Subgroups — D₃×ΓL(1,𝔽₈)×C₂₉⋊C₇ #38784652

Order 25578.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×ΓL(1,𝔽₈)×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₇×C₂₉⋊C₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×ΓL(1,𝔽₈)×C₂₉⋊C₇	—	3	1	no	maximal
4	C₃×C₇×C₂₉⋊C₇	C₂×C₃	1	1	yes	characteristic, complemented
5	ΓL(1,𝔽₈)×C₂₉⋊C₇	—	2	1	no	—
6	ΓL(1,𝔽₈)×C₂₉⋊C₇	D₃	1	1	yes	characteristic, direct product factor
7	D₃×ΓL(1,𝔽₈)×C₂₉	C₇	1	1	yes	maximal, characteristic, complemented
8	C₃×D₃×C₂₉⋊C₇	—	7	1	no	maximal
9	C₂×C₇×C₂₉⋊C₇	—	3	1	no	Hall
10	C₃×ΓL(1,𝔽₈)×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
11	C₃²×C₂₉⋊C₇	—	7	1	no	—
12	C₇×C₂₉⋊C₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	D₃×C₇×C₂₉	C₃×C₇	1	1	yes	characteristic, complemented
14	C₂×ΓL(1,𝔽₈)×C₂₉	—	3	1	no	—
15	C₂×C₃×C₂₉⋊C₇	—	21	1	no	—
16	D₃×C₂₉⋊C₇	—	3	2	no	—
17	D₃×C₂₉⋊C₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
18	D₃×C₇×ΓL(1,𝔽₈)	—	29	1	no	maximal, Hall
19	C₃×C₇×C₂₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
20	ΓL(1,𝔽₈)×C₂₉	—	2	1	no	—
21	ΓL(1,𝔽₈)×C₂₉	D₃×C₇	1	1	yes	characteristic, complemented
22	C₃×C₂₉⋊C₇	—	3	2	no	—
23	C₃×C₂₉⋊C₇	—	7	1	no	—
24	C₃×C₂₉⋊C₇	—	14	1	no	—
25	C₃×C₂₉⋊C₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
26	C₃×D₃×C₂₉	—	7	1	no	Hall
27	C₃×C₇×ΓL(1,𝔽₈)	—	29	1	no	Hall
28	C₂×C₇×C₂₉	—	3	1	no	—
29	C₂×C₂₉⋊C₇	—	3	1	no	—
30	C₂×C₂₉⋊C₇	—	9	2	no	—
31	D₃×C₇²	—	29	1	no	—
32	C₂×C₇×ΓL(1,𝔽₈)	—	87	1	no	—
33	C₃²×C₂₉	—	7	1	no	Hall
34	C₇×C₂₉	C₃×D₃×C₇	1	1	yes	characteristic, complemented
35	C₂₉⋊C₇	—	3	2	no	—
36	C₂₉⋊C₇	D₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
37	C₂×C₃×C₂₉	—	21	1	no	—
38	D₃×C₂₉	C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
39	C₃×C₇²	—	29	1	no	—
40	C₇×ΓL(1,𝔽₈)	—	29	1	no	—
41	C₇×ΓL(1,𝔽₈)	—	58	1	no	—
42	C₃×D₃×C₇	—	203	1	no	—
43	D₃×ΓL(1,𝔽₈)	C₂₉⋊C₇	1	1	yes	characteristic, direct product factor
44	C₂×C₇²	—	87	1	no	Hall
45	C₃×C₂₉	—	7	1	no	—
46	C₃×C₂₉	—	14	1	no	—
47	C₃×C₂₉	C₂×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
48	C₃²×C₇	—	203	1	no	—
49	C₃×ΓL(1,𝔽₈)	C₂×C₂₉⋊C₇	1	1	yes	characteristic, complemented
50	C₂×C₂₉	—	3	1	no	Hall
51	C₇²	—	29	1	no	Sylow
52	C₂×C₃×C₇	—	609	1	no	—
53	D₃×C₇	—	29	1	no	—
54	D₃×C₇	—	87	2	no	—
55	D₃×C₇	C₃×C₂₉⋊C₇	1	1	yes	characteristic, complemented
56	C₂×ΓL(1,𝔽₈)	—	3	1	no	—
57	C₂₉	D₃×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
58	C₃×C₇	—	29	1	no	—
59	C₃×C₇	—	87	2	no	—
60	C₃×C₇	—	406	1	no	—
61	C₃×C₇	—	203	1	no	—
62	C₃×C₇	C₂×C₃×C₂₉⋊C₇	1	1	yes	characteristic, complemented
63	ΓL(1,𝔽₈)	—	2	1	no	—
64	ΓL(1,𝔽₈)	D₃×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor
65	C₃×D₃	—	7	1	no	Hall
66	C₂×C₇	—	3	1	no	—
67	C₂×C₇	—	261	2	no	—
68	C₂×C₇	—	87	1	no	—
69	C₃²	—	7	1	no	Sylow
70	C₇	—	29	1	no	—
71	C₇	—	87	2	no	—
72	C₇	C₃×D₃×C₂₉⋊C₇	1	1	yes	characteristic, complemented
73	C₂×C₃	—	21	1	no	—
74	D₃	ΓL(1,𝔽₈)×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor
75	C₃	—	7	1	no	—
76	C₃	—	14	1	no	—
77	C₃	C₂×ΓL(1,𝔽₈)×C₂₉⋊C₇	1	1	yes	characteristic, complemented
78	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₂₉	C₂×C₃×C₇
LCS	G ▷ C₃×C₇×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×ΓL(1,𝔽₈)×C₂₉⋊C₇	C₂	semidirect
2. D₃×C₇×C₂₉⋊C₇	C₃	semidirect
4. C₃×C₇×C₂₉⋊C₇	C₂×C₃	semidirect
6. ΓL(1,𝔽₈)×C₂₉⋊C₇	D₃	direct (N × H)
7. D₃×ΓL(1,𝔽₈)×C₂₉	C₇	semidirect
10. C₃×ΓL(1,𝔽₈)×C₂₉	C₂×C₇	semidirect
12. C₇×C₂₉⋊C₇	C₃×D₃	semidirect
13. D₃×C₇×C₂₉	C₃×C₇	semidirect
17. D₃×C₂₉⋊C₇	ΓL(1,𝔽₈)	direct (N × H)
19. C₃×C₇×C₂₉	C₂×C₃×C₇	semidirect
21. ΓL(1,𝔽₈)×C₂₉	D₃×C₇	semidirect
25. C₃×C₂₉⋊C₇	C₂×ΓL(1,𝔽₈)	semidirect
34. C₇×C₂₉	C₃×D₃×C₇	semidirect
36. C₂₉⋊C₇	D₃×ΓL(1,𝔽₈)	direct (N × H)
38. D₃×C₂₉	C₇×ΓL(1,𝔽₈)	semidirect
43. D₃×ΓL(1,𝔽₈)	C₂₉⋊C₇	direct (N × H)
47. C₃×C₂₉	C₂×C₇×ΓL(1,𝔽₈)	semidirect
49. C₃×ΓL(1,𝔽₈)	C₂×C₂₉⋊C₇	semidirect
55. D₃×C₇	C₃×C₂₉⋊C₇	semidirect
57. C₂₉	D₃×C₇×ΓL(1,𝔽₈)	semidirect
62. C₃×C₇	C₂×C₃×C₂₉⋊C₇	semidirect
64. ΓL(1,𝔽₈)	D₃×C₂₉⋊C₇	direct (N × H)
72. C₇	C₃×D₃×C₂₉⋊C₇	semidirect
74. D₃	ΓL(1,𝔽₈)×C₂₉⋊C₇	direct (N × H)
77. C₃	C₂×ΓL(1,𝔽₈)×C₂₉⋊C₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×ΓL(1,𝔽₈)×C₂₉⋊C₇	2
D₃×C₇×C₂₉⋊C₇	3
C₂×ΓL(1,𝔽₈)×C₂₉⋊C₇	3
D₃×ΓL(1,𝔽₈)×C₂₉	7
C₃×D₃×C₂₉⋊C₇	7
D₃×C₇×ΓL(1,𝔽₈)	29

Subgroups — D3×ΓL(1,𝔽8)×C29⋊C7 #38784652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×ΓL(1,𝔽₈)×C₂₉⋊C₇ #38784652