Subgroups — C₃×#14578912 #21419432

Order 7533.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14578912	C₃	1	27	yes	maximal, direct product factor
2	C₃×#11719689	C₃	1	2	yes	maximal, complemented
3	C₃×#11719686	C₃	1	3	yes	maximal, complemented
4	C₃×#11719687	C₃	1	3	yes	maximal, complemented
5	C₃×C₃²⋊(C₃₁⋊C₃)	C₃	1	1	yes	maximal, characteristic
6	C₃×C₉×C₃₁⋊C₃	C₃	1	3	yes	maximal, complemented
7	C₃²×C₉×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃³×C₃₁	C₃²	1	1	yes	characteristic
9	C₃²×C₃₁⋊C₃	C₃²	1	3	yes	—
10	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
11	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
12	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
13	C₃×C₉×C₃₁	C₃²	1	9	yes	complemented
14	C₃²⋊(C₃₁⋊C₃)	C₃²	1	9	yes	—
15	#11719689	C₃²	1	18	yes	complemented
16	C₃×C₃₁⋊C₉	C₃²	1	6	yes	—
17	#11719687	C₃²	1	27	yes	complemented
18	#11719686	C₃²	1	27	yes	complemented
19	C₉×C₃₁⋊C₃	C₃²	1	27	yes	complemented
20	C₃²×C₃₁	—	3	3	no	—
21	C₃²×C₃₁	C₃³	1	3	yes	—
22	C₃²×C₃₁	C₃³	1	1	yes	characteristic
23	C₃×C₃₁⋊C₃	—	3	9	no	—
24	C₃×C₃₁⋊C₃	C₃³	1	9	yes	—
25	C₉×C₃₁	C₃³	1	3	yes	—
26	C₉×C₃₁	C₃³	1	3	yes	—
27	C₉×C₃₁	C₃³	1	3	yes	—
28	C₃₁⋊C₉	C₃³	1	18	yes	—
29	C₃×#737	—	31	1	no	maximal, Sylow
30	C₃×C₃₁	—	3	3	no	—
31	C₃×C₃₁	#737	1	3	yes	complemented
32	C₃×C₃₁	C₃⁴	1	1	yes	characteristic
33	C₃₁⋊C₃	—	3	9	no	—
34	#737	—	31	27	no	—
35	C₃×3₋¹⁺²	—	31	2	no	—
36	C₃×3₋¹⁺²	—	31	3	no	—
37	C₃×3₋¹⁺²	—	31	3	no	—
38	C₃×H(3,𝔽₃)	—	31	1	no	—
39	C₃²×C₉	—	31	3	no	—
40	C₃²×C₉	C₃₁⋊C₃	1	1	yes	characteristic, complemented
41	C₃₁	C₃×#737	1	1	yes	characteristic, complemented, Sylow
42	C₃³	—	31	3	no	—
43	C₃³	C₃×C₃₁⋊C₃	1	1	yes	characteristic
44	3₋¹⁺²	—	31	18	no	—
45	3₋¹⁺²	—	31	27	no	—
46	3₋¹⁺²	—	31	27	no	—
47	H(3,𝔽₃)	—	31	9	no	—
48	C₃×C₉	—	31	6	no	—
49	C₃×C₉	—	31	27	no	—
50	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
51	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
52	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
53	C₃×C₉	C₃×C₃₁⋊C₃	1	9	yes	complemented
54	C₃²	—	3	3	no	—
55	C₃²	—	31	9	no	—
56	C₃²	—	93	9	no	—
57	C₃²	C₃²×C₃₁⋊C₃	1	3	yes	—
58	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
59	C₉	—	31	18	no	—
60	C₉	C₃²×C₃₁⋊C₃	1	3	yes	—
61	C₉	C₃²×C₃₁⋊C₃	1	3	yes	—
62	C₉	C₃²×C₃₁⋊C₃	1	3	yes	—
63	C₃	—	3	3	no	—
64	C₃	—	93	9	no	—
65	C₃	#14578912	1	3	yes	direct product factor
66	C₃	C₃³×C₃₁⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃×C₃₁⋊C₃
commutator	C₃×C₃₁	C₃⁴
Frattini	C₃	C₃³×C₃₁⋊C₃
Fitting	C₃²×C₉×C₃₁	C₃
socle	C₃²×C₃₁	C₃³
hypercenter	C₃²×C₉	C₃₁⋊C₃
hypocenter	C₃₁	C₃×#737
LCS	G ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. #14578912	C₃	direct (N × H)
2. C₃×#11719689	C₃	semidirect
3. C₃×#11719686	C₃	semidirect
4. C₃×#11719687	C₃	semidirect
6. C₃×C₉×C₃₁⋊C₃	C₃	semidirect
7. C₃²×C₉×C₃₁	C₃	semidirect
13. C₃×C₉×C₃₁	C₃²	semidirect
15. #11719689	C₃²	semidirect
17. #11719687	C₃²	semidirect
18. #11719686	C₃²	semidirect
19. C₉×C₃₁⋊C₃	C₃²	semidirect
31. C₃×C₃₁	#737	semidirect
40. C₃²×C₉	C₃₁⋊C₃	semidirect
41. C₃₁	C₃×#737	semidirect
53. C₃×C₉	C₃×C₃₁⋊C₃	semidirect
65. C₃	#14578912	direct (N × H)

Subgroups — C3×#14578912 #21419432

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#14578912 #21419432