Subgroups — #36380069

Order 22599.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#11719689	C₃	1	3	yes	maximal
2	#21419216	C₃	1	3	yes	maximal
3	#21419213	C₃	1	3	yes	maximal
4	#21419207	C₃	1	3	yes	maximal
5	C₃₁×#6887	C₃	1	1	yes	maximal, characteristic
6	C₃×#11719689	C₃²	1	3	yes	—
7	(C₃₁⋊C₉)⋊C₉	—	3	6	no	—
8	C₃²⋊(C₃₁⋊C₉)	C₃²	1	3	yes	—
9	C₃²⋊(C₃₁⋊C₉)	C₃²	1	3	yes	—
10	C₉×C₃₁⋊C₉	—	3	3	no	—
11	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
12	C₃₁×C₉⋊C₉	—	3	2	no	—
13	C₃₁×C₃²⋊C₉	C₃²	1	3	yes	—
14	C₉²×C₃₁	—	3	1	no	—
15	C₃³×C₃₁	C₃³	1	1	yes	characteristic
16	C₃×C₉×C₃₁	—	3	3	no	—
17	C₃×C₉×C₃₁	—	3	3	no	—
18	C₃×C₉×C₃₁	H(3,𝔽₃)	1	2	yes	—
19	C₃×C₉×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
20	#11719689	—	3	9	no	—
21	C₃×C₃₁⋊C₉	—	3	3	no	—
22	C₃×C₃₁⋊C₉	—	3	3	no	—
23	C₃×C₃₁⋊C₉	—	3	3	no	—
24	#10624588	—	31	1	no	maximal, Sylow
25	C₃²×C₃₁	—	3	1	no	—
26	C₃²×C₃₁	—	3	3	no	—
27	C₃²×C₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	C₉×C₃₁	—	3	2	no	—
29	C₉×C₃₁	—	9	3	no	—
30	C₉×C₃₁	#733	1	3	yes	—
31	C₃₁⋊C₉	—	3	9	no	—
32	C₃₁⋊C₉	—	9	3	no	—
33	C₃₁⋊C₉	—	9	3	no	—
34	C₉×3₋¹⁺²	—	31	3	no	—
35	#6887	C₃₁⋊C₃	1	1	yes	characteristic
36	#6861	—	31	3	no	—
37	#6860	—	31	3	no	—
38	#6858	—	31	3	no	—
39	C₃×C₃₁	—	9	1	no	—
40	C₃×C₃₁	C₃×#733	1	1	yes	characteristic
41	C₃×C₃₁	#6908	1	3	yes	—
42	C₃×3₋¹⁺²	—	31	3	no	—
43	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
44	C₉⋊C₉	—	3	2	no	—
45	C₉⋊C₉	—	93	6	no	—
46	C₃²⋊C₉	—	31	3	no	—
47	C₃²⋊C₉	—	31	3	no	—
48	C₃²⋊C₉	C₃×C₃₁⋊C₃	1	3	yes	—
49	C₉²	—	3	1	no	—
50	C₉²	—	93	3	no	—
51	C₃₁	#10624588	1	1	yes	characteristic, complemented, Sylow
52	C₃³	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
53	3₋¹⁺²	—	93	9	no	—
54	C₃×C₉	—	3	3	no	—
55	C₃×C₉	—	3	3	no	—
56	C₃×C₉	—	93	3	no	—
57	C₃×C₉	—	93	3	no	—
58	C₃×C₉	—	93	3	no	—
59	C₃×C₉	C₃²⋊(C₃₁⋊C₃)	1	2	yes	—
60	C₃×C₉	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
61	C₃²	—	3	1	no	—
62	C₃²	—	3	3	no	—
63	C₃²	C₃×C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
64	C₉	—	3	2	no	—
65	C₉	—	9	3	no	—
66	C₉	—	279	3	no	—
67	C₉	—	279	3	no	—
68	C₉	—	93	9	no	—
69	C₉	#14578902	1	3	yes	—
70	C₃	—	9	1	no	—
71	C₃	C₃×#14578902	1	1	yes	characteristic
72	C₃	#21419388	1	3	yes	—

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₃₁⋊C₃)
commutator, prime radical, cosocle	C₃³×C₃₁	C₃³
Frattini	C₃³	C₃²×C₃₁⋊C₃
Fitting	C₃₁×#6887	C₃
socle	C₃²×C₃₁	C₃×H(3,𝔽₃)
hypercenter	#6887	C₃₁⋊C₃
hypocenter	C₃₁	#10624588
LCS	G ▷ C₃³×C₃₁ ▷ C₃²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
51. C₃₁	#10624588	semidirect

Maximal subgroups

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

subgroup	index
C₉×#11719689	3
#21419216	3
#21419213	3
#21419207	3
C₃₁×#6887	3
#10624588	31