Subgroups — #28356614

Order 13851.

936 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987547	C₃	1	2	yes	maximal
2	C₃×#13095331	C₃	1	1	yes	maximal, characteristic
3	#17987518	C₃	1	24	yes	maximal, complemented
4	C₃×#13095321	C₃	1	12	yes	maximal, complemented
5	C₁₉×3₋¹⁺⁴	C₃	1	1	yes	maximal, characteristic
6	#13095331	—	3	9	no	—
7	#13095331	—	3	18	no	—
8	C₃×#10587025	C₃²	1	24	yes	—
9	C₃×#10587025	C₃²	1	8	yes	—
10	C₃²×#4294	C₃²	1	4	yes	—
11	#13095321	C₃²	1	9	yes	—
12	#13095321	C₃²	1	72	yes	—
13	C₁₉×#737	—	3	9	no	—
14	C₃×C₁₉×3₋¹⁺²	C₃²	1	12	yes	—
15	C₃×C₁₉×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
16	#10624933	—	19	1	no	maximal, Sylow
17	C₃³×C₁₉	C₃³	1	4	yes	—
18	C₁₉×3₋¹⁺²	—	3	24	no	—
19	C₁₉×3₋¹⁺²	C₃³	1	9	yes	—
20	C₁₉×H(3,𝔽₃)	H(3,𝔽₃)	1	9	yes	—
21	C₃×C₉×C₁₉	—	3	12	no	—
22	#10587025	—	3	48	no	—
23	#10587025	—	3	24	no	—
24	#10587025	C₃³	1	18	yes	—
25	C₃×#4294	—	3	12	no	—
26	C₃×#4294	—	3	24	no	—
27	C₃×#4294	C₃³	1	1	yes	characteristic
28	C₃×#4294	C₃³	1	8	yes	—
29	3₋¹⁺⁴	—	19	2	no	—
30	3₋¹⁺⁴	C₁₉⋊C₃	1	1	yes	characteristic
31	C₃×#737	—	19	1	no	—
32	#6912	—	19	24	no	—
33	C₃×#733	—	19	12	no	—
34	C₃²×C₁₉	—	9	4	no	—
35	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	12	yes	—
36	C₃²×C₁₉	C₃⁴	1	1	yes	characteristic
37	C₉×C₁₉	—	3	9	no	—
38	#4294	—	3	1	no	—
39	#4294	—	3	18	no	—
40	#4294	—	3	8	no	—
41	#737	—	3	9	no	—
42	#737	—	57	9	no	—
43	#737	—	57	18	no	—
44	C₃×3₋¹⁺²	—	19	8	no	—
45	C₃×3₋¹⁺²	—	19	24	no	—
46	C₃×3₋¹⁺²	C₃×C₁₉⋊C₃	1	12	yes	—
47	C₃×H(3,𝔽₃)	C₃×C₁₉⋊C₃	1	1	yes	characteristic
48	C₃²×C₉	—	19	4	no	—
49	#733	—	19	72	no	—
50	#733	—	19	9	no	—
51	C₃×C₁₉	—	3	1	no	—
52	C₃×C₁₉	—	3	12	no	—
53	C₃×C₁₉	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
54	C₃³	C₃²×C₁₉⋊C₃	1	4	yes	—
55	3₋¹⁺²	—	3	24	no	—
56	3₋¹⁺²	—	19	18	no	—
57	3₋¹⁺²	—	57	24	no	—
58	3₋¹⁺²	—	57	48	no	—
59	3₋¹⁺²	C₃²×C₁₉⋊C₃	1	9	yes	—
60	H(3,𝔽₃)	C₃²⋊(C₁₉⋊C₃)	1	9	yes	—
61	C₃×C₉	—	3	12	no	—
62	C₃×C₉	—	19	1	no	—
63	C₃×C₉	—	19	8	no	—
64	C₃×C₉	—	57	12	no	—
65	C₃×C₉	—	57	24	no	—
66	C₁₉	#10624933	1	1	yes	characteristic, complemented, Sylow
67	C₃²	—	9	4	no	—
68	C₃²	C₃×C₃²⋊(C₁₉⋊C₃)	1	12	yes	—
69	C₃²	C₃³×C₁₉⋊C₃	1	1	yes	characteristic
70	C₉	—	3	9	no	—
71	C₉	—	57	1	no	—
72	C₉	—	57	8	no	—
73	C₉	—	57	18	no	—
74	C₃	—	3	1	no	—
75	C₃	—	3	12	no	—
76	C₃	C₃²×C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃²×C₃²⋊(C₁₉⋊C₃)
commutator, cosocle	C₃²×C₁₉	C₃⁴
Frattini	C₃²	C₃³×C₁₉⋊C₃
Fitting	C₁₉×3₋¹⁺⁴	C₃
socle	C₃×C₁₉	C₃²×H(3,𝔽₃)
prime radical	C₃×C₁₉×H(3,𝔽₃)	C₃²
hypercenter	3₋¹⁺⁴	C₁₉⋊C₃
hypocenter	C₁₉	#10624933
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃×H(3,𝔽₃) ◁ 3₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
3. #17987518	C₃	semidirect
4. C₃×#13095321	C₃	semidirect
66. C₁₉	#10624933	semidirect

Maximal subgroups

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

subgroup	index
#17987547	3
C₃×#13095331	3
#17987518	3
C₃×#13095321	3
C₁₉×3₋¹⁺⁴	3
#10624933	19