Subgroups — #36379869

Order 22599.

458 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14578887	C₃	1	1	yes	maximal, characteristic
2	C₃×#14578886	C₃	1	1	yes	maximal, characteristic
3	C₃×(C₃₁⋊C₉)⋊C₉	C₃	1	9	yes	maximal
4	C₃×C₉×C₃₁⋊C₉	C₃	1	1	yes	maximal, characteristic
5	C₃×C₃₁×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
6	C₃²×C₃₁⋊C₉	C₃²	1	3	yes	—
7	C₃²×C₃₁⋊C₉	C₃²	1	3	yes	—
8	C₃²×C₃₁⋊C₉	C₃²	1	3	yes	—
9	#14578887	—	3	3	no	—
10	#14578886	—	3	3	no	—
11	(C₃₁⋊C₉)⋊C₉	—	3	27	no	—
12	C₉×C₃₁⋊C₉	C₉	1	9	yes	complemented
13	C₃²×C₉×C₃₁	C₃²	1	3	yes	—
14	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
15	C₃₁×C₉⋊C₉	—	3	3	no	—
16	C₃³×C₃₁	C₃³	1	1	yes	characteristic
17	C₃×C₉×C₃₁	—	3	3	no	—
18	C₃×C₉×C₃₁	—	3	9	no	—
19	C₃×C₉×C₃₁	C₃×C₉	1	3	yes	—
20	C₃×C₉×C₃₁	3₋¹⁺²	1	3	yes	—
21	C₃×C₉×C₃₁	3₋¹⁺²	1	3	yes	—
22	C₃×C₉×C₃₁	3₋¹⁺²	1	3	yes	—
23	C₃×C₃₁⋊C₉	—	3	9	no	—
24	C₃×C₃₁⋊C₉	—	3	9	no	—
25	C₃×C₃₁⋊C₉	—	3	3	no	—
26	C₃×C₃₁⋊C₉	—	3	3	no	—
27	C₃×C₃₁⋊C₉	C₃×C₉	1	9	yes	—
28	C₃×C₃₁⋊C₉	3₋¹⁺²	1	27	yes	—
29	#10624554	—	31	1	no	maximal, Sylow
30	C₃²×C₃₁	C₃²×C₉	1	1	yes	characteristic
31	C₃²×C₃₁	C₃×3₋¹⁺²	1	9	yes	—
32	C₃²×C₃₁	C₃×3₋¹⁺²	1	1	yes	characteristic
33	C₃²×C₃₁	C₃×3₋¹⁺²	1	1	yes	characteristic
34	C₃²×C₃₁	C₃×3₋¹⁺²	1	1	yes	characteristic
35	C₉×C₃₁	—	9	3	no	—
36	C₉×C₃₁	C₉⋊C₉	1	9	yes	complemented
37	C₃₁⋊C₉	—	9	3	no	—
38	C₃₁⋊C₉	—	9	3	no	—
39	C₃₁⋊C₉	C₉⋊C₉	1	27	yes	complemented
40	C₃×C₉⋊C₉	—	31	9	no	—
41	C₃×C₉⋊C₉	—	31	1	no	—
42	C₃×C₉⋊C₉	—	31	1	no	—
43	C₃×C₉⋊C₉	C₃₁⋊C₃	1	1	yes	characteristic
44	C₃×C₉²	—	31	1	no	—
45	C₃×C₃₁	C₃×C₉⋊C₉	1	3	yes	—
46	C₃×C₃₁	C₃×C₉⋊C₉	1	1	yes	characteristic
47	C₃×C₃₁	#6900	1	3	yes	—
48	C₃×C₃₁	#6900	1	3	yes	—
49	C₃×C₃₁	#6900	1	3	yes	—
50	C₃²×C₉	—	31	3	no	—
51	C₃²×C₉	—	31	3	no	—
52	C₃²×C₉	—	31	3	no	—
53	C₃²×C₉	C₃×C₃₁⋊C₃	1	3	yes	—
54	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
55	C₉⋊C₉	—	3	3	no	—
56	C₉⋊C₉	—	93	27	no	—
57	C₉⋊C₉	—	93	3	no	—
58	C₉⋊C₉	—	93	3	no	—
59	C₉²	—	31	9	no	—
60	C₃₁	#10624554	1	1	yes	characteristic, complemented, Sylow
61	C₃³	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
62	C₃×C₉	—	3	9	no	—
63	C₃×C₉	—	3	3	no	—
64	C₃×C₉	—	31	9	no	—
65	C₃×C₉	—	31	27	no	—
66	C₃×C₉	—	93	9	no	—
67	C₃×C₉	—	93	9	no	—
68	C₃×C₉	—	93	3	no	—
69	C₃×C₉	—	93	3	no	—
70	C₃×C₉	C₉×C₃₁⋊C₃	1	3	yes	—
71	C₃×C₉	#11719686	1	3	yes	—
72	C₃×C₉	#11719687	1	3	yes	—
73	C₃×C₉	#11719689	1	3	yes	—
74	C₃²	C₃×C₉×C₃₁⋊C₃	1	1	yes	characteristic
75	C₃²	3₋¹⁺²×C₃₁⋊C₃	1	9	yes	—
76	C₃²	C₃×#11719687	1	1	yes	characteristic
77	C₃²	C₃×#11719686	1	1	yes	characteristic
78	C₃²	C₃×#11719689	1	1	yes	characteristic
79	C₉	—	9	3	no	—
80	C₉	—	279	3	no	—
81	C₉	—	279	3	no	—
82	C₉	—	31	27	no	—
83	C₉	(C₃₁⋊C₉)⋊C₉	1	9	yes	complemented
84	C₃	C₉⋊C₉×C₃₁⋊C₃	1	3	yes	—
85	C₃	C₃×(C₃₁⋊C₉)⋊C₉	1	1	yes	characteristic
86	C₃	#21419359	1	3	yes	—
87	C₃	#21419362	1	3	yes	—
88	C₃	#21419363	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₃₁⋊C₃
commutator	C₃²×C₃₁	C₃²×C₉
Fitting	C₃×C₃₁×C₉⋊C₉	C₃
socle, prime radical, cosocle	C₃³×C₃₁	C₃³
hypercenter	C₃×C₉⋊C₉	C₃₁⋊C₃
hypocenter	C₃₁	#10624554
LCS	G ▷ C₃²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃³ ◁ C₃×C₉⋊C₉

Complements

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

N	H ≅ G/N	type
12. C₉×C₃₁⋊C₉	C₉	semidirect
36. C₉×C₃₁	C₉⋊C₉	semidirect
39. C₃₁⋊C₉	C₉⋊C₉	semidirect
60. C₃₁	#10624554	semidirect
83. C₉	(C₃₁⋊C₉)⋊C₉	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
C₃×(C₃₁⋊C₉)⋊C₉	3
C₃×C₉×C₃₁⋊C₉	3
C₃×C₃₁×C₉⋊C₉	3
#10624554	31