Subgroups — #41008555

Order 26973.

230 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582704	C₃	1	3	yes	maximal, complemented
2	#22582703	C₃	1	3	yes	maximal, complemented
3	C₃²⋊#11758603	C₃	1	3	yes	maximal
4	C₉×#11758603	C₃	1	3	yes	maximal, complemented
5	C₃×C₉×#66524	C₃	1	1	yes	maximal, characteristic
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	2	yes	—
11	C₉×#66524	C₉	1	2	yes	—
12	C₉×#66524	C₃²	1	1	yes	characteristic
13	C₉×#66524	C₃²	1	1	yes	characteristic
14	C₉×#66524	C₃²	1	1	yes	characteristic
15	C₃²×C₉×C₃₇	C₉	1	1	yes	characteristic
16	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
17	C₃×C₉×C₃₇	C₂₇	1	9	yes	complemented
18	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
19	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
20	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
21	C₃×#66524	—	3	6	no	—
22	C₃×#66524	—	3	3	no	—
23	C₃×#66524	C₃×C₉	1	2	yes	—
24	C₃×#66524	C₃×C₉	1	2	yes	—
25	C₃×#66524	C₃×C₉	1	2	yes	—
26	C₃×#66524	C₃×C₉	1	2	yes	—
27	C₃×#66524	C₃³	1	1	yes	characteristic
28	#11758603	—	3	9	no	—
29	#10624710	—	37	1	no	maximal, Sylow
30	C₃²×C₃₇	—	3	1	no	—
31	C₃²×C₃₇	—	3	2	no	—
32	C₃²×C₃₇	C₃×C₂₇	1	3	yes	—
33	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
34	C₉×C₃₇	C₃×C₂₇	1	3	yes	—
35	C₉×C₃₇	C₃×C₂₇	1	3	yes	—
36	C₉×C₃₇	C₃×C₂₇	1	3	yes	—
37	#66524	—	3	2	no	—
38	#66524	—	3	2	no	—
39	#66524	—	3	2	no	—
40	#66524	C₂₇⋊C₃	1	6	yes	—
41	#66524	#737	1	3	yes	—
42	C₃×C₉²	—	37	1	no	—
43	C₉⋊C₂₇	—	37	3	no	—
44	C₉⋊C₂₇	—	37	3	no	—
45	C₃²⋊C₂₇	—	37	3	no	—
46	C₉×C₂₇	—	37	3	no	—
47	C₃×C₃₇	—	3	3	no	—
48	C₃×C₃₇	#6887	1	1	yes	characteristic
49	C₃×C₃₇	C₃²×C₂₇	1	1	yes	characteristic
50	C₃×C₃₇	C₃×C₂₇⋊C₃	1	2	yes	—
51	C₃²×C₉	—	37	2	no	—
52	C₃²×C₉	—	37	1	no	—
53	C₃²×C₉	#66526	1	1	yes	characteristic
54	C₃×C₂₇	—	37	9	no	—
55	C₉²	—	37	2	no	—
56	C₉²	—	37	2	no	—
57	C₉²	—	37	1	no	—
58	C₉²	—	37	1	no	—
59	C₉²	—	37	2	no	—
60	C₉²	—	37	1	no	—
61	C₃₇	#10624710	1	1	yes	characteristic, complemented, Sylow
62	C₃³	C₃×#66526	1	1	yes	characteristic
63	C₃×C₉	—	37	2	no	—
64	C₃×C₉	—	37	1	no	—
65	C₃×C₉	—	37	2	no	—
66	C₃×C₉	—	37	2	no	—
67	C₃×C₉	—	37	2	no	—
68	C₃×C₉	—	111	3	no	—
69	C₃×C₉	—	111	6	no	—
70	C₃×C₉	#11758603	1	9	yes	complemented
71	C₃×C₉	C₃×#66526	1	1	yes	characteristic
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	—	3	1	no	—
76	C₃²	—	3	2	no	—
77	C₃²	C₃×#11758603	1	3	yes	—
78	C₃²	C₃²×#66526	1	1	yes	characteristic
79	C₉	—	37	3	no	—
80	C₉	—	37	6	no	—
81	C₉	—	111	2	no	—
82	C₉	—	111	2	no	—
83	C₉	—	111	2	no	—
84	C₉	C₃×#11758603	1	3	yes	—
85	C₉	C₃×#11758603	1	3	yes	—
86	C₉	C₃×#11758603	1	3	yes	—
87	C₃	—	3	3	no	—
88	C₃	#22582722	1	1	yes	characteristic
89	C₃	C₃²×#11758603	1	1	yes	characteristic
90	C₃	(C₃₇⋊C₃)⋊(C₂₇⋊C₃)	1	2	yes	—

	subgroup	G/H
center	C₃×C₉	C₃×#66526
commutator	C₃×C₃₇	C₃²×C₂₇
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	#10624710
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
1. #22582704	C₃	semidirect
2. #22582703	C₃	semidirect
4. C₉×#11758603	C₃	semidirect
17. C₃×C₉×C₃₇	C₂₇	semidirect
61. C₃₇	#10624710	semidirect
70. C₃×C₉	#11758603	semidirect

Maximal subgroups

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

subgroup	index
#22582704	3
#22582703	3
C₃²⋊#11758603	3
C₉×#11758603	3
C₃×C₉×#66524	3
#10624710	37