Subgroups — C₂×C₃×C₄₉×D₄₃ #38760266

Order 25284.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₉×D₄₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₄₃×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₉×D₄₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₄₃×C₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₄₉×D₄₃	C₂×C₃	1	2	yes	direct product factor
6	C₂×C₄₃×C₄₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₃×C₇×D₄₃	C₇	1	1	yes	maximal, characteristic
8	C₄₃×C₄₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₇×C₄₃	C₂×C₇	1	1	yes	characteristic
10	C₃×C₇×D₄₃	C₂×C₇	1	2	yes	—
11	C₂×C₇×D₄₃	C₃×C₇	1	1	yes	characteristic
12	C₃×C₇×C₄₃	C₂²×C₇	1	1	yes	characteristic
13	C₂×C₇×C₄₃	C₂×C₃×C₇	1	1	yes	characteristic
14	C₇×D₄₃	C₂×C₃×C₇	1	2	yes	—
15	C₂²×C₃×C₄₉	—	43	1	no	maximal, Hall
16	C₂×C₃×D₄₃	C₄₉	1	1	yes	characteristic, direct product factor, Hall
17	C₇×C₄₃	C₂²×C₃×C₇	1	1	yes	characteristic
18	C₂×C₃×C₄₉	—	43	2	no	—
19	C₂×C₃×C₄₉	D₄₃	1	1	yes	characteristic, direct product factor
20	C₂×C₃×C₄₃	C₂×C₄₉	1	1	yes	characteristic, complemented
21	C₃×D₄₃	C₂×C₄₉	1	2	yes	direct product factor
22	C₂²×C₄₉	—	43	1	no	Hall
23	C₂×D₄₃	C₃×C₄₉	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₄₉	C₂×D₄₃	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₄₃	C₂²×C₄₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₄₉	—	43	2	no	—
27	C₂×C₄₉	C₃×D₄₃	1	1	yes	characteristic, direct product factor
28	C₂×C₄₃	C₂×C₃×C₄₉	1	1	yes	characteristic, complemented
29	D₄₃	C₂×C₃×C₄₉	1	2	yes	direct product factor
30	C₂²×C₃×C₇	—	43	1	no	—
31	C₄₉	C₂×C₃×D₄₃	1	1	yes	characteristic, direct product factor, Sylow
32	C₄₃	C₂²×C₃×C₄₉	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃×C₇	—	43	2	no	—
34	C₂×C₃×C₇	C₇×D₄₃	1	1	yes	characteristic
35	C₂²×C₇	—	43	1	no	—
36	C₃×C₇	C₂×C₇×D₄₃	1	1	yes	characteristic
37	C₂×C₇	—	43	2	no	—
38	C₂×C₇	C₃×C₇×D₄₃	1	1	yes	characteristic
39	C₂²×C₃	—	43	1	no	Hall
40	C₇	C₂×C₃×C₇×D₄₃	1	1	yes	characteristic
41	C₂×C₃	—	43	2	no	—
42	C₂×C₃	C₄₉×D₄₃	1	1	yes	characteristic, direct product factor
43	C₂²	—	43	1	no	Sylow
44	C₃	C₂×C₄₉×D₄₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	43	2	no	—
46	C₂	C₃×C₄₉×D₄₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₄₉	D₄₃
commutator, hypocenter	C₄₃	C₂²×C₃×C₄₉
Frattini	C₇	C₂×C₃×C₇×D₄₃
Fitting	C₂×C₃×C₄₃×C₄₉	C₂
socle	C₂×C₃×C₇×C₄₃	C₂×C₇
prime radical	C₂×C₃×C₇×D₄₃	C₇
cosocle	C₇×C₄₃	C₂²×C₃×C₇
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂×C₃×C₄₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₄₉×D₄₃	C₂	direct (N × H)
2. C₂×C₃×C₄₃×C₄₉	C₂	semidirect
3. C₂×C₄₉×D₄₃	C₃	direct (N × H)
4. C₃×C₄₃×C₄₉	C₂²	semidirect
5. C₄₉×D₄₃	C₂×C₃	direct (N × H)
6. C₂×C₄₃×C₄₉	C₂×C₃	semidirect
8. C₄₃×C₄₉	C₂²×C₃	semidirect
16. C₂×C₃×D₄₃	C₄₉	direct (N × H)
19. C₂×C₃×C₄₉	D₄₃	direct (N × H)
20. C₂×C₃×C₄₃	C₂×C₄₉	semidirect
21. C₃×D₄₃	C₂×C₄₉	direct (N × H)
23. C₂×D₄₃	C₃×C₄₉	direct (N × H)
24. C₃×C₄₉	C₂×D₄₃	direct (N × H)
25. C₃×C₄₃	C₂²×C₄₉	semidirect
27. C₂×C₄₉	C₃×D₄₃	direct (N × H)
28. C₂×C₄₃	C₂×C₃×C₄₉	semidirect
29. D₄₃	C₂×C₃×C₄₉	direct (N × H)
31. C₄₉	C₂×C₃×D₄₃	direct (N × H)
32. C₄₃	C₂²×C₃×C₄₉	semidirect
42. C₂×C₃	C₄₉×D₄₃	direct (N × H)
44. C₃	C₂×C₄₉×D₄₃	direct (N × H)
46. C₂	C₃×C₄₉×D₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄₉×D₄₃	2
C₂×C₃×C₄₃×C₄₉	2
C₂×C₄₉×D₄₃	3
C₂×C₃×C₇×D₄₃	7
C₂²×C₃×C₄₉	43

Subgroups — C2×C3×C49×D43 #38760266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄₉×D₄₃ #38760266