Subgroups — C₇×D₂₂₈₉ #44545271

Order 32046.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₇₆₃	—	3	1	no	maximal, Hall
3	C₇²×C₁₀₉	D₃	1	1	yes	characteristic, complemented, Hall
4	D₂₂₈₉	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₇×D₃₂₇	—	7	1	no	maximal
6	C₃×C₇×C₁₀₉	—	2	3	no	—
7	C₃×C₇×C₁₀₉	D₇	1	1	yes	characteristic, complemented
8	C₃×C₇×C₁₀₉	C₂×C₇	1	1	yes	characteristic, complemented
9	D₇₆₃	—	3	1	no	—
10	C₇×D₁₀₉	—	21	1	no	—
11	C₇×C₁₀₉	—	2	3	no	—
12	C₇×C₁₀₉	D₃×C₇	1	1	yes	characteristic, complemented
13	C₇×C₁₀₉	D₂₁	1	1	yes	characteristic, complemented
14	D₃₂₇	—	7	1	no	Hall
15	C₃×C₁₀₉	C₇×D₇	1	1	yes	characteristic, complemented, Hall
16	C₇×D₂₁	—	109	1	no	maximal, Hall
17	D₁₀₉	—	21	1	no	Hall
18	C₃×C₇²	D₁₀₉	1	1	yes	characteristic, complemented, Hall
19	C₁₀₉	C₇×D₂₁	1	1	yes	characteristic, complemented, Sylow
20	C₇×D₇	—	327	1	no	Hall
21	C₇²	D₃₂₇	1	1	yes	characteristic, complemented, Sylow
22	D₂₁	—	109	1	no	—
23	D₃×C₇	—	763	1	no	—
24	C₃×C₇	—	2	3	no	—
25	C₃×C₇	C₇×D₁₀₉	1	1	yes	characteristic, complemented
26	C₃×C₇	D₇₆₃	1	1	yes	characteristic, complemented
27	C₂×C₇	—	2289	1	no	—
28	D₇	—	327	1	no	—
29	C₇	—	2	3	no	—
30	C₇	C₇×D₃₂₇	1	1	yes	characteristic, complemented
31	C₇	D₂₂₈₉	1	1	yes	characteristic, direct product factor
32	D₃	—	763	1	no	Hall
33	C₃	C₇×D₇₆₃	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	2289	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₂₂₈₉
commutator, cosocle, hypocenter	C₃×C₇×C₁₀₉	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₀₉	C₂
LCS	G ▷ C₃×C₇×C₁₀₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇²×C₁₀₉	C₂	semidirect
3. C₇²×C₁₀₉	D₃	semidirect
4. D₂₂₈₉	C₇	direct (N × H)
7. C₃×C₇×C₁₀₉	D₇	semidirect
8. C₃×C₇×C₁₀₉	C₂×C₇	semidirect
12. C₇×C₁₀₉	D₃×C₇	semidirect
13. C₇×C₁₀₉	D₂₁	semidirect
15. C₃×C₁₀₉	C₇×D₇	semidirect
18. C₃×C₇²	D₁₀₉	semidirect
19. C₁₀₉	C₇×D₂₁	semidirect
21. C₇²	D₃₂₇	semidirect
25. C₃×C₇	C₇×D₁₀₉	semidirect
26. C₃×C₇	D₇₆₃	semidirect
30. C₇	C₇×D₃₂₇	semidirect
31. C₇	D₂₂₈₉	direct (N × H)
33. C₃	C₇×D₇₆₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇²×C₁₀₉	2
C₇×D₇₆₃	3
D₂₂₈₉	7
C₇×D₃₂₇	7
C₇×D₂₁	109

Subgroups — C7×D2289 #44545271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₂₂₈₉ #44545271