Subgroups — C₇×D₂₁×C₄₃ #27162458

Order 12642.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₇×C₄₃	—	3	1	no	maximal, Hall
3	C₇²×C₄₃	D₃	1	1	yes	characteristic, complemented, Hall
4	D₂₁×C₄₃	C₇	1	1	yes	maximal, characteristic, direct product factor
5	D₃×C₇×C₄₃	—	7	1	no	maximal
6	C₃×C₇×C₄₃	—	2	3	no	—
7	C₃×C₇×C₄₃	D₇	1	1	yes	characteristic, complemented
8	C₃×C₇×C₄₃	C₂×C₇	1	1	yes	characteristic, complemented
9	C₂×C₇×C₄₃	—	21	1	no	—
10	D₇×C₄₃	—	3	1	no	—
11	C₇×C₄₃	—	2	3	no	—
12	C₇×C₄₃	D₃×C₇	1	1	yes	characteristic, complemented
13	C₇×C₄₃	D₂₁	1	1	yes	characteristic, direct product factor
14	C₇×D₂₁	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	D₃×C₄₃	—	7	1	no	Hall
16	C₃×C₇²	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
17	C₃×C₄₃	C₇×D₇	1	1	yes	characteristic, complemented, Hall
18	C₇×D₇	—	3	1	no	Hall
19	C₂×C₄₃	—	21	1	no	Hall
20	C₇²	D₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
21	C₄₃	C₇×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
22	D₂₁	C₇×C₄₃	1	1	yes	characteristic, direct product factor
23	D₃×C₇	—	7	1	no	—
24	C₃×C₇	—	2	3	no	—
25	C₃×C₇	D₇×C₄₃	1	1	yes	characteristic, complemented
26	C₃×C₇	C₂×C₇×C₄₃	1	1	yes	characteristic, complemented
27	C₂×C₇	—	21	1	no	—
28	D₇	—	3	1	no	—
29	C₇	—	2	3	no	—
30	C₇	D₃×C₇×C₄₃	1	1	yes	characteristic, complemented
31	C₇	D₂₁×C₄₃	1	1	yes	characteristic, direct product factor
32	D₃	—	7	1	no	Hall
33	C₃	C₇×D₇×C₄₃	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	21	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₇²×C₄₃	C₂	semidirect
3. C₇²×C₄₃	D₃	semidirect
4. D₂₁×C₄₃	C₇	direct (N × H)
7. C₃×C₇×C₄₃	D₇	semidirect
8. C₃×C₇×C₄₃	C₂×C₇	semidirect
12. C₇×C₄₃	D₃×C₇	semidirect
13. C₇×C₄₃	D₂₁	direct (N × H)
14. C₇×D₂₁	C₄₃	direct (N × H)
16. C₃×C₇²	C₂×C₄₃	semidirect
17. C₃×C₄₃	C₇×D₇	semidirect
20. C₇²	D₃×C₄₃	semidirect
21. C₄₃	C₇×D₂₁	direct (N × H)
22. D₂₁	C₇×C₄₃	direct (N × H)
25. C₃×C₇	D₇×C₄₃	semidirect
26. C₃×C₇	C₂×C₇×C₄₃	semidirect
30. C₇	D₃×C₇×C₄₃	semidirect
31. C₇	D₂₁×C₄₃	direct (N × H)
33. C₃	C₇×D₇×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇²×C₄₃	2
C₇×D₇×C₄₃	3
D₂₁×C₄₃	7
D₃×C₇×C₄₃	7
C₇×D₂₁	43

Subgroups — C7×D21×C43 #27162458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₂₁×C₄₃ #27162458