Subgroups — C₉×#14578892 #36380951

Order 22599.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14578892	C₃	1	3	yes	maximal
2	#21419222	C₃	1	6	yes	maximal, complemented
3	C₉×C₃₁⋊C₂₇	C₃	1	3	yes	maximal, complemented
4	C₃×C₉²×C₃₁	C₃	1	1	yes	maximal, characteristic
5	#14578892	C₉	1	27	yes	direct product factor
6	C₃×C₃₁⋊C₂₇	C₃²	1	9	yes	—
7	C₃²×C₉×C₃₁	C₉	1	3	yes	—
8	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
9	C₉²×C₃₁	C₉	1	6	yes	—
10	C₉²×C₃₁	C₃²	1	2	yes	—
11	C₉²×C₃₁	C₃²	1	1	yes	characteristic
12	C₃³×C₃₁	C₃×C₉	1	1	yes	characteristic
13	C₃×C₉×C₃₁	—	3	9	no	—
14	C₃×C₉×C₃₁	C₃×C₉	1	6	yes	—
15	C₃×C₉×C₃₁	C₃×C₉	1	2	yes	—
16	C₃×C₉×C₃₁	C₃×C₉	1	9	yes	—
17	C₃×C₉×C₃₁	C₃×C₉	1	3	yes	—
18	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
19	C₃₁⋊C₂₇	C₃×C₉	1	27	yes	complemented
20	C₉×C₂₇⋊C₃	—	31	1	no	maximal, Sylow
21	C₃²×C₃₁	—	3	3	no	—
22	C₃²×C₃₁	C₉²	1	3	yes	—
23	C₃²×C₃₁	C₃²×C₉	1	1	yes	characteristic
24	C₉×C₃₁	—	3	6	no	—
25	C₉×C₃₁	C₉²	1	6	yes	—
26	C₉×C₃₁	C₂₇⋊C₃	1	9	yes	complemented
27	C₉×C₃₁	C₃²×C₉	1	3	yes	—
28	C₃×C₂₇⋊C₃	—	31	3	no	—
29	C₃×C₉²	C₃₁⋊C₃	1	1	yes	characteristic
30	#6864	—	31	6	no	—
31	C₉×C₂₇	—	31	3	no	—
32	C₃×C₃₁	—	3	3	no	—
33	C₃×C₃₁	C₃×C₉²	1	1	yes	characteristic
34	C₃×C₃₁	C₃×C₂₇⋊C₃	1	3	yes	—
35	C₃²×C₉	C₃₁⋊C₉	1	3	yes	—
36	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
37	C₂₇⋊C₃	—	31	27	no	—
38	C₃×C₂₇	—	31	9	no	—
39	C₉²	C₃₁⋊C₉	1	6	yes	—
40	C₉²	C₃×C₃₁⋊C₃	1	2	yes	—
41	C₉²	C₃×C₃₁⋊C₃	1	1	yes	characteristic
42	C₃₁	C₉×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
43	C₃³	C₃×C₃₁⋊C₉	1	1	yes	characteristic
44	C₃×C₉	—	3	9	no	—
45	C₃×C₉	C₉×C₃₁⋊C₃	1	9	yes	—
46	C₃×C₉	C₃×C₃₁⋊C₉	1	6	yes	—
47	C₃×C₉	C₃×C₃₁⋊C₉	1	2	yes	—
48	C₃×C₉	C₃×C₃₁⋊C₉	1	3	yes	—
49	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
50	C₂₇	—	31	27	no	—
51	C₃²	—	3	3	no	—
52	C₃²	C₉×C₃₁⋊C₉	1	3	yes	—
53	C₃²	C₃²×C₃₁⋊C₉	1	1	yes	characteristic
54	C₉	—	3	6	no	—
55	C₉	C₉×C₃₁⋊C₉	1	6	yes	—
56	C₉	#14578892	1	9	yes	direct product factor
57	C₉	C₃×C₉×C₃₁⋊C₃	1	3	yes	—
58	C₃	—	3	3	no	—
59	C₃	C₃×C₉×C₃₁⋊C₉	1	1	yes	characteristic
60	C₃	C₃×#14578892	1	3	yes	—

	subgroup	G/H
center	C₉²	C₃×C₃₁⋊C₃
commutator	C₃×C₃₁	C₃×C₉²
Frattini	C₃×C₉	C₃²×C₃₁⋊C₃
Fitting	C₃×C₉²×C₃₁	C₃
socle	C₃²×C₃₁	C₃²×C₉
prime radical	C₃³×C₃₁	C₃×C₉
cosocle	C₃×C₉×C₃₁	C₃³
hypercenter	C₃×C₉²	C₃₁⋊C₃
hypocenter	C₃₁	C₉×C₂₇⋊C₃
LCS	G ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₉² ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
2. #21419222	C₃	semidirect
3. C₉×C₃₁⋊C₂₇	C₃	semidirect
5. #14578892	C₉	direct (N × H)
19. C₃₁⋊C₂₇	C₃×C₉	semidirect
26. C₉×C₃₁	C₂₇⋊C₃	semidirect
42. C₃₁	C₉×C₂₇⋊C₃	semidirect
56. C₉	#14578892	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×#14578892	3
#21419222	3
C₉×C₃₁⋊C₂₇	3
C₃×C₉²×C₃₁	3
C₉×C₂₇⋊C₃	31

Subgroups — C9×#14578892 #36380951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#14578892 #36380951