Subgroups — #23782891

Order 10449.

160 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, complemented
2	C₃×C₃²⋊(C₄₃⋊C₃)	C₃	1	2	yes	maximal, complemented
3	#16812512	C₃	1	9	yes	maximal, complemented
4	C₃×H(3,𝔽₃)×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃²×C₄₃⋊C₃	—	3	2	no	—
6	#11923958	—	3	2	no	—
7	#11923958	—	3	1	no	—
8	C₃²⋊(C₄₃⋊C₃)	—	3	2	no	—
9	C₃²⋊(C₄₃⋊C₃)	—	3	2	no	—
10	C₃²⋊(C₄₃⋊C₃)	C₃²	1	6	yes	complemented
11	C₃×C₄₃⋊C₉	C₃²	1	3	yes	complemented
12	C₃³×C₄₃	—	3	1	no	—
13	C₃³×C₄₃	C₃²	1	1	yes	characteristic
14	H(3,𝔽₃)×C₄₃	—	3	2	no	—
15	H(3,𝔽₃)×C₄₃	C₃²	1	3	yes	complemented
16	C₃²×C₄₃	—	3	3	no	—
17	C₃²×C₄₃	—	9	1	no	—
18	C₃²×C₄₃	—	9	3	no	—
19	C₃²×C₄₃	H(3,𝔽₃)	1	2	yes	—
20	C₃²×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃²×C₄₃	C₃³	1	1	yes	characteristic
22	C₃×C₄₃⋊C₃	—	3	6	no	—
23	C₃×C₄₃⋊C₃	—	9	6	no	—
24	C₄₃⋊C₉	—	3	3	no	—
25	#6911	—	43	1	no	maximal, Sylow
26	C₃×C₄₃	—	3	2	no	—
27	C₃×C₄₃	—	3	1	no	—
28	C₃×C₄₃	—	3	1	no	—
29	C₃×C₄₃	—	9	3	no	—
30	C₃×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
31	C₄₃⋊C₃	—	9	6	no	—
32	C₃×3₋¹⁺²	—	43	1	no	—
33	C₃×H(3,𝔽₃)	—	43	2	no	—
34	C₃×H(3,𝔽₃)	C₄₃⋊C₃	1	1	yes	characteristic, complemented
35	#732	—	43	9	no	—
36	C₄₃	#6911	1	1	yes	characteristic, complemented, Sylow
37	C₃³	—	3	1	no	—
38	C₃³	—	129	2	no	—
39	C₃³	C₃×C₄₃⋊C₃	1	1	yes	characteristic
40	3₋¹⁺²	—	129	2	no	—
41	3₋¹⁺²	—	129	1	no	—
42	H(3,𝔽₃)	—	3	2	no	—
43	H(3,𝔽₃)	—	43	6	no	—
44	H(3,𝔽₃)	—	129	2	no	—
45	H(3,𝔽₃)	—	129	2	no	—
46	H(3,𝔽₃)	C₃×C₄₃⋊C₃	1	3	yes	complemented
47	C₃×C₉	—	43	3	no	—
48	C₃²	—	3	3	no	—
49	C₃²	—	9	1	no	—
50	C₃²	—	9	3	no	—
51	C₃²	—	129	6	no	—
52	C₃²	—	387	6	no	—
53	C₃²	C₃²⋊(C₄₃⋊C₃)	1	2	yes	—
54	C₃²	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
55	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
56	C₉	—	129	3	no	—
57	C₃	—	3	1	no	—
58	C₃	—	3	2	no	—
59	C₃	—	3	1	no	—
60	C₃	—	9	3	no	—
61	C₃	—	387	6	no	—
62	C₃	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×C₃²⋊(C₄₃⋊C₃)
commutator, cosocle	C₃²×C₄₃	C₃³
Frattini	C₃²	C₃²×C₄₃⋊C₃
Fitting	C₃×H(3,𝔽₃)×C₄₃	C₃
socle	C₃×C₄₃	C₃×H(3,𝔽₃)
hypercenter	C₃×H(3,𝔽₃)	C₄₃⋊C₃
hypocenter	C₄₃	#6911
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃×#11923958	C₃	semidirect
2. C₃×C₃²⋊(C₄₃⋊C₃)	C₃	semidirect
3. #16812512	C₃	semidirect
4. C₃×H(3,𝔽₃)×C₄₃	C₃	semidirect
10. C₃²⋊(C₄₃⋊C₃)	C₃²	semidirect
11. C₃×C₄₃⋊C₉	C₃²	semidirect
15. H(3,𝔽₃)×C₄₃	C₃²	semidirect
34. C₃×H(3,𝔽₃)	C₄₃⋊C₃	semidirect
36. C₄₃	#6911	semidirect
46. H(3,𝔽₃)	C₃×C₄₃⋊C₃	semidirect