Subgroups — C₃×#16812525 #23782918

Order 10449.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812525	C₃	1	27	yes	maximal, direct product factor
2	C₃×#11923958	C₃	1	2	yes	maximal, complemented
3	C₃×#11923957	C₃	1	3	yes	maximal, complemented
4	C₃×#11923956	C₃	1	3	yes	maximal, complemented
5	C₃×C₃²⋊(C₄₃⋊C₃)	C₃	1	1	yes	maximal, characteristic
6	C₃×C₉×C₄₃⋊C₃	C₃	1	3	yes	maximal, complemented
7	C₃²×C₉×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₄₃⋊C₃	C₃²	1	3	yes	—
9	#11923958	C₃²	1	18	yes	complemented
10	#11923957	C₃²	1	27	yes	complemented
11	#11923956	C₃²	1	27	yes	complemented
12	C₃²⋊(C₄₃⋊C₃)	C₃²	1	9	yes	—
13	C₃×C₄₃⋊C₉	C₃²	1	6	yes	—
14	C₉×C₄₃⋊C₃	C₃²	1	27	yes	complemented
15	C₃³×C₄₃	C₃²	1	1	yes	characteristic
16	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
17	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
18	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
19	C₃×C₉×C₄₃	C₃²	1	9	yes	complemented
20	C₃²×C₄₃	—	3	3	no	—
21	C₃²×C₄₃	C₃³	1	3	yes	—
22	C₃²×C₄₃	C₃³	1	1	yes	characteristic
23	C₃×C₄₃⋊C₃	—	3	9	no	—
24	C₃×C₄₃⋊C₃	C₃³	1	9	yes	—
25	C₉×C₄₃	C₃³	1	3	yes	—
26	C₉×C₄₃	C₃³	1	3	yes	—
27	C₉×C₄₃	C₃³	1	3	yes	—
28	C₄₃⋊C₉	C₃³	1	18	yes	—
29	C₃×#737	—	43	1	no	maximal, Sylow
30	C₃×C₄₃	—	3	3	no	—
31	C₃×C₄₃	#737	1	3	yes	complemented
32	C₃×C₄₃	C₃⁴	1	1	yes	characteristic
33	C₄₃⋊C₃	—	3	9	no	—
34	#737	—	43	27	no	—
35	C₃×3₋¹⁺²	—	43	2	no	—
36	C₃×3₋¹⁺²	—	43	3	no	—
37	C₃×3₋¹⁺²	—	43	3	no	—
38	C₃×H(3,𝔽₃)	—	43	1	no	—
39	C₃²×C₉	—	43	3	no	—
40	C₃²×C₉	C₄₃⋊C₃	1	1	yes	characteristic, complemented
41	C₄₃	C₃×#737	1	1	yes	characteristic, complemented, Sylow
42	C₃³	—	43	3	no	—
43	C₃³	C₃×C₄₃⋊C₃	1	1	yes	characteristic
44	3₋¹⁺²	—	43	18	no	—
45	3₋¹⁺²	—	43	27	no	—
46	3₋¹⁺²	—	43	27	no	—
47	H(3,𝔽₃)	—	43	9	no	—
48	C₃×C₉	—	43	6	no	—
49	C₃×C₉	—	43	27	no	—
50	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
51	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
52	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
53	C₃×C₉	C₃×C₄₃⋊C₃	1	9	yes	complemented
54	C₃²	—	3	3	no	—
55	C₃²	—	43	9	no	—
56	C₃²	—	129	9	no	—
57	C₃²	C₃²×C₄₃⋊C₃	1	3	yes	—
58	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
59	C₉	—	43	18	no	—
60	C₉	C₃²×C₄₃⋊C₃	1	3	yes	—
61	C₉	C₃²×C₄₃⋊C₃	1	3	yes	—
62	C₉	C₃²×C₄₃⋊C₃	1	3	yes	—
63	C₃	—	3	3	no	—
64	C₃	—	129	9	no	—
65	C₃	#16812525	1	3	yes	direct product factor
66	C₃	C₃³×C₄₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃×C₄₃⋊C₃
commutator, cosocle	C₃×C₄₃	C₃⁴
Frattini	C₃	C₃³×C₄₃⋊C₃
Fitting	C₃²×C₉×C₄₃	C₃
socle	C₃²×C₄₃	C₃³
prime radical	C₃×C₃²⋊(C₄₃⋊C₃)	C₃
hypercenter	C₃²×C₉	C₄₃⋊C₃
hypocenter	C₄₃	C₃×#737
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. #16812525	C₃	direct (N × H)
2. C₃×#11923958	C₃	semidirect
3. C₃×#11923957	C₃	semidirect
4. C₃×#11923956	C₃	semidirect
6. C₃×C₉×C₄₃⋊C₃	C₃	semidirect
7. C₃²×C₉×C₄₃	C₃	semidirect
9. #11923958	C₃²	semidirect
10. #11923957	C₃²	semidirect
11. #11923956	C₃²	semidirect
14. C₉×C₄₃⋊C₃	C₃²	semidirect
19. C₃×C₉×C₄₃	C₃²	semidirect
31. C₃×C₄₃	#737	semidirect
40. C₃²×C₉	C₄₃⋊C₃	semidirect
41. C₄₃	C₃×#737	semidirect
53. C₃×C₉	C₃×C₄₃⋊C₃	semidirect
65. C₃	#16812525	direct (N × H)

Subgroups — C3×#16812525 #23782918

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#16812525 #23782918