Subgroups — #14550880

Order 2187.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624688	C₃	1	4	yes	maximal
2	#10624497	C₃	1	8	yes	maximal
3	#10624496	C₃	1	1	yes	maximal, characteristic
4	C₃³×C₉	C₃²	1	1	yes	characteristic
5	#6887	—	3	4	no	—
6	#6868	—	3	4	no	—
7	#6867	—	3	4	no	—
8	#6866	C₃²	1	4	yes	—
9	#6866	C₃²	1	8	yes	—
10	C₃⁴	C₃³	1	1	yes	characteristic
11	C₃²×C₉	—	3	8	no	—
12	C₃²×C₉	—	3	4	no	—
13	C₃²×C₉	H(3,𝔽₃)	1	2	yes	—
14	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
15	C₉⋊C₉	—	9	8	no	—
16	C₃²⋊C₉	—	3	4	no	—
17	C₃²⋊C₉	—	3	8	no	—
18	C₉²	—	9	4	no	—
19	C₃³	—	3	4	no	—
20	C₃³	—	9	3	no	—
21	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
22	C₃×C₉	—	3	8	no	—
23	C₃×C₉	—	9	8	no	—
24	C₃×C₉	—	9	1	no	—
25	C₃×C₉	—	9	4	no	—
26	C₃×C₉	—	9	8	no	—
27	C₃×C₉	#731	1	8	yes	—
28	C₃×C₉	#731	1	4	yes	—
29	C₃²	—	9	1	no	—
30	C₃²	—	9	12	no	—
31	C₃²	—	9	1	no	—
32	C₃²	C₃×#731	1	4	yes	—
33	C₉	—	9	2	no	—
34	C₉	—	27	4	no	—
35	C₉	—	27	8	no	—
36	C₉	#6862	1	8	yes	—
37	C₉	#6862	1	1	yes	characteristic
38	C₃	—	3	4	no	—
39	C₃	—	9	3	no	—
40	C₃	C₃×#6862	1	1	yes	characteristic

	subgroup	G/H
center	C₉	#6862
commutator, Frattini, prime radical, cosocle	C₃⁴	C₃³
socle	C₃	C₃×#6862
LCS	G ▷ C₃⁴ ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉ ◁ C₃²×C₉ ◁ C₃³×C₉ ◁ G
LECS	G ▷ C₃⁴ ▷ C₃³ ▷ C₃ ▷ C₁

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