Subgroups — C₃×D₇×D₈₇ #20300650

Order 7308.

88 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	C₃×C₇×D₈₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₈₇	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×D₇×D₂₉	—	3	1	no	maximal
6	C₃²×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₆₀₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×D₈₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×D₂₀₃	—	3	1	no	—
10	C₃×D₇×C₂₉	—	2	1	no	—
11	C₃×D₇×C₂₉	D₃	1	1	yes	characteristic, complemented
12	C₃×D₇×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
13	C₃×C₇×D₂₉	—	3	1	no	—
14	C₂×C₃×D₈₇	—	7	1	no	maximal, Hall
15	D₇×D₂₉	—	3	1	no	Hall
16	C₃×C₇×C₂₉	—	2	1	no	—
17	C₃×C₇×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented
18	C₃×C₇×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented
19	C₂×C₃²×C₂₉	—	7	1	no	—
20	C₃×D₈₇	—	7	1	no	—
21	C₃×D₈₇	D₇	1	1	yes	characteristic, direct product factor
22	D₂₀₃	—	3	1	no	—
23	C₇×D₂₉	—	3	1	no	—
24	D₇×C₂₉	C₃×D₃	1	1	yes	characteristic, complemented
25	C₂×D₈₇	—	7	1	no	—
26	C₂×C₃×D₂₉	—	21	1	no	—
27	C₃²×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
28	C₃×D₃×D₇	—	29	1	no	maximal, Hall
29	C₇×C₂₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₂₉	—	7	1	no	—
31	C₂×C₃×C₂₉	—	7	1	no	—
32	C₂×C₃×C₂₉	—	14	1	no	—
33	D₈₇	—	7	1	no	—
34	D₈₇	C₃×D₇	1	1	yes	characteristic, direct product factor
35	C₃×D₂₉	—	3	1	no	—
36	C₃×D₂₉	—	21	1	no	—
37	C₃×D₂₁	—	29	1	no	—
38	C₃×D₃×C₇	—	29	1	no	—
39	C₃²×D₇	D₂₉	1	1	yes	characteristic, complemented
40	C₂×D₂₉	—	21	1	no	Hall
41	C₃×C₂₉	—	2	1	no	—
42	C₃×C₂₉	D₃×D₇	1	1	yes	characteristic, complemented
43	C₃×C₂₉	C₂×C₃×D₇	1	1	yes	characteristic, complemented
44	C₂×C₃×D₇	—	87	1	no	—
45	D₃×D₇	—	29	1	no	—
46	C₃²×C₇	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
47	C₂×C₂₉	—	7	1	no	—
48	D₂₉	—	3	1	no	—
49	D₂₉	—	21	1	no	—
50	C₂×C₃×C₇	—	87	1	no	—
51	D₂₁	—	29	1	no	—
52	C₃×D₇	—	2	1	no	—
53	C₃×D₇	—	87	1	no	—
54	C₃×D₇	C₃×D₂₉	1	1	yes	characteristic, complemented
55	C₃×D₇	D₈₇	1	1	yes	characteristic, direct product factor
56	D₃×C₇	—	29	1	no	—
57	C₂×C₃×D₃	—	203	1	no	Hall
58	C₂₉	C₃×D₃×D₇	1	1	yes	characteristic, complemented, Sylow
59	C₂×D₇	—	87	1	no	Hall
60	C₃×C₇	—	2	1	no	—
61	C₃×C₇	C₂×C₃×D₂₉	1	1	yes	characteristic, complemented
62	C₃×C₇	C₂×D₈₇	1	1	yes	characteristic, complemented
63	C₂×C₃²	—	7	1	no	—
64	C₃×D₃	—	29	1	no	—
65	C₃×D₃	—	203	1	no	—
66	C₂×C₇	—	87	1	no	—
67	D₇	—	87	1	no	—
68	D₇	C₃×D₈₇	1	1	yes	characteristic, direct product factor
69	C₂²×C₃	—	609	1	no	—
70	C₂×D₃	—	203	1	no	—
71	C₃²	D₇×D₂₉	1	1	yes	characteristic, complemented, Sylow
72	C₇	C₂×C₃×D₈₇	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	7	1	no	—
74	C₂×C₃	—	7	1	no	—
75	C₂×C₃	—	14	1	no	—
76	C₂×C₃	—	87	1	no	—
77	C₂×C₃	—	609	1	no	—
78	D₃	—	29	1	no	—
79	D₃	—	203	1	no	—
80	C₂²	—	609	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	C₃×D₇×D₂₉	1	1	yes	characteristic, complemented
83	C₃	D₇×D₈₇	1	1	yes	characteristic, direct product factor
84	C₂	—	7	1	no	—
85	C₂	—	87	1	no	—
86	C₂	—	609	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₇×D₈₇
commutator, hypocenter	C₃×C₇×C₂₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₂₉	C₂²
LCS	G ▷ C₃×C₇×C₂₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₆₀₉	C₂	semidirect
2. C₃×C₇×D₈₇	C₂	semidirect
3. C₃²×D₇×C₂₉	C₂	semidirect
4. D₇×D₈₇	C₃	direct (N × H)
6. C₃²×C₇×C₂₉	C₂²	semidirect
7. D₆₀₉	C₂×C₃	semidirect
8. C₇×D₈₇	C₂×C₃	semidirect
11. C₃×D₇×C₂₉	D₃	semidirect
12. C₃×D₇×C₂₉	C₂×C₃	semidirect
17. C₃×C₇×C₂₉	C₂×D₃	semidirect
18. C₃×C₇×C₂₉	C₂²×C₃	semidirect
21. C₃×D₈₇	D₇	direct (N × H)
24. D₇×C₂₉	C₃×D₃	semidirect
27. C₃²×C₂₉	C₂×D₇	semidirect
29. C₇×C₂₉	C₂×C₃×D₃	semidirect
34. D₈₇	C₃×D₇	direct (N × H)
39. C₃²×D₇	D₂₉	semidirect
42. C₃×C₂₉	D₃×D₇	semidirect
43. C₃×C₂₉	C₂×C₃×D₇	semidirect
46. C₃²×C₇	C₂×D₂₉	semidirect
54. C₃×D₇	C₃×D₂₉	semidirect
55. C₃×D₇	D₈₇	direct (N × H)
58. C₂₉	C₃×D₃×D₇	semidirect
61. C₃×C₇	C₂×C₃×D₂₉	semidirect
62. C₃×C₇	C₂×D₈₇	semidirect
68. D₇	C₃×D₈₇	direct (N × H)
71. C₃²	D₇×D₂₉	semidirect
72. C₇	C₂×C₃×D₈₇	semidirect
82. C₃	C₃×D₇×D₂₉	semidirect
83. C₃	D₇×D₈₇	direct (N × H)

Subgroups — C3×D7×D87 #20300650

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₇×D₈₇ #20300650