Subgroups — C₃×D₁₁×D₈₉ #26044339

Order 11748.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₉₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₁×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₁×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₁×D₈₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₁×C₈₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₉₇₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₁×D₈₉	C₂×C₃	1	1	yes	characteristic, complemented
8	D₁₁×C₈₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×C₃×D₈₉	—	11	1	no	maximal, Hall
10	C₁₁×C₈₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₈₉	—	11	1	no	—
12	C₃×D₈₉	—	11	1	no	—
13	C₃×D₈₉	D₁₁	1	1	yes	characteristic, direct product factor
14	C₂×D₈₉	—	11	1	no	Hall
15	C₃×C₈₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₈₉	—	11	1	no	—
17	D₈₉	—	11	1	no	—
18	D₈₉	C₃×D₁₁	1	1	yes	characteristic, direct product factor
19	C₂×C₃×D₁₁	—	89	1	no	maximal, Hall
20	C₈₉	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₁₁	—	89	1	no	—
22	C₃×D₁₁	—	89	1	no	—
23	C₃×D₁₁	D₈₉	1	1	yes	characteristic, direct product factor
24	C₂×D₁₁	—	89	1	no	Hall
25	C₃×C₁₁	C₂×D₈₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₁	—	89	1	no	—
27	D₁₁	—	89	1	no	—
28	D₁₁	C₃×D₈₉	1	1	yes	characteristic, direct product factor
29	C₂²×C₃	—	979	1	no	Hall
30	C₁₁	C₂×C₃×D₈₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	11	1	no	—
32	C₂×C₃	—	89	1	no	—
33	C₂×C₃	—	979	1	no	—
34	C₂²	—	979	1	no	Sylow
35	C₃	D₁₁×D₈₉	1	1	yes	characteristic, direct product factor, Sylow
36	C₂	—	11	1	no	—
37	C₂	—	89	1	no	—
38	C₂	—	979	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₁₁×D₈₉
commutator, cosocle, hypocenter	C₁₁×C₈₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₈₉	C₂²
LCS	G ▷ C₁₁×C₈₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₉₇₉	C₂	semidirect
2. C₃×D₁₁×C₈₉	C₂	semidirect
3. C₃×C₁₁×D₈₉	C₂	semidirect
4. D₁₁×D₈₉	C₃	direct (N × H)
5. C₃×C₁₁×C₈₉	C₂²	semidirect
6. D₉₇₉	C₂×C₃	semidirect
7. C₁₁×D₈₉	C₂×C₃	semidirect
8. D₁₁×C₈₉	C₂×C₃	semidirect
10. C₁₁×C₈₉	C₂²×C₃	semidirect
13. C₃×D₈₉	D₁₁	direct (N × H)
15. C₃×C₈₉	C₂×D₁₁	semidirect
18. D₈₉	C₃×D₁₁	direct (N × H)
20. C₈₉	C₂×C₃×D₁₁	semidirect
23. C₃×D₁₁	D₈₉	direct (N × H)
25. C₃×C₁₁	C₂×D₈₉	semidirect
28. D₁₁	C₃×D₈₉	direct (N × H)
30. C₁₁	C₂×C₃×D₈₉	semidirect
35. C₃	D₁₁×D₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₉₇₉	2
C₃×D₁₁×C₈₉	2
C₃×C₁₁×D₈₉	2
D₁₁×D₈₉	3
C₂×C₃×D₈₉	11
C₂×C₃×D₁₁	89

Subgroups — C3×D11×D89 #26044339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₁₁×D₈₉ #26044339