Subgroups — #14548235

Order 2187.

485 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
2	#10624811	C₃	1	9	yes	maximal, complemented
3	#10624733	C₃	1	2	yes	maximal, complemented
4	#10624732	C₃	1	1	yes	maximal, characteristic
5	C₃³×C₉	C₃²	1	1	yes	characteristic
6	C₃³×C₉	C₃²	1	3	yes	—
7	C₃×#733	—	3	6	no	—
8	C₃×#732	—	3	3	no	—
9	#6891	C₃²	1	6	yes	—
10	C₃²⋊H(3,𝔽₃)	C₃²	1	3	yes	—
11	C₃×C₉⋊C₉	—	3	9	no	—
12	C₃×C₉⋊C₉	—	3	3	no	—
13	H(3,𝔽₃)⋊C₉	—	3	27	no	—
14	C₃⁴	C₃³	1	1	yes	characteristic
15	C₃×3₋¹⁺²	—	3	6	no	—
16	C₃×H(3,𝔽₃)	—	3	9	no	—
17	C₃×H(3,𝔽₃)	—	3	3	no	—
18	C₃²×C₉	—	3	3	no	—
19	C₃²×C₉	—	3	9	no	—
20	C₃²×C₉	—	3	3	no	—
21	C₃²×C₉	—	3	3	no	—
22	C₃²×C₉	—	3	3	no	—
23	C₃²×C₉	—	9	9	no	—
24	C₃²×C₉	H(3,𝔽₃)	1	3	yes	—
25	C₃²×C₉	H(3,𝔽₃)	1	9	yes	—
26	#733	—	9	18	no	—
27	#732	—	9	9	no	—
28	C₉⋊C₉	—	3	27	no	—
29	C₃²⋊C₉	—	3	18	no	—
30	C₃³	—	3	9	no	—
31	C₃³	—	3	3	no	—
32	C₃³	—	9	3	no	—
33	C₃³	C₃×H(3,𝔽₃)	1	3	yes	—
34	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
35	3₋¹⁺²	—	9	18	no	—
36	H(3,𝔽₃)	—	9	27	no	—
37	H(3,𝔽₃)	—	9	9	no	—
38	C₃×C₉	—	3	27	no	—
39	C₃×C₉	—	3	3	no	—
40	C₃×C₉	—	3	6	no	—
41	C₃×C₉	—	3	9	no	—
42	C₃×C₉	—	9	9	no	—
43	C₃×C₉	—	9	9	no	—
44	C₃×C₉	—	9	9	no	—
45	C₃×C₉	—	9	9	no	—
46	C₃×C₉	—	9	6	no	—
47	C₃×C₉	#732	1	9	yes	—
48	C₃²	—	3	27	no	—
49	C₃²	—	3	3	no	—
50	C₃²	—	3	3	no	—
51	C₃²	—	3	3	no	—
52	C₃²	—	3	3	no	—
53	C₃²	—	27	3	no	—
54	C₃²	—	27	9	no	—
55	C₃²	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
56	C₃²	C₃×#732	1	3	yes	—
57	C₃²	#6913	1	9	yes	—
58	C₉	—	3	9	no	—
59	C₉	—	9	9	no	—
60	C₉	—	27	6	no	—
61	C₃	—	3	9	no	—
62	C₃	—	3	3	no	—
63	C₃	—	81	3	no	—
64	C₃	#10624732	1	1	yes	characteristic
65	C₃	#10624739	1	3	yes	—

	subgroup	G/H
center, socle	C₃²	C₃²⋊H(3,𝔽₃)
commutator, Frattini, cosocle	C₃⁴	C₃³
prime radical	#10624732	C₃
LCS	G ▷ C₃⁴ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃² ◁ C₃⁴ ◁ G
LECS	G ▷ C₃⁴ ▷ C₃² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₉⋊C₉	C₃	semidirect
2. #10624811	C₃	semidirect
3. #10624733	C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₉⋊C₉	3
#10624811	3
#10624733	3
#10624732	3