Subgroups — C₃×#10624906 #14555306

Order 2187.

3668 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624906	C₃	1	81	yes	maximal, direct product factor
2	C₃×#6898	C₃	1	9	yes	maximal, complemented
3	C₃×#6897	C₃	1	9	yes	maximal, complemented
4	C₃×#6894	C₃	1	12	yes	maximal, complemented
5	C₃×#6891	C₃	1	2	yes	maximal
6	C₃×C₉×3₋¹⁺²	C₃	1	6	yes	maximal, complemented
7	C₃²×C₃²⋊C₉	C₃	1	2	yes	maximal
8	C₃⁵	C₃²	1	1	yes	characteristic
9	C₃²×3₋¹⁺²	C₃²	1	6	yes	—
10	C₃³×C₉	C₃²	1	6	yes	—
11	#6898	C₃²	1	243	yes	complemented
12	#6897	C₃²	1	243	yes	complemented
13	#6894	C₃²	1	324	yes	complemented
14	#6891	C₃²	1	54	yes	—
15	C₉×3₋¹⁺²	C₃²	1	162	yes	complemented
16	C₃×C₉⋊C₉	C₃²	1	36	yes	complemented
17	C₃×C₉⋊C₉	C₃²	1	36	yes	complemented
18	C₃×C₃²⋊C₉	C₃²	1	2	yes	—
19	C₃×C₃²⋊C₉	C₃²	1	4	yes	—
20	C₃×C₃²⋊C₉	C₃²	1	6	yes	—
21	C₃×C₃²⋊C₉	C₃²	1	6	yes	—
22	C₃×C₃²⋊C₉	C₃²	1	54	yes	—
23	C₃×C₃²⋊C₉	C₃²	1	6	yes	—
24	C₃×C₃²⋊C₉	C₃²	1	6	yes	—
25	C₃×C₃²⋊C₉	C₃²	1	6	yes	—
26	C₃×C₉²	C₃²	1	9	yes	complemented
27	C₃⁴	—	3	18	no	—
28	C₃⁴	—	9	6	no	—
29	C₃⁴	C₃³	1	1	yes	characteristic
30	C₃⁴	C₃³	1	1	yes	characteristic
31	C₃⁴	C₃³	1	2	yes	—
32	C₃⁴	C₃³	1	9	yes	—
33	C₃×3₋¹⁺²	—	3	54	no	—
34	C₃×3₋¹⁺²	C₃³	1	54	yes	—
35	C₃²×C₉	—	9	18	no	—
36	C₃²×C₉	C₃³	1	6	yes	—
37	C₃²×C₉	C₃³	1	12	yes	—
38	C₃²×C₉	C₃³	1	18	yes	—
39	C₃²×C₉	C₃³	1	54	yes	—
40	C₉⋊C₉	C₃³	1	324	yes	complemented
41	C₉⋊C₉	C₃³	1	324	yes	complemented
42	C₃²⋊C₉	C₃³	1	18	yes	—
43	C₃²⋊C₉	C₃³	1	36	yes	—
44	C₃²⋊C₉	C₃³	1	54	yes	—
45	C₃²⋊C₉	C₃³	1	54	yes	—
46	C₃²⋊C₉	C₃³	1	54	yes	—
47	C₃²⋊C₉	C₃³	1	54	yes	—
48	C₃²⋊C₉	C₃³	1	54	yes	—
49	C₉²	C₃³	1	81	yes	complemented
50	C₃³	—	3	6	no	—
51	C₃³	—	3	6	no	—
52	C₃³	—	3	6	no	—
53	C₃³	—	3	54	no	—
54	C₃³	—	3	6	no	—
55	C₃³	—	3	6	no	—
56	C₃³	—	3	6	no	—
57	C₃³	—	3	6	no	—
58	C₃³	—	9	18	no	—
59	C₃³	—	9	81	no	—
60	C₃³	#737	1	18	yes	—
61	C₃³	C₃⁴	1	3	yes	—
62	C₃³	C₃⁴	1	3	yes	—
63	C₃³	C₃⁴	1	6	yes	—
64	C₃³	C₃⁴	1	1	yes	characteristic
65	3₋¹⁺²	—	3	162	no	—
66	C₃×C₉	—	3	54	no	—
67	C₃×C₉	—	3	18	no	—
68	C₃×C₉	—	3	36	no	—
69	C₃×C₉	—	9	54	no	—
70	C₃×C₉	C₃⁴	1	18	yes	—
71	C₃×C₉	C₃⁴	1	54	yes	—
72	C₃×C₉	C₃⁴	1	36	yes	—
73	C₃²	—	3	54	no	—
74	C₃²	—	3	6	no	—
75	C₃²	—	3	6	no	—
76	C₃²	—	3	6	no	—
77	C₃²	—	3	6	no	—
78	C₃²	—	3	6	no	—
79	C₃²	—	3	6	no	—
80	C₃²	—	3	6	no	—
81	C₃²	—	9	81	no	—
82	C₃²	—	9	9	no	—
83	C₃²	—	9	9	no	—
84	C₃²	C₃×#737	1	18	yes	—
85	C₃²	C₃×#737	1	6	yes	—
86	C₃²	3₋¹⁺⁴	1	6	yes	—
87	C₃²	C₃⁵	1	1	yes	characteristic
88	C₉	—	3	54	no	—
89	C₉	—	3	18	no	—
90	C₉	—	3	36	no	—
91	C₃	—	3	18	no	—
92	C₃	—	9	3	no	—
93	C₃	—	9	3	no	—
94	C₃	#10624906	1	9	yes	direct product factor
95	C₃	C₃²×#737	1	2	yes	—
96	C₃	C₃×3₋¹⁺⁴	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. #10624906	C₃	direct (N × H)
2. C₃×#6898	C₃	semidirect
3. C₃×#6897	C₃	semidirect
4. C₃×#6894	C₃	semidirect
6. C₃×C₉×3₋¹⁺²	C₃	semidirect
11. #6898	C₃²	semidirect
12. #6897	C₃²	semidirect
13. #6894	C₃²	semidirect
15. C₉×3₋¹⁺²	C₃²	semidirect
16. C₃×C₉⋊C₉	C₃²	semidirect
17. C₃×C₉⋊C₉	C₃²	semidirect
26. C₃×C₉²	C₃²	semidirect
40. C₉⋊C₉	C₃³	semidirect
41. C₉⋊C₉	C₃³	semidirect
49. C₉²	C₃³	semidirect
94. C₃	#10624906	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624906	3
C₃×#6898	3
C₃×#6897	3
C₃×#6894	3
C₃×#6891	3
C₃×C₉×3₋¹⁺²	3
C₃²×C₃²⋊C₉	3

Subgroups — C3×#10624906 #14555306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10624906 #14555306