Subgroups — C₃×#16812511 #23782866

Order 10449.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11923958	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×C₃²⋊(C₄₃⋊C₃)	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	#16812511	C₃	1	9	yes	maximal, direct product factor
5	C₃×3₋¹⁺²×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₄₃⋊C₃	—	3	1	no	—
7	#11923958	—	3	2	no	—
8	#11923958	C₃²	1	3	yes	complemented
9	C₃²⋊(C₄₃⋊C₃)	—	3	2	no	—
10	C₃²⋊(C₄₃⋊C₃)	C₃²	1	3	yes	—
11	C₃×C₄₃⋊C₉	—	3	2	no	—
12	C₃×C₄₃⋊C₉	—	3	1	no	—
13	C₃×C₄₃⋊C₉	—	3	1	no	—
14	C₃×C₄₃⋊C₉	C₃²	1	3	yes	complemented
15	C₃³×C₄₃	C₃²	1	1	yes	characteristic
16	3₋¹⁺²×C₄₃	—	3	2	no	—
17	3₋¹⁺²×C₄₃	C₃²	1	3	yes	complemented
18	C₃×C₉×C₄₃	—	3	1	no	—
19	C₃²×C₄₃	—	3	3	no	—
20	C₃²×C₄₃	H(3,𝔽₃)	1	2	yes	—
21	C₃²×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
22	C₃²×C₄₃	C₃³	1	1	yes	characteristic
23	C₃×C₄₃⋊C₃	—	3	3	no	—
24	C₃×C₄₃⋊C₃	—	9	3	no	—
25	C₉×C₄₃	—	3	3	no	—
26	C₄₃⋊C₉	—	3	3	no	—
27	C₄₃⋊C₉	—	3	3	no	—
28	C₃×#731	—	43	1	no	maximal, Sylow
29	C₃×C₄₃	—	3	2	no	—
30	C₃×C₄₃	—	3	1	no	—
31	C₃×C₄₃	#731	1	3	yes	complemented
32	C₃×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
33	C₄₃⋊C₃	—	9	3	no	—
34	C₃×3₋¹⁺²	—	43	1	no	—
35	C₃×3₋¹⁺²	C₄₃⋊C₃	1	1	yes	characteristic, complemented
36	C₃×H(3,𝔽₃)	—	43	1	no	—
37	C₃²×C₉	—	43	1	no	—
38	#731	—	43	9	no	—
39	C₄₃	C₃×#731	1	1	yes	characteristic, complemented, Sylow
40	C₃³	—	129	1	no	—
41	C₃³	C₃×C₄₃⋊C₃	1	1	yes	characteristic
42	3₋¹⁺²	—	3	2	no	—
43	3₋¹⁺²	—	43	3	no	—
44	3₋¹⁺²	—	129	2	no	—
45	3₋¹⁺²	C₃×C₄₃⋊C₃	1	3	yes	complemented
46	H(3,𝔽₃)	—	43	3	no	—
47	H(3,𝔽₃)	—	129	2	no	—
48	C₃×C₉	—	3	1	no	—
49	C₃×C₉	—	43	3	no	—
50	C₃×C₉	—	129	2	no	—
51	C₃×C₉	—	129	1	no	—
52	C₃×C₉	—	129	1	no	—
53	C₃²	—	3	3	no	—
54	C₃²	—	129	3	no	—
55	C₃²	—	387	3	no	—
56	C₃²	C₃²⋊(C₄₃⋊C₃)	1	2	yes	—
57	C₃²	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
58	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
59	C₉	—	3	3	no	—
60	C₉	—	129	3	no	—
61	C₉	—	129	3	no	—
62	C₃	—	3	2	no	—
63	C₃	—	3	1	no	—
64	C₃	—	387	3	no	—
65	C₃	#16812511	1	3	yes	direct product factor
66	C₃	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊(C₄₃⋊C₃)
commutator, cosocle	C₃²×C₄₃	C₃³
Frattini	C₃²	C₃²×C₄₃⋊C₃
Fitting	C₃×3₋¹⁺²×C₄₃	C₃
socle	C₃²×C₄₃	H(3,𝔽₃)
prime radical	C₃×C₃²⋊(C₄₃⋊C₃)	C₃
hypercenter	C₃×3₋¹⁺²	C₄₃⋊C₃
hypocenter	C₄₃	C₃×#731
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. C₃×#11923958	C₃	semidirect
3. C₃²×C₄₃⋊C₉	C₃	semidirect
4. #16812511	C₃	direct (N × H)
5. C₃×3₋¹⁺²×C₄₃	C₃	semidirect
8. #11923958	C₃²	semidirect
14. C₃×C₄₃⋊C₉	C₃²	semidirect
17. 3₋¹⁺²×C₄₃	C₃²	semidirect
31. C₃×C₄₃	#731	semidirect
35. C₃×3₋¹⁺²	C₄₃⋊C₃	semidirect
39. C₄₃	C₃×#731	semidirect
45. 3₋¹⁺²	C₃×C₄₃⋊C₃	semidirect
65. C₃	#16812511	direct (N × H)

Subgroups — C3×#16812511 #23782866

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#16812511 #23782866