Subgroups — #23782848

Order 10449.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11923956	C₃	1	3	yes	maximal
2	C₃×#11923956	C₃	1	1	yes	maximal, characteristic
3	#16812499	C₃	1	1	yes	maximal, characteristic, complemented
4	(C₄₃⋊C₉)⋊C₉	C₃	1	6	yes	maximal, complemented
5	C₉×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
6	C₄₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃²×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
8	#11923956	—	3	3	no	—
9	#11923956	—	3	9	no	—
10	C₃×C₄₃⋊C₉	C₃²	1	2	yes	—
11	C₃×C₄₃⋊C₉	C₃²	1	3	yes	—
12	C₃×C₄₃⋊C₉	C₃²	1	3	yes	—
13	C₃×C₉×C₄₃	C₃²	1	3	yes	—
14	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
15	C₃²×C₄₃	C₃³	1	1	yes	characteristic
16	C₃×C₄₃⋊C₃	—	3	3	no	—
17	C₃×C₄₃⋊C₃	—	3	1	no	—
18	C₉×C₄₃	—	3	3	no	—
19	C₉×C₄₃	3₋¹⁺²	1	3	yes	complemented
20	C₄₃⋊C₉	—	3	3	no	—
21	C₄₃⋊C₉	—	3	2	no	—
22	C₄₃⋊C₉	3₋¹⁺²	1	9	yes	complemented
23	#6900	—	43	1	no	maximal, Sylow
24	C₃×C₄₃	C₃×3₋¹⁺²	1	3	yes	—
25	C₃×C₄₃	C₃×3₋¹⁺²	1	1	yes	characteristic
26	C₄₃⋊C₃	—	9	1	no	—
27	C₃×3₋¹⁺²	—	43	3	no	—
28	C₃×3₋¹⁺²	—	43	1	no	—
29	C₉⋊C₉	—	43	6	no	—
30	C₉⋊C₉	—	43	1	no	—
31	C₉⋊C₉	C₄₃⋊C₃	1	1	yes	characteristic, complemented
32	C₉²	—	43	1	no	—
33	C₄₃	#6900	1	1	yes	characteristic, complemented, Sylow
34	C₃³	—	43	1	no	—
35	3₋¹⁺²	—	129	9	no	—
36	3₋¹⁺²	—	129	3	no	—
37	C₃×C₉	—	43	3	no	—
38	C₃×C₉	—	43	3	no	—
39	C₃×C₉	—	43	2	no	—
40	C₃×C₉	C₃×C₄₃⋊C₃	1	3	yes	—
41	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
42	C₃²	—	129	3	no	—
43	C₃²	—	129	1	no	—
44	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
45	C₉	—	3	3	no	—
46	C₉	—	43	9	no	—
47	C₉	—	129	3	no	—
48	C₉	—	129	2	no	—
49	C₉	#11923956	1	3	yes	complemented
50	C₃	—	387	1	no	—
51	C₃	3₋¹⁺²×C₄₃⋊C₃	1	3	yes	—
52	C₃	C₃×#11923956	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₄₃⋊C₃
commutator, socle, cosocle	C₃²×C₄₃	C₃³
Fitting	C₄₃×C₉⋊C₉	C₃
prime radical	C₃²×C₄₃⋊C₃	C₃²
hypercenter	C₉⋊C₉	C₄₃⋊C₃
hypocenter	C₄₃	#6900
LCS	G ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

Complements

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

N	H ≅ G/N	type
3. #16812499	C₃	semidirect
4. (C₄₃⋊C₉)⋊C₉	C₃	semidirect
5. C₉×C₄₃⋊C₉	C₃	semidirect
6. C₄₃×C₉⋊C₉	C₃	semidirect
19. C₉×C₄₃	3₋¹⁺²	semidirect
22. C₄₃⋊C₉	3₋¹⁺²	semidirect
31. C₉⋊C₉	C₄₃⋊C₃	semidirect
33. C₄₃	#6900	semidirect
49. C₉	#11923956	semidirect