Subgroups — #41005050

Order 26973.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688500	C₃	1	3	yes	maximal
2	C₉×C₂₇×C₃₇	C₃	1	1	yes	maximal, characteristic
3	#15688500	—	3	3	no	—
4	C₃×C₂₇×C₃₇	C₉	1	2	yes	—
5	C₃×C₂₇×C₃₇	C₃²	1	1	yes	characteristic
6	C₉²×C₃₇	C₉	1	1	yes	characteristic
7	C₃×C₉×C₃₇	C₂₇	1	2	yes	—
8	C₃×C₉×C₃₇	C₂₇	1	1	yes	characteristic
9	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
10	C₂₇×C₃₇	—	3	2	no	—
11	C₂₇×C₃₇	3₋¹⁺²	1	3	yes	—
12	C₉⋊C₈₁	—	37	1	no	maximal, Sylow
13	C₃²×C₃₇	C₃×C₂₇	1	1	yes	characteristic
14	C₉×C₃₇	—	3	2	no	—
15	C₉×C₃₇	C₈₁	1	3	yes	complemented
16	C₉×C₃₇	C₉⋊C₉	1	1	yes	characteristic
17	C₉×C₃₇	C₂₇⋊C₃	1	2	yes	—
18	C₃×C₈₁	—	37	3	no	—
19	C₉×C₂₇	C₃₇⋊C₃	1	1	yes	characteristic
20	C₃×C₃₇	C₉⋊C₂₇	1	1	yes	characteristic
21	C₃×C₃₇	C₃×C₈₁	1	1	yes	characteristic
22	C₃×C₃₇	C₈₁⋊C₃	1	2	yes	—
23	C₃×C₂₇	#66524	1	2	yes	—
24	C₃×C₂₇	C₃×C₃₇⋊C₃	1	1	yes	characteristic
25	C₉²	#66524	1	1	yes	characteristic
26	C₈₁	—	111	3	no	—
27	C₃₇	C₉⋊C₈₁	1	1	yes	characteristic, complemented, Sylow
28	C₃×C₉	#11758601	1	2	yes	—
29	C₃×C₉	#11758601	1	1	yes	characteristic
30	C₃×C₉	C₃×#66524	1	1	yes	characteristic
31	C₂₇	—	3	2	no	—
32	C₂₇	#11758605	1	3	yes	—
33	C₃²	C₃×#11758601	1	1	yes	characteristic
34	C₉	—	3	2	no	—
35	C₉	#15688500	1	3	yes	complemented
36	C₉	#15688505	1	1	yes	characteristic
37	C₉	#15688511	1	2	yes	—
38	C₃	#22582489	1	1	yes	characteristic
39	C₃	C₃×#15688500	1	1	yes	characteristic
40	C₃	#22582500	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃×C₂₇	C₃×C₃₇⋊C₃
commutator	C₃×C₃₇	C₃×C₈₁
Fitting	C₉×C₂₇×C₃₇	C₃
socle, prime radical	C₃²×C₃₇	C₃×C₂₇
cosocle	C₃×C₂₇×C₃₇	C₃²
hypercenter	C₉×C₂₇	C₃₇⋊C₃
hypocenter	C₃₇	C₉⋊C₈₁
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃×C₂₇ ◁ C₉×C₂₇

Complements

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

N	H ≅ G/N	type
15. C₉×C₃₇	C₈₁	semidirect
27. C₃₇	C₉⋊C₈₁	semidirect
35. C₉	#15688500	semidirect

Maximal subgroups

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

subgroup	index
C₃×#15688500	3
C₉×C₂₇×C₃₇	3
C₉⋊C₈₁	37