Subgroups — #41008483

Order 26973.

428 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688541	C₃	1	3	yes	maximal, complemented
2	#22582690	C₃	1	9	yes	maximal, complemented
3	C₃²×C₉×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
4	#15688541	—	3	9	no	—
5	C₃×#11758603	C₃²	1	9	yes	complemented
6	C₃³×C₃₇⋊C₃	C₉	1	1	yes	characteristic
7	C₃²×#66524	C₉	1	1	yes	characteristic
8	C₃²×#66524	C₃²	1	1	yes	characteristic
9	C₃×C₉×C₃₇⋊C₃	—	3	3	no	—
10	C₃×C₉×C₃₇⋊C₃	—	3	6	no	—
11	C₃×C₉×C₃₇⋊C₃	C₉	1	6	yes	—
12	C₃×C₉×C₃₇⋊C₃	C₃²	1	3	yes	—
13	C₃²×C₉×C₃₇	C₉	1	1	yes	characteristic
14	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
15	C₃²×C₃₇⋊C₃	—	3	3	no	—
16	C₃²×C₃₇⋊C₃	—	3	9	no	—
17	C₃²×C₃₇⋊C₃	C₃×C₉	1	3	yes	—
18	C₃×C₉×C₃₇	—	3	3	no	—
19	C₃×C₉×C₃₇	C₃×C₉	1	3	yes	—
20	C₃×#66524	—	3	3	no	—
21	C₃×#66524	C₃×C₉	1	3	yes	—
22	C₃×#66524	C₃×C₉	1	2	yes	—
23	C₃×#66524	H(3,𝔽₃)	1	3	yes	—
24	C₃×#66524	3₋¹⁺²	1	6	yes	—
25	C₃×#66524	C₃³	1	1	yes	characteristic
26	C₉×C₃₇⋊C₃	—	3	18	no	—
27	C₉×C₃₇⋊C₃	—	3	3	no	—
28	C₉×C₃₇⋊C₃	—	3	6	no	—
29	#11758603	—	3	9	no	—
30	#10624683	—	37	1	no	maximal, Sylow
31	C₃²×C₃₇	—	3	3	no	—
32	C₃²×C₃₇	C₃²⋊C₉	1	3	yes	—
33	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
34	C₃×C₃₇⋊C₃	—	3	27	no	—
35	C₃×C₃₇⋊C₃	—	3	3	no	—
36	C₃×C₃₇⋊C₃	—	3	6	no	—
37	C₃×C₃₇⋊C₃	C₂₇⋊C₃	1	9	yes	complemented
38	C₉×C₃₇	—	3	3	no	—
39	#66524	—	3	3	no	—
40	#66524	C₃²⋊C₉	1	6	yes	—
41	#66524	C₃×H(3,𝔽₃)	1	1	yes	characteristic
42	#66524	C₃×3₋¹⁺²	1	2	yes	—
43	C₃³×C₉	—	37	1	no	—
44	C₃×C₂₇⋊C₃	—	37	3	no	—
45	C₃²⋊C₂₇	—	37	9	no	—
46	C₃×C₃₇	—	3	3	no	—
47	C₃×C₃₇	C₃×C₃²⋊C₉	1	1	yes	characteristic
48	C₃×C₃₇	C₃×C₂₇⋊C₃	1	3	yes	—
49	C₃₇⋊C₃	—	3	9	no	—
50	C₃⁴	—	37	1	no	—
51	C₃²×C₉	—	37	1	no	—
52	C₃²×C₉	—	37	1	no	—
53	C₃²×C₉	—	37	6	no	—
54	C₃²×C₉	—	37	3	no	—
55	C₃²×C₉	—	111	3	no	—
56	C₃²×C₉	—	111	6	no	—
57	C₃²×C₉	#66526	1	1	yes	characteristic
58	C₂₇⋊C₃	—	111	9	no	—
59	C₃×C₂₇	—	37	9	no	—
60	C₃₇	#10624683	1	1	yes	characteristic, complemented, Sylow
61	C₃³	—	37	3	no	—
62	C₃³	—	111	9	no	—
63	C₃³	—	111	3	no	—
64	C₃³	C₃×#66526	1	1	yes	characteristic
65	C₃×C₉	—	3	3	no	—
66	C₃×C₉	—	37	3	no	—
67	C₃×C₉	—	37	6	no	—
68	C₃×C₉	—	37	2	no	—
69	C₃×C₉	—	37	1	no	—
70	C₃×C₉	—	37	3	no	—
71	C₃×C₉	—	111	3	no	—
72	C₃×C₉	—	111	18	no	—
73	C₃×C₉	—	111	6	no	—
74	C₃×C₉	—	111	3	no	—
75	C₃×C₉	C₃×#66526	1	3	yes	—
76	C₂₇	—	111	9	no	—
77	C₃²	—	3	3	no	—
78	C₃²	—	37	9	no	—
79	C₃²	—	111	27	no	—
80	C₃²	—	111	3	no	—
81	C₃²	—	111	6	no	—
82	C₃²	C₃²⋊#66526	1	3	yes	—
83	C₃²	C₃²×#66526	1	1	yes	characteristic
84	C₉	—	3	3	no	—
85	C₉	—	37	1	no	—
86	C₉	—	37	6	no	—
87	C₉	—	37	2	no	—
88	C₉	—	111	3	no	—
89	C₃	—	3	3	no	—
90	C₃	—	111	9	no	—
91	C₃	C₃×C₃²⋊#66526	1	1	yes	characteristic
92	C₃	(C₃₇⋊C₃)⋊(C₂₇⋊C₃)	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×#66526
commutator, socle	C₃²×C₃₇	C₃²×C₉
Fitting	C₃²×C₉×C₃₇	C₉
prime radical	C₃³×C₃₇⋊C₃	C₉
cosocle	C₃×#66524	C₃³
hypercenter	C₃²×C₉	#66526
hypocenter	C₃₇	#10624683
LCS	G ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. C₃×#15688541	C₃	semidirect
2. #22582690	C₃	semidirect
5. C₃×#11758603	C₃²	semidirect
37. C₃×C₃₇⋊C₃	C₂₇⋊C₃	semidirect
60. C₃₇	#10624683	semidirect

Maximal subgroups

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

subgroup	index
C₃×#15688541	3
#22582690	3
C₃²×C₉×C₃₇⋊C₃	3
#10624683	37