Subgroups — #23782817

Order 10449.

124 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	#16812500	C₃	1	3	yes	maximal, complemented
4	(C₄₃⋊C₉)⋊C₉	C₃	1	3	yes	maximal, complemented
5	(C₄₃⋊C₉)⋊C₉	C₃	1	3	yes	maximal, complemented
6	C₃²⋊(C₄₃⋊C₉)	C₃	1	1	yes	maximal, characteristic
7	C₄₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
8	#11923958	—	3	3	no	—
9	C₃×C₄₃⋊C₉	—	3	3	no	—
10	C₃×C₄₃⋊C₉	C₃²	1	3	yes	—
11	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
12	C₃×C₄₃⋊C₉	C₃²	1	3	yes	—
13	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
14	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
15	C₃³×C₄₃	C₃²	1	1	yes	characteristic
16	C₃×C₉×C₄₃	C₃²	1	3	yes	—
17	C₃²×C₄₃	—	3	1	no	—
18	C₃²×C₄₃	—	3	1	no	—
19	C₃²×C₄₃	—	3	1	no	—
20	C₃²×C₄₃	3₋¹⁺²	1	3	yes	—
21	C₃²×C₄₃	C₃³	1	1	yes	characteristic
22	C₉×C₄₃	—	3	3	no	—
23	C₄₃⋊C₉	—	3	1	no	—
24	C₄₃⋊C₉	—	3	1	no	—
25	C₄₃⋊C₉	—	3	3	no	—
26	C₄₃⋊C₉	—	3	3	no	—
27	C₄₃⋊C₉	3₋¹⁺²	1	3	yes	complemented
28	#6894	—	43	1	no	maximal, Sylow
29	C₃×C₄₃	—	3	3	no	—
30	C₃×C₄₃	C₃×3₋¹⁺²	1	1	yes	characteristic
31	C₃×C₄₃	C₃×3₋¹⁺²	1	1	yes	characteristic
32	C₃×C₄₃	#737	1	1	yes	characteristic
33	C₃×C₄₃	#737	1	1	yes	characteristic
34	C₃×3₋¹⁺²	—	43	1	no	—
35	C₃²×C₉	—	43	1	no	—
36	C₉⋊C₉	—	43	3	no	—
37	C₉⋊C₉	—	43	3	no	—
38	C₉⋊C₉	—	43	3	no	—
39	C₃²⋊C₉	—	43	1	no	—
40	C₃²⋊C₉	C₄₃⋊C₃	1	1	yes	characteristic
41	C₄₃	#6894	1	1	yes	characteristic, complemented, Sylow
42	C₃³	C₃×C₄₃⋊C₃	1	1	yes	characteristic
43	3₋¹⁺²	—	129	3	no	—
44	C₃×C₉	—	43	1	no	—
45	C₃×C₉	—	43	3	no	—
46	C₃×C₉	—	43	1	no	—
47	C₃×C₉	—	43	1	no	—
48	C₃×C₉	—	43	3	no	—
49	C₃×C₉	—	129	3	no	—
50	C₃×C₉	C₃×C₄₃⋊C₃	1	3	yes	—
51	C₃²	—	3	1	no	—
52	C₃²	—	3	1	no	—
53	C₃²	—	3	1	no	—
54	C₃²	#11923956	1	3	yes	—
55	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
56	C₉	—	3	3	no	—
57	C₉	—	43	3	no	—
58	C₉	—	129	1	no	—
59	C₉	—	129	1	no	—
60	C₉	—	129	3	no	—
61	C₉	—	129	3	no	—
62	C₃	—	3	3	no	—
63	C₃	3₋¹⁺²×C₄₃⋊C₃	1	1	yes	characteristic
64	C₃	C₃×#11923956	1	1	yes	characteristic
65	C₃	#16812524	1	1	yes	characteristic
66	C₃	#16812526	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	#6894
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
3. #16812500	C₃	semidirect
4. (C₄₃⋊C₉)⋊C₉	C₃	semidirect
5. (C₄₃⋊C₉)⋊C₉	C₃	semidirect
27. C₄₃⋊C₉	3₋¹⁺²	semidirect
41. C₄₃	#6894	semidirect