Subgroups — #23782828

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	#16812500	C₃	1	1	yes	maximal, characteristic, complemented
5	(C₄₃⋊C₉)⋊C₉	C₃	1	2	yes	maximal, complemented
6	(C₄₃⋊C₉)⋊C₉	C₃	1	2	yes	maximal, complemented
7	(C₃×C₄₃⋊C₃)⋊C₉	C₃	1	2	yes	maximal
8	C₉×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
9	C₄₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
10	C₃²×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
11	#11923957	—	3	3	no	—
12	#11923956	—	3	3	no	—
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	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
17	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
18	C₃×C₉×C₄₃	C₃²	1	2	yes	—
19	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
20	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
21	C₃²×C₄₃	C₃³	1	1	yes	characteristic
22	C₃×C₄₃⋊C₃	—	3	1	no	—
23	C₃×C₄₃⋊C₃	—	3	1	no	—
24	C₃×C₄₃⋊C₃	—	3	2	no	—
25	C₉×C₄₃	—	3	1	no	—
26	C₉×C₄₃	—	3	2	no	—
27	C₉×C₄₃	3₋¹⁺²	1	3	yes	complemented
28	C₄₃⋊C₉	—	3	1	no	—
29	C₄₃⋊C₉	—	3	2	no	—
30	C₄₃⋊C₉	—	3	2	no	—
31	C₄₃⋊C₉	—	3	2	no	—
32	C₄₃⋊C₉	3₋¹⁺²	1	3	yes	complemented
33	#6896	—	43	1	no	maximal, Sylow
34	C₃×C₄₃	C₃×3₋¹⁺²	1	1	yes	characteristic
35	C₃×C₄₃	C₃×3₋¹⁺²	1	1	yes	characteristic
36	C₃×C₄₃	#737	1	2	yes	—
37	C₄₃⋊C₃	—	9	1	no	—
38	C₃×3₋¹⁺²	—	43	1	no	—
39	C₃×3₋¹⁺²	—	43	1	no	—
40	C₉⋊C₉	—	43	2	no	—
41	C₉⋊C₉	—	43	2	no	—
42	C₉⋊C₉	—	43	2	no	—
43	C₉⋊C₉	—	43	1	no	—
44	C₉⋊C₉	C₄₃⋊C₃	1	1	yes	characteristic, complemented
45	C₃²⋊C₉	—	43	2	no	—
46	C₉²	—	43	1	no	—
47	C₄₃	#6896	1	1	yes	characteristic, complemented, Sylow
48	C₃³	—	43	1	no	—
49	3₋¹⁺²	—	129	3	no	—
50	3₋¹⁺²	—	129	3	no	—
51	C₃×C₉	—	43	1	no	—
52	C₃×C₉	—	43	2	no	—
53	C₃×C₉	—	43	2	no	—
54	C₃×C₉	—	43	1	no	—
55	C₃×C₉	—	43	2	no	—
56	C₃×C₉	C₃×C₄₃⋊C₃	1	2	yes	—
57	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
58	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
59	C₃²	—	129	1	no	—
60	C₃²	—	129	1	no	—
61	C₃²	—	129	2	no	—
62	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
63	C₉	—	3	1	no	—
64	C₉	—	3	2	no	—
65	C₉	—	43	3	no	—
66	C₉	—	129	1	no	—
67	C₉	—	129	2	no	—
68	C₉	—	129	2	no	—
69	C₉	—	129	2	no	—
70	C₉	#11923956	1	3	yes	complemented
71	C₃	—	387	1	no	—
72	C₃	3₋¹⁺²×C₄₃⋊C₃	1	1	yes	characteristic
73	C₃	C₃×#11923956	1	1	yes	characteristic
74	C₃	#16812526	1	2	yes	—

	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	#6896
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. #16812500	C₃	semidirect
4. #16812500	C₃	semidirect
5. (C₄₃⋊C₉)⋊C₉	C₃	semidirect
6. (C₄₃⋊C₉)⋊C₉	C₃	semidirect
8. C₉×C₄₃⋊C₉	C₃	semidirect
9. C₄₃×C₉⋊C₉	C₃	semidirect
27. C₉×C₄₃	3₋¹⁺²	semidirect
32. C₄₃⋊C₉	3₋¹⁺²	semidirect
44. C₉⋊C₉	C₄₃⋊C₃	semidirect
47. C₄₃	#6896	semidirect
70. C₉	#11923956	semidirect