Finite Group Databasebeta

← #16779964

Subgroups — #16779964

Order 3328.

562 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131512C211yesmaximal, characteristic
2#13131512C211yesmaximal, characteristic
3#13129724C214yesmaximal, complemented
4#13117231C211yesmaximal, characteristic
5C22×C4×Dic13C2211yescharacteristic
6#11719169—21no—
7#11719169—21no—
8#11719130C412yescomplemented
9#11719130C2212yes—
10#11719129—21no—
11#11719129C412yescomplemented
12#11719128—21no—
13#11719128C412yescomplemented
14#11719125—21no—
15#11719125—21no—
16C4×#6122—21no—
17C4×#6122C2212yes—
18#11719119—21no—
19#11719119C412yescomplemented
20C13×#380C411yescharacteristic
21#11718873C411yescharacteristic
22#11718638—21no—
23C4⋊C4×Dic13—21no—
24#11718604—21no—
25C22⋊C4×Dic13—21no—
26#11718312C412yes—
27#11718309C2212yes—
28C23×C4×C13C2×C411yescharacteristic
29C23×Dic13D411yescharacteristic
30C23×Dic13D411yescharacteristic
31C2×#6122—22no—
32C2×#6122—22no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C22⋊C4—21no—
35C2×C22⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4×Dic13—22no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13C2×C411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13Q811yescharacteristic
48C2×C4×Dic13Q811yescharacteristic
49C2×C4×Dic13C2311yescharacteristic
50C22⋊#1057—22no—
51C22⋊#1057—22no—
52C22⋊#1057—22no—
53C22⋊#1057—22no—
54#88112—22no—
55#88112—22no—
56#88110—22no—
57#88110C2×C414yes—
58C4⋊#1057—22no—
59C4⋊#1057C2×C414yes—
60C4×#1057—22no—
61C4×#1057—22no—
62C13×#95C2×C412yes—
63#88071—22no—
64#88071—22no—
65#88071—22no—
66#88071C2×C412yes—
67#8070—131nomaximal, Sylow
68C24×C13C22⋊C411yescharacteristic
69C22×C4×C13—22no—
70C22×C4×C13—42no—
71C22×C4×C13C4211yescharacteristic
72C22×C4×C13C4211yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C4⋊C411yescharacteristic
75C22×C4×C13C4⋊C411yescharacteristic
76C22×C4×C13C22×C411yescharacteristic
77C22×Dic13—22no—
78C22×Dic13—42no—
79C22×Dic13—41no—
80C22×Dic13—41no—
81C22×Dic13C22⋊C411yescharacteristic
82C22×Dic13C22⋊C411yescharacteristic
83C22×Dic13C22⋊C411yescharacteristic
84C22×Dic13C22⋊C411yescharacteristic
85C22×Dic13C22⋊C411yescharacteristic
86C22×Dic13C22⋊C411yescharacteristic
87C22×Dic13C4⋊C411yescharacteristic
88C22×Dic13C4⋊C411yescharacteristic
89C22×Dic13C4⋊C411yescharacteristic
90C22×Dic13C4⋊C411yescharacteristic
91C22×Dic13C2×D411yescharacteristic
92C22×Dic13C2×D411yescharacteristic
93#6122—42no—
94#6122—42no—
95#6122—44no—
96C2×#1057—24no—
97C2×#1057—24no—
98C13×C4⋊C4—42no—
99C13×C22⋊C4—42no—
100C22⋊Dic13—42no—
101C4⋊Dic13—42no—
102C4×Dic13—44no—
103C4×Dic13C4211yescharacteristic
104C4×Dic13C4211yescharacteristic
105C4×Dic13C22⋊C411yescharacteristic
106C4×Dic13C22⋊C411yescharacteristic
107C4×Dic13C22⋊C411yescharacteristic
108C4×Dic13C22⋊C411yescharacteristic
109C4×Dic13C4⋊C411yescharacteristic
110C4×Dic13C4⋊C411yescharacteristic
111C4×Dic13C4⋊C411yescharacteristic
112C4×Dic13C4⋊C411yescharacteristic
113C4×Dic13C4⋊C411yescharacteristic
114C4×Dic13C4⋊C411yescharacteristic
115C4×Dic13C22×C411yescharacteristic
116C4×Dic13C22×C411yescharacteristic
117C4×Dic13C2×D411yescharacteristic
118C4×Dic13C2×Q811yescharacteristic
119#2920—131no—
120#2920—131no—
121#2283—131no—
122#1300—134no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13#9511yescharacteristic
128C23×C13#9511yescharacteristic
129C23×C13C2×C22⋊C411yescharacteristic
130C2×C4×C13—22no—
131C2×C4×C13—22no—
132C2×C4×C13—22no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—42no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13#9511yescharacteristic
140C2×C4×C13#9511yescharacteristic
141C2×C4×C13C2×C4211yescharacteristic
142C2×C4×C13C2×C4⋊C411yescharacteristic
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—22no—
148C2×Dic13—22no—
149C2×Dic13—22no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—42no—
158C2×Dic13—42no—
159C2×Dic13—42no—
160C2×Dic13#9511yescharacteristic
161C2×Dic13#9511yescharacteristic
162C2×Dic13#9511yescharacteristic
163C2×Dic13#9511yescharacteristic
164C2×Dic13C2×C22⋊C411yescharacteristic
165C2×Dic13C2×C22⋊C411yescharacteristic
166C2×Dic13C2×C4⋊C411yescharacteristic
167C2×Dic13C2×C4⋊C411yescharacteristic
168#1057—44no—
169#1057—44no—
170C22×C42—131no—
171#432—132no—
172#432—132no—
173#432—132no—
174#432—261no—
175#431—132no—
176#431—261no—
177#431—261no—
178#431—261no—
179#423—132no—
180#423—261no—
181#407—261no—
182#407—261no—
183C4×M16—132no—
184C4×M16—261no—
185#383—132no—
186#382—261no—
187#381—261no—
188#380—131no—
189#380#26111yescharacteristic
190C4×C4⋊C4—261no—
191C4×C22⋊C4—261no—
192#376—132no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—42no—
202C22×C13—42no—
203C22×C13C2×#9511yescharacteristic
204C22×C13#42111yescharacteristic
205C22×C13#42111yescharacteristic
206C4×C13—21no—
207C4×C13—21no—
208C4×C13—21no—
209C4×C13—82no—
210C4×C13#34412yes—
211Dic13—21no—
212Dic13—21no—
213Dic13—21no—
214Dic13—21no—
215Dic13—21no—
216Dic13—21no—
217Dic13—21no—
218Dic13—82no—
219Dic13#42112yes—
220C23×C4—131no—
221C23×C4—131no—
222C23×C4C2×#26111yescharacteristic
223C2×M16—262no—
224C2×M16—262no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—261no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—261no—
229C2×C42—131no—
230C2×C42—131no—
231C2×C42—131no—
232C2×C42—131no—
233C2×C42—131no—
234C2×C42—131no—
235C2×C42—131no—
236C2×C42—131no—
237C2×C42—131no—
238C2×C42—131no—
239C2×C42—131no—
240C2×C42—131no—
241C2×C42—262no—
242C4⋊C8—134no—
243C4⋊C8—262no—
244C4⋊C8—262no—
245C4⋊C8—262no—
246C22⋊C8—262no—
247C22⋊C8—262no—
248C22⋊C8—262no—
249C22⋊C8—262no—
250#97—134no—
251#97—262no—
252C4×C8—262no—
253C4×C8—262no—
254#95—132no—
255#95—262no—
256#95—262no—
257#95—262no—
258#95C2×#26112yes—
259C2×C13—21no—
260C2×C13—21no—
261C2×C13—41no—
262C2×C13—41no—
263C2×C13#173311yescharacteristic
264C2×C13#173311yescharacteristic
265C2×C13C2×#34411yescharacteristic
266C24C22⋊#26111yescharacteristic
267C22×C4—22no—
268C22×C4—42no—
269C22×C4—131no—
270C22×C4—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—262no—
282C22×C4—522no—
283C22×C4—521no—
284C22×C4—521no—
285C22×C4C4×#26111yescharacteristic
286C22×C4C4×#26111yescharacteristic
287C22×C4C4⋊#26111yescharacteristic
288C22×C4C4⋊#26111yescharacteristic
289C22×C4C22⋊#26111yescharacteristic
290C22×C4C22×#26111yescharacteristic
291M16—524no—
292M16—522no—
293M16—522no—
294C2×C8—264no—
295C2×C8—264no—
296C4⋊C4—42no—
297C4⋊C4—522no—
298C22⋊C4—42no—
299C22⋊C4—522no—
300C42—131no—
301C42—131no—
302C42—131no—
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—131no—
316C42—524no—
317C13#807011yescharacteristic, complemented, Sylow
318C23—21no—
319C23—21no—
320C23—41no—
321C23—41no—
322C23(C2×#261)⋊C411yescharacteristic
323C23(C2×#261)⋊C411yescharacteristic
324C23C2×C22⋊#26111yescharacteristic
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—131no—
335C2×C4—131no—
336C2×C4—131no—
337C2×C4—131no—
338C2×C4—131no—
339C2×C4—131no—
340C2×C4—131no—
341C2×C4—131no—
342C2×C4—262no—
343C2×C4—262no—
344C2×C4—262no—
345C2×C4—261no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—521no—
350C2×C4—521no—
351C2×C4—521no—
352C2×C4—521no—
353C2×C4—521no—
354C2×C4—521no—
355C2×C4—521no—
356C2×C4—522no—
357C2×C4—522no—
358C2×C4—522no—
359C2×C4(C2×#261)⋊C411yescharacteristic
360C2×C4(C2×#261)⋊C411yescharacteristic
361C2×C4C2×C4×#26111yescharacteristic
362C2×C4C2×C4⋊#26111yescharacteristic
363C8—524no—
364C8—524no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—42no—
374C22—42no—
375C22C2×(C2×#261)⋊C411yescharacteristic
376C22#1171914011yescharacteristic
377C22#1171915511yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—82no—
382C4—132no—
383C4—261no—
384C4—261no—
385C4—261no—
386C4—261no—
387C4—261no—
388C4—261no—
389C4—261no—
390C4—1042no—
391C4#1171823912yes—
392C2—21no—
393C2—21no—
394C2—41no—
395C2—41no—
396C2#1313051511yescharacteristic
397C2#1313051711yescharacteristic
398C2C2×#1171823911yescharacteristic
subgroupG/H
centerC22C2×(C2×#261)⋊C4
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#380C4
socleC22×C13C2×#95
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#380#261
hypocenterC13#8070
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #13129724C2semidirect
8. #11719130C4semidirect
11. #11719129C4semidirect
13. #11719128C4semidirect
19. #11719119C4semidirect
317. C13#8070semidirect

Maximal subgroups

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

subgroupindex
#131315122
#131297242
#131172312
#807013