Subgroups — #28353274

Order 13851.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095320	C₃	1	1	yes	maximal, characteristic
2	#17987445	C₃	1	1	yes	maximal, characteristic, complemented
3	#17987337	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#6895	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃×C₃²⋊(C₁₉⋊C₃)	—	3	1	no	—
6	#13095320	—	3	3	no	—
7	#13095305	—	3	3	no	—
8	C₃²⋊#4294	—	3	1	no	—
9	C₃²⋊#4294	—	3	1	no	—
10	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
11	C₁₉×C₉⋊C₉	—	3	3	no	—
12	C₁₉×C₃²⋊C₉	—	3	1	no	—
13	#10624484	—	19	1	no	maximal, Sylow
14	C₃³×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
15	C₃²×C₁₉⋊C₃	—	9	1	no	—
16	C₃×C₉×C₁₉	—	3	3	no	—
17	C₃×C₉×C₁₉	—	3	1	no	—
18	C₃×C₉×C₁₉	—	3	1	no	—
19	C₃×C₉×C₁₉	—	3	1	no	—
20	C₃×C₉×C₁₉	—	3	1	no	—
21	C₃²⋊(C₁₉⋊C₃)	—	3	3	no	—
22	C₃²⋊(C₁₉⋊C₃)	—	9	1	no	—
23	C₃²⋊(C₁₉⋊C₃)	—	9	1	no	—
24	C₃×#4294	—	3	3	no	—
25	C₃×#4294	—	9	1	no	—
26	C₃×#732	—	19	1	no	—
27	#6895	—	19	1	no	—
28	#6895	C₁₉⋊C₃	1	1	yes	characteristic, complemented
29	#6867	—	19	1	no	—
30	C₃²×C₁₉	—	9	1	no	—
31	C₃²×C₁₉	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
32	C₃²×C₁₉	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
33	C₃²×C₁₉	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
34	C₃²×C₁₉	#731	1	1	yes	characteristic
35	C₃×C₁₉⋊C₃	—	9	3	no	—
36	C₃×C₁₉⋊C₃	—	27	3	no	—
37	C₉×C₁₉	—	9	3	no	—
38	C₉×C₁₉	—	9	1	no	—
39	#4294	—	9	3	no	—
40	#4294	—	27	1	no	—
41	C₃×H(3,𝔽₃)	—	57	1	no	—
42	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
43	#732	—	57	3	no	—
44	C₉⋊C₉	—	3	3	no	—
45	C₉⋊C₉	—	57	3	no	—
46	C₃²⋊C₉	—	3	1	no	—
47	C₃²⋊C₉	—	57	1	no	—
48	C₃²⋊C₉	—	57	1	no	—
49	C₃×C₁₉	—	3	1	no	—
50	C₃×C₁₉	—	3	1	no	—
51	C₃×C₁₉	—	3	1	no	—
52	C₃×C₁₉	—	3	1	no	—
53	C₃×C₁₉	#6857	1	1	yes	characteristic
54	C₁₉⋊C₃	—	27	3	no	—
55	C₃³	—	171	1	no	—
56	C₃³	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
57	H(3,𝔽₃)	—	57	3	no	—
58	H(3,𝔽₃)	—	171	1	no	—
59	H(3,𝔽₃)	—	171	1	no	—
60	C₃×C₉	—	3	3	no	—
61	C₃×C₉	—	3	1	no	—
62	C₃×C₉	—	3	1	no	—
63	C₃×C₉	—	3	1	no	—
64	C₃×C₉	—	3	1	no	—
65	C₃×C₉	—	57	3	no	—
66	C₃×C₉	—	171	1	no	—
67	C₁₉	#10624484	1	1	yes	characteristic, complemented, Sylow
68	C₃²	—	513	3	no	—
69	C₃²	—	9	1	no	—
70	C₃²	—	171	3	no	—
71	C₃²	#13095314	1	1	yes	characteristic
72	C₃²	#13095315	1	1	yes	characteristic
73	C₃²	#13095315	1	1	yes	characteristic
74	C₃²	#13095318	1	1	yes	characteristic
75	C₉	—	513	1	no	—
76	C₉	—	9	3	no	—
77	C₉	—	9	1	no	—
78	C₉	—	171	3	no	—
79	C₃	—	513	3	no	—
80	C₃	—	3	1	no	—
81	C₃	—	3	1	no	—
82	C₃	—	3	1	no	—
83	C₃	—	3	1	no	—
84	C₃	#17987311	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#17987311
commutator, cosocle	C₃²×C₉×C₁₉	C₃²
Frattini	C₃²×C₉	C₃×C₁₉⋊C₃
Fitting	C₁₉×#6895	C₃
socle	C₃×C₁₉	#6857
prime radical	C₃×#13095320	C₃
hypercenter	#6895	C₁₉⋊C₃
hypocenter	C₁₉	#10624484
LCS	G ▷ C₃²×C₉×C₁₉ ▷ C₃³×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ #6895

Complements

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

N	H ≅ G/N	type
2. #17987445	C₃	semidirect
3. #17987337	C₃	semidirect
4. C₁₉×#6895	C₃	semidirect
28. #6895	C₁₉⋊C₃	semidirect
67. C₁₉	#10624484	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095320	3
#17987445	3
#17987337	3
C₁₉×#6895	3
#10624484	19