Subgroups — #36379859

Order 22599.

374 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14578887	C₃	1	3	yes	maximal
2	C₃×#14578886	C₃	1	3	yes	maximal
3	C₃₁⋊#6855	C₃	1	6	yes	maximal
4	C₃×C₉²×C₃₁	C₃	1	1	yes	maximal, characteristic
5	C₃²×C₃₁⋊C₉	C₃²	1	9	yes	—
6	#14578887	—	3	9	no	—
7	#14578886	—	3	9	no	—
8	C₃²×C₉×C₃₁	C₃²	1	2	yes	—
9	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
10	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
11	C₉²×C₃₁	C₉	1	9	yes	complemented
12	C₃³×C₃₁	C₃³	1	1	yes	characteristic
13	C₃×C₉×C₃₁	—	3	6	no	—
14	C₃×C₉×C₃₁	C₃×C₉	1	6	yes	—
15	C₃×C₉×C₃₁	C₃×C₉	1	3	yes	—
16	C₃×C₉×C₃₁	C₃×C₉	1	3	yes	—
17	C₃×C₉×C₃₁	3₋¹⁺²	1	9	yes	—
18	C₃×C₉×C₃₁	3₋¹⁺²	1	9	yes	—
19	C₃×C₃₁⋊C₉	—	3	9	no	—
20	C₃×C₃₁⋊C₉	—	3	9	no	—
21	C₃×C₃₁⋊C₉	—	3	18	no	—
22	#10624550	—	31	1	no	maximal, Sylow
23	C₃²×C₃₁	C₃²×C₉	1	1	yes	characteristic
24	C₃²×C₃₁	C₃×3₋¹⁺²	1	3	yes	—
25	C₃²×C₃₁	C₃×3₋¹⁺²	1	3	yes	—
26	C₃²×C₃₁	#737	1	6	yes	—
27	C₉×C₃₁	—	3	6	no	—
28	C₉×C₃₁	C₉⋊C₉	1	9	yes	complemented
29	C₉×C₃₁	C₉⋊C₉	1	9	yes	complemented
30	C₃₁⋊C₉	—	9	9	no	—
31	C₃×C₉⋊C₉	—	31	3	no	—
32	C₃×C₉⋊C₉	—	31	3	no	—
33	C₃×C₉²	C₃₁⋊C₃	1	1	yes	characteristic
34	#6855	—	31	6	no	—
35	C₃×C₃₁	C₃×C₉⋊C₉	1	1	yes	characteristic
36	C₃×C₃₁	C₃×C₉⋊C₉	1	1	yes	characteristic
37	C₃×C₃₁	#6887	1	2	yes	—
38	C₃×C₃₁	#6896	1	9	yes	—
39	C₃²×C₉	—	31	9	no	—
40	C₃²×C₉	C₃×C₃₁⋊C₃	1	2	yes	—
41	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
42	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
43	C₉⋊C₉	—	93	9	no	—
44	C₉⋊C₉	—	93	9	no	—
45	C₉²	C₃₁⋊C₉	1	9	yes	complemented
46	C₃₁	#10624550	1	1	yes	characteristic, complemented, Sylow
47	C₃³	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
48	C₃×C₉	—	3	6	no	—
49	C₃×C₉	—	93	9	no	—
50	C₃×C₉	—	93	9	no	—
51	C₃×C₉	—	93	18	no	—
52	C₃×C₉	#11719686	1	9	yes	—
53	C₃×C₉	#11719687	1	9	yes	—
54	C₃×C₉	C₃×C₃₁⋊C₉	1	6	yes	—
55	C₃×C₉	C₃×C₃₁⋊C₉	1	3	yes	—
56	C₃×C₉	C₃×C₃₁⋊C₉	1	3	yes	—
57	C₃²	C₃²×C₃₁⋊C₉	1	1	yes	characteristic
58	C₃²	C₃×#11719687	1	3	yes	—
59	C₃²	C₃×#11719686	1	3	yes	—
60	C₃²	#14578912	1	6	yes	—
61	C₉	—	3	6	no	—
62	C₉	—	279	9	no	—
63	C₉	#14578886	1	9	yes	complemented
64	C₉	#14578887	1	9	yes	complemented
65	C₃	C₃×#14578886	1	1	yes	characteristic
66	C₃	C₃×#14578887	1	1	yes	characteristic
67	C₃	#21419296	1	2	yes	—
68	C₃	#21419339	1	9	yes	—

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₃₁⋊C₃
commutator	C₃²×C₃₁	C₃²×C₉
Fitting	C₃×C₉²×C₃₁	C₃
socle, prime radical, cosocle	C₃³×C₃₁	C₃³
hypercenter	C₃×C₉²	C₃₁⋊C₃
hypocenter	C₃₁	#10624550
LCS	G ▷ C₃²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃³ ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
11. C₉²×C₃₁	C₉	semidirect
28. C₉×C₃₁	C₉⋊C₉	semidirect
29. C₉×C₃₁	C₉⋊C₉	semidirect
45. C₉²	C₃₁⋊C₉	semidirect
46. C₃₁	#10624550	semidirect
63. C₉	#14578886	semidirect
64. C₉	#14578887	semidirect

Maximal subgroups

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

subgroup	index
C₃×#14578887	3
C₃×#14578886	3
C₃₁⋊#6855	3
C₃×C₉²×C₃₁	3
#10624550	31