Subgroups — C₂×ΓL(1,𝔽₈)×D₈₇ #20300641

Order 7308.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×ΓL(1,𝔽₈)×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	ΓL(1,𝔽₈)×D₈₇	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇×D₈₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×ΓL(1,𝔽₈)×D₂₉	—	3	1	no	maximal
5	C₃×ΓL(1,𝔽₈)×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₇×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×D₈₇	C₂×C₃	1	2	yes	complemented
8	C₂×ΓL(1,𝔽₈)×C₂₉	—	2	1	no	—
9	C₂×ΓL(1,𝔽₈)×C₂₉	D₃	1	1	yes	characteristic, complemented
10	ΓL(1,𝔽₈)×D₂₉	—	3	2	no	—
11	C₂×C₃×D₈₇	—	7	1	no	maximal, Hall
12	C₂×C₇×D₂₉	—	3	1	no	Hall
13	C₃×C₇×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented
14	ΓL(1,𝔽₈)×C₂₉	—	2	1	no	—
15	ΓL(1,𝔽₈)×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented
16	C₂×C₃²×C₂₉	—	7	1	no	—
17	C₃×D₈₇	—	7	2	no	—
18	C₂×C₇×C₂₉	C₃×D₃	1	1	yes	characteristic, complemented
19	C₇×D₂₉	—	3	2	no	—
20	C₂×D₈₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
21	C₂×C₃×D₂₉	—	21	1	no	—
22	C₃²×C₂₉	—	7	1	no	Hall
23	C₂×D₃×ΓL(1,𝔽₈)	—	29	1	no	maximal, Hall
24	C₇×C₂₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₂₉	—	7	1	no	—
26	C₂×C₃×C₂₉	—	14	1	no	—
27	C₂×C₃×C₂₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
28	D₈₇	C₂×ΓL(1,𝔽₈)	1	2	yes	direct product factor
29	C₃×D₂₉	—	21	2	no	—
30	C₂×C₃×ΓL(1,𝔽₈)	D₂₉	1	1	yes	characteristic, complemented
31	D₃×ΓL(1,𝔽₈)	—	29	2	no	—
32	C₂×D₂₉	—	3	1	no	Hall
33	C₃×C₂₉	—	7	1	no	—
34	C₃×C₂₉	—	14	1	no	—
35	C₃×C₂₉	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
36	C₂×D₃×C₇	—	29	1	no	—
37	C₂²×ΓL(1,𝔽₈)	—	87	1	no	—
38	C₃×ΓL(1,𝔽₈)	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
39	C₂×C₂₉	D₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
40	D₂₉	—	3	2	no	—
41	C₂×C₃×C₇	C₃×D₂₉	1	1	yes	characteristic, complemented
42	D₃×C₇	—	29	2	no	—
43	C₂×ΓL(1,𝔽₈)	—	2	1	no	—
44	C₂×ΓL(1,𝔽₈)	—	87	2	no	—
45	C₂×ΓL(1,𝔽₈)	D₈₇	1	1	yes	characteristic, direct product factor
46	C₂×C₃×D₃	—	203	1	no	Hall
47	C₂₉	C₂×D₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₇	—	87	1	no	Hall
49	C₃×C₇	C₂×C₃×D₂₉	1	1	yes	characteristic, complemented
50	ΓL(1,𝔽₈)	—	2	1	no	—
51	ΓL(1,𝔽₈)	C₂×D₈₇	1	1	yes	characteristic, direct product factor
52	C₂×C₃²	—	7	1	no	—
53	C₃×D₃	—	203	2	no	—
54	C₂×C₇	—	87	2	no	—
55	C₂×C₇	C₃×D₈₇	1	1	yes	characteristic, complemented
56	C₂²×C₃	—	609	1	no	—
57	C₂×D₃	—	29	1	no	—
58	C₃²	—	7	1	no	Sylow
59	C₇	C₂×C₃×D₈₇	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₃	—	7	1	no	—
61	C₂×C₃	—	14	1	no	—
62	C₂×C₃	—	609	2	no	—
63	C₂×C₃	ΓL(1,𝔽₈)×D₂₉	1	1	yes	characteristic, complemented
64	D₃	—	29	2	no	—
65	C₂²	—	87	1	no	Sylow
66	C₃	—	7	1	no	—
67	C₃	—	14	1	no	—
68	C₃	C₂×ΓL(1,𝔽₈)×D₂₉	1	1	yes	characteristic, complemented
69	C₂	—	87	2	no	—
70	C₂	ΓL(1,𝔽₈)×D₈₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	ΓL(1,𝔽₈)×D₈₇
commutator, hypocenter	C₃×C₇×C₂₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₂₉	C₂×C₃
LCS	G ▷ C₃×C₇×C₂₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×ΓL(1,𝔽₈)×C₂₉	C₂	semidirect
2. ΓL(1,𝔽₈)×D₈₇	C₂	direct (N × H)
3. C₂×C₇×D₈₇	C₃	semidirect
5. C₃×ΓL(1,𝔽₈)×C₂₉	C₂²	semidirect
6. C₂×C₃×C₇×C₂₉	C₂×C₃	semidirect
7. C₇×D₈₇	C₂×C₃	semidirect
9. C₂×ΓL(1,𝔽₈)×C₂₉	D₃	semidirect
13. C₃×C₇×C₂₉	C₂²×C₃	semidirect
15. ΓL(1,𝔽₈)×C₂₉	C₂×D₃	semidirect
18. C₂×C₇×C₂₉	C₃×D₃	semidirect
20. C₂×D₈₇	ΓL(1,𝔽₈)	direct (N × H)
24. C₇×C₂₉	C₂×C₃×D₃	semidirect
27. C₂×C₃×C₂₉	C₂×ΓL(1,𝔽₈)	semidirect
28. D₈₇	C₂×ΓL(1,𝔽₈)	direct (N × H)
30. C₂×C₃×ΓL(1,𝔽₈)	D₂₉	semidirect
35. C₃×C₂₉	C₂²×ΓL(1,𝔽₈)	semidirect
38. C₃×ΓL(1,𝔽₈)	C₂×D₂₉	semidirect
39. C₂×C₂₉	D₃×ΓL(1,𝔽₈)	semidirect
41. C₂×C₃×C₇	C₃×D₂₉	semidirect
45. C₂×ΓL(1,𝔽₈)	D₈₇	direct (N × H)
47. C₂₉	C₂×D₃×ΓL(1,𝔽₈)	semidirect
49. C₃×C₇	C₂×C₃×D₂₉	semidirect
51. ΓL(1,𝔽₈)	C₂×D₈₇	direct (N × H)
55. C₂×C₇	C₃×D₈₇	semidirect
59. C₇	C₂×C₃×D₈₇	semidirect
63. C₂×C₃	ΓL(1,𝔽₈)×D₂₉	semidirect
68. C₃	C₂×ΓL(1,𝔽₈)×D₂₉	semidirect
70. C₂	ΓL(1,𝔽₈)×D₈₇	direct (N × H)

Subgroups — C2×ΓL(1,𝔽8)×D87 #20300641

Conjugacy classes of subgroups

Complements

Subgroups — C₂×ΓL(1,𝔽₈)×D₈₇ #20300641