Subgroups — C₃×C₁₁×Dic₃×C₅₉ #37552513

Order 23364.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₁×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₁₁×Dic₃×C₅₉	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₄×C₁₁×C₅₉	—	3	1	no	maximal
4	C₃²×C₁₁×C₅₉	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₁×C₅₉	—	2	1	no	—
6	C₂×C₃×C₁₁×C₅₉	D₃	1	1	yes	characteristic
7	C₂×C₃×C₁₁×C₅₉	C₂×C₃	1	1	yes	characteristic
8	C₄×C₁₁×C₅₉	—	3	1	no	Hall
9	C₃×Dic₃×C₅₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₁₁×C₅₉	—	2	1	no	—
11	C₃×C₁₁×C₅₉	Dic₃	1	1	yes	characteristic, direct product factor
12	C₃×C₁₁×C₅₉	C₃×C₄	1	1	yes	characteristic, complemented
13	C₂×C₁₁×C₅₉	C₃×D₃	1	1	yes	characteristic
14	C₂×C₃²×C₅₉	C₂×C₁₁	1	1	yes	characteristic
15	C₃×C₄×C₅₉	—	3	1	no	—
16	Dic₃×C₅₉	C₃×C₁₁	1	1	yes	characteristic, direct product factor
17	C₁₁×C₅₉	C₃×Dic₃	1	1	yes	characteristic, direct product factor, Hall
18	C₃²×C₅₉	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
19	C₃×C₁₁×Dic₃	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂×C₃×C₅₉	—	2	1	no	—
21	C₂×C₃×C₅₉	D₃×C₁₁	1	1	yes	characteristic
22	C₂×C₃×C₅₉	C₂×C₃×C₁₁	1	1	yes	characteristic
23	C₄×C₅₉	—	3	1	no	Hall
24	C₂×C₃²×C₁₁	C₂×C₅₉	1	1	yes	characteristic
25	C₃×C₅₉	—	2	1	no	—
26	C₃×C₅₉	C₁₁×Dic₃	1	1	yes	characteristic, direct product factor
27	C₃×C₅₉	C₃×C₄×C₁₁	1	1	yes	characteristic, complemented
28	C₃×C₄×C₁₁	—	3	1	no	—
29	C₁₁×Dic₃	C₃×C₅₉	1	1	yes	characteristic, direct product factor
30	C₂×C₅₉	C₃×D₃×C₁₁	1	1	yes	characteristic
31	C₃²×C₁₁	C₄×C₅₉	1	1	yes	characteristic, complemented, Hall
32	C₂×C₃×C₁₁	—	2	1	no	—
33	C₂×C₃×C₁₁	D₃×C₅₉	1	1	yes	characteristic
34	C₂×C₃×C₁₁	C₂×C₃×C₅₉	1	1	yes	characteristic
35	C₅₉	C₃×C₁₁×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₄×C₁₁	—	3	1	no	Hall
37	C₃×Dic₃	C₁₁×C₅₉	1	1	yes	characteristic, direct product factor, Hall
38	C₃×C₁₁	—	2	1	no	—
39	C₃×C₁₁	Dic₃×C₅₉	1	1	yes	characteristic, direct product factor
40	C₃×C₁₁	C₃×C₄×C₅₉	1	1	yes	characteristic, complemented
41	C₂×C₁₁	C₃×D₃×C₅₉	1	1	yes	characteristic
42	C₂×C₃²	C₂×C₁₁×C₅₉	1	1	yes	characteristic
43	C₃×C₄	—	3	1	no	—
44	Dic₃	C₃×C₁₁×C₅₉	1	1	yes	characteristic, direct product factor
45	C₁₁	C₃×Dic₃×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
46	C₃²	C₄×C₁₁×C₅₉	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	2	1	no	—
48	C₂×C₃	C₂×C₃×C₁₁×C₅₉	1	1	yes	characteristic
49	C₂×C₃	D₃×C₁₁×C₅₉	1	1	yes	characteristic
50	C₄	—	3	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×C₄×C₁₁×C₅₉	1	1	yes	characteristic, complemented
53	C₃	C₁₁×Dic₃×C₅₉	1	1	yes	characteristic, direct product factor
54	C₂	C₃×D₃×C₁₁×C₅₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₁×C₅₉	D₃
commutator, hypocenter	C₃	C₃×C₄×C₁₁×C₅₉
Frattini	C₂	C₃×D₃×C₁₁×C₅₉
Fitting, socle, prime radical	C₂×C₃²×C₁₁×C₅₉	C₂
cosocle	C₂×C₃	C₂×C₃×C₁₁×C₅₉
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₁₁×C₅₉

Complements

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

N	H ≅ G/N	type
2. C₁₁×Dic₃×C₅₉	C₃	direct (N × H)
4. C₃²×C₁₁×C₅₉	C₄	semidirect
9. C₃×Dic₃×C₅₉	C₁₁	direct (N × H)
11. C₃×C₁₁×C₅₉	Dic₃	direct (N × H)
12. C₃×C₁₁×C₅₉	C₃×C₄	semidirect
16. Dic₃×C₅₉	C₃×C₁₁	direct (N × H)
17. C₁₁×C₅₉	C₃×Dic₃	direct (N × H)
18. C₃²×C₅₉	C₄×C₁₁	semidirect
19. C₃×C₁₁×Dic₃	C₅₉	direct (N × H)
26. C₃×C₅₉	C₁₁×Dic₃	direct (N × H)
27. C₃×C₅₉	C₃×C₄×C₁₁	semidirect
29. C₁₁×Dic₃	C₃×C₅₉	direct (N × H)
31. C₃²×C₁₁	C₄×C₅₉	semidirect
35. C₅₉	C₃×C₁₁×Dic₃	direct (N × H)
37. C₃×Dic₃	C₁₁×C₅₉	direct (N × H)
39. C₃×C₁₁	Dic₃×C₅₉	direct (N × H)
40. C₃×C₁₁	C₃×C₄×C₅₉	semidirect
44. Dic₃	C₃×C₁₁×C₅₉	direct (N × H)
45. C₁₁	C₃×Dic₃×C₅₉	direct (N × H)
46. C₃²	C₄×C₁₁×C₅₉	semidirect
52. C₃	C₃×C₄×C₁₁×C₅₉	semidirect
53. C₃	C₁₁×Dic₃×C₅₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₁₁×C₅₉	2
C₁₁×Dic₃×C₅₉	3
C₃×C₄×C₁₁×C₅₉	3
C₃×Dic₃×C₅₉	11
C₃×C₁₁×Dic₃	59

Subgroups — C3×C11×Dic3×C59 #37552513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁×Dic₃×C₅₉ #37552513