Subgroups — C₃×#17987383 #28355773

Order 13851.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095322	C₃	1	2	yes	maximal
2	C₃×#13095307	C₃	1	1	yes	maximal, characteristic
3	#17987383	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₁₉×#733	C₃	1	1	yes	maximal, characteristic
5	C₃×#10587025	—	3	2	no	—
6	C₃²×#4294	—	3	1	no	—
7	#13095322	—	3	4	no	—
8	#13095322	C₃²	1	6	yes	—
9	#13095307	—	3	2	no	—
10	#13095307	C₃²	1	3	yes	—
11	C₃×C₁₉×3₋¹⁺²	—	3	1	no	—
12	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
13	C₁₉×#733	—	3	2	no	—
14	C₁₉×#733	C₃²	1	3	yes	—
15	C₃×#6882	—	19	1	no	maximal, Sylow
16	C₃³×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
17	C₁₉×3₋¹⁺²	—	3	3	no	—
18	C₁₉×3₋¹⁺²	—	9	2	no	—
19	C₃×C₉×C₁₉	—	3	2	no	—
20	C₃×C₉×C₁₉	—	3	1	no	—
21	C₃×C₉×C₁₉	—	9	1	no	—
22	C₃×C₉×C₁₉	H(3,𝔽₃)	1	2	yes	—
23	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
24	#10587025	—	3	6	no	—
25	#10587025	—	9	4	no	—
26	C₃×#4294	—	3	3	no	—
27	C₃×#4294	—	9	3	no	—
28	C₃×#4294	—	9	2	no	—
29	C₃×#733	—	19	2	no	—
30	C₃×#733	C₁₉⋊C₃	1	1	yes	characteristic
31	C₃×C₉⋊C₉	—	19	1	no	—
32	#6882	—	19	9	no	—
33	C₃²×C₁₉	—	3	3	no	—
34	C₃²×C₁₉	#732	1	2	yes	—
35	C₃²×C₁₉	#732	1	1	yes	characteristic
36	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
37	C₉×C₁₉	—	3	2	no	—
38	C₉×C₁₉	—	3	1	no	—
39	C₉×C₁₉	—	9	3	no	—
40	#4294	—	9	3	no	—
41	#4294	—	9	6	no	—
42	C₃×3₋¹⁺²	—	3	1	no	—
43	C₃×3₋¹⁺²	—	57	2	no	—
44	C₃²×C₉	—	57	1	no	—
45	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
46	#733	—	3	2	no	—
47	#733	—	19	6	no	—
48	#733	—	57	4	no	—
49	#733	C₃×C₁₉⋊C₃	1	3	yes	—
50	C₉⋊C₉	—	19	3	no	—
51	C₉⋊C₉	—	57	2	no	—
52	C₃×C₁₉	—	3	1	no	—
53	C₃×C₁₉	—	3	2	no	—
54	C₃×C₁₉	#6882	1	3	yes	complemented
55	C₃×C₁₉	C₃×#732	1	1	yes	characteristic
56	C₃³	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
57	3₋¹⁺²	—	3	3	no	—
58	3₋¹⁺²	—	9	2	no	—
59	3₋¹⁺²	—	57	6	no	—
60	3₋¹⁺²	—	171	4	no	—
61	C₃×C₉	—	3	2	no	—
62	C₃×C₉	—	3	1	no	—
63	C₃×C₉	—	9	1	no	—
64	C₃×C₉	—	57	3	no	—
65	C₃×C₉	—	171	3	no	—
66	C₃×C₉	—	171	2	no	—
67	C₃×C₉	C₃²⋊(C₁₉⋊C₃)	1	2	yes	—
68	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
69	C₁₉	C₃×#6882	1	1	yes	characteristic, complemented, Sylow
70	C₃²	—	3	3	no	—
71	C₃²	#13095319	1	2	yes	—
72	C₃²	#13095319	1	1	yes	characteristic
73	C₃²	C₃×C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
74	C₉	—	3	2	no	—
75	C₉	—	3	1	no	—
76	C₉	—	9	3	no	—
77	C₉	—	171	3	no	—
78	C₉	—	171	6	no	—
79	C₃	—	3	1	no	—
80	C₃	—	3	2	no	—
81	C₃	#17987383	1	3	yes	direct product factor
82	C₃	C₃×#13095319	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	#13095319
commutator, cosocle	C₃×C₉×C₁₉	C₃³
Frattini	C₃×C₉	C₃²×C₁₉⋊C₃
Fitting	C₃×C₁₉×#733	C₃
socle	C₃²×C₁₉	#732
prime radical	C₃³×C₁₉	H(3,𝔽₃)
hypercenter	C₃×#733	C₁₉⋊C₃
hypocenter	C₁₉	C₃×#6882
LCS	G ▷ C₃×C₉×C₁₉ ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²×C₉ ◁ C₃×#733

Complements

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

N	H ≅ G/N	type
3. #17987383	C₃	direct (N × H)
54. C₃×C₁₉	#6882	semidirect
69. C₁₉	C₃×#6882	semidirect
81. C₃	#17987383	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#13095322	3
C₃×#13095307	3
#17987383	3
C₃×C₁₉×#733	3
C₃×#6882	19

Subgroups — C3×#17987383 #28355773

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#17987383 #28355773