Subgroups — C₂×D₄₃×#3861 #38760509

Order 25284.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#3861	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄₃×#3861	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇²×D₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₄₃×#3861	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	8	no	maximal
8	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×ΓL(1,𝔽₈)×C₄₃	—	7	8	no	—
10	ΓL(1,𝔽₈)×D₄₃	—	7	16	no	—
11	C₂×C₇×D₄₃	ΓL(1,𝔽₈)	1	8	yes	complemented
12	ΓL(1,𝔽₈)×C₄₃	—	7	8	no	—
13	C₂×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
14	C₇×D₄₃	C₂×ΓL(1,𝔽₈)	1	16	yes	complemented
15	C₂²×#3861	—	43	1	no	maximal, Hall
16	C₂×C₃×D₄₃	—	49	1	no	Hall
17	C₇×C₄₃	C₂²×ΓL(1,𝔽₈)	1	8	yes	complemented
18	C₂×#3861	—	43	2	no	—
19	C₂×#3861	D₄₃	1	1	yes	characteristic, direct product factor
20	C₂×C₃×C₄₃	—	49	1	no	—
21	C₃×D₄₃	—	49	2	no	—
22	C₂²×C₇²	—	43	1	no	Hall
23	C₂×D₄₃	#3861	1	1	yes	characteristic, direct product factor, Hall
24	#3861	C₂×D₄₃	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₄₃	—	49	1	no	Hall
26	C₂×C₇²	—	43	2	no	—
27	C₂×C₇²	C₃×D₄₃	1	1	yes	characteristic, complemented
28	C₂×C₄₃	C₂×#3861	1	1	yes	characteristic, complemented
29	D₄₃	C₂×#3861	1	2	yes	direct product factor
30	C₂²×ΓL(1,𝔽₈)	—	301	8	no	—
31	C₇²	C₂×C₃×D₄₃	1	1	yes	characteristic, complemented, Sylow
32	C₄₃	C₂²×#3861	1	1	yes	characteristic, complemented, Sylow
33	C₂×ΓL(1,𝔽₈)	—	7	8	no	—
34	C₂×ΓL(1,𝔽₈)	—	301	16	no	—
35	C₂²×C₇	—	43	8	no	—
36	ΓL(1,𝔽₈)	—	7	8	no	—
37	C₂×C₇	—	43	16	no	—
38	C₂×C₇	ΓL(1,𝔽₈)×D₄₃	1	8	yes	complemented
39	C₂²×C₃	—	2107	1	no	Hall
40	C₇	C₂×ΓL(1,𝔽₈)×D₄₃	1	8	yes	complemented
41	C₂×C₃	—	49	1	no	—
42	C₂×C₃	—	2107	2	no	—
43	C₂²	—	43	1	no	Sylow
44	C₃	—	49	1	no	Sylow
45	C₂	—	43	2	no	—
46	C₂	D₄₃×#3861	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₄₃×#3861
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×#3861	C₂	semidirect
2. D₄₃×#3861	C₂	direct (N × H)
3. C₂×C₇²×D₄₃	C₃	semidirect
4. C₄₃×#3861	C₂²	semidirect
5. C₇²×D₄₃	C₂×C₃	semidirect
6. C₂×C₇²×C₄₃	C₂×C₃	semidirect
8. C₇²×C₄₃	C₂²×C₃	semidirect
11. C₂×C₇×D₄₃	ΓL(1,𝔽₈)	semidirect
13. C₂×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	semidirect
14. C₇×D₄₃	C₂×ΓL(1,𝔽₈)	semidirect
17. C₇×C₄₃	C₂²×ΓL(1,𝔽₈)	semidirect
19. C₂×#3861	D₄₃	direct (N × H)
23. C₂×D₄₃	#3861	direct (N × H)
24. #3861	C₂×D₄₃	direct (N × H)
27. C₂×C₇²	C₃×D₄₃	semidirect
28. C₂×C₄₃	C₂×#3861	semidirect
29. D₄₃	C₂×#3861	direct (N × H)
31. C₇²	C₂×C₃×D₄₃	semidirect
32. C₄₃	C₂²×#3861	semidirect
38. C₂×C₇	ΓL(1,𝔽₈)×D₄₃	semidirect
40. C₇	C₂×ΓL(1,𝔽₈)×D₄₃	semidirect
46. C₂	D₄₃×#3861	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×#3861	2
D₄₃×#3861	2
C₂×C₇²×D₄₃	3
C₂×ΓL(1,𝔽₈)×D₄₃	7
C₂²×#3861	43

Subgroups — C2×D43×#3861 #38760509

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄₃×#3861 #38760509