Subgroups — #28353214

Order 13851.

174 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987405	C₃	1	3	yes	maximal
2	C₁₉×#6887	C₃	1	1	yes	maximal, characteristic
3	#13095307	—	3	3	no	—
4	#13095306	C₉	1	9	yes	complemented
5	C₃²⋊#4294	—	3	3	no	—
6	C₉×#4294	—	3	3	no	—
7	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
8	C₁₉×C₉⋊C₉	—	3	2	no	—
9	C₁₉×C₃²⋊C₉	—	3	1	no	—
10	C₉²×C₁₉	C₉	1	3	yes	complemented
11	#10624470	—	19	1	no	maximal, Sylow
12	C₃³×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃×C₉×C₁₉	—	3	3	no	—
14	C₃×C₉×C₁₉	C₃×C₉	1	3	yes	—
15	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
16	C₃×C₉×C₁₉	3₋¹⁺²	1	3	yes	—
17	C₃×C₉×C₁₉	3₋¹⁺²	1	3	yes	—
18	C₃×C₉×C₁₉	3₋¹⁺²	1	2	yes	—
19	C₃×#4294	—	3	9	no	—
20	#6887	—	19	3	no	—
21	#6887	C₁₉⋊C₃	1	1	yes	characteristic
22	C₃²×C₁₉	—	9	1	no	—
23	C₃²×C₁₉	C₃²⋊C₉	1	3	yes	—
24	C₃²×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
25	C₉×C₁₉	—	9	3	no	—
26	C₉×C₁₉	C₉²	1	1	yes	characteristic
27	C₉×C₁₉	C₉⋊C₉	1	6	yes	—
28	C₉×C₁₉	C₉⋊C₉	1	1	yes	characteristic
29	C₉×C₁₉	C₉⋊C₉	1	1	yes	characteristic
30	#4294	—	9	9	no	—
31	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
32	C₉⋊C₉	—	3	2	no	—
33	C₉⋊C₉	—	19	9	no	—
34	C₉⋊C₉	—	57	3	no	—
35	C₃²⋊C₉	—	3	1	no	—
36	C₃²⋊C₉	—	57	3	no	—
37	C₉²	—	57	3	no	—
38	C₉²	#4294	1	3	yes	complemented
39	C₃×C₁₉	—	3	3	no	—
40	C₃×C₁₉	—	3	1	no	—
41	C₃×C₁₉	#6855	1	1	yes	characteristic
42	C₃³	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
43	C₃×C₉	—	3	3	no	—
44	C₃×C₉	—	57	9	no	—
45	C₃×C₉	C₉×C₁₉⋊C₃	1	3	yes	—
46	C₃×C₉	#10587022	1	3	yes	—
47	C₃×C₉	#10587023	1	3	yes	—
48	C₃×C₉	C₃×#4294	1	1	yes	characteristic
49	C₃×C₉	#10587025	1	2	yes	—
50	C₁₉	#10624470	1	1	yes	characteristic, complemented, Sylow
51	C₃²	—	9	1	no	—
52	C₃²	#13095303	1	3	yes	—
53	C₃²	C₃²⋊#4294	1	1	yes	characteristic
54	C₉	—	9	3	no	—
55	C₉	—	171	9	no	—
56	C₉	C₉×#4294	1	1	yes	characteristic
57	C₉	#13095305	1	6	yes	—
58	C₉	#13095306	1	1	yes	characteristic
59	C₉	#13095307	1	1	yes	characteristic
60	C₃	—	3	1	no	—
61	C₃	—	3	3	no	—
62	C₃	#17987308	1	1	yes	characteristic

	subgroup	G/H
center	C₉	#13095306
commutator	C₉×C₁₉	C₉²
Frattini	C₃²×C₉	C₃×C₁₉⋊C₃
Fitting	C₁₉×#6887	C₃
socle	C₃×C₁₉	#6855
prime radical	C₃³×C₁₉	H(3,𝔽₃)
cosocle	C₃²×C₉×C₁₉	C₃²
hypercenter	#6887	C₁₉⋊C₃
hypocenter	C₁₉	#10624470
LCS	G ▷ C₉×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₉ ◁ C₃²×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
4. #13095306	C₉	semidirect
10. C₉²×C₁₉	C₉	semidirect
38. C₉²	#4294	semidirect
50. C₁₉	#10624470	semidirect

Maximal subgroups

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

subgroup	index
#17987405	3
C₁₉×#6887	3
#10624470	19