Subgroups — C₃×#26014629 #46798678

Order 33777.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26014629	C₃	1	27	yes	maximal, direct product factor
2	C₃×#16836730	C₃	1	2	yes	maximal, complemented
3	C₃×#16836729	C₃	1	3	yes	maximal, complemented
4	C₃×#16836728	C₃	1	3	yes	maximal, complemented
5	C₃×C₃²⋊(C₁₃₉⋊C₃)	C₃	1	1	yes	maximal, characteristic
6	C₃×C₉×C₁₃₉⋊C₃	C₃	1	3	yes	maximal, complemented
7	C₃²×C₉×C₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₁₃₉⋊C₃	C₃²	1	3	yes	—
9	#16836730	C₃²	1	18	yes	complemented
10	#16836729	C₃²	1	27	yes	complemented
11	#16836728	C₃²	1	27	yes	complemented
12	C₃²⋊(C₁₃₉⋊C₃)	C₃²	1	9	yes	—
13	C₃×C₁₃₉⋊C₉	C₃²	1	6	yes	—
14	C₉×C₁₃₉⋊C₃	C₃²	1	27	yes	complemented
15	C₃³×C₁₃₉	C₃²	1	1	yes	characteristic
16	C₃×C₉×C₁₃₉	C₃²	1	1	yes	characteristic
17	C₃×C₉×C₁₃₉	C₃²	1	1	yes	characteristic
18	C₃×C₉×C₁₃₉	C₃²	1	1	yes	characteristic
19	C₃×C₉×C₁₃₉	C₃²	1	9	yes	complemented
20	C₃²×C₁₃₉	—	3	3	no	—
21	C₃²×C₁₃₉	C₃³	1	3	yes	—
22	C₃²×C₁₃₉	C₃³	1	1	yes	characteristic
23	C₃×C₁₃₉⋊C₃	—	3	9	no	—
24	C₃×C₁₃₉⋊C₃	C₃³	1	9	yes	—
25	C₉×C₁₃₉	C₃³	1	3	yes	—
26	C₉×C₁₃₉	C₃³	1	3	yes	—
27	C₉×C₁₃₉	C₃³	1	3	yes	—
28	C₁₃₉⋊C₉	C₃³	1	18	yes	—
29	C₃×C₁₃₉	—	3	3	no	—
30	C₃×C₁₃₉	#737	1	3	yes	complemented
31	C₃×C₁₃₉	C₃⁴	1	1	yes	characteristic
32	C₁₃₉⋊C₃	—	3	9	no	—
33	C₃×#737	—	139	1	no	maximal, Sylow
34	C₁₃₉	C₃×#737	1	1	yes	characteristic, complemented, Sylow
35	#737	—	139	27	no	—
36	C₃×3₋¹⁺²	—	139	2	no	—
37	C₃×3₋¹⁺²	—	139	3	no	—
38	C₃×3₋¹⁺²	—	139	3	no	—
39	C₃×H(3,𝔽₃)	—	139	1	no	—
40	C₃²×C₉	—	139	3	no	—
41	C₃²×C₉	C₁₃₉⋊C₃	1	1	yes	characteristic, complemented
42	C₃³	—	139	3	no	—
43	C₃³	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
44	3₋¹⁺²	—	139	18	no	—
45	3₋¹⁺²	—	139	27	no	—
46	3₋¹⁺²	—	139	27	no	—
47	H(3,𝔽₃)	—	139	9	no	—
48	C₃×C₉	—	139	6	no	—
49	C₃×C₉	—	139	27	no	—
50	C₃×C₉	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
51	C₃×C₉	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
52	C₃×C₉	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
53	C₃×C₉	C₃×C₁₃₉⋊C₃	1	9	yes	complemented
54	C₃²	—	3	3	no	—
55	C₃²	—	139	9	no	—
56	C₃²	—	417	9	no	—
57	C₃²	C₃²×C₁₃₉⋊C₃	1	3	yes	—
58	C₃²	C₃²×C₁₃₉⋊C₃	1	1	yes	characteristic
59	C₉	—	139	18	no	—
60	C₉	C₃²×C₁₃₉⋊C₃	1	3	yes	—
61	C₉	C₃²×C₁₃₉⋊C₃	1	3	yes	—
62	C₉	C₃²×C₁₃₉⋊C₃	1	3	yes	—
63	C₃	—	3	3	no	—
64	C₃	—	417	9	no	—
65	C₃	#26014629	1	3	yes	direct product factor
66	C₃	C₃³×C₁₃₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃×C₁₃₉⋊C₃
commutator, cosocle	C₃×C₁₃₉	C₃⁴
Frattini	C₃	C₃³×C₁₃₉⋊C₃
Fitting	C₃²×C₉×C₁₃₉	C₃
socle	C₃²×C₁₃₉	C₃³
prime radical	C₃×C₃²⋊(C₁₃₉⋊C₃)	C₃
hypercenter	C₃²×C₉	C₁₃₉⋊C₃
hypocenter	C₁₃₉	C₃×#737
LCS	G ▷ C₃×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. #26014629	C₃	direct (N × H)
2. C₃×#16836730	C₃	semidirect
3. C₃×#16836729	C₃	semidirect
4. C₃×#16836728	C₃	semidirect
6. C₃×C₉×C₁₃₉⋊C₃	C₃	semidirect
7. C₃²×C₉×C₁₃₉	C₃	semidirect
9. #16836730	C₃²	semidirect
10. #16836729	C₃²	semidirect
11. #16836728	C₃²	semidirect
14. C₉×C₁₃₉⋊C₃	C₃²	semidirect
19. C₃×C₉×C₁₃₉	C₃²	semidirect
30. C₃×C₁₃₉	#737	semidirect
34. C₁₃₉	C₃×#737	semidirect
41. C₃²×C₉	C₁₃₉⋊C₃	semidirect
53. C₃×C₉	C₃×C₁₃₉⋊C₃	semidirect
65. C₃	#26014629	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#26014629	3
C₃×#16836730	3
C₃×#16836729	3
C₃×#16836728	3
C₃×C₃²⋊(C₁₃₉⋊C₃)	3
C₃×C₉×C₁₃₉⋊C₃	3
C₃²×C₉×C₁₃₉	3
C₃×#737	139

Subgroups — C3×#26014629 #46798678

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#26014629 #46798678