Subgroups — #14546302

Order 2187.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6869	C₃	1	1	yes	maximal, characteristic
2	#10624688	C₃	1	1	yes	maximal, characteristic
3	#10624683	C₃	1	2	yes	maximal
4	C₃³×C₉	C₃²	1	1	yes	characteristic
5	C₃×C₂₇⋊C₃	—	3	2	no	—
6	C₃×C₂₇⋊C₃	—	3	1	no	—
7	#6887	—	3	1	no	—
8	#6869	—	3	3	no	—
9	#6868	—	3	1	no	—
10	#6867	—	3	1	no	—
11	#6866	C₉	1	3	yes	—
12	C₃²⋊C₂₇	—	3	6	no	—
13	C₃⁴	C₃×C₉	1	1	yes	characteristic
14	C₃²×C₉	—	3	2	no	—
15	C₃²×C₉	—	3	1	no	—
16	C₃²×C₉	—	3	1	no	—
17	C₃²×C₉	—	3	2	no	—
18	C₃²×C₉	—	3	1	no	—
19	C₃²×C₉	—	3	1	no	—
20	C₃²×C₉	—	3	2	no	—
21	C₃²×C₉	—	3	2	no	—
22	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
23	C₃²×C₉	3₋¹⁺²	1	1	yes	characteristic
24	C₃²×C₉	3₋¹⁺²	1	1	yes	characteristic
25	C₂₇⋊C₃	—	3	3	no	—
26	C₂₇⋊C₃	—	9	2	no	—
27	C₂₇⋊C₃	—	9	2	no	—
28	C₂₇⋊C₃	—	9	2	no	—
29	C₂₇⋊C₃	—	9	2	no	—
30	C₃×C₂₇	—	3	6	no	—
31	C₃×C₂₇	—	9	1	no	—
32	C₉⋊C₉	—	9	1	no	—
33	C₉⋊C₉	—	9	1	no	—
34	C₃²⋊C₉	—	3	3	no	—
35	C₉²	—	9	1	no	—
36	C₃³	—	3	2	no	—
37	C₃³	—	3	1	no	—
38	C₃³	—	3	1	no	—
39	C₃³	—	9	3	no	—
40	C₃³	C₃²⋊C₉	1	1	yes	characteristic
41	C₃×C₉	—	3	1	no	—
42	C₃×C₉	—	3	1	no	—
43	C₃×C₉	—	3	1	no	—
44	C₃×C₉	—	3	1	no	—
45	C₃×C₉	—	3	2	no	—
46	C₃×C₉	—	3	2	no	—
47	C₃×C₉	—	9	1	no	—
48	C₃×C₉	—	9	2	no	—
49	C₃×C₉	—	9	1	no	—
50	C₃×C₉	—	9	2	no	—
51	C₃×C₉	—	9	1	no	—
52	C₃×C₉	—	9	2	no	—
53	C₃×C₉	—	9	3	no	—
54	C₃×C₉	AΣL(1,𝔽₂₇)	1	2	yes	—
55	C₃×C₉	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
56	C₃×C₉	#731	1	1	yes	characteristic
57	C₃×C₉	#731	1	2	yes	—
58	C₃×C₉	#732	1	1	yes	characteristic
59	C₃×C₉	#732	1	1	yes	characteristic
60	C₃×C₉	#733	1	2	yes	—
61	C₃×C₉	#733	1	2	yes	—
62	C₂₇	—	9	6	no	—
63	C₂₇	—	9	3	no	—
64	C₃²	—	3	6	no	—
65	C₃²	—	9	1	no	—
66	C₃²	—	9	3	no	—
67	C₃²	—	9	3	no	—
68	C₃²	—	9	4	no	—
69	C₃²	—	9	1	no	—
70	C₃²	#6868	1	1	yes	characteristic
71	C₃²	H(3,𝔽₃)⋊C₉	1	1	yes	characteristic
72	C₃²	3₋¹⁺²⋊C₉	1	2	yes	—
73	C₉	—	9	1	no	—
74	C₉	—	9	1	no	—
75	C₉	—	27	3	no	—
76	C₉	#6856	1	1	yes	characteristic
77	C₉	#6858	1	2	yes	—
78	C₉	#6859	1	1	yes	characteristic
79	C₉	#6860	1	2	yes	—
80	C₉	#6861	1	1	yes	characteristic
81	C₉	#6861	1	2	yes	—
82	C₃	—	3	1	no	—
83	C₃	—	3	2	no	—
84	C₃	—	3	1	no	—
85	C₃	—	9	3	no	—
86	C₃	#10624451	1	1	yes	characteristic

	subgroup	G/H
center	C₉	#6856
commutator, prime radical	C₃⁴	C₃×C₉
Frattini, cosocle	C₃³×C₉	C₃²
socle	C₃	#10624451
LCS	G ▷ C₃⁴ ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉ ◁ C₃²×C₉ ◁ C₃³×C₉ ◁ G
LECS	G ▷ C₃³×C₉ ▷ C₃³ ▷ C₃ ▷ C₁

Maximal subgroups

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

subgroup	index
C₃×#6869	3
#10624688	3
#10624683	3