Subgroups — D₃×D₁₇×C₈₉ #31827771

Order 18156.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×D₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₇×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₇×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₇×C₈₉	—	3	1	no	maximal, Hall
5	C₃×C₁₇×C₈₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₇×C₈₉	—	3	1	no	—
7	D₁₇×C₈₉	—	3	1	no	—
8	D₁₇×C₈₉	D₃	1	1	yes	characteristic, direct product factor
9	C₁₇×C₈₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₃×C₈₉	—	17	1	no	maximal, Hall
11	C₂×C₃×C₈₉	—	17	1	no	—
12	D₃×C₈₉	—	17	1	no	—
13	D₃×C₈₉	D₁₇	1	1	yes	characteristic, direct product factor
14	C₂²×C₈₉	—	51	1	no	Hall
15	C₃×C₈₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
16	D₃×D₁₇	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₈₉	—	3	1	no	—
18	C₂×C₈₉	—	17	1	no	—
19	C₂×C₈₉	—	51	1	no	—
20	D₅₁	C₂×C₈₉	1	1	yes	characteristic, complemented
21	C₃×D₁₇	C₂×C₈₉	1	1	yes	characteristic, complemented
22	D₃×C₁₇	C₂×C₈₉	1	1	yes	characteristic, complemented
23	C₈₉	D₃×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×D₁₇	—	3	1	no	Hall
25	C₃×C₁₇	C₂²×C₈₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₇	—	3	1	no	—
27	D₁₇	—	3	1	no	—
28	D₁₇	D₃×C₈₉	1	1	yes	characteristic, direct product factor
29	C₁₇	C₂×D₃×C₈₉	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	17	1	no	Hall
31	C₂×C₃	—	17	1	no	—
32	D₃	—	17	1	no	—
33	D₃	D₁₇×C₈₉	1	1	yes	characteristic, direct product factor
34	C₂²	—	51	1	no	Sylow
35	C₃	C₂×D₁₇×C₈₉	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	17	1	no	—
38	C₂	—	51	1	no	—

	subgroup	G/H
center, hypercenter	C₈₉	D₃×D₁₇
commutator, cosocle, hypocenter	C₃×C₁₇	C₂²×C₈₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₇×C₈₉	C₂²
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₈₉

Complements

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

N	H ≅ G/N	type
1. C₈₉×D₅₁	C₂	semidirect
2. D₃×C₁₇×C₈₉	C₂	semidirect
3. C₃×D₁₇×C₈₉	C₂	semidirect
5. C₃×C₁₇×C₈₉	C₂²	semidirect
8. D₁₇×C₈₉	D₃	direct (N × H)
9. C₁₇×C₈₉	C₂×D₃	semidirect
13. D₃×C₈₉	D₁₇	direct (N × H)
15. C₃×C₈₉	C₂×D₁₇	semidirect
16. D₃×D₁₇	C₈₉	direct (N × H)
20. D₅₁	C₂×C₈₉	semidirect
21. C₃×D₁₇	C₂×C₈₉	semidirect
22. D₃×C₁₇	C₂×C₈₉	semidirect
23. C₈₉	D₃×D₁₇	direct (N × H)
25. C₃×C₁₇	C₂²×C₈₉	semidirect
28. D₁₇	D₃×C₈₉	direct (N × H)
29. C₁₇	C₂×D₃×C₈₉	semidirect
33. D₃	D₁₇×C₈₉	direct (N × H)
35. C₃	C₂×D₁₇×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×D₅₁	2
D₃×C₁₇×C₈₉	2
C₃×D₁₇×C₈₉	2
C₂×D₁₇×C₈₉	3
C₂×D₃×C₈₉	17
D₃×D₁₇	89

Subgroups — D3×D17×C89 #31827771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₁₇×C₈₉ #31827771