Subgroups — C₃×#10624690 #14554114

Order 2187.

2096 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₃²⋊C₉	C₃	1	3	yes	maximal
3	#10624690	C₃	1	27	yes	maximal, direct product factor
4	C₃×#6867	C₃	1	9	yes	maximal, complemented
5	C₃⁵	C₃²	1	1	yes	characteristic
6	C₃²×3₋¹⁺²	—	3	6	no	—
7	C₃²×3₋¹⁺²	—	3	3	no	—
8	C₃²×3₋¹⁺²	—	3	18	no	—
9	C₃²×3₋¹⁺²	C₉	1	27	yes	complemented
10	C₃²×3₋¹⁺²	C₃²	1	9	yes	—
11	C₃³×C₉	—	3	3	no	—
12	C₃³×C₉	C₃²	1	3	yes	—
13	C₃×C₃²⋊C₉	—	3	18	no	—
14	C₃×C₃²⋊C₉	—	3	6	no	—
15	C₃×C₃²⋊C₉	C₃²	1	9	yes	—
16	C₃×C₃²⋊C₉	C₃²	1	27	yes	—
17	#6867	C₃²	1	81	yes	complemented
18	C₃⁴	—	9	9	no	—
19	C₃⁴	C₃×C₉	1	9	yes	—
20	C₃⁴	H(3,𝔽₃)	1	3	yes	—
21	C₃⁴	H(3,𝔽₃)	1	6	yes	—
22	C₃⁴	3₋¹⁺²	1	18	yes	—
23	C₃⁴	C₃³	1	1	yes	characteristic
24	C₃⁴	C₃³	1	3	yes	—
25	C₃×3₋¹⁺²	—	3	81	no	—
26	C₃×3₋¹⁺²	—	3	162	no	—
27	C₃×3₋¹⁺²	—	3	27	no	—
28	C₃×3₋¹⁺²	—	3	54	no	—
29	C₃×3₋¹⁺²	C₃×C₉	1	81	yes	complemented
30	C₃²×C₉	—	3	6	no	—
31	C₃²×C₉	—	3	3	no	—
32	C₃²×C₉	—	3	18	no	—
33	C₃²×C₉	—	3	27	no	—
34	C₃²×C₉	—	3	9	no	—
35	C₃²×C₉	—	9	27	no	—
36	C₃²×C₉	C₃×C₉	1	27	yes	complemented
37	C₃²×C₉	C₃³	1	9	yes	—
38	C₃²⋊C₉	—	3	18	no	—
39	C₃²⋊C₉	—	3	54	no	—
40	C₃²⋊C₉	C₃³	1	27	yes	—
41	C₃³	—	3	9	no	—
42	C₃³	—	3	18	no	—
43	C₃³	—	3	9	no	—
44	C₃³	—	9	27	no	—
45	C₃³	—	9	18	no	—
46	C₃³	—	9	54	no	—
47	C₃³	—	9	9	no	—
48	C₃³	C₃²⋊C₉	1	27	yes	—
49	C₃³	C₃²⋊C₉	1	54	yes	—
50	C₃³	C₃²×C₉	1	3	yes	—
51	C₃³	C₃²×C₉	1	9	yes	—
52	C₃³	C₃×H(3,𝔽₃)	1	2	yes	—
53	C₃³	C₃×H(3,𝔽₃)	1	9	yes	—
54	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
55	C₃³	C₃×3₋¹⁺²	1	6	yes	—
56	C₃³	C₃×3₋¹⁺²	1	18	yes	—
57	C₃³	C₃⁴	1	1	yes	characteristic
58	3₋¹⁺²	—	3	243	no	—
59	C₃×C₉	—	3	9	no	—
60	C₃×C₉	—	3	18	no	—
61	C₃×C₉	—	3	54	no	—
62	C₃×C₉	—	3	27	no	—
63	C₃×C₉	—	3	27	no	—
64	C₃×C₉	—	9	81	no	—
65	C₃×C₉	—	9	27	no	—
66	C₃×C₉	C₃²×C₉	1	27	yes	complemented
67	C₃²	—	3	9	no	—
68	C₃²	—	3	18	no	—
69	C₃²	—	3	6	no	—
70	C₃²	—	3	3	no	—
71	C₃²	—	3	81	no	—
72	C₃²	—	3	9	no	—
73	C₃²	—	3	18	no	—
74	C₃²	—	9	54	no	—
75	C₃²	—	9	9	no	—
76	C₃²	—	9	18	no	—
77	C₃²	C₃×C₃²⋊C₉	1	6	yes	—
78	C₃²	C₃×C₃²⋊C₉	1	27	yes	—
79	C₃²	C₃×C₃²⋊C₉	1	3	yes	—
80	C₃²	#6910	1	9	yes	—
81	C₃²	C₃³×C₉	1	1	yes	characteristic
82	C₃²	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
83	C₃²	C₃²×3₋¹⁺²	1	2	yes	—
84	C₉	—	3	27	no	—
85	C₉	—	9	27	no	—
86	C₃	—	3	1	no	—
87	C₃	—	3	2	no	—
88	C₃	—	3	27	no	—
89	C₃	—	3	6	no	—
90	C₃	#10624690	1	9	yes	direct product factor
91	C₃	C₃²×C₃²⋊C₉	1	1	yes	characteristic
92	C₃	C₃×#6910	1	3	yes	—

	subgroup	G/H
center, socle	C₃³	C₃×H(3,𝔽₃)
commutator	C₃²	C₃³×C₉
Frattini, cosocle	C₃³	C₃⁴
prime radical	C₃⁵	C₃²
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃³ ◁ C₃⁵ ◁ G
LECS	G ▷ C₃³ ▷ C₃ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #10624690	C₃	direct (N × H)
4. C₃×#6867	C₃	semidirect
9. C₃²×3₋¹⁺²	C₉	semidirect
17. #6867	C₃²	semidirect
29. C₃×3₋¹⁺²	C₃×C₉	semidirect
36. C₃²×C₉	C₃×C₉	semidirect
66. C₃×C₉	C₃²×C₉	semidirect
90. C₃	#10624690	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×3₋¹⁺²	3
C₃²×C₃²⋊C₉	3
#10624690	3
C₃×#6867	3

Subgroups — C3×#10624690 #14554114

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10624690 #14554114