Subgroups — C₂×D₄₃×#3862 #38760529

Order 25284.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#3862	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄₃×#3862	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇²×D₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₄₃×#3862	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇²×D₄₃	C₂×C₃	1	2	yes	complemented
6	C₂×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×ΓL(1,𝔽₈)×D₄₃	—	7	2	no	maximal
8	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×ΓL(1,𝔽₈)×C₄₃	—	7	2	no	—
10	ΓL(1,𝔽₈)×D₄₃	—	7	4	no	—
11	C₂×C₇×D₄₃	—	3	2	no	—
12	C₂×C₇×D₄₃	ΓL(1,𝔽₈)	1	2	yes	complemented
13	ΓL(1,𝔽₈)×C₄₃	—	7	2	no	—
14	C₂×C₇×C₄₃	—	3	2	no	—
15	C₂×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
16	C₇×D₄₃	—	3	4	no	—
17	C₇×D₄₃	C₂×ΓL(1,𝔽₈)	1	4	yes	complemented
18	C₂²×#3862	—	43	1	no	maximal, Hall
19	C₂×C₃×D₄₃	—	49	1	no	Hall
20	C₇×C₄₃	—	3	2	no	—
21	C₇×C₄₃	C₂²×ΓL(1,𝔽₈)	1	2	yes	complemented
22	C₂×#3862	—	43	2	no	—
23	C₂×#3862	D₄₃	1	1	yes	characteristic, direct product factor
24	C₂×C₃×C₄₃	—	49	1	no	—
25	C₃×D₄₃	—	49	2	no	—
26	C₂²×C₇²	—	43	1	no	Hall
27	C₂×D₄₃	#3862	1	1	yes	characteristic, direct product factor, Hall
28	#3862	C₂×D₄₃	1	1	yes	characteristic, direct product factor, Hall
29	C₃×C₄₃	—	49	1	no	Hall
30	C₂×C₇²	—	43	2	no	—
31	C₂×C₇²	C₃×D₄₃	1	1	yes	characteristic, complemented
32	C₂×C₄₃	C₂×#3862	1	1	yes	characteristic, complemented
33	D₄₃	C₂×#3862	1	2	yes	direct product factor
34	C₂²×ΓL(1,𝔽₈)	—	301	2	no	—
35	C₇²	C₂×C₃×D₄₃	1	1	yes	characteristic, complemented, Sylow
36	C₄₃	C₂²×#3862	1	1	yes	characteristic, complemented, Sylow
37	C₂×ΓL(1,𝔽₈)	—	7	2	no	—
38	C₂×ΓL(1,𝔽₈)	—	301	4	no	—
39	C₂²×C₇	—	43	2	no	—
40	C₂²×C₇	—	129	2	no	—
41	ΓL(1,𝔽₈)	—	7	2	no	—
42	C₂×C₇	—	3	2	no	—
43	C₂×C₇	—	43	4	no	—
44	C₂×C₇	—	129	4	no	—
45	C₂×C₇	ΓL(1,𝔽₈)×D₄₃	1	2	yes	complemented
46	C₂²×C₃	—	2107	1	no	Hall
47	C₇	—	3	2	no	—
48	C₇	C₂×ΓL(1,𝔽₈)×D₄₃	1	2	yes	complemented
49	C₂×C₃	—	49	1	no	—
50	C₂×C₃	—	2107	2	no	—
51	C₂²	—	43	1	no	Sylow
52	C₃	—	49	1	no	Sylow
53	C₂	—	43	2	no	—
54	C₂	D₄₃×#3862	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₄₃×#3862
commutator, cosocle, hypocenter	C₇²×C₄₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₄₃	C₂×C₃
LCS	G ▷ C₇²×C₄₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#3862	C₂	semidirect
2. D₄₃×#3862	C₂	direct (N × H)
3. C₂×C₇²×D₄₃	C₃	semidirect
4. C₄₃×#3862	C₂²	semidirect
5. C₇²×D₄₃	C₂×C₃	semidirect
6. C₂×C₇²×C₄₃	C₂×C₃	semidirect
8. C₇²×C₄₃	C₂²×C₃	semidirect
12. C₂×C₇×D₄₃	ΓL(1,𝔽₈)	semidirect
15. C₂×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	semidirect
17. C₇×D₄₃	C₂×ΓL(1,𝔽₈)	semidirect
21. C₇×C₄₃	C₂²×ΓL(1,𝔽₈)	semidirect
23. C₂×#3862	D₄₃	direct (N × H)
27. C₂×D₄₃	#3862	direct (N × H)
28. #3862	C₂×D₄₃	direct (N × H)
31. C₂×C₇²	C₃×D₄₃	semidirect
32. C₂×C₄₃	C₂×#3862	semidirect
33. D₄₃	C₂×#3862	direct (N × H)
35. C₇²	C₂×C₃×D₄₃	semidirect
36. C₄₃	C₂²×#3862	semidirect
45. C₂×C₇	ΓL(1,𝔽₈)×D₄₃	semidirect
48. C₇	C₂×ΓL(1,𝔽₈)×D₄₃	semidirect
54. C₂	D₄₃×#3862	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#3862	2
D₄₃×#3862	2
C₂×C₇²×D₄₃	3
C₂×ΓL(1,𝔽₈)×D₄₃	7
C₂²×#3862	43

Subgroups — C2×D43×#3862 #38760529

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄₃×#3862 #38760529