Subgroups — #41008306

Order 26973.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582703	C₃	1	1	yes	maximal, characteristic
2	#22582703	C₃	1	1	yes	maximal, characteristic
3	#22582703	C₃	1	1	yes	maximal, characteristic
4	#22582463	C₃	1	1	yes	maximal, characteristic
5	C₃×#11758603	—	3	1	no	—
6	C₃×#11758603	—	3	1	no	—
7	C₃×#11758603	—	3	1	no	—
8	C₃×#11758601	C₉	1	1	yes	characteristic
9	C₃×#11758601	C₉	1	1	yes	characteristic
10	C₉×#66524	C₃²	1	1	yes	characteristic
11	C₃×C₂₇×C₃₇	C₉	1	1	yes	characteristic
12	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
13	C₃×#66524	3₋¹⁺²	1	1	yes	characteristic
14	C₃×#66524	3₋¹⁺²	1	1	yes	characteristic
15	C₃×#66524	3₋¹⁺²	1	1	yes	characteristic
16	#11758603	—	9	1	no	—
17	#11758603	—	9	1	no	—
18	#11758603	—	9	1	no	—
19	C₂₇×C₃₇	—	3	1	no	—
20	#11758601	—	3	1	no	—
21	#11758601	C₂₇	1	3	yes	complemented
22	#10624462	—	37	1	no	maximal, Sylow
23	C₃²×C₃₇	C₉⋊C₉	1	1	yes	characteristic
24	C₉×C₃₇	C₃×C₂₇	1	1	yes	characteristic
25	C₉×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
26	C₉×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
27	#66524	—	3	1	no	—
28	#66524	—	3	1	no	—
29	#66524	—	3	1	no	—
30	C₉⋊C₂₇	—	37	1	no	—
31	C₉⋊C₂₇	—	37	1	no	—
32	C₉⋊C₂₇	—	37	1	no	—
33	#6864	—	37	1	no	—
34	C₃×C₃₇	C₉⋊C₂₇	1	1	yes	characteristic
35	C₃×C₃₇	#6875	1	1	yes	characteristic
36	C₃×C₃₇	#6875	1	1	yes	characteristic
37	C₃×C₃₇	#6875	1	1	yes	characteristic
38	C₃×C₂₇	—	37	1	no	—
39	C₃×C₂₇	—	37	1	no	—
40	C₃×C₂₇	—	111	1	no	—
41	C₃×C₂₇	—	111	1	no	—
42	C₃×C₂₇	—	111	1	no	—
43	C₃×C₂₇	#66526	1	1	yes	characteristic
44	C₉²	—	37	1	no	—
45	C₃₇	#10624462	1	1	yes	characteristic, complemented, Sylow
46	C₃×C₉	—	37	1	no	—
47	C₃×C₉	—	37	1	no	—
48	C₃×C₉	—	37	1	no	—
49	C₃×C₉	C₃×#66526	1	1	yes	characteristic
50	C₂₇	—	3	1	no	—
51	C₂₇	—	37	3	no	—
52	C₂₇	—	333	1	no	—
53	C₂₇	—	333	1	no	—
54	C₂₇	—	333	1	no	—
55	C₂₇	—	111	1	no	—
56	C₃²	#15688537	1	1	yes	characteristic
57	C₉	—	111	1	no	—
58	C₉	—	111	1	no	—
59	C₉	—	111	1	no	—
60	C₉	(C₃₇⋊C₃)⋊C₂₇	1	1	yes	characteristic
61	C₉	#15688541	1	1	yes	characteristic
62	C₉	#15688543	1	1	yes	characteristic
63	C₃	#22582705	1	1	yes	characteristic
64	C₃	#22582707	1	1	yes	characteristic
65	C₃	#22582709	1	1	yes	characteristic
66	C₃	#22582711	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	#15688537
commutator	C₉×C₃₇	C₃×C₂₇
Frattini	C₃×C₉	C₃×#66526
Fitting	C₃×C₂₇×C₃₇	C₉
socle, prime radical	C₃²×C₃₇	C₉⋊C₉
cosocle	C₉×#66524	C₃²
hypercenter	C₃×C₂₇	#66526
hypocenter	C₃₇	#10624462
LCS	G ▷ C₉×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₃×C₉ ◁ C₃×C₂₇

Complements

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

N	H ≅ G/N	type
21. #11758601	C₂₇	semidirect
45. C₃₇	#10624462	semidirect

Maximal subgroups

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

subgroup	index
#22582703	3
#22582463	3
#10624462	37