Subgroups — C₉×#13095311 #28354604

Order 13851.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095311	C₃	1	3	yes	maximal
2	C₉²×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	#17987330	C₃	1	6	yes	maximal, complemented
4	C₉×#10587018	C₃	1	2	yes	maximal, complemented
5	C₉×C₁₉×C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃×C₉×C₁₉⋊C₃	C₉	1	3	yes	—
7	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
8	#13095311	C₉	1	27	yes	direct product factor
9	C₃×#10587018	C₃²	1	6	yes	—
10	C₉×#4294	C₉	1	6	yes	—
11	C₉×#4294	C₃²	1	2	yes	—
12	C₃×C₁₉×C₂₇	C₃²	1	3	yes	—
13	C₉²×C₁₉	C₃²	1	1	yes	characteristic
14	C₉×C₂₇⋊C₃	—	19	1	no	maximal, Sylow
15	C₃²×C₁₉⋊C₃	C₃×C₉	1	1	yes	characteristic
16	C₃×C₉×C₁₉	C₃×C₉	1	3	yes	—
17	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
18	C₃×#4294	C₃×C₉	1	6	yes	—
19	C₃×#4294	C₃×C₉	1	2	yes	—
20	C₉×C₁₉⋊C₃	—	3	9	no	—
21	C₉×C₁₉⋊C₃	C₃×C₉	1	9	yes	—
22	C₁₉×C₂₇	C₃×C₉	1	9	yes	complemented
23	#10587018	C₃×C₉	1	18	yes	complemented
24	C₃×C₂₇⋊C₃	—	19	3	no	—
25	C₃×C₉²	—	19	1	no	—
26	#6864	—	19	6	no	—
27	C₉×C₂₇	—	19	2	no	—
28	C₉×C₂₇	C₁₉⋊C₃	1	1	yes	characteristic, complemented
29	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
30	C₃×C₁₉⋊C₃	—	3	3	no	—
31	C₃×C₁₉⋊C₃	C₉²	1	3	yes	—
32	C₉×C₁₉	C₂₇⋊C₃	1	9	yes	complemented
33	C₉×C₁₉	C₃²×C₉	1	3	yes	—
34	#4294	—	3	6	no	—
35	#4294	C₉²	1	6	yes	—
36	C₃²×C₉	—	19	1	no	—
37	C₃²×C₉	—	19	3	no	—
38	C₂₇⋊C₃	—	19	27	no	—
39	C₃×C₂₇	—	19	6	no	—
40	C₃×C₂₇	C₃×C₁₉⋊C₃	1	3	yes	—
41	C₉²	—	19	6	no	—
42	C₉²	—	19	2	no	—
43	C₉²	C₃×C₁₉⋊C₃	1	1	yes	characteristic
44	C₃×C₁₉	C₃×C₉²	1	1	yes	characteristic
45	C₃×C₁₉	C₃×C₂₇⋊C₃	1	3	yes	—
46	C₁₉⋊C₃	—	3	3	no	—
47	C₃³	—	19	1	no	—
48	C₃×C₉	—	19	2	no	—
49	C₃×C₉	—	19	9	no	—
50	C₃×C₉	—	19	6	no	—
51	C₃×C₉	—	57	9	no	—
52	C₃×C₉	C₉×C₁₉⋊C₃	1	3	yes	—
53	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
54	C₂₇	—	19	18	no	—
55	C₂₇	C₉×C₁₉⋊C₃	1	9	yes	complemented
56	C₁₉	C₉×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
57	C₃²	—	19	3	no	—
58	C₃²	—	57	3	no	—
59	C₃²	C₃×C₉×C₁₉⋊C₃	1	1	yes	characteristic
60	C₉	—	19	6	no	—
61	C₉	—	57	6	no	—
62	C₉	#13095311	1	9	yes	direct product factor
63	C₉	C₃×C₉×C₁₉⋊C₃	1	3	yes	—
64	C₃	—	57	3	no	—
65	C₃	C₉²×C₁₉⋊C₃	1	1	yes	characteristic
66	C₃	C₃×#13095311	1	3	yes	—

	subgroup	G/H
center	C₉²	C₃×C₁₉⋊C₃
commutator	C₃×C₁₉	C₃×C₉²
Frattini	C₃×C₉	C₃²×C₁₉⋊C₃
Fitting	C₉×C₁₉×C₂₇	C₃
socle	C₃²×C₁₉	C₃²×C₉
prime radical	C₃²×C₁₉⋊C₃	C₃×C₉
cosocle	C₃×C₉×C₁₉	C₃³
hypercenter	C₉×C₂₇	C₁₉⋊C₃
hypocenter	C₁₉	C₉×C₂₇⋊C₃
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₉² ◁ C₉×C₂₇

Complements

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

N	H ≅ G/N	type
3. #17987330	C₃	semidirect
4. C₉×#10587018	C₃	semidirect
5. C₉×C₁₉×C₂₇	C₃	semidirect
8. #13095311	C₉	direct (N × H)
22. C₁₉×C₂₇	C₃×C₉	semidirect
23. #10587018	C₃×C₉	semidirect
28. C₉×C₂₇	C₁₉⋊C₃	semidirect
32. C₉×C₁₉	C₂₇⋊C₃	semidirect
55. C₂₇	C₉×C₁₉⋊C₃	semidirect
56. C₁₉	C₉×C₂₇⋊C₃	semidirect
62. C₉	#13095311	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×#13095311	3
C₉²×C₁₉⋊C₃	3
#17987330	3
C₉×#10587018	3
C₉×C₁₉×C₂₇	3
C₉×C₂₇⋊C₃	19

Subgroups — C9×#13095311 #28354604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#13095311 #28354604