Subgroups — #14552049

Order 2187.

884 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6887	C₃	1	1	yes	maximal, characteristic
2	#10624559	C₃	1	18	yes	maximal, complemented
3	#10624557	C₃	1	9	yes	maximal
4	C₉×C₉⋊C₉	C₃	1	6	yes	maximal, complemented
5	C₉×C₃²⋊C₉	C₃	1	3	yes	maximal
6	#10624544	C₃	1	2	yes	maximal, complemented
7	C₉³	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃³×C₉	C₃²	1	1	yes	characteristic
9	#6887	C₉	1	27	yes	complemented
10	C₃×C₉⋊C₉	C₃²	1	18	yes	—
11	C₃×C₉⋊C₉	C₃²	1	6	yes	—
12	C₃×C₃²⋊C₉	C₃²	1	9	yes	—
13	C₃×C₃²⋊C₉	C₃²	1	3	yes	—
14	C₃×C₉²	C₃²	1	9	yes	—
15	C₃×C₉²	C₃²	1	3	yes	—
16	C₃×C₉²	C₃²	1	6	yes	—
17	C₃×C₉²	C₃²	1	1	yes	characteristic
18	C₃×C₉²	C₃²	1	2	yes	—
19	#6855	C₃²	1	18	yes	—
20	#6855	C₃²	1	18	yes	—
21	#6855	C₃²	1	36	yes	—
22	C₃⁴	C₃³	1	1	yes	characteristic
23	C₃²×C₉	—	3	9	no	—
24	C₃²×C₉	C₃×C₉	1	9	yes	—
25	C₃²×C₉	C₃³	1	18	yes	—
26	C₃²×C₉	C₃³	1	2	yes	—
27	C₃²×C₉	C₃³	1	3	yes	—
28	C₃²×C₉	C₃³	1	6	yes	—
29	C₃²×C₉	C₃³	1	9	yes	—
30	C₃²×C₉	C₃³	1	1	yes	characteristic
31	C₉⋊C₉	—	3	54	no	—
32	C₉⋊C₉	C₃×C₉	1	54	yes	—
33	C₃²⋊C₉	—	3	27	no	—
34	C₃²⋊C₉	C₃×C₉	1	27	yes	—
35	C₉²	—	3	27	no	—
36	C₉²	—	3	9	no	—
37	C₉²	—	3	18	no	—
38	C₉²	C₃×C₉	1	9	yes	—
39	C₉²	C₃×C₉	1	18	yes	—
40	C₃³	—	3	9	no	—
41	C₃³	—	3	3	no	—
42	C₃³	C₃²×C₉	1	3	yes	—
43	C₃³	C₃⁴	1	1	yes	characteristic
44	C₃×C₉	—	3	9	no	—
45	C₃×C₉	—	3	9	no	—
46	C₃×C₉	—	3	18	no	—
47	C₃×C₉	—	3	18	no	—
48	C₃×C₉	—	3	6	no	—
49	C₃×C₉	—	3	27	no	—
50	C₃×C₉	—	3	18	no	—
51	C₃×C₉	—	3	18	no	—
52	C₃×C₉	—	3	36	no	—
53	C₃×C₉	C₃²×C₉	1	9	yes	—
54	C₃×C₉	C₃²×C₉	1	18	yes	—
55	C₃×C₉	C₃²×C₉	1	6	yes	—
56	C₃×C₉	C₃²×C₉	1	3	yes	—
57	C₃×C₉	#737	1	27	yes	—
58	C₃×C₉	#737	1	9	yes	—
59	C₃²	—	3	3	no	—
60	C₃²	—	3	9	no	—
61	C₃²	—	9	9	no	—
62	C₃²	C₃³×C₉	1	1	yes	characteristic
63	C₃²	C₃×#737	1	3	yes	—
64	C₃²	C₃×#737	1	9	yes	—
65	C₉	—	3	6	no	—
66	C₉	—	3	9	no	—
67	C₉	—	3	18	no	—
68	C₉	—	3	27	no	—
69	C₉	—	9	18	no	—
70	C₉	#6887	1	9	yes	—
71	C₃	—	9	3	no	—
72	C₃	C₃×#6887	1	1	yes	characteristic
73	C₃	C₉×#737	1	3	yes	—
74	C₃	#10624877	1	9	yes	—

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

Complements

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

N	H ≅ G/N	type
2. #10624559	C₃	semidirect
4. C₉×C₉⋊C₉	C₃	semidirect
6. #10624544	C₃	semidirect
7. C₉³	C₃	semidirect
9. #6887	C₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×#6887	3
#10624559	3
#10624557	3
C₉×C₉⋊C₉	3
C₉×C₃²⋊C₉	3
#10624544	3
C₉³	3