Subgroups — #28353726

Order 13851.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#10587025	C₃	1	3	yes	maximal
2	#17987325	C₃	1	3	yes	maximal
3	#17987322	C₃	1	3	yes	maximal
4	#17987316	C₃	1	3	yes	maximal
5	C₁₉×#6887	C₃	1	1	yes	maximal, characteristic
6	C₃×#10587025	C₃²	1	3	yes	—
7	#13095305	—	3	6	no	—
8	C₃²⋊#4294	C₃²	1	3	yes	—
9	C₃²⋊#4294	C₃²	1	3	yes	—
10	C₉×#4294	—	3	3	no	—
11	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
12	C₁₉×C₉⋊C₉	—	3	2	no	—
13	C₁₉×C₃²⋊C₉	C₃²	1	3	yes	—
14	C₉²×C₁₉	—	3	1	no	—
15	#10624588	—	19	1	no	maximal, Sylow
16	C₃³×C₁₉	C₃³	1	1	yes	characteristic
17	C₃×C₉×C₁₉	—	3	3	no	—
18	C₃×C₉×C₁₉	—	3	3	no	—
19	C₃×C₉×C₁₉	H(3,𝔽₃)	1	2	yes	—
20	C₃×C₉×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
21	#10587025	—	3	9	no	—
22	C₃×#4294	—	3	3	no	—
23	C₃×#4294	—	3	3	no	—
24	C₃×#4294	—	3	3	no	—
25	C₉×3₋¹⁺²	—	19	3	no	—
26	#6887	C₁₉⋊C₃	1	1	yes	characteristic
27	#6861	—	19	3	no	—
28	#6860	—	19	3	no	—
29	#6858	—	19	3	no	—
30	C₃²×C₁₉	—	3	1	no	—
31	C₃²×C₁₉	—	3	3	no	—
32	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
33	C₉×C₁₉	—	3	2	no	—
34	C₉×C₁₉	—	9	3	no	—
35	C₉×C₁₉	#733	1	3	yes	—
36	#4294	—	3	9	no	—
37	#4294	—	9	3	no	—
38	#4294	—	9	3	no	—
39	C₃×3₋¹⁺²	—	19	3	no	—
40	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
41	C₉⋊C₉	—	3	2	no	—
42	C₉⋊C₉	—	57	6	no	—
43	C₃²⋊C₉	—	19	3	no	—
44	C₃²⋊C₉	—	19	3	no	—
45	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	3	yes	—
46	C₉²	—	3	1	no	—
47	C₉²	—	57	3	no	—
48	C₃×C₁₉	—	9	1	no	—
49	C₃×C₁₉	C₃×#733	1	1	yes	characteristic
50	C₃×C₁₉	#6908	1	3	yes	—
51	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
52	3₋¹⁺²	—	57	9	no	—
53	C₃×C₉	—	3	3	no	—
54	C₃×C₉	—	3	3	no	—
55	C₃×C₉	—	57	3	no	—
56	C₃×C₉	—	57	3	no	—
57	C₃×C₉	—	57	3	no	—
58	C₃×C₉	C₃²⋊(C₁₉⋊C₃)	1	2	yes	—
59	C₃×C₉	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
60	C₁₉	#10624588	1	1	yes	characteristic, complemented, Sylow
61	C₃²	—	3	1	no	—
62	C₃²	—	3	3	no	—
63	C₃²	C₃×C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
64	C₉	—	3	2	no	—
65	C₉	—	9	3	no	—
66	C₉	—	57	9	no	—
67	C₉	—	171	3	no	—
68	C₉	—	171	3	no	—
69	C₉	#13095322	1	3	yes	—
70	C₃	—	9	1	no	—
71	C₃	C₃×#13095322	1	1	yes	characteristic
72	C₃	#17987497	1	3	yes	—

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₁₉⋊C₃)
commutator, prime radical, cosocle	C₃³×C₁₉	C₃³
Frattini	C₃³	C₃²×C₁₉⋊C₃
Fitting	C₁₉×#6887	C₃
socle	C₃²×C₁₉	C₃×H(3,𝔽₃)
hypercenter	#6887	C₁₉⋊C₃
hypocenter	C₁₉	#10624588
LCS	G ▷ C₃³×C₁₉ ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
60. C₁₉	#10624588	semidirect

Maximal subgroups

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

subgroup	index
C₉×#10587025	3
#17987325	3
#17987322	3
#17987316	3
C₁₉×#6887	3
#10624588	19