Finite Group Databasebeta

← #16779976

Subgroups — #16779976

Order 3328.

698 conjugacy classes of subgroups.

The subgroup lattice has 412 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
4C2×#11718309C211yesmaximal, characteristic
5C22×C4×Dic13—21no—
6C22×C4×Dic13C2211yescharacteristic
7#11719169—21no—
8#11719169—21no—
9#11719130C412yescomplemented
10#11719130C2212yes—
11#11719129—21no—
12#11719129C412yescomplemented
13#11719128—21no—
14#11719128C412yescomplemented
15#11719125—21no—
16#11719125—21no—
17C4×#6122—21no—
18C4×#6122C2212yes—
19#11719119—21no—
20#11719119C412yescomplemented
21C2×C13×#95C411yescharacteristic
22C2×#88071—21no—
23C2×#88071C411yescharacteristic
24#11718309—21no—
25#11718309—21no—
26#11718309C412yes—
27#11718309C2212yes—
28C23×C4×C13—21no—
29C23×C4×C13C2×C411yescharacteristic
30C23×Dic13—21no—
31C23×Dic13D411yescharacteristic
32C23×Dic13D411yescharacteristic
33C2×#6122—22no—
34C2×#6122—22no—
35C2×C4×Dic13—28no—
36C2×C4×Dic13—22no—
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×C414yescomplemented
58C4⋊#1057—22no—
59C4⋊#1057C2×C414yescomplemented
60C4×#1057—22no—
61C4×#1057—22no—
62C13×#95—21no—
63C13×#95C2×C412yes—
64#88071—21no—
65#88071—22no—
66#88071—22no—
67#88071C2×C412yes—
68#8072—131nomaximal, Sylow
69C24×C13C22⋊C411yescharacteristic
70C22×C4×C13—24no—
71C22×C4×C13—22no—
72C22×C4×C13—42no—
73C22×C4×C13—42no—
74C22×C4×C13—42no—
75C22×C4×C13C4211yescharacteristic
76C22×C4×C13C4211yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C4⋊C411yescharacteristic
79C22×C4×C13C4⋊C411yescharacteristic
80C22×C4×C13C22×C411yescharacteristic
81C22×Dic13—24no—
82C22×Dic13—24no—
83C22×Dic13—22no—
84C22×Dic13—41no—
85C22×Dic13—41no—
86C22×Dic13—42no—
87C22×Dic13—42no—
88C22×Dic13C22⋊C411yescharacteristic
89C22×Dic13C22⋊C411yescharacteristic
90C22×Dic13C22⋊C411yescharacteristic
91C22×Dic13C22⋊C411yescharacteristic
92C22×Dic13C22⋊C411yescharacteristic
93C22×Dic13C22⋊C411yescharacteristic
94C22×Dic13C4⋊C411yescharacteristic
95C22×Dic13C4⋊C411yescharacteristic
96C22×Dic13C4⋊C411yescharacteristic
97C22×Dic13C4⋊C411yescharacteristic
98C22×Dic13C2×D411yescharacteristic
99C22×Dic13C2×D411yescharacteristic
100#6122—42no—
101#6122—42no—
102#6122—44no—
103C2×#1057—24no—
104C2×#1057—24no—
105C4×Dic13—28no—
106C4×Dic13—28no—
107C4×Dic13C4211yescharacteristic
108C4×Dic13C4211yescharacteristic
109C4×Dic13C22⋊C411yescharacteristic
110C4×Dic13C22⋊C411yescharacteristic
111C4×Dic13C22⋊C411yescharacteristic
112C4×Dic13C22⋊C411yescharacteristic
113C4×Dic13C4⋊C411yescharacteristic
114C4×Dic13C4⋊C411yescharacteristic
115C4×Dic13C4⋊C411yescharacteristic
116C4×Dic13C4⋊C411yescharacteristic
117C4×Dic13C4⋊C411yescharacteristic
118C4×Dic13C4⋊C411yescharacteristic
119C4×Dic13C22×C411yescharacteristic
120C4×Dic13C22×C411yescharacteristic
121C4×Dic13C2×D411yescharacteristic
122C4×Dic13C2×Q811yescharacteristic
123#2920—131no—
124#2920—131no—
125C2×#376—131no—
126#1300—134no—
127C23×C13—22no—
128C23×C13—22no—
129C23×C13—21no—
130C23×C13—21no—
131C23×C13#9511yescharacteristic
132C23×C13#9511yescharacteristic
133C23×C13C2×C22⋊C411yescharacteristic
134C2×C4×C13—22no—
135C2×C4×C13—22no—
136C2×C4×C13—24no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—48no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13#9511yescharacteristic
145C2×C4×C13#9511yescharacteristic
146C2×C4×C13C2×C4211yescharacteristic
147C2×C4×C13C2×C4⋊C411yescharacteristic
148C2×Dic13—22no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—21no—
153C2×Dic13—22no—
154C2×Dic13—22no—
155C2×Dic13—22no—
156C2×Dic13—22no—
157C2×Dic13—24no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—48no—
163C2×Dic13—42no—
164C2×Dic13—42no—
165C2×Dic13#9511yescharacteristic
166C2×Dic13#9511yescharacteristic
167C2×Dic13#9511yescharacteristic
168C2×Dic13#9511yescharacteristic
169C2×Dic13#10414yes—
170C2×Dic13C2×C22⋊C411yescharacteristic
171C2×Dic13C2×C22⋊C411yescharacteristic
172C2×Dic13C2×C4⋊C411yescharacteristic
173C2×Dic13C2×C4⋊C411yescharacteristic
174#1057—44no—
175#1057—44no—
176C22×C42—131no—
177C22×C42—261no—
178#432—132no—
179#432—132no—
180#432—132no—
181#432—261no—
182#431—132no—
183#431—261no—
184#431—261no—
185#431—261no—
186#423—132no—
187#423—261no—
188#407—261no—
189#407—261no—
190C4×M16—132no—
191C4×M16—261no—
192#376—132no—
193#376—132no—
194#376—261no—
195#376—261no—
196C2×#95—131no—
197C2×#95—261no—
198C2×#95#26111yescharacteristic
199C22×C13—24no—
200C22×C13—24no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13#33912yes—
208C22×C13#34412yes—
209C22×C13C2×#9511yescharacteristic
210C22×C13#42111yescharacteristic
211C22×C13#42111yescharacteristic
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—21no—
216C4×C13—44no—
217Dic13—21no—
218Dic13—21no—
219Dic13—21no—
220Dic13—21no—
221Dic13—21no—
222Dic13—21no—
223Dic13—44no—
224Dic13#33912yes—
225Dic13C2×#10412yes—
226C23×C4—21no—
227C23×C4—131no—
228C23×C4—131no—
229C23×C4—261no—
230C23×C4C2×#26111yescharacteristic
231C2×M16—262no—
232C2×M16—262no—
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—131no—
242C2×C42—131no—
243C2×C42—131no—
244C2×C42—131no—
245C2×C42—262no—
246C2×C42—262no—
247C2×C42—268no—
248C4⋊C8—134no—
249C4⋊C8—262no—
250C4⋊C8—262no—
251C4⋊C8—262no—
252C22⋊C8—262no—
253C22⋊C8—262no—
254C22⋊C8—262no—
255C22⋊C8—262no—
256#97—134no—
257#97—262no—
258C4×C8—262no—
259C4×C8—262no—
260#95—21no—
261#95—132no—
262#95—262no—
263#95—262no—
264#95—261no—
265#95C2×#26112yes—
266C2×C13—21no—
267C2×C13—21no—
268C2×C13—22no—
269C2×C13—22no—
270C2×C13C2×#33911yescharacteristic
271C2×C13#173311yescharacteristic
272C2×C13C2×#34411yescharacteristic
273C24C22⋊#26111yescharacteristic
274C22×C4—24no—
275C22×C4—22no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
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—264no—
292C22×C4—264no—
293C22×C4—262no—
294C22×C4—521no—
295C22×C4—521no—
296C22×C4—522no—
297C22×C4—522no—
298C22×C4C4×#26111yescharacteristic
299C22×C4C4×#26111yescharacteristic
300C22×C4C4⋊#26111yescharacteristic
301C22×C4C4⋊#26111yescharacteristic
302C22×C4C22⋊#26111yescharacteristic
303C22×C4C22×#26111yescharacteristic
304M16—524no—
305M16—522no—
306M16—522no—
307C2×C8—264no—
308C2×C8—264no—
309C42—131no—
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—131no—
323C42—131no—
324C42—131no—
325C42—268no—
326C42—268no—
327C13#807211yescharacteristic, complemented, Sylow
328C23—22no—
329C23—22no—
330C23—21no—
331C23—21no—
332C23(C2×#261)⋊C411yescharacteristic
333C23(C2×#261)⋊C411yescharacteristic
334C23C2×C22⋊#26111yescharacteristic
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—24no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—48no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—134no—
346C2×C4—131no—
347C2×C4—131no—
348C2×C4—131no—
349C2×C4—131no—
350C2×C4—131no—
351C2×C4—131no—
352C2×C4—131no—
353C2×C4—131no—
354C2×C4—262no—
355C2×C4—262no—
356C2×C4—262no—
357C2×C4—262no—
358C2×C4—262no—
359C2×C4—261no—
360C2×C4—261no—
361C2×C4—261no—
362C2×C4—261no—
363C2×C4—264no—
364C2×C4—521no—
365C2×C4—521no—
366C2×C4—521no—
367C2×C4—521no—
368C2×C4—528no—
369C2×C4—522no—
370C2×C4—522no—
371C2×C4(C2×#261)⋊C411yescharacteristic
372C2×C4(C2×#261)⋊C411yescharacteristic
373C2×C4C2×C4×#26111yescharacteristic
374C2×C4C2×C4⋊#26111yescharacteristic
375C8—524no—
376C8—524no—
377C22—24no—
378C22—24no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22#1171823412yes—
386C22#1171823912yes—
387C22C2×(C2×#261)⋊C411yescharacteristic
388C22#1171914011yescharacteristic
389C22#1171915511yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—44no—
395C4—132no—
396C4—132no—
397C4—261no—
398C4—261no—
399C4—261no—
400C4—261no—
401C4—261no—
402C4—261no—
403C4—524no—
404C2—21no—
405C2—21no—
406C2—22no—
407C2—22no—
408C2C2×#1171823411yescharacteristic
409C2#1313051511yescharacteristic
410C2C2×#1171823911yescharacteristic
subgroupG/H
centerC22C2×(C2×#261)⋊C4
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC2×C13×#95C4
socleC22×C13C2×#95
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#95#261
hypocenterC13#8072
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. #13129724C2semidirect
9. #11719130C4semidirect
12. #11719129C4semidirect
14. #11719128C4semidirect
20. #11719119C4semidirect
57. #88110C2×C4semidirect
59. C4⋊#1057C2×C4semidirect
327. C13#8072semidirect

Maximal subgroups

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

subgroupindex
#131315122
#131297242
C2×#117183092
#807213