Subgroups — C₃×#16812512 #23782868

Order 10449.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊(C₄₃⋊C₃)	C₃	1	2	yes	maximal, complemented
2	C₃²×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
3	#16812512	C₃	1	9	yes	maximal, direct product factor
4	C₃×H(3,𝔽₃)×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃²×C₄₃⋊C₃	—	3	2	no	—
6	C₃²⋊(C₄₃⋊C₃)	—	3	4	no	—
7	C₃²⋊(C₄₃⋊C₃)	C₃²	1	6	yes	complemented
8	C₃×C₄₃⋊C₉	—	3	2	no	—
9	C₃×C₄₃⋊C₉	—	3	1	no	—
10	C₃×C₄₃⋊C₉	C₃²	1	3	yes	complemented
11	C₃³×C₄₃	—	3	1	no	—
12	C₃³×C₄₃	C₃²	1	1	yes	characteristic
13	H(3,𝔽₃)×C₄₃	—	3	2	no	—
14	H(3,𝔽₃)×C₄₃	C₃²	1	3	yes	complemented
15	C₃²×C₄₃	—	3	3	no	—
16	C₃²×C₄₃	—	3	3	no	—
17	C₃²×C₄₃	—	9	3	no	—
18	C₃²×C₄₃	H(3,𝔽₃)	1	2	yes	—
19	C₃²×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
20	C₃²×C₄₃	C₃³	1	1	yes	characteristic
21	C₃×C₄₃⋊C₃	—	3	6	no	—
22	C₃×C₄₃⋊C₃	—	9	6	no	—
23	C₄₃⋊C₉	—	3	3	no	—
24	C₃×#732	—	43	1	no	maximal, Sylow
25	C₃×C₄₃	—	3	2	no	—
26	C₃×C₄₃	—	3	1	no	—
27	C₃×C₄₃	—	9	3	no	—
28	C₃×C₄₃	#732	1	3	yes	complemented
29	C₃×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
30	C₄₃⋊C₃	—	9	6	no	—
31	C₃×H(3,𝔽₃)	—	43	2	no	—
32	C₃×H(3,𝔽₃)	C₄₃⋊C₃	1	1	yes	characteristic, complemented
33	C₃²×C₉	—	43	1	no	—
34	#732	—	43	9	no	—
35	C₄₃	C₃×#732	1	1	yes	characteristic, complemented, Sylow
36	C₃³	—	3	1	no	—
37	C₃³	—	129	2	no	—
38	C₃³	C₃×C₄₃⋊C₃	1	1	yes	characteristic
39	H(3,𝔽₃)	—	3	2	no	—
40	H(3,𝔽₃)	—	43	6	no	—
41	H(3,𝔽₃)	—	129	4	no	—
42	H(3,𝔽₃)	C₃×C₄₃⋊C₃	1	3	yes	complemented
43	C₃×C₉	—	43	3	no	—
44	C₃×C₉	—	129	2	no	—
45	C₃×C₉	—	129	1	no	—
46	C₃²	—	3	3	no	—
47	C₃²	—	3	3	no	—
48	C₃²	—	9	3	no	—
49	C₃²	—	129	6	no	—
50	C₃²	—	387	6	no	—
51	C₃²	C₃²⋊(C₄₃⋊C₃)	1	2	yes	—
52	C₃²	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
53	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
54	C₉	—	129	3	no	—
55	C₃	—	3	2	no	—
56	C₃	—	3	1	no	—
57	C₃	—	9	3	no	—
58	C₃	—	387	6	no	—
59	C₃	#16812512	1	3	yes	direct product factor
60	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×H(3,𝔽₃)×C₄₃	C₃
socle	C₃²×C₄₃	H(3,𝔽₃)
hypercenter	C₃×H(3,𝔽₃)	C₄₃⋊C₃
hypocenter	C₄₃	C₃×#732
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃×C₃²⋊(C₄₃⋊C₃)	C₃	semidirect
2. C₃²×C₄₃⋊C₉	C₃	semidirect
3. #16812512	C₃	direct (N × H)
4. C₃×H(3,𝔽₃)×C₄₃	C₃	semidirect
7. C₃²⋊(C₄₃⋊C₃)	C₃²	semidirect
10. C₃×C₄₃⋊C₉	C₃²	semidirect
14. H(3,𝔽₃)×C₄₃	C₃²	semidirect
28. C₃×C₄₃	#732	semidirect
32. C₃×H(3,𝔽₃)	C₄₃⋊C₃	semidirect
35. C₄₃	C₃×#732	semidirect
42. H(3,𝔽₃)	C₃×C₄₃⋊C₃	semidirect
59. C₃	#16812512	direct (N × H)

Subgroups — C3×#16812512 #23782868

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#16812512 #23782868