Subgroups — #14546248

Order 2187.

114 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	C₉	1	2	yes	—
5	C₃×C₉⋊C₉	C₉	1	1	yes	characteristic
6	C₃×C₉²	—	3	1	no	—
7	C₃×C₉²	C₃²	1	1	yes	characteristic
8	C₃²⋊C₂₇	—	3	2	no	—
9	C₃²⋊C₂₇	—	3	1	no	—
10	#6855	—	3	1	no	—
11	#6855	—	3	1	no	—
12	C₃²×C₉	—	3	1	no	—
13	C₃²×C₉	—	3	2	no	—
14	C₃²×C₉	C₃×C₉	1	1	yes	characteristic
15	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
16	C₃²×C₉	3₋¹⁺²	1	1	yes	characteristic
17	C₃²×C₉	3₋¹⁺²	1	1	yes	characteristic
18	C₃×C₂₇	—	9	2	no	—
19	C₃×C₂₇	—	9	1	no	—
20	C₉⋊C₉	—	3	6	no	—
21	C₉⋊C₉	—	3	2	no	—
22	C₉⋊C₉	C₂₇	1	3	yes	complemented
23	C₉²	—	3	1	no	—
24	C₉²	—	3	2	no	—
25	C₉²	—	9	1	no	—
26	C₉²	—	9	1	no	—
27	C₉²	—	9	1	no	—
28	C₃³	C₃²⋊C₉	1	1	yes	characteristic
29	C₃×C₉	—	3	1	no	—
30	C₃×C₉	—	3	2	no	—
31	C₃×C₉	—	3	1	no	—
32	C₃×C₉	—	3	1	no	—
33	C₃×C₉	—	3	1	no	—
34	C₃×C₉	—	3	3	no	—
35	C₃×C₉	—	3	1	no	—
36	C₃×C₉	—	3	1	no	—
37	C₃×C₉	—	3	6	no	—
38	C₃×C₉	—	9	1	no	—
39	C₃×C₉	—	9	2	no	—
40	C₃×C₉	—	9	1	no	—
41	C₃×C₉	—	9	2	no	—
42	C₃×C₉	—	9	1	no	—
43	C₃×C₉	—	9	2	no	—
44	C₃×C₉	—	9	1	no	—
45	C₃×C₉	—	9	1	no	—
46	C₃×C₉	C₃×C₂₇	1	1	yes	characteristic
47	C₃×C₉	C₂₇⋊C₃	1	2	yes	—
48	C₃×C₉	#732	1	1	yes	characteristic
49	C₃×C₉	#733	1	2	yes	—
50	C₂₇	—	27	2	no	—
51	C₂₇	—	27	1	no	—
52	C₃²	—	3	1	no	—
53	C₃²	—	3	1	no	—
54	C₃²	—	3	1	no	—
55	C₃²	C₃²⋊C₂₇	1	1	yes	characteristic
56	C₃²	#6868	1	1	yes	characteristic
57	C₃²	#6869	1	2	yes	—
58	C₉	—	3	2	no	—
59	C₉	—	3	1	no	—
60	C₉	—	3	2	no	—
61	C₉	—	9	3	no	—
62	C₉	—	9	6	no	—
63	C₉	—	9	1	no	—
64	C₉	—	9	1	no	—
65	C₉	#6881	1	1	yes	characteristic
66	C₉	#6882	1	1	yes	characteristic
67	C₉	#6883	1	1	yes	characteristic
68	C₃	—	3	1	no	—
69	C₃	—	3	2	no	—
70	C₃	#10624446	1	1	yes	characteristic
71	C₃	#10624521	1	1	yes	characteristic
72	C₃	#10624522	1	1	yes	characteristic
73	C₃	#10624523	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	#732
commutator	C₃×C₉	C₃×C₂₇
Frattini, cosocle	C₃×C₉²	C₃²
socle	C₃²	#6868
prime radical	C₃³	C₃²⋊C₉
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ C₃×C₉² ◁ G
LECS	G ▷ C₃×C₉² ▷ C₃³ ▷ C₃ ▷ C₁

Complements

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

N	H ≅ G/N	type
22. C₉⋊C₉	C₂₇	semidirect

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