Subgroups — C₃×#10624493 #14550852

Order 2187.

302 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6868	C₃	1	1	yes	maximal, characteristic
2	C₃×#6868	C₃	1	2	yes	maximal
3	C₃×#6855	C₃	1	1	yes	maximal, characteristic
4	#10624493	C₃	1	9	yes	maximal, direct product factor
5	C₃³×C₉	—	3	1	no	—
6	C₃³×C₉	C₃²	1	1	yes	characteristic
7	C₃×C₃²⋊C₉	—	3	1	no	—
8	C₃×C₃²⋊C₉	—	3	2	no	—
9	#6868	—	3	2	no	—
10	#6868	—	3	4	no	—
11	#6868	C₃²	1	3	yes	—
12	#6868	C₃²	1	6	yes	—
13	#6855	—	3	2	no	—
14	#6855	C₃²	1	3	yes	—
15	C₃⁴	H(3,𝔽₃)	1	1	yes	characteristic
16	C₃²×C₉	—	3	9	no	—
17	C₃²×C₉	—	3	3	no	—
18	C₃²×C₉	—	3	2	no	—
19	C₃²×C₉	—	3	1	no	—
20	C₃²×C₉	—	3	6	no	—
21	C₃²×C₉	—	3	3	no	—
22	C₃²×C₉	—	9	3	no	—
23	C₃²×C₉	—	9	3	no	—
24	C₃²×C₉	—	9	3	no	—
25	C₃²×C₉	—	9	1	no	—
26	C₃²×C₉	—	9	2	no	—
27	C₃²×C₉	H(3,𝔽₃)	1	2	yes	—
28	C₃²×C₉	C₃³	1	1	yes	characteristic
29	C₃²⋊C₉	—	3	3	no	—
30	C₃²⋊C₉	—	3	6	no	—
31	C₃²⋊C₉	—	9	2	no	—
32	C₃²⋊C₉	—	9	4	no	—
33	C₃³	—	3	3	no	—
34	C₃³	—	3	3	no	—
35	C₃³	—	3	3	no	—
36	C₃³	#731	1	3	yes	—
37	C₃³	#732	1	2	yes	—
38	C₃³	#732	1	1	yes	characteristic
39	C₃³	#733	1	6	yes	—
40	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
41	C₃×C₉	—	3	9	no	—
42	C₃×C₉	—	3	2	no	—
43	C₃×C₉	—	3	1	no	—
44	C₃×C₉	—	3	2	no	—
45	C₃×C₉	—	3	1	no	—
46	C₃×C₉	—	3	4	no	—
47	C₃×C₉	—	3	2	no	—
48	C₃×C₉	—	9	3	no	—
49	C₃×C₉	—	9	3	no	—
50	C₃×C₉	—	9	27	no	—
51	C₃×C₉	—	9	6	no	—
52	C₃×C₉	—	9	3	no	—
53	C₃×C₉	—	9	3	no	—
54	C₃×C₉	—	9	3	no	—
55	C₃×C₉	—	9	6	no	—
56	C₃×C₉	—	27	3	no	—
57	C₃×C₉	—	27	6	no	—
58	C₃²	—	3	1	no	—
59	C₃²	—	3	2	no	—
60	C₃²	—	3	1	no	—
61	C₃²	—	3	2	no	—
62	C₃²	—	3	1	no	—
63	C₃²	—	3	2	no	—
64	C₃²	—	3	9	no	—
65	C₃²	—	3	18	no	—
66	C₃²	#6861	1	6	yes	—
67	C₃²	#6861	1	3	yes	—
68	C₃²	#6878	1	3	yes	—
69	C₃²	#6881	1	3	yes	—
70	C₃²	#6882	1	3	yes	—
71	C₃²	C₃×#731	1	1	yes	characteristic
72	C₃²	C₃×#732	1	1	yes	characteristic
73	C₃²	C₃×#733	1	2	yes	—
74	C₉	—	9	9	no	—
75	C₉	—	9	2	no	—
76	C₉	—	9	1	no	—
77	C₉	—	27	3	no	—
78	C₉	—	27	6	no	—
79	C₃	—	3	1	no	—
80	C₃	—	3	6	no	—
81	C₃	—	3	2	no	—
82	C₃	#10624493	1	9	yes	direct product factor
83	C₃	C₃×#6861	1	1	yes	characteristic
84	C₃	C₃×#6878	1	1	yes	characteristic
85	C₃	C₃×#6881	1	1	yes	characteristic
86	C₃	C₃×#6882	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃³	#732
commutator, Frattini, cosocle	C₃²×C₉	C₃³
prime radical	C₃⁴	H(3,𝔽₃)
LCS	G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃³ ◁ C₃⁴ ◁ C₃³×C₉ ◁ G
LECS	G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁

Complements

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

N	H ≅ G/N	type
4. #10624493	C₃	direct (N × H)
82. C₃	#10624493	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#6868	3
C₃×#6855	3
#10624493	3

Subgroups — C3×#10624493 #14550852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10624493 #14550852