Subgroups — C₃×ΓL(1,𝔽₈)×D₂₉⋊C₇ #38784648

Order 25578.

112 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	C₃×C₇×D₂₉⋊C₇	C₃	1	1	yes	maximal, characteristic, complemented
3	ΓL(1,𝔽₈)×D₂₉⋊C₇	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₇×C₂₉⋊C₇	C₂×C₃	1	1	yes	characteristic, complemented
5	ΓL(1,𝔽₈)×C₂₉⋊C₇	C₂×C₃	1	3	yes	complemented
6	C₃×ΓL(1,𝔽₈)×D₂₉	C₇	1	1	yes	maximal, characteristic, complemented
7	C₃²×D₂₉⋊C₇	—	7	1	no	maximal
8	C₇×D₂₉⋊C₇	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×ΓL(1,𝔽₈)×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
10	C₃²×C₂₉⋊C₇	—	7	1	no	—
11	C₇×C₂₉⋊C₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₇×D₂₉	C₃×C₇	1	1	yes	characteristic, complemented
13	ΓL(1,𝔽₈)×D₂₉	C₃×C₇	1	3	yes	complemented
14	C₃×D₂₉⋊C₇	—	3	2	no	—
15	C₃×D₂₉⋊C₇	—	7	3	no	—
16	C₃×D₂₉⋊C₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
17	C₂×C₃×C₇×ΓL(1,𝔽₈)	—	29	1	no	maximal, Hall
18	C₃×C₇×C₂₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
19	ΓL(1,𝔽₈)×C₂₉	C₂×C₃×C₇	1	3	yes	complemented
20	C₃×C₂₉⋊C₇	—	3	2	no	—
21	C₃×C₂₉⋊C₇	—	7	3	no	—
22	C₃×C₂₉⋊C₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
23	C₃²×D₂₉	—	7	1	no	Hall
24	C₃×C₇×ΓL(1,𝔽₈)	—	29	1	no	Hall
25	C₇×D₂₉	C₃²×C₇	1	1	yes	characteristic, complemented
26	D₂₉⋊C₇	—	3	2	no	—
27	D₂₉⋊C₇	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
28	C₂×C₃×C₇²	—	29	1	no	—
29	C₂×C₇×ΓL(1,𝔽₈)	—	29	3	no	—
30	C₃²×C₂₉	—	7	1	no	Hall
31	C₇×C₂₉	C₂×C₃²×C₇	1	1	yes	characteristic, complemented
32	C₂₉⋊C₇	—	3	2	no	—
33	C₂₉⋊C₇	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
34	C₃×D₂₉	—	7	3	no	—
35	C₃×D₂₉	C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
36	C₃×C₇²	—	29	1	no	—
37	C₇×ΓL(1,𝔽₈)	—	29	3	no	—
38	C₂×C₃²×C₇	—	203	1	no	—
39	C₂×C₃×ΓL(1,𝔽₈)	—	29	1	no	—
40	C₂×C₇²	—	29	1	no	Hall
41	C₃×C₂₉	—	7	3	no	—
42	C₃×C₂₉	C₂×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
43	C₃²×C₇	—	203	1	no	—
44	C₃×ΓL(1,𝔽₈)	D₂₉⋊C₇	1	1	yes	characteristic, direct product factor
45	D₂₉	C₃×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
46	C₇²	—	29	1	no	Sylow
47	C₂×C₃×C₇	—	29	1	no	—
48	C₂×C₃×C₇	—	29	1	no	—
49	C₂×C₃×C₇	—	87	2	no	—
50	C₂×C₃×C₇	—	203	3	no	—
51	C₂×ΓL(1,𝔽₈)	—	29	3	no	—
52	C₂₉	C₂×C₃×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
53	C₃×C₇	—	29	1	no	—
54	C₃×C₇	—	87	2	no	—
55	C₃×C₇	—	203	3	no	—
56	C₃×C₇	C₃×D₂₉⋊C₇	1	1	yes	characteristic, complemented
57	ΓL(1,𝔽₈)	C₃×D₂₉⋊C₇	1	3	yes	direct product factor
58	C₂×C₃²	—	203	1	no	Hall
59	C₂×C₇	—	29	1	no	—
60	C₂×C₇	—	29	1	no	—
61	C₂×C₇	—	87	2	no	—
62	C₃²	—	7	1	no	Sylow
63	C₇	—	29	1	no	—
64	C₇	—	87	2	no	—
65	C₇	C₃²×D₂₉⋊C₇	1	1	yes	characteristic, complemented
66	C₂×C₃	—	29	1	no	—
67	C₂×C₃	—	203	3	no	—
68	C₃	—	7	3	no	—
69	C₃	ΓL(1,𝔽₈)×D₂₉⋊C₇	1	1	yes	characteristic, direct product factor
70	C₂	—	29	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	ΓL(1,𝔽₈)×D₂₉⋊C₇
commutator, cosocle, hypocenter	C₇×C₂₉	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₂₉	C₂×C₃×C₇
LCS	G ▷ C₇×C₂₉
UCS	C₁ ◁ C₃

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. C₃×C₇×D₂₉⋊C₇	C₃	semidirect
3. ΓL(1,𝔽₈)×D₂₉⋊C₇	C₃	direct (N × H)
4. C₃×C₇×C₂₉⋊C₇	C₂×C₃	semidirect
5. ΓL(1,𝔽₈)×C₂₉⋊C₇	C₂×C₃	semidirect
6. C₃×ΓL(1,𝔽₈)×D₂₉	C₇	semidirect
8. C₇×D₂₉⋊C₇	C₃²	semidirect
9. C₃×ΓL(1,𝔽₈)×C₂₉	C₂×C₇	semidirect
11. C₇×C₂₉⋊C₇	C₂×C₃²	semidirect
12. C₃×C₇×D₂₉	C₃×C₇	semidirect
13. ΓL(1,𝔽₈)×D₂₉	C₃×C₇	semidirect
16. C₃×D₂₉⋊C₇	ΓL(1,𝔽₈)	direct (N × H)
18. C₃×C₇×C₂₉	C₂×C₃×C₇	semidirect
19. ΓL(1,𝔽₈)×C₂₉	C₂×C₃×C₇	semidirect
22. C₃×C₂₉⋊C₇	C₂×ΓL(1,𝔽₈)	semidirect
25. C₇×D₂₉	C₃²×C₇	semidirect
27. D₂₉⋊C₇	C₃×ΓL(1,𝔽₈)	direct (N × H)
31. C₇×C₂₉	C₂×C₃²×C₇	semidirect
33. C₂₉⋊C₇	C₂×C₃×ΓL(1,𝔽₈)	semidirect
35. C₃×D₂₉	C₇×ΓL(1,𝔽₈)	semidirect
42. C₃×C₂₉	C₂×C₇×ΓL(1,𝔽₈)	semidirect
44. C₃×ΓL(1,𝔽₈)	D₂₉⋊C₇	direct (N × H)
45. D₂₉	C₃×C₇×ΓL(1,𝔽₈)	semidirect
52. C₂₉	C₂×C₃×C₇×ΓL(1,𝔽₈)	semidirect
56. C₃×C₇	C₃×D₂₉⋊C₇	semidirect
57. ΓL(1,𝔽₈)	C₃×D₂₉⋊C₇	direct (N × H)
65. C₇	C₃²×D₂₉⋊C₇	semidirect
69. C₃	ΓL(1,𝔽₈)×D₂₉⋊C₇	direct (N × H)

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
C₃×C₇×D₂₉⋊C₇	3
ΓL(1,𝔽₈)×D₂₉⋊C₇	3
C₃×ΓL(1,𝔽₈)×D₂₉	7
C₃²×D₂₉⋊C₇	7
C₂×C₃×C₇×ΓL(1,𝔽₈)	29

Subgroups — C3×ΓL(1,𝔽8)×D29⋊C7 #38784648

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×ΓL(1,𝔽₈)×D₂₉⋊C₇ #38784648