Subgroups — C₃×#14578913 #21419433

Order 7533.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14578913	C₃	1	27	yes	maximal, direct product factor
2	C₃×#11719689	C₃	1	1	yes	maximal, characteristic, 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	C₃²×C₃₁⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃×C₉×C₃₁⋊C₃	C₃	1	3	yes	maximal, complemented
8	C₃×3₋¹⁺²×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
9	C₃³×C₃₁	C₃²	1	1	yes	characteristic
10	C₃²×C₃₁⋊C₃	C₃²	1	3	yes	—
11	3₋¹⁺²×C₃₁	C₃²	1	9	yes	complemented
12	C₃×C₉×C₃₁	C₃²	1	3	yes	—
13	C₃²⋊(C₃₁⋊C₃)	C₃²	1	9	yes	—
14	#11719689	C₃²	1	9	yes	complemented
15	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
16	C₃×C₃₁⋊C₉	C₃²	1	3	yes	—
17	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
18	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
19	C₃×C₃₁⋊C₉	C₃²	1	9	yes	complemented
20	#11719687	C₃²	1	27	yes	complemented
21	#11719686	C₃²	1	27	yes	complemented
22	C₉×C₃₁⋊C₃	C₃²	1	27	yes	complemented
23	C₃²×C₃₁	—	3	3	no	—
24	C₃²×C₃₁	C₃³	1	3	yes	—
25	C₃²×C₃₁	C₃³	1	1	yes	characteristic
26	C₃×C₃₁⋊C₃	—	3	9	no	—
27	C₃×C₃₁⋊C₃	C₃³	1	9	yes	—
28	C₉×C₃₁	C₃³	1	9	yes	—
29	C₃₁⋊C₉	C₃³	1	3	yes	—
30	C₃₁⋊C₉	C₃³	1	9	yes	—
31	C₃₁⋊C₉	C₃³	1	3	yes	—
32	C₃₁⋊C₉	C₃³	1	3	yes	—
33	C₃×#737	—	31	1	no	maximal, Sylow
34	C₃×C₃₁	—	3	3	no	—
35	C₃×C₃₁	#737	1	3	yes	complemented
36	C₃×C₃₁	C₃⁴	1	1	yes	characteristic
37	C₃₁⋊C₃	—	3	9	no	—
38	#737	—	31	27	no	—
39	C₃×3₋¹⁺²	—	31	1	no	—
40	C₃×3₋¹⁺²	—	31	3	no	—
41	C₃×3₋¹⁺²	—	31	3	no	—
42	C₃×3₋¹⁺²	C₃₁⋊C₃	1	1	yes	characteristic, complemented
43	C₃×H(3,𝔽₃)	—	31	1	no	—
44	C₃²×C₉	—	31	1	no	—
45	C₃²×C₉	—	31	3	no	—
46	C₃₁	C₃×#737	1	1	yes	characteristic, complemented, Sylow
47	C₃³	—	31	3	no	—
48	C₃³	C₃×C₃₁⋊C₃	1	1	yes	characteristic
49	3₋¹⁺²	—	31	9	no	—
50	3₋¹⁺²	—	31	27	no	—
51	3₋¹⁺²	—	31	27	no	—
52	3₋¹⁺²	C₃×C₃₁⋊C₃	1	9	yes	complemented
53	H(3,𝔽₃)	—	31	9	no	—
54	C₃×C₉	—	31	9	no	—
55	C₃×C₉	—	31	1	no	—
56	C₃×C₉	—	31	3	no	—
57	C₃×C₉	—	31	1	no	—
58	C₃×C₉	—	31	1	no	—
59	C₃×C₉	—	31	27	no	—
60	C₃×C₉	C₃×C₃₁⋊C₃	1	3	yes	—
61	C₃²	—	3	3	no	—
62	C₃²	—	31	9	no	—
63	C₃²	—	93	9	no	—
64	C₃²	C₃²×C₃₁⋊C₃	1	3	yes	—
65	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
66	C₉	—	31	3	no	—
67	C₉	—	31	9	no	—
68	C₉	—	31	3	no	—
69	C₉	—	31	3	no	—
70	C₉	C₃²×C₃₁⋊C₃	1	9	yes	—
71	C₃	—	3	3	no	—
72	C₃	—	93	9	no	—
73	C₃	#14578913	1	3	yes	direct product factor
74	C₃	C₃³×C₃₁⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²×C₃₁⋊C₃
commutator	C₃×C₃₁	C₃⁴
Frattini	C₃	C₃³×C₃₁⋊C₃
Fitting	C₃×3₋¹⁺²×C₃₁	C₃
socle	C₃²×C₃₁	C₃³
hypercenter	C₃×3₋¹⁺²	C₃₁⋊C₃
hypocenter	C₃₁	C₃×#737
LCS	G ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃² ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. #14578913	C₃	direct (N × H)
2. C₃×#11719689	C₃	semidirect
3. C₃×#11719686	C₃	semidirect
4. C₃×#11719687	C₃	semidirect
6. C₃²×C₃₁⋊C₉	C₃	semidirect
7. C₃×C₉×C₃₁⋊C₃	C₃	semidirect
8. C₃×3₋¹⁺²×C₃₁	C₃	semidirect
11. 3₋¹⁺²×C₃₁	C₃²	semidirect
14. #11719689	C₃²	semidirect
19. C₃×C₃₁⋊C₉	C₃²	semidirect
20. #11719687	C₃²	semidirect
21. #11719686	C₃²	semidirect
22. C₉×C₃₁⋊C₃	C₃²	semidirect
35. C₃×C₃₁	#737	semidirect
42. C₃×3₋¹⁺²	C₃₁⋊C₃	semidirect
46. C₃₁	C₃×#737	semidirect
52. 3₋¹⁺²	C₃×C₃₁⋊C₃	semidirect
73. C₃	#14578913	direct (N × H)

Subgroups — C3×#14578913 #21419433

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#14578913 #21419433