Subgroups — D₇×C₃⋊D₈₇ #20300658

Order 7308.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₆₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₃⋊D₈₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₈₇	—	3	4	no	maximal
5	C₃²×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₆₀₉	—	3	4	no	—
7	C₇×D₈₇	—	3	4	no	—
8	C₃×D₇×C₂₉	D₃	1	4	yes	complemented
9	C₂×C₃⋊D₈₇	—	7	1	no	maximal, Hall
10	D₇×D₂₉	—	9	1	no	Hall
11	C₃×C₇×C₂₉	C₂×D₃	1	4	yes	complemented
12	C₂×C₃²×C₂₉	—	7	1	no	—
13	C₃⋊D₈₇	—	7	1	no	—
14	C₃⋊D₈₇	D₇	1	1	yes	characteristic, direct product factor
15	D₂₀₃	—	9	1	no	—
16	C₇×D₂₉	—	9	1	no	—
17	D₇×C₂₉	C₃⋊D₃	1	1	yes	characteristic, complemented
18	C₂×D₈₇	—	21	4	no	—
19	C₃²×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	D₇×C₃⋊D₃	—	29	1	no	maximal, Hall
21	C₇×C₂₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₂₉	—	7	4	no	—
23	D₈₇	—	3	4	no	—
24	D₈₇	—	21	4	no	—
25	C₃⋊D₂₁	—	29	1	no	—
26	C₇×C₃⋊D₃	—	29	1	no	—
27	C₃²×D₇	D₂₉	1	1	yes	characteristic, complemented
28	C₂×D₂₉	—	63	1	no	Hall
29	C₃×C₂₉	D₃×D₇	1	4	yes	complemented
30	D₃×D₇	—	87	4	no	—
31	C₃²×C₇	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
32	C₂×C₂₉	—	7	1	no	—
33	D₂₉	—	9	1	no	—
34	D₂₉	—	63	1	no	—
35	D₂₁	—	87	4	no	—
36	C₃×D₇	D₈₇	1	4	yes	complemented
37	D₃×C₇	—	87	4	no	—
38	C₂×C₃⋊D₃	—	203	1	no	Hall
39	C₂₉	D₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
40	C₂×D₇	—	261	1	no	Hall
41	C₃×C₇	C₂×D₈₇	1	4	yes	complemented
42	C₂×C₃²	—	7	1	no	—
43	C₃⋊D₃	—	29	1	no	—
44	C₃⋊D₃	—	203	1	no	—
45	C₂×C₇	—	261	1	no	—
46	D₇	—	261	1	no	—
47	D₇	C₃⋊D₈₇	1	1	yes	characteristic, direct product factor
48	C₂×D₃	—	609	4	no	—
49	C₃²	D₇×D₂₉	1	1	yes	characteristic, complemented, Sylow
50	C₇	C₂×C₃⋊D₈₇	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	7	4	no	—
52	D₃	—	87	4	no	—
53	D₃	—	609	4	no	—
54	C₂²	—	1827	1	no	Sylow
55	C₃	D₇×D₈₇	1	4	yes	complemented
56	C₂	—	261	1	no	—
57	C₂	—	7	1	no	—
58	C₂	—	1827	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₆₀₉	C₂	semidirect
2. C₇×C₃⋊D₈₇	C₂	semidirect
3. C₃²×D₇×C₂₉	C₂	semidirect
5. C₃²×C₇×C₂₉	C₂²	semidirect
8. C₃×D₇×C₂₉	D₃	semidirect
11. C₃×C₇×C₂₉	C₂×D₃	semidirect
14. C₃⋊D₈₇	D₇	direct (N × H)
17. D₇×C₂₉	C₃⋊D₃	semidirect
19. C₃²×C₂₉	C₂×D₇	semidirect
21. C₇×C₂₉	C₂×C₃⋊D₃	semidirect
27. C₃²×D₇	D₂₉	semidirect
29. C₃×C₂₉	D₃×D₇	semidirect
31. C₃²×C₇	C₂×D₂₉	semidirect
36. C₃×D₇	D₈₇	semidirect
39. C₂₉	D₇×C₃⋊D₃	semidirect
41. C₃×C₇	C₂×D₈₇	semidirect
47. D₇	C₃⋊D₈₇	direct (N × H)
49. C₃²	D₇×D₂₉	semidirect
50. C₇	C₂×C₃⋊D₈₇	semidirect
55. C₃	D₇×D₈₇	semidirect

Subgroups — D7×C3⋊D87 #20300658

Conjugacy classes of subgroups

Complements

Subgroups — D₇×C₃⋊D₈₇ #20300658