Subgroups — C₂×C₁₇×D₂₆₁ #31801630

Order 17748.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×D₂₆₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₁₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×D₈₇	—	3	1	no	maximal
4	C₉×C₁₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₇×D₈₇	—	3	2	no	—
6	C₂×C₃×C₁₇×C₂₉	D₃	1	1	yes	characteristic
7	C₂×C₁₇×D₂₉	—	9	1	no	Hall
8	C₃×C₁₇×C₂₉	C₂×D₃	1	1	yes	characteristic
9	C₂×D₂₆₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₇×C₂₉	D₉	1	1	yes	characteristic, complemented
11	C₁₇×D₂₉	—	9	2	no	—
12	C₂×C₁₇×D₉	—	29	1	no	maximal, Hall
13	C₂×C₉×C₂₉	C₂×C₁₇	1	1	yes	characteristic, complemented
14	D₂₆₁	C₂×C₁₇	1	2	yes	direct product factor
15	C₁₇×C₂₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
16	C₂×D₈₇	—	3	1	no	—
17	C₂×C₉×C₁₇	D₂₉	1	1	yes	characteristic, complemented
18	C₁₇×D₉	—	29	2	no	—
19	C₉×C₂₉	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
20	C₂×D₃×C₁₇	—	87	1	no	—
21	C₂×C₃×C₂₉	D₃×C₁₇	1	1	yes	characteristic
22	D₈₇	—	3	2	no	—
23	C₉×C₁₇	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
24	C₂×D₂₉	—	9	1	no	Hall
25	C₂×C₃×C₁₇	D₈₇	1	1	yes	characteristic
26	D₃×C₁₇	—	87	2	no	—
27	C₃×C₂₉	C₂×D₃×C₁₇	1	1	yes	characteristic
28	C₂²×C₁₇	—	261	1	no	Hall
29	C₂×C₂₉	C₁₇×D₉	1	1	yes	characteristic, complemented
30	D₂₉	—	9	2	no	—
31	C₃×C₁₇	C₂×D₈₇	1	1	yes	characteristic
32	C₂×D₉	—	29	1	no	Hall
33	C₂×C₁₇	—	261	2	no	—
34	C₂×C₁₇	D₂₆₁	1	1	yes	characteristic, direct product factor
35	C₂₉	C₂×C₁₇×D₉	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₉	C₁₇×D₂₉	1	1	yes	characteristic, complemented
37	D₉	—	29	2	no	—
38	C₁₇	C₂×D₂₆₁	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×D₃	—	87	1	no	—
40	C₉	C₂×C₁₇×D₂₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	C₁₇×D₈₇	1	1	yes	characteristic
42	D₃	—	87	2	no	—
43	C₂²	—	261	1	no	Sylow
44	C₃	C₂×C₁₇×D₈₇	1	1	yes	characteristic
45	C₂	—	261	2	no	—
46	C₂	C₁₇×D₂₆₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	D₂₆₁
commutator, cosocle, hypocenter	C₉×C₂₉	C₂²×C₁₇
Frattini	C₃	C₂×C₁₇×D₈₇
Fitting	C₂×C₉×C₁₇×C₂₉	C₂
socle	C₂×C₃×C₁₇×C₂₉	D₃
LCS	G ▷ C₉×C₂₉
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×D₂₆₁	C₂	direct (N × H)
2. C₂×C₉×C₁₇×C₂₉	C₂	semidirect
4. C₉×C₁₇×C₂₉	C₂²	semidirect
9. C₂×D₂₆₁	C₁₇	direct (N × H)
10. C₂×C₁₇×C₂₉	D₉	semidirect
13. C₂×C₉×C₂₉	C₂×C₁₇	semidirect
14. D₂₆₁	C₂×C₁₇	direct (N × H)
15. C₁₇×C₂₉	C₂×D₉	semidirect
17. C₂×C₉×C₁₇	D₂₉	semidirect
19. C₉×C₂₉	C₂²×C₁₇	semidirect
23. C₉×C₁₇	C₂×D₂₉	semidirect
29. C₂×C₂₉	C₁₇×D₉	semidirect
34. C₂×C₁₇	D₂₆₁	direct (N × H)
35. C₂₉	C₂×C₁₇×D₉	semidirect
36. C₂×C₉	C₁₇×D₂₉	semidirect
38. C₁₇	C₂×D₂₆₁	direct (N × H)
40. C₉	C₂×C₁₇×D₂₉	semidirect
46. C₂	C₁₇×D₂₆₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×D₂₆₁	2
C₂×C₉×C₁₇×C₂₉	2
C₂×C₁₇×D₈₇	3
C₂×D₂₆₁	17
C₂×C₁₇×D₉	29

Subgroups — C2×C17×D261 #31801630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×D₂₆₁ #31801630