Subgroups — C₉×#6875 #14550273

Order 2187.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6875	C₃	1	3	yes	maximal
2	C₉×C₂₇⋊C₃	C₃	1	2	yes	maximal
3	C₉×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₉×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
5	#10624472	C₃	1	6	yes	maximal
6	C₃×C₂₇⋊C₃	C₃²	1	6	yes	—
7	C₃×C₂₇⋊C₃	C₃²	1	2	yes	—
8	C₃×C₂₇⋊C₃	C₃²	1	1	yes	characteristic
9	C₃×C₉⋊C₉	C₃²	1	3	yes	—
10	C₃×C₉²	—	3	1	no	—
11	C₃×C₉²	C₃²	1	1	yes	characteristic
12	#6875	C₉	1	27	yes	direct product factor
13	#6864	—	3	4	no	—
14	#6864	C₉	1	6	yes	complemented
15	C₉×C₂₇	—	3	2	no	—
16	C₉×C₂₇	C₉	1	3	yes	complemented
17	#6855	—	3	2	no	—
18	C₃²×C₉	—	3	3	no	—
19	C₃²×C₉	3₋¹⁺²	1	1	yes	characteristic
20	C₃²×C₉	3₋¹⁺²	1	2	yes	—
21	C₃²×C₉	C₃³	1	1	yes	characteristic
22	C₂₇⋊C₃	—	3	6	no	—
23	C₂₇⋊C₃	—	3	12	no	—
24	C₂₇⋊C₃	C₃×C₉	1	18	yes	—
25	C₂₇⋊C₃	C₃×C₉	1	9	yes	—
26	C₃×C₂₇	—	3	6	no	—
27	C₃×C₂₇	C₃×C₉	1	6	yes	—
28	C₃×C₂₇	C₃×C₉	1	3	yes	—
29	C₉⋊C₉	—	3	6	no	—
30	C₉⋊C₉	C₃×C₉	1	9	yes	—
31	C₉²	—	9	3	no	—
32	C₉²	C₃×C₉	1	2	yes	—
33	C₉²	C₃×C₉	1	1	yes	characteristic
34	C₉²	3₋¹⁺²	1	4	yes	—
35	C₉²	3₋¹⁺²	1	2	yes	—
36	C₃³	C₃×3₋¹⁺²	1	1	yes	characteristic
37	C₃×C₉	—	3	3	no	—
38	C₃×C₉	—	3	9	no	—
39	C₃×C₉	—	9	2	no	—
40	C₃×C₉	—	9	3	no	—
41	C₃×C₉	—	9	6	no	—
42	C₃×C₉	C₉⋊C₉	1	2	yes	—
43	C₃×C₉	C₉⋊C₉	1	4	yes	—
44	C₃×C₉	C₉⋊C₉	1	2	yes	—
45	C₃×C₉	C₉⋊C₉	1	1	yes	characteristic
46	C₃×C₉	C₃²×C₉	1	1	yes	characteristic
47	C₃×C₉	C₃²×C₉	1	3	yes	—
48	C₃×C₉	C₃×3₋¹⁺²	1	2	yes	—
49	C₃×C₉	#737	1	6	yes	—
50	C₂₇	—	3	6	no	—
51	C₂₇	—	3	18	no	—
52	C₂₇	C₉²	1	9	yes	complemented
53	C₃²	—	3	1	no	—
54	C₃²	—	3	2	no	—
55	C₃²	C₃×C₉⋊C₉	1	1	yes	characteristic
56	C₃²	C₉×3₋¹⁺²	1	3	yes	—
57	C₉	—	3	2	no	—
58	C₉	—	3	4	no	—
59	C₉	—	3	2	no	—
60	C₉	—	9	9	no	—
61	C₉	#6875	1	3	yes	direct product factor
62	C₉	C₃×C₉²	1	1	yes	characteristic
63	C₉	#6887	1	2	yes	—
64	C₉	C₉×3₋¹⁺²	1	6	yes	—
65	C₃	—	3	3	no	—
66	C₃	C₉×C₉⋊C₉	1	1	yes	characteristic
67	C₃	C₃×#6875	1	1	yes	characteristic
68	C₃	#10624709	1	2	yes	—

	subgroup	G/H
center	C₃×C₉	C₉⋊C₉
commutator	C₉	C₃×C₉²
Frattini, cosocle	C₃²×C₉	C₃³
socle	C₃²	C₃×C₉⋊C₉
prime radical	C₃³	C₃×3₋¹⁺²
LCS	G ▷ C₉ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₉ ◁ C₃×C₉² ◁ G
LECS	G ▷ C₃²×C₉ ▷ C₃ ▷ C₁

Complements

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

N	H ≅ G/N	type
12. #6875	C₉	direct (N × H)
14. #6864	C₉	semidirect
16. C₉×C₂₇	C₉	semidirect
52. C₂₇	C₉²	semidirect
61. C₉	#6875	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#6875	3
C₉×C₂₇⋊C₃	3
C₉×C₉⋊C₉	3
#10624472	3

Subgroups — C9×#6875 #14550273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#6875 #14550273