Subgroups — #23782792

Order 10449.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11923958	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic
3	(C₄₃⋊C₉)⋊C₉	C₃	1	6	yes	maximal, complemented
4	C₃²⋊(C₄₃⋊C₉)	C₃	1	1	yes	maximal, characteristic
5	C₉×C₄₃⋊C₉	C₃	1	3	yes	maximal, complemented
6	C₄₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
7	#11923958	C₉	1	9	yes	complemented
8	C₃×C₄₃⋊C₉	—	3	3	no	—
9	C₃×C₄₃⋊C₉	C₃²	1	3	yes	—
10	C₃×C₄₃⋊C₉	C₃²	1	2	yes	—
11	C₃×C₄₃⋊C₉	C₃²	1	3	yes	—
12	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
13	C₃³×C₄₃	C₃²	1	1	yes	characteristic
14	C₃×C₉×C₄₃	C₃²	1	3	yes	—
15	C₃²×C₄₃	—	3	1	no	—
16	C₃²×C₄₃	—	3	1	no	—
17	C₃²×C₄₃	—	3	1	no	—
18	C₃²×C₄₃	C₃×C₉	1	3	yes	—
19	C₃²×C₄₃	C₃³	1	1	yes	characteristic
20	C₉×C₄₃	—	3	3	no	—
21	C₄₃⋊C₉	—	3	2	no	—
22	C₄₃⋊C₉	—	3	3	no	—
23	C₄₃⋊C₉	C₃×C₉	1	9	yes	complemented
24	C₄₃⋊C₉	3₋¹⁺²	1	3	yes	complemented
25	C₉×3₋¹⁺²	—	43	1	no	maximal, Sylow
26	C₃×C₄₃	—	3	3	no	—
27	C₃×C₄₃	C₃²×C₉	1	1	yes	characteristic
28	C₃×C₄₃	C₃×3₋¹⁺²	1	1	yes	characteristic
29	C₃×C₄₃	#737	1	1	yes	characteristic
30	C₃×C₄₃	#737	1	1	yes	characteristic
31	C₃×3₋¹⁺²	—	43	1	no	—
32	C₃²×C₉	—	43	1	no	—
33	C₉⋊C₉	—	43	6	no	—
34	C₃²⋊C₉	—	43	1	no	—
35	C₃²⋊C₉	C₄₃⋊C₃	1	1	yes	characteristic
36	C₉²	—	43	3	no	—
37	C₄₃	C₉×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
38	C₃³	C₃×C₄₃⋊C₃	1	1	yes	characteristic
39	3₋¹⁺²	—	43	9	no	—
40	C₃×C₉	—	43	1	no	—
41	C₃×C₉	—	43	3	no	—
42	C₃×C₉	—	43	3	no	—
43	C₃×C₉	—	43	2	no	—
44	C₃×C₉	—	129	3	no	—
45	C₃×C₉	C₃×C₄₃⋊C₃	1	3	yes	—
46	C₃²	—	3	1	no	—
47	C₃²	—	3	1	no	—
48	C₃²	—	3	1	no	—
49	C₃²	C₉×C₄₃⋊C₃	1	3	yes	—
50	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
51	C₉	—	3	3	no	—
52	C₉	—	43	9	no	—
53	C₉	—	43	3	no	—
54	C₉	—	129	2	no	—
55	C₉	—	129	3	no	—
56	C₃	—	3	3	no	—
57	C₃	C₃×C₉×C₄₃⋊C₃	1	1	yes	characteristic
58	C₃	3₋¹⁺²×C₄₃⋊C₃	1	1	yes	characteristic
59	C₃	#16812524	1	1	yes	characteristic
60	C₃	#16812526	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₄₃⋊C₃
commutator	C₃×C₄₃	C₃²×C₉
Fitting	C₄₃×C₃²⋊C₉	C₃
socle, cosocle	C₃²×C₄₃	C₃³
prime radical	C₃³×C₄₃	C₃²
hypercenter	C₃²⋊C₉	C₄₃⋊C₃
hypocenter	C₄₃	C₉×3₋¹⁺²
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
3. (C₄₃⋊C₉)⋊C₉	C₃	semidirect
5. C₉×C₄₃⋊C₉	C₃	semidirect
7. #11923958	C₉	semidirect
23. C₄₃⋊C₉	C₃×C₉	semidirect
24. C₄₃⋊C₉	3₋¹⁺²	semidirect
37. C₄₃	C₉×3₋¹⁺²	semidirect