Subgroups — C₃×#10624872 #14555298

Order 2187.

4958 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×C₉	C₃	1	1	yes	maximal, characteristic
2	#10624872	C₃	1	81	yes	maximal, direct product factor
3	C₃×#6895	C₃	1	6	yes	maximal, complemented
4	C₃×#6894	C₃	1	18	yes	maximal, complemented
5	C₃×#6891	C₃	1	3	yes	maximal
6	C₃×C₉×3₋¹⁺²	C₃	1	9	yes	maximal, complemented
7	C₃×#6887	C₃	1	3	yes	maximal, complemented
8	C₃⁵	C₃²	1	1	yes	characteristic
9	C₃²×3₋¹⁺²	C₃²	1	9	yes	—
10	C₃³×C₉	—	3	27	no	—
11	C₃³×C₉	C₃²	1	6	yes	—
12	C₃³×C₉	C₃²	1	2	yes	—
13	C₃³×C₉	C₃²	1	27	yes	—
14	C₃³×C₉	C₃²	1	3	yes	—
15	C₃³×C₉	C₃²	1	1	yes	characteristic
16	#6895	C₃²	1	162	yes	complemented
17	#6894	C₃²	1	486	yes	complemented
18	#6891	C₃²	1	81	yes	—
19	C₉×3₋¹⁺²	C₃²	1	243	yes	complemented
20	#6887	C₃²	1	81	yes	complemented
21	C₃×C₉⋊C₉	C₃²	1	18	yes	complemented
22	C₃×C₉⋊C₉	C₃²	1	54	yes	complemented
23	C₃×C₃²⋊C₉	C₃²	1	9	yes	—
24	C₃×C₃²⋊C₉	C₃²	1	18	yes	—
25	C₃×C₉²	C₃²	1	9	yes	complemented
26	C₃⁴	—	3	9	no	—
27	C₃⁴	—	3	27	no	—
28	C₃⁴	C₃³	1	9	yes	—
29	C₃⁴	C₃³	1	1	yes	characteristic
30	C₃⁴	C₃³	1	3	yes	—
31	C₃×3₋¹⁺²	—	3	81	no	—
32	C₃×3₋¹⁺²	C₃³	1	81	yes	—
33	C₃²×C₉	—	3	18	no	—
34	C₃²×C₉	—	3	54	no	—
35	C₃²×C₉	—	3	27	no	—
36	C₃²×C₉	—	3	243	no	—
37	C₃²×C₉	3₋¹⁺²	1	27	yes	complemented
38	C₃²×C₉	C₃³	1	6	yes	—
39	C₃²×C₉	C₃³	1	27	yes	—
40	C₃²×C₉	C₃³	1	54	yes	—
41	C₃²×C₉	C₃³	1	18	yes	—
42	C₃²×C₉	C₃³	1	27	yes	—
43	C₃²×C₉	C₃³	1	2	yes	—
44	C₃²×C₉	C₃³	1	9	yes	—
45	C₃²×C₉	C₃³	1	1	yes	characteristic
46	C₉⋊C₉	C₃³	1	162	yes	complemented
47	C₉⋊C₉	C₃³	1	486	yes	complemented
48	C₃²⋊C₉	C₃³	1	81	yes	—
49	C₃²⋊C₉	C₃³	1	162	yes	—
50	C₉²	C₃³	1	81	yes	complemented
51	C₃³	—	3	243	no	—
52	C₃³	—	3	27	no	—
53	C₃³	—	3	9	no	—
54	C₃³	—	3	81	no	—
55	C₃³	—	3	9	no	—
56	C₃³	—	3	18	no	—
57	C₃³	C₃×3₋¹⁺²	1	9	yes	—
58	C₃³	#737	1	27	yes	—
59	C₃³	C₃⁴	1	3	yes	—
60	C₃³	C₃⁴	1	9	yes	—
61	C₃³	C₃⁴	1	1	yes	characteristic
62	3₋¹⁺²	—	3	243	no	—
63	C₃×C₉	—	3	54	no	—
64	C₃×C₉	—	3	18	no	—
65	C₃×C₉	—	3	81	no	—
66	C₃×C₉	—	3	81	no	—
67	C₃×C₉	—	3	162	no	—
68	C₃×C₉	C₃×3₋¹⁺²	1	18	yes	—
69	C₃×C₉	C₃×3₋¹⁺²	1	9	yes	—
70	C₃×C₉	C₃×3₋¹⁺²	1	81	yes	complemented
71	C₃×C₉	C₃⁴	1	81	yes	—
72	C₃×C₉	C₃⁴	1	18	yes	—
73	C₃×C₉	C₃⁴	1	3	yes	—
74	C₃×C₉	C₃⁴	1	6	yes	—
75	C₃²	—	3	243	no	—
76	C₃²	—	3	27	no	—
77	C₃²	—	3	81	no	—
78	C₃²	—	3	9	no	—
79	C₃²	—	3	9	no	—
80	C₃²	—	3	18	no	—
81	C₃²	C₃²×3₋¹⁺²	1	9	yes	—
82	C₃²	C₃²×3₋¹⁺²	1	3	yes	—
83	C₃²	C₃×#737	1	27	yes	—
84	C₃²	C₃×#737	1	9	yes	—
85	C₃²	C₃⁵	1	1	yes	characteristic
86	C₉	—	3	18	no	—
87	C₉	—	3	81	no	—
88	C₉	C₃²×3₋¹⁺²	1	18	yes	—
89	C₉	C₃²×3₋¹⁺²	1	9	yes	—
90	C₃	—	3	9	no	—
91	C₃	—	3	27	no	—
92	C₃	#10624872	1	9	yes	direct product factor
93	C₃	C₃³×3₋¹⁺²	1	1	yes	characteristic
94	C₃	C₃²×#737	1	3	yes	—

	subgroup	G/H
center	C₃²×C₉	C₃³
commutator, Frattini, cosocle	C₃²	C₃⁵
socle	C₃³	C₃⁴
prime radical	C₃⁵	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₉ ◁ G
LECS	G ▷ C₃² ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #10624872	C₃	direct (N × H)
3. C₃×#6895	C₃	semidirect
4. C₃×#6894	C₃	semidirect
6. C₃×C₉×3₋¹⁺²	C₃	semidirect
7. C₃×#6887	C₃	semidirect
16. #6895	C₃²	semidirect
17. #6894	C₃²	semidirect
19. C₉×3₋¹⁺²	C₃²	semidirect
20. #6887	C₃²	semidirect
21. C₃×C₉⋊C₉	C₃²	semidirect
22. C₃×C₉⋊C₉	C₃²	semidirect
25. C₃×C₉²	C₃²	semidirect
37. C₃²×C₉	3₋¹⁺²	semidirect
46. C₉⋊C₉	C₃³	semidirect
47. C₉⋊C₉	C₃³	semidirect
50. C₉²	C₃³	semidirect
70. C₃×C₉	C₃×3₋¹⁺²	semidirect
92. C₃	#10624872	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃⁴×C₉	3
#10624872	3
C₃×#6895	3
C₃×#6894	3
C₃×#6891	3
C₃×C₉×3₋¹⁺²	3
C₃×#6887	3

Subgroups — C3×#10624872 #14555298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10624872 #14555298