Subgroups — C₉×C₉⋊C₂₇ #14550265

Order 2187.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉⋊C₂₇	C₃	1	3	yes	maximal
2	C₃×C₉×C₂₇	C₃	1	3	yes	maximal
3	C₉³	C₃	1	1	yes	maximal, characteristic
4	#10624463	C₃	1	6	yes	maximal
5	C₃²×C₂₇	C₃²	1	9	yes	—
6	C₃×C₉²	C₉	1	6	yes	—
7	C₃×C₉²	C₉	1	3	yes	—
8	C₃×C₉²	C₃²	1	2	yes	—
9	C₃×C₉²	C₃²	1	1	yes	characteristic
10	C₃×C₉²	C₃²	1	1	yes	characteristic
11	C₉⋊C₂₇	C₉	1	27	yes	direct product factor
12	C₉×C₂₇	—	3	9	no	—
13	C₃²×C₉	C₃×C₉	1	2	yes	—
14	C₃²×C₉	C₃×C₉	1	6	yes	—
15	C₃²×C₉	C₃×C₉	1	1	yes	characteristic
16	C₃²×C₉	C₃×C₉	1	3	yes	—
17	C₃²×C₉	C₃³	1	1	yes	characteristic
18	C₃×C₂₇	—	3	9	no	—
19	C₃×C₂₇	—	3	18	no	—
20	C₃×C₂₇	C₃×C₉	1	27	yes	—
21	C₉²	—	3	18	no	—
22	C₉²	—	3	6	no	—
23	C₉²	C₂₇	1	27	yes	complemented
24	C₉²	C₃×C₉	1	9	yes	—
25	C₉²	3₋¹⁺²	1	9	yes	—
26	C₃³	C₃²×C₉	1	1	yes	characteristic
27	C₃×C₉	—	3	6	no	—
28	C₃×C₉	—	3	6	no	—
29	C₃×C₉	—	3	12	no	—
30	C₃×C₉	C₉²	1	6	yes	—
31	C₃×C₉	C₉²	1	3	yes	—
32	C₃×C₉	C₉⋊C₉	1	9	yes	—
33	C₃×C₉	C₃×C₂₇	1	18	yes	—
34	C₃×C₉	C₃×C₂₇	1	9	yes	—
35	C₃×C₉	C₃×C₂₇	1	9	yes	—
36	C₃×C₉	C₂₇⋊C₃	1	18	yes	—
37	C₃×C₉	C₃²×C₉	1	3	yes	—
38	C₃×C₉	C₃×3₋¹⁺²	1	3	yes	—
39	C₃×C₉	#737	1	6	yes	—
40	C₂₇	—	3	27	no	—
41	C₃²	C₃×C₉²	1	1	yes	characteristic
42	C₃²	C₃×C₉⋊C₉	1	1	yes	characteristic
43	C₃²	#6887	1	2	yes	—
44	C₃²	C₃²×C₂₇	1	3	yes	—
45	C₃²	C₃×C₂₇⋊C₃	1	6	yes	—
46	C₉	—	3	6	no	—
47	C₉	—	3	18	no	—
48	C₉	C₉×C₂₇	1	9	yes	complemented
49	C₉	C₉⋊C₂₇	1	27	yes	direct product factor
50	C₉	C₉×3₋¹⁺²	1	9	yes	—
51	C₃	C₉×C₉⋊C₉	1	1	yes	characteristic
52	C₃	C₃×C₉×C₂₇	1	1	yes	characteristic
53	C₃	C₉×C₂₇⋊C₃	1	2	yes	—
54	C₃	C₃×C₉⋊C₂₇	1	3	yes	—
55	C₃	#10624710	1	6	yes	—

	subgroup	G/H
center	C₃×C₉²	C₃²
commutator	C₃	C₃×C₉×C₂₇
Frattini, cosocle	C₃²×C₉	C₃³
socle, prime radical	C₃³	C₃²×C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ 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
11. C₉⋊C₂₇	C₉	direct (N × H)
23. C₉²	C₂₇	semidirect
48. C₉	C₉×C₂₇	semidirect
49. C₉	C₉⋊C₂₇	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×C₉⋊C₂₇	3
C₃×C₉×C₂₇	3
C₉³	3
#10624463	3

Subgroups — C9×C9⋊C27 #14550265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₉⋊C₂₇ #14550265