Subgroups — C₃×(C₃×C₄₃⋊C₃)⋊C₉ #23782773

Order 10449.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
2. C₃²×C₄₃⋊C₉	C₃	semidirect
3. (C₃×C₄₃⋊C₃)⋊C₉	C₃	direct (N × H)
4. C₃²×C₉×C₄₃	C₃	semidirect
8. C₃²×C₄₃⋊C₃	C₉	semidirect
11. C₃×C₄₃⋊C₉	C₃²	semidirect
14. C₃×C₉×C₄₃	C₃²	semidirect
24. C₃×C₄₃⋊C₃	C₃×C₉	semidirect
28. C₃×C₄₃	C₃²⋊C₉	semidirect
36. C₃²×C₉	C₄₃⋊C₃	semidirect
38. C₄₃	C₃×C₃²⋊C₉	semidirect
48. C₃×C₉	C₃×C₄₃⋊C₃	semidirect
62. C₃	(C₃×C₄₃⋊C₃)⋊C₉	direct (N × H)

Subgroups — C3×(C3×C43⋊C3)⋊C9 #23782773

Conjugacy classes of subgroups

Complements

Subgroups — C₃×(C₃×C₄₃⋊C₃)⋊C₉ #23782773