Subgroups — #11744748⋊A₄ #24925607

Order 10836.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#11744749	C₃	1	1	yes	maximal, characteristic, complemented
2	C₄₃×C₂²⋊ΓL(1,𝔽₈)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇×C₂²⋊(C₄₃⋊C₃)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×#11744748	C₃	1	1	yes	maximal, characteristic, complemented
5	ΓL(1,𝔽₈)×C₄₃⋊C₃	—	4	1	no	maximal, Hall
6	C₂×#11744748	—	3	1	no	—
7	A₄×C₄₃⋊C₃	—	7	1	no	maximal, Hall
8	C₂²×C₇×C₄₃	C₃²	1	1	yes	characteristic, complemented, Hall
9	#11744749	—	4	1	no	—
10	#11744748	A₄	1	1	yes	characteristic, complemented
11	C₇×C₄₃⋊C₃	—	4	1	no	—
12	ΓL(1,𝔽₈)×C₄₃	—	4	1	no	—
13	C₂×C₇×C₄₃	—	3	1	no	—
14	C₂²⋊(C₄₃⋊C₃)	—	7	1	no	—
15	C₂²⋊(C₄₃⋊C₃)	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
16	A₄×C₄₃	—	7	1	no	—
17	C₂²×C₄₃⋊C₃	—	7	1	no	—
18	C₃×C₄₃⋊C₃	—	28	1	no	Hall
19	C₇×C₄₃	C₃×A₄	1	1	yes	characteristic, complemented, Hall
20	C₂×C₄₃⋊C₃	—	21	1	no	—
21	A₄×ΓL(1,𝔽₈)	—	43	1	no	maximal, Hall
22	C₂²×C₄₃	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
23	C₃×C₄₃	—	28	1	no	—
24	C₄₃⋊C₃	—	4	1	no	—
25	C₄₃⋊C₃	—	7	1	no	—
26	C₄₃⋊C₃	—	28	1	no	—
27	C₂×C₄₃	—	3	1	no	—
28	C₂²⋊ΓL(1,𝔽₈)	—	43	1	no	—
29	C₂²⋊ΓL(1,𝔽₈)	C₄₃⋊C₃	1	1	yes	characteristic, complemented
30	C₇×A₄	—	43	1	no	—
31	C₂²×ΓL(1,𝔽₈)	—	43	1	no	—
32	C₃×ΓL(1,𝔽₈)	—	172	1	no	Hall
33	C₄₃	A₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
34	C₂×ΓL(1,𝔽₈)	—	129	1	no	—
35	C₃×A₄	—	301	1	no	Hall
36	C₂²×C₇	C₃×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
37	C₃×C₇	—	172	1	no	—
38	ΓL(1,𝔽₈)	—	4	1	no	—
39	ΓL(1,𝔽₈)	—	43	1	no	—
40	ΓL(1,𝔽₈)	—	172	1	no	—
41	C₂×C₇	—	3	1	no	—
42	C₂²×C₃	—	301	1	no	—
43	A₄	—	7	1	no	—
44	A₄	—	43	1	no	—
45	A₄	—	301	1	no	—
46	C₃²	—	1204	1	no	Sylow
47	C₇	A₄×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	—	903	1	no	—
49	C₂²	ΓL(1,𝔽₈)×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
50	C₃	—	28	1	no	—
51	C₃	—	301	1	no	—
52	C₃	—	172	1	no	—
53	C₃	—	1204	1	no	—
54	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂²×C₇×C₄₃	C₃²
LCS	G ▷ C₂²×C₇×C₄₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂²⋊#11744749	C₃	semidirect
2. C₄₃×C₂²⋊ΓL(1,𝔽₈)	C₃	semidirect
3. C₇×C₂²⋊(C₄₃⋊C₃)	C₃	semidirect
4. C₂²×#11744748	C₃	semidirect
8. C₂²×C₇×C₄₃	C₃²	semidirect
10. #11744748	A₄	semidirect
15. C₂²⋊(C₄₃⋊C₃)	ΓL(1,𝔽₈)	semidirect
19. C₇×C₄₃	C₃×A₄	semidirect
22. C₂²×C₄₃	C₃×ΓL(1,𝔽₈)	semidirect
29. C₂²⋊ΓL(1,𝔽₈)	C₄₃⋊C₃	semidirect
33. C₄₃	A₄×ΓL(1,𝔽₈)	semidirect
36. C₂²×C₇	C₃×C₄₃⋊C₃	semidirect
47. C₇	A₄×C₄₃⋊C₃	semidirect
49. C₂²	ΓL(1,𝔽₈)×C₄₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²⋊#11744749	3
C₄₃×C₂²⋊ΓL(1,𝔽₈)	3
C₇×C₂²⋊(C₄₃⋊C₃)	3
C₂²×#11744748	3
ΓL(1,𝔽₈)×C₄₃⋊C₃	4
A₄×C₄₃⋊C₃	7
A₄×ΓL(1,𝔽₈)	43

Subgroups — #11744748⋊A4 #24925607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #11744748⋊A₄ #24925607