Subgroups — C₂²×C₃×C₄₃⋊C₄₉ #38760237

Order 25284.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄₃⋊C₄₉	C₂	direct (N × H)
2. C₂²×C₄₃⋊C₄₉	C₃	direct (N × H)
3. C₃×C₄₃⋊C₄₉	C₂²	direct (N × H)
4. C₂×C₄₃⋊C₄₉	C₂×C₃	direct (N × H)
6. C₄₃⋊C₄₉	C₂²×C₃	direct (N × H)
12. C₂²×C₃×C₄₃	C₄₉	semidirect
15. C₂×C₃×C₄₃	C₂×C₄₉	semidirect
17. C₂²×C₄₃	C₃×C₄₉	semidirect
19. C₃×C₄₃	C₂²×C₄₉	semidirect
21. C₂×C₄₃	C₂×C₃×C₄₉	semidirect
24. C₄₃	C₂²×C₃×C₄₉	semidirect
29. C₂²×C₃	C₄₃⋊C₄₉	direct (N × H)
31. C₂×C₃	C₂×C₄₃⋊C₄₉	direct (N × H)
32. C₂²	C₃×C₄₃⋊C₄₉	direct (N × H)
33. C₃	C₂²×C₄₃⋊C₄₉	direct (N × H)
34. C₂	C₂×C₃×C₄₃⋊C₄₉	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×C₃×C₄₃⋊C₄₉	2
C₂²×C₄₃⋊C₄₉	3
C₂²×C₃×C₇×C₄₃	7
C₂²×C₃×C₄₉	43

Subgroups — C22×C3×C43⋊C49 #38760237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₄₃⋊C₄₉ #38760237