Subgroups — #14550330

Order 2187.

488 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	#10624683	C₃	1	3	yes	maximal
3	#10624467	C₃	1	9	yes	maximal, complemented
4	C₃³×C₉	C₉	1	3	yes	—
5	C₃³×C₉	C₃²	1	1	yes	characteristic
6	C₃×C₂₇⋊C₃	C₃²	1	9	yes	—
7	C₃×C₉²	—	3	3	no	—
8	C₃×C₉²	—	3	6	no	—
9	C₃×C₉²	C₉	1	6	yes	—
10	C₃×C₉²	C₃²	1	3	yes	—
11	C₃²⋊C₂₇	—	3	9	no	—
12	C₃⁴	C₃×C₉	1	1	yes	characteristic
13	C₃²×C₉	—	3	6	no	—
14	C₃²×C₉	—	3	3	no	—
15	C₃²×C₉	—	3	9	no	—
16	C₃²×C₉	—	3	27	no	—
17	C₃²×C₉	C₃×C₉	1	9	yes	—
18	C₃²×C₉	C₃×C₉	1	2	yes	—
19	C₃²×C₉	H(3,𝔽₃)	1	3	yes	—
20	C₃²×C₉	3₋¹⁺²	1	6	yes	—
21	C₃²×C₉	C₃³	1	1	yes	characteristic
22	C₂₇⋊C₃	—	3	27	no	—
23	C₃×C₂₇	—	3	9	no	—
24	C₉²	—	3	18	no	—
25	C₉²	—	3	3	no	—
26	C₉²	—	3	6	no	—
27	C₃³	—	3	9	no	—
28	C₃³	—	3	3	no	—
29	C₃³	C₃²⋊C₉	1	3	yes	—
30	C₃³	C₃²×C₉	1	1	yes	characteristic
31	C₃×C₉	—	3	54	no	—
32	C₃×C₉	—	3	27	no	—
33	C₃×C₉	—	3	9	no	—
34	C₃×C₉	—	3	6	no	—
35	C₃×C₉	—	3	9	no	—
36	C₃×C₉	—	3	18	no	—
37	C₃×C₉	—	3	27	no	—
38	C₃×C₉	C₃²⋊C₉	1	6	yes	—
39	C₃×C₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
40	C₃×C₉	C₃×3₋¹⁺²	1	2	yes	—
41	C₃×C₉	#737	1	9	yes	—
42	C₂₇	—	9	9	no	—
43	C₃²	—	3	27	no	—
44	C₃²	—	3	3	no	—
45	C₃²	—	3	6	no	—
46	C₃²	—	3	3	no	—
47	C₃²	#6869	1	9	yes	—
48	C₃²	C₃×C₃²⋊C₉	1	1	yes	characteristic
49	C₃²	#6887	1	3	yes	—
50	C₉	—	3	6	no	—
51	C₉	—	3	27	no	—
52	C₉	#6893	1	3	yes	—
53	C₉	#6895	1	6	yes	—
54	C₃	—	3	9	no	—
55	C₃	—	3	3	no	—
56	C₃	#10624549	1	1	yes	characteristic
57	C₃	C₃×#6869	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
3. #10624467	C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₉²	3
#10624683	3
#10624467	3