Subgroups — C₉×C₃²⋊C₂₇ #14550239

Order 2187.

647 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₉²	C₃	1	1	yes	maximal, characteristic
2	C₃×C₃²⋊C₂₇	C₃	1	3	yes	maximal
3	C₃×C₉×C₂₇	C₃	1	3	yes	maximal, complemented
4	#10624463	C₃	1	6	yes	maximal, complemented
5	C₃³×C₉	C₉	1	3	yes	—
6	C₃³×C₉	C₃²	1	1	yes	characteristic
7	C₃²×C₂₇	C₃²	1	9	yes	—
8	C₃×C₉²	—	3	3	no	—
9	C₃×C₉²	—	3	6	no	—
10	C₃×C₉²	C₉	1	6	yes	—
11	C₃×C₉²	C₃²	1	2	yes	—
12	C₃×C₉²	C₃²	1	1	yes	characteristic
13	C₃²⋊C₂₇	C₉	1	27	yes	direct product factor
14	C₉×C₂₇	—	3	9	no	—
15	C₃⁴	C₃×C₉	1	1	yes	characteristic
16	C₃²×C₉	—	3	9	no	—
17	C₃²×C₉	—	3	18	no	—
18	C₃²×C₉	—	3	1	no	—
19	C₃²×C₉	—	3	2	no	—
20	C₃²×C₉	—	3	6	no	—
21	C₃²×C₉	C₂₇	1	27	yes	complemented
22	C₃²×C₉	C₃×C₉	1	2	yes	—
23	C₃²×C₉	C₃×C₉	1	9	yes	—
24	C₃²×C₉	C₃×C₉	1	6	yes	—
25	C₃²×C₉	C₃×C₉	1	3	yes	—
26	C₃²×C₉	C₃³	1	1	yes	characteristic
27	C₃×C₂₇	—	3	9	no	—
28	C₃×C₂₇	—	3	18	no	—
29	C₃×C₂₇	C₃×C₉	1	27	yes	complemented
30	C₉²	—	3	18	no	—
31	C₉²	—	3	2	no	—
32	C₉²	—	3	4	no	—
33	C₉²	H(3,𝔽₃)	1	3	yes	—
34	C₉²	3₋¹⁺²	1	6	yes	—
35	C₃³	—	3	1	no	—
36	C₃³	—	3	2	no	—
37	C₃³	—	3	6	no	—
38	C₃³	C₉²	1	3	yes	—
39	C₃³	C₃×C₂₇	1	9	yes	—
40	C₃³	C₃²×C₉	1	1	yes	characteristic
41	C₃×C₉	—	3	2	no	—
42	C₃×C₉	—	3	6	no	—
43	C₃×C₉	—	3	4	no	—
44	C₃×C₉	—	3	12	no	—
45	C₃×C₉	—	3	81	no	—
46	C₃×C₉	—	3	9	no	—
47	C₃×C₉	—	3	18	no	—
48	C₃×C₉	C₉²	1	6	yes	—
49	C₃×C₉	C₃²⋊C₉	1	9	yes	—
50	C₃×C₉	C₃×C₂₇	1	18	yes	—
51	C₃×C₉	C₃×C₂₇	1	9	yes	—
52	C₃×C₉	C₂₇⋊C₃	1	18	yes	—
53	C₃×C₉	C₃²×C₉	1	3	yes	—
54	C₃×C₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
55	C₃×C₉	C₃×3₋¹⁺²	1	2	yes	—
56	C₃×C₉	#737	1	6	yes	—
57	C₂₇	—	3	27	no	—
58	C₃²	—	3	3	no	—
59	C₃²	—	3	6	no	—
60	C₃²	—	3	9	no	—
61	C₃²	—	3	18	no	—
62	C₃²	C₉×C₂₇	1	9	yes	complemented
63	C₃²	C₃×C₉²	1	1	yes	characteristic
64	C₃²	C₃×C₃²⋊C₉	1	1	yes	characteristic
65	C₃²	#6887	1	2	yes	—
66	C₃²	C₃²×C₂₇	1	3	yes	—
67	C₃²	C₃×C₂₇⋊C₃	1	6	yes	—
68	C₉	—	3	6	no	—
69	C₉	—	3	18	no	—
70	C₉	C₃²⋊C₂₇	1	27	yes	direct product factor
71	C₉	C₉×H(3,𝔽₃)	1	3	yes	—
72	C₉	C₉×3₋¹⁺²	1	6	yes	—
73	C₃	—	3	9	no	—
74	C₃	C₉×C₃²⋊C₉	1	1	yes	characteristic
75	C₃	C₃×C₉×C₂₇	1	1	yes	characteristic
76	C₃	C₉×C₂₇⋊C₃	1	2	yes	—
77	C₃	C₃×C₃²⋊C₂₇	1	3	yes	—
78	C₃	#10624710	1	6	yes	—

	subgroup	G/H
center	C₃×C₉²	C₃²
commutator	C₃	C₃×C₉×C₂₇
Frattini, cosocle	C₃²×C₉	C₃³
socle	C₃³	C₃²×C₉
prime radical	C₃⁴	C₃×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
3. C₃×C₉×C₂₇	C₃	semidirect
4. #10624463	C₃	semidirect
13. C₃²⋊C₂₇	C₉	direct (N × H)
21. C₃²×C₉	C₂₇	semidirect
29. C₃×C₂₇	C₃×C₉	semidirect
62. C₃²	C₉×C₂₇	semidirect
70. C₉	C₃²⋊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
C₃²×C₉²	3
C₃×C₃²⋊C₂₇	3
C₃×C₉×C₂₇	3
#10624463	3

Subgroups — C9×C32⋊C27 #14550239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₃²⋊C₂₇ #14550239