Subgroups — C₃⋊D₃×D₁₇×C₅₉ #49115694

Order 36108.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₁₇×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×C₃⋊D₃×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×C₃⋊D₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₁₇×C₅₉	—	3	4	no	maximal
5	C₃²×C₁₇×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅₉×D₅₁	—	3	4	no	—
7	D₃×C₁₇×C₅₉	—	3	4	no	—
8	C₃×D₁₇×C₅₉	D₃	1	4	yes	complemented
9	C₂×D₁₇×C₅₉	—	9	1	no	Hall
10	C₃×C₁₇×C₅₉	C₂×D₃	1	4	yes	complemented
11	C₂×C₃⋊D₃×C₅₉	—	17	1	no	maximal, Hall
12	C₂×C₁₇×C₅₉	—	9	1	no	—
13	D₁₇×C₅₉	—	9	1	no	—
14	D₁₇×C₅₉	C₃⋊D₃	1	1	yes	characteristic, direct product factor
15	C₂×C₃²×C₅₉	—	17	1	no	—
16	C₃⋊D₃×C₅₉	—	17	1	no	—
17	C₃⋊D₃×C₅₉	D₁₇	1	1	yes	characteristic, direct product factor
18	C₁₇×C₅₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
19	C₂×D₃×C₅₉	—	51	4	no	—
20	C₃⋊D₃×D₁₇	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₃²×C₅₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₅₉	—	17	4	no	—
23	D₃×C₅₉	—	3	4	no	—
24	D₃×C₅₉	—	51	4	no	—
25	C₃⋊D₅₁	C₂×C₅₉	1	1	yes	characteristic, complemented
26	C₁₇×C₃⋊D₃	C₂×C₅₉	1	1	yes	characteristic, complemented
27	C₃²×D₁₇	C₂×C₅₉	1	1	yes	characteristic, complemented
28	C₂²×C₅₉	—	153	1	no	Hall
29	D₃×D₁₇	—	3	4	no	—
30	C₃×C₅₉	D₃×D₁₇	1	4	yes	complemented
31	C₃²×C₁₇	C₂²×C₅₉	1	1	yes	characteristic, complemented, Hall
32	C₂×C₅₉	—	9	1	no	—
33	C₂×C₅₉	—	17	1	no	—
34	C₂×C₅₉	—	153	1	no	—
35	D₅₁	—	3	4	no	—
36	C₃×D₁₇	D₃×C₅₉	1	4	yes	complemented
37	D₃×C₁₇	—	3	4	no	—
38	C₂×D₁₇	—	9	1	no	Hall
39	C₅₉	C₃⋊D₃×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×C₁₇	C₂×D₃×C₅₉	1	4	yes	complemented
41	C₂×C₃⋊D₃	—	17	1	no	Hall
42	C₂×C₁₇	—	9	1	no	—
43	D₁₇	—	9	1	no	—
44	D₁₇	C₃⋊D₃×C₅₉	1	1	yes	characteristic, direct product factor
45	C₂×C₃²	—	17	1	no	—
46	C₃⋊D₃	—	17	1	no	—
47	C₃⋊D₃	D₁₇×C₅₉	1	1	yes	characteristic, direct product factor
48	C₁₇	C₂×C₃⋊D₃×C₅₉	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₃	—	51	4	no	—
50	C₃²	C₂×D₁₇×C₅₉	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	17	4	no	—
52	D₃	—	3	4	no	—
53	D₃	—	51	4	no	—
54	C₂²	—	153	1	no	Sylow
55	C₃	D₃×D₁₇×C₅₉	1	4	yes	complemented
56	C₂	—	9	1	no	—
57	C₂	—	17	1	no	—
58	C₂	—	153	1	no	—

	subgroup	G/H
center, hypercenter	C₅₉	C₃⋊D₃×D₁₇
commutator, cosocle, hypocenter	C₃²×C₁₇	C₂²×C₅₉
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇×C₅₉	C₂²
LCS	G ▷ C₃²×C₁₇
UCS	C₁ ◁ C₅₉

Complements

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

N	H ≅ G/N	type
1. C₃²×D₁₇×C₅₉	C₂	semidirect
2. C₁₇×C₃⋊D₃×C₅₉	C₂	semidirect
3. C₅₉×C₃⋊D₅₁	C₂	semidirect
5. C₃²×C₁₇×C₅₉	C₂²	semidirect
8. C₃×D₁₇×C₅₉	D₃	semidirect
10. C₃×C₁₇×C₅₉	C₂×D₃	semidirect
14. D₁₇×C₅₉	C₃⋊D₃	direct (N × H)
17. C₃⋊D₃×C₅₉	D₁₇	direct (N × H)
18. C₁₇×C₅₉	C₂×C₃⋊D₃	semidirect
20. C₃⋊D₃×D₁₇	C₅₉	direct (N × H)
21. C₃²×C₅₉	C₂×D₁₇	semidirect
25. C₃⋊D₅₁	C₂×C₅₉	semidirect
26. C₁₇×C₃⋊D₃	C₂×C₅₉	semidirect
27. C₃²×D₁₇	C₂×C₅₉	semidirect
30. C₃×C₅₉	D₃×D₁₇	semidirect
31. C₃²×C₁₇	C₂²×C₅₉	semidirect
36. C₃×D₁₇	D₃×C₅₉	semidirect
39. C₅₉	C₃⋊D₃×D₁₇	direct (N × H)
40. C₃×C₁₇	C₂×D₃×C₅₉	semidirect
44. D₁₇	C₃⋊D₃×C₅₉	direct (N × H)
47. C₃⋊D₃	D₁₇×C₅₉	direct (N × H)
48. C₁₇	C₂×C₃⋊D₃×C₅₉	semidirect
50. C₃²	C₂×D₁₇×C₅₉	semidirect
55. C₃	D₃×D₁₇×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₃²×D₁₇×C₅₉	2
C₁₇×C₃⋊D₃×C₅₉	2
C₅₉×C₃⋊D₅₁	2
D₃×D₁₇×C₅₉	3
C₂×C₃⋊D₃×C₅₉	17
C₃⋊D₃×D₁₇	59

Subgroups — C3⋊D3×D17×C59 #49115694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×D₁₇×C₅₉ #49115694