Subgroups — #28355799

Order 13851.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095322	C₃	1	3	yes	maximal
2	#17987385	C₃	1	9	yes	maximal, complemented
3	C₁₉×#6887	C₃	1	1	yes	maximal, characteristic
4	C₃×#10587025	—	3	3	no	—
5	#13095322	—	3	3	no	—
6	#13095322	—	3	3	no	—
7	#13095322	C₃²	1	9	yes	—
8	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
9	C₁₉×C₉⋊C₉	—	3	1	no	—
10	C₁₉×C₉⋊C₉	C₃²	1	3	yes	—
11	C₁₉×C₃²⋊C₉	—	3	1	no	—
12	C₉²×C₁₉	—	3	1	no	—
13	#10624847	—	19	1	no	maximal, Sylow
14	C₃³×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
15	C₃×C₉×C₁₉	—	3	3	no	—
16	C₃×C₉×C₁₉	—	3	3	no	—
17	C₃×C₉×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
18	C₃×C₉×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
19	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
20	#10587025	—	3	9	no	—
21	#10587025	—	9	6	no	—
22	C₃×#4294	—	9	3	no	—
23	C₃×#733	—	19	3	no	—
24	#6887	C₁₉⋊C₃	1	1	yes	characteristic
25	#6882	—	19	9	no	—
26	C₃²×C₁₉	—	9	1	no	—
27	C₃²×C₁₉	#732	1	3	yes	—
28	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
29	C₉×C₁₉	—	3	1	no	—
30	C₉×C₁₉	—	3	1	no	—
31	C₉×C₁₉	—	3	1	no	—
32	C₉×C₁₉	—	9	3	no	—
33	#4294	—	9	9	no	—
34	C₃×3₋¹⁺²	—	57	3	no	—
35	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
36	#733	—	19	9	no	—
37	#733	—	57	3	no	—
38	#733	—	57	3	no	—
39	C₉⋊C₉	—	3	1	no	—
40	C₉⋊C₉	C₃×C₁₉⋊C₃	1	3	yes	—
41	C₃²⋊C₉	—	3	1	no	—
42	C₉²	—	3	1	no	—
43	C₃×C₁₉	—	3	1	no	—
44	C₃×C₁₉	—	3	3	no	—
45	C₃×C₁₉	C₃×#732	1	1	yes	characteristic
46	C₃³	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
47	3₋¹⁺²	—	57	9	no	—
48	3₋¹⁺²	—	171	6	no	—
49	C₃×C₉	—	3	3	no	—
50	C₃×C₉	—	3	3	no	—
51	C₃×C₉	—	171	3	no	—
52	C₃×C₉	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
53	C₃×C₉	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
54	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
55	C₁₉	#10624847	1	1	yes	characteristic, complemented, Sylow
56	C₃²	—	9	1	no	—
57	C₃²	#13095320	1	3	yes	—
58	C₃²	C₃×C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
59	C₉	—	3	1	no	—
60	C₉	—	3	1	no	—
61	C₉	—	3	1	no	—
62	C₉	—	9	3	no	—
63	C₉	—	171	9	no	—
64	C₃	—	3	1	no	—
65	C₃	—	3	3	no	—
66	C₃	C₃×#13095320	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×#13095320
commutator, cosocle	C₃×C₉×C₁₉	C₃³
Frattini	C₃×C₉	C₃²×C₁₉⋊C₃
Fitting	C₁₉×#6887	C₃
socle	C₃×C₁₉	C₃×#732
prime radical	C₃³×C₁₉	H(3,𝔽₃)
hypercenter	#6887	C₁₉⋊C₃
hypocenter	C₁₉	#10624847
LCS	G ▷ C₃×C₉×C₁₉ ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
2. #17987385	C₃	semidirect
55. C₁₉	#10624847	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095322	3
#17987385	3
C₁₉×#6887	3
#10624847	19