Subgroups — #28354853

Order 13851.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987480	C₃	1	3	yes	maximal, complemented
2	C₃×#13095312	C₃	1	1	yes	maximal, characteristic, complemented
3	#17987353	C₃	1	3	yes	maximal, complemented
4	#17987350	C₃	1	3	yes	maximal, complemented
5	#17987341	C₃	1	2	yes	maximal, complemented
6	C₁₉×#6908	C₃	1	1	yes	maximal, characteristic
7	#13095312	—	3	3	no	—
8	#13095312	—	3	6	no	—
9	#13095312	C₃²	1	6	yes	—
10	C₃×#10587018	—	3	3	no	—
11	C₃×#10587018	C₃²	1	1	yes	characteristic
12	C₃×#10587018	C₃²	1	1	yes	characteristic
13	C₃×#10587018	C₃²	1	1	yes	characteristic
14	C₁₉×#737	C₃²	1	3	yes	—
15	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
16	C₁₉×#733	C₉	1	2	yes	—
17	C₁₉×#732	C₉	1	1	yes	characteristic
18	C₁₉×#731	C₉	1	3	yes	—
19	C₁₉×AΣL(1,𝔽₂₇)	C₉	1	3	yes	—
20	#10624725	—	19	1	no	maximal, Sylow
21	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
22	C₁₉×3₋¹⁺²	—	3	6	no	—
23	C₁₉×3₋¹⁺²	C₃×C₉	1	6	yes	—
24	C₁₉×H(3,𝔽₃)	C₃×C₉	1	3	yes	—
25	C₃×C₉×C₁₉	—	3	1	no	—
26	C₃×C₉×C₁₉	—	3	3	no	—
27	C₃×C₉×C₁₉	—	3	2	no	—
28	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
29	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
30	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
31	#10587018	—	3	6	no	—
32	#10587018	—	3	1	no	—
33	#10587018	—	3	1	no	—
34	#10587018	H(3,𝔽₃)	1	3	yes	—
35	#6908	C₁₉⋊C₃	1	1	yes	characteristic
36	#6903	—	19	3	no	—
37	C₃×C₂₇⋊C₃	—	19	1	no	—
38	#6873	—	19	3	no	—
39	#6872	—	19	3	no	—
40	#6869	—	19	2	no	—
41	C₃²×C₁₉	—	3	1	no	—
42	C₃²×C₁₉	—	3	3	no	—
43	C₃²×C₁₉	—	9	1	no	—
44	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
45	C₉×C₁₉	—	3	1	no	—
46	C₉×C₁₉	—	3	1	no	—
47	C₉×C₁₉	—	3	6	no	—
48	C₉×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
49	C₉×C₁₉	#737	1	2	yes	—
50	#737	C₃×C₁₉⋊C₃	1	3	yes	—
51	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
52	#733	#4294	1	2	yes	—
53	#732	#4294	1	1	yes	characteristic
54	#731	#4294	1	3	yes	—
55	AΣL(1,𝔽₂₇)	#4294	1	3	yes	—
56	C₂₇⋊C₃	—	19	6	no	—
57	C₂₇⋊C₃	—	57	3	no	—
58	C₂₇⋊C₃	—	57	6	no	—
59	C₃×C₂₇	—	19	1	no	—
60	C₃×C₂₇	—	19	1	no	—
61	C₃×C₂₇	—	19	1	no	—
62	C₃×C₂₇	—	57	3	no	—
63	C₃×C₁₉	—	3	1	no	—
64	C₃×C₁₉	—	9	3	no	—
65	C₃×C₁₉	—	9	1	no	—
66	C₃×C₁₉	C₉×H(3,𝔽₃)	1	1	yes	characteristic
67	C₃³	C₃×#4294	1	1	yes	characteristic
68	3₋¹⁺²	—	3	6	no	—
69	3₋¹⁺²	C₃×#4294	1	6	yes	—
70	H(3,𝔽₃)	C₃×#4294	1	3	yes	—
71	C₃×C₉	—	3	3	no	—
72	C₃×C₉	—	3	1	no	—
73	C₃×C₉	—	3	2	no	—
74	C₃×C₉	C₃×#4294	1	1	yes	characteristic
75	C₃×C₉	C₃×#4294	1	1	yes	characteristic
76	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
77	C₂₇	—	19	3	no	—
78	C₂₇	—	57	1	no	—
79	C₂₇	—	57	1	no	—
80	C₂₇	—	57	6	no	—
81	C₁₉	#10624725	1	1	yes	characteristic, complemented, Sylow
82	C₃²	—	3	1	no	—
83	C₃²	—	3	3	no	—
84	C₃²	—	9	1	no	—
85	C₃²	C₃²×#4294	1	1	yes	characteristic
86	C₉	—	3	1	no	—
87	C₉	—	3	1	no	—
88	C₉	—	3	6	no	—
89	C₉	H(3,𝔽₃)×C₁₉⋊C₃	1	1	yes	characteristic
90	C₉	#13095331	1	2	yes	—
91	C₃	—	3	1	no	—
92	C₃	—	9	1	no	—
93	C₃	—	9	3	no	—
94	C₃	H(3,𝔽₃)×#4294	1	1	yes	characteristic

	subgroup	G/H
center	C₉	H(3,𝔽₃)×C₁₉⋊C₃
commutator	C₃²×C₁₉	C₃²×C₉
Frattini	C₃×C₉	C₃²×C₁₉⋊C₃
Fitting, prime radical	C₁₉×#6908	C₃
socle	C₃×C₁₉	C₉×H(3,𝔽₃)
cosocle	C₃×C₉×C₁₉	C₃³
hypercenter	#6908	C₁₉⋊C₃
hypocenter	C₁₉	#10624725
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₉ ◁ C₃×C₉ ◁ #6908

Complements

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

N	H ≅ G/N	type
1. #17987480	C₃	semidirect
2. C₃×#13095312	C₃	semidirect
3. #17987353	C₃	semidirect
4. #17987350	C₃	semidirect
5. #17987341	C₃	semidirect
81. C₁₉	#10624725	semidirect

Maximal subgroups

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

subgroup	index
#17987480	3
C₃×#13095312	3
#17987353	3
#17987350	3
#17987341	3
C₁₉×#6908	3
#10624725	19