Subgroups — C₇×C₄₃×D₆₃ #49181608

Order 37926.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₉×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₂₁×C₄₃	—	3	1	no	maximal
3	C₃×C₇²×C₄₃	D₃	1	1	yes	characteristic
4	C₄₃×D₆₃	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₇×D₉×C₄₃	—	7	1	no	maximal
6	C₇×D₇×C₄₃	—	9	1	no	Hall
7	C₇×C₉×C₄₃	—	2	3	no	—
8	C₇×C₉×C₄₃	D₇	1	1	yes	characteristic, complemented
9	C₇×C₉×C₄₃	C₂×C₇	1	1	yes	characteristic, complemented
10	C₇²×C₄₃	D₉	1	1	yes	characteristic, complemented, Hall
11	D₂₁×C₄₃	—	3	1	no	—
12	D₃×C₇×C₄₃	—	21	1	no	—
13	C₃×C₇×C₄₃	—	2	3	no	—
14	C₃×C₇×C₄₃	D₃×C₇	1	1	yes	characteristic
15	C₃×C₇×C₄₃	D₂₁	1	1	yes	characteristic
16	C₇×D₆₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	D₉×C₄₃	—	7	1	no	Hall
18	C₂×C₇×C₄₃	—	63	1	no	—
19	D₇×C₄₃	—	9	1	no	—
20	C₇²×C₉	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
21	C₉×C₄₃	C₇×D₇	1	1	yes	characteristic, complemented, Hall
22	C₇×C₄₃	—	2	3	no	—
23	C₇×C₄₃	C₇×D₉	1	1	yes	characteristic, complemented
24	C₇×C₄₃	D₆₃	1	1	yes	characteristic, direct product factor
25	C₇×D₂₁	—	3	1	no	—
26	D₃×C₄₃	—	21	1	no	—
27	C₃×C₇²	D₃×C₄₃	1	1	yes	characteristic
28	C₃×C₄₃	C₇×D₂₁	1	1	yes	characteristic
29	D₆₃	C₇×C₄₃	1	1	yes	characteristic, direct product factor
30	C₇×D₉	—	7	1	no	—
31	C₇×D₇	—	9	1	no	Hall
32	C₂×C₄₃	—	63	1	no	Hall
33	C₇×C₉	—	2	3	no	—
34	C₇×C₉	D₇×C₄₃	1	1	yes	characteristic, complemented
35	C₇×C₉	C₂×C₇×C₄₃	1	1	yes	characteristic, complemented
36	C₇²	D₉×C₄₃	1	1	yes	characteristic, complemented, Sylow
37	C₄₃	C₇×D₆₃	1	1	yes	characteristic, direct product factor, Sylow
38	D₂₁	—	3	1	no	—
39	D₃×C₇	—	21	1	no	—
40	C₃×C₇	—	2	3	no	—
41	C₃×C₇	D₃×C₇×C₄₃	1	1	yes	characteristic
42	C₃×C₇	D₂₁×C₄₃	1	1	yes	characteristic
43	D₉	—	7	1	no	Hall
44	C₂×C₇	—	63	1	no	—
45	D₇	—	9	1	no	—
46	C₉	C₇×D₇×C₄₃	1	1	yes	characteristic, complemented, Sylow
47	C₇	—	2	3	no	—
48	C₇	C₇×D₉×C₄₃	1	1	yes	characteristic, complemented
49	C₇	C₄₃×D₆₃	1	1	yes	characteristic, direct product factor
50	D₃	—	21	1	no	—
51	C₃	C₇×D₂₁×C₄₃	1	1	yes	characteristic
52	C₂	—	63	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₄₃	D₆₃
commutator, cosocle, hypocenter	C₇×C₉	C₂×C₇×C₄₃
Frattini	C₃	C₇×D₂₁×C₄₃
Fitting	C₇²×C₉×C₄₃	C₂
socle	C₃×C₇²×C₄₃	D₃
LCS	G ▷ C₇×C₉
UCS	C₁ ◁ C₇×C₄₃

Complements

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

N	H ≅ G/N	type
1. C₇²×C₉×C₄₃	C₂	semidirect
4. C₄₃×D₆₃	C₇	direct (N × H)
8. C₇×C₉×C₄₃	D₇	semidirect
9. C₇×C₉×C₄₃	C₂×C₇	semidirect
10. C₇²×C₄₃	D₉	semidirect
16. C₇×D₆₃	C₄₃	direct (N × H)
20. C₇²×C₉	C₂×C₄₃	semidirect
21. C₉×C₄₃	C₇×D₇	semidirect
23. C₇×C₄₃	C₇×D₉	semidirect
24. C₇×C₄₃	D₆₃	direct (N × H)
29. D₆₃	C₇×C₄₃	direct (N × H)
34. C₇×C₉	D₇×C₄₃	semidirect
35. C₇×C₉	C₂×C₇×C₄₃	semidirect
36. C₇²	D₉×C₄₃	semidirect
37. C₄₃	C₇×D₆₃	direct (N × H)
46. C₉	C₇×D₇×C₄₃	semidirect
48. C₇	C₇×D₉×C₄₃	semidirect
49. C₇	C₄₃×D₆₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇²×C₉×C₄₃	2
C₇×D₂₁×C₄₃	3
C₄₃×D₆₃	7
C₇×D₉×C₄₃	7
C₇×D₆₃	43

Subgroups — C7×C43×D63 #49181608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₄₃×D₆₃ #49181608