Subgroups — #23782902

Order 10449.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812524	C₃	1	3	yes	maximal, complemented
2	C₃×#11923956	C₃	1	1	yes	maximal, characteristic, complemented
3	#16812515	C₃	1	2	yes	maximal, complemented
4	#16812509	C₃	1	3	yes	maximal, complemented
5	#16812506	C₃	1	3	yes	maximal, complemented
6	C₄₃×#732	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃²×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
8	#11923958	—	3	6	no	—
9	#11923958	C₃²	1	6	yes	—
10	#11923956	—	3	3	no	—
11	C₃×C₄₃⋊C₉	—	3	3	no	—
12	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
13	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
14	H(3,𝔽₃)×C₄₃	C₃²	1	3	yes	—
15	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
16	C₃²×C₄₃	—	3	3	no	—
17	C₃²×C₄₃	C₃³	1	1	yes	characteristic
18	C₃×C₄₃⋊C₃	—	3	1	no	—
19	C₃×C₄₃⋊C₃	—	9	1	no	—
20	C₉×C₄₃	—	3	1	no	—
21	C₄₃⋊C₉	—	3	6	no	—
22	C₄₃⋊C₉	—	3	1	no	—
23	C₄₃⋊C₉	H(3,𝔽₃)	1	3	yes	—
24	#6913	—	43	1	no	maximal, Sylow
25	C₃×C₄₃	—	3	1	no	—
26	C₃×C₄₃	—	9	3	no	—
27	C₃×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	C₄₃⋊C₃	—	9	1	no	—
29	#737	—	43	3	no	—
30	C₃×3₋¹⁺²	—	43	1	no	—
31	#733	—	43	2	no	—
32	#732	C₄₃⋊C₃	1	1	yes	characteristic, complemented
33	#731	—	43	3	no	—
34	AΣL(1,𝔽₂₇)	—	43	3	no	—
35	C₄₃	#6913	1	1	yes	characteristic, complemented, Sylow
36	C₃³	—	43	1	no	—
37	3₋¹⁺²	—	43	6	no	—
38	3₋¹⁺²	—	129	3	no	—
39	3₋¹⁺²	—	129	6	no	—
40	H(3,𝔽₃)	C₃×C₄₃⋊C₃	1	3	yes	—
41	C₃×C₉	—	43	1	no	—
42	C₃×C₉	—	43	1	no	—
43	C₃×C₉	—	129	3	no	—
44	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
45	C₃²	—	3	3	no	—
46	C₃²	—	129	1	no	—
47	C₃²	—	387	1	no	—
48	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
49	C₉	—	3	1	no	—
50	C₉	—	43	3	no	—
51	C₉	—	129	1	no	—
52	C₉	—	129	6	no	—
53	C₃	—	3	1	no	—
54	C₃	—	9	3	no	—
55	C₃	—	387	1	no	—
56	C₃	H(3,𝔽₃)×C₄₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃	H(3,𝔽₃)×C₄₃⋊C₃
commutator, cosocle	C₃²×C₄₃	C₃³
Frattini	C₃²	C₃²×C₄₃⋊C₃
Fitting	C₄₃×#732	C₃
socle	C₃×C₄₃	C₃×H(3,𝔽₃)
hypercenter	#732	C₄₃⋊C₃
hypocenter	C₄₃	#6913
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃² ◁ #732

Complements

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

N	H ≅ G/N	type
1. #16812524	C₃	semidirect
2. C₃×#11923956	C₃	semidirect
3. #16812515	C₃	semidirect
4. #16812509	C₃	semidirect
5. #16812506	C₃	semidirect
6. C₄₃×#732	C₃	semidirect
32. #732	C₄₃⋊C₃	semidirect
35. C₄₃	#6913	semidirect