Finite Group Databasebeta

← D53×#2866 #27590134

Subgroups — D53×#2866 #27590134

Order 13568.

2186 conjugacy classes of subgroups; only the 591 normal subgroups are shown.

normal subgroups only

This group has 2186 conjugacy classes of subgroups — too many to draw. Only its 591 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283108C217yesmaximal, complemented
2#20283107C211yesmaximal, characteristic, complemented
3#20283106C217yesmaximal, complemented
4#388×D53C217yesmaximal
5#387×D53C217yesmaximal, complemented
6C43×D53C211yesmaximal, characteristic, complemented
7C53×#2866C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D53C2217yes—
9C2×C22⋊C4×D53C2217yes—
10C2×C42×D53C2217yes—
11#16810517C2217yes—
12#16810516C2217yes—
13#16810515C2217yes—
14#16810514C2217yes—
15#16810513C2217yes—
16#16810512C2217yes—
17#16810511C2217yes—
18#16810510C2217yescomplemented
19#16810509C2217yescomplemented
20#16810508C2217yescomplemented
21#16810507C2217yescomplemented
22#16810506C2217yescomplemented
23#16810505C2217yescomplemented
24#16810504C2217yescomplemented
25#95×D53C2217yes—
26#95×D53C2217yes—
27C42×Dic53C2217yescomplemented
28C53×#388C2217yes—
29C53×#387C2217yescomplemented
30C43×C53C2211yescharacteristic, complemented
31C24×D53C2311yescharacteristic
32C22×C4×D53C2317yes—
33C22×C4×D53C2317yes—
34C2×C4⋊Dic53C2317yes—
35C2×#11719919C2317yes—
36C2×#11719919C2317yes—
37C4⋊C4×D53—228no—
38C2×C22⋊Dic53C2317yes—
39C2×#11719921C2317yes—
40C2×#11719921C2317yes—
41C22⋊C4×D53—228no—
42C2×C4×Dic53C2317yes—
43C2×C4×Dic53C2317yes—
44C2×C4×Dic53C2317yes—
45C42×D53—228no—
46#13133124C2317yes—
47#13133124C2317yes—
48#13133124C2317yes—
49#13133124C2317yes—
50#13133124C2317yes—
51#13133124C2317yes—
52C2×C4⋊C4×C53C2317yes—
53C2×C22⋊C4×C53C2317yes—
54C2×C42×C53C2317yes—
55#95×C53C2317yes—
56#95×C53C2317yes—
57C24×C53C2411yescharacteristic
58C23×D53—214no—
59C23×D53C2411yescharacteristic
60C23×D53C2411yescharacteristic
61C22×C4×C53C2417yes—
62C22×C4×C53C2417yes—
63C22×Dic53C2417yes—
64C22×Dic53C2417yes—
65C2×C4×D53—214no—
66C2×C4×D53—214no—
67C2×C4×D53—214no—
68C2×C4×D53—214no—
69C2×C4×D53—214no—
70C2×C4×D53#41128yes—
71C4⋊C4×C53—214no—
72C22⋊C4×C53—214no—
73C42×C53—214no—
74C22⋊Dic53—214no—
75#11719921—214no—
76#11719921—214no—
77C4⋊Dic53—214no—
78#11719919—214no—
79#11719919—214no—
80C4×Dic53—214no—
81C4×Dic53—214no—
82C4×Dic53—214no—
83C23×C53—27no—
84C23×C53C2511yescharacteristic
85C22×D53—27no—
86C22×D53—428no—
87C22×D53C2×#41114yes—
88C2×C4×C53—27no—
89C2×C4×C53—27no—
90C2×C4×C53—27no—
91C2×C4×C53—27no—
92C2×C4×C53—27no—
93C2×C4×C53C2×#41114yes—
94C2×Dic53—27no—
95C2×Dic53—27no—
96C2×Dic53—27no—
97C2×Dic53—27no—
98C2×Dic53—27no—
99C2×Dic53C2×#41114yes—
100C4×D53—256no—
101C4×D53—428no—
102C2×#2866—531nomaximal, Sylow
103C22×C53—47no—
104C22×C53C22×#4117yes—
105C2×D53—47no—
106C2×D53—88no—
107C2×D53#529128yes—
108C4×C53—214no—
109C4×C53—47no—
110Dic53—214no—
111Dic53—47no—
112#2866—537no—
113#2866—537no—
114#2866—531no—
115#2866D5311yescharacteristic, direct product factor
116C2×#388—537no—
117C2×#387—537no—
118C2×C43—531no—
119C2×C53—81no—
120C2×C53C2×#52917yes—
121D53—81no—
122D53#286618yesdirect product factor
123C22×C4⋊C4—537no—
124C22×C22⋊C4—537no—
125C22×C42—537no—
126#388—537no—
127#388—537no—
128#388—537no—
129#388—537no—
130#388—537no—
131#388—537no—
132#388—537no—
133#388C2×D5317yes—
134#387—537no—
135#387—537no—
136#387—537no—
137#387—537no—
138#387—537no—
139#387—537no—
140#387—537no—
141#387C2×D5317yescomplemented
142C2×#95—537no—
143C2×#95—537no—
144C43—537no—
145C43C2×D5311yescharacteristic, complemented
146C53C2×#286611yescharacteristic, complemented, Sylow
147C25—531no—
148C23×C4—537no—
149C23×C4—537no—
150C2×C4⋊C4—537no—
151C2×C4⋊C4—537no—
152C2×C4⋊C4—537no—
153C2×C4⋊C4—10628no—
154C2×C4⋊C4C22×D5317yes—
155C2×C22⋊C4—537no—
156C2×C22⋊C4—537no—
157C2×C22⋊C4—537no—
158C2×C22⋊C4—10628no—
159C2×C22⋊C4C22×D5317yes—
160C2×C42—537no—
161C2×C42—537no—
162C2×C42—537no—
163C2×C42—10628no—
164C2×C42C22×D5317yes—
165#95—537no—
166#95—537no—
167#95—537no—
168#95—537no—
169#95—537no—
170#95—537no—
171#95C22×D5317yes—
172#95C22×D5317yes—
173C24—531no—
174C24—531no—
175C24—10614no—
176C24C23×D5311yescharacteristic
177C22×C4—537no—
178C22×C4—5328no—
179C22×C4—537no—
180C22×C4—10614no—
181C22×C4—10614no—
182C22×C4—10614no—
183C22×C4—10614no—
184C22×C4—10614no—
185C22×C4C23×D5317yes—
186C22×C4C23×D5317yes—
187C4⋊C4—214no—
188C4⋊C4—10614no—
189C4⋊C4—10614no—
190C4⋊C4—10614no—
191C22⋊C4—214no—
192C22⋊C4—10614no—
193C22⋊C4—10614no—
194C22⋊C4—10614no—
195C42—214no—
196C42—10614no—
197C42—10614no—
198C42—10614no—
199C23—27no—
200C23—5314no—
201C23—1067no—
202C23—21228no—
203C23C24×D5311yescharacteristic
204C2×C4—27no—
205C2×C4—27no—
206C2×C4—27no—
207C2×C4—27no—
208C2×C4—27no—
209C2×C4—5314no—
210C2×C4—10656no—
211C2×C4—1067no—
212C2×C4—1067no—
213C2×C4—1067no—
214C2×C4—1067no—
215C2×C4—1067no—
216C2×C4—21228no—
217C2×C4#41×D53114yes—
218C22—47no—
219C22—5328no—
220C22—4248no—
221C22—2127no—
222C22C2×#41×D5317yes—
223C4—214no—
224C4—47no—
225C4—10614no—
226C4—2127no—
227C2—81no—
228C2—538no—
229C2—4241no—
230C2#529×D5317yes—
subgroupG/H
center, FrattiniC23C24×D53
commutator, socle, cosocleC23×C53C25
FittingC53×#2866C2
prime radicalC24×D53C23
hypercenter#2866D53
hypocenterC53C2×#2866
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23 ◁ #2866

Complements

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

NH ≅ G/Ntype
1. #20283108C2semidirect
2. #20283107C2semidirect
3. #20283106C2semidirect
5. #387×D53C2semidirect
6. C43×D53C2semidirect
7. C53×#2866C2semidirect
18. #16810510C22semidirect
19. #16810509C22semidirect
20. #16810508C22semidirect
21. #16810507C22semidirect
22. #16810506C22semidirect
23. #16810505C22semidirect
24. #16810504C22semidirect
27. C42×Dic53C22semidirect
29. C53×#387C22semidirect
30. C43×C53C22semidirect
115. #2866D53direct (N × H)
122. D53#2866direct (N × H)
141. #387C2×D53semidirect
145. C43C2×D53semidirect
146. C53C2×#2866semidirect

Maximal subgroups

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

subgroupindex
#202831082
#202831072
#202831062
#388×D532
#387×D532
C43×D532
C53×#28662
C2×#286653