Subgroups — #36379804

Order 22599.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21419258	C₃	1	3	yes	maximal
2	C₃₁×#6864	C₃	1	1	yes	maximal, characteristic
3	C₃₁⋊C₈₁	—	3	3	no	—
4	C₃×C₂₇×C₃₁	C₉	1	1	yes	characteristic
5	C₃×C₂₇×C₃₁	C₉	1	1	yes	characteristic
6	C₃×C₂₇×C₃₁	C₃²	1	1	yes	characteristic
7	C₉²×C₃₁	C₉	1	1	yes	characteristic
8	C₃×C₉×C₃₁	—	3	1	no	—
9	C₃×C₉×C₃₁	C₃×C₉	1	1	yes	characteristic
10	C₂₇×C₃₁	—	3	1	no	—
11	C₂₇×C₃₁	C₂₇	1	3	yes	—
12	C₂₇×C₃₁	3₋¹⁺²	1	3	yes	—
13	#10624532	—	31	1	no	maximal, Sylow
14	C₃²×C₃₁	C₂₇⋊C₃	1	1	yes	characteristic
15	C₉×C₃₁	—	9	1	no	—
16	C₉×C₃₁	C₉⋊C₉	1	1	yes	characteristic
17	C₉×C₃₁	C₃×C₂₇	1	1	yes	characteristic
18	C₉×C₃₁	C₂₇⋊C₃	1	1	yes	characteristic
19	C₈₁⋊C₃	—	31	3	no	—
20	#6864	C₃₁⋊C₃	1	1	yes	characteristic
21	C₃×C₃₁	—	3	1	no	—
22	C₃×C₃₁	C₉⋊C₂₇	1	1	yes	characteristic
23	C₃×C₂₇	C₃₁⋊C₉	1	1	yes	characteristic
24	C₃×C₂₇	C₃₁⋊C₉	1	1	yes	characteristic
25	C₃×C₂₇	C₃×C₃₁⋊C₃	1	1	yes	characteristic
26	C₉²	C₃₁⋊C₉	1	1	yes	characteristic
27	C₈₁	—	93	3	no	—
28	C₃₁	#10624532	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₉	—	3	1	no	—
30	C₃×C₉	C₃×C₃₁⋊C₉	1	1	yes	characteristic
31	C₂₇	—	3	1	no	—
32	C₂₇	C₃₁⋊C₂₇	1	3	yes	—
33	C₂₇	#11719686	1	3	yes	—
34	C₃²	#14578892	1	1	yes	characteristic
35	C₉	—	9	1	no	—
36	C₉	#14578886	1	1	yes	characteristic
37	C₉	C₃×C₃₁⋊C₂₇	1	1	yes	characteristic
38	C₉	#14578892	1	1	yes	characteristic
39	C₃	—	3	1	no	—
40	C₃	#21419247	1	1	yes	characteristic

	subgroup	G/H
center	C₉	#14578886
commutator	C₉×C₃₁	C₃×C₂₇
Frattini	C₃×C₂₇	C₃×C₃₁⋊C₃
Fitting	C₃₁×#6864	C₃
socle	C₃×C₃₁	C₉⋊C₂₇
prime radical	C₃²×C₃₁	C₂₇⋊C₃
cosocle	C₃×C₂₇×C₃₁	C₃²
hypercenter	#6864	C₃₁⋊C₃
hypocenter	C₃₁	#10624532
LCS	G ▷ C₉×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₉ ◁ C₃×C₂₇ ◁ #6864

Complements

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

N	H ≅ G/N	type
28. C₃₁	#10624532	semidirect

Maximal subgroups

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

subgroup	index
#21419258	3
C₃₁×#6864	3
#10624532	31