Subgroups — C₃×#10624684 #14554107

Order 2187.

1664 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#737	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₂₇⋊C₃	C₃	1	2	yes	maximal, complemented
3	C₃³×C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
4	#10624684	C₃	1	27	yes	maximal, direct product factor
5	C₃×C₃²⋊C₂₇	C₃	1	9	yes	maximal, complemented
6	C₃×#737	—	3	9	no	—
7	C₃×#737	—	3	18	no	—
8	C₃×#737	C₉	1	18	yes	—
9	C₃×#737	C₃²	1	9	yes	—
10	C₃²×3₋¹⁺²	C₉	1	2	yes	—
11	C₃²×3₋¹⁺²	C₉	1	6	yes	—
12	C₃²×H(3,𝔽₃)	C₉	1	1	yes	characteristic
13	C₃³×C₉	C₃²	1	3	yes	—
14	C₃³×C₉	C₃²	1	1	yes	characteristic
15	C₃×C₂₇⋊C₃	—	3	18	no	—
16	C₃×C₂₇⋊C₃	C₃²	1	18	yes	complemented
17	C₃²×C₂₇	—	3	9	no	—
18	C₃²×C₂₇	C₃²	1	3	yes	—
19	C₃²×C₂₇	C₃²	1	6	yes	—
20	C₃²×C₂₇	C₃²	1	9	yes	complemented
21	C₃²⋊C₂₇	C₃²	1	81	yes	complemented
22	C₃⁴	C₃×C₉	1	3	yes	—
23	C₃⁴	C₃×C₉	1	1	yes	characteristic
24	#737	—	3	162	no	—
25	#737	—	3	27	no	—
26	#737	—	3	54	no	—
27	C₃×3₋¹⁺²	—	3	18	no	—
28	C₃×3₋¹⁺²	—	3	54	no	—
29	C₃×3₋¹⁺²	C₃×C₉	1	18	yes	—
30	C₃×3₋¹⁺²	C₃×C₉	1	54	yes	—
31	C₃×H(3,𝔽₃)	—	3	9	no	—
32	C₃×H(3,𝔽₃)	C₃×C₉	1	9	yes	—
33	C₃²×C₉	—	3	9	no	—
34	C₃²×C₉	—	3	18	no	—
35	C₃²×C₉	C₃×C₉	1	6	yes	—
36	C₃²×C₉	C₃×C₉	1	18	yes	—
37	C₃²×C₉	C₃×C₉	1	2	yes	—
38	C₃²×C₉	C₃×C₉	1	6	yes	—
39	C₃²×C₉	H(3,𝔽₃)	1	9	yes	—
40	C₃²×C₉	3₋¹⁺²	1	18	yes	—
41	C₃²×C₉	C₃³	1	9	yes	—
42	C₃²×C₉	C₃³	1	3	yes	—
43	C₃²×C₉	C₃³	1	1	yes	characteristic
44	C₂₇⋊C₃	—	3	54	no	—
45	C₃×C₂₇	—	3	9	no	—
46	C₃×C₂₇	—	3	27	no	—
47	C₃×C₂₇	—	3	18	no	—
48	C₃×C₂₇	C₃³	1	9	yes	—
49	C₃×C₂₇	C₃³	1	18	yes	—
50	C₃³	—	3	9	no	—
51	C₃³	—	3	9	no	—
52	C₃³	—	3	27	no	—
53	C₃³	C₃²⋊C₉	1	9	yes	—
54	C₃³	C₃²×C₉	1	9	yes	—
55	C₃³	C₃²×C₉	1	3	yes	—
56	C₃³	C₃²×C₉	1	1	yes	characteristic
57	3₋¹⁺²	—	3	54	no	—
58	3₋¹⁺²	—	3	162	no	—
59	H(3,𝔽₃)	—	3	27	no	—
60	C₃×C₉	—	3	18	no	—
61	C₃×C₉	—	3	9	no	—
62	C₃×C₉	—	3	18	no	—
63	C₃×C₉	—	3	54	no	—
64	C₃×C₉	C₃²⋊C₉	1	18	yes	—
65	C₃×C₉	C₃²⋊C₉	1	54	yes	—
66	C₃×C₉	C₃²×C₉	1	18	yes	—
67	C₃×C₉	C₃²×C₉	1	2	yes	—
68	C₃×C₉	C₃²×C₉	1	6	yes	—
69	C₃×C₉	C₃×H(3,𝔽₃)	1	3	yes	—
70	C₃×C₉	C₃×H(3,𝔽₃)	1	9	yes	—
71	C₃×C₉	C₃×3₋¹⁺²	1	6	yes	—
72	C₃×C₉	C₃×3₋¹⁺²	1	18	yes	—
73	C₃×C₉	C₃⁴	1	1	yes	characteristic
74	C₂₇	—	3	9	no	—
75	C₂₇	—	3	18	no	—
76	C₃²	—	3	9	no	—
77	C₃²	—	3	27	no	—
78	C₃²	—	3	9	no	—
79	C₃²	—	3	27	no	—
80	C₃²	—	9	27	no	—
81	C₃²	C₃×C₃²⋊C₉	1	9	yes	—
82	C₃²	C₃×C₃²⋊C₉	1	3	yes	—
83	C₃²	#6903	1	9	yes	—
84	C₃²	C₃³×C₉	1	1	yes	characteristic
85	C₉	—	3	18	no	—
86	C₉	C₃×C₃²⋊C₉	1	6	yes	—
87	C₉	C₃×C₃²⋊C₉	1	18	yes	—
88	C₉	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
89	C₉	C₃²×3₋¹⁺²	1	2	yes	—
90	C₃	—	3	9	no	—
91	C₃	—	9	9	no	—
92	C₃	#10624684	1	9	yes	direct product factor
93	C₃	C₃²×C₃²⋊C₉	1	1	yes	characteristic
94	C₃	C₃×#6903	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₃²×C₂₇⋊C₃	C₃	semidirect
3. C₃³×C₂₇	C₃	semidirect
4. #10624684	C₃	direct (N × H)
5. C₃×C₃²⋊C₂₇	C₃	semidirect
16. C₃×C₂₇⋊C₃	C₃²	semidirect
20. C₃²×C₂₇	C₃²	semidirect
21. C₃²⋊C₂₇	C₃²	semidirect
92. C₃	#10624684	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#737	3
C₃²×C₂₇⋊C₃	3
C₃³×C₂₇	3
#10624684	3
C₃×C₃²⋊C₂₇	3

Subgroups — C3×#10624684 #14554107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10624684 #14554107