Subgroups — C₉×#15688541 #41008470

Order 26973.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688541	C₃	1	3	yes	maximal
2	#22582688	C₃	1	6	yes	maximal, complemented
3	C₉×#11758603	C₃	1	3	yes	maximal, complemented
4	C₃×C₉×#66524	C₃	1	1	yes	maximal, characteristic
5	#15688541	C₉	1	27	yes	direct product factor
6	C₃×#11758603	C₃²	1	9	yes	—
7	C₃²×#66524	C₉	1	2	yes	—
8	C₃²×#66524	C₃²	1	1	yes	characteristic
9	C₉×#66524	C₉	1	2	yes	—
10	C₉×#66524	C₉	1	4	yes	—
11	C₉×#66524	C₃²	1	1	yes	characteristic
12	C₉×#66524	C₃²	1	2	yes	—
13	C₃²×C₉×C₃₇	C₉	1	1	yes	characteristic
14	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
15	C₃×C₉×C₃₇	—	3	3	no	—
16	C₃×C₉×C₃₇	C₃×C₉	1	2	yes	—
17	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
18	C₃×#66524	—	3	6	no	—
19	C₃×#66524	C₃×C₉	1	4	yes	—
20	C₃×#66524	C₃×C₉	1	2	yes	—
21	C₃×#66524	C₃×C₉	1	9	yes	—
22	C₃×#66524	C₃×C₉	1	2	yes	—
23	C₃×#66524	C₃³	1	1	yes	characteristic
24	#11758603	C₃×C₉	1	27	yes	complemented
25	C₉×C₂₇⋊C₃	—	37	1	no	maximal, Sylow
26	C₃²×C₃₇	—	3	2	no	—
27	C₃²×C₃₇	—	3	1	no	—
28	C₃²×C₃₇	C₉²	1	3	yes	—
29	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
30	C₉×C₃₇	—	3	2	no	—
31	C₉×C₃₇	C₂₇⋊C₃	1	3	yes	complemented
32	#66524	—	3	4	no	—
33	#66524	C₉²	1	6	yes	—
34	#66524	C₂₇⋊C₃	1	6	yes	complemented
35	#66524	C₃²×C₉	1	3	yes	—
36	C₃×C₂₇⋊C₃	—	37	3	no	—
37	C₃×C₉²	—	37	1	no	—
38	#6864	—	37	6	no	—
39	C₉×C₂₇	—	37	3	no	—
40	C₃×C₃₇	—	3	3	no	—
41	C₃×C₃₇	C₃×C₉²	1	1	yes	characteristic
42	C₃×C₃₇	C₃×C₂₇⋊C₃	1	1	yes	characteristic
43	C₃×C₃₇	C₃×C₂₇⋊C₃	1	2	yes	—
44	C₃²×C₉	—	37	1	no	—
45	C₃²×C₉	—	37	2	no	—
46	C₃²×C₉	#66526	1	1	yes	characteristic
47	C₂₇⋊C₃	—	37	27	no	—
48	C₃×C₂₇	—	37	9	no	—
49	C₉²	—	37	4	no	—
50	C₉²	—	37	2	no	—
51	C₉²	—	37	2	no	—
52	C₉²	—	37	1	no	—
53	C₃₇	C₉×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
54	C₃³	C₃×#66526	1	1	yes	characteristic
55	C₃×C₉	—	3	3	no	—
56	C₃×C₉	—	37	9	no	—
57	C₃×C₉	—	37	2	no	—
58	C₃×C₉	—	37	2	no	—
59	C₃×C₉	—	37	1	no	—
60	C₃×C₉	—	37	4	no	—
61	C₃×C₉	—	111	6	no	—
62	C₃×C₉	C₃×#66526	1	2	yes	—
63	C₃×C₉	C₃×#66526	1	1	yes	characteristic
64	C₂₇	—	37	27	no	—
65	C₃²	—	3	1	no	—
66	C₃²	—	3	2	no	—
67	C₃²	C₉×#66526	1	3	yes	—
68	C₃²	C₃²×#66526	1	1	yes	characteristic
69	C₉	—	3	2	no	—
70	C₉	—	37	3	no	—
71	C₉	—	37	6	no	—
72	C₉	—	37	6	no	—
73	C₉	—	111	4	no	—
74	C₉	#15688541	1	3	yes	direct product factor
75	C₃	—	3	3	no	—
76	C₃	C₃×C₉×#66526	1	1	yes	characteristic
77	C₃	C₃×#15688541	1	1	yes	characteristic
78	C₃	(C₃₇⋊C₃)⋊(C₂₇⋊C₃)	1	2	yes	—

	subgroup	G/H
center	C₃×C₉	C₃×#66526
commutator	C₃×C₃₇	C₃×C₉²
Frattini	C₃²	C₃²×#66526
Fitting	C₃²×C₉×C₃₇	C₉
socle	C₃²×C₃₇	C₃²×C₉
prime radical	C₃³×C₃₇	C₃×C₉
cosocle	C₃×#66524	C₃³
hypercenter	C₃²×C₉	#66526
hypocenter	C₃₇	C₉×C₂₇⋊C₃
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
2. #22582688	C₃	semidirect
3. C₉×#11758603	C₃	semidirect
5. #15688541	C₉	direct (N × H)
24. #11758603	C₃×C₉	semidirect
31. C₉×C₃₇	C₂₇⋊C₃	semidirect
34. #66524	C₂₇⋊C₃	semidirect
53. C₃₇	C₉×C₂₇⋊C₃	semidirect
74. C₉	#15688541	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×#15688541	3
#22582688	3
C₉×#11758603	3
C₃×C₉×#66524	3
C₉×C₂₇⋊C₃	37

Subgroups — C9×#15688541 #41008470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#15688541 #41008470