Subgroups — #41008534

Order 26973.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688542	C₃	1	3	yes	maximal
2	#22582706	C₃	1	6	yes	maximal, complemented
3	#22582704	C₃	1	3	yes	maximal, complemented
4	C₉²×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
5	#15688542	—	3	9	no	—
6	C₃×#11758603	C₃²	1	9	yes	—
7	C₃×C₉×C₃₇⋊C₃	C₉	1	1	yes	characteristic
8	C₃×C₉×C₃₇⋊C₃	C₉	1	2	yes	—
9	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
10	C₉×#66524	C₉	1	2	yes	—
11	C₉×#66524	C₉	1	2	yes	—
12	C₉×#66524	C₉	1	1	yes	characteristic
13	C₉×#66524	C₃²	1	1	yes	characteristic
14	C₉×#66524	C₃²	1	2	yes	—
15	C₉²×C₃₇	C₉	1	1	yes	characteristic
16	C₃²×C₃₇⋊C₃	C₃×C₉	1	1	yes	characteristic
17	C₃×C₉×C₃₇	C₃×C₉	1	2	yes	—
18	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
19	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
20	C₃×#66524	C₃×C₉	1	2	yes	—
21	C₃×#66524	C₃×C₉	1	2	yes	—
22	C₃×#66524	C₃×C₉	1	1	yes	characteristic
23	C₃×#66524	C₃×C₉	1	2	yes	—
24	C₃×#66524	C₃³	1	1	yes	characteristic
25	C₉×C₃₇⋊C₃	—	3	3	no	—
26	C₉×C₃₇⋊C₃	—	3	6	no	—
27	C₉×C₃₇⋊C₃	3₋¹⁺²	1	9	yes	—
28	#11758603	—	3	9	no	—
29	#10624706	—	37	1	no	maximal, Sylow
30	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
31	C₃×C₃₇⋊C₃	—	3	2	no	—
32	C₃×C₃₇⋊C₃	—	3	1	no	—
33	C₃×C₃₇⋊C₃	C₉⋊C₉	1	3	yes	—
34	C₉×C₃₇	—	3	2	no	—
35	C₉×C₃₇	C₉⋊C₉	1	3	yes	—
36	C₉×C₃₇	C₂₇⋊C₃	1	3	yes	complemented
37	#66524	—	3	2	no	—
38	#66524	—	3	2	no	—
39	#66524	C₉⋊C₉	1	3	yes	—
40	#66524	C₂₇⋊C₃	1	6	yes	complemented
41	#66524	C₃×3₋¹⁺²	1	3	yes	—
42	C₃×C₂₇⋊C₃	—	37	3	no	—
43	C₃×C₉²	—	37	1	no	—
44	C₉⋊C₂₇	—	37	3	no	—
45	C₉⋊C₂₇	—	37	6	no	—
46	C₃×C₃₇	C₃×C₉⋊C₉	1	1	yes	characteristic
47	C₃×C₃₇	C₃×C₂₇⋊C₃	1	2	yes	—
48	C₃×C₃₇	C₃×C₂₇⋊C₃	1	1	yes	characteristic
49	C₃₇⋊C₃	—	3	3	no	—
50	C₃²×C₉	—	37	1	no	—
51	C₃²×C₉	—	37	2	no	—
52	C₃²×C₉	—	37	1	no	—
53	C₂₇⋊C₃	—	111	9	no	—
54	C₃×C₂₇	—	37	9	no	—
55	C₉²	—	37	1	no	—
56	C₉²	—	37	2	no	—
57	C₉²	—	37	2	no	—
58	C₉²	—	37	2	no	—
59	C₉²	—	37	1	no	—
60	C₉²	#66526	1	1	yes	characteristic
61	C₃₇	#10624706	1	1	yes	characteristic, complemented, Sylow
62	C₃³	—	37	1	no	—
63	C₃×C₉	—	37	1	no	—
64	C₃×C₉	—	37	2	no	—
65	C₃×C₉	—	37	1	no	—
66	C₃×C₉	—	37	9	no	—
67	C₃×C₉	—	37	2	no	—
68	C₃×C₉	—	37	2	no	—
69	C₃×C₉	—	111	6	no	—
70	C₃×C₉	—	111	3	no	—
71	C₃×C₉	C₃×#66526	1	2	yes	—
72	C₃×C₉	C₃×#66526	1	1	yes	characteristic
73	C₃×C₉	C₃×#66526	1	1	yes	characteristic
74	C₂₇	—	111	9	no	—
75	C₃²	—	37	3	no	—
76	C₃²	—	111	2	no	—
77	C₃²	—	111	1	no	—
78	C₃²	C₃²×#66526	1	1	yes	characteristic
79	C₉	—	3	2	no	—
80	C₉	—	37	3	no	—
81	C₉	—	37	3	no	—
82	C₉	—	37	6	no	—
83	C₉	—	111	2	no	—
84	C₉	—	111	2	no	—
85	C₉	#15688538	1	3	yes	—
86	C₉	#15688542	1	3	yes	complemented
87	C₃	—	111	3	no	—
88	C₃	C₃×#15688538	1	1	yes	characteristic
89	C₃	(C₃₇⋊C₃)⋊(C₂₇⋊C₃)	1	2	yes	—
90	C₃	C₃×#15688542	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃²×#66526
commutator, socle	C₃²×C₃₇	C₃²×C₉
Fitting	C₉²×C₃₇	C₉
prime radical	C₃²×C₃₇⋊C₃	C₃×C₉
cosocle	C₃×#66524	C₃³
hypercenter	C₉²	#66526
hypocenter	C₃₇	#10624706
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
2. #22582706	C₃	semidirect
3. #22582704	C₃	semidirect
36. C₉×C₃₇	C₂₇⋊C₃	semidirect
40. #66524	C₂₇⋊C₃	semidirect
61. C₃₇	#10624706	semidirect
86. C₉	#15688542	semidirect

Maximal subgroups

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

subgroup	index
C₃×#15688542	3
#22582706	3
#22582704	3
C₉²×C₃₇⋊C₃	3
#10624706	37