Finite Group Databasebeta

← #15755421

Subgroups — #15755421

Order 3328.

818 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 131 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#13114919C211yesmaximal, characteristic, complemented
2#13114913C211yesmaximal, characteristic, complemented
3#13113365C214yesmaximal, complemented
4C2×C13×#540C211yesmaximal, characteristic
5C13×#540—28no—
6C2×C13×#127C411yescharacteristic, complemented
7C2×C13×#125C411yescharacteristic, complemented
8C2×C13×#123—22no—
9C2×C13×#121—22no—
10C2×C13×#121C2212yes—
11C2×C4×D4×C13C412yescomplemented
12C2×C13×#117C2211yescharacteristic
13#11718872C2212yes—
14#11718868C2212yes—
15#11718129—28no—
16#11718122—22no—
17#11718118—22no—
18C22×D4×C13—22no—
19C22×D4×C13—22no—
20C22×D4×C13C2×C412yes—
21C23×C4×C13—22no—
22C23×C4×C13C2311yescharacteristic
23C13×#127—24no—
24C13×#125—24no—
25C13×#123—216no—
26C13×#121—216no—
27C13×#121—24no—
28C13×#121D418yes—
29C4×D4×C13—24no—
30C4×D4×C13—24no—
31C13×#117—24no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4C2×C412yes—
34C2×C13×C4⋊C4D412yes—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4D412yes—
38C2×C42×C13C2×C411yescharacteristic
39C2×C42×C13C2×C411yescharacteristic
40C2×C22⋊Dic13—22no—
41C2×#6099—22no—
42#88071—24no—
43C22⋊#1055—24no—
44#8518—131nomaximal, Sylow
45C24×C13—22no—
46C24×C13C2×D411yescharacteristic
47C2×D4×C13—28no—
48C2×D4×C13—28no—
49C2×D4×C13—22no—
50C2×D4×C13—44no—
51C2×D4×C13—84no—
52C2×D4×C13—84no—
53C2×D4×C13C22⋊C414yes—
54C22×C4×C13—22no—
55C22×C4×C13—28no—
56C22×C4×C13—42no—
57C22×C4×C13—84no—
58C22×C4×C13C22⋊C412yes—
59C22×C4×C13C22⋊C412yes—
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D414yes—
63C22×Dic13—42no—
64C13×C4⋊C4—28no—
65C13×C4⋊C4—22no—
66C13×C4⋊C4—24no—
67C13×C4⋊C4C22⋊C414yes—
68C13×C22⋊C4—28no—
69C13×C22⋊C4—24no—
70C13×C22⋊C4—28no—
71C42×C13—22no—
72C42×C13—22no—
73C22⋊Dic13—44no—
74#6099—44no—
75C2×#1055—42no—
76C2×#540D1311yescharacteristic
77#1822—131no—
78#1820—131no—
79#1510—134no—
80C23×C13—22no—
81C23×C13—24no—
82C23×C13—42no—
83C23×C13—44no—
84C23×C13—44no—
85C23×C13—44no—
86C23×C13C2×C22⋊C411yescharacteristic
87C23×C13#12012yes—
88D4×C13—44no—
89D4×C13—44no—
90D4×C13—88no—
91D4×C13—88no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—24no—
97C2×C4×C13—44no—
98C2×C4×C13—44no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—88no—
102C2×C4×C13C2×C22⋊C412yes—
103C2×C4×C13#12012yes—
104C2×Dic13—82no—
105C2×Dic13—84no—
106#1055—82no—
107#540—28no—
108C2×#127Dic1311yescharacteristic, complemented
109C2×#125Dic1311yescharacteristic, complemented
110C2×#123—22no—
111C2×#121—22no—
112C2×#121C2×D1312yes—
113C2×C4×D4Dic1312yescomplemented
114C2×#117C2×D1311yescharacteristic
115#407—132no—
116#381—132no—
117#343—262no—
118#342—262no—
119#327—268no—
120C22×C13—22no—
121C22×C13—24no—
122C22×C13—22no—
123C22×C13—44no—
124C22×C13—44no—
125C22×C13—44no—
126C22×C13—82no—
127C22×C13—88no—
128C22×C13#37911yescharacteristic
129C22×C13#41012yes—
130C4×C13—22no—
131C4×C13—22no—
132C4×C13—44no—
133C4×C13—42no—
134C4×C13—42no—
135Dic13—162no—
136C22×D4—22no—
137C22×D4—22no—
138C22×D4C2×Dic1312yes—
139C23×C4—22no—
140C23×C4C22×D1311yescharacteristic
141C2×M16—262no—
142#127—24no—
143#125—24no—
144#123—216no—
145#121—216no—
146#121—24no—
147#121C22⋊D1318yes—
148C4×D4—24no—
149C4×D4—24no—
150#117—24no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4C2×Dic1312yes—
153C2×C4⋊C4C22⋊D1312yes—
154C2×C22⋊C4—22no—
155C2×C22⋊C4—22no—
156C2×C22⋊C4—262no—
157C2×C22⋊C4C22⋊D1312yes—
158C2×C42C2×Dic1311yescharacteristic
159C2×C42C2×Dic1311yescharacteristic
160C22⋊C8—264no—
161#95—264no—
162C2×C13—22no—
163C2×C13—42no—
164C2×C13—84no—
165C2×C13#178211yescharacteristic
166C2×C13#179512yes—
167C24—22no—
168C24C2×C22⋊D1311yescharacteristic
169C2×D4—28no—
170C2×D4—28no—
171C2×D4—22no—
172C2×D4—44no—
173C2×D4—84no—
174C2×D4—84no—
175C2×D4C22⋊Dic1314yes—
176C22×C4—22no—
177C22×C4—28no—
178C22×C4—42no—
179C22×C4—84no—
180C22×C4—522no—
181C22×C4C22⋊Dic1312yes—
182C22×C4C22⋊Dic1312yes—
183C22×C4C22×Dic1311yescharacteristic
184C22×C4C2×C22⋊D1311yescharacteristic
185C22×C4C2×C22⋊D1314yes—
186M16—524no—
187C2×C8—522no—
188C4⋊C4—28no—
189C4⋊C4—22no—
190C4⋊C4—24no—
191C4⋊C4C22⋊Dic1314yes—
192C22⋊C4—28no—
193C22⋊C4—24no—
194C22⋊C4—28no—
195C22⋊C4—524no—
196C42—22no—
197C42—22no—
198C13#851811yescharacteristic, complemented, Sylow
199C23—22no—
200C23—24no—
201C23—42no—
202C23—44no—
203C23—44no—
204C23—44no—
205C23C2×C22⋊Dic1311yescharacteristic
206C23#8820712yes—
207D4—44no—
208D4—44no—
209D4—88no—
210D4—88no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—24no—
216C2×C4—44no—
217C2×C4—44no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—88no—
221C2×C4—1042no—
222C2×C4—1044no—
223C2×C4C2×C22⋊Dic1312yes—
224C2×C4#8820712yes—
225C8—1042no—
226C22—22no—
227C22—22no—
228C22—24no—
229C22—44no—
230C22—44no—
231C22—44no—
232C22—82no—
233C22—88no—
234C22#1171890112yes—
235C22#1171890811yescharacteristic
236C4—22no—
237C4—22no—
238C4—44no—
239C4—42no—
240C4—42no—
241C4—2082no—
242C2—22no—
243C2—42no—
244C2—84no—
245C2#1311475411yescharacteristic
246C2#1311480612yes—
subgroupG/H
centerC22#11718908
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
Fitting, prime radicalC2×C13×#540C2
socleC22×C13#379
cosocleC23×C4×C13C23
hypercenterC2×#540D13
hypocenterC13#8518
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #13114919C2semidirect
2. #13114913C2semidirect
3. #13113365C2semidirect
6. C2×C13×#127C4semidirect
7. C2×C13×#125C4semidirect
11. C2×C4×D4×C13C4semidirect
108. C2×#127Dic13semidirect
109. C2×#125Dic13semidirect
113. C2×C4×D4Dic13semidirect
198. C13#8518semidirect

Maximal subgroups

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

subgroupindex
#131149192
#131149132
#131133652
C2×C13×#5402
#851813