Subgroups — C₃×#10624706 #14554145

Order 2187.

1016 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₇⋊C₃	C₃	1	3	yes	maximal
2	C₃²×C₉²	C₃	1	1	yes	maximal, characteristic
3	#10624706	C₃	1	27	yes	maximal, direct product factor
4	C₃×C₉⋊C₂₇	C₃	1	9	yes	maximal, complemented
5	C₃³×C₉	C₉	1	3	yes	—
6	C₃³×C₉	C₃²	1	1	yes	characteristic
7	C₃×C₂₇⋊C₃	—	3	27	no	—
8	C₃×C₂₇⋊C₃	C₃²	1	27	yes	—
9	C₃²×C₂₇	C₃²	1	9	yes	—
10	C₃×C₉²	C₉	1	2	yes	—
11	C₃×C₉²	C₉	1	18	yes	—
12	C₃×C₉²	C₉	1	3	yes	—
13	C₃×C₉²	C₉	1	1	yes	characteristic
14	C₃×C₉²	C₃²	1	9	yes	—
15	C₃×C₉²	C₃²	1	3	yes	—
16	C₉⋊C₂₇	C₃²	1	81	yes	complemented
17	C₃⁴	C₃×C₉	1	1	yes	characteristic
18	C₃²×C₉	—	3	27	no	—
19	C₃²×C₉	C₃×C₉	1	6	yes	—
20	C₃²×C₉	C₃×C₉	1	27	yes	—
21	C₃²×C₉	C₃×C₉	1	1	yes	characteristic
22	C₃²×C₉	C₃×C₉	1	1	yes	characteristic
23	C₃²×C₉	C₃×C₉	1	6	yes	—
24	C₃²×C₉	C₃×C₉	1	3	yes	—
25	C₃²×C₉	3₋¹⁺²	1	27	yes	—
26	C₃²×C₉	C₃³	1	3	yes	—
27	C₃²×C₉	C₃³	1	1	yes	characteristic
28	C₂₇⋊C₃	—	3	81	no	—
29	C₃×C₂₇	—	3	27	no	—
30	C₃×C₂₇	C₃³	1	27	yes	—
31	C₉²	C₃×C₉	1	18	yes	—
32	C₉²	C₃×C₉	1	27	yes	—
33	C₉²	C₃×C₉	1	18	yes	—
34	C₉²	C₃×C₉	1	9	yes	—
35	C₉²	C₃³	1	9	yes	—
36	C₃³	—	3	9	no	—
37	C₃³	C₉⋊C₉	1	9	yes	—
38	C₃³	C₃²×C₉	1	3	yes	—
39	C₃³	C₃²×C₉	1	1	yes	characteristic
40	C₃×C₉	—	3	18	no	—
41	C₃×C₉	—	3	81	no	—
42	C₃×C₉	C₉⋊C₉	1	54	yes	—
43	C₃×C₉	C₉⋊C₉	1	9	yes	—
44	C₃×C₉	C₉⋊C₉	1	9	yes	—
45	C₃×C₉	C₂₇⋊C₃	1	27	yes	complemented
46	C₃×C₉	C₃²×C₉	1	18	yes	—
47	C₃×C₉	C₃²×C₉	1	3	yes	—
48	C₃×C₉	C₃²×C₉	1	3	yes	—
49	C₃×C₉	C₃²×C₉	1	2	yes	—
50	C₃×C₉	C₃²×C₉	1	9	yes	—
51	C₃×C₉	C₃×3₋¹⁺²	1	9	yes	—
52	C₃×C₉	C₃×3₋¹⁺²	1	27	yes	—
53	C₃×C₉	C₃⁴	1	1	yes	characteristic
54	C₂₇	—	3	27	no	—
55	C₃²	—	3	9	no	—
56	C₃²	—	3	27	no	—
57	C₃²	C₃×C₉⋊C₉	1	9	yes	—
58	C₃²	C₃×C₉⋊C₉	1	3	yes	—
59	C₃²	C₃×C₂₇⋊C₃	1	9	yes	—
60	C₃²	C₃³×C₉	1	1	yes	characteristic
61	C₉	—	3	18	no	—
62	C₉	C₃×C₉⋊C₉	1	9	yes	—
63	C₉	C₃×C₉⋊C₉	1	9	yes	—
64	C₉	C₃×C₉⋊C₉	1	6	yes	—
65	C₉	C₃×C₂₇⋊C₃	1	27	yes	complemented
66	C₉	C₃²×3₋¹⁺²	1	3	yes	—
67	C₃	—	3	9	no	—
68	C₃	#10624706	1	9	yes	direct product factor
69	C₃	C₃²×C₉⋊C₉	1	1	yes	characteristic
70	C₃	C₃²×C₂₇⋊C₃	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
3. #10624706	C₃	direct (N × H)
4. C₃×C₉⋊C₂₇	C₃	semidirect
16. C₉⋊C₂₇	C₃²	semidirect
45. C₃×C₉	C₂₇⋊C₃	semidirect
65. C₉	C₃×C₂₇⋊C₃	semidirect
68. C₃	#10624706	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₂₇⋊C₃	3
C₃²×C₉²	3
#10624706	3
C₃×C₉⋊C₂₇	3

Subgroups — C3×#10624706 #14554145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10624706 #14554145