Subgroups — #36379729

Order 22599.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21419228	C₃	1	3	yes	maximal
2	C₃₁×#6887	C₃	1	1	yes	maximal, characteristic
3	C₃²⋊(C₃₁⋊C₉)	—	3	3	no	—
4	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
5	C₃₁×C₉⋊C₉	—	3	2	no	—
6	C₃₁×C₃²⋊C₉	—	3	1	no	—
7	C₉²×C₃₁	C₉	1	3	yes	complemented
8	C₃³×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
9	C₃×C₉×C₃₁	—	3	3	no	—
10	C₃×C₉×C₃₁	—	3	3	no	—
11	C₃×C₉×C₃₁	C₃×C₉	1	1	yes	characteristic
12	C₃×C₉×C₃₁	3₋¹⁺²	1	2	yes	—
13	C₃×C₃₁⋊C₉	—	9	3	no	—
14	#10624513	—	31	1	no	maximal, Sylow
15	C₃²×C₃₁	—	9	1	no	—
16	C₃²×C₃₁	C₃²⋊C₉	1	1	yes	characteristic
17	C₃²×C₃₁	#731	1	3	yes	—
18	C₉×C₃₁	—	3	1	no	—
19	C₉×C₃₁	—	3	2	no	—
20	C₉×C₃₁	—	9	3	no	—
21	C₃₁⋊C₉	—	27	3	no	—
22	#6887	C₃₁⋊C₃	1	1	yes	characteristic
23	#6867	—	31	3	no	—
24	C₃×C₃₁	—	3	3	no	—
25	C₃×C₃₁	—	3	1	no	—
26	C₃×C₃₁	#6867	1	1	yes	characteristic
27	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
28	C₉⋊C₉	—	3	2	no	—
29	C₃²⋊C₉	—	3	1	no	—
30	C₃²⋊C₉	—	93	3	no	—
31	C₉²	C₃₁⋊C₉	1	3	yes	complemented
32	C₃₁	#10624513	1	1	yes	characteristic, complemented, Sylow
33	C₃³	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
34	C₃×C₉	—	3	3	no	—
35	C₃×C₉	—	3	3	no	—
36	C₃×C₉	—	279	3	no	—
37	C₃×C₉	C₃×C₃₁⋊C₉	1	1	yes	characteristic
38	C₃×C₉	#11719689	1	2	yes	—
39	C₃²	—	9	1	no	—
40	C₃²	C₃²⋊(C₃₁⋊C₉)	1	1	yes	characteristic
41	C₃²	#14578897	1	3	yes	—
42	C₉	—	3	1	no	—
43	C₉	—	3	2	no	—
44	C₉	—	9	3	no	—
45	C₉	—	837	3	no	—
46	C₃	—	3	1	no	—
47	C₃	—	3	3	no	—
48	C₃	#21419228	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#21419228
commutator	C₃×C₉×C₃₁	C₃×C₉
Frattini	C₃²×C₉	C₃×C₃₁⋊C₃
Fitting	C₃₁×#6887	C₃
socle	C₃×C₃₁	#6867
prime radical	C₃³×C₃₁	H(3,𝔽₃)
cosocle	C₃²×C₉×C₃₁	C₃²
hypercenter	#6887	C₃₁⋊C₃
hypocenter	C₃₁	#10624513
LCS	G ▷ C₃×C₉×C₃₁ ▷ C₃²×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
7. C₉²×C₃₁	C₉	semidirect
31. C₉²	C₃₁⋊C₉	semidirect
32. C₃₁	#10624513	semidirect

Maximal subgroups

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

subgroup	index
#21419228	3
C₃₁×#6887	3
#10624513	31