Subgroups — #28353308

Order 13851.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095322	C₃	1	1	yes	maximal, characteristic
2	#17987339	C₃	1	1	yes	maximal, characteristic
3	#17987308	C₃	1	1	yes	maximal, characteristic
4	C₁₉×#6868	C₃	1	1	yes	maximal, characteristic
5	C₃×#10587025	—	3	1	no	—
6	C₃²×#4294	—	3	1	no	—
7	#13095322	—	3	3	no	—
8	C₃²⋊#4294	—	3	1	no	—
9	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
10	C₁₉×C₃²⋊C₉	—	3	1	no	—
11	#10624490	—	19	1	no	maximal, Sylow
12	C₃³×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃×C₉×C₁₉	—	3	1	no	—
14	C₃×C₉×C₁₉	—	3	1	no	—
15	C₃×C₉×C₁₉	—	3	1	no	—
16	C₃×C₉×C₁₉	—	3	1	no	—
17	C₃×C₉×C₁₉	—	9	1	no	—
18	#10587025	—	3	3	no	—
19	#10587025	—	9	1	no	—
20	#10587025	—	9	1	no	—
21	C₃×#4294	—	3	3	no	—
22	C₃×#4294	—	9	1	no	—
23	C₃×#4294	—	9	1	no	—
24	C₃×#4294	—	9	1	no	—
25	C₃×#4294	—	9	1	no	—
26	C₃×#4294	—	9	1	no	—
27	C₃×#733	—	19	1	no	—
28	#6868	—	19	1	no	—
29	#6868	C₁₉⋊C₃	1	1	yes	characteristic
30	#6855	—	19	1	no	—
31	C₃²×C₁₉	—	3	1	no	—
32	C₃²×C₁₉	—	3	1	no	—
33	C₃²×C₁₉	—	3	1	no	—
34	C₃²×C₁₉	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
35	C₃²×C₁₉	#731	1	1	yes	characteristic
36	C₃²×C₁₉	#731	1	1	yes	characteristic
37	C₃²×C₁₉	#732	1	1	yes	characteristic
38	C₉×C₁₉	—	9	1	no	—
39	C₉×C₁₉	—	27	1	no	—
40	#4294	—	9	3	no	—
41	#4294	—	9	3	no	—
42	#4294	—	27	1	no	—
43	C₃×3₋¹⁺²	—	57	1	no	—
44	C₃²×C₉	—	57	1	no	—
45	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
46	#733	—	57	3	no	—
47	C₃²⋊C₉	—	3	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	#6859	1	1	yes	characteristic
53	C₃×C₁₉	#6878	1	1	yes	characteristic
54	C₃×C₁₉	#6882	1	1	yes	characteristic
55	C₃×C₁₉	#6883	1	1	yes	characteristic
56	C₃³	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
57	3₋¹⁺²	—	57	3	no	—
58	3₋¹⁺²	—	171	1	no	—
59	3₋¹⁺²	—	171	1	no	—
60	C₃×C₉	—	3	1	no	—
61	C₃×C₉	—	3	1	no	—
62	C₃×C₉	—	3	1	no	—
63	C₃×C₉	—	3	1	no	—
64	C₃×C₉	—	9	1	no	—
65	C₃×C₉	—	57	3	no	—
66	C₃×C₉	—	171	1	no	—
67	C₃×C₉	—	171	1	no	—
68	C₃×C₉	—	171	1	no	—
69	C₃×C₉	—	171	1	no	—
70	C₃×C₉	—	171	1	no	—
71	C₁₉	#10624490	1	1	yes	characteristic, complemented, Sylow
72	C₃²	—	3	1	no	—
73	C₃²	—	3	1	no	—
74	C₃²	—	3	1	no	—
75	C₃²	#13095315	1	1	yes	characteristic
76	C₃²	#13095317	1	1	yes	characteristic
77	C₃²	#13095318	1	1	yes	characteristic
78	C₃²	#13095319	1	1	yes	characteristic
79	C₉	—	513	1	no	—
80	C₉	—	9	1	no	—
81	C₉	—	27	1	no	—
82	C₉	—	171	3	no	—
83	C₉	—	171	3	no	—
84	C₃	—	3	1	no	—
85	C₃	—	3	1	no	—
86	C₃	—	3	1	no	—
87	C₃	#17987320	1	1	yes	characteristic
88	C₃	#17987372	1	1	yes	characteristic
89	C₃	#17987384	1	1	yes	characteristic
90	C₃	#17987391	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	#13095319
commutator, cosocle	C₃²×C₉×C₁₉	C₃²
Frattini	C₃²×C₉	C₃×C₁₉⋊C₃
Fitting	C₁₉×#6868	C₃
socle	C₃²×C₁₉	#732
prime radical	C₃³×C₁₉	H(3,𝔽₃)
hypercenter	#6868	C₁₉⋊C₃
hypocenter	C₁₉	#10624490
LCS	G ▷ C₃²×C₉×C₁₉ ▷ C₃³×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²×C₉ ◁ #6868

Complements

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

N	H ≅ G/N	type
71. C₁₉	#10624490	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
#17987339	3
#17987308	3
C₁₉×#6868	3
#10624490	19