — C₂×C₇×C₃⋊D₁₂₉ #24925675

Order 10836.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊D₁₂₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₁₂₉	—	3	4	no	maximal
4	C₃²×C₇×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×C₄₃	D₃	1	4	yes	complemented
6	C₇×D₁₂₉	—	3	8	no	—
7	C₂×C₃⋊D₁₂₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×D₄₃	—	9	1	no	Hall
9	C₃×C₇×C₄₃	C₂×D₃	1	4	yes	complemented
10	C₂×C₃²×C₄₃	C₂×C₇	1	1	yes	characteristic, complemented
11	C₃⋊D₁₂₉	C₂×C₇	1	2	yes	direct product factor
12	C₂×C₇×C₄₃	C₃⋊D₃	1	1	yes	characteristic, complemented
13	C₇×D₄₃	—	9	2	no	—
14	C₂×D₁₂₉	—	3	4	no	—
15	C₃²×C₄₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₇×C₄₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₄₃	D₃×C₇	1	4	yes	complemented
18	D₁₂₉	—	3	8	no	—
19	C₂×C₇×C₃⋊D₃	—	43	1	no	maximal, Hall
20	C₂×D₄₃	—	9	1	no	Hall
21	C₃×C₄₃	C₂×D₃×C₇	1	4	yes	complemented
22	C₂×C₃²×C₇	D₄₃	1	1	yes	characteristic, complemented
23	C₇×C₃⋊D₃	—	43	2	no	—
24	C₂×C₄₃	C₇×C₃⋊D₃	1	1	yes	characteristic, complemented
25	D₄₃	—	9	2	no	—
26	C₂×D₃×C₇	—	129	4	no	—
27	C₃²×C₇	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
28	C₄₃	C₂×C₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃×C₇	D₁₂₉	1	4	yes	complemented
30	D₃×C₇	—	129	8	no	—
31	C₂×C₃⋊D₃	—	43	1	no	Hall
32	C₂²×C₇	—	387	1	no	Hall
33	C₃×C₇	C₂×D₁₂₉	1	4	yes	complemented
34	C₂×C₃²	C₇×D₄₃	1	1	yes	characteristic, complemented
35	C₃⋊D₃	—	43	2	no	—
36	C₂×C₇	—	387	2	no	—
37	C₂×C₇	C₃⋊D₁₂₉	1	1	yes	characteristic, direct product factor
38	C₂×D₃	—	129	4	no	—
39	C₃²	C₂×C₇×D₄₃	1	1	yes	characteristic, complemented, Sylow
40	C₇	C₂×C₃⋊D₁₂₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	C₇×D₁₂₉	1	4	yes	complemented
42	D₃	—	129	8	no	—
43	C₂²	—	387	1	no	Sylow
44	C₃	C₂×C₇×D₁₂₉	1	4	yes	complemented
45	C₂	—	387	2	no	—
46	C₂	C₇×C₃⋊D₁₂₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	C₃⋊D₁₂₉
commutator, cosocle, hypocenter	C₃²×C₄₃	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₄₃	C₂
LCS	G ▷ C₃²×C₄₃
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₃⋊D₁₂₉	C₂	direct (N × H)
2. C₂×C₃²×C₇×C₄₃	C₂	semidirect
4. C₃²×C₇×C₄₃	C₂²	semidirect
5. C₂×C₃×C₇×C₄₃	D₃	semidirect
7. C₂×C₃⋊D₁₂₉	C₇	direct (N × H)
9. C₃×C₇×C₄₃	C₂×D₃	semidirect
10. C₂×C₃²×C₄₃	C₂×C₇	semidirect
11. C₃⋊D₁₂₉	C₂×C₇	direct (N × H)
12. C₂×C₇×C₄₃	C₃⋊D₃	semidirect
15. C₃²×C₄₃	C₂²×C₇	semidirect
16. C₇×C₄₃	C₂×C₃⋊D₃	semidirect
17. C₂×C₃×C₄₃	D₃×C₇	semidirect
21. C₃×C₄₃	C₂×D₃×C₇	semidirect
22. C₂×C₃²×C₇	D₄₃	semidirect
24. C₂×C₄₃	C₇×C₃⋊D₃	semidirect
27. C₃²×C₇	C₂×D₄₃	semidirect
28. C₄₃	C₂×C₇×C₃⋊D₃	semidirect
29. C₂×C₃×C₇	D₁₂₉	semidirect
33. C₃×C₇	C₂×D₁₂₉	semidirect
34. C₂×C₃²	C₇×D₄₃	semidirect
37. C₂×C₇	C₃⋊D₁₂₉	direct (N × H)
39. C₃²	C₂×C₇×D₄₃	semidirect
40. C₇	C₂×C₃⋊D₁₂₉	direct (N × H)
41. C₂×C₃	C₇×D₁₂₉	semidirect
44. C₃	C₂×C₇×D₁₂₉	semidirect
46. C₂	C₇×C₃⋊D₁₂₉	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×C₃⋊D₁₂₉	2
C₂×C₃²×C₇×C₄₃	2
C₂×C₇×D₁₂₉	3
C₂×C₃⋊D₁₂₉	7
C₂×C₇×C₃⋊D₃	43

Subgroups — C2×C7×C3⋊D129 #24925675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₃⋊D₁₂₉ #24925675