Finite Group Databasebeta

← #15772559

Subgroups — #15772559

Order 3328.

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

normal subgroups only

This group has 462 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#13119835C211yesmaximal, characteristic
2#13113160C211yesmaximal, characteristic, complemented
3#13112767C214yesmaximal, complemented
4C13×#1467C211yesmaximal, characteristic, complemented
5C2×C4×Q8×C13C2211yescharacteristic
6C2×#88201C412yes—
7C2×#88128C411yescharacteristic
8C13×#432—21no—
9#11718652—21no—
10#11718652—21no—
11#11718649C2212yes—
12#11718600—21no—
13#11718600—21no—
14C4×C4⋊Dic13C411yescharacteristic
15#11718586—21no—
16C13×#324—21no—
17C13×#324C2212yes—
18#11718120—21no—
19#11718120C2212yes—
20C22×Q8×C13C2×C411yescharacteristic
21C22×D52—21no—
22C22×D52—21no—
23C22×D52C2×C412yes—
24C4×Q8×C13—41no—
25C4×Q8×C13—41no—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4C2311yescharacteristic
29C2×C42×C13C2×C411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C42×C13D411yescharacteristic
32#88201—44no—
33C2×#6103—22no—
34C2×#6103—22no—
35C2×#6103—22no—
36C2×#6103—22no—
37C2×C4⋊Dic13—21no—
38C2×C4×Dic13C2×C412yes—
39#88128—41no—
40#88128—41no—
41C13×C4⋊C8—41no—
42C13×C22⋊C8—22no—
43C13×#97—41no—
44#88071—21no—
45C22⋊#1055—22no—
46C4⋊#1055—41no—
47C4×#1055—41no—
48#11567—131nomaximal, Sylow
49C23×D13—22no—
50C2×Q8×C13—22no—
51C2×Q8×C13—22no—
52C2×Q8×C13—41no—
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22×C411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×Dic13—22no—
61C2×D52—24no—
62C2×D52—42no—
63C2×D52—42no—
64C2×D52—42no—
65C2×D52—42no—
66C2×D52—42no—
67C2×D52—41no—
68C2×D52—41no—
69C2×D52—82no—
70C2×C8×C13—42no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—41no—
74C42×C13—21no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—21no—
80#6103—44no—
81#6103—44no—
82#6103—82no—
83#6103—82no—
84C4⋊Dic13—42no—
85C4×Dic13—42no—
86C2×#1055—42no—
87#2548—131no—
88#1467D1311yescharacteristic, complemented
89#1461—131no—
90#1318—134no—
91C23×C13C2×C22⋊C411yescharacteristic
92C22×D13—42no—
93C22×D13—42no—
94C22×D13—42no—
95C22×D13—42no—
96C22×D13—42no—
97C22×D13—42no—
98C22×D13—42no—
99Q8×C13—44no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—22no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13#9911yescharacteristic
115C2×C4×C13#9911yescharacteristic
116C2×C4×C13#10012yes—
117C2×C4×C13#13112yes—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121D52—82no—
122D52—84no—
123D52—84no—
124D52—82no—
125C8×C13—82no—
126#1055—82no—
127C2×#127—131no—
128C2×#124—132no—
129C2×C4×Q8C2×D1311yescharacteristic
130#432—21no—
131#431—261no—
132#394—261no—
133#394—261no—
134#390—132no—
135#390—261no—
136#390—261no—
137C4×C4⋊C4—131no—
138#324—21no—
139#324—132no—
140#324—261no—
141#324C2×D1312yes—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13#40811yescharacteristic
145C22×C13C2×#9911yescharacteristic
146C22×C13C2×#10011yescharacteristic
147C2×D13—82no—
148C2×D13—82no—
149C2×D13—82no—
150C2×D13—82no—
151C2×D13—82no—
152C2×D13—82no—
153C2×D13—82no—
154C4×C13—21no—
155C4×C13—22no—
156C4×C13—22no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13#35512yes—
162Dic13—82no—
163C22×Q8C4×D1311yescharacteristic
164C22×D4—132no—
165C22×D4—261no—
166C22×D4—261no—
167#127—521no—
168#127—521no—
169#124—524no—
170C4×Q8—41no—
171C4×Q8—41no—
172C2×C4⋊C4—261no—
173C2×C4⋊C4D5211yescharacteristic
174C2×C4⋊C4C22⋊D1311yescharacteristic
175C2×C4⋊C4C22×D1311yescharacteristic
176C2×C22⋊C4—262no—
177C2×C22⋊C4—262no—
178C2×C22⋊C4—262no—
179C2×C22⋊C4—262no—
180C2×C42—132no—
181C2×C42C4×D1311yescharacteristic
182C2×C42D5211yescharacteristic
183C2×C42C22⋊D1311yescharacteristic
184C4⋊C8—41no—
185C4⋊C8—521no—
186C22⋊C8—22no—
187C22⋊C8—262no—
188#97—41no—
189C4×C8—521no—
190#95—261no—
191C2×C13—21no—
192C2×C13—21no—
193C2×C13#147111yescharacteristic
194C2×C13#212811yescharacteristic
195C2×C13C2×#35511yescharacteristic
196D13—162no—
197C24—262no—
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—41no—
201C2×D4—264no—
202C2×D4—522no—
203C2×D4—522no—
204C2×D4—522no—
205C2×D4—522no—
206C2×D4—522no—
207C2×D4—521no—
208C2×D4—521no—
209C2×D4—1042no—
210C22×C4—262no—
211C22×C4#610311yescharacteristic
212C22×C4#610311yescharacteristic
213C22×C4#610311yescharacteristic
214C22×C4#610311yescharacteristic
215C22×C4C2×C4×D1311yescharacteristic
216C22×C4C2×D5211yescharacteristic
217C22×C4C2×C22⋊D1311yescharacteristic
218C2×C8—42no—
219C2×C8—522no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—522no—
224C22⋊C4—524no—
225C22⋊C4—524no—
226C22⋊C4—1042no—
227C22⋊C4—1042no—
228C42—21no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—522no—
235C13#1156711yescharacteristic, complemented, Sylow
236C23—522no—
237C23—522no—
238C23—522no—
239C23—522no—
240C23—522no—
241C23—522no—
242C23—522no—
243C23C2×#610311yescharacteristic
244Q8—44no—
245D4—1044no—
246D4—1042no—
247D4—1044no—
248D4—1042no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—522no—
264C2×C4—522no—
265C2×C4—522no—
266C2×C4#8804611yescharacteristic
267C2×C4#8804611yescharacteristic
268C2×C4#8806312yes—
269C2×C4#8816112yes—
270C8—82no—
271C8—1042no—
272C22—21no—
273C22—21no—
274C22—1042no—
275C22—1042no—
276C22—1042no—
277C22—1042no—
278C22—1042no—
279C22—1042no—
280C22—1042no—
281C22C2×#8804611yescharacteristic
282C22#1171879011yescharacteristic
283C22C2×#8806311yescharacteristic
284C4—21no—
285C4—22no—
286C4—22no—
287C4—41no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—1042no—
292C4#1171806912yes—
293C2—21no—
294C2—21no—
295C2—2082no—
296C2#1311319711yescharacteristic
297C2#1311650711yescharacteristic
298C2C2×#1171806911yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1467C2
socleC22×C13C2×#99
prime radicalC2×#88128C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1467D13
hypocenterC13#11567
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
2. #13113160C2semidirect
3. #13112767C2semidirect
4. C13×#1467C2semidirect
88. #1467D13semidirect
235. C13#11567semidirect

Maximal subgroups

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

subgroupindex
#131198352
#131131602
#131127672
C13×#14672
#1156713