Finite Group Databasebeta

← #15839226

Subgroups — #15839226

Order 3328.

982 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 982 conjugacy classes of subgroups — too many to draw. Only its 179 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#13125216C211yesmaximal, characteristic, complemented
2#13124935C212yesmaximal, complemented
3#13114064C218yesmaximal, complemented
4#13113562C211yesmaximal, characteristic, complemented
5#13113279C212yesmaximal, complemented
6C2×C13×#555C211yesmaximal, characteristic
7C13×#555—22no—
8C13×#555—24no—
9C13×#555C2214yes—
10C2×C13×C4⋊Q8C2211yescharacteristic
11C2×C13×#124—22no—
12C2×C13×#121—22no—
13C2×C4×D4×C13C2212yes—
14C2×C13×#117—22no—
15#11719175C2211yescharacteristic
16#11718886—22no—
17#11718879—22no—
18#11718743—22no—
19#11718742C2214yescomplemented
20#11718680C2214yescomplemented
21#11718679—24no—
22#11718668C2214yescomplemented
23#11718631—22no—
24#11718587C2212yes—
25C4×#6099C2211yescharacteristic
26#11718138C2214yescomplemented
27D4⋊#1055C2218yescomplemented
28C22×Q8×C13D412yes—
29C22×D4×C13—22no—
30C22×D4×C13D412yes—
31C23×C4×C13—22no—
32C13×C4⋊Q8—22no—
33C13×C4⋊Q8D412yes—
34C13×C4⋊Q8C2312yes—
35C13×#124—28no—
36C13×#124—28no—
37C13×#121—28no—
38C13×#121—28no—
39C4×D4×C13—22no—
40C4×D4×C13—22no—
41C4×D4×C13D414yes—
42C4×D4×C13C2314yes—
43C13×#117—28no—
44C13×#117—28no—
45C2×C13×C4⋊C4—22no—
46C2×C13×C4⋊C4D412yes—
47C2×C13×C22⋊C4—24no—
48C2×C13×C22⋊C4—22no—
49C2×C42×C13—22no—
50C2×C42×C13C2311yescharacteristic
51C2×#6105—24no—
52#88180—21no—
53#88178—22no—
54C2×#6099—21no—
55#88124—21no—
56#88123C2312yes—
57C4×Dic26—22no—
58#88075—28no—
59#88072—24no—
60C22⋊#1055—22no—
61#88050—24no—
62#88047—24no—
63C4⋊#1055C2314yes—
64#88043—22no—
65#88043—21no—
66C4×#1055C2312yes—
67#18552—131nomaximal, Sylow
68C24×C13—22no—
69C2×Q8×C13—22no—
70C2×Q8×C13—44no—
71C2×Q8×C13C2×D414yes—
72C2×D4×C13—28no—
73C2×D4×C13—22no—
74C2×D4×C13—44no—
75C2×D4×C13—84no—
76C2×D4×C13C2×D414yes—
77C22×C4×C13—22no—
78C22×C4×C13—22no—
79C22×C4×C13—24no—
80C22×C4×C13—24no—
81C22×C4×C13—48no—
82C22×C4×C13C2×D412yes—
83C22×C4×C13C2×D411yescharacteristic
84C2×Dic26—22no—
85C13×C4⋊C4—24no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—24no—
88C13×C4⋊C4C2×D414yes—
89C13×C22⋊C4—216no—
90C13×C22⋊C4—24no—
91C13×C22⋊C4—24no—
92C42×C13—28no—
93C42×C13C2×D412yes—
94C42×C13C2×D411yescharacteristic
95C42×C13C2411yescharacteristic
96C22⋊Dic13—41no—
97#6105—48no—
98C4⋊Dic13—22no—
99C4⋊Dic13—22no—
100#6101—42no—
101C4×Dic13—41no—
102#6099—42no—
103C2×#1055—24no—
104C2×#1055—22no—
105C2×#555D1311yescharacteristic
106#3139—131no—
107#3110—132no—
108#1646—138no—
109#1558—131no—
110#1490—132no—
111C23×C13—24no—
112C23×C13—44no—
113C23×C13—44no—
114C23×C13—44no—
115C23×C13#12011yescharacteristic
116Q8×C13—44no—
117Q8×C13—82no—
118D4×C13—24no—
119D4×C13—24no—
120D4×C13—44no—
121D4×C13—88no—
122C2×C4×C13—22no—
123C2×C4×C13—24no—
124C2×C4×C13—24no—
125C2×C4×C13—24no—
126C2×C4×C13—48no—
127C2×C4×C13—44no—
128C2×C4×C13—44no—
129C2×C4×C13—48no—
130C2×C4×C13#12011yescharacteristic
131C2×C4×C13#12012yes—
132C2×C4×C13C22×D411yescharacteristic
133C2×C4×C13C22×D412yes—
134C2×Dic13—42no—
135Dic26—44no—
136#1055—42no—
137#1055—44no—
138#555—22no—
139#555—24no—
140#555C2×D1314yes—
141#533—131no—
142C2×C4⋊Q8C2×D1311yescharacteristic
143C2×#124—22no—
144C2×#121—22no—
145C2×C4×D4C2×D1312yes—
146C2×#117—22no—
147#491—262no—
148#487—134no—
149#484—262no—
150#474—134no—
151#461—134no—
152#450—262no—
153#440—264no—
154#432—132no—
155#419—262no—
156C4×M16—131no—
157#333—134no—
158D4⋊C8—138no—
159C22×C13—22no—
160C22×C13—44no—
161C22×C13—44no—
162C22×C13—44no—
163C22×C13—88no—
164C22×C13#45512yes—
165C22×C13C2×#12011yescharacteristic
166C4×C13—22no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—44no—
170C4×C13—44no—
171C4×C13#57514yes—
172Dic13—82no—
173C22×Q8C22⋊D1312yes—
174C22×D4—22no—
175C22×D4C22⋊D1312yes—
176C23×C4—22no—
177C2×SD16—264no—
178C2×M16—261no—
179C4⋊Q8—22no—
180C4⋊Q8—132no—
181C4⋊Q8C22⋊D1312yes—
182C4⋊Q8C22×D1312yes—
183#125—261no—
184#124—28no—
185#124—28no—
186C22⋊Q8—262no—
187#121—28no—
188#121—28no—
189C4×Q8—262no—
190C4×D4—22no—
191C4×D4—22no—
192C4×D4C22⋊D1314yes—
193C4×D4C22×D1314yes—
194#117—28no—
195#117—28no—
196#117—261no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4C22⋊D1312yes—
199C2×C22⋊C4—24no—
200C2×C22⋊C4—22no—
201C2×C42—22no—
202C2×C42C22×D1311yescharacteristic
203#107—264no—
204C4⋊C8—134no—
205#103—268no—
206#103—264no—
207#102—264no—
208C22⋊C8—262no—
209#97—261no—
210#97—262no—
211C4×C8—132no—
212C2×C13—22no—
213C2×C13—84no—
214C2×C13#300512yes—
215C2×C13C2×#45511yescharacteristic
216C24—22no—
217C2×Q8—22no—
218C2×Q8—44no—
219C2×Q8—262no—
220C2×Q8C2×C22⋊D1314yes—
221C2×D4—28no—
222C2×D4—22no—
223C2×D4—44no—
224C2×D4—84no—
225C2×D4C2×C22⋊D1314yes—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—24no—
229C22×C4—24no—
230C22×C4—48no—
231C22×C4C2×C22⋊D1312yes—
232C22×C4C2×C22⋊D1311yescharacteristic
233SD16—528no—
234M16—522no—
235C2×C8—262no—
236C2×C8—264no—
237C4⋊C4—24no—
238C4⋊C4—22no—
239C4⋊C4—24no—
240C4⋊C4—262no—
241C4⋊C4—262no—
242C4⋊C4—522no—
243C4⋊C4C2×C22⋊D1314yes—
244C22⋊C4—216no—
245C22⋊C4—24no—
246C22⋊C4—24no—
247C22⋊C4—521no—
248C42—28no—
249C42—521no—
250C42C2×C22⋊D1311yescharacteristic
251C42C2×C22⋊D1312yes—
252C42C23×D1311yescharacteristic
253C13#1855211yescharacteristic, complemented, Sylow
254C23—24no—
255C23—44no—
256C23—44no—
257C23—44no—
258C23#8820711yescharacteristic
259Q8—44no—
260Q8—82no—
261Q8—524no—
262D4—24no—
263D4—24no—
264D4—44no—
265D4—88no—
266C2×C4—22no—
267C2×C4—24no—
268C2×C4—24no—
269C2×C4—24no—
270C2×C4—48no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—48no—
274C2×C4—522no—
275C2×C4#8820711yescharacteristic
276C2×C4#8820712yes—
277C2×C4C22×C22⋊D1311yescharacteristic
278C2×C4C22×C22⋊D1312yes—
279C8—522no—
280C8—524no—
281C22—22no—
282C22—44no—
283C22—44no—
284C22—44no—
285C22—88no—
286C22#1171890312yes—
287C22C2×#8820711yescharacteristic
288C4—21no—
289C4—21no—
290C4—22no—
291C4—44no—
292C4—44no—
293C4—1042no—
294C4#1171952714yes—
295C2—22no—
296C2—84no—
297C2#1312407812yes—
298C2C2×#1171890311yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
Fitting, prime radicalC2×C13×#555C2
socleC22×C13C2×#120
hypercenterC2×#555D13
hypocenterC13#18552
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. #13125216C2semidirect
2. #13124935C2semidirect
3. #13114064C2semidirect
4. #13113562C2semidirect
5. #13113279C2semidirect
19. #11718742C22semidirect
20. #11718680C22semidirect
22. #11718668C22semidirect
26. #11718138C22semidirect
27. D4⋊#1055C22semidirect
253. C13#18552semidirect

Maximal subgroups

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

subgroupindex
#131252162
#131249352
#131140642
#131135622
#131132792
C2×C13×#5552
#1855213