Subgroups — C₃×#10624902 #14555309

Order 2187.

3668 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624902	C₃	1	81	yes	maximal, direct product factor
2	C₃×#6898	C₃	1	9	yes	maximal, complemented
3	C₃×#6896	C₃	1	9	yes	maximal, complemented
4	C₃×#6895	C₃	1	12	yes	maximal, complemented
5	C₃×#6891	C₃	1	2	yes	maximal
6	C₃×#6887	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	#6896	C₃²	1	243	yes	complemented
13	#6895	C₃²	1	324	yes	complemented
14	#6891	C₃²	1	54	yes	—
15	#6887	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	12	yes	—
24	C₃×C₃²⋊C₉	C₃²	1	6	yes	—
25	C₃×C₉²	C₃²	1	9	yes	complemented
26	C₃⁴	—	3	18	no	—
27	C₃⁴	—	9	6	no	—
28	C₃⁴	C₃³	1	1	yes	characteristic
29	C₃⁴	C₃³	1	1	yes	characteristic
30	C₃⁴	C₃³	1	2	yes	—
31	C₃⁴	C₃³	1	9	yes	—
32	C₃×3₋¹⁺²	—	9	18	no	—
33	C₃×3₋¹⁺²	C₃³	1	54	yes	—
34	C₃²×C₉	—	3	54	no	—
35	C₃²×C₉	C₃³	1	54	yes	—
36	C₃²×C₉	C₃³	1	6	yes	—
37	C₃²×C₉	C₃³	1	12	yes	—
38	C₃²×C₉	C₃³	1	18	yes	—
39	C₉⋊C₉	C₃³	1	324	yes	complemented
40	C₉⋊C₉	C₃³	1	324	yes	complemented
41	C₃²⋊C₉	C₃³	1	18	yes	—
42	C₃²⋊C₉	C₃³	1	36	yes	—
43	C₃²⋊C₉	C₃³	1	54	yes	—
44	C₃²⋊C₉	C₃³	1	54	yes	—
45	C₃²⋊C₉	C₃³	1	108	yes	—
46	C₃²⋊C₉	C₃³	1	54	yes	—
47	C₉²	C₃³	1	81	yes	complemented
48	C₃³	—	3	6	no	—
49	C₃³	—	3	12	no	—
50	C₃³	—	3	54	no	—
51	C₃³	—	3	6	no	—
52	C₃³	—	3	6	no	—
53	C₃³	—	3	6	no	—
54	C₃³	—	3	6	no	—
55	C₃³	—	9	18	no	—
56	C₃³	—	9	81	no	—
57	C₃³	#737	1	18	yes	—
58	C₃³	C₃⁴	1	3	yes	—
59	C₃³	C₃⁴	1	3	yes	—
60	C₃³	C₃⁴	1	6	yes	—
61	C₃³	C₃⁴	1	1	yes	characteristic
62	3₋¹⁺²	—	9	54	no	—
63	C₃×C₉	—	3	162	no	—
64	C₃×C₉	—	3	18	no	—
65	C₃×C₉	—	3	36	no	—
66	C₃×C₉	—	3	54	no	—
67	C₃×C₉	C₃⁴	1	18	yes	—
68	C₃×C₉	C₃⁴	1	54	yes	—
69	C₃×C₉	C₃⁴	1	36	yes	—
70	C₃²	—	3	54	no	—
71	C₃²	—	3	6	no	—
72	C₃²	—	3	12	no	—
73	C₃²	—	3	6	no	—
74	C₃²	—	3	6	no	—
75	C₃²	—	3	6	no	—
76	C₃²	—	3	6	no	—
77	C₃²	—	9	81	no	—
78	C₃²	—	9	9	no	—
79	C₃²	—	9	9	no	—
80	C₃²	C₃×#737	1	18	yes	—
81	C₃²	C₃×#737	1	6	yes	—
82	C₃²	3₋¹⁺⁴	1	6	yes	—
83	C₃²	C₃⁵	1	1	yes	characteristic
84	C₉	—	3	18	no	—
85	C₉	—	3	36	no	—
86	C₉	—	3	54	no	—
87	C₃	—	3	18	no	—
88	C₃	—	9	3	no	—
89	C₃	—	9	3	no	—
90	C₃	#10624902	1	9	yes	direct product factor
91	C₃	C₃²×#737	1	2	yes	—
92	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. #10624902	C₃	direct (N × H)
2. C₃×#6898	C₃	semidirect
3. C₃×#6896	C₃	semidirect
4. C₃×#6895	C₃	semidirect
6. C₃×#6887	C₃	semidirect
11. #6898	C₃²	semidirect
12. #6896	C₃²	semidirect
13. #6895	C₃²	semidirect
15. #6887	C₃²	semidirect
16. C₃×C₉⋊C₉	C₃²	semidirect
17. C₃×C₉⋊C₉	C₃²	semidirect
25. C₃×C₉²	C₃²	semidirect
39. C₉⋊C₉	C₃³	semidirect
40. C₉⋊C₉	C₃³	semidirect
47. C₉²	C₃³	semidirect
90. C₃	#10624902	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624902	3
C₃×#6898	3
C₃×#6896	3
C₃×#6895	3
C₃×#6891	3
C₃×#6887	3
C₃²×C₃²⋊C₉	3

Subgroups — C3×#10624902 #14555309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10624902 #14555309