Subgroups — C₃×#16812508 #23782862

Order 10449.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×#11923958	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃²⋊(C₄₃⋊C₃)	C₃	1	1	yes	maximal, characteristic, complemented
4	#16812508	C₃	1	9	yes	maximal, direct product factor
5	C₃×3₋¹⁺²×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₄₃⋊C₃	—	3	2	no	—
7	C₃²×C₄₃⋊C₃	—	3	1	no	—
8	C₃²×C₄₃⋊C₃	—	3	9	no	—
9	C₃²×C₄₃⋊C₃	—	3	1	no	—
10	C₃²×C₄₃⋊C₃	C₃²	1	3	yes	complemented
11	#11923958	—	3	2	no	—
12	#11923958	C₃²	1	3	yes	complemented
13	C₃²⋊(C₄₃⋊C₃)	—	3	2	no	—
14	C₃²⋊(C₄₃⋊C₃)	C₃²	1	3	yes	complemented
15	C₃×C₄₃⋊C₉	—	3	1	no	—
16	C₃³×C₄₃	C₃²	1	1	yes	characteristic
17	3₋¹⁺²×C₄₃	—	3	2	no	—
18	3₋¹⁺²×C₄₃	C₃²	1	3	yes	complemented
19	C₃×C₉×C₄₃	—	3	1	no	—
20	C₃²×C₄₃	—	3	3	no	—
21	C₃²×C₄₃	H(3,𝔽₃)	1	2	yes	—
22	C₃²×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
23	C₃²×C₄₃	C₃³	1	1	yes	characteristic
24	C₃×C₄₃⋊C₃	—	3	18	no	—
25	C₃×C₄₃⋊C₃	—	3	9	no	—
26	C₃×C₄₃⋊C₃	—	3	3	no	—
27	C₃×C₄₃⋊C₃	—	3	9	no	—
28	C₃×C₄₃⋊C₃	—	3	3	no	—
29	C₃×C₄₃⋊C₃	—	9	3	no	—
30	C₉×C₄₃	—	3	3	no	—
31	C₄₃⋊C₉	—	3	3	no	—
32	C₃×AΣL(1,𝔽₂₇)	—	43	1	no	maximal, Sylow
33	C₃×C₄₃	—	3	2	no	—
34	C₃×C₄₃	—	3	1	no	—
35	C₃×C₄₃	AΣL(1,𝔽₂₇)	1	3	yes	complemented
36	C₃×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
37	C₄₃⋊C₃	—	3	9	no	—
38	C₄₃⋊C₃	—	9	3	no	—
39	C₃⁴	—	43	1	no	—
40	C₃×3₋¹⁺²	—	43	1	no	—
41	C₃×3₋¹⁺²	C₄₃⋊C₃	1	1	yes	characteristic, complemented
42	C₃×H(3,𝔽₃)	—	43	1	no	—
43	AΣL(1,𝔽₂₇)	—	43	9	no	—
44	C₄₃	C₃×AΣL(1,𝔽₂₇)	1	1	yes	characteristic, complemented, Sylow
45	C₃³	—	43	3	no	—
46	C₃³	—	129	9	no	—
47	C₃³	—	129	2	no	—
48	C₃³	—	129	1	no	—
49	C₃³	—	129	1	no	—
50	C₃³	C₃×C₄₃⋊C₃	1	1	yes	characteristic
51	3₋¹⁺²	—	3	2	no	—
52	3₋¹⁺²	—	43	3	no	—
53	3₋¹⁺²	—	129	2	no	—
54	3₋¹⁺²	C₃×C₄₃⋊C₃	1	3	yes	complemented
55	H(3,𝔽₃)	—	43	3	no	—
56	H(3,𝔽₃)	—	129	2	no	—
57	C₃×C₉	—	3	1	no	—
58	C₃×C₉	—	129	1	no	—
59	C₃²	—	3	3	no	—
60	C₃²	—	129	9	no	—
61	C₃²	—	129	18	no	—
62	C₃²	—	129	9	no	—
63	C₃²	—	129	3	no	—
64	C₃²	—	129	3	no	—
65	C₃²	—	387	3	no	—
66	C₃²	C₃²⋊(C₄₃⋊C₃)	1	2	yes	—
67	C₃²	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
68	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
69	C₉	—	3	3	no	—
70	C₉	—	129	3	no	—
71	C₃	—	3	2	no	—
72	C₃	—	3	1	no	—
73	C₃	—	129	9	no	—
74	C₃	—	387	3	no	—
75	C₃	#16812508	1	3	yes	direct product factor
76	C₃	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊(C₄₃⋊C₃)
commutator, cosocle	C₃²×C₄₃	C₃³
Frattini	C₃²	C₃²×C₄₃⋊C₃
Fitting	C₃×3₋¹⁺²×C₄₃	C₃
socle	C₃²×C₄₃	H(3,𝔽₃)
hypercenter	C₃×3₋¹⁺²	C₄₃⋊C₃
hypocenter	C₄₃	C₃×AΣL(1,𝔽₂₇)
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. C₃³×C₄₃⋊C₃	C₃	semidirect
2. C₃×#11923958	C₃	semidirect
3. C₃×C₃²⋊(C₄₃⋊C₃)	C₃	semidirect
4. #16812508	C₃	direct (N × H)
5. C₃×3₋¹⁺²×C₄₃	C₃	semidirect
10. C₃²×C₄₃⋊C₃	C₃²	semidirect
12. #11923958	C₃²	semidirect
14. C₃²⋊(C₄₃⋊C₃)	C₃²	semidirect
18. 3₋¹⁺²×C₄₃	C₃²	semidirect
35. C₃×C₄₃	AΣL(1,𝔽₂₇)	semidirect
41. C₃×3₋¹⁺²	C₄₃⋊C₃	semidirect
44. C₄₃	C₃×AΣL(1,𝔽₂₇)	semidirect
54. 3₋¹⁺²	C₃×C₄₃⋊C₃	semidirect
75. C₃	#16812508	direct (N × H)

Subgroups — C3×#16812508 #23782862

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#16812508 #23782862