Subgroups — C₁₇×(C₃⋊D₃)⋊D₅₉ #49115682

Order 36108.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×D₁₇₇	C₂	1	2	yes	maximal, complemented
2	C₁₇×C₃⋊D₃×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×C₁₇×D₅₉	—	3	2	no	maximal
4	C₃²×C₁₇×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₇×D₁₇₇	D₃	1	2	yes	complemented
6	D₃×C₁₇×C₅₉	—	3	2	no	—
7	D₃×C₁₇×C₅₉	—	6	1	no	—
8	C₃×C₁₇×D₅₉	—	3	2	no	—
9	C₂×C₁₇×D₅₉	—	9	1	no	Hall
10	C₃×C₁₇×C₅₉	—	2	1	no	—
11	C₃×C₁₇×C₅₉	C₂×D₃	1	2	yes	complemented
12	(C₃⋊D₃)⋊D₅₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₁₇×C₅₉	—	9	1	no	—
14	C₁₇×D₅₉	—	3	2	no	—
15	C₃⋊D₃×C₅₉	C₂×C₁₇	1	1	yes	characteristic, complemented
16	C₃×D₁₇₇	C₂×C₁₇	1	2	yes	complemented
17	C₁₇×C₅₉	D₃²	1	1	yes	characteristic, complemented, Hall
18	D₃×D₅₉	—	3	2	no	—
19	D₃²×C₁₇	—	59	1	no	maximal, Hall
20	C₃²×C₅₉	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
21	D₁₇₇	D₃×C₁₇	1	2	yes	complemented
22	C₃×D₅₉	—	3	2	no	—
23	D₃×C₅₉	—	3	2	no	—
24	D₃×C₅₉	—	6	1	no	—
25	C₁₇×C₃⋊D₃	D₅₉	1	1	yes	characteristic, complemented
26	C₃×D₃×C₁₇	—	59	2	no	—
27	C₂×D₅₉	—	9	1	no	Hall
28	C₂×D₃×C₁₇	—	177	2	no	—
29	C₃×C₅₉	—	2	1	no	—
30	C₃×C₅₉	C₂×D₃×C₁₇	1	2	yes	complemented
31	C₃²×C₁₇	C₂×D₅₉	1	1	yes	characteristic, complemented, Hall
32	C₂×C₅₉	—	9	1	no	—
33	D₅₉	—	3	2	no	—
34	C₂×C₃×C₁₇	—	177	2	no	—
35	D₃×C₁₇	—	3	2	no	—
36	D₃×C₁₇	—	6	1	no	—
37	D₃×C₁₇	—	59	2	no	—
38	C₂²×C₁₇	—	531	1	no	Hall
39	C₅₉	D₃²×C₁₇	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₁₇	—	2	1	no	—
41	C₃×C₁₇	D₃×D₅₉	1	2	yes	complemented
42	D₃²	—	59	1	no	Hall
43	C₂×C₁₇	—	9	1	no	—
44	C₂×C₁₇	—	177	2	no	—
45	C₃⋊D₃	C₁₇×D₅₉	1	1	yes	characteristic, complemented
46	C₃×D₃	—	59	2	no	—
47	C₁₇	(C₃⋊D₃)⋊D₅₉	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×D₃	—	177	2	no	—
49	C₃²	C₂×C₁₇×D₅₉	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	177	2	no	—
51	D₃	—	3	2	no	—
52	D₃	—	6	1	no	—
53	D₃	—	59	2	no	—
54	C₂²	—	531	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₃×C₁₇×D₅₉	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	177	2	no	—

	subgroup	G/H
center, hypercenter	C₁₇	(C₃⋊D₃)⋊D₅₉
commutator, cosocle, hypocenter	C₃²×C₅₉	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇×C₅₉	C₂²
LCS	G ▷ C₃²×C₅₉
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₇×D₁₇₇	C₂	semidirect
2. C₁₇×C₃⋊D₃×C₅₉	C₂	semidirect
4. C₃²×C₁₇×C₅₉	C₂²	semidirect
5. C₁₇×D₁₇₇	D₃	semidirect
11. C₃×C₁₇×C₅₉	C₂×D₃	semidirect
12. (C₃⋊D₃)⋊D₅₉	C₁₇	direct (N × H)
15. C₃⋊D₃×C₅₉	C₂×C₁₇	semidirect
16. C₃×D₁₇₇	C₂×C₁₇	semidirect
17. C₁₇×C₅₉	D₃²	semidirect
20. C₃²×C₅₉	C₂²×C₁₇	semidirect
21. D₁₇₇	D₃×C₁₇	semidirect
25. C₁₇×C₃⋊D₃	D₅₉	semidirect
30. C₃×C₅₉	C₂×D₃×C₁₇	semidirect
31. C₃²×C₁₇	C₂×D₅₉	semidirect
39. C₅₉	D₃²×C₁₇	semidirect
41. C₃×C₁₇	D₃×D₅₉	semidirect
45. C₃⋊D₃	C₁₇×D₅₉	semidirect
47. C₁₇	(C₃⋊D₃)⋊D₅₉	direct (N × H)
49. C₃²	C₂×C₁₇×D₅₉	semidirect
56. C₃	D₃×C₁₇×D₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₇×D₁₇₇	2
C₁₇×C₃⋊D₃×C₅₉	2
D₃×C₁₇×D₅₉	3
(C₃⋊D₃)⋊D₅₉	17
D₃²×C₁₇	59

Subgroups — C17×(C3⋊D3)⋊D59 #49115682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×(C₃⋊D₃)⋊D₅₉ #49115682