Subgroups — #14546670

Order 2187.

353 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6895	C₃	1	1	yes	maximal, characteristic
2	#10624548	C₃	1	1	yes	maximal, characteristic
3	C₉×C₃²⋊C₉	C₃	1	2	yes	maximal
4	#10624450	C₃	1	3	yes	maximal
5	#10624450	C₃	1	6	yes	maximal
6	C₃³×C₉	C₃²	1	1	yes	characteristic
7	#6895	—	3	6	no	—
8	#6895	C₉	1	9	yes	complemented
9	C₃×C₉⋊C₉	—	3	2	no	—
10	C₃×C₉⋊C₉	—	3	1	no	—
11	C₃×C₉⋊C₉	—	3	1	no	—
12	C₃×C₃²⋊C₉	C₃²	1	6	yes	—
13	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
14	C₃×C₃²⋊C₉	C₃²	1	2	yes	—
15	C₃×C₃²⋊C₉	C₃²	1	3	yes	—
16	C₃×C₉²	—	3	2	no	—
17	#6855	—	3	2	no	—
18	#6855	—	3	2	no	—
19	#6855	—	3	2	no	—
20	C₃⁴	C₃³	1	1	yes	characteristic
21	C₃²×C₉	—	3	6	no	—
22	C₃²×C₉	—	3	1	no	—
23	C₃²×C₉	—	3	2	no	—
24	C₃²×C₉	—	3	3	no	—
25	C₃²×C₉	—	9	2	no	—
26	C₃²×C₉	—	9	1	no	—
27	C₃²×C₉	C₃×C₉	1	3	yes	—
28	C₃²×C₉	H(3,𝔽₃)	1	2	yes	—
29	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
30	C₃²×C₉	3₋¹⁺²	1	6	yes	—
31	C₉⋊C₉	—	3	18	no	—
32	C₉⋊C₉	—	3	9	no	—
33	C₉⋊C₉	—	9	3	no	—
34	C₃²⋊C₉	—	3	4	no	—
35	C₃²⋊C₉	—	3	2	no	—
36	C₃²⋊C₉	—	3	18	no	—
37	C₃²⋊C₉	—	9	3	no	—
38	C₃²⋊C₉	C₃×C₉	1	6	yes	—
39	C₃²⋊C₉	C₃×C₉	1	3	yes	—
40	C₉²	—	9	6	no	—
41	C₃³	—	3	3	no	—
42	C₃³	—	3	6	no	—
43	C₃³	—	3	2	no	—
44	C₃³	—	3	1	no	—
45	C₃³	C₃²×C₉	1	1	yes	characteristic
46	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
47	C₃³	C₃×3₋¹⁺²	1	2	yes	—
48	C₃×C₉	—	3	2	no	—
49	C₃×C₉	—	3	1	no	—
50	C₃×C₉	—	3	2	no	—
51	C₃×C₉	—	3	2	no	—
52	C₃×C₉	—	3	2	no	—
53	C₃×C₉	—	3	6	no	—
54	C₃×C₉	—	3	3	no	—
55	C₃×C₉	—	3	18	no	—
56	C₃×C₉	—	9	3	no	—
57	C₃×C₉	—	9	6	no	—
58	C₃×C₉	—	9	6	no	—
59	C₃×C₉	—	9	3	no	—
60	C₃×C₉	—	9	6	no	—
61	C₃×C₉	—	9	6	no	—
62	C₃×C₉	—	9	6	no	—
63	C₃×C₉	—	9	3	no	—
64	C₃×C₉	—	9	6	no	—
65	C₃×C₉	—	9	3	no	—
66	C₃×C₉	C₃²⋊C₉	1	6	yes	—
67	C₃×C₉	C₃²⋊C₉	1	3	yes	—
68	C₃²	—	3	1	no	—
69	C₃²	—	3	2	no	—
70	C₃²	—	3	2	no	—
71	C₃²	—	3	4	no	—
72	C₃²	—	3	1	no	—
73	C₃²	—	3	2	no	—
74	C₃²	—	9	6	no	—
75	C₃²	—	9	3	no	—
76	C₃²	C₃×C₃²⋊C₉	1	1	yes	characteristic
77	C₃²	#6908	1	6	yes	—
78	C₃²	#6910	1	2	yes	—
79	C₃²	#6910	1	1	yes	characteristic
80	C₃²	#6913	1	3	yes	—
81	C₉	—	3	6	no	—
82	C₉	—	3	3	no	—
83	C₉	—	9	18	no	—
84	C₉	—	9	6	no	—
85	C₉	—	9	3	no	—
86	C₉	—	27	3	no	—
87	C₃	—	9	1	no	—
88	C₃	—	9	2	no	—
89	C₃	#10624624	1	6	yes	—
90	C₃	#10624625	1	3	yes	—
91	C₃	#10624690	1	1	yes	characteristic
92	C₃	#10624697	1	2	yes	—
93	C₃	#10624700	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃³	C₃×H(3,𝔽₃)
commutator	C₃³	C₃²×C₉
Frattini, prime radical, cosocle	C₃⁴	C₃³
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃³ ◁ C₃³×C₉ ◁ G
LECS	G ▷ C₃⁴ ▷ C₃² ▷ C₁

Complements

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

N	H ≅ G/N	type
8. #6895	C₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×#6895	3
#10624548	3
C₉×C₃²⋊C₉	3
#10624450	3