Subgroups — D₃×D₈₉⋊C₁₁ #26044331

Order 11748.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(D₈₉⋊C₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₈₉⋊C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₈₉⋊C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈₉⋊C₁₁	—	3	1	no	maximal, Hall
5	C₃×C₈₉⋊C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₈₉⋊C₁₁	—	3	1	no	—
7	D₈₉⋊C₁₁	—	3	1	no	—
8	D₈₉⋊C₁₁	D₃	1	1	yes	characteristic, direct product factor
9	D₃×D₈₉	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
10	C₈₉⋊C₁₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₂₆₇	C₂×C₁₁	1	1	yes	characteristic, complemented
12	C₃×D₈₉	C₂×C₁₁	1	1	yes	characteristic, complemented
13	D₃×C₈₉	C₂×C₁₁	1	1	yes	characteristic, complemented
14	C₂×D₈₉	—	3	1	no	Hall
15	C₃×C₈₉	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₈₉	—	3	1	no	—
17	D₈₉	—	3	1	no	—
18	D₈₉	D₃×C₁₁	1	1	yes	characteristic, complemented
19	C₂×D₃×C₁₁	—	89	1	no	maximal, Hall
20	C₈₉	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₁₁	—	89	1	no	—
22	D₃×C₁₁	—	89	1	no	—
23	D₃×C₁₁	—	89	1	no	—
24	C₂²×C₁₁	—	267	1	no	Hall
25	C₃×C₁₁	—	89	1	no	Hall
26	C₂×C₁₁	—	267	1	no	—
27	C₂×C₁₁	—	267	1	no	—
28	C₂×C₁₁	—	89	1	no	—
29	C₂×D₃	—	89	1	no	Hall
30	C₁₁	—	89	1	no	Sylow
31	C₂×C₃	—	89	1	no	—
32	D₃	—	89	1	no	—
33	D₃	D₈₉⋊C₁₁	1	1	yes	characteristic, direct product factor
34	C₂²	—	267	1	no	Sylow
35	C₃	C₂×D₈₉⋊C₁₁	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	267	1	no	—
38	C₂	—	89	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃⋊(D₈₉⋊C₁₁)	C₂	semidirect
2. D₃×C₈₉⋊C₁₁	C₂	semidirect
3. C₃×D₈₉⋊C₁₁	C₂	semidirect
5. C₃×C₈₉⋊C₁₁	C₂²	semidirect
8. D₈₉⋊C₁₁	D₃	direct (N × H)
9. D₃×D₈₉	C₁₁	semidirect
10. C₈₉⋊C₁₁	C₂×D₃	semidirect
11. D₂₆₇	C₂×C₁₁	semidirect
12. C₃×D₈₉	C₂×C₁₁	semidirect
13. D₃×C₈₉	C₂×C₁₁	semidirect
15. C₃×C₈₉	C₂²×C₁₁	semidirect
18. D₈₉	D₃×C₁₁	semidirect
20. C₈₉	C₂×D₃×C₁₁	semidirect
33. D₃	D₈₉⋊C₁₁	direct (N × H)
35. C₃	C₂×D₈₉⋊C₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(D₈₉⋊C₁₁)	2
D₃×C₈₉⋊C₁₁	2
C₃×D₈₉⋊C₁₁	2
C₂×D₈₉⋊C₁₁	3
D₃×D₈₉	11
C₂×D₃×C₁₁	89

Subgroups — D3×D89⋊C11 #26044331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₈₉⋊C₁₁ #26044331