Subgroups — C₂×C₄₃×#64418 #38760481

Order 25284.

68 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	C₄₃×#64418	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇×D₇×C₄₃	—	3	1	no	maximal, Hall
4	C₄₃×#3862	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×D₇×C₄₃	—	3	2	no	—
6	C₂×C₇²×C₄₃	D₃	1	1	yes	characteristic, complemented
7	C₇²×C₄₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×ΓL(1,𝔽₈)×C₄₃	—	14	1	no	—
9	C₂²×C₇×C₄₃	—	21	1	no	—
10	C₂×D₇×C₄₃	—	3	1	no	—
11	ΓL(1,𝔽₈)×C₄₃	—	14	1	no	—
12	C₂×C₇×C₄₃	—	2	1	no	—
13	C₂×C₇×C₄₃	—	3	1	no	—
14	C₂×C₇×C₄₃	—	3	1	no	—
15	C₂×C₇×C₄₃	—	21	2	no	—
16	D₇×C₄₃	—	3	2	no	—
17	C₂×#64418	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂×D₃×C₄₃	—	49	1	no	maximal, Hall
19	C₇×C₄₃	—	2	1	no	—
20	C₇×C₄₃	—	3	1	no	—
21	C₇×C₄₃	—	3	1	no	—
22	C₂×#3862	C₂×C₄₃	1	1	yes	characteristic, complemented
23	#64418	C₂×C₄₃	1	2	yes	direct product factor
24	C₂×C₃×C₄₃	—	49	1	no	—
25	D₃×C₄₃	—	49	2	no	—
26	C₂×C₇×D₇	—	3	1	no	Hall
27	C₂²×C₄₃	—	21	1	no	Hall
28	#3862	C₂²×C₄₃	1	1	yes	characteristic, complemented, Hall
29	C₃×C₄₃	—	49	1	no	Hall
30	C₂×C₇²	D₃×C₄₃	1	1	yes	characteristic, complemented
31	C₇×D₇	—	3	2	no	—
32	C₂×C₄₃	—	21	2	no	—
33	C₂×C₄₃	#64418	1	1	yes	characteristic, direct product factor
34	C₇²	C₂×D₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
35	C₄₃	C₂×#64418	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×ΓL(1,𝔽₈)	—	14	1	no	—
37	C₂²×C₇	—	21	1	no	—
38	C₂×D₇	—	3	1	no	—
39	ΓL(1,𝔽₈)	—	14	1	no	—
40	C₂×C₇	—	2	1	no	—
41	C₂×C₇	—	3	1	no	—
42	C₂×C₇	—	3	1	no	—
43	C₂×C₇	—	21	2	no	—
44	D₇	—	3	2	no	—
45	C₂×D₃	—	49	1	no	Hall
46	C₇	—	2	1	no	—
47	C₇	—	3	1	no	—
48	C₇	—	3	1	no	—
49	C₂×C₃	—	49	1	no	—
50	D₃	—	49	2	no	—
51	C₂²	—	21	1	no	Sylow
52	C₃	—	49	1	no	Sylow
53	C₂	—	21	2	no	—
54	C₂	C₄₃×#64418	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₄₃	#64418
commutator, cosocle, hypocenter	#3862	C₂²×C₄₃
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₄₃	D₃
LCS	G ▷ #3862
UCS	C₁ ◁ C₂×C₄₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#3862	C₂	semidirect
2. C₄₃×#64418	C₂	direct (N × H)
4. C₄₃×#3862	C₂²	semidirect
6. C₂×C₇²×C₄₃	D₃	semidirect
7. C₇²×C₄₃	C₂×D₃	semidirect
17. C₂×#64418	C₄₃	direct (N × H)
22. C₂×#3862	C₂×C₄₃	semidirect
23. #64418	C₂×C₄₃	direct (N × H)
28. #3862	C₂²×C₄₃	semidirect
30. C₂×C₇²	D₃×C₄₃	semidirect
33. C₂×C₄₃	#64418	direct (N × H)
34. C₇²	C₂×D₃×C₄₃	semidirect
35. C₄₃	C₂×#64418	direct (N × H)
54. C₂	C₄₃×#64418	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
C₄₃×#64418	2
C₂×C₇×D₇×C₄₃	3
C₂×#64418	43
C₂×D₃×C₄₃	49

Subgroups — C2×C43×#64418 #38760481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#64418 #38760481