Finite Group Databasebeta

← #16779864

Subgroups — #16779864

Order 3328.

696 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131515C211yesmaximal, characteristic
2#13131283C211yesmaximal, characteristic
3#13129717C214yesmaximal
4C4×#88146C211yesmaximal, characteristic
5C2×#88146—21no—
6C2×C42×D13C2211yescharacteristic
7#11719136—21no—
8#11719135—21no—
9C4×C22⋊#261C2212yes—
10#11719128—21no—
11#11719127C2212yes—
12#11719125—21no—
13#11719061C412yescomplemented
14#11719060C412yescomplemented
15C4×C4⋊#261—21no—
16#11719057—21no—
17#11719055—21no—
18#11719053C412yescomplemented
19#11719049—21no—
20C4×#6118C412yescomplemented
21C4×C13×C4⋊C4C411yescharacteristic, complemented
22C4⋊C4×Dic13—21no—
23C4×#6103—21no—
24C4×C4⋊Dic13C411yescharacteristic, complemented
25C42×Dic13—21no—
26#11718327C2212yes—
27#11718309C412yescomplemented
28C22×C4×D13D411yescharacteristic
29C22×C4×D13D411yescharacteristic
30C22×C4×D13C2311yescharacteristic
31C2×C22⋊#261—22no—
32C2×C4⋊#261—22no—
33C2×C4×#261—22no—
34C2×#6118C2×C414yes—
35C2×C13×C4⋊C4—21no—
36C2×C42×C13—21no—
37C2×C42×C13C2×C411yescharacteristic
38C2×#6103—22no—
39C2×C4⋊Dic13—21no—
40C2×C4×Dic13—22no—
41C2×C4×Dic13—21no—
42C2×C4×Dic13—22no—
43C2×C4×Dic13C2×C411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46#88146—28no—
47C42×D13C2×C411yescharacteristic
48C42×D13C2×C411yescharacteristic
49C42×D13C2×C411yescharacteristic
50C42×D13C2×C411yescharacteristic
51C42×D13D411yescharacteristic
52C42×D13D411yescharacteristic
53C42×D13Q811yescharacteristic
54C42×D13Q811yescharacteristic
55C22⋊#1057—22no—
56(C2×#261)⋊C4—22no—
57(C2×#261)⋊C4—22no—
58(C2×#261)⋊C4—22no—
59(C2×#261)⋊C4C2×C414yes—
60#88112—22no—
61#88112—22no—
62#88111—22no—
63#88110—22no—
64C4×#1057—22no—
65C13×#95C2×C412yes—
66#88071—22no—
67#88071C2×C412yes—
68#8052—131nomaximal, Sylow
69C23×D13C2×D411yescharacteristic
70C22×#261—24no—
71C22×C4×C13—22no—
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22×C411yescharacteristic
75C22×Dic13—22no—
76C22×Dic13C22⋊C411yescharacteristic
77C22×Dic13C22⋊C411yescharacteristic
78C22×Dic13C2×D411yescharacteristic
79C2×C4×D13—24no—
80C2×C4×D13—42no—
81C2×C4×D13—41no—
82C2×C4×D13—41no—
83C2×C4×D13C22⋊C411yescharacteristic
84C2×C4×D13C22⋊C411yescharacteristic
85C2×C4×D13C22⋊C411yescharacteristic
86C2×C4×D13C22⋊C411yescharacteristic
87C2×C4×D13C4⋊C411yescharacteristic
88C2×C4×D13C4⋊C411yescharacteristic
89C2×C4×D13C4⋊C411yescharacteristic
90C2×C4×D13C4⋊C411yescharacteristic
91C2×C4×D13C22×C411yescharacteristic
92C2×C4×D13C22×C411yescharacteristic
93C2×C4×D13C2×D411yescharacteristic
94C2×C4×D13C2×Q811yescharacteristic
95C22⋊#261—42no—
96C22⋊#261—42no—
97C2×#1057—24no—
98C4⋊#261—44no—
99C4×#261—44no—
100#6118—44no—
101C13×C4⋊C4—24no—
102C42×C13—42no—
103C42×C13C4211yescharacteristic
104C42×C13C4211yescharacteristic
105C42×C13C4⋊C411yescharacteristic
106C42×C13C4⋊C411yescharacteristic
107#6103—28no—
108C4⋊Dic13—24no—
109C4×Dic13—28no—
110C4×Dic13—44no—
111C4×Dic13—42no—
112C4×Dic13C4211yescharacteristic
113C4×Dic13C4211yescharacteristic
114C4×Dic13C22⋊C411yescharacteristic
115C4×Dic13C22⋊C411yescharacteristic
116C4×Dic13C22⋊C411yescharacteristic
117C4×Dic13C22⋊C411yescharacteristic
118C4×Dic13C4⋊C411yescharacteristic
119C4×Dic13C4⋊C411yescharacteristic
120C4×Dic13C4⋊C411yescharacteristic
121C4×Dic13C4⋊C411yescharacteristic
122C4×Dic13C4⋊C411yescharacteristic
123C4×Dic13C4⋊C411yescharacteristic
124#2920—131no—
125#2283—131no—
126C4×#117—131no—
127#1297—134no—
128C23×C13C2×C22⋊C411yescharacteristic
129C22×D13—21no—
130C22×D13—21no—
131C22×D13—22no—
132C22×D13—41no—
133C22×D13C2×C22⋊C411yescharacteristic
134C22×D13C2×C4⋊C411yescharacteristic
135C2×#261—44no—
136C2×#261—44no—
137C2×#261—44no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—22no—
141C2×C4×C13—24no—
142C2×C4×C13—41no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13#9511yescharacteristic
146C2×C4×C13#9511yescharacteristic
147C2×C4×C13#9511yescharacteristic
148C2×C4×C13#9511yescharacteristic
149C2×C4×C13C2×C4211yescharacteristic
150C2×C4×C13C2×C4⋊C411yescharacteristic
151C2×Dic13—21no—
152C2×Dic13—21no—
153C2×Dic13—22no—
154C2×Dic13—22no—
155C2×Dic13—24no—
156C2×Dic13—42no—
157C2×Dic13—42no—
158C2×Dic13#9511yescharacteristic
159C2×Dic13#9511yescharacteristic
160C2×Dic13#9511yescharacteristic
161C2×Dic13#9511yescharacteristic
162C2×Dic13C2×C22⋊C411yescharacteristic
163C2×Dic13C2×C4⋊C411yescharacteristic
164C4×D13—22no—
165C4×D13—22no—
166C4×D13—22no—
167C4×D13—22no—
168C4×D13—22no—
169C4×D13—41no—
170C4×D13—41no—
171C4×D13—41no—
172C4×D13—41no—
173C4×D13—41no—
174C4×D13—41no—
175C4×D13#10414yes—
176#1057—44no—
177C2×#117—261no—
178C22×C42—131no—
179#432—261no—
180#432—261no—
181#431—261no—
182#431—261no—
183#423—132no—
184#407—132no—
185C4×M16—132no—
186#383—132no—
187#382—132no—
188#381—261no—
189#380—261no—
190C4×C4⋊C4—131no—
191C4×C4⋊C4—261no—
192C4×C4⋊C4—261no—
193C4×C4⋊C4#26111yescharacteristic, complemented
194C4×C22⋊C4—132no—
195C4×C22⋊C4—132no—
196C4×C22⋊C4—261no—
197#376—132no—
198#376—261no—
199C43—261no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13C2×#9511yescharacteristic
203C22×C13#42111yescharacteristic
204C22×C13#42111yescharacteristic
205C2×D13—21no—
206C2×D13—21no—
207C2×D13—21no—
208C2×D13—21no—
209C2×D13—21no—
210C2×D13—42no—
211C2×D13—42no—
212C2×D13C2×#10412yes—
213#261—84no—
214C4×C13—21no—
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—44no—
220C4×C13#33912yes—
221Dic13—21no—
222Dic13—21no—
223Dic13—21no—
224Dic13—21no—
225Dic13—44no—
226Dic13#33912yes—
227Dic13#41012yes—
228C23×C4—131no—
229C23×C4—131no—
230C23×C4—131no—
231C2×M16—134no—
232#117—268no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—261no—
235C2×C4⋊C4—262no—
236C2×C22⋊C4—262no—
237C2×C22⋊C4—262no—
238C2×C42—21no—
239C2×C42—131no—
240C2×C42—131no—
241C2×C42—131no—
242C2×C42—131no—
243C2×C42—131no—
244C2×C42—131no—
245C2×C42—131no—
246C2×C42—131no—
247C2×C42—131no—
248C2×C42—131no—
249C2×C42—131no—
250C2×C42—262no—
251C2×C42—262no—
252C2×C42—262no—
253C2×C42—261no—
254C2×C42C2×#26111yescharacteristic
255C4⋊C8—262no—
256C4⋊C8—262no—
257C22⋊C8—262no—
258C22⋊C8—262no—
259#97—262no—
260C4×C8—262no—
261#95—134no—
262#95—132no—
263#95—262no—
264#95—262no—
265#95—262no—
266#95—262no—
267#95C2×#26112yes—
268C2×C13—21no—
269C2×C13—21no—
270C2×C13C2×#33911yescharacteristic
271C2×C13#173311yescharacteristic
272C2×C13#174011yescharacteristic
273D13—22no—
274D13—41no—
275C24—131no—
276C22×C4—22no—
277C22×C4—131no—
278C22×C4—131no—
279C22×C4—131no—
280C22×C4—131no—
281C22×C4—131no—
282C22×C4—131no—
283C22×C4—131no—
284C22×C4—131no—
285C22×C4—131no—
286C22×C4—131no—
287C22×C4—131no—
288C22×C4—131no—
289C22×C4—131no—
290C22×C4—131no—
291C22×C4—131no—
292C22×C4—264no—
293C22×C4—262no—
294C22×C4—264no—
295C22×C4—521no—
296C22×C4—521no—
297C22×C4—522no—
298C22×C4C22⋊#26111yescharacteristic
299C22×C4C22⋊#26111yescharacteristic
300C22×C4C22×#26111yescharacteristic
301M16—524no—
302C2×C8—264no—
303C4⋊C4—24no—
304C4⋊C4—264no—
305C4⋊C4—524no—
306C22⋊C4—268no—
307C22⋊C4—522no—
308C22⋊C4—522no—
309C42—42no—
310C42—131no—
311C42—131no—
312C42—131no—
313C42—131no—
314C42—131no—
315C42—131no—
316C42—131no—
317C42—131no—
318C42—131no—
319C42—131no—
320C42—131no—
321C42—131no—
322C42—268no—
323C42—522no—
324C42—524no—
325C42—524no—
326C42C4×#26111yescharacteristic
327C42C4×#26111yescharacteristic
328C42C4⋊#26111yescharacteristic
329C42C4⋊#26111yescharacteristic
330C13#805211yescharacteristic, complemented, Sylow
331C23—131no—
332C23—131no—
333C23—262no—
334C23—261no—
335C23—261no—
336C23—521no—
337C23C2×C22⋊#26111yescharacteristic
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—131no—
346C2×C4—131no—
347C2×C4—134no—
348C2×C4—131no—
349C2×C4—131no—
350C2×C4—131no—
351C2×C4—131no—
352C2×C4—262no—
353C2×C4—262no—
354C2×C4—262no—
355C2×C4—262no—
356C2×C4—262no—
357C2×C4—262no—
358C2×C4—261no—
359C2×C4—261no—
360C2×C4—262no—
361C2×C4—264no—
362C2×C4—521no—
363C2×C4—521no—
364C2×C4—521no—
365C2×C4—521no—
366C2×C4—521no—
367C2×C4—521no—
368C2×C4—522no—
369C2×C4—522no—
370C2×C4—524no—
371C2×C4—524no—
372C2×C4—524no—
373C2×C4(C2×#261)⋊C411yescharacteristic
374C2×C4(C2×#261)⋊C411yescharacteristic
375C2×C4(C2×#261)⋊C411yescharacteristic
376C2×C4(C2×#261)⋊C411yescharacteristic
377C2×C4C2×C4×#26111yescharacteristic
378C2×C4C2×C4⋊#26111yescharacteristic
379C8—524no—
380C22—21no—
381C22—21no—
382C22—132no—
383C22—261no—
384C22—261no—
385C22—261no—
386C22—261no—
387C22—261no—
388C22—522no—
389C22—522no—
390C22C2×(C2×#261)⋊C411yescharacteristic
391C22#1171914011yescharacteristic
392C22#1171915511yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—44no—
399C4—132no—
400C4—132no—
401C4—261no—
402C4—261no—
403C4—261no—
404C4—261no—
405C4—524no—
406C4—1044no—
407C4#1171823412yes—
408C2—21no—
409C2—21no—
410C2—262no—
411C2—521no—
412C2C2×#1171823411yescharacteristic
413C2#1313051511yescharacteristic
414C2#1313053411yescharacteristic
subgroupG/H
centerC22C2×(C2×#261)⋊C4
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC4×C13×C4⋊C4C4
socleC22×C13C2×#95
prime radicalC23×D13C2×D4
cosocleC22×C4×D13C23
hypercenterC4×C4⋊C4#261
hypocenterC13#8052
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
13. #11719061C4semidirect
14. #11719060C4semidirect
18. #11719053C4semidirect
20. C4×#6118C4semidirect
21. C4×C13×C4⋊C4C4semidirect
24. C4×C4⋊Dic13C4semidirect
27. #11718309C4semidirect
193. C4×C4⋊C4#261semidirect
330. C13#8052semidirect

Maximal subgroups

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

subgroupindex
#131315152
#131312832
#131297172
C4×#881462
#805213