Subgroups — #14550355

Order 2187.

323 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	C₉³	C₃	1	1	yes	maximal, characteristic
3	#10624463	C₃	1	9	yes	maximal
4	C₃²×C₂₇	C₃²	1	9	yes	—
5	C₃×C₉²	C₉	1	6	yes	—
6	C₃×C₉²	C₉	1	2	yes	—
7	C₃×C₉²	C₉	1	1	yes	characteristic
8	C₃×C₉²	C₃²	1	3	yes	—
9	C₃×C₉²	C₃²	1	1	yes	characteristic
10	C₉⋊C₂₇	—	3	9	no	—
11	C₃²×C₉	C₃×C₉	1	2	yes	—
12	C₃²×C₉	C₃×C₉	1	3	yes	—
13	C₃²×C₉	C₃×C₉	1	6	yes	—
14	C₃²×C₉	C₃×C₉	1	1	yes	characteristic
15	C₃²×C₉	C₃³	1	1	yes	characteristic
16	C₃×C₂₇	—	3	9	no	—
17	C₃×C₂₇	—	3	27	no	—
18	C₉²	—	3	18	no	—
19	C₉²	—	3	6	no	—
20	C₉²	—	3	9	no	—
21	C₉²	C₂₇	1	9	yes	complemented
22	C₉²	3₋¹⁺²	1	9	yes	—
23	C₃³	C₃²×C₉	1	1	yes	characteristic
24	C₃×C₉	—	3	3	no	—
25	C₃×C₉	—	3	6	no	—
26	C₃×C₉	—	3	6	no	—
27	C₃×C₉	—	3	6	no	—
28	C₃×C₉	—	3	6	no	—
29	C₃×C₉	—	3	6	no	—
30	C₃×C₉	C₉⋊C₉	1	6	yes	—
31	C₃×C₉	C₉⋊C₉	1	3	yes	—
32	C₃×C₉	C₃×C₂₇	1	9	yes	—
33	C₃×C₉	C₃×C₂₇	1	3	yes	—
34	C₃×C₉	C₂₇⋊C₃	1	18	yes	—
35	C₃×C₉	C₂₇⋊C₃	1	6	yes	—
36	C₃×C₉	C₃×3₋¹⁺²	1	3	yes	—
37	C₃×C₉	#737	1	9	yes	—
38	C₂₇	—	9	9	no	—
39	C₃²	C₃×C₉⋊C₉	1	1	yes	characteristic
40	C₃²	#6887	1	3	yes	—
41	C₃²	C₃²×C₂₇	1	1	yes	characteristic
42	C₃²	C₃×C₂₇⋊C₃	1	2	yes	—
43	C₃²	C₃×C₂₇⋊C₃	1	6	yes	—
44	C₉	—	3	6	no	—
45	C₉	—	3	9	no	—
46	C₉	—	3	18	no	—
47	C₉	C₉⋊C₂₇	1	9	yes	—
48	C₉	#6899	1	9	yes	—
49	C₃	#10624553	1	1	yes	characteristic
50	C₃	C₃×C₉⋊C₂₇	1	1	yes	characteristic
51	C₃	#10624706	1	2	yes	—
52	C₃	#10624710	1	3	yes	—
53	C₃	#10624711	1	6	yes	—

	subgroup	G/H
center, Frattini, cosocle	C₃²×C₉	C₃³
commutator	C₃²	C₃²×C₂₇
socle, prime radical	C₃³	C₃²×C₉
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₉ ◁ G
LECS	G ▷ C₃²×C₉ ▷ C₃ ▷ C₁

Complements

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

N	H ≅ G/N	type
21. C₉²	C₂₇	semidirect

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
C₉³	3
#10624463	3