Subgroups — #14546323

Order 2187.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
2	#10624446	C₃	1	2	yes	maximal
3	#10624446	C₃	1	1	yes	maximal, characteristic
4	C₃×C₉⋊C₉	—	3	1	no	—
5	C₃×C₉²	—	3	1	no	—
6	C₃×C₉²	C₃²	1	1	yes	characteristic
7	C₃²⋊C₂₇	—	3	2	no	—
8	C₃²⋊C₂₇	—	3	1	no	—
9	#6855	—	3	1	no	—
10	#6855	C₉	1	3	yes	—
11	C₃²×C₉	—	3	3	no	—
12	C₃²×C₉	C₃×C₉	1	1	yes	characteristic
13	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
14	C₃²×C₉	3₋¹⁺²	1	1	yes	characteristic
15	C₃²×C₉	3₋¹⁺²	1	1	yes	characteristic
16	C₃×C₂₇	—	9	2	no	—
17	C₃×C₂₇	—	9	1	no	—
18	C₉⋊C₉	—	3	9	no	—
19	C₉²	—	3	1	no	—
20	C₉²	—	3	2	no	—
21	C₉²	—	9	1	no	—
22	C₉²	—	9	1	no	—
23	C₉²	—	9	1	no	—
24	C₃³	C₃²⋊C₉	1	1	yes	characteristic
25	C₃×C₉	—	3	1	no	—
26	C₃×C₉	—	3	1	no	—
27	C₃×C₉	—	3	1	no	—
28	C₃×C₉	—	3	1	no	—
29	C₃×C₉	—	3	3	no	—
30	C₃×C₉	—	3	9	no	—
31	C₃×C₉	—	3	1	no	—
32	C₃×C₉	—	3	1	no	—
33	C₃×C₉	—	3	3	no	—
34	C₃×C₉	—	9	3	no	—
35	C₃×C₉	—	9	3	no	—
36	C₃×C₉	—	9	3	no	—
37	C₃×C₉	—	9	1	no	—
38	C₃×C₉	#732	1	1	yes	characteristic
39	C₃×C₉	#733	1	2	yes	—
40	C₂₇	—	27	2	no	—
41	C₂₇	—	27	1	no	—
42	C₃²	—	3	1	no	—
43	C₃²	—	3	1	no	—
44	C₃²	—	3	1	no	—
45	C₃²	#6868	1	1	yes	characteristic
46	C₃²	#6872	1	3	yes	—
47	C₉	—	3	3	no	—
48	C₉	—	3	2	no	—
49	C₉	—	9	9	no	—
50	C₉	—	9	1	no	—
51	C₉	—	9	1	no	—
52	C₉	#6881	1	1	yes	characteristic
53	C₉	#6882	1	1	yes	characteristic
54	C₉	#6883	1	1	yes	characteristic
55	C₃	—	3	3	no	—
56	C₃	#10624458	1	1	yes	characteristic
57	C₃	#10624520	1	1	yes	characteristic
58	C₃	#10624521	1	1	yes	characteristic
59	C₃	#10624523	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	#732
commutator	C₃²×C₉	C₃×C₉
Frattini, cosocle	C₃×C₉²	C₃²
socle	C₃²	#6868
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×C₉⋊C₉	3
#10624446	3