Subgroups — #41008538

Order 26973.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688543	C₃	1	3	yes	maximal
2	#22582706	C₃	1	9	yes	maximal, complemented
3	C₉²×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
4	#15688543	—	3	9	no	—
5	C₃×#11758603	C₃²	1	9	yes	—
6	C₃×C₉×C₃₇⋊C₃	C₉	1	3	yes	—
7	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
8	C₉×#66524	C₉	1	1	yes	characteristic
9	C₉×#66524	C₉	1	3	yes	—
10	C₉×#66524	C₉	1	1	yes	characteristic
11	C₉×#66524	C₃²	1	3	yes	—
12	C₉²×C₃₇	C₉	1	1	yes	characteristic
13	C₃²×C₃₇⋊C₃	C₃×C₉	1	1	yes	characteristic
14	C₃×C₉×C₃₇	C₃×C₉	1	3	yes	—
15	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
16	C₃×#66524	C₃×C₉	1	3	yes	—
17	C₃×#66524	C₃×C₉	1	1	yes	characteristic
18	C₃×#66524	C₃×C₉	1	3	yes	—
19	C₃×#66524	C₃³	1	1	yes	characteristic
20	C₉×C₃₇⋊C₃	—	3	9	no	—
21	C₉×C₃₇⋊C₃	3₋¹⁺²	1	9	yes	—
22	#11758603	—	3	9	no	—
23	#10624706	—	37	1	no	maximal, Sylow
24	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
25	C₃×C₃₇⋊C₃	—	3	3	no	—
26	C₃×C₃₇⋊C₃	C₉⋊C₉	1	3	yes	—
27	C₉×C₃₇	—	3	3	no	—
28	C₉×C₃₇	C₉⋊C₉	1	3	yes	—
29	#66524	—	3	3	no	—
30	#66524	C₉⋊C₉	1	3	yes	—
31	#66524	C₂₇⋊C₃	1	9	yes	complemented
32	#66524	C₃×3₋¹⁺²	1	3	yes	—
33	C₃×C₂₇⋊C₃	—	37	3	no	—
34	C₃×C₉²	—	37	1	no	—
35	C₉⋊C₂₇	—	37	9	no	—
36	C₃×C₃₇	C₃×C₉⋊C₉	1	1	yes	characteristic
37	C₃×C₃₇	C₃×C₂₇⋊C₃	1	3	yes	—
38	C₃₇⋊C₃	—	3	3	no	—
39	C₃²×C₉	—	37	1	no	—
40	C₃²×C₉	—	37	3	no	—
41	C₂₇⋊C₃	—	111	9	no	—
42	C₃×C₂₇	—	37	9	no	—
43	C₉²	—	37	1	no	—
44	C₉²	—	37	3	no	—
45	C₉²	—	37	1	no	—
46	C₉²	—	37	3	no	—
47	C₉²	#66526	1	1	yes	characteristic
48	C₃₇	#10624706	1	1	yes	characteristic, complemented, Sylow
49	C₃³	—	37	1	no	—
50	C₃×C₉	—	37	1	no	—
51	C₃×C₉	—	37	3	no	—
52	C₃×C₉	—	37	1	no	—
53	C₃×C₉	—	37	9	no	—
54	C₃×C₉	—	37	3	no	—
55	C₃×C₉	—	111	9	no	—
56	C₃×C₉	C₃×#66526	1	3	yes	—
57	C₃×C₉	C₃×#66526	1	1	yes	characteristic
58	C₂₇	—	111	9	no	—
59	C₃²	—	37	3	no	—
60	C₃²	—	111	3	no	—
61	C₃²	C₃²×#66526	1	1	yes	characteristic
62	C₉	—	3	3	no	—
63	C₉	—	37	3	no	—
64	C₉	—	37	3	no	—
65	C₉	—	37	9	no	—
66	C₉	—	111	3	no	—
67	C₉	#15688538	1	3	yes	—
68	C₃	—	111	3	no	—
69	C₃	C₃×#15688538	1	1	yes	characteristic
70	C₃	(C₃₇⋊C₃)⋊(C₂₇⋊C₃)	1	3	yes	—

	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
31. #66524	C₂₇⋊C₃	semidirect
48. C₃₇	#10624706	semidirect

Maximal subgroups

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

subgroup	index
C₃×#15688543	3
#22582706	3
C₉²×C₃₇⋊C₃	3
#10624706	37