Subgroups — C₂×C₄₃×#64424 #38760510

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	C₄₃×#64424	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₄₃×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₄₃×#3861	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₄₃×C₇⋊D₇	C₂×C₃	1	2	yes	complemented
6	C₂×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×AGL(1,𝔽₇)×C₄₃	—	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	AGL(1,𝔽₇)×C₄₃	—	7	16	no	—
11	C₂×D₇×C₄₃	—	7	8	no	—
12	ΓL(1,𝔽₈)×C₄₃	—	7	8	no	—
13	C₂×C₇×C₄₃	AGL(1,𝔽₇)	1	8	yes	complemented
14	D₇×C₄₃	—	7	16	no	—
15	C₂×#64424	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂²×C₃×C₄₃	—	49	1	no	Hall
17	C₇×C₄₃	C₂×AGL(1,𝔽₇)	1	8	yes	complemented
18	C₂×#3861	C₂×C₄₃	1	1	yes	characteristic, complemented
19	#64424	C₂×C₄₃	1	2	yes	direct product factor
20	C₂×C₃×C₄₃	—	49	2	no	—
21	C₂×C₃×C₄₃	—	49	1	no	—
22	C₂×C₇⋊D₇	C₃×C₄₃	1	1	yes	characteristic, complemented, Hall
23	C₂²×C₄₃	—	49	1	no	Hall
24	#3861	C₂²×C₄₃	1	1	yes	characteristic, complemented, Hall
25	C₃×C₄₃	—	49	1	no	Hall
26	C₂×C₇²	C₂×C₃×C₄₃	1	1	yes	characteristic, complemented
27	C₇⋊D₇	C₂×C₃×C₄₃	1	2	yes	complemented
28	C₂×C₄₃	—	49	2	no	—
29	C₂×C₄₃	#64424	1	1	yes	characteristic, direct product factor
30	C₂×AGL(1,𝔽₇)	—	7	8	no	—
31	C₇²	C₂²×C₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
32	C₄₃	C₂×#64424	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×ΓL(1,𝔽₈)	—	7	8	no	—
34	AGL(1,𝔽₇)	—	7	16	no	—
35	C₂×D₇	—	7	8	no	—
36	ΓL(1,𝔽₈)	—	7	8	no	—
37	C₂×C₇	AGL(1,𝔽₇)×C₄₃	1	8	yes	complemented
38	D₇	—	7	16	no	—
39	C₂²×C₃	—	49	1	no	Hall
40	C₇	C₂×AGL(1,𝔽₇)×C₄₃	1	8	yes	complemented
41	C₂×C₃	—	49	2	no	—
42	C₂×C₃	—	49	1	no	—
43	C₂²	—	49	1	no	Sylow
44	C₃	—	49	1	no	Sylow
45	C₂	—	49	2	no	—
46	C₂	C₄₃×#64424	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₄₃	#64424
commutator, cosocle, hypocenter	C₇²	C₂²×C₃×C₄₃
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₄₃	C₂×C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₄₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#3861	C₂	semidirect
2. C₄₃×#64424	C₂	direct (N × H)
3. C₂×C₄₃×C₇⋊D₇	C₃	semidirect
4. C₄₃×#3861	C₂²	semidirect
5. C₄₃×C₇⋊D₇	C₂×C₃	semidirect
6. C₂×C₇²×C₄₃	C₂×C₃	semidirect
8. C₇²×C₄₃	C₂²×C₃	semidirect
13. C₂×C₇×C₄₃	AGL(1,𝔽₇)	semidirect
15. C₂×#64424	C₄₃	direct (N × H)
17. C₇×C₄₃	C₂×AGL(1,𝔽₇)	semidirect
18. C₂×#3861	C₂×C₄₃	semidirect
19. #64424	C₂×C₄₃	direct (N × H)
22. C₂×C₇⋊D₇	C₃×C₄₃	semidirect
24. #3861	C₂²×C₄₃	semidirect
26. C₂×C₇²	C₂×C₃×C₄₃	semidirect
27. C₇⋊D₇	C₂×C₃×C₄₃	semidirect
29. C₂×C₄₃	#64424	direct (N × H)
31. C₇²	C₂²×C₃×C₄₃	semidirect
32. C₄₃	C₂×#64424	direct (N × H)
37. C₂×C₇	AGL(1,𝔽₇)×C₄₃	semidirect
40. C₇	C₂×AGL(1,𝔽₇)×C₄₃	semidirect
46. C₂	C₄₃×#64424	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
C₄₃×#64424	2
C₂×C₄₃×C₇⋊D₇	3
C₂×AGL(1,𝔽₇)×C₄₃	7
C₂×#64424	43

Subgroups — C2×C43×#64424 #38760510

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#64424 #38760510