Subgroups — #28353201

Order 13851.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095312	C₃	1	3	yes	maximal
2	C₁₉×#6887	C₃	1	1	yes	maximal, characteristic
3	#13095312	—	3	3	no	—
4	#13095312	—	3	3	no	—
5	#13095312	—	3	3	no	—
6	C₃×#10587018	C₉	1	9	yes	complemented
7	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
8	C₁₉×C₉⋊C₉	—	3	1	no	—
9	C₁₉×C₉⋊C₉	—	3	1	no	—
10	C₁₉×C₃²⋊C₉	—	3	1	no	—
11	C₉²×C₁₉	C₉	1	3	yes	—
12	#10624465	—	19	1	no	maximal, Sylow
13	C₃³×C₁₉	3₋¹⁺²	1	1	yes	characteristic
14	C₃×C₉×C₁₉	—	3	3	no	—
15	C₃×C₉×C₁₉	C₃×C₉	1	3	yes	—
16	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
17	C₃×C₉×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
18	C₃×C₉×C₁₉	3₋¹⁺²	1	3	yes	—
19	C₃×C₉×C₁₉	3₋¹⁺²	1	3	yes	—
20	C₃×C₉×C₁₉	3₋¹⁺²	1	1	yes	characteristic
21	#10587018	—	3	9	no	—
22	C₃×C₂₇⋊C₃	—	19	3	no	—
23	#6887	C₁₉⋊C₃	1	1	yes	characteristic
24	C₃²×C₁₉	—	9	1	no	—
25	C₃²×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
26	C₃²×C₁₉	C₉⋊C₉	1	3	yes	—
27	C₉×C₁₉	—	9	3	no	—
28	C₉×C₁₉	C₉²	1	1	yes	characteristic
29	C₉×C₁₉	C₃²⋊C₉	1	3	yes	—
30	C₉×C₁₉	C₉⋊C₉	1	3	yes	—
31	C₉×C₁₉	C₉⋊C₉	1	1	yes	characteristic
32	C₉×C₁₉	C₉⋊C₉	1	1	yes	characteristic
33	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
34	C₂₇⋊C₃	—	57	3	no	—
35	C₂₇⋊C₃	—	57	3	no	—
36	C₂₇⋊C₃	—	57	3	no	—
37	C₃×C₂₇	—	19	9	no	—
38	C₉⋊C₉	—	3	1	no	—
39	C₉⋊C₉	—	3	1	no	—
40	C₃²⋊C₉	—	3	1	no	—
41	C₉²	#4294	1	3	yes	—
42	C₃×C₁₉	—	3	1	no	—
43	C₃×C₁₉	—	3	3	no	—
44	C₃×C₁₉	#6855	1	1	yes	characteristic
45	C₃³	#10587025	1	1	yes	characteristic
46	C₃×C₉	—	3	3	no	—
47	C₃×C₉	C₉×C₁₉⋊C₃	1	3	yes	—
48	C₃×C₉	#10587022	1	3	yes	—
49	C₃×C₉	#10587023	1	3	yes	—
50	C₃×C₉	C₃×#4294	1	1	yes	characteristic
51	C₃×C₉	#10587025	1	1	yes	characteristic
52	C₃×C₉	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
53	C₂₇	—	57	9	no	—
54	C₁₉	#10624465	1	1	yes	characteristic, complemented, Sylow
55	C₃²	—	9	1	no	—
56	C₃²	C₃²⋊#4294	1	1	yes	characteristic
57	C₃²	#13095305	1	3	yes	—
58	C₉	—	9	3	no	—
59	C₉	C₉×#4294	1	1	yes	characteristic
60	C₉	#13095303	1	3	yes	—
61	C₉	#13095305	1	3	yes	—
62	C₉	#13095306	1	1	yes	characteristic
63	C₉	#13095307	1	1	yes	characteristic
64	C₃	—	3	1	no	—
65	C₃	—	3	3	no	—
66	C₃	#17987308	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₉×#4294
commutator	C₉×C₁₉	C₉²
Frattini	C₃²×C₉	C₃×C₁₉⋊C₃
Fitting	C₁₉×#6887	C₃
socle	C₃×C₁₉	#6855
prime radical	C₃³×C₁₉	3₋¹⁺²
cosocle	C₃²×C₉×C₁₉	C₃²
hypercenter	#6887	C₁₉⋊C₃
hypocenter	C₁₉	#10624465
LCS	G ▷ C₉×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
6. C₃×#10587018	C₉	semidirect
54. C₁₉	#10624465	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095312	3
C₁₉×#6887	3
#10624465	19