Subgroups — C₃×D₃₃⋊D₆₁ #37563539

Order 24156.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₆₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₁×D₁₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₆₁×D₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₃⋊D₆₁	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×D₁₁×D₆₁	—	3	1	no	maximal
6	C₃²×C₁₁×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₆₁×D₃₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₁×D₁₈₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×D₆₇₁	—	2	1	no	—
10	C₃×D₆₇₁	D₃	1	1	yes	characteristic, complemented
11	C₃×D₆₇₁	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×D₁₁×C₆₁	—	3	1	no	—
13	C₃×C₁₁×D₆₁	—	3	1	no	—
14	D₁₁×D₆₁	—	3	1	no	Hall
15	C₃×D₃×D₆₁	—	11	1	no	maximal, Hall
16	C₃×C₁₁×C₆₁	—	2	1	no	—
17	C₃×C₁₁×C₆₁	C₂×D₃	1	1	yes	characteristic, complemented
18	C₃×C₁₁×C₆₁	C₂²×C₃	1	1	yes	characteristic, complemented
19	D₆₇₁	C₃×D₃	1	1	yes	characteristic, complemented
20	C₁₁×D₆₁	—	3	1	no	—
21	D₁₁×C₆₁	—	3	1	no	—
22	C₃×D₁₈₃	D₁₁	1	1	yes	characteristic, complemented
23	C₃×D₃×C₆₁	—	11	1	no	—
24	C₃²×D₆₁	—	11	1	no	—
25	C₂×C₃×D₆₁	—	33	1	no	—
26	D₃×D₆₁	—	11	1	no	—
27	C₁₁×C₆₁	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
28	C₃²×C₆₁	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
29	C₃×D₃×D₁₁	—	61	1	no	maximal, Hall
30	C₂×C₃×C₆₁	—	33	1	no	—
31	D₁₈₃	C₃×D₁₁	1	1	yes	characteristic, complemented
32	C₃×D₆₁	—	3	1	no	—
33	C₃×D₆₁	—	11	1	no	—
34	C₃×D₆₁	—	11	1	no	—
35	C₃×D₆₁	—	22	1	no	—
36	D₃×C₆₁	—	11	1	no	—
37	C₂×D₆₁	—	33	1	no	Hall
38	C₃×D₃₃	D₆₁	1	1	yes	characteristic, complemented
39	C₃×D₃×C₁₁	—	61	1	no	—
40	C₃²×D₁₁	—	61	1	no	—
41	C₃×C₆₁	—	2	1	no	—
42	C₃×C₆₁	D₃×D₁₁	1	1	yes	characteristic, complemented
43	C₃×C₆₁	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented
44	C₂×C₃×D₁₁	—	183	1	no	—
45	D₃×D₁₁	—	61	1	no	—
46	C₂×C₆₁	—	33	1	no	—
47	D₆₁	—	3	1	no	—
48	D₆₁	—	11	1	no	—
49	C₃²×C₁₁	C₂×D₆₁	1	1	yes	characteristic, complemented, Hall
50	C₂×C₃×C₁₁	—	183	1	no	—
51	D₃₃	C₃×D₆₁	1	1	yes	characteristic, complemented
52	C₃×D₁₁	—	3	1	no	—
53	C₃×D₁₁	—	61	1	no	—
54	C₃×D₁₁	—	61	1	no	—
55	C₃×D₁₁	—	122	1	no	—
56	D₃×C₁₁	—	61	1	no	—
57	C₆₁	C₃×D₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
58	C₂×D₁₁	—	183	1	no	Hall
59	C₂×C₃×D₃	—	671	1	no	Hall
60	C₃×C₁₁	—	2	1	no	—
61	C₃×C₁₁	D₃×D₆₁	1	1	yes	characteristic, complemented
62	C₃×C₁₁	C₂×C₃×D₆₁	1	1	yes	characteristic, complemented
63	C₂×C₁₁	—	183	1	no	—
64	D₁₁	—	3	1	no	—
65	D₁₁	—	61	1	no	—
66	C₂×C₃²	—	671	1	no	—
67	C₃×D₃	—	11	1	no	—
68	C₃×D₃	—	61	1	no	—
69	C₂²×C₃	—	2013	1	no	—
70	C₂×D₃	—	671	1	no	—
71	C₁₁	C₃×D₃×D₆₁	1	1	yes	characteristic, complemented, Sylow
72	C₃²	D₁₁×D₆₁	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	33	1	no	—
74	C₂×C₃	—	1342	1	no	—
75	C₂×C₃	—	671	1	no	—
76	C₂×C₃	—	671	1	no	—
77	C₂×C₃	—	183	1	no	—
78	D₃	—	11	1	no	—
79	D₃	—	61	1	no	—
80	C₂²	—	2013	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	C₃×D₁₁×D₆₁	1	1	yes	characteristic, complemented
83	C₃	D₃₃⋊D₆₁	1	1	yes	characteristic, direct product factor
84	C₂	—	33	1	no	—
85	C₂	—	671	1	no	—
86	C₂	—	183	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₃₃⋊D₆₁
commutator, cosocle, hypocenter	C₃×C₁₁×C₆₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₆₁	C₂²
LCS	G ▷ C₃×C₁₁×C₆₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×D₆₇₁	C₂	semidirect
2. C₃×C₁₁×D₁₈₃	C₂	semidirect
3. C₃×C₆₁×D₃₃	C₂	semidirect
4. D₃₃⋊D₆₁	C₃	direct (N × H)
6. C₃²×C₁₁×C₆₁	C₂²	semidirect
7. C₆₁×D₃₃	C₂×C₃	semidirect
8. C₁₁×D₁₈₃	C₂×C₃	semidirect
10. C₃×D₆₇₁	D₃	semidirect
11. C₃×D₆₇₁	C₂×C₃	semidirect
17. C₃×C₁₁×C₆₁	C₂×D₃	semidirect
18. C₃×C₁₁×C₆₁	C₂²×C₃	semidirect
19. D₆₇₁	C₃×D₃	semidirect
22. C₃×D₁₈₃	D₁₁	semidirect
27. C₁₁×C₆₁	C₂×C₃×D₃	semidirect
28. C₃²×C₆₁	C₂×D₁₁	semidirect
31. D₁₈₃	C₃×D₁₁	semidirect
38. C₃×D₃₃	D₆₁	semidirect
42. C₃×C₆₁	D₃×D₁₁	semidirect
43. C₃×C₆₁	C₂×C₃×D₁₁	semidirect
49. C₃²×C₁₁	C₂×D₆₁	semidirect
51. D₃₃	C₃×D₆₁	semidirect
57. C₆₁	C₃×D₃×D₁₁	semidirect
61. C₃×C₁₁	D₃×D₆₁	semidirect
62. C₃×C₁₁	C₂×C₃×D₆₁	semidirect
71. C₁₁	C₃×D₃×D₆₁	semidirect
72. C₃²	D₁₁×D₆₁	semidirect
82. C₃	C₃×D₁₁×D₆₁	semidirect
83. C₃	D₃₃⋊D₆₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×D₆₇₁	2
C₃×C₁₁×D₁₈₃	2
C₃×C₆₁×D₃₃	2
D₃₃⋊D₆₁	3
C₃×D₁₁×D₆₁	3
C₃×D₃×D₆₁	11
C₃×D₃×D₁₁	61

Subgroups — C3×D33⋊D61 #37563539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃₃⋊D₆₁ #37563539