Finite Group Databasebeta

← #16787211

Subgroups — #16787211

Order 3328.

444 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 74 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#13130091C211yesmaximal, characteristic
2#13130075C211yesmaximal, characteristic
3#13129762C214yesmaximal, complemented
4#13119138C211yesmaximal, characteristic
5C22×C13×C4⋊C4C411yescharacteristic
6C2×#88183C412yes—
7C2×C4×C22⋊D13C2211yescharacteristic
8#11719127—21no—
9#11719125—21no—
10#11718873C411yescharacteristic
11#11718872C2212yes—
12#11718654—21no—
13#11718648—21no—
14#11718641—21no—
15#11718634—21no—
16#11718305C2212yes—
17#11718305C2212yes—
18#11718287—21no—
19#11718286—21no—
20C23×C4×C13C2×C412yes—
21C23×C4×C13C2×C411yescharacteristic
22C22×C22⋊D13C2×C411yescharacteristic
23C22×C4×D13D411yescharacteristic
24C2×#6118—41no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—41no—
28C2×C13×C4⋊C4—41no—
29C2×C22⋊Dic13C2×C412yes—
30C2×C22⋊Dic13C2311yescharacteristic
31#88183—44no—
32C4×C22⋊D13—41no—
33C4×C22⋊D13—41no—
34C2×#6103—22no—
35C2×#6103D411yescharacteristic
36C2×C4⋊Dic13—21no—
37C2×#6101—22no—
38C2×#6101D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C22⋊#1057—22no—
41C22⋊#1057—22no—
42#88112—41no—
43#88111—41no—
44C4×#1057—41no—
45#88071—21no—
46#88071—22no—
47#88071—22no—
48#11562—131nomaximal, Sylow
49C24×C13C22×C411yescharacteristic
50C23×D13C22⋊C411yescharacteristic
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—22no—
54C22×C4×C13—24no—
55C22×C4×C13—42no—
56C22×C4×C13—42no—
57C22×C4×C13—42no—
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C2×C22⋊D13—22no—
61C2×C22⋊D13—22no—
62C2×C22⋊D13—41no—
63C22×Dic13—22no—
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C2×D411yescharacteristic
66C22×Dic13C2×D411yescharacteristic
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×C4×D13—42no—
70C2×#1057—42no—
71C2×#1057—42no—
72#6118—82no—
73C13×C4⋊C4—42no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C22⋊Dic13—41no—
77C22⋊Dic13—42no—
78#6103—41no—
79#6103—44no—
80C4⋊Dic13—42no—
81#6101—41no—
82#6101—44no—
83C4×Dic13—21no—
84C4×Dic13—21no—
85#2486—131no—
86#1465—131no—
87#1460—131no—
88#1317—134no—
89C23×C13—21no—
90C23×C13—21no—
91C23×C13—41no—
92C23×C13—41no—
93C23×C13C2×C22⋊C411yescharacteristic
94C23×C13#13112yes—
95C22×D13—21no—
96C22×D13—21no—
97C22×D13—21no—
98C22×D13—41no—
99C22×D13—41no—
100C2×C4×C13—22no—
101C2×C4×C13—21no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—41no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—84no—
109C2×C4×C13#9911yescharacteristic
110C2×C4×C13#9911yescharacteristic
111C22⋊D13—44no—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—41no—
117C2×Dic13—41no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13#10012yes—
122C4×D13—42no—
123C4×D13—81no—
124#1057—82no—
125#1057—82no—
126C2×#123—132no—
127C2×C4×D4—131no—
128C22×C4⋊C4#26111yescharacteristic
129#431—261no—
130#407—261no—
131#398—261no—
132#397—261no—
133#389—261no—
134#381—132no—
135#380—131no—
136#380—261no—
137#324—261no—
138#323—132no—
139#323—132no—
140#323—261no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—22no—
144C22×C13—42no—
145C22×C13—42no—
146C22×C13—41no—
147C22×C13—41no—
148C22×C13#40811yescharacteristic
149C22×C13C2×#9911yescharacteristic
150C22×C13C2×#10011yescharacteristic
151C2×D13—42no—
152C2×D13—41no—
153C2×D13—41no—
154C2×D13—41no—
155C2×D13—81no—
156C4×C13—21no—
157C4×C13—41no—
158C4×C13—82no—
159C4×C13#35212yes—
160Dic13—22no—
161Dic13—41no—
162Dic13—41no—
163Dic13—82no—
164C22×D4—131no—
165C23×C4—131no—
166C23×C4C2×#26112yes—
167C23×C4C2×#26111yescharacteristic
168C2×M16—521no—
169#123—524no—
170C4×D4—521no—
171C4×D4—521no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—41no—
176C2×C4⋊C4—131no—
177C2×C4⋊C4—262no—
178C2×C4⋊C4—261no—
179C2×C22⋊C4—131no—
180C2×C22⋊C4—131no—
181C2×C22⋊C4—132no—
182C2×C22⋊C4—262no—
183C2×C42—131no—
184C4⋊C8—521no—
185C22⋊C8—262no—
186C22⋊C8—262no—
187C22⋊C8—521no—
188C4×C8—521no—
189#95—262no—
190#95—262no—
191#95—261no—
192C2×C13—21no—
193C2×C13—21no—
194C2×C13—42no—
195C2×C13#147111yescharacteristic
196C2×C13C2×#35211yescharacteristic
197C2×C13#212311yescharacteristic
198D13—81no—
199C24—131no—
200C24C22×#26111yescharacteristic
201C2×D4—262no—
202C2×D4—262no—
203C2×D4—521no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—24no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—131no—
212C22×C4—131no—
213C22×C4—131no—
214C22×C4—261no—
215C22×C4—261no—
216C22×C4—262no—
217C22×C4—522no—
218C22×C4C22⋊#26111yescharacteristic
219C22×C4C22⋊#26111yescharacteristic
220M16—1042no—
221C2×C8—522no—
222C2×C8—522no—
223C4⋊C4—42no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—521no—
227C4⋊C4—522no—
228C4⋊C4—524no—
229C22⋊C4—521no—
230C22⋊C4—524no—
231C22⋊C4—521no—
232C22⋊C4—522no—
233C42—261no—
234C42—261no—
235C13#1156211yescharacteristic, complemented, Sylow
236C23—21no—
237C23—21no—
238C23—41no—
239C23—41no—
240C23—261no—
241C23—261no—
242C23—261no—
243C23—521no—
244C23—521no—
245C23#8823812yes—
246C23C2×C22⋊#26111yescharacteristic
247D4—524no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—84no—
257C2×C4—132no—
258C2×C4—261no—
259C2×C4—261no—
260C2×C4—261no—
261C2×C4—261no—
262C2×C4—522no—
263C2×C4—521no—
264C2×C4—521no—
265C2×C4—522no—
266C2×C4—522no—
267C2×C4—522no—
268C2×C4—1041no—
269C2×C4#8811911yescharacteristic
270C2×C4#8811911yescharacteristic
271C8—1042no—
272C8—1042no—
273C22—21no—
274C22—21no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—41no—
279C22—41no—
280C22—522no—
281C22—521no—
282C22—521no—
283C22—521no—
284C22—1041no—
285C22#1171914711yescharacteristic
286C22D13⋊#10011yescharacteristic
287C22C2×#8811911yescharacteristic
288C4—21no—
289C4—41no—
290C4—82no—
291C4—262no—
292C4—521no—
293C4—521no—
294C4—1042no—
295C4#1171828812yes—
296C2—21no—
297C2—21no—
298C2—42no—
299C2—1041no—
300C2#1313011111yescharacteristic
301C2C2×#1171828811yescharacteristic
302C2#1313109811yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC24×C13C22×C4
FrattiniC24C22×#261
FittingC22×C13×C4⋊C4C4
socleC22×C13C2×#99
prime radicalC22×C22⋊D13C2×C4
cosocleC2×C22⋊Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#11562
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13129762C2semidirect
235. C13#11562semidirect

Maximal subgroups

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

subgroupindex
#131300912
#131300752
#131297622
#131191382
#1156213