Subgroups — #28354613

Order 13851.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095312	C₃	1	1	yes	maximal, characteristic
2	C₃²×#10587018	C₃	1	1	yes	maximal, characteristic
3	#17987405	C₃	1	1	yes	maximal, characteristic
4	#17987330	C₃	1	3	yes	maximal, complemented
5	#17987329	C₃	1	3	yes	maximal, complemented
6	C₂₇×#4294	C₃	1	3	yes	maximal, complemented
7	C₃×C₁₉×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
8	#13095312	C₉	1	9	yes	complemented
9	C₃×#10587018	C₉	1	9	yes	complemented
10	C₃×#10587018	C₃²	1	1	yes	characteristic
11	C₃×#10587018	C₃²	1	3	yes	—
12	C₃×#10587018	C₃²	1	1	yes	characteristic
13	C₃×#10587018	C₃²	1	1	yes	characteristic
14	#13095307	C₉	1	3	yes	—
15	#13095306	C₉	1	3	yes	—
16	C₃²⋊#4294	C₉	1	3	yes	—
17	C₉×#4294	C₃²	1	3	yes	—
18	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
19	C₁₉×C₂₇⋊C₃	C₉	1	9	yes	complemented
20	C₃×C₁₉×C₂₇	C₃²	1	3	yes	—
21	#10624681	—	19	1	no	maximal, Sylow
22	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
23	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
24	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
25	C₃×C₉×C₁₉	C₃×C₉	1	3	yes	—
26	C₃×C₉×C₁₉	C₃×C₉	1	3	yes	—
27	C₃×C₉×C₁₉	C₃×C₉	1	3	yes	—
28	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
29	C₃×#4294	C₃×C₉	1	9	yes	—
30	C₁₉×C₂₇	C₃×C₉	1	9	yes	—
31	#10587018	C₃×C₉	1	3	yes	—
32	#10587018	C₃×C₉	1	3	yes	—
33	#10587018	C₃×C₉	1	3	yes	—
34	#10587018	C₃×C₉	1	9	yes	—
35	C₃×C₂₇⋊C₃	—	19	1	no	—
36	C₃×C₂₇⋊C₃	C₁₉⋊C₃	1	1	yes	characteristic
37	C₃²×C₂₇	—	19	1	no	—
38	#6887	—	19	1	no	—
39	#6864	—	19	3	no	—
40	#6864	—	19	3	no	—
41	C₉×C₂₇	—	19	3	no	—
42	C₃²×C₁₉	—	3	3	no	—
43	C₃²×C₁₉	C₉²	1	3	yes	—
44	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
45	C₉×C₁₉	C₉²	1	3	yes	—
46	C₉×C₁₉	C₉²	1	3	yes	—
47	C₉×C₁₉	C₃²×C₉	1	1	yes	characteristic
48	C₉×C₁₉	C₃²×C₉	1	1	yes	characteristic
49	C₉×C₁₉	C₃²×C₉	1	1	yes	characteristic
50	#4294	—	3	9	no	—
51	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
52	C₂₇⋊C₃	—	19	9	no	—
53	C₂₇⋊C₃	#4294	1	9	yes	complemented
54	C₃×C₂₇	—	19	9	no	—
55	C₃×C₂₇	—	19	1	no	—
56	C₃×C₂₇	—	19	3	no	—
57	C₃×C₂₇	—	19	1	no	—
58	C₃×C₂₇	—	19	1	no	—
59	C₃×C₂₇	C₃×C₁₉⋊C₃	1	3	yes	—
60	C₉⋊C₉	—	19	3	no	—
61	C₉⋊C₉	—	19	3	no	—
62	C₃²⋊C₉	—	19	3	no	—
63	C₉²	—	19	3	no	—
64	C₃×C₁₉	—	3	3	no	—
65	C₃×C₁₉	C₃×C₉²	1	1	yes	characteristic
66	C₃×C₁₉	#6903	1	3	yes	—
67	C₃³	C₉×C₁₉⋊C₃	1	1	yes	characteristic
68	C₃×C₉	—	19	9	no	—
69	C₃×C₉	C₉×C₁₉⋊C₃	1	1	yes	characteristic
70	C₃×C₉	C₉×C₁₉⋊C₃	1	1	yes	characteristic
71	C₃×C₉	C₉×C₁₉⋊C₃	1	3	yes	—
72	C₃×C₉	C₉×C₁₉⋊C₃	1	3	yes	—
73	C₃×C₉	C₃×#4294	1	3	yes	—
74	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
75	C₂₇	—	19	3	no	—
76	C₂₇	—	19	3	no	—
77	C₂₇	—	19	3	no	—
78	C₂₇	—	19	9	no	—
79	C₂₇	C₃×#4294	1	9	yes	—
80	C₁₉	#10624681	1	1	yes	characteristic, complemented, Sylow
81	C₃²	—	3	3	no	—
82	C₃²	C₉×#4294	1	3	yes	—
83	C₃²	C₃×C₉×C₁₉⋊C₃	1	1	yes	characteristic
84	C₉	—	57	9	no	—
85	C₉	C₉×#4294	1	3	yes	—
86	C₉	C₉×#4294	1	3	yes	—
87	C₉	C₃×C₉×C₁₉⋊C₃	1	1	yes	characteristic
88	C₉	C₃×C₉×C₁₉⋊C₃	1	1	yes	characteristic
89	C₉	C₃²×#4294	1	1	yes	characteristic
90	C₃	—	3	3	no	—
91	C₃	C₃×C₉×#4294	1	1	yes	characteristic
92	C₃	#17987481	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃×C₉	C₃²×C₁₉⋊C₃
commutator	C₃×C₁₉	C₃×C₉²
Fitting	C₃×C₁₉×C₂₇⋊C₃	C₃
socle	C₃²×C₁₉	C₃²×C₉
prime radical	C₃³×C₁₉	C₃×C₉
cosocle	C₃×C₉×C₁₉	C₃³
hypercenter	C₃×C₂₇⋊C₃	C₁₉⋊C₃
hypocenter	C₁₉	#10624681
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃×C₉ ◁ C₃×C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
4. #17987330	C₃	semidirect
5. #17987329	C₃	semidirect
6. C₂₇×#4294	C₃	semidirect
8. #13095312	C₉	semidirect
9. C₃×#10587018	C₉	semidirect
19. C₁₉×C₂₇⋊C₃	C₉	semidirect
53. C₂₇⋊C₃	#4294	semidirect
80. C₁₉	#10624681	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095312	3
C₃²×#10587018	3
#17987405	3
#17987330	3
#17987329	3
C₂₇×#4294	3
C₃×C₁₉×C₂₇⋊C₃	3
#10624681	19