Finite Group Databasebeta

← #16779863

Subgroups — #16779863

Order 3328.

696 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131283C211yesmaximal, characteristic
2C4×#88237C211yesmaximal, characteristic
3#13129716C214yesmaximal
4#13123468C211yesmaximal, characteristic
5C2×#88237—21no—
6C2×C42×D13C2211yescharacteristic
7#11719136—21no—
8#11719135—21no—
9C4×C22⋊#261—21no—
10C4×C22⋊#261C2212yes—
11C4×C22⋊#261C2212yes—
12#11719061C412yescomplemented
13#11719060C412yescomplemented
14C4×C4⋊#261—21no—
15C4×C4⋊#261—21no—
16C4×C4⋊#261C412yescomplemented
17#11719057—21no—
18#11719057C412yescomplemented
19C42×#261—21no—
20C13×#423C411yescharacteristic, complemented
21#11718787C2212yes—
22M16×Dic13C412yescomplemented
23#11718585C411yescharacteristic, complemented
24#11718496—21no—
25#11718496—21no—
26#11718494—21no—
27#11718494—21no—
28C22×C4×D13D411yescharacteristic
29C22×C4×D13D411yescharacteristic
30C22×C4×D13C2311yescharacteristic
31C2×C22⋊#261—22no—
32C2×C22⋊#261—22no—
33#88237—28no—
34C2×C4⋊#261—22no—
35C2×C4⋊#261—22no—
36C2×C4×#261—22no—
37C2×C4×#261—22no—
38C2×C4×#261—22no—
39C2×C4×#261—22no—
40C2×C13×M16C2×C412yes—
41C2×C42×C13C2×C411yescharacteristic
42C2×C4×Dic13C2×C411yescharacteristic
43C2×C4×Dic13Q811yescharacteristic
44C2×C4×Dic13Q811yescharacteristic
45C2×#6099C2×C412yes—
46C42×D13C2×C411yescharacteristic
47C42×D13C2×C411yescharacteristic
48C42×D13C2×C411yescharacteristic
49C42×D13C2×C411yescharacteristic
50C42×D13D411yescharacteristic
51C42×D13D411yescharacteristic
52C42×D13D411yescharacteristic
53C42×D13D411yescharacteristic
54(C2×#261)⋊C4—22no—
55(C2×#261)⋊C4—22no—
56(C2×#261)⋊C4—22no—
57(C2×#261)⋊C4—22no—
58(C2×#261)⋊C4C2×C414yes—
59(C2×#261)⋊C4C2×C414yes—
60C13×C4⋊C8—21no—
61C13×C4⋊C8—21no—
62#88060—22no—
63#88060—22no—
64#88055—22no—
65C8×Dic13—22no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68#8052—131nomaximal, Sylow
69C23×D13C2×D411yescharacteristic
70C22×#261—24no—
71C22×#261—24no—
72C22×C4×C13C4⋊C411yescharacteristic
73C22×C4×C13C4⋊C411yescharacteristic
74C22×C4×C13C22×C411yescharacteristic
75C22×Dic13C4⋊C411yescharacteristic
76C22×Dic13C4⋊C411yescharacteristic
77C22×Dic13C2×Q811yescharacteristic
78C2×C4×D13—24no—
79C2×C4×D13—41no—
80C2×C4×D13—41no—
81C2×C4×D13—42no—
82C2×C4×D13C22⋊C411yescharacteristic
83C2×C4×D13C22⋊C411yescharacteristic
84C2×C4×D13C22⋊C411yescharacteristic
85C2×C4×D13C22⋊C411yescharacteristic
86C2×C4×D13C22⋊C411yescharacteristic
87C2×C4×D13C22⋊C411yescharacteristic
88C2×C4×D13C22⋊C411yescharacteristic
89C2×C4×D13C22⋊C411yescharacteristic
90C2×C4×D13C22×C411yescharacteristic
91C2×C4×D13C22×C411yescharacteristic
92C2×C4×D13C2×D411yescharacteristic
93C2×C4×D13C2×D411yescharacteristic
94C22⋊#261—28no—
95C22⋊#261—44no—
96C4⋊#261—28no—
97C4⋊#261—44no—
98C4×#261—28no—
99C4×#261—44no—
100C4×#261—42no—
101C4×#261—42no—
102C4×#261—42no—
103C4×#261—42no—
104C13×M16—42no—
105C2×C8×C13—22no—
106C42×C13C4211yescharacteristic
107C42×C13C4211yescharacteristic
108C42×C13C22⋊C411yescharacteristic
109C42×C13C22⋊C411yescharacteristic
110C4×Dic13C4211yescharacteristic
111C4×Dic13C4211yescharacteristic
112C4×Dic13C22⋊C411yescharacteristic
113C4×Dic13C22⋊C411yescharacteristic
114C4×Dic13C4⋊C411yescharacteristic
115C4×Dic13C4⋊C411yescharacteristic
116C4×Dic13C4⋊C411yescharacteristic
117C4×Dic13C4⋊C411yescharacteristic
118C4×Dic13C4⋊C411yescharacteristic
119C4×Dic13C4⋊C411yescharacteristic
120C4×Dic13C4⋊C411yescharacteristic
121C4×Dic13C4⋊C411yescharacteristic
122#6099—42no—
123C2×#1055—22no—
124#2920—131no—
125#2283—131no—
126C4×#117—131no—
127#1297—134no—
128C23×C13C2×C4⋊C411yescharacteristic
129C22×D13—22no—
130C22×D13—22no—
131C22×D13—41no—
132C22×D13C2×C22⋊C411yescharacteristic
133C22×D13C2×C22⋊C411yescharacteristic
134C2×#261—28no—
135C2×#261—44no—
136C2×#261—44no—
137C2×#261—44no—
138C2×#261—44no—
139C2×#261—44no—
140C2×C4×C13—22no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—41no—
144C2×C4×C13#9511yescharacteristic
145C2×C4×C13#9511yescharacteristic
146C2×C4×C13#9511yescharacteristic
147C2×C4×C13#9511yescharacteristic
148C2×C4×C13C2×C4211yescharacteristic
149C2×C4×C13C2×C22⋊C411yescharacteristic
150C2×Dic13—22no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13#9511yescharacteristic
154C2×Dic13#9511yescharacteristic
155C2×Dic13#9511yescharacteristic
156C2×Dic13#9511yescharacteristic
157C2×Dic13C2×C4⋊C411yescharacteristic
158C2×Dic13C2×C4⋊C411yescharacteristic
159C4×D13—22no—
160C4×D13—22no—
161C4×D13—22no—
162C4×D13—22no—
163C4×D13—21no—
164C4×D13—21no—
165C4×D13—21no—
166C4×D13—21no—
167C4×D13—22no—
168C4×D13—41no—
169C4×D13—41no—
170C4×D13—41no—
171C4×D13—41no—
172C4×D13#10414yes—
173C8×C13—42no—
174#1055—42no—
175C2×#117—261no—
176C22×C42—131no—
177#432—261no—
178#432—261no—
179#431—261no—
180#431—261no—
181#423—131no—
182#423#26111yescharacteristic, complemented
183#407—132no—
184C4×M16—132no—
185#383—132no—
186#382—132no—
187#381—261no—
188#380—261no—
189C4×C4⋊C4—132no—
190C4×C4⋊C4—261no—
191C4×C4⋊C4—261no—
192C4×C22⋊C4—132no—
193C4×C22⋊C4—132no—
194C4×C22⋊C4—261no—
195#376—132no—
196#376—261no—
197C43—261no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13C2×#9511yescharacteristic
202C2×D13—21no—
203C2×D13—21no—
204C2×D13—21no—
205C2×D13—21no—
206C2×D13—44no—
207C2×D13C2×#10412yes—
208C2×D13#42112yes—
209#261—48no—
210#261—84no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—21no—
215C4×C13#33912yes—
216C4×C13#41011yescharacteristic
217C4×C13#41011yescharacteristic
218Dic13—21no—
219Dic13—21no—
220Dic13—21no—
221Dic13—21no—
222Dic13—21no—
223Dic13#33912yes—
224C23×C4—131no—
225C23×C4—131no—
226C23×C4—131no—
227C2×M16—132no—
228C2×M16C2×#26112yes—
229#117—268no—
230C2×C4⋊C4—262no—
231C2×C4⋊C4—262no—
232C2×C22⋊C4—262no—
233C2×C22⋊C4—262no—
234C2×C42—131no—
235C2×C42—131no—
236C2×C42—131no—
237C2×C42—131no—
238C2×C42—131no—
239C2×C42—131no—
240C2×C42—131no—
241C2×C42—131no—
242C2×C42—131no—
243C2×C42—131no—
244C2×C42—131no—
245C2×C42—262no—
246C2×C42—262no—
247C2×C42—262no—
248C2×C42—262no—
249C2×C42C2×#26111yescharacteristic
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—261no—
253C4⋊C8—261no—
254C22⋊C8—262no—
255C22⋊C8—262no—
256#97—262no—
257C4×C8—262no—
258#95—134no—
259#95—134no—
260#95—262no—
261#95—262no—
262#95—262no—
263#95—262no—
264C2×C13—41no—
265C2×C13C2×#33911yescharacteristic
266C2×C13#173311yescharacteristic
267C2×C13#174011yescharacteristic
268D13—22no—
269D13—22no—
270C24—131no—
271C22×C4—131no—
272C22×C4—131no—
273C22×C4—131no—
274C22×C4—131no—
275C22×C4—131no—
276C22×C4—131no—
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—264no—
287C22×C4—264no—
288C22×C4—264no—
289C22×C4—521no—
290C22×C4—521no—
291C22×C4—522no—
292C22×C4C4⋊#26111yescharacteristic
293C22×C4C4⋊#26111yescharacteristic
294C22×C4C22×#26111yescharacteristic
295M16—42no—
296M16—522no—
297C2×C8—22no—
298C2×C8—262no—
299C4⋊C4—268no—
300C4⋊C4—524no—
301C22⋊C4—268no—
302C22⋊C4—524no—
303C42—131no—
304C42—131no—
305C42—131no—
306C42—131no—
307C42—131no—
308C42—131no—
309C42—131no—
310C42—131no—
311C42—131no—
312C42—131no—
313C42—131no—
314C42—131no—
315C42—268no—
316C42—524no—
317C42—522no—
318C42—522no—
319C42—522no—
320C42—522no—
321C42C4×#26111yescharacteristic
322C42C4×#26111yescharacteristic
323C42C22⋊#26111yescharacteristic
324C42C22⋊#26111yescharacteristic
325C13#805211yescharacteristic, complemented, Sylow
326C23—131no—
327C23—131no—
328C23—262no—
329C23—262no—
330C23—521no—
331C23C2×C4⋊#26111yescharacteristic
332C2×C4—22no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—131no—
337C2×C4—134no—
338C2×C4—131no—
339C2×C4—131no—
340C2×C4—131no—
341C2×C4—131no—
342C2×C4—131no—
343C2×C4—262no—
344C2×C4—262no—
345C2×C4—262no—
346C2×C4—262no—
347C2×C4—262no—
348C2×C4—262no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—261no—
353C2×C4—268no—
354C2×C4—521no—
355C2×C4—521no—
356C2×C4—521no—
357C2×C4—521no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—524no—
361C2×C4—524no—
362C2×C4—524no—
363C2×C4—524no—
364C2×C4—524no—
365C2×C4(C2×#261)⋊C411yescharacteristic
366C2×C4(C2×#261)⋊C411yescharacteristic
367C2×C4(C2×#261)⋊C411yescharacteristic
368C2×C4(C2×#261)⋊C411yescharacteristic
369C2×C4C2×C4×#26111yescharacteristic
370C2×C4C2×C22⋊#26111yescharacteristic
371C8—42no—
372C8—522no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—132no—
377C22—132no—
378C22—261no—
379C22—261no—
380C22—261no—
381C22—261no—
382C22—524no—
383C22C2×(C2×#261)⋊C411yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—132no—
389C4—261no—
390C4—261no—
391C4—261no—
392C4—261no—
393C4—261no—
394C4—528no—
395C4—1044no—
396C4#1171827212yes—
397C4#1171914211yescharacteristic
398C4#1171915611yescharacteristic
399C2—41no—
400C2—262no—
401C2—262no—
402C2C2×#1171827211yescharacteristic
403C2#1313051811yescharacteristic
404C2#1313053611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#423C4
socleC22×C13C2×#95
prime radicalC23×D13C2×D4
cosocleC22×C4×D13C23
hypercenter#423#261
hypocenterC13#8052
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
12. #11719061C4semidirect
13. #11719060C4semidirect
16. C4×C4⋊#261C4semidirect
18. #11719057C4semidirect
20. C13×#423C4semidirect
22. M16×Dic13C4semidirect
23. #11718585C4semidirect
182. #423#261semidirect
325. C13#8052semidirect

Maximal subgroups

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

subgroupindex
#131312832
C4×#882372
#131297162
#131234682
#805213