Subgroups — #14551441

Order 2187.

221 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₈₁⋊C₃	C₃	1	2	yes	maximal
2	C₃²×C₈₁	C₃	1	1	yes	maximal, characteristic
3	#10624681	C₃	1	1	yes	maximal, characteristic
4	#10624499	C₃	1	6	yes	maximal, complemented
5	C₉×C₈₁	C₃	1	3	yes	maximal, complemented
6	C₃×C₂₇⋊C₃	C₉	1	2	yes	—
7	C₃²×C₂₇	C₃²	1	1	yes	characteristic
8	#6887	C₉	1	1	yes	characteristic
9	C₈₁⋊C₃	C₉	1	18	yes	complemented
10	C₃×C₈₁	C₉	1	9	yes	complemented
11	C₃×C₈₁	C₃²	1	2	yes	—
12	C₃×C₈₁	C₃²	1	6	yes	—
13	C₃×C₈₁	C₃²	1	1	yes	characteristic
14	#6864	C₉	1	6	yes	—
15	C₉×C₂₇	C₃²	1	3	yes	—
16	C₃²×C₉	C₃×C₉	1	1	yes	characteristic
17	C₂₇⋊C₃	C₂₇	1	18	yes	—
18	C₃×C₂₇	C₃×C₉	1	2	yes	—
19	C₃×C₂₇	C₃×C₉	1	3	yes	—
20	C₃×C₂₇	C₃×C₉	1	6	yes	—
21	C₃×C₂₇	C₃×C₉	1	6	yes	—
22	C₃×C₂₇	C₃³	1	1	yes	characteristic
23	C₉⋊C₉	C₂₇	1	6	yes	—
24	C₃²⋊C₉	C₂₇	1	3	yes	—
25	C₉²	C₃×C₉	1	3	yes	—
26	C₈₁	C₃×C₉	1	6	yes	—
27	C₈₁	C₃×C₉	1	3	yes	—
28	C₈₁	C₃×C₉	1	18	yes	—
29	C₃³	C₃×C₂₇	1	1	yes	characteristic
30	C₃×C₉	C₉²	1	3	yes	—
31	C₃×C₉	C₃×C₂₇	1	9	yes	—
32	C₃×C₉	C₃×C₂₇	1	2	yes	—
33	C₃×C₉	C₃×C₂₇	1	6	yes	—
34	C₃×C₉	C₃²×C₉	1	1	yes	characteristic
35	C₂₇	C₉²	1	6	yes	—
36	C₂₇	C₃×C₂₇	1	18	yes	—
37	C₂₇	C₃²×C₉	1	1	yes	characteristic
38	C₂₇	C₃²×C₉	1	2	yes	—
39	C₃²	—	3	3	no	—
40	C₃²	C₉×C₂₇	1	3	yes	—
41	C₃²	C₃²×C₂₇	1	1	yes	characteristic
42	C₉	—	3	9	no	—
43	C₉	C₉×C₂₇	1	6	yes	—
44	C₉	C₃×C₉²	1	1	yes	characteristic
45	C₉	C₃²×C₂₇	1	2	yes	—
46	C₃	—	3	3	no	—
47	C₃	C₃×C₉×C₂₇	1	1	yes	characteristic
48	C₃	#10624833	1	3	yes	—

	subgroup	G/H
center	C₃×C₈₁	C₃²
commutator	C₃	C₃×C₉×C₂₇
Frattini, cosocle	C₃×C₂₇	C₃³
socle	C₃²	C₃²×C₂₇
prime radical	C₃³	C₃×C₂₇
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₈₁ ◁ G
LECS	G ▷ C₃×C₂₇ ▷ C₉ ▷ C₃ ▷ C₁

Complements

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

N	H ≅ G/N	type
4. #10624499	C₃	semidirect
5. C₉×C₈₁	C₃	semidirect
9. C₈₁⋊C₃	C₉	semidirect
10. C₃×C₈₁	C₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₈₁⋊C₃	3
C₃²×C₈₁	3
#10624681	3
#10624499	3
C₉×C₈₁	3