Subgroups — #14550324

Order 2187.

344 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6887	C₃	1	1	yes	maximal, characteristic
2	C₃×C₃²⋊C₂₇	C₃	1	3	yes	maximal
3	#10624463	C₃	1	9	yes	maximal, complemented
4	C₃³×C₉	C₃²	1	1	yes	characteristic
5	C₃²×C₂₇	C₃²	1	9	yes	—
6	#6887	—	3	3	no	—
7	#6887	—	3	6	no	—
8	C₃×C₉⋊C₉	C₉	1	6	yes	—
9	C₃×C₃²⋊C₉	C₉	1	3	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	3	no	—
14	C₃²×C₉	—	3	6	no	—
15	C₃²×C₉	C₃×C₉	1	9	yes	—
16	C₃²×C₉	C₃×C₉	1	2	yes	—
17	C₃²×C₉	H(3,𝔽₃)	1	3	yes	—
18	C₃²×C₉	3₋¹⁺²	1	6	yes	—
19	C₃²×C₉	C₃³	1	1	yes	characteristic
20	C₃×C₂₇	—	3	9	no	—
21	C₃×C₂₇	—	3	9	no	—
22	C₃×C₂₇	—	3	18	no	—
23	C₉⋊C₉	—	3	18	no	—
24	C₃²⋊C₉	—	3	9	no	—
25	C₉²	—	3	3	no	—
26	C₉²	—	3	6	no	—
27	C₃³	—	3	1	no	—
28	C₃³	—	3	2	no	—
29	C₃³	—	3	3	no	—
30	C₃³	—	3	6	no	—
31	C₃³	C₃²⋊C₉	1	3	yes	—
32	C₃³	C₃²×C₉	1	1	yes	characteristic
33	C₃×C₉	—	3	2	no	—
34	C₃×C₉	—	3	4	no	—
35	C₃×C₉	—	3	9	no	—
36	C₃×C₉	—	3	18	no	—
37	C₃×C₉	—	3	9	no	—
38	C₃×C₉	—	3	9	no	—
39	C₃×C₉	—	3	18	no	—
40	C₃×C₉	C₃²⋊C₉	1	6	yes	—
41	C₃×C₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
42	C₃×C₉	C₃×3₋¹⁺²	1	2	yes	—
43	C₃×C₉	#737	1	3	yes	—
44	C₃×C₉	#737	1	6	yes	—
45	C₂₇	—	9	9	no	—
46	C₃²	—	3	3	no	—
47	C₃²	—	3	9	no	—
48	C₃²	—	9	1	no	—
49	C₃²	—	9	2	no	—
50	C₃²	—	9	6	no	—
51	C₃²	C₃×C₃²⋊C₉	1	1	yes	characteristic
52	C₃²	#6887	1	1	yes	characteristic
53	C₃²	#6887	1	2	yes	—
54	C₃²	#6903	1	3	yes	—
55	C₃²	#6903	1	6	yes	—
56	C₉	—	3	6	no	—
57	C₉	—	9	9	no	—
58	C₉	#6893	1	3	yes	—
59	C₉	#6895	1	6	yes	—
60	C₃	—	9	3	no	—
61	C₃	#10624549	1	1	yes	characteristic
62	C₃	#10624684	1	3	yes	—
63	C₃	#10624712	1	1	yes	characteristic
64	C₃	#10624713	1	2	yes	—
65	C₃	#10624713	1	6	yes	—

	subgroup	G/H
center, Frattini, cosocle	C₃²×C₉	C₃³
commutator, socle	C₃³	C₃²×C₉
prime radical	C₃⁴	C₃×C₉
LCS	G ▷ C₃³ ▷ 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
3. #10624463	C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×#6887	3
C₃×C₃²⋊C₂₇	3
#10624463	3