Finite Group Databasebeta

← #15772519

Subgroups — #15772519

Order 3328.

446 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 87 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#13119144C211yesmaximal, characteristic
2#13113154C211yesmaximal, characteristic
3#13112765C214yesmaximal, complemented
4C13×#1466C211yesmaximal, characteristic
5C2×C4×D4×C13C2211yescharacteristic
6C2×#88189C412yes—
7C22×C4⋊Dic13C411yescharacteristic
8C13×#432—21no—
9#11718873—21no—
10#11718873C411yescharacteristic
11C2×C22⋊#1055—21no—
12#11718644—21no—
13#11718614—21no—
14#11718604C2212yes—
15#11718589—21no—
16C13×#323—21no—
17C13×#323C2212yes—
18#11718120—21no—
19#11718117C2212yes—
20C22×D4×C13C2×C411yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×Dic13C2×C412yes—
24C4×D4×C13—41no—
25C4×D4×C13—41no—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C13×C22⋊C4D411yescharacteristic
28C2×C13×C22⋊C4C2311yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C22⋊Dic13—22no—
31C2×C22⋊Dic13C2×C412yes—
32#88189—44no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—41no—
37C2×C4⋊Dic13—41no—
38C2×#6101—22no—
39C22×#1055—41no—
40C13×C4⋊C8—41no—
41C13×C22⋊C8—22no—
42C13×#97—41no—
43#88071—21no—
44#88071—22no—
45#88071—22no—
46C22⋊#1055—22no—
47C22⋊#1055—41no—
48#11558—131nomaximal, Sylow
49C24×C13C22⋊C411yescharacteristic
50C24×C13C22×C411yescharacteristic
51C2×D4×C13—22no—
52C2×D4×C13—22no—
53C2×D4×C13—41no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—42no—
59C22×C4×C13—42no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×Dic13—22no—
66C22×Dic13—22no—
67C22×Dic13—24no—
68C22×Dic13—42no—
69C22×Dic13—42no—
70C2×C8×C13—42no—
71C13×C4⋊C4—41no—
72C13×C22⋊C4—41no—
73C13×C22⋊C4—41no—
74C42×C13—21no—
75C42×C13—21no—
76C22⋊Dic13—44no—
77C22⋊Dic13—42no—
78C4⋊Dic13—42no—
79C4⋊Dic13—42no—
80C4⋊Dic13—41no—
81C4⋊Dic13—41no—
82#6101—44no—
83C2×#1055—42no—
84C2×#1055—82no—
85#2486—131no—
86#1466D1311yescharacteristic
87#1459—131no—
88#1317—134no—
89C23×C13—21no—
90C23×C13—21no—
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—41no—
94C23×C13—41no—
95C23×C13—41no—
96C23×C13—41no—
97C23×C13#10012yes—
98C23×C13C2×C22⋊C411yescharacteristic
99C23×C13#13112yes—
100D4×C13—44no—
101C2×C4×C13—22no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—81no—
115C2×C4×C13#9911yescharacteristic
116C2×C4×C13#9911yescharacteristic
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122C2×Dic13—42no—
123C2×Dic13—84no—
124C8×C13—82no—
125#1055—82no—
126C2×#123—132no—
127C2×C4×D4C2×D1311yescharacteristic
128C22×C4⋊C4—131no—
129#432—21no—
130C2×C22⋊C8—261no—
131#398—261no—
132#397—261no—
133#389—261no—
134#381—132no—
135#380—131no—
136#380—261no—
137#324—261no—
138#323—21no—
139#323—132no—
140#323C2×D1312yes—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—22no—
144C22×C13—22no—
145C22×C13—42no—
146C22×C13—42no—
147C22×C13—42no—
148C22×C13—41no—
149C22×C13—41no—
150C22×C13—41no—
151C22×C13—41no—
152C22×C13—81no—
153C22×C13#40811yescharacteristic
154C22×C13C2×#9911yescharacteristic
155C22×C13C2×#10011yescharacteristic
156C4×C13—21no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13#35212yes—
162Dic13—82no—
163Dic13—82no—
164C22×D4C4×D1311yescharacteristic
165C23×C4—132no—
166C23×C4C4×D1311yescharacteristic
167C23×C4D5211yescharacteristic
168C22×C8—521no—
169#123—524no—
170C4×D4—41no—
171C4×D4—41no—
172C2×C4⋊C4—261no—
173C2×C4⋊C4—262no—
174C2×C4⋊C4—261no—
175C2×C4⋊C4—261no—
176C2×C4⋊C4—521no—
177C2×C4⋊C4—521no—
178C2×C4⋊C4D5211yescharacteristic
179C2×C22⋊C4—132no—
180C2×C22⋊C4—262no—
181C2×C22⋊C4C22⋊D1311yescharacteristic
182C2×C22⋊C4C22×D1311yescharacteristic
183C2×C42C22⋊D1311yescharacteristic
184C4⋊C8—41no—
185C22⋊C8—22no—
186C22⋊C8—262no—
187C22⋊C8—521no—
188#97—41no—
189#95—261no—
190#95—262no—
191#95—262no—
192C2×C13—21no—
193C2×C13—21no—
194C2×C13—42no—
195C2×C13—42no—
196C2×C13#147111yescharacteristic
197C2×C13C2×#35211yescharacteristic
198C2×C13#212311yescharacteristic
199C24#610311yescharacteristic
200C24C2×C4×D1311yescharacteristic
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—41no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—262no—
211C22×C4—262no—
212C22×C4—264no—
213C22×C4—522no—
214C22×C4—522no—
215C22×C4#610311yescharacteristic
216C22×C4#610311yescharacteristic
217C22×C4#610311yescharacteristic
218C22×C4C2×D5211yescharacteristic
219C22×C4C2×C22⋊D1311yescharacteristic
220C2×C8—42no—
221C2×C8—522no—
222C2×C8—1042no—
223C4⋊C4—41no—
224C4⋊C4—522no—
225C4⋊C4—524no—
226C4⋊C4—522no—
227C4⋊C4—521no—
228C4⋊C4—521no—
229C22⋊C4—41no—
230C22⋊C4—41no—
231C22⋊C4—524no—
232C22⋊C4—522no—
233C42—21no—
234C42—21no—
235C13#1155811yescharacteristic, complemented, Sylow
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—41no—
241C23—41no—
242C23—41no—
243C23—41no—
244C23#8806312yes—
245C23#8816112yes—
246C23C2×#610311yescharacteristic
247D4—44no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—81no—
262C2×C4—522no—
263C2×C4—522no—
264C2×C4—522no—
265C2×C4—522no—
266C2×C4—522no—
267C2×C4—522no—
268C2×C4—1044no—
269C2×C4#8804611yescharacteristic
270C2×C4#8804611yescharacteristic
271C8—82no—
272C8—1042no—
273C22—21no—
274C22—21no—
275C22—22no—
276C22—22no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—81no—
285C22C2×#8804611yescharacteristic
286C22#1171879011yescharacteristic
287C22C2×#8806311yescharacteristic
288C4—21no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—1042no—
294C4—1042no—
295C4#1171806812yes—
296C2—21no—
297C2—21no—
298C2—42no—
299C2—42no—
300C2#1311319711yescharacteristic
301C2C2×#1171806811yescharacteristic
302C2#1311648911yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC24×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1466C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C13×C22⋊C4C23
hypercenter#1466D13
hypocenterC13#11558
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #13112765C2semidirect
235. C13#11558semidirect

Maximal subgroups

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

subgroupindex
#131191442
#131131542
#131127652
C13×#14662
#1155813