Subgroups — #23782823

Order 10449.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11923958	C₃	1	2	yes	maximal
2	#16812500	C₃	1	1	yes	maximal, characteristic, complemented
3	#16812499	C₃	1	1	yes	maximal, characteristic, complemented
4	(C₄₃⋊C₉)⋊C₉	C₃	1	2	yes	maximal, complemented
5	(C₄₃⋊C₉)⋊C₉	C₃	1	2	yes	maximal, complemented
6	(C₄₃⋊C₉)⋊C₉	C₃	1	2	yes	maximal, complemented
7	C₃²⋊(C₄₃⋊C₉)	C₃	1	1	yes	maximal, characteristic
8	C₉×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
9	C₄₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
10	#11923958	—	3	6	no	—
11	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
12	C₃×C₄₃⋊C₉	C₃²	1	2	yes	—
13	C₃×C₄₃⋊C₉	C₃²	1	2	yes	—
14	C₃×C₄₃⋊C₉	C₃²	1	2	yes	—
15	C₃×C₄₃⋊C₉	C₃²	1	2	yes	—
16	C₃³×C₄₃	C₃²	1	1	yes	characteristic
17	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
18	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
19	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
20	C₃²×C₄₃	—	3	2	no	—
21	C₃²×C₄₃	—	3	1	no	—
22	C₃²×C₄₃	—	3	1	no	—
23	C₃²×C₄₃	C₃³	1	1	yes	characteristic
24	C₉×C₄₃	—	3	1	no	—
25	C₉×C₄₃	—	3	1	no	—
26	C₉×C₄₃	—	3	1	no	—
27	C₄₃⋊C₉	—	3	2	no	—
28	C₄₃⋊C₉	—	3	2	no	—
29	C₄₃⋊C₉	—	3	1	no	—
30	C₄₃⋊C₉	—	3	2	no	—
31	C₄₃⋊C₉	3₋¹⁺²	1	6	yes	complemented
32	#6896	—	43	1	no	maximal, Sylow
33	C₃×C₄₃	—	9	1	no	—
34	C₃×C₄₃	C₃×3₋¹⁺²	1	2	yes	—
35	C₃×C₄₃	#737	1	1	yes	characteristic
36	C₃×C₄₃	#737	1	1	yes	characteristic
37	C₃×3₋¹⁺²	—	43	2	no	—
38	C₉⋊C₉	—	43	2	no	—
39	C₉⋊C₉	—	43	2	no	—
40	C₉⋊C₉	—	43	2	no	—
41	C₉⋊C₉	—	43	1	no	—
42	C₉⋊C₉	—	43	1	no	—
43	C₃²⋊C₉	—	43	1	no	—
44	C₃²⋊C₉	C₄₃⋊C₃	1	1	yes	characteristic
45	C₉²	—	43	1	no	—
46	C₄₃	#6896	1	1	yes	characteristic, complemented, Sylow
47	C₃³	C₃×C₄₃⋊C₃	1	1	yes	characteristic
48	3₋¹⁺²	—	129	6	no	—
49	C₃×C₉	—	43	2	no	—
50	C₃×C₉	—	43	1	no	—
51	C₃×C₉	—	43	2	no	—
52	C₃×C₉	—	43	2	no	—
53	C₃×C₉	—	43	2	no	—
54	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
55	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
56	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
57	C₃²	—	3	2	no	—
58	C₃²	—	3	1	no	—
59	C₃²	—	3	1	no	—
60	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
61	C₉	—	3	1	no	—
62	C₉	—	3	1	no	—
63	C₉	—	3	1	no	—
64	C₉	—	43	6	no	—
65	C₉	—	129	2	no	—
66	C₉	—	129	2	no	—
67	C₉	—	129	1	no	—
68	C₉	—	129	2	no	—
69	C₃	—	9	1	no	—
70	C₃	3₋¹⁺²×C₄₃⋊C₃	1	2	yes	—
71	C₃	#16812524	1	1	yes	characteristic
72	C₃	#16812525	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₄₃⋊C₃
commutator, socle, cosocle	C₃²×C₄₃	C₃³
Fitting	C₄₃×C₃²⋊C₉	C₃
prime radical	C₃³×C₄₃	C₃²
hypercenter	C₃²⋊C₉	C₄₃⋊C₃
hypocenter	C₄₃	#6896
LCS	G ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
2. #16812500	C₃	semidirect
3. #16812499	C₃	semidirect
4. (C₄₃⋊C₉)⋊C₉	C₃	semidirect
5. (C₄₃⋊C₉)⋊C₉	C₃	semidirect
6. (C₄₃⋊C₉)⋊C₉	C₃	semidirect
8. C₉×C₄₃⋊C₉	C₃	semidirect
31. C₄₃⋊C₉	3₋¹⁺²	semidirect
46. C₄₃	#6896	semidirect