Subgroups — D₃×C₁₇×D₃₃ #20269697

Order 6732.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₃⋊D₃₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₇×D₃₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₇×D₃₃	—	3	1	no	maximal
5	D₃×C₁₇×D₁₁	—	3	1	no	maximal
6	C₃²×C₁₁×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₁×C₁₇	—	3	1	no	—
8	C₁₇×D₃₃	—	3	1	no	—
9	C₁₇×D₃₃	—	3	1	no	—
10	C₁₇×D₃₃	—	6	1	no	—
11	C₁₇×D₃₃	D₃	1	1	yes	characteristic, direct product factor
12	D₃×C₁₁×C₁₇	D₃	1	1	yes	characteristic, complemented
13	C₃×C₁₇×D₁₁	—	3	1	no	—
14	C₂×C₁₇×D₁₁	—	9	1	no	Hall
15	D₃²×C₁₇	—	11	1	no	maximal, Hall
16	C₃×C₁₁×C₁₇	—	2	1	no	—
17	C₃×C₁₁×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented
18	C₃×C₁₁×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented
19	D₃×D₃₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂×C₁₁×C₁₇	—	3	1	no	—
21	C₁₇×D₁₁	—	3	1	no	—
22	C₁₇×D₁₁	—	9	1	no	—
23	C₁₇×C₃⋊D₃	—	11	1	no	—
24	C₃×D₃×C₁₇	—	11	1	no	—
25	C₃×D₃×C₁₇	D₁₁	1	1	yes	characteristic, complemented
26	C₂×D₃×C₁₇	—	33	1	no	—
27	C₂×D₃×C₁₇	—	33	1	no	—
28	C₃⋊D₃₃	C₂×C₁₇	1	1	yes	characteristic, complemented
29	C₃×D₃₃	C₂×C₁₇	1	1	yes	characteristic, complemented
30	C₃×D₃×C₁₁	C₂×C₁₇	1	1	yes	characteristic, complemented
31	C₁₁×C₁₇	D₃²	1	1	yes	characteristic, complemented, Hall
32	C₃²×C₁₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
33	C₂×D₃₃	—	3	1	no	—
34	D₃×D₁₁	—	3	1	no	—
35	C₂×C₃×C₁₇	—	3	1	no	—
36	C₂×C₃×C₁₇	—	33	1	no	—
37	D₃×C₁₇	—	11	1	no	—
38	D₃×C₁₇	—	33	1	no	—
39	D₃×C₁₇	—	33	1	no	—
40	D₃×C₁₇	—	66	1	no	—
41	D₃×C₁₇	D₃₃	1	1	yes	characteristic, direct product factor
42	C₃²×C₁₁	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
43	C₂²×C₁₇	—	99	1	no	Hall
44	C₂×C₃×C₁₁	—	3	1	no	—
45	D₃₃	—	3	1	no	—
46	D₃₃	—	3	1	no	—
47	D₃₃	—	6	1	no	—
48	D₃₃	D₃×C₁₇	1	1	yes	characteristic, direct product factor
49	C₃×D₁₁	—	3	1	no	—
50	D₃×C₁₁	D₃×C₁₇	1	1	yes	characteristic, complemented
51	C₃×C₁₇	—	2	1	no	—
52	C₃×C₁₇	D₃×D₁₁	1	1	yes	characteristic, complemented
53	C₃×C₁₇	C₂×D₃₃	1	1	yes	characteristic, complemented
54	C₂×D₁₁	—	9	1	no	Hall
55	D₃²	—	11	1	no	Hall
56	C₂×C₁₇	—	3	1	no	—
57	C₂×C₁₇	—	33	1	no	—
58	C₂×C₁₇	—	99	1	no	—
59	C₃×C₁₁	—	2	1	no	—
60	C₃×C₁₁	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented
61	C₃×C₁₁	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented
62	C₂×C₁₁	—	3	1	no	—
63	D₁₁	—	3	1	no	—
64	D₁₁	—	9	1	no	—
65	C₃⋊D₃	—	11	1	no	—
66	C₃×D₃	—	11	1	no	—
67	C₃×D₃	C₁₇×D₁₁	1	1	yes	characteristic, complemented
68	C₁₇	D₃×D₃₃	1	1	yes	characteristic, direct product factor, Sylow
69	C₂×D₃	—	33	1	no	—
70	C₂×D₃	—	33	1	no	—
71	C₁₁	D₃²×C₁₇	1	1	yes	characteristic, complemented, Sylow
72	C₃²	C₂×C₁₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	33	1	no	—
75	D₃	—	11	1	no	—
76	D₃	—	33	1	no	—
77	D₃	—	33	1	no	—
78	D₃	—	66	1	no	—
79	D₃	C₁₇×D₃₃	1	1	yes	characteristic, direct product factor
80	C₂²	—	99	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×C₁₇×D₁₁	1	1	yes	characteristic, complemented
83	C₃	C₂×C₁₇×D₃₃	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	33	1	no	—
86	C₂	—	99	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇	D₃×D₃₃
commutator, hypocenter	C₃²×C₁₁	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₁₇	C₂²
LCS	G ▷ C₃²×C₁₁
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₃⋊D₃₃	C₂	semidirect
2. C₃×C₁₇×D₃₃	C₂	semidirect
3. C₃×D₃×C₁₁×C₁₇	C₂	semidirect
6. C₃²×C₁₁×C₁₇	C₂²	semidirect
11. C₁₇×D₃₃	D₃	direct (N × H)
12. D₃×C₁₁×C₁₇	D₃	semidirect
17. C₃×C₁₁×C₁₇	C₂×D₃	semidirect
18. C₃×C₁₁×C₁₇	C₂×D₃	semidirect
19. D₃×D₃₃	C₁₇	direct (N × H)
25. C₃×D₃×C₁₇	D₁₁	semidirect
28. C₃⋊D₃₃	C₂×C₁₇	semidirect
29. C₃×D₃₃	C₂×C₁₇	semidirect
30. C₃×D₃×C₁₁	C₂×C₁₇	semidirect
31. C₁₁×C₁₇	D₃²	semidirect
32. C₃²×C₁₇	C₂×D₁₁	semidirect
41. D₃×C₁₇	D₃₃	direct (N × H)
42. C₃²×C₁₁	C₂²×C₁₇	semidirect
48. D₃₃	D₃×C₁₇	direct (N × H)
50. D₃×C₁₁	D₃×C₁₇	semidirect
52. C₃×C₁₇	D₃×D₁₁	semidirect
53. C₃×C₁₇	C₂×D₃₃	semidirect
60. C₃×C₁₁	C₂×D₃×C₁₇	semidirect
61. C₃×C₁₁	C₂×D₃×C₁₇	semidirect
67. C₃×D₃	C₁₇×D₁₁	semidirect
68. C₁₇	D₃×D₃₃	direct (N × H)
71. C₁₁	D₃²×C₁₇	semidirect
72. C₃²	C₂×C₁₇×D₁₁	semidirect
79. D₃	C₁₇×D₃₃	direct (N × H)
82. C₃	D₃×C₁₇×D₁₁	semidirect
83. C₃	C₂×C₁₇×D₃₃	semidirect

Subgroups — D3×C17×D33 #20269697

Conjugacy classes of subgroups

Complements

Subgroups — D₃×C₁₇×D₃₃ #20269697