Finite Group Databasebeta

← #14731044

Subgroups — #14731044

Order 2816.

1004 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079561C211yesmaximal, characteristic, complemented
2C2×#10622683C211yesmaximal, characteristic, complemented
3#13078431C211yesmaximal, characteristic, complemented
4#13067809C214yesmaximal, complemented
5#13067802C214yesmaximal, complemented
6#13067284C211yesmaximal, characteristic, complemented
7#13067071C211yesmaximal, characteristic, complemented
8#13066998C211yesmaximal, characteristic, complemented
9C11×#3508C211yesmaximal, characteristic
10C11×#559—21no—
11C11×#559C2212yes—
12C11×#550—21no—
13C11×#550C2212yes—
14C11×#546—22no—
15C11×#546—22no—
16C11×#540—22no—
17C11×#535—21no—
18C11×#533C2211yescharacteristic
19C11×#532—21no—
20C11×#532—21no—
21C2×C11×#127C2211yescharacteristic
22C11×#518—21no—
23C4×C11×#41C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25#10622845—21no—
26C2×#66896—22no—
27#10622706—21no—
28#10622705—21no—
29#10622683—22no—
30#10622683C2214yes—
31#10622663—22no—
32#10622644C2214yescomplemented
33#10622634—21no—
34#10622633C2212yescomplemented
35#10622621—21no—
36#10622620C2212yescomplemented
37#10622608—21no—
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622182C2214yes—
42Q8⋊(C11⋊C8)C2212yescomplemented
43Q8⋊(C11⋊C8)C2214yescomplemented
44D4⋊(C11⋊C8)C2212yescomplemented
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41D411yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11D412yes—
51C22×Dic22—21no—
52C11×C4⋊Q8D411yescharacteristic
53C11×C4⋊Q8D411yescharacteristic
54C11×#127—22no—
55C11×#127—21no—
56C11×#127—21no—
57C11×#127D412yes—
58C11×#127C2312yes—
59C11×#125—21no—
60C11×#124—22no—
61C11×#124—22no—
62C11×#124—22no—
63C11×#123—24no—
64C11×#123—24no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8D412yes—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121—22no—
70C11×#121—24no—
71C11×#121—24no—
72C11×#121—22no—
73C11×#120—24no—
74C4×Q8×C11—21no—
75C4×Q8×C11D411yescharacteristic
76C4×Q8×C11C2311yescharacteristic
77C4×Q8×C11C2312yes—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11D411yescharacteristic
87C4×D4×C11C2311yescharacteristic
88C11×#117—21no—
89C11×#117—21no—
90C11×#117D411yescharacteristic
91C2×C11×C22⋊C4—24no—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94C2×#4326—24no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×#4318—21no—
98C22×C11⋊C8—21no—
99#66922—21no—
100#66922—21no—
101#66922—21no—
102#66922C2312yes—
103#66899—22no—
104#66896—28no—
105#66896—22no—
106C22⋊(C11⋊C8)—21no—
107#66874—24no—
108#66872—22no—
109#66871—22no—
110C4⋊(C11⋊C8)—21no—
111C4⋊(C11⋊C8)C2312yes—
112C4⋊(C11⋊C8)C2312yes—
113C4×C11⋊C8—21no—
114C4×C11⋊C8—21no—
115C4×C11⋊C8C2312yes—
116#18635—111nomaximal, Sylow
117C24×C11—22no—
118C11×#41—22no—
119C11×#41—22no—
120C11×#41—84no—
121C11×#41—84no—
122C2×Q8×C11—21no—
123C2×Q8×C11C2×D411yescharacteristic
124C2×Q8×C11C2×D412yes—
125C2×D4×C11—21no—
126C2×D4×C11—24no—
127C2×D4×C11—24no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—44no—
134C2×D4×C11—42no—
135C2×D4×C11—42no—
136C2×D4×C11—82no—
137C2×D4×C11C2×D411yescharacteristic
138C2×D4×C11C2×D414yes—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×Dic11—41no—
148C2×Dic22—22no—
149C2×Dic22—41no—
150C2×Dic22—82no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4C2×D411yescharacteristic
159C11×C4⋊C4C2×D411yescharacteristic
160C11×C4⋊C4C2×D412yes—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—21no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—21no—
168C11×C22⋊C4—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—22no—
173C42×C11C2×D411yescharacteristic
174C42×C11C2×D411yescharacteristic
175C42×C11C2×D411yescharacteristic
176C42×C11C2411yescharacteristic
177#4326—84no—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11—41no—
181C4⋊Dic11—41no—
182#4318—42no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—42no—
187#3508D1111yescharacteristic
188#3209—111no—
189C2×#486—111no—
190#3079—111no—
191#1641—114no—
192#1640—114no—
193#1545—111no—
194#1493—111no—
195#1476—111no—
196C23×C11—24no—
197C23×C11—21no—
198C23×C11—44no—
199C23×C11—82no—
200C23×C11—82no—
201C23×C11#12011yescharacteristic
202Q8×C11—21no—
203Q8×C11—21no—
204Q8×C11—24no—
205Q8×C11—42no—
206D4×C11—21no—
207D4×C11—21no—
208D4×C11—44no—
209D4×C11—42no—
210D4×C11—42no—
211D4×C11—42no—
212D4×C11—44no—
213D4×C11—44no—
214D4×C11—44no—
215D4×C11—82no—
216D4×C11—84no—
217D4×C11—84no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—84no—
229C2×C4×C11—84no—
230C2×C4×C11#12011yescharacteristic
231C2×C4×C11#12011yescharacteristic
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11#13512yes—
234C2×C4×C11#13712yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×Dic11—42no—
239C2×Dic11—82no—
240Dic22—44no—
241Dic22—82no—
242C11⋊C8—42no—
243C11⋊C8—42no—
244C11⋊C8—42no—
245#559—21no—
246#559C2×D1112yes—
247#550—21no—
248#550C2×D1112yes—
249#546—22no—
250#546—22no—
251#540—22no—
252#535—21no—
253#533C2×D1111yescharacteristic
254#532—21no—
255#532—21no—
256C2×C4⋊Q8—111no—
257C2×#127C2×D1111yescharacteristic
258#518—21no—
259C4×#41C2×D1111yescharacteristic
260#494—221no—
261#487—221no—
262#486—114no—
263#486—222no—
264#477—221no—
265#476—221no—
266#475—112no—
267#474—112no—
268#462—114no—
269#451—222no—
270#431—111no—
271#428—221no—
272#423—111no—
273#417—221no—
274C2×#102—222no—
275C2×C4×C8—111no—
276#331—114no—
277Q8⋊C8—112no—
278Q8⋊C8—114no—
279D4⋊C8—112no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—41no—
283C22×C11—44no—
284C22×C11—41no—
285C22×C11—44no—
286C22×C11—41no—
287C22×C11—44no—
288C22×C11—164no—
289C22×C11#45212yes—
290C22×C11C2×#12011yescharacteristic
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—41no—
294C4×C11—41no—
295C4×C11—42no—
296C4×C11—41no—
297C4×C11—42no—
298C4×C11#45212yes—
299C4×C11#45512yes—
300C4×C11C2×#13511yescharacteristic
301C4×C11C2×#13711yescharacteristic
302C4×C11#57612yes—
303Dic11—82no—
304C2×#41—22no—
305C2×#41—22no—
306C2×#41C22⋊D1111yescharacteristic
307C22×Q8—221no—
308C22×D4—21no—
309C22×D4—21no—
310C22×D4C22⋊D1112yes—
311C2×Q16—224no—
312C2×M16—221no—
313C22×C8—221no—
314C4⋊Q8—112no—
315C4⋊Q8—221no—
316C4⋊Q8—221no—
317C4⋊Q8—221no—
318C4⋊Q8C22⋊D1111yescharacteristic
319C4⋊Q8C22⋊D1111yescharacteristic
320#127—22no—
321#127—21no—
322#127—21no—
323#127C22⋊D1112yes—
324#127C22×D1112yes—
325#125—21no—
326#124—22no—
327#124—22no—
328#124—22no—
329#123—24no—
330#123—24no—
331C22⋊Q8—21no—
332C22⋊Q8C22⋊D1112yes—
333#121—22no—
334#121—22no—
335#121—22no—
336#121—24no—
337#121—24no—
338#121—22no—
339#120—24no—
340C4×Q8—21no—
341C4×Q8C22⋊D1111yescharacteristic
342C4×Q8C22×D1111yescharacteristic
343C4×Q8C22×D1112yes—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4C22⋊D1111yescharacteristic
353C4×D4C22×D1111yescharacteristic
354#117—21no—
355#117—21no—
356#117C22⋊D1111yescharacteristic
357C2×C4⋊C4—221no—
358C2×C4⋊C4—221no—
359C2×C22⋊C4—24no—
360C2×C42—21no—
361C2×C42C22×D1111yescharacteristic
362#107—222no—
363#106—222no—
364C4⋊C8—112no—
365C4⋊C8—112no—
366C4⋊C8—221no—
367#103—222no—
368#103—224no—
369#102—228no—
370#102—222no—
371C22⋊C8—221no—
372C4×C8—112no—
373C4×C8—221no—
374C4×C8—221no—
375C2×C11—22no—
376C2×C11—81no—
377C2×C11—84no—
378C2×C11C2×#45211yescharacteristic
379C2×C11#300811yescharacteristic
380C2×C11C2×#45511yescharacteristic
381C24—22no—
382#41—22no—
383#41—22no—
384#41—84no—
385#41—84no—
386C2×Q8—21no—
387C2×Q8—222no—
388C2×Q8—441no—
389C2×Q8—882no—
390C2×Q8C2×C22⋊D1111yescharacteristic
391C2×Q8C2×C22⋊D1112yes—
392C2×D4—21no—
393C2×D4—24no—
394C2×D4—24no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—44no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—82no—
404C2×D4C2×C22⋊D1111yescharacteristic
405C2×D4C2×C22⋊D1114yes—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—441no—
412C22×C4C2×C22⋊D1111yescharacteristic
413C22×C4C2×C22⋊D1111yescharacteristic
414C22×C4C2×C22⋊D1111yescharacteristic
415Q16—884no—
416M16—442no—
417C2×C8—222no—
418C2×C8—222no—
419C2×C8—222no—
420C2×C8—442no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—222no—
429C4⋊C4—222no—
430C4⋊C4—441no—
431C4⋊C4—441no—
432C4⋊C4C2×C22⋊D1112yes—
433C4⋊C4C2×C22⋊D1111yescharacteristic
434C4⋊C4C2×C22⋊D1111yescharacteristic
435C22⋊C4—24no—
436C22⋊C4—24no—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—21no—
440C22⋊C4—22no—
441C22⋊C4—21no—
442C22⋊C4—21no—
443C42—21no—
444C42—21no—
445C42—21no—
446C42—22no—
447C42C2×C22⋊D1111yescharacteristic
448C42C2×C22⋊D1111yescharacteristic
449C42C2×C22⋊D1111yescharacteristic
450C42C23×D1111yescharacteristic
451C11#1863511yescharacteristic, complemented, Sylow
452C23—24no—
453C23—21no—
454C23—44no—
455C23—82no—
456C23—82no—
457C23#6700611yescharacteristic
458Q8—21no—
459Q8—21no—
460Q8—24no—
461Q8—42no—
462Q8—444no—
463Q8—882no—
464D4—21no—
465D4—21no—
466D4—44no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—44no—
471D4—44no—
472D4—44no—
473D4—82no—
474D4—84no—
475D4—84no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—84no—
487C2×C4—84no—
488C2×C4—442no—
489C2×C4—882no—
490C2×C4#6700312yes—
491C2×C4#6700412yes—
492C2×C4#6700611yescharacteristic
493C2×C4#6700611yescharacteristic
494C2×C4#6700611yescharacteristic
495C2×C4C22×C22⋊D1111yescharacteristic
496C2×C4C22×C22⋊D1111yescharacteristic
497C2×C4C22×C22⋊D1111yescharacteristic
498C8—442no—
499C8—442no—
500C8—442no—
501C22—21no—
502C22—21no—
503C22—41no—
504C22—44no—
505C22—41no—
506C22—44no—
507C22—41no—
508C22—44no—
509C22—164no—
510C22#1062285212yes—
511C22C2×#6700611yescharacteristic
512C4—21no—
513C4—21no—
514C4—41no—
515C4—41no—
516C4—42no—
517C4—41no—
518C4—42no—
519C4—882no—
520C4#1062285212yes—
521C4#1062285512yes—
522C4C2×#6700311yescharacteristic
523C4C2×#6700411yescharacteristic
524C4#1062336612yes—
525C2—22no—
526C2—84no—
527C2—81no—
528C2C2×#1062285211yescharacteristic
529C2#1307788411yescharacteristic
530C2C2×#1062285511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3508C2
socleC22×C11C2×#120
hypercenter#3508D11
hypocenterC11#18635
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #13079561C2semidirect
2. C2×#10622683C2semidirect
3. #13078431C2semidirect
4. #13067809C2semidirect
5. #13067802C2semidirect
6. #13067284C2semidirect
7. #13067071C2semidirect
8. #13066998C2semidirect
32. #10622644C22semidirect
34. #10622633C22semidirect
36. #10622620C22semidirect
42. Q8⋊(C11⋊C8)C22semidirect
43. Q8⋊(C11⋊C8)C22semidirect
44. D4⋊(C11⋊C8)C22semidirect
451. C11#18635semidirect

Maximal subgroups

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

subgroupindex
#130795612
C2×#106226832
#130784312
#130678092
#130678022
#130672842
#130670712
#130669982
C11×#35082
#1863511