Subgroups — C₃×C₇×D₂₆₇ #26014261

Order 11214.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₂₆₇	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₇×D₈₉	—	3	1	no	maximal
4	C₃×C₇×C₈₉	—	2	1	no	—
5	C₃×C₇×C₈₉	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇×C₈₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×D₂₆₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×D₈₉	—	3	1	no	Hall
9	C₃²×C₈₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₈₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	D₂₆₇	C₃×C₇	1	1	yes	characteristic, direct product factor
12	C₃×D₈₉	—	3	1	no	—
13	C₃×C₈₉	—	2	1	no	—
14	C₃×C₈₉	D₃×C₇	1	1	yes	characteristic, complemented
15	C₃×C₈₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
16	D₈₉	—	3	1	no	Hall
17	C₃×D₃×C₇	—	89	1	no	maximal, Hall
18	C₈₉	C₃×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
19	C₃²×C₇	D₈₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₇	—	267	1	no	—
21	D₃×C₇	—	89	1	no	—
22	C₃×C₇	—	2	1	no	—
23	C₃×C₇	C₃×D₈₉	1	1	yes	characteristic, complemented
24	C₃×C₇	D₂₆₇	1	1	yes	characteristic, direct product factor
25	C₃×D₃	—	89	1	no	Hall
26	C₂×C₇	—	267	1	no	Hall
27	C₃²	C₇×D₈₉	1	1	yes	characteristic, complemented, Sylow
28	C₇	C₃×D₂₆₇	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₃	—	267	1	no	—
30	D₃	—	89	1	no	—
31	C₃	—	2	1	no	—
32	C₃	C₃×C₇×D₈₉	1	1	yes	characteristic, complemented
33	C₃	C₇×D₂₆₇	1	1	yes	characteristic, direct product factor
34	C₂	—	267	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇	D₂₆₇
commutator, cosocle, hypocenter	C₃×C₈₉	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₈₉	C₂
LCS	G ▷ C₃×C₈₉
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₈₉	C₂	semidirect
2. C₇×D₂₆₇	C₃	direct (N × H)
5. C₃×C₇×C₈₉	D₃	semidirect
6. C₃×C₇×C₈₉	C₂×C₃	semidirect
7. C₃×D₂₆₇	C₇	direct (N × H)
9. C₃²×C₈₉	C₂×C₇	semidirect
10. C₇×C₈₉	C₃×D₃	semidirect
11. D₂₆₇	C₃×C₇	direct (N × H)
14. C₃×C₈₉	D₃×C₇	semidirect
15. C₃×C₈₉	C₂×C₃×C₇	semidirect
18. C₈₉	C₃×D₃×C₇	semidirect
19. C₃²×C₇	D₈₉	semidirect
23. C₃×C₇	C₃×D₈₉	semidirect
24. C₃×C₇	D₂₆₇	direct (N × H)
27. C₃²	C₇×D₈₉	semidirect
28. C₇	C₃×D₂₆₇	direct (N × H)
32. C₃	C₃×C₇×D₈₉	semidirect
33. C₃	C₇×D₂₆₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₇×C₈₉	2
C₇×D₂₆₇	3
C₃×C₇×D₈₉	3
C₃×D₂₆₇	7
C₃×D₃×C₇	89

Subgroups — C3×C7×D267 #26014261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×D₂₆₇ #26014261