Subgroups — #28356732

Order 13851.

174 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987589	C₃	1	3	yes	maximal
2	#17987403	C₃	1	1	yes	maximal, characteristic
3	#13095339	C₉	1	9	yes	complemented
4	#13095338	—	3	3	no	—
5	C₃²⋊#4296	—	3	3	no	—
6	C₉×#4296	—	3	3	no	—
7	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
8	#13095305	—	3	2	no	—
9	#13095303	—	3	1	no	—
10	C₉×#4294	C₉	1	2	yes	complemented
11	C₉²×C₁₉	C₉	1	1	yes	characteristic, complemented
12	#10624470	—	19	1	no	maximal, Sylow
13	C₃²×C₁₉⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
14	C₃×#4296	—	3	9	no	—
15	C₃×C₉×C₁₉	—	3	1	no	—
16	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
17	C₃×#4294	—	3	2	no	—
18	C₃×#4294	3₋¹⁺²	1	2	yes	—
19	C₉×C₁₉⋊C₃	C₃×C₉	1	3	yes	—
20	C₉×C₁₉⋊C₃	3₋¹⁺²	1	3	yes	—
21	C₉×C₁₉⋊C₃	3₋¹⁺²	1	3	yes	—
22	#6887	—	19	1	no	—
23	#6887	—	19	3	no	—
24	C₃²×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
25	C₃×C₁₉⋊C₃	—	9	1	no	—
26	C₃×C₁₉⋊C₃	C₃²⋊C₉	1	3	yes	—
27	#4296	—	9	9	no	—
28	C₉×C₁₉	—	9	1	no	—
29	C₉×C₁₉	C₉²	1	1	yes	characteristic
30	C₉×C₁₉	C₉⋊C₉	1	1	yes	characteristic
31	C₉×C₁₉	C₉⋊C₉	1	1	yes	characteristic
32	#4294	—	9	2	no	—
33	#4294	C₉⋊C₉	1	6	yes	—
34	C₃²×C₉	—	19	1	no	—
35	C₉⋊C₉	—	19	9	no	—
36	C₉⋊C₉	—	57	2	no	—
37	C₉⋊C₉	—	57	3	no	—
38	C₃²⋊C₉	—	57	1	no	—
39	C₃²⋊C₉	—	57	3	no	—
40	C₉²	—	19	2	no	—
41	C₉²	—	57	3	no	—
42	C₉²	#4296	1	1	yes	characteristic, complemented
43	C₃×C₁₉	—	3	1	no	—
44	C₃×C₁₉	#6855	1	1	yes	characteristic
45	C₁₉⋊C₃	—	3	3	no	—
46	C₃³	—	19	1	no	—
47	C₃×C₉	—	3	1	no	—
48	C₃×C₉	—	19	2	no	—
49	C₃×C₉	—	19	3	no	—
50	C₃×C₉	—	19	3	no	—
51	C₃×C₉	—	19	3	no	—
52	C₃×C₉	—	57	9	no	—
53	C₃×C₉	—	57	2	no	—
54	C₃×C₉	C₃×#4296	1	1	yes	characteristic
55	C₁₉	#10624470	1	1	yes	characteristic, complemented, Sylow
56	C₃²	—	19	3	no	—
57	C₃²	—	171	1	no	—
58	C₃²	C₃²⋊#4296	1	1	yes	characteristic
59	C₉	—	9	1	no	—
60	C₉	—	19	6	no	—
61	C₉	—	171	2	no	—
62	C₉	—	171	9	no	—
63	C₉	C₉×#4296	1	1	yes	characteristic
64	C₉	#13095338	1	1	yes	characteristic
65	C₉	#13095339	1	1	yes	characteristic
66	C₃	—	3	1	no	—
67	C₃	—	57	3	no	—
68	C₃	(C₃×#4296)⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₉	#13095339
commutator	C₉×C₁₉	C₉²
Frattini	C₃×C₉	C₃×#4296
Fitting	C₉²×C₁₉	C₉
socle	C₃×C₁₉	#6855
prime radical	C₃²×C₁₉⋊C₃	H(3,𝔽₃)
cosocle	C₃×C₉×C₁₉⋊C₃	C₃²
hypercenter	C₉²	#4296
hypocenter	C₁₉	#10624470
LCS	G ▷ C₉×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₉ ◁ C₃×C₉ ◁ C₉²

Complements

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

N	H ≅ G/N	type
3. #13095339	C₉	semidirect
10. C₉×#4294	C₉	semidirect
11. C₉²×C₁₉	C₉	semidirect
42. C₉²	#4296	semidirect
55. C₁₉	#10624470	semidirect

Maximal subgroups

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

subgroup	index
#17987589	3
#17987403	3
#10624470	19