Subgroups — #28353249

Order 13851.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095322	C₃	1	1	yes	maximal, characteristic
2	#17987337	C₃	1	2	yes	maximal
3	C₃×C₁₉×#733	C₃	1	1	yes	maximal, characteristic
4	C₃×#10587025	—	3	1	no	—
5	#13095322	—	3	3	no	—
6	C₃²⋊#4294	—	3	2	no	—
7	C₃×C₁₉×3₋¹⁺²	—	3	1	no	—
8	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
9	C₁₉×#733	—	3	3	no	—
10	#10624479	—	19	1	no	maximal, Sylow
11	C₃³×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
12	C₁₉×3₋¹⁺²	—	3	3	no	—
13	C₁₉×3₋¹⁺²	—	9	2	no	—
14	C₃×C₉×C₁₉	—	3	1	no	—
15	C₃×C₉×C₁₉	—	3	1	no	—
16	C₃×C₉×C₁₉	—	3	2	no	—
17	C₃×C₉×C₁₉	—	9	1	no	—
18	#10587025	—	3	3	no	—
19	#10587025	—	9	2	no	—
20	C₃×#4294	—	9	1	no	—
21	C₃×#4294	—	9	2	no	—
22	C₃×#733	—	19	1	no	—
23	C₃×#733	C₁₉⋊C₃	1	1	yes	characteristic
24	#6867	—	19	2	no	—
25	C₃²×C₁₉	—	9	1	no	—
26	C₃²×C₁₉	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
27	C₃²×C₁₉	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
28	C₃²×C₁₉	#732	1	2	yes	—
29	C₉×C₁₉	—	9	1	no	—
30	C₉×C₁₉	—	9	3	no	—
31	#4294	—	9	3	no	—
32	#4294	—	27	2	no	—
33	C₃×3₋¹⁺²	—	3	1	no	—
34	C₃×3₋¹⁺²	—	57	1	no	—
35	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
36	#733	—	3	3	no	—
37	#733	—	57	3	no	—
38	C₃²⋊C₉	—	57	2	no	—
39	C₃×C₁₉	—	3	2	no	—
40	C₃×C₁₉	—	3	1	no	—
41	C₃×C₁₉	—	3	1	no	—
42	C₃×C₁₉	#6856	1	1	yes	characteristic
43	C₃³	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
44	3₋¹⁺²	—	3	3	no	—
45	3₋¹⁺²	—	9	2	no	—
46	3₋¹⁺²	—	57	3	no	—
47	3₋¹⁺²	—	171	2	no	—
48	C₃×C₉	—	3	1	no	—
49	C₃×C₉	—	3	1	no	—
50	C₃×C₉	—	3	2	no	—
51	C₃×C₉	—	9	1	no	—
52	C₃×C₉	—	171	2	no	—
53	C₃×C₉	—	171	1	no	—
54	C₁₉	#10624479	1	1	yes	characteristic, complemented, Sylow
55	C₃²	—	9	1	no	—
56	C₃²	#13095313	1	1	yes	characteristic
57	C₃²	#13095314	1	1	yes	characteristic
58	C₃²	#13095319	1	2	yes	—
59	C₉	—	513	2	no	—
60	C₉	—	9	1	no	—
61	C₉	—	9	3	no	—
62	C₉	—	171	3	no	—
63	C₃	—	3	2	no	—
64	C₃	—	3	1	no	—
65	C₃	—	3	1	no	—
66	C₃	#17987309	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#17987309
commutator, cosocle	C₃²×C₉×C₁₉	C₃²
Frattini	C₃²×C₉	C₃×C₁₉⋊C₃
Fitting	C₃×C₁₉×#733	C₃
socle	C₃×C₁₉	#6856
prime radical	C₃³×C₁₉	H(3,𝔽₃)
hypercenter	C₃×#733	C₁₉⋊C₃
hypocenter	C₁₉	#10624479
LCS	G ▷ C₃²×C₉×C₁₉ ▷ C₃³×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ C₃×#733

Complements

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

N	H ≅ G/N	type
54. C₁₉	#10624479	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
#17987337	3
C₃×C₁₉×#733	3
#10624479	19