Subgroups — C₃×#21419228 #36380973

Order 22599.

476 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊(C₃₁⋊C₉)	C₃	1	3	yes	maximal
2	#21419228	C₃	1	9	yes	maximal, direct product factor
3	C₃³×C₉×C₃₁	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₃₁⋊C₉	—	3	3	no	—
5	C₃²⋊(C₃₁⋊C₉)	—	3	6	no	—
6	C₃²⋊(C₃₁⋊C₉)	C₃²	1	9	yes	—
7	C₃⁴×C₃₁	C₃²	1	1	yes	characteristic
8	C₃²×C₉×C₃₁	—	3	2	no	—
9	C₃²×C₉×C₃₁	—	3	1	no	—
10	C₃²×C₉×C₃₁	—	3	6	no	—
11	C₃²×C₉×C₃₁	C₉	1	9	yes	complemented
12	C₃²×C₉×C₃₁	C₃²	1	3	yes	—
13	C₃³×C₃₁	—	3	9	no	—
14	C₃³×C₃₁	C₃×C₉	1	3	yes	—
15	C₃³×C₃₁	H(3,𝔽₃)	1	2	yes	—
16	C₃³×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
17	C₃³×C₃₁	3₋¹⁺²	1	6	yes	—
18	C₃³×C₃₁	C₃³	1	1	yes	characteristic
19	C₃×C₉×C₃₁	—	3	18	no	—
20	C₃×C₉×C₃₁	—	3	9	no	—
21	C₃×C₉×C₃₁	—	3	3	no	—
22	C₃×C₉×C₃₁	—	3	6	no	—
23	C₃×C₉×C₃₁	C₃×C₉	1	9	yes	complemented
24	C₃×C₃₁⋊C₉	—	3	9	no	—
25	C₃×C₃₁⋊C₉	—	9	9	no	—
26	C₃×#6867	—	31	1	no	maximal, Sylow
27	C₃²×C₃₁	—	3	9	no	—
28	C₃²×C₃₁	—	3	18	no	—
29	C₃²×C₃₁	—	3	6	no	—
30	C₃²×C₃₁	—	3	3	no	—
31	C₃²×C₃₁	C₃²⋊C₉	1	6	yes	—
32	C₃²×C₃₁	C₃²⋊C₉	1	3	yes	—
33	C₃²×C₃₁	#731	1	9	yes	—
34	C₃²×C₃₁	C₃²×C₉	1	1	yes	characteristic
35	C₃²×C₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
36	C₃²×C₃₁	C₃×3₋¹⁺²	1	2	yes	—
37	C₉×C₃₁	—	3	9	no	—
38	C₃₁⋊C₉	—	9	9	no	—
39	C₃³×C₉	C₃₁⋊C₃	1	1	yes	characteristic
40	C₃×C₃²⋊C₉	—	31	3	no	—
41	#6867	—	31	9	no	—
42	C₃×C₃₁	—	3	6	no	—
43	C₃×C₃₁	—	3	1	no	—
44	C₃×C₃₁	—	3	2	no	—
45	C₃×C₃₁	#6867	1	9	yes	complemented
46	C₃×C₃₁	C₃×C₃²⋊C₉	1	1	yes	characteristic
47	C₃×C₃₁	C₃×#731	1	3	yes	—
48	C₃⁴	C₃×C₃₁⋊C₃	1	1	yes	characteristic
49	C₃²×C₉	—	3	6	no	—
50	C₃²×C₉	—	3	2	no	—
51	C₃²×C₉	—	3	1	no	—
52	C₃²×C₉	—	93	3	no	—
53	C₃²×C₉	C₃₁⋊C₉	1	9	yes	complemented
54	C₃²×C₉	C₃×C₃₁⋊C₃	1	3	yes	—
55	C₃²⋊C₉	—	31	9	no	—
56	C₃²⋊C₉	—	93	6	no	—
57	C₃₁	C₃×#6867	1	1	yes	characteristic, complemented, Sylow
58	C₃³	—	3	9	no	—
59	C₃³	C₃×C₃₁⋊C₉	1	3	yes	—
60	C₃³	#11719689	1	6	yes	—
61	C₃³	C₃²⋊(C₃₁⋊C₃)	1	2	yes	—
62	C₃³	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
63	C₃³	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
64	C₃×C₉	—	3	18	no	—
65	C₃×C₉	—	3	9	no	—
66	C₃×C₉	—	3	3	no	—
67	C₃×C₉	—	3	6	no	—
68	C₃×C₉	—	279	9	no	—
69	C₃×C₉	—	93	9	no	—
70	C₃×C₉	C₃×C₃₁⋊C₉	1	9	yes	complemented
71	C₃²	—	3	6	no	—
72	C₃²	—	3	3	no	—
73	C₃²	—	3	9	no	—
74	C₃²	—	3	18	no	—
75	C₃²	C₃²⋊(C₃₁⋊C₉)	1	6	yes	—
76	C₃²	C₃²⋊(C₃₁⋊C₉)	1	3	yes	—
77	C₃²	#14578897	1	9	yes	—
78	C₃²	C₃²×C₃₁⋊C₉	1	1	yes	characteristic
79	C₃²	C₃×C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
80	C₃²	C₃×#11719689	1	2	yes	—
81	C₉	—	3	9	no	—
82	C₉	—	279	9	no	—
83	C₃	—	3	6	no	—
84	C₃	—	3	1	no	—
85	C₃	—	3	2	no	—
86	C₃	#21419228	1	9	yes	direct product factor
87	C₃	C₃×C₃²⋊(C₃₁⋊C₉)	1	1	yes	characteristic
88	C₃	C₃×#14578897	1	3	yes	—

	subgroup	G/H
center	C₃³	C₃²⋊(C₃₁⋊C₃)
commutator	C₃²×C₃₁	C₃²×C₉
Frattini	C₃³	C₃²×C₃₁⋊C₃
Fitting	C₃³×C₉×C₃₁	C₃
socle	C₃³×C₃₁	H(3,𝔽₃)
prime radical	C₃⁴×C₃₁	C₃²
cosocle	C₃³×C₃₁	C₃³
hypercenter	C₃³×C₉	C₃₁⋊C₃
hypocenter	C₃₁	C₃×#6867
LCS	G ▷ C₃²×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃³ ◁ C₃⁴ ◁ C₃³×C₉

Complements

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

N	H ≅ G/N	type
2. #21419228	C₃	direct (N × H)
11. C₃²×C₉×C₃₁	C₉	semidirect
23. C₃×C₉×C₃₁	C₃×C₉	semidirect
45. C₃×C₃₁	#6867	semidirect
53. C₃²×C₉	C₃₁⋊C₉	semidirect
57. C₃₁	C₃×#6867	semidirect
70. C₃×C₉	C₃×C₃₁⋊C₉	semidirect
86. C₃	#21419228	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₃²⋊(C₃₁⋊C₉)	3
#21419228	3
C₃³×C₉×C₃₁	3
C₃×#6867	31

Subgroups — C3×#21419228 #36380973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#21419228 #36380973