Subgroups — #28355756

Order 13851.

186 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	#17987405	C₃	1	1	yes	maximal, characteristic
3	#17987376	C₃	1	9	yes	maximal, complemented
4	C₃×C₁₉×#733	C₃	1	1	yes	maximal, characteristic
5	C₃×#10587025	—	3	2	no	—
6	#13095322	—	3	2	no	—
7	#13095322	—	3	2	no	—
8	#13095322	C₃²	1	6	yes	—
9	#13095307	—	3	1	no	—
10	#13095306	—	3	1	no	—
11	C₃²⋊#4294	—	3	1	no	—
12	C₉×#4294	C₃²	1	3	yes	—
13	C₃×C₁₉×3₋¹⁺²	—	3	1	no	—
14	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
15	C₁₉×#733	—	3	1	no	—
16	C₁₉×#733	—	3	1	no	—
17	C₁₉×#733	C₃²	1	3	yes	—
18	#10624840	—	19	1	no	maximal, Sylow
19	C₃³×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
20	C₁₉×3₋¹⁺²	—	3	3	no	—
21	C₁₉×3₋¹⁺²	—	9	2	no	—
22	C₃×C₉×C₁₉	—	3	2	no	—
23	C₃×C₉×C₁₉	—	3	1	no	—
24	C₃×C₉×C₁₉	—	9	1	no	—
25	C₃×C₉×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
26	C₃×C₉×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
27	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
28	#10587025	—	3	6	no	—
29	#10587025	—	9	2	no	—
30	#10587025	—	9	2	no	—
31	C₃×#4294	—	3	3	no	—
32	C₃×#4294	—	9	2	no	—
33	C₃×#733	—	19	2	no	—
34	C₃×#733	C₁₉⋊C₃	1	1	yes	characteristic
35	#6887	—	19	1	no	—
36	#6880	—	19	9	no	—
37	C₃²×C₁₉	—	9	1	no	—
38	C₃²×C₁₉	#732	1	2	yes	—
39	C₃²×C₁₉	#732	1	1	yes	characteristic
40	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
41	C₉×C₁₉	—	3	1	no	—
42	C₉×C₁₉	—	3	1	no	—
43	C₉×C₁₉	—	3	1	no	—
44	C₉×C₁₉	—	9	3	no	—
45	#4294	—	9	3	no	—
46	#4294	—	9	6	no	—
47	C₃×3₋¹⁺²	—	3	1	no	—
48	C₃×3₋¹⁺²	—	57	2	no	—
49	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
50	#733	—	3	1	no	—
51	#733	—	3	1	no	—
52	#733	—	19	6	no	—
53	#733	—	57	2	no	—
54	#733	—	57	2	no	—
55	#733	C₃×C₁₉⋊C₃	1	3	yes	—
56	C₉⋊C₉	—	57	1	no	—
57	C₉⋊C₉	—	57	1	no	—
58	C₃²⋊C₉	—	57	1	no	—
59	C₉²	—	19	3	no	—
60	C₃×C₁₉	—	3	1	no	—
61	C₃×C₁₉	—	3	2	no	—
62	C₃×C₁₉	—	3	1	no	—
63	C₃×C₁₉	C₃×#732	1	1	yes	characteristic
64	C₃³	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
65	3₋¹⁺²	—	3	3	no	—
66	3₋¹⁺²	—	9	2	no	—
67	3₋¹⁺²	—	57	6	no	—
68	3₋¹⁺²	—	171	2	no	—
69	3₋¹⁺²	—	171	2	no	—
70	C₃×C₉	—	3	1	no	—
71	C₃×C₉	—	3	2	no	—
72	C₃×C₉	—	9	1	no	—
73	C₃×C₉	—	57	3	no	—
74	C₃×C₉	—	171	2	no	—
75	C₃×C₉	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
76	C₃×C₉	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
77	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
78	C₁₉	#10624840	1	1	yes	characteristic, complemented, Sylow
79	C₃²	—	9	1	no	—
80	C₃²	#13095319	1	1	yes	characteristic
81	C₃²	#13095319	1	2	yes	—
82	C₃²	C₃×C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
83	C₉	—	3	1	no	—
84	C₉	—	3	1	no	—
85	C₉	—	3	1	no	—
86	C₉	—	9	3	no	—
87	C₉	—	171	3	no	—
88	C₉	—	171	6	no	—
89	C₃	—	3	1	no	—
90	C₃	—	3	1	no	—
91	C₃	—	3	2	no	—
92	C₃	C₃×#13095319	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×#13095319
commutator, cosocle	C₃×C₉×C₁₉	C₃³
Frattini	C₃×C₉	C₃²×C₁₉⋊C₃
Fitting	C₃×C₁₉×#733	C₃
socle	C₃×C₁₉	C₃×#732
prime radical	C₃³×C₁₉	H(3,𝔽₃)
hypercenter	C₃×#733	C₁₉⋊C₃
hypocenter	C₁₉	#10624840
LCS	G ▷ C₃×C₉×C₁₉ ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ C₃×#733

Complements

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

N	H ≅ G/N	type
3. #17987376	C₃	semidirect
78. C₁₉	#10624840	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095322	3
#17987405	3
#17987376	3
C₃×C₁₉×#733	3
#10624840	19