Subgroups — #14554147

Order 2187.

818 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	C₃×#6887	C₃	1	1	yes	maximal, characteristic
3	#10624707	C₃	1	27	yes	maximal, complemented
4	#10624706	C₃	1	9	yes	maximal, complemented
5	C₃³×C₉	C₃²	1	1	yes	characteristic
6	C₃×C₂₇⋊C₃	—	3	27	no	—
7	C₃×C₂₇⋊C₃	C₃²	1	9	yes	—
8	C₃×C₂₇⋊C₃	C₃²	1	18	yes	—
9	C₃²×C₂₇	C₃²	1	9	yes	—
10	#6887	C₉	1	18	yes	—
11	#6887	C₃²	1	9	yes	—
12	C₃×C₉⋊C₉	C₉	1	6	yes	—
13	C₃×C₃²⋊C₉	C₉	1	3	yes	—
14	C₃×C₉²	C₃²	1	3	yes	—
15	C₉⋊C₂₇	C₃²	1	81	yes	complemented
16	C₃⁴	C₃×C₉	1	1	yes	characteristic
17	C₃²×C₉	C₃×C₉	1	9	yes	—
18	C₃²×C₉	C₃×C₉	1	2	yes	—
19	C₃²×C₉	C₃×C₉	1	6	yes	—
20	C₃²×C₉	3₋¹⁺²	1	27	yes	—
21	C₃²×C₉	C₃³	1	1	yes	characteristic
22	C₃²×C₉	C₃³	1	3	yes	—
23	C₂₇⋊C₃	—	3	27	no	—
24	C₂₇⋊C₃	—	3	54	no	—
25	C₃×C₂₇	—	3	27	no	—
26	C₃×C₂₇	C₃³	1	27	yes	—
27	C₉⋊C₉	C₃×C₉	1	54	yes	—
28	C₃²⋊C₉	C₃×C₉	1	27	yes	—
29	C₉²	C₃×C₉	1	18	yes	—
30	C₉²	C₃³	1	9	yes	—
31	C₃³	—	9	3	no	—
32	C₃³	C₉⋊C₉	1	9	yes	—
33	C₃³	C₃²×C₉	1	3	yes	—
34	C₃³	C₃²×C₉	1	1	yes	characteristic
35	C₃×C₉	—	9	9	no	—
36	C₃×C₉	C₉⋊C₉	1	18	yes	—
37	C₃×C₉	C₉⋊C₉	1	54	yes	—
38	C₃×C₉	C₃²×C₉	1	27	yes	—
39	C₃×C₉	C₃²×C₉	1	2	yes	—
40	C₃×C₉	C₃²×C₉	1	6	yes	—
41	C₃×C₉	C₃×3₋¹⁺²	1	9	yes	—
42	C₃×C₉	C₃×3₋¹⁺²	1	9	yes	—
43	C₃×C₉	C₃×3₋¹⁺²	1	18	yes	—
44	C₃×C₉	C₃⁴	1	1	yes	characteristic
45	C₂₇	—	3	27	no	—
46	C₃²	—	3	3	no	—
47	C₃²	—	3	9	no	—
48	C₃²	—	9	9	no	—
49	C₃²	C₃×C₉⋊C₉	1	9	yes	—
50	C₃²	C₃×C₉⋊C₉	1	3	yes	—
51	C₃²	C₃³×C₉	1	1	yes	characteristic
52	C₉	—	3	27	no	—
53	C₉	C₃×C₉⋊C₉	1	6	yes	—
54	C₉	C₃×C₉⋊C₉	1	18	yes	—
55	C₉	C₃²×3₋¹⁺²	1	3	yes	—
56	C₃	—	3	3	no	—
57	C₃	—	3	9	no	—
58	C₃	C₃²×C₉⋊C₉	1	1	yes	characteristic
59	C₃	#10624918	1	3	yes	—

	subgroup	G/H
center, Frattini, cosocle	C₃×C₉	C₃⁴
commutator, socle	C₃²	C₃³×C₉
prime radical	C₃⁴	C₃×C₉
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃×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. #10624707	C₃	semidirect
4. #10624706	C₃	semidirect
15. C₉⋊C₂₇	C₃²	semidirect

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
C₃×#6887	3
#10624707	3
#10624706	3