Subgroups — #41006342

Order 26973.

230 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582490	C₃	1	3	yes	maximal, complemented
2	#22582489	C₃	1	3	yes	maximal, complemented
3	C₃²⋊#11758601	C₃	1	3	yes	maximal
4	C₉×#11758601	C₃	1	3	yes	maximal, complemented
5	C₃×C₉²×C₃₇	C₃	1	1	yes	maximal, characteristic
6	C₃×#11758601	C₃²	1	9	yes	—
7	C₃²×C₉×C₃₇	C₉	1	2	yes	—
8	C₃²×C₉×C₃₇	C₉	1	1	yes	characteristic
9	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
10	C₉²×C₃₇	C₉	1	2	yes	—
11	C₉²×C₃₇	C₉	1	2	yes	—
12	C₉²×C₃₇	C₉	1	2	yes	—
13	C₉²×C₃₇	C₃²	1	1	yes	characteristic
14	C₉²×C₃₇	C₃²	1	1	yes	characteristic
15	C₉²×C₃₇	C₃²	1	1	yes	characteristic
16	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
17	C₃×C₉×C₃₇	—	3	6	no	—
18	C₃×C₉×C₃₇	—	3	3	no	—
19	C₃×C₉×C₃₇	C₂₇	1	9	yes	complemented
20	C₃×C₉×C₃₇	C₃×C₉	1	2	yes	—
21	C₃×C₉×C₃₇	C₃×C₉	1	2	yes	—
22	C₃×C₉×C₃₇	C₃×C₉	1	2	yes	—
23	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
24	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
25	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
26	C₃×C₉×C₃₇	C₃×C₉	1	2	yes	—
27	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
28	#11758601	—	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	—	3	2	no	—
35	C₉×C₃₇	—	3	2	no	—
36	C₉×C₃₇	—	3	2	no	—
37	C₉×C₃₇	C₃×C₂₇	1	3	yes	—
38	C₉×C₃₇	C₃×C₂₇	1	3	yes	—
39	C₉×C₃₇	C₃×C₂₇	1	3	yes	—
40	C₉×C₃₇	C₂₇⋊C₃	1	6	yes	—
41	C₉×C₃₇	#737	1	3	yes	—
42	C₃×C₉²	C₃₇⋊C₃	1	1	yes	characteristic
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	#66524	1	2	yes	—
52	C₃²×C₉	#66524	1	1	yes	characteristic
53	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
54	C₃×C₂₇	—	37	9	no	—
55	C₉²	#66524	1	2	yes	—
56	C₉²	#66524	1	2	yes	—
57	C₉²	#66524	1	2	yes	—
58	C₉²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
59	C₉²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
60	C₉²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
61	C₃₇	#10624710	1	1	yes	characteristic, complemented, Sylow
62	C₃³	C₃×#66524	1	1	yes	characteristic
63	C₃×C₉	—	3	6	no	—
64	C₃×C₉	—	3	3	no	—
65	C₃×C₉	#11758601	1	9	yes	complemented
66	C₃×C₉	C₃×#66524	1	2	yes	—
67	C₃×C₉	C₃×#66524	1	2	yes	—
68	C₃×C₉	C₃×#66524	1	2	yes	—
69	C₃×C₉	C₃×#66524	1	1	yes	characteristic
70	C₃×C₉	C₃×#66524	1	1	yes	characteristic
71	C₃×C₉	C₃×#66524	1	1	yes	characteristic
72	C₃×C₉	C₃×#66524	1	2	yes	—
73	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
74	C₂₇	—	111	9	no	—
75	C₃²	—	3	1	no	—
76	C₃²	—	3	2	no	—
77	C₃²	C₃×#11758601	1	3	yes	—
78	C₃²	C₃²×#66524	1	1	yes	characteristic
79	C₉	—	3	2	no	—
80	C₉	—	3	2	no	—
81	C₉	—	3	2	no	—
82	C₉	C₃×#11758601	1	3	yes	—
83	C₉	C₃×#11758601	1	3	yes	—
84	C₉	C₃×#11758601	1	3	yes	—
85	C₉	#15688511	1	6	yes	—
86	C₉	#15688531	1	3	yes	—
87	C₃	—	3	3	no	—
88	C₃	#22582538	1	1	yes	characteristic
89	C₃	C₃²×#11758601	1	1	yes	characteristic
90	C₃	C₃×#15688511	1	2	yes	—

	subgroup	G/H
center	C₉²	C₃×C₃₇⋊C₃
commutator	C₃×C₃₇	C₃²×C₂₇
Frattini	C₃×C₉	C₃²×C₃₇⋊C₃
Fitting	C₃×C₉²×C₃₇	C₃
socle	C₃²×C₃₇	C₃²×C₉
prime radical	C₃³×C₃₇	C₃×C₉
cosocle	C₃×C₉×C₃₇	C₃³
hypercenter	C₃×C₉²	C₃₇⋊C₃
hypocenter	C₃₇	#10624710
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₉² ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
1. #22582490	C₃	semidirect
2. #22582489	C₃	semidirect
4. C₉×#11758601	C₃	semidirect
19. C₃×C₉×C₃₇	C₂₇	semidirect
61. C₃₇	#10624710	semidirect
65. C₃×C₉	#11758601	semidirect

Maximal subgroups

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

subgroup	index
#22582490	3
#22582489	3
C₃²⋊#11758601	3
C₉×#11758601	3
C₃×C₉²×C₃₇	3
#10624710	37