Subgroups — C₉×#15688509 #41006196

Order 26973.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688509	C₃	1	3	yes	maximal
2	C₉²×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	#22582462	C₃	1	6	yes	maximal, complemented
4	C₉×#11758601	C₃	1	2	yes	maximal, complemented
5	C₉×C₂₇×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃×C₉×C₃₇⋊C₃	C₉	1	3	yes	—
7	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
8	#15688509	C₉	1	27	yes	direct product factor
9	C₃×#11758601	C₃²	1	6	yes	—
10	C₉×#66524	C₉	1	6	yes	—
11	C₉×#66524	C₃²	1	2	yes	—
12	C₃×C₂₇×C₃₇	C₃²	1	3	yes	—
13	C₉²×C₃₇	C₃²	1	1	yes	characteristic
14	C₃²×C₃₇⋊C₃	C₃×C₉	1	1	yes	characteristic
15	C₃×C₉×C₃₇	C₃×C₉	1	3	yes	—
16	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
17	C₃×#66524	C₃×C₉	1	6	yes	—
18	C₃×#66524	C₃×C₉	1	2	yes	—
19	C₉×C₃₇⋊C₃	—	3	9	no	—
20	C₉×C₃₇⋊C₃	C₃×C₉	1	9	yes	—
21	C₂₇×C₃₇	C₃×C₉	1	9	yes	complemented
22	#11758601	C₃×C₉	1	18	yes	complemented
23	C₉×C₂₇⋊C₃	—	37	1	no	maximal, Sylow
24	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
25	C₃×C₃₇⋊C₃	—	3	3	no	—
26	C₃×C₃₇⋊C₃	C₉²	1	3	yes	—
27	C₉×C₃₇	C₂₇⋊C₃	1	9	yes	complemented
28	C₉×C₃₇	C₃²×C₉	1	3	yes	—
29	#66524	—	3	6	no	—
30	#66524	C₉²	1	6	yes	—
31	C₃×C₂₇⋊C₃	—	37	3	no	—
32	C₃×C₉²	—	37	1	no	—
33	#6864	—	37	6	no	—
34	C₉×C₂₇	—	37	2	no	—
35	C₉×C₂₇	C₃₇⋊C₃	1	1	yes	characteristic, complemented
36	C₃×C₃₇	C₃×C₉²	1	1	yes	characteristic
37	C₃×C₃₇	C₃×C₂₇⋊C₃	1	3	yes	—
38	C₃₇⋊C₃	—	3	3	no	—
39	C₃²×C₉	—	37	1	no	—
40	C₃²×C₉	—	37	3	no	—
41	C₂₇⋊C₃	—	37	27	no	—
42	C₃×C₂₇	—	37	6	no	—
43	C₃×C₂₇	C₃×C₃₇⋊C₃	1	3	yes	—
44	C₉²	—	37	6	no	—
45	C₉²	—	37	2	no	—
46	C₉²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
47	C₃₇	C₉×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
48	C₃³	—	37	1	no	—
49	C₃×C₉	—	37	2	no	—
50	C₃×C₉	—	37	9	no	—
51	C₃×C₉	—	37	6	no	—
52	C₃×C₉	—	111	9	no	—
53	C₃×C₉	C₉×C₃₇⋊C₃	1	3	yes	—
54	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
55	C₂₇	—	37	18	no	—
56	C₂₇	C₉×C₃₇⋊C₃	1	9	yes	complemented
57	C₃²	—	37	3	no	—
58	C₃²	—	111	3	no	—
59	C₃²	C₃×C₉×C₃₇⋊C₃	1	1	yes	characteristic
60	C₉	—	37	6	no	—
61	C₉	—	111	6	no	—
62	C₉	#15688509	1	9	yes	direct product factor
63	C₉	C₃×C₉×C₃₇⋊C₃	1	3	yes	—
64	C₃	—	111	3	no	—
65	C₃	C₉²×C₃₇⋊C₃	1	1	yes	characteristic
66	C₃	C₃×#15688509	1	3	yes	—

	subgroup	G/H
center	C₉²	C₃×C₃₇⋊C₃
commutator	C₃×C₃₇	C₃×C₉²
Frattini	C₃×C₉	C₃²×C₃₇⋊C₃
Fitting	C₉×C₂₇×C₃₇	C₃
socle	C₃²×C₃₇	C₃²×C₉
prime radical	C₃²×C₃₇⋊C₃	C₃×C₉
cosocle	C₃×C₉×C₃₇	C₃³
hypercenter	C₉×C₂₇	C₃₇⋊C₃
hypocenter	C₃₇	C₉×C₂₇⋊C₃
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₉² ◁ C₉×C₂₇

Complements

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

N	H ≅ G/N	type
3. #22582462	C₃	semidirect
4. C₉×#11758601	C₃	semidirect
5. C₉×C₂₇×C₃₇	C₃	semidirect
8. #15688509	C₉	direct (N × H)
21. C₂₇×C₃₇	C₃×C₉	semidirect
22. #11758601	C₃×C₉	semidirect
27. C₉×C₃₇	C₂₇⋊C₃	semidirect
35. C₉×C₂₇	C₃₇⋊C₃	semidirect
47. C₃₇	C₉×C₂₇⋊C₃	semidirect
56. C₂₇	C₉×C₃₇⋊C₃	semidirect
62. C₉	#15688509	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#15688509	3
C₉²×C₃₇⋊C₃	3
#22582462	3
C₉×#11758601	3
C₉×C₂₇×C₃₇	3
C₉×C₂₇⋊C₃	37

Subgroups — C9×#15688509 #41006196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#15688509 #41006196