Subgroups — C₉×#14578902 #36381141

Order 22599.

274 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14578902	C₃	1	1	yes	maximal, characteristic
2	C₉×#11719689	C₃	1	3	yes	maximal
3	#21419238	C₃	1	6	yes	maximal
4	#21419230	C₃	1	2	yes	maximal
5	C₃×C₉²×C₃₁	C₃	1	1	yes	maximal, characteristic
6	C₃×#11719689	C₃²	1	3	yes	—
7	#14578902	C₉	1	9	yes	direct product factor
8	(C₃₁⋊C₉)⋊C₉	—	3	6	no	—
9	C₃²⋊(C₃₁⋊C₉)	C₃²	1	6	yes	—
10	C₉×C₃₁⋊C₉	—	3	3	no	—
11	C₃²×C₉×C₃₁	C₃²	1	2	yes	—
12	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
13	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
14	C₉²×C₃₁	—	3	2	no	—
15	C₉²×C₃₁	—	3	1	no	—
16	C₃³×C₃₁	C₃³	1	1	yes	characteristic
17	C₃×C₉×C₃₁	—	3	1	no	—
18	C₃×C₉×C₃₁	—	3	2	no	—
19	C₃×C₉×C₃₁	—	3	2	no	—
20	C₃×C₉×C₃₁	—	3	3	no	—
21	C₃×C₉×C₃₁	—	3	6	no	—
22	C₃×C₉×C₃₁	C₃×C₉	1	3	yes	—
23	C₃×C₉×C₃₁	H(3,𝔽₃)	1	2	yes	—
24	C₃×C₉×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
25	#11719689	—	3	6	no	—
26	#11719689	C₃×C₉	1	9	yes	—
27	C₃×C₃₁⋊C₉	—	3	3	no	—
28	C₃×C₃₁⋊C₉	—	3	6	no	—
29	C₉×#733	—	31	1	no	maximal, Sylow
30	C₃²×C₃₁	—	3	1	no	—
31	C₃²×C₃₁	—	3	2	no	—
32	C₃²×C₃₁	C₃²×C₉	1	1	yes	characteristic
33	C₃²×C₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
34	C₃²×C₃₁	#737	1	2	yes	—
35	C₉×C₃₁	—	3	3	no	—
36	C₉×C₃₁	—	3	2	no	—
37	C₉×C₃₁	—	3	6	no	—
38	C₉×C₃₁	#733	1	3	yes	complemented
39	C₃₁⋊C₉	—	3	9	no	—
40	C₃₁⋊C₉	—	9	6	no	—
41	C₃×#733	—	31	1	no	—
42	C₉×3₋¹⁺²	—	31	3	no	—
43	C₃×C₉²	C₃₁⋊C₃	1	1	yes	characteristic
44	3₋¹⁺²⋊C₉	—	31	6	no	—
45	#6868	—	31	2	no	—
46	C₃×C₃₁	—	3	1	no	—
47	C₃×C₃₁	—	3	2	no	—
48	C₃×C₃₁	C₉×H(3,𝔽₃)	1	1	yes	characteristic
49	C₃×C₃₁	C₃×#733	1	1	yes	characteristic
50	C₃×C₃₁	#6908	1	2	yes	—
51	C₃×3₋¹⁺²	—	31	3	no	—
52	C₃²×C₉	C₃×C₃₁⋊C₃	1	2	yes	—
53	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
54	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
55	#733	—	31	9	no	—
56	C₉⋊C₉	—	93	6	no	—
57	C₃²⋊C₉	—	31	6	no	—
58	C₉²	—	3	2	no	—
59	C₉²	—	3	1	no	—
60	C₉²	—	93	3	no	—
61	C₃₁	C₉×#733	1	1	yes	characteristic, complemented, Sylow
62	C₃³	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
63	3₋¹⁺²	—	31	9	no	—
64	3₋¹⁺²	—	93	6	no	—
65	C₃×C₉	—	3	1	no	—
66	C₃×C₉	—	3	2	no	—
67	C₃×C₉	—	3	2	no	—
68	C₃×C₉	—	3	3	no	—
69	C₃×C₉	—	3	6	no	—
70	C₃×C₉	—	93	6	no	—
71	C₃×C₉	—	93	3	no	—
72	C₃×C₉	C₉×C₃₁⋊C₃	1	3	yes	—
73	C₃×C₉	C₃²⋊(C₃₁⋊C₃)	1	2	yes	—
74	C₃×C₉	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
75	C₃²	—	3	1	no	—
76	C₃²	—	3	2	no	—
77	C₃²	C₃×C₉×C₃₁⋊C₃	1	1	yes	characteristic
78	C₃²	C₃×C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
79	C₃²	#14578912	1	2	yes	—
80	C₉	—	3	3	no	—
81	C₉	—	3	2	no	—
82	C₉	—	3	6	no	—
83	C₉	—	279	6	no	—
84	C₉	—	93	9	no	—
85	C₉	#14578902	1	3	yes	direct product factor
86	C₃	—	3	1	no	—
87	C₃	—	3	2	no	—
88	C₃	C₉×C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
89	C₃	C₃×#14578902	1	1	yes	characteristic
90	C₃	#21419391	1	2	yes	—

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₃₁⋊C₃)
commutator	C₃²×C₃₁	C₃²×C₉
Frattini	C₃³	C₃²×C₃₁⋊C₃
Fitting	C₃×C₉²×C₃₁	C₃
socle	C₃²×C₃₁	C₃×H(3,𝔽₃)
prime radical, cosocle	C₃³×C₃₁	C₃³
hypercenter	C₃×C₉²	C₃₁⋊C₃
hypocenter	C₃₁	C₉×#733
LCS	G ▷ C₃²×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
7. #14578902	C₉	direct (N × H)
38. C₉×C₃₁	#733	semidirect
61. C₃₁	C₉×#733	semidirect
85. C₉	#14578902	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×#14578902	3
C₉×#11719689	3
#21419238	3
#21419230	3
C₃×C₉²×C₃₁	3
C₉×#733	31

Subgroups — C9×#14578902 #36381141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#14578902 #36381141