Finite Group Databasebeta

← #15755426

Subgroups — #15755426

Order 3328.

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

normal subgroups only

This group has 754 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#13113369C212yesmaximal, complemented
4#13113365C212yesmaximal
5C2×C13×#542C211yesmaximal, characteristic
6C13×#542—24no—
7C13×#542—24no—
8C2×C13×C4⋊Q8C411yescharacteristic, complemented
9C2×C13×#126—21no—
10C2×C13×#124—21no—
11C2×C13×#124C411yescharacteristic, complemented
12C2×C13×#123—21no—
13C2×C13×C22⋊Q8—21no—
14C2×C13×C22⋊Q8C2211yescharacteristic
15C2×C13×#121C2211yescharacteristic
16C2×C4×Q8×C13C411yescharacteristic, complemented
17C2×C4×D4×C13C411yescharacteristic, complemented
18C2×C13×#117C2211yescharacteristic
19#11718872C2212yes—
20#11718868C2212yes—
21#11718130—24no—
22#11718129—24no—
23#11718122—21no—
24#11718122—21no—
25#11718118—21no—
26#11718118—21no—
27C22×Q8×C13—21no—
28C22×Q8×C13C2×C411yescharacteristic
29C22×D4×C13—21no—
30C22×D4×C13C2×C411yescharacteristic
31C23×C4×C13—21no—
32C23×C4×C13C2311yescharacteristic
33C13×C4⋊Q8—22no—
34C13×C4⋊Q8—22no—
35C13×#126—28no—
36C13×#124—28no—
37C13×#124—22no—
38C13×#124—22no—
39C13×#123—28no—
40C13×C22⋊Q8—28no—
41C13×C22⋊Q8—22no—
42C13×C22⋊Q8D414yes—
43C13×#121—22no—
44C13×#121D414yes—
45C4×Q8×C13—22no—
46C4×Q8×C13—22no—
47C4×D4×C13—22no—
48C4×D4×C13—22no—
49C13×#117—22no—
50C13×#117—22no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4C2×C411yescharacteristic
55C2×C13×C4⋊C4C2×C411yescharacteristic
56C2×C13×C4⋊C4D411yescharacteristic
57C2×C13×C4⋊C4D411yescharacteristic
58C2×C13×C22⋊C4—21no—
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4D411yescharacteristic
64C2×C13×C22⋊C4D411yescharacteristic
65C2×C42×C13—21no—
66C2×C42×C13C2×C411yescharacteristic
67C2×C42×C13C2×C411yescharacteristic
68C2×C22⋊Dic13—22no—
69C2×#6099—22no—
70#88071—22no—
71#88071—22no—
72C22⋊#1055—22no—
73C22⋊#1055—22no—
74#8519—131nomaximal, Sylow
75C24×C13—21no—
76C24×C13C2×D411yescharacteristic
77C2×Q8×C13—24no—
78C2×Q8×C13—21no—
79C2×Q8×C13—42no—
80C2×Q8×C13—82no—
81C2×Q8×C13C22⋊C412yes—
82C2×D4×C13—24no—
83C2×D4×C13—21no—
84C2×D4×C13—42no—
85C2×D4×C13—82no—
86C2×D4×C13C22⋊C412yes—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—24no—
91C22×C4×C13—42no—
92C22×C4×C13—82no—
93C22×C4×C13C22⋊C411yescharacteristic
94C22×C4×C13C22⋊C411yescharacteristic
95C22×C4×C13C22⋊C411yescharacteristic
96C22×C4×C13C22⋊C411yescharacteristic
97C22×C4×C13C22×C411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D412yes—
100C22×C4×C13C2×D412yes—
101C22×Dic13—42no—
102C13×C4⋊C4—24no—
103C13×C4⋊C4—24no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—24no—
107C13×C4⋊C4—22no—
108C13×C4⋊C4—22no—
109C13×C4⋊C4C22⋊C412yes—
110C13×C4⋊C4C22⋊C412yes—
111C13×C22⋊C4—24no—
112C13×C22⋊C4—24no—
113C13×C22⋊C4—24no—
114C13×C22⋊C4—24no—
115C13×C22⋊C4—22no—
116C13×C22⋊C4—22no—
117C13×C22⋊C4—24no—
118C42×C13—24no—
119C42×C13—21no—
120C42×C13—21no—
121C42×C13—21no—
122C42×C13—21no—
123C22⋊Dic13—44no—
124#6099—44no—
125C2×#1055—42no—
126C2×#542D1311yescharacteristic
127#1822—131no—
128#1820—131no—
129#1511—132no—
130#1510—132no—
131C23×C13—22no—
132C23×C13—22no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13—42no—
136C23×C13—42no—
137C23×C13—42no—
138C23×C13C2×C22⋊C411yescharacteristic
139C23×C13#12012yes—
140Q8×C13—42no—
141Q8×C13—42no—
142Q8×C13—84no—
143D4×C13—42no—
144D4×C13—42no—
145D4×C13—84no—
146C2×C4×C13—22no—
147C2×C4×C13—22no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—22no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—22no—
154C2×C4×C13—22no—
155C2×C4×C13—42no—
156C2×C4×C13—42no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—84no—
165C2×C4×C13C2×C22⋊C411yescharacteristic
166C2×C4×C13C2×C22⋊C411yescharacteristic
167C2×C4×C13#12012yes—
168C2×Dic13—82no—
169C2×Dic13—82no—
170C2×Dic13—82no—
171#1055—82no—
172#542—24no—
173#542—24no—
174C2×C4⋊Q8Dic1311yescharacteristic, complemented
175C2×#126—21no—
176C2×#124—21no—
177C2×#124Dic1311yescharacteristic, complemented
178C2×#123—21no—
179C2×C22⋊Q8—21no—
180C2×C22⋊Q8C2×D1311yescharacteristic
181C2×#121C2×D1311yescharacteristic
182C2×C4×Q8Dic1311yescharacteristic, complemented
183C2×C4×D4Dic1311yescharacteristic, complemented
184C2×#117C2×D1311yescharacteristic
185#407—132no—
186#381—132no—
187#343—261no—
188#343—261no—
189#342—261no—
190#342—261no—
191#328—264no—
192#327—264no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—22no—
196C22×C13—22no—
197C22×C13—22no—
198C22×C13—42no—
199C22×C13—42no—
200C22×C13—42no—
201C22×C13—82no—
202C22×C13—84no—
203C22×C13#37911yescharacteristic
204C22×C13#41012yes—
205C4×C13—22no—
206C4×C13—21no—
207C4×C13—21no—
208C4×C13—42no—
209C4×C13—42no—
210C4×C13—41no—
211C4×C13—41no—
212C4×C13—41no—
213C4×C13—41no—
214C4×C13—42no—
215Dic13—162no—
216C22×Q8—21no—
217C22×Q8C2×Dic1311yescharacteristic
218C22×D4—21no—
219C22×D4C2×Dic1311yescharacteristic
220C23×C4—21no—
221C23×C4C22×D1311yescharacteristic
222C2×M16—262no—
223C4⋊Q8—22no—
224C4⋊Q8—22no—
225#126—28no—
226#124—28no—
227#124—22no—
228#124—22no—
229#123—28no—
230C22⋊Q8—28no—
231C22⋊Q8—22no—
232C22⋊Q8C22⋊D1314yes—
233#121—22no—
234#121C22⋊D1314yes—
235C4×Q8—22no—
236C4×Q8—22no—
237C4×D4—22no—
238C4×D4—22no—
239#117—22no—
240#117—22no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4C2×Dic1311yescharacteristic
245C2×C4⋊C4C2×Dic1311yescharacteristic
246C2×C4⋊C4C22⋊D1311yescharacteristic
247C2×C4⋊C4C22⋊D1311yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—262no—
254C2×C22⋊C4C22⋊D1311yescharacteristic
255C2×C22⋊C4C22⋊D1311yescharacteristic
256C2×C42—21no—
257C2×C42C2×Dic1311yescharacteristic
258C2×C42C2×Dic1311yescharacteristic
259C22⋊C8—262no—
260C22⋊C8—262no—
261#95—262no—
262#95—262no—
263C2×C13—22no—
264C2×C13—42no—
265C2×C13—82no—
266C2×C13#178211yescharacteristic
267C2×C13#179511yescharacteristic
268C2×C13#179611yescharacteristic
269C24—21no—
270C24C2×C22⋊D1311yescharacteristic
271C2×Q8—24no—
272C2×Q8—21no—
273C2×Q8—42no—
274C2×Q8—82no—
275C2×Q8C22⋊Dic1312yes—
276C2×D4—24no—
277C2×D4—21no—
278C2×D4—42no—
279C2×D4—82no—
280C2×D4C22⋊Dic1312yes—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—24no—
285C22×C4—42no—
286C22×C4—82no—
287C22×C4—522no—
288C22×C4C22⋊Dic1311yescharacteristic
289C22×C4C22⋊Dic1311yescharacteristic
290C22×C4C22⋊Dic1311yescharacteristic
291C22×C4C22⋊Dic1311yescharacteristic
292C22×C4C22×Dic1311yescharacteristic
293C22×C4C2×C22⋊D1311yescharacteristic
294C22×C4C2×C22⋊D1312yes—
295C22×C4C2×C22⋊D1312yes—
296M16—524no—
297C2×C8—522no—
298C4⋊C4—24no—
299C4⋊C4—24no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—24no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4C22⋊Dic1312yes—
306C4⋊C4C22⋊Dic1312yes—
307C22⋊C4—24no—
308C22⋊C4—24no—
309C22⋊C4—24no—
310C22⋊C4—24no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—24no—
314C22⋊C4—524no—
315C42—24no—
316C42—21no—
317C42—21no—
318C42—21no—
319C42—21no—
320C13#851911yescharacteristic, complemented, Sylow
321C23—22no—
322C23—22no—
323C23—41no—
324C23—41no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23C2×C22⋊Dic1311yescharacteristic
329C23#8820712yes—
330Q8—42no—
331Q8—42no—
332Q8—84no—
333D4—42no—
334D4—42no—
335D4—84no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—84no—
355C2×C4—1042no—
356C2×C4—1042no—
357C2×C4—1042no—
358C2×C4C2×C22⋊Dic1311yescharacteristic
359C2×C4C2×C22⋊Dic1311yescharacteristic
360C2×C4#8820712yes—
361C8—1042no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—42no—
368C22—42no—
369C22—42no—
370C22—82no—
371C22—84no—
372C22#1171890112yes—
373C22#1171890811yescharacteristic
374C4—22no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—42no—
379C4—42no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—2082no—
385C2—22no—
386C2—42no—
387C2—82no—
388C2#1311475411yescharacteristic
389C2#1311480611yescharacteristic
390C2#1311481111yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#542C2
socleC22×C13#379
prime radicalC2×C13×#121C22
cosocleC23×C4×C13C23
hypercenterC2×#542D13
hypocenterC13#8519
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. #13114919C2semidirect
2. #13114913C2semidirect
3. #13113369C2semidirect
8. C2×C13×C4⋊Q8C4semidirect
11. C2×C13×#124C4semidirect
16. C2×C4×Q8×C13C4semidirect
17. C2×C4×D4×C13C4semidirect
174. C2×C4⋊Q8Dic13semidirect
177. C2×#124Dic13semidirect
182. C2×C4×Q8Dic13semidirect
183. C2×C4×D4Dic13semidirect
320. C13#8519semidirect

Maximal subgroups

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

subgroupindex
#131149192
#131149132
#131133692
#131133652
C2×C13×#5422
#851913