Subgroups — #41008445

Order 26973.

374 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688538	C₃	1	3	yes	maximal
2	C₃×#15688537	C₃	1	3	yes	maximal
3	(C₃×#66526)⋊C₉	C₃	1	6	yes	maximal
4	C₉²×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
5	C₃²×#66526	C₃²	1	9	yes	—
6	#15688538	—	3	9	no	—
7	#15688537	—	3	9	no	—
8	C₃×C₉×C₃₇⋊C₃	C₃²	1	2	yes	—
9	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
10	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
11	C₉×#66524	C₉	1	2	yes	complemented
12	C₉×#66524	C₉	1	2	yes	complemented
13	C₉×#66524	C₉	1	4	yes	complemented
14	C₉²×C₃₇	C₉	1	1	yes	characteristic, complemented
15	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
16	C₃×#66526	—	3	9	no	—
17	C₃×#66526	—	3	9	no	—
18	C₃×#66526	—	3	18	no	—
19	C₃×C₉×C₃₇	C₃×C₉	1	2	yes	—
20	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
21	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
22	C₃×#66524	C₃×C₉	1	4	yes	—
23	C₃×#66524	C₃×C₉	1	2	yes	—
24	C₃×#66524	C₃×C₉	1	2	yes	—
25	C₉×C₃₇⋊C₃	—	3	6	no	—
26	C₉×C₃₇⋊C₃	3₋¹⁺²	1	9	yes	—
27	C₉×C₃₇⋊C₃	3₋¹⁺²	1	9	yes	—
28	#10624550	—	37	1	no	maximal, Sylow
29	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
30	C₃×C₃₇⋊C₃	C₃×3₋¹⁺²	1	3	yes	—
31	C₃×C₃₇⋊C₃	C₃×3₋¹⁺²	1	3	yes	—
32	C₃×C₃₇⋊C₃	#737	1	6	yes	—
33	#66526	—	9	9	no	—
34	C₉×C₃₇	—	3	2	no	—
35	C₉×C₃₇	C₉⋊C₉	1	3	yes	complemented
36	C₉×C₃₇	C₉⋊C₉	1	3	yes	complemented
37	#66524	—	3	4	no	—
38	#66524	C₉⋊C₉	1	6	yes	complemented
39	#66524	C₉⋊C₉	1	6	yes	complemented
40	C₃×C₉⋊C₉	—	37	3	no	—
41	C₃×C₉⋊C₉	—	37	3	no	—
42	C₃×C₉²	—	37	1	no	—
43	#6855	—	37	6	no	—
44	C₃×C₃₇	C₃×C₉⋊C₉	1	1	yes	characteristic
45	C₃×C₃₇	C₃×C₉⋊C₉	1	1	yes	characteristic
46	C₃×C₃₇	#6887	1	2	yes	—
47	C₃₇⋊C₃	#6896	1	9	yes	—
48	C₃²×C₉	—	37	1	no	—
49	C₃²×C₉	—	37	1	no	—
50	C₃²×C₉	—	37	2	no	—
51	C₃²×C₉	—	37	9	no	—
52	C₉⋊C₉	—	111	9	no	—
53	C₉⋊C₉	—	111	9	no	—
54	C₉²	—	37	4	no	—
55	C₉²	—	37	2	no	—
56	C₉²	—	37	2	no	—
57	C₉²	#66526	1	1	yes	characteristic, complemented
58	C₃₇	#10624550	1	1	yes	characteristic, complemented, Sylow
59	C₃³	—	37	1	no	—
60	C₃×C₉	—	37	2	no	—
61	C₃×C₉	—	37	2	no	—
62	C₃×C₉	—	37	9	no	—
63	C₃×C₉	—	37	9	no	—
64	C₃×C₉	—	37	4	no	—
65	C₃×C₉	—	111	6	no	—
66	C₃×C₉	—	111	9	no	—
67	C₃×C₉	—	111	9	no	—
68	C₃×C₉	—	111	18	no	—
69	C₃×C₉	C₃×#66526	1	2	yes	—
70	C₃×C₉	C₃×#66526	1	1	yes	characteristic
71	C₃×C₉	C₃×#66526	1	1	yes	characteristic
72	C₃²	—	37	3	no	—
73	C₃²	—	37	3	no	—
74	C₃²	—	37	6	no	—
75	C₃²	C₃²×#66526	1	1	yes	characteristic
76	C₉	—	3	2	no	—
77	C₉	—	37	6	no	—
78	C₉	—	37	6	no	—
79	C₉	—	333	9	no	—
80	C₉	—	111	4	no	—
81	C₉	#15688537	1	3	yes	complemented
82	C₉	#15688538	1	3	yes	complemented
83	C₃	—	37	9	no	—
84	C₃	C₃×#15688537	1	1	yes	characteristic
85	C₃	C₃×#15688538	1	1	yes	characteristic
86	C₃	#22582722	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×#66526
commutator, socle	C₃²×C₃₇	C₃²×C₉
Fitting	C₉²×C₃₇	C₉
prime radical, cosocle	C₃²×C₃₇⋊C₃	C₃³
hypercenter	C₉²	#66526
hypocenter	C₃₇	#10624550
LCS	G ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₉²

Complements

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

N	H ≅ G/N	type
11. C₉×#66524	C₉	semidirect
12. C₉×#66524	C₉	semidirect
13. C₉×#66524	C₉	semidirect
14. C₉²×C₃₇	C₉	semidirect
35. C₉×C₃₇	C₉⋊C₉	semidirect
36. C₉×C₃₇	C₉⋊C₉	semidirect
38. #66524	C₉⋊C₉	semidirect
39. #66524	C₉⋊C₉	semidirect
57. C₉²	#66526	semidirect
58. C₃₇	#10624550	semidirect
81. C₉	#15688537	semidirect
82. C₉	#15688538	semidirect

Maximal subgroups

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

subgroup	index
C₃×#15688538	3
C₃×#15688537	3
(C₃×#66526)⋊C₉	3
C₉²×C₃₇⋊C₃	3
#10624550	37