Subgroups — #23782825

Order 10449.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11923957	C₃	1	1	yes	maximal, characteristic
2	C₃×#11923956	C₃	1	1	yes	maximal, characteristic
3	#16812500	C₃	1	2	yes	maximal, complemented
4	#16812499	C₃	1	2	yes	maximal, complemented
5	(C₄₃⋊C₉)⋊C₉	C₃	1	4	yes	maximal, complemented
6	(C₃×C₄₃⋊C₃)⋊C₉	C₃	1	2	yes	maximal
7	C₉²×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
9	#11923957	—	3	3	no	—
10	#11923956	—	3	3	no	—
11	C₃×C₄₃⋊C₉	C₃²	1	4	yes	—
12	C₃×C₄₃⋊C₉	C₃²	1	2	yes	—
13	C₃×C₄₃⋊C₉	C₃²	1	2	yes	—
14	C₃×C₉×C₄₃	C₃²	1	2	yes	—
15	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
16	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
17	C₃²×C₄₃	C₃³	1	1	yes	characteristic
18	C₃×C₄₃⋊C₃	—	3	1	no	—
19	C₃×C₄₃⋊C₃	—	3	1	no	—
20	C₃×C₄₃⋊C₃	—	3	2	no	—
21	C₉×C₄₃	—	3	2	no	—
22	C₉×C₄₃	3₋¹⁺²	1	3	yes	complemented
23	C₉×C₄₃	3₋¹⁺²	1	3	yes	complemented
24	C₄₃⋊C₉	—	3	2	no	—
25	C₄₃⋊C₉	—	3	2	no	—
26	C₄₃⋊C₉	—	3	4	no	—
27	#6896	—	43	1	no	maximal, Sylow
28	C₃×C₄₃	C₃×3₋¹⁺²	1	1	yes	characteristic
29	C₃×C₄₃	C₃×3₋¹⁺²	1	1	yes	characteristic
30	C₃×C₄₃	#737	1	2	yes	—
31	C₄₃⋊C₃	—	9	1	no	—
32	C₃×3₋¹⁺²	—	43	1	no	—
33	C₃×3₋¹⁺²	—	43	1	no	—
34	C₉⋊C₉	—	43	4	no	—
35	C₉⋊C₉	—	43	2	no	—
36	C₉⋊C₉	—	43	2	no	—
37	C₃²⋊C₉	—	43	2	no	—
38	C₉²	C₄₃⋊C₃	1	1	yes	characteristic, complemented
39	C₄₃	#6896	1	1	yes	characteristic, complemented, Sylow
40	C₃³	—	43	1	no	—
41	3₋¹⁺²	—	129	3	no	—
42	3₋¹⁺²	—	129	3	no	—
43	C₃×C₉	—	43	4	no	—
44	C₃×C₉	—	43	2	no	—
45	C₃×C₉	—	43	2	no	—
46	C₃×C₉	C₃×C₄₃⋊C₃	1	2	yes	—
47	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
48	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
49	C₃²	—	129	1	no	—
50	C₃²	—	129	1	no	—
51	C₃²	—	129	2	no	—
52	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
53	C₉	—	3	2	no	—
54	C₉	—	129	2	no	—
55	C₉	—	129	2	no	—
56	C₉	—	129	4	no	—
57	C₉	#11923956	1	3	yes	complemented
58	C₉	#11923957	1	3	yes	complemented
59	C₃	—	387	1	no	—
60	C₃	C₃×#11923956	1	1	yes	characteristic
61	C₃	C₃×#11923957	1	1	yes	characteristic
62	C₃	#16812525	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₄₃⋊C₃
commutator, socle, cosocle	C₃²×C₄₃	C₃³
Fitting	C₉²×C₄₃	C₃
prime radical	C₃²×C₄₃⋊C₃	C₃²
hypercenter	C₉²	C₄₃⋊C₃
hypocenter	C₄₃	#6896
LCS	G ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₉²

Complements

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

N	H ≅ G/N	type
3. #16812500	C₃	semidirect
4. #16812499	C₃	semidirect
5. (C₄₃⋊C₉)⋊C₉	C₃	semidirect
7. C₉²×C₄₃	C₃	semidirect
22. C₉×C₄₃	3₋¹⁺²	semidirect
23. C₉×C₄₃	3₋¹⁺²	semidirect
38. C₉²	C₄₃⋊C₃	semidirect
39. C₄₃	#6896	semidirect
57. C₉	#11923956	semidirect
58. C₉	#11923957	semidirect