Subgroups — #41005053

Order 26973.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582500	C₃	1	1	yes	maximal, characteristic
2	#22582500	C₃	1	1	yes	maximal, characteristic
3	#22582463	C₃	1	1	yes	maximal, characteristic
4	C₃₇×C₈₁⋊C₃	C₃	1	1	yes	maximal, characteristic
5	C₃×#11758601	C₉	1	1	yes	characteristic
6	C₃×#11758601	C₉	1	1	yes	characteristic
7	C₉×#66524	C₉	1	1	yes	characteristic
8	#15688500	—	3	1	no	—
9	#15688500	—	3	1	no	—
10	C₃×C₂₇×C₃₇	C₃²	1	1	yes	characteristic
11	C₃₇×C₈₁	—	3	1	no	—
12	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
13	C₃×#66524	—	3	1	no	—
14	C₂₇×C₃₇	3₋¹⁺²	1	1	yes	characteristic
15	C₂₇×C₃₇	3₋¹⁺²	1	1	yes	characteristic
16	C₂₇×C₃₇	3₋¹⁺²	1	1	yes	characteristic
17	#11758601	—	3	1	no	—
18	#11758601	C₂₇	1	3	yes	—
19	#10624532	—	37	1	no	maximal, Sylow
20	C₃²×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
21	C₉×C₃₇	C₉⋊C₉	1	1	yes	characteristic
22	C₉×C₃₇	C₃×C₂₇	1	1	yes	characteristic
23	C₉×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
24	#66524	—	9	1	no	—
25	C₈₁⋊C₃	—	37	1	no	—
26	C₈₁⋊C₃	—	37	1	no	—
27	C₈₁⋊C₃	C₃₇⋊C₃	1	1	yes	characteristic
28	#6864	—	37	1	no	—
29	C₃×C₃₇	—	3	1	no	—
30	C₃×C₃₇	C₉⋊C₂₇	1	1	yes	characteristic
31	C₃×C₂₇	—	37	1	no	—
32	C₃×C₂₇	—	37	1	no	—
33	C₃×C₂₇	C₃×C₃₇⋊C₃	1	1	yes	characteristic
34	C₉²	—	37	1	no	—
35	C₈₁	—	3	1	no	—
36	C₈₁	—	111	1	no	—
37	C₈₁	—	111	1	no	—
38	C₃₇	#10624532	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₉	—	111	1	no	—
40	C₃×C₉	C₉×C₃₇⋊C₃	1	1	yes	characteristic
41	C₂₇	—	37	3	no	—
42	C₂₇	—	111	1	no	—
43	C₂₇	#11758605	1	1	yes	characteristic
44	C₂₇	#11758606	1	1	yes	characteristic
45	C₂₇	#11758608	1	1	yes	characteristic
46	C₃²	#15688510	1	1	yes	characteristic
47	C₉	—	333	1	no	—
48	C₉	#15688504	1	1	yes	characteristic
49	C₉	C₂₇×C₃₇⋊C₃	1	1	yes	characteristic
50	C₉	#15688509	1	1	yes	characteristic
51	C₃	—	3	1	no	—
52	C₃	#22582488	1	1	yes	characteristic

	subgroup	G/H
center	C₉	#15688504
commutator	C₉×C₃₇	C₃×C₂₇
Frattini	C₃×C₂₇	C₃×C₃₇⋊C₃
Fitting	C₃₇×C₈₁⋊C₃	C₃
socle	C₃×C₃₇	C₉⋊C₂₇
prime radical	C₃²×C₃₇	C₂₇⋊C₃
cosocle	C₃×C₂₇×C₃₇	C₃²
hypercenter	C₈₁⋊C₃	C₃₇⋊C₃
hypocenter	C₃₇	#10624532
LCS	G ▷ C₉×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₉ ◁ C₃×C₂₇ ◁ C₈₁⋊C₃

Complements

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

N	H ≅ G/N	type
38. C₃₇	#10624532	semidirect

Maximal subgroups

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

subgroup	index
#22582500	3
#22582463	3
C₃₇×C₈₁⋊C₃	3
#10624532	37