Subgroups — C₃²×C₁₁×#66772 #46778069

Order 33660.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₁×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₁×#66772	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅×C₁₁×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃²×C₁₁×#595	—	5	1	no	maximal, Hall
5	C₃×C₅×C₁₁×D₁₇	C₂×C₃	1	4	yes	—
6	C₁₁×#66772	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₁₁×D₁₇	D₅	1	1	yes	characteristic
8	C₃²×#66772	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅×C₁₁×C₁₇	C₃×C₄	1	4	yes	complemented
10	C₃×C₁₁×#595	—	5	4	no	—
11	C₃²×C₁₁×Dic₅	—	17	1	no	maximal, Hall
12	C₅×C₁₁×D₁₇	C₂×C₃²	1	1	yes	characteristic
13	C₃²×C₁₁×C₁₇	Dic₅	1	1	yes	characteristic, complemented, Hall
14	C₃²×C₅×D₁₇	C₂×C₁₁	1	1	yes	characteristic
15	C₃×C₁₁×D₁₇	C₃×D₅	1	4	yes	—
16	C₃×#66772	C₃×C₁₁	1	4	yes	direct product factor
17	C₂×C₃²×C₅×C₁₁	—	17	1	no	—
18	C₅×C₁₁×C₁₇	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
19	C₃²×C₅×C₁₇	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
20	C₁₁×#595	—	5	1	no	Hall
21	C₃×C₁₁×Dic₅	—	17	4	no	—
22	C₃²×#595	—	5	1	no	Hall
23	C₃×C₁₁×C₁₇	C₃×Dic₅	1	4	yes	complemented
24	C₃×C₅×D₁₇	C₂×C₃×C₁₁	1	4	yes	—
25	C₃²×C₅×C₁₁	#595	1	1	yes	characteristic, complemented, Hall
26	C₃²×C₄×C₁₁	—	85	1	no	Hall
27	C₁₁×D₁₇	C₃²×D₅	1	1	yes	characteristic
28	#66772	C₃²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₃×C₅×C₁₁	—	17	4	no	—
30	C₃²×D₁₇	D₅×C₁₁	1	1	yes	characteristic
31	C₃×C₅×C₁₇	C₃×C₄×C₁₁	1	4	yes	complemented
32	C₁₁×Dic₅	—	17	1	no	Hall
33	C₃×#595	—	5	4	no	—
34	C₂×C₃²×C₁₁	—	17	1	no	—
35	C₁₁×C₁₇	C₃²×Dic₅	1	1	yes	characteristic, complemented, Hall
36	C₃²×Dic₅	—	17	1	no	Hall
37	C₅×D₁₇	C₂×C₃²×C₁₁	1	1	yes	characteristic
38	C₃×C₅×C₁₁	C₃×#595	1	4	yes	complemented
39	C₃²×C₁₇	C₁₁×Dic₅	1	1	yes	characteristic, complemented, Hall
40	C₃×C₄×C₁₁	—	85	4	no	—
41	C₂×C₅×C₁₁	—	17	1	no	—
42	C₃×D₁₇	C₃×D₅×C₁₁	1	4	yes	—
43	C₃²×C₁₁	#66772	1	1	yes	characteristic, direct product factor, Hall
44	C₂×C₃²×C₅	—	17	1	no	—
45	C₅×C₁₇	C₃²×C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
46	#595	—	5	1	no	Hall
47	C₂×C₃×C₁₁	—	17	4	no	—
48	C₃×Dic₅	—	17	4	no	—
49	C₅×C₁₁	C₃²×#595	1	1	yes	characteristic, complemented, Hall
50	C₃×C₁₇	C₃×C₁₁×Dic₅	1	4	yes	complemented
51	C₃²×C₅	C₁₁×#595	1	1	yes	characteristic, complemented, Hall
52	C₄×C₁₁	—	85	1	no	Hall
53	C₃²×C₄	—	85	1	no	Hall
54	D₁₇	C₃²×D₅×C₁₁	1	1	yes	characteristic
55	C₃×C₁₁	C₃×#66772	1	4	yes	direct product factor
56	C₂×C₃×C₅	—	17	4	no	—
57	C₂×C₁₁	—	17	1	no	—
58	Dic₅	—	17	1	no	Hall
59	C₂×C₃²	—	17	1	no	—
60	C₁₇	C₃²×C₁₁×Dic₅	1	1	yes	characteristic, complemented, Sylow
61	C₃×C₅	C₃×C₁₁×#595	1	4	yes	complemented
62	C₃×C₄	—	85	4	no	—
63	C₁₁	C₃²×#66772	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₅	—	17	1	no	—
65	C₃²	C₁₁×#66772	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×C₃	—	17	4	no	—
67	C₅	C₃²×C₁₁×#595	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	85	1	no	Sylow
69	C₃	C₃×C₁₁×#66772	1	4	yes	direct product factor
70	C₂	—	17	1	no	—

	subgroup	G/H
center, hypercenter	C₃²×C₁₁	#66772
commutator, hypocenter	C₅×C₁₇	C₃²×C₄×C₁₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₁×C₁₇	C₄
prime radical	C₃²×C₅×C₁₁×D₁₇	C₂
cosocle	C₅×D₁₇	C₂×C₃²×C₁₁
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₃²×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₁×#66772	C₃	direct (N × H)
3. C₃²×C₅×C₁₁×C₁₇	C₄	semidirect
6. C₁₁×#66772	C₃²	direct (N × H)
8. C₃²×#66772	C₁₁	direct (N × H)
9. C₃×C₅×C₁₁×C₁₇	C₃×C₄	semidirect
13. C₃²×C₁₁×C₁₇	Dic₅	semidirect
16. C₃×#66772	C₃×C₁₁	direct (N × H)
18. C₅×C₁₁×C₁₇	C₃²×C₄	semidirect
19. C₃²×C₅×C₁₇	C₄×C₁₁	semidirect
23. C₃×C₁₁×C₁₇	C₃×Dic₅	semidirect
25. C₃²×C₅×C₁₁	#595	semidirect
28. #66772	C₃²×C₁₁	direct (N × H)
31. C₃×C₅×C₁₇	C₃×C₄×C₁₁	semidirect
35. C₁₁×C₁₇	C₃²×Dic₅	semidirect
38. C₃×C₅×C₁₁	C₃×#595	semidirect
39. C₃²×C₁₇	C₁₁×Dic₅	semidirect
43. C₃²×C₁₁	#66772	direct (N × H)
45. C₅×C₁₇	C₃²×C₄×C₁₁	semidirect
49. C₅×C₁₁	C₃²×#595	semidirect
50. C₃×C₁₇	C₃×C₁₁×Dic₅	semidirect
51. C₃²×C₅	C₁₁×#595	semidirect
55. C₃×C₁₁	C₃×#66772	direct (N × H)
60. C₁₇	C₃²×C₁₁×Dic₅	semidirect
61. C₃×C₅	C₃×C₁₁×#595	semidirect
63. C₁₁	C₃²×#66772	direct (N × H)
65. C₃²	C₁₁×#66772	direct (N × H)
67. C₅	C₃²×C₁₁×#595	semidirect
69. C₃	C₃×C₁₁×#66772	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×C₅×C₁₁×D₁₇	2
C₃×C₁₁×#66772	3
C₃²×C₁₁×#595	5
C₃²×#66772	11
C₃²×C₁₁×Dic₅	17

Subgroups — C32×C11×#66772 #46778069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₁₁×#66772 #46778069