Subgroups — C₃×3₋¹⁺²×C₁₃₉⋊C₃ #46798672

Order 33777.

576 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	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	3₋¹⁺²×C₁₃₉⋊C₃	C₃	1	27	yes	maximal, direct product factor
6	C₃×C₉×C₁₃₉⋊C₃	C₃	1	3	yes	maximal, complemented
7	C₃×3₋¹⁺²×C₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₁₃₉⋊C₃	—	3	9	no	—
9	C₃²×C₁₃₉⋊C₃	C₃²	1	9	yes	—
10	C₃²×C₁₃₉⋊C₃	C₃²	1	1	yes	characteristic
11	C₃²×C₁₃₉⋊C₃	C₃²	1	1	yes	characteristic
12	C₃²×C₁₃₉⋊C₃	C₃²	1	1	yes	characteristic
13	#16836730	C₃²	1	18	yes	complemented
14	#16836729	C₃²	1	27	yes	complemented
15	#16836728	C₃²	1	27	yes	complemented
16	C₃×C₁₃₉⋊C₉	C₃²	1	6	yes	complemented
17	C₉×C₁₃₉⋊C₃	C₃²	1	27	yes	complemented
18	C₃³×C₁₃₉	C₃²	1	1	yes	characteristic
19	3₋¹⁺²×C₁₃₉	C₃²	1	9	yes	complemented
20	C₃×C₉×C₁₃₉	C₃²	1	3	yes	complemented
21	C₃²×C₁₃₉	—	3	3	no	—
22	C₃²×C₁₃₉	C₃³	1	3	yes	—
23	C₃²×C₁₃₉	C₃³	1	1	yes	characteristic
24	C₃×C₁₃₉⋊C₃	—	3	3	no	—
25	C₃×C₁₃₉⋊C₃	—	3	3	no	—
26	C₃×C₁₃₉⋊C₃	—	3	27	no	—
27	C₃×C₁₃₉⋊C₃	3₋¹⁺²	1	9	yes	direct product factor
28	C₃×C₁₃₉⋊C₃	C₃³	1	3	yes	—
29	C₃×C₁₃₉⋊C₃	C₃³	1	3	yes	—
30	C₃×C₁₃₉⋊C₃	C₃³	1	3	yes	—
31	C₉×C₁₃₉	C₃³	1	9	yes	complemented
32	C₁₃₉⋊C₉	C₃³	1	18	yes	complemented
33	C₃×C₁₃₉	—	3	3	no	—
34	C₃×C₁₃₉	C₃×3₋¹⁺²	1	3	yes	complemented
35	C₃×C₁₃₉	C₃⁴	1	1	yes	characteristic
36	C₁₃₉⋊C₃	—	3	3	no	—
37	C₁₃₉⋊C₃	—	3	3	no	—
38	C₁₃₉⋊C₃	C₃×3₋¹⁺²	1	9	yes	direct product factor
39	C₃²×3₋¹⁺²	—	139	1	no	maximal, Sylow
40	C₁₃₉	C₃²×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
41	C₃⁴	—	139	1	no	—
42	C₃×3₋¹⁺²	—	139	2	no	—
43	C₃×3₋¹⁺²	—	139	27	no	—
44	C₃×3₋¹⁺²	—	139	3	no	—
45	C₃×3₋¹⁺²	—	139	3	no	—
46	C₃×3₋¹⁺²	C₁₃₉⋊C₃	1	1	yes	characteristic, direct product factor
47	C₃²×C₉	—	139	3	no	—
48	C₃³	—	139	1	no	—
49	C₃³	—	139	9	no	—
50	C₃³	—	139	1	no	—
51	C₃³	—	139	1	no	—
52	C₃³	—	417	9	no	—
53	C₃³	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
54	3₋¹⁺²	—	139	18	no	—
55	3₋¹⁺²	—	139	27	no	—
56	3₋¹⁺²	—	139	27	no	—
57	3₋¹⁺²	C₃×C₁₃₉⋊C₃	1	9	yes	direct product factor
58	C₃×C₉	—	139	6	no	—
59	C₃×C₉	—	139	27	no	—
60	C₃×C₉	C₃×C₁₃₉⋊C₃	1	3	yes	complemented
61	C₃²	—	3	3	no	—
62	C₃²	—	139	9	no	—
63	C₃²	—	139	3	no	—
64	C₃²	—	139	3	no	—
65	C₃²	—	139	3	no	—
66	C₃²	—	417	27	no	—
67	C₃²	—	417	3	no	—
68	C₃²	—	417	3	no	—
69	C₃²	C₃²×C₁₃₉⋊C₃	1	3	yes	—
70	C₃²	C₃²×C₁₃₉⋊C₃	1	1	yes	characteristic
71	C₉	—	139	18	no	—
72	C₉	C₃²×C₁₃₉⋊C₃	1	9	yes	complemented
73	C₃	—	3	3	no	—
74	C₃	—	139	9	no	—
75	C₃	—	417	3	no	—
76	C₃	—	417	3	no	—
77	C₃	3₋¹⁺²×C₁₃₉⋊C₃	1	3	yes	direct product factor
78	C₃	C₃³×C₁₃₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²×C₁₃₉⋊C₃
commutator, cosocle	C₃×C₁₃₉	C₃⁴
Frattini	C₃	C₃³×C₁₃₉⋊C₃
Fitting	C₃×3₋¹⁺²×C₁₃₉	C₃
socle	C₃²×C₁₃₉	C₃³
prime radical	C₃³×C₁₃₉⋊C₃	C₃
hypercenter	C₃×3₋¹⁺²	C₁₃₉⋊C₃
hypocenter	C₁₃₉	C₃²×3₋¹⁺²
LCS	G ▷ C₃×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₃² ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
2. C₃×#16836730	C₃	semidirect
3. C₃×#16836729	C₃	semidirect
4. C₃×#16836728	C₃	semidirect
5. 3₋¹⁺²×C₁₃₉⋊C₃	C₃	direct (N × H)
6. C₃×C₉×C₁₃₉⋊C₃	C₃	semidirect
7. C₃×3₋¹⁺²×C₁₃₉	C₃	semidirect
13. #16836730	C₃²	semidirect
14. #16836729	C₃²	semidirect
15. #16836728	C₃²	semidirect
16. C₃×C₁₃₉⋊C₉	C₃²	semidirect
17. C₉×C₁₃₉⋊C₃	C₃²	semidirect
19. 3₋¹⁺²×C₁₃₉	C₃²	semidirect
20. C₃×C₉×C₁₃₉	C₃²	semidirect
27. C₃×C₁₃₉⋊C₃	3₋¹⁺²	direct (N × H)
31. C₉×C₁₃₉	C₃³	semidirect
32. C₁₃₉⋊C₉	C₃³	semidirect
34. C₃×C₁₃₉	C₃×3₋¹⁺²	semidirect
38. C₁₃₉⋊C₃	C₃×3₋¹⁺²	direct (N × H)
40. C₁₃₉	C₃²×3₋¹⁺²	semidirect
46. C₃×3₋¹⁺²	C₁₃₉⋊C₃	direct (N × H)
57. 3₋¹⁺²	C₃×C₁₃₉⋊C₃	direct (N × H)
60. C₃×C₉	C₃×C₁₃₉⋊C₃	semidirect
72. C₉	C₃²×C₁₃₉⋊C₃	semidirect
77. C₃	3₋¹⁺²×C₁₃₉⋊C₃	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
C₃×#16836730	3
C₃×#16836729	3
C₃×#16836728	3
3₋¹⁺²×C₁₃₉⋊C₃	3
C₃×C₉×C₁₃₉⋊C₃	3
C₃×3₋¹⁺²×C₁₃₉	3
C₃²×3₋¹⁺²	139

Subgroups — C3×3−1+2×C139⋊C3 #46798672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×3₋¹⁺²×C₁₃₉⋊C₃ #46798672