Subgroups — C₇²×Dic₃×C₄₃ #38760367

Order 25284.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇²×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇²×C₄₃	—	3	1	no	maximal, Hall
3	C₃×C₇²×C₄₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇²×C₄₃	D₃	1	1	yes	characteristic
5	C₇×Dic₃×C₄₃	C₇	1	8	yes	maximal, direct product factor
6	C₇²×C₄₃	Dic₃	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₇×C₄₃	C₂×C₇	1	8	yes	—
8	C₄×C₇×C₄₃	—	3	8	no	—
9	C₃×C₇×C₄₃	C₄×C₇	1	8	yes	complemented
10	C₂×C₇×C₄₃	D₃×C₇	1	8	yes	—
11	C₇²×Dic₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	Dic₃×C₄₃	C₇²	1	1	yes	characteristic, direct product factor, Hall
13	C₇×C₄₃	C₇×Dic₃	1	8	yes	direct product factor
14	C₂×C₃×C₇²	C₂×C₄₃	1	1	yes	characteristic
15	C₂×C₃×C₄₃	C₂×C₇²	1	1	yes	characteristic
16	C₄×C₇²	—	3	1	no	Hall
17	C₄×C₄₃	—	3	1	no	Hall
18	C₃×C₇²	C₄×C₄₃	1	1	yes	characteristic, complemented, Hall
19	C₃×C₄₃	C₄×C₇²	1	1	yes	characteristic, complemented, Hall
20	C₂×C₇²	D₃×C₄₃	1	1	yes	characteristic
21	C₂×C₄₃	D₃×C₇²	1	1	yes	characteristic
22	C₇×Dic₃	C₇×C₄₃	1	8	yes	direct product factor
23	C₇²	Dic₃×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₄₃	C₇²×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₃×C₇	C₂×C₇×C₄₃	1	8	yes	—
26	C₄×C₇	—	3	8	no	—
27	C₃×C₇	C₄×C₇×C₄₃	1	8	yes	complemented
28	C₂×C₇	D₃×C₇×C₄₃	1	8	yes	—
29	Dic₃	C₇²×C₄₃	1	1	yes	characteristic, direct product factor, Hall
30	C₇	C₇×Dic₃×C₄₃	1	8	yes	direct product factor
31	C₂×C₃	C₂×C₇²×C₄₃	1	1	yes	characteristic
32	C₄	—	3	1	no	Sylow
33	C₃	C₄×C₇²×C₄₃	1	1	yes	characteristic, complemented, Sylow
34	C₂	D₃×C₇²×C₄₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇²×C₄₃	D₃
commutator, hypocenter	C₃	C₄×C₇²×C₄₃
Frattini	C₂	D₃×C₇²×C₄₃
Fitting, socle, prime radical	C₂×C₃×C₇²×C₄₃	C₂
cosocle	C₂×C₃	C₂×C₇²×C₄₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₇²×C₄₃

Complements

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

N	H ≅ G/N	type
3. C₃×C₇²×C₄₃	C₄	semidirect
5. C₇×Dic₃×C₄₃	C₇	direct (N × H)
6. C₇²×C₄₃	Dic₃	direct (N × H)
9. C₃×C₇×C₄₃	C₄×C₇	semidirect
11. C₇²×Dic₃	C₄₃	direct (N × H)
12. Dic₃×C₄₃	C₇²	direct (N × H)
13. C₇×C₄₃	C₇×Dic₃	direct (N × H)
18. C₃×C₇²	C₄×C₄₃	semidirect
19. C₃×C₄₃	C₄×C₇²	semidirect
22. C₇×Dic₃	C₇×C₄₃	direct (N × H)
23. C₇²	Dic₃×C₄₃	direct (N × H)
24. C₄₃	C₇²×Dic₃	direct (N × H)
27. C₃×C₇	C₄×C₇×C₄₃	semidirect
29. Dic₃	C₇²×C₄₃	direct (N × H)
30. C₇	C₇×Dic₃×C₄₃	direct (N × H)
33. C₃	C₄×C₇²×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇²×C₄₃	2
C₄×C₇²×C₄₃	3
C₇×Dic₃×C₄₃	7
C₇²×Dic₃	43

Subgroups — C72×Dic3×C43 #38760367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇²×Dic₃×C₄₃ #38760367