Subgroups — C₉×#14578887 #36379844

Order 22599.

482 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×C₉×C₃₁⋊C₉	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	C₉	1	27	yes	direct product factor
7	C₉×C₃₁⋊C₉	—	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	9	yes	—
16	C₃×C₉×C₃₁	C₃×C₉	1	3	yes	—
17	C₃×C₉×C₃₁	C₃×C₉	1	3	yes	—
18	C₃×C₉×C₃₁	3₋¹⁺²	1	9	yes	—
19	C₃×C₃₁⋊C₉	—	3	9	no	—
20	C₃×C₃₁⋊C₉	—	3	18	no	—
21	C₃×C₃₁⋊C₉	C₃×C₉	1	27	yes	—
22	C₉×C₉⋊C₉	—	31	1	no	maximal, Sylow
23	C₃²×C₃₁	C₃²×C₉	1	3	yes	—
24	C₃²×C₃₁	C₃²×C₉	1	1	yes	characteristic
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	C₉²	1	9	yes	complemented
29	C₉×C₃₁	C₉⋊C₉	1	9	yes	complemented
30	C₃₁⋊C₉	—	3	27	no	—
31	C₃×C₉⋊C₉	—	31	3	no	—
32	C₃×C₉²	—	31	3	no	—
33	C₃×C₉²	C₃₁⋊C₃	1	1	yes	characteristic
34	#6855	—	31	6	no	—
35	C₃×C₃₁	C₃×C₉²	1	1	yes	characteristic
36	C₃×C₃₁	C₃×C₉⋊C₉	1	1	yes	characteristic
37	C₃×C₃₁	#6887	1	2	yes	—
38	C₃×C₃₁	C₉×3₋¹⁺²	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	—	31	27	no	—
44	C₉²	—	93	9	no	—
45	C₉²	C₃₁⋊C₉	1	9	yes	complemented
46	C₃₁	C₉×C₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
47	C₃³	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
48	C₃×C₉	—	3	6	no	—
49	C₃×C₉	—	31	27	no	—
50	C₃×C₉	—	93	9	no	—
51	C₃×C₉	—	93	18	no	—
52	C₃×C₉	C₉×C₃₁⋊C₃	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	C₃×C₉×C₃₁⋊C₃	1	3	yes	—
58	C₃²	C₃²×C₃₁⋊C₉	1	1	yes	characteristic
59	C₃²	C₃×#11719687	1	3	yes	—
60	C₃²	#14578912	1	6	yes	—
61	C₉	—	3	6	no	—
62	C₉	—	93	27	no	—
63	C₉	C₉×C₃₁⋊C₉	1	9	yes	complemented
64	C₉	#14578887	1	9	yes	direct product factor
65	C₃	C₃×C₉×C₃₁⋊C₉	1	1	yes	characteristic
66	C₃	C₃×#14578887	1	1	yes	characteristic
67	C₃	#21419296	1	2	yes	—
68	C₃	C₉×#11719687	1	9	yes	—

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

Complements

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

N	H ≅ G/N	type
6. #14578887	C₉	direct (N × H)
11. C₉²×C₃₁	C₉	semidirect
28. C₉×C₃₁	C₉²	semidirect
29. C₉×C₃₁	C₉⋊C₉	semidirect
45. C₉²	C₃₁⋊C₉	semidirect
46. C₃₁	C₉×C₉⋊C₉	semidirect
63. C₉	C₉×C₃₁⋊C₉	semidirect
64. C₉	#14578887	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×#14578887	3
C₃×C₉×C₃₁⋊C₉	3
C₃₁⋊#6855	3
C₃×C₉²×C₃₁	3
C₉×C₉⋊C₉	31

Subgroups — C9×#14578887 #36379844

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#14578887 #36379844