Subgroups — #28355757

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	#17987377	C₃	1	9	yes	maximal, complemented
3	C₁₉×#6887	C₃	1	1	yes	maximal, characteristic
4	C₃×#10587025	—	3	3	no	—
5	#13095322	—	3	6	no	—
6	#13095322	C₃²	1	9	yes	—
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	C₃²	1	3	yes	—
11	#10624840	—	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	—	3	3	no	—
15	C₃×C₉×C₁₉	H(3,𝔽₃)	1	2	yes	—
16	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
17	#10587025	—	3	9	no	—
18	#10587025	—	9	6	no	—
19	C₃×#4294	—	9	3	no	—
20	C₃×#733	—	19	3	no	—
21	#6887	C₁₉⋊C₃	1	1	yes	characteristic
22	#6880	—	19	9	no	—
23	C₃²×C₁₉	—	9	1	no	—
24	C₃²×C₁₉	#732	1	3	yes	—
25	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
26	C₉×C₁₉	—	3	2	no	—
27	C₉×C₁₉	—	3	1	no	—
28	C₉×C₁₉	—	9	3	no	—
29	#4294	—	9	9	no	—
30	C₃×3₋¹⁺²	—	57	3	no	—
31	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
32	#733	—	19	9	no	—
33	#733	—	57	6	no	—
34	C₉⋊C₉	—	3	2	no	—
35	C₃²⋊C₉	—	3	1	no	—
36	C₉²	C₃×C₁₉⋊C₃	1	3	yes	—
37	C₃×C₁₉	—	3	1	no	—
38	C₃×C₁₉	—	3	3	no	—
39	C₃×C₁₉	C₃×#732	1	1	yes	characteristic
40	C₃³	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
41	3₋¹⁺²	—	57	9	no	—
42	3₋¹⁺²	—	171	6	no	—
43	C₃×C₉	—	3	3	no	—
44	C₃×C₉	—	3	3	no	—
45	C₃×C₉	—	171	3	no	—
46	C₃×C₉	C₃²⋊(C₁₉⋊C₃)	1	2	yes	—
47	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
48	C₁₉	#10624840	1	1	yes	characteristic, complemented, Sylow
49	C₃²	—	9	1	no	—
50	C₃²	#13095320	1	3	yes	—
51	C₃²	C₃×C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
52	C₉	—	3	2	no	—
53	C₉	—	3	1	no	—
54	C₉	—	9	3	no	—
55	C₉	—	171	9	no	—
56	C₃	—	3	1	no	—
57	C₃	—	3	3	no	—
58	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	#10624840
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. #17987377	C₃	semidirect
48. C₁₉	#10624840	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
#17987377	3
C₁₉×#6887	3
#10624840	19