Subgroups — #14546310

Order 2187.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#733	C₃	1	1	yes	maximal, characteristic
2	C₃×#6864	C₃	1	1	yes	maximal, characteristic
3	#10624446	C₃	1	2	yes	maximal
4	C₃×#733	C₉	1	1	yes	characteristic
5	C₃²×C₂₇	—	3	1	no	—
6	C₉×3₋¹⁺²	—	3	1	no	—
7	C₃×C₉²	C₃²	1	1	yes	characteristic
8	3₋¹⁺²⋊C₉	—	3	2	no	—
9	#6868	C₉	1	2	yes	—
10	C₃²⋊C₂₇	—	3	2	no	—
11	#6864	—	3	3	no	—
12	C₃×3₋¹⁺²	—	3	1	no	—
13	C₃²×C₉	C₃×C₉	1	1	yes	characteristic
14	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
15	C₃²×C₉	3₋¹⁺²	1	2	yes	—
16	#733	—	3	3	no	—
17	C₃×C₂₇	—	3	6	no	—
18	C₃×C₂₇	—	3	3	no	—
19	C₃×C₂₇	—	3	3	no	—
20	C₃×C₂₇	—	9	2	no	—
21	C₉⋊C₉	—	9	1	no	—
22	C₉⋊C₉	—	9	1	no	—
23	C₃²⋊C₉	—	3	2	no	—
24	C₉²	—	3	1	no	—
25	C₉²	—	3	1	no	—
26	C₉²	—	3	1	no	—
27	C₉²	—	9	1	no	—
28	C₃³	C₃²⋊C₉	1	1	yes	characteristic
29	3₋¹⁺²	—	3	3	no	—
30	3₋¹⁺²	—	9	1	no	—
31	3₋¹⁺²	—	9	1	no	—
32	C₃×C₉	—	3	2	no	—
33	C₃×C₉	—	3	1	no	—
34	C₃×C₉	—	3	1	no	—
35	C₃×C₉	—	3	1	no	—
36	C₃×C₉	—	3	2	no	—
37	C₃×C₉	—	3	1	no	—
38	C₃×C₉	—	3	1	no	—
39	C₃×C₉	—	9	1	no	—
40	C₃×C₉	—	9	2	no	—
41	C₃×C₉	—	9	2	no	—
42	C₃×C₉	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
43	C₃×C₉	#731	1	1	yes	characteristic
44	C₃×C₉	#732	1	1	yes	characteristic
45	C₂₇	—	3	9	no	—
46	C₂₇	—	27	2	no	—
47	C₃²	—	3	1	no	—
48	C₃²	—	3	2	no	—
49	C₃²	#6869	1	1	yes	characteristic
50	C₃²	H(3,𝔽₃)⋊C₉	1	1	yes	characteristic
51	C₃²	#6872	1	1	yes	characteristic
52	C₃²	#6873	1	1	yes	characteristic
53	C₉	—	3	1	no	—
54	C₉	—	3	1	no	—
55	C₉	—	9	2	no	—
56	C₉	—	9	1	no	—
57	C₉	—	9	3	no	—
58	C₉	—	27	2	no	—
59	C₉	#6878	1	2	yes	—
60	C₉	#6880	1	1	yes	characteristic
61	C₃	—	3	1	no	—
62	C₃	—	3	1	no	—
63	C₃	—	3	1	no	—
64	C₃	#10624453	1	1	yes	characteristic
65	C₃	#10624525	1	1	yes	characteristic
66	C₃	#10624530	1	2	yes	—

	subgroup	G/H
center	C₃×C₉	#732
commutator	C₃²×C₉	C₃×C₉
Frattini, cosocle	C₃×C₉²	C₃²
socle	C₃²	H(3,𝔽₃)⋊C₉
prime radical	C₃³	C₃²⋊C₉
LCS	G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ C₃×C₉² ◁ G
LECS	G ▷ C₃×C₉² ▷ C₃³ ▷ C₃ ▷ C₁

Maximal subgroups

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

subgroup	index
C₉×#733	3
C₃×#6864	3
#10624446	3