Subgroups — C₃×(C₄₃⋊C₉)⋊C₉ #23782776

Order 10449.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic
4	(C₄₃⋊C₉)⋊C₉	C₃	1	9	yes	maximal, direct product factor
5	C₃²×C₉×C₄₃	C₃	1	1	yes	maximal, characteristic
6	C₃×C₄₃⋊C₉	—	3	3	no	—
7	C₃×C₄₃⋊C₉	—	3	3	no	—
8	C₃×C₄₃⋊C₉	C₉	1	9	yes	complemented
9	C₃×C₄₃⋊C₉	C₃²	1	3	yes	—
10	C₃×C₄₃⋊C₉	C₃²	1	3	yes	—
11	C₃×C₄₃⋊C₉	C₃²	1	3	yes	—
12	C₃³×C₄₃	C₃²	1	1	yes	characteristic
13	C₃×C₉×C₄₃	—	3	3	no	—
14	C₃×C₉×C₄₃	C₃²	1	3	yes	—
15	C₃²×C₄₃	C₃×C₉	1	3	yes	—
16	C₃²×C₄₃	3₋¹⁺²	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	C₉×C₄₃	—	3	3	no	—
21	C₄₃⋊C₉	—	3	3	no	—
22	C₄₃⋊C₉	—	3	3	no	—
23	C₄₃⋊C₉	C₃×C₉	1	9	yes	complemented
24	C₃×C₉⋊C₉	—	43	1	no	maximal, Sylow
25	C₃×C₄₃	C₉⋊C₉	1	9	yes	complemented
26	C₃×C₄₃	C₃²×C₉	1	1	yes	characteristic
27	C₃×C₄₃	C₃×3₋¹⁺²	1	1	yes	characteristic
28	C₃×C₄₃	C₃×3₋¹⁺²	1	1	yes	characteristic
29	C₃×C₄₃	C₃×3₋¹⁺²	1	1	yes	characteristic
30	C₃²×C₉	—	43	1	no	—
31	C₃²×C₉	—	43	1	no	—
32	C₃²×C₉	—	43	1	no	—
33	C₃²×C₉	C₄₃⋊C₃	1	1	yes	characteristic
34	C₉⋊C₉	—	43	9	no	—
35	C₄₃	C₃×C₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
36	C₃³	C₃×C₄₃⋊C₃	1	1	yes	characteristic
37	C₃×C₉	—	3	3	no	—
38	C₃×C₉	—	43	9	no	—
39	C₃×C₉	—	43	3	no	—
40	C₃×C₉	—	43	3	no	—
41	C₃×C₉	—	43	3	no	—
42	C₃×C₉	—	129	3	no	—
43	C₃×C₉	—	129	3	no	—
44	C₃×C₉	C₃×C₄₃⋊C₃	1	3	yes	—
45	C₃²	C₉×C₄₃⋊C₃	1	3	yes	—
46	C₃²	#11923956	1	3	yes	—
47	C₃²	#11923957	1	3	yes	—
48	C₃²	#11923958	1	3	yes	—
49	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
50	C₉	—	3	3	no	—
51	C₉	—	43	9	no	—
52	C₉	—	129	3	no	—
53	C₉	—	129	3	no	—
54	C₃	(C₄₃⋊C₉)⋊C₉	1	9	yes	direct product factor
55	C₃	C₃×C₉×C₄₃⋊C₃	1	1	yes	characteristic
56	C₃	C₃×#11923956	1	1	yes	characteristic
57	C₃	C₃×#11923957	1	1	yes	characteristic
58	C₃	C₃×#11923958	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, prime radical	C₃³×C₄₃	C₃²
cosocle	C₃²×C₄₃	C₃³
hypercenter	C₃²×C₉	C₄₃⋊C₃
hypocenter	C₄₃	C₃×C₉⋊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
4. (C₄₃⋊C₉)⋊C₉	C₃	direct (N × H)
8. C₃×C₄₃⋊C₉	C₉	semidirect
23. C₄₃⋊C₉	C₃×C₉	semidirect
25. C₃×C₄₃	C₉⋊C₉	semidirect
35. C₄₃	C₃×C₉⋊C₉	semidirect
54. C₃	(C₄₃⋊C₉)⋊C₉	direct (N × H)

Subgroups — C3×(C43⋊C9)⋊C9 #23782776

Conjugacy classes of subgroups

Complements

Subgroups — C₃×(C₄₃⋊C₉)⋊C₉ #23782776