Subgroups — C₃×(C₃×C₁₃₉⋊C₃)⋊C₉ #46798533

Order 33777.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
2. C₃²×C₁₃₉⋊C₉	C₃	semidirect
3. (C₃×C₁₃₉⋊C₃)⋊C₉	C₃	direct (N × H)
4. C₃²×C₉×C₁₃₉	C₃	semidirect
8. C₃²×C₁₃₉⋊C₃	C₉	semidirect
11. C₃×C₁₃₉⋊C₉	C₃²	semidirect
14. C₃×C₉×C₁₃₉	C₃²	semidirect
24. C₃×C₁₃₉⋊C₃	C₃×C₉	semidirect
27. C₃×C₁₃₉	C₃²⋊C₉	semidirect
34. C₁₃₉	C₃×C₃²⋊C₉	semidirect
37. C₃²×C₉	C₁₃₉⋊C₃	semidirect
48. C₃×C₉	C₃×C₁₃₉⋊C₃	semidirect
62. C₃	(C₃×C₁₃₉⋊C₃)⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₁₃₉⋊C₃	3
C₃²×C₁₃₉⋊C₉	3
(C₃×C₁₃₉⋊C₃)⋊C₉	3
C₃²×C₉×C₁₃₉	3
C₃×C₃²⋊C₉	139

Subgroups — C3×(C3×C139⋊C3)⋊C9 #46798533

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×(C₃×C₁₃₉⋊C₃)⋊C₉ #46798533