Subgroups — A₄×ΓL(1,𝔽₈)×C₂₉ #20300633

Order 7308.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₂²⋊ΓL(1,𝔽₈)	C₃	1	2	yes	maximal, complemented
2	C₇×A₄×C₂₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂²×ΓL(1,𝔽₈)×C₂₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×ΓL(1,𝔽₈)×C₂₉	—	4	1	no	maximal, Hall
5	C₂×ΓL(1,𝔽₈)×C₂₉	—	3	1	no	—
6	C₃×A₄×C₂₉	—	7	1	no	maximal, Hall
7	C₂²×C₇×C₂₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇×C₂₉	—	4	1	no	—
9	ΓL(1,𝔽₈)×C₂₉	—	4	2	no	—
10	ΓL(1,𝔽₈)×C₂₉	A₄	1	1	yes	characteristic, direct product factor
11	C₂×C₇×C₂₉	—	3	1	no	—
12	C₂²×C₃×C₂₉	—	7	1	no	—
13	A₄×C₂₉	—	7	2	no	—
14	A₄×C₂₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
15	C₃²×C₂₉	—	28	1	no	Hall
16	A₄×ΓL(1,𝔽₈)	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₇×C₂₉	C₃×A₄	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₂₉	—	21	1	no	—
19	C₂²×C₂₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
20	C₃×C₂₉	—	4	1	no	—
21	C₃×C₂₉	—	7	1	no	—
22	C₃×C₂₉	—	28	2	no	—
23	C₂²⋊ΓL(1,𝔽₈)	C₃×C₂₉	1	2	yes	complemented
24	C₇×A₄	C₃×C₂₉	1	1	yes	characteristic, complemented
25	C₂²×ΓL(1,𝔽₈)	C₃×C₂₉	1	1	yes	characteristic, complemented
26	C₃×ΓL(1,𝔽₈)	—	4	1	no	Hall
27	C₂×C₂₉	—	3	1	no	—
28	C₂×ΓL(1,𝔽₈)	—	3	1	no	—
29	C₃×A₄	—	7	1	no	Hall
30	C₂₉	A₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Sylow
31	C₂²×C₇	C₃²×C₂₉	1	1	yes	characteristic, complemented, Hall
32	C₃×C₇	—	4	1	no	—
33	ΓL(1,𝔽₈)	—	4	2	no	—
34	ΓL(1,𝔽₈)	A₄×C₂₉	1	1	yes	characteristic, direct product factor
35	C₂×C₇	—	3	1	no	—
36	C₂²×C₃	—	7	1	no	—
37	A₄	—	7	2	no	—
38	A₄	ΓL(1,𝔽₈)×C₂₉	1	1	yes	characteristic, direct product factor
39	C₃²	—	28	1	no	Sylow
40	C₇	C₃×A₄×C₂₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	21	1	no	—
42	C₂²	C₃×ΓL(1,𝔽₈)×C₂₉	1	1	yes	characteristic, complemented, Sylow
43	C₃	—	4	1	no	—
44	C₃	—	7	1	no	—
45	C₃	—	28	2	no	—
46	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₂₉	A₄×ΓL(1,𝔽₈)
commutator, hypocenter	C₂²×C₇	C₃²×C₂₉
Frattini	C₁	G
Fitting, socle	C₂²×C₇×C₂₉	C₃²
LCS	G ▷ C₂²×C₇
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂₉×C₂²⋊ΓL(1,𝔽₈)	C₃	semidirect
2. C₇×A₄×C₂₉	C₃	semidirect
3. C₂²×ΓL(1,𝔽₈)×C₂₉	C₃	semidirect
7. C₂²×C₇×C₂₉	C₃²	semidirect
10. ΓL(1,𝔽₈)×C₂₉	A₄	direct (N × H)
14. A₄×C₂₉	ΓL(1,𝔽₈)	direct (N × H)
16. A₄×ΓL(1,𝔽₈)	C₂₉	direct (N × H)
17. C₇×C₂₉	C₃×A₄	semidirect
19. C₂²×C₂₉	C₃×ΓL(1,𝔽₈)	semidirect
23. C₂²⋊ΓL(1,𝔽₈)	C₃×C₂₉	semidirect
24. C₇×A₄	C₃×C₂₉	semidirect
25. C₂²×ΓL(1,𝔽₈)	C₃×C₂₉	semidirect
30. C₂₉	A₄×ΓL(1,𝔽₈)	direct (N × H)
31. C₂²×C₇	C₃²×C₂₉	semidirect
34. ΓL(1,𝔽₈)	A₄×C₂₉	direct (N × H)
38. A₄	ΓL(1,𝔽₈)×C₂₉	direct (N × H)
40. C₇	C₃×A₄×C₂₉	semidirect
42. C₂²	C₃×ΓL(1,𝔽₈)×C₂₉	semidirect

Subgroups — A4×ΓL(1,𝔽8)×C29 #20300633

Conjugacy classes of subgroups

Complements

Subgroups — A₄×ΓL(1,𝔽₈)×C₂₉ #20300633