Finite Group Databasebeta

← #14720735

Subgroups — #14720735

Order 2816.

948 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082209C211yesmaximal, characteristic
2#13077282C211yesmaximal, characteristic, complemented
3#13067086C211yesmaximal, characteristic, complemented
4#13067082C211yesmaximal, characteristic, complemented
5#13067077C211yesmaximal, characteristic, complemented
6#13067064C211yesmaximal, characteristic, complemented
7#13067056C211yesmaximal, characteristic, complemented
8#13067051C211yesmaximal, characteristic, complemented
9#13067034C211yesmaximal, characteristic, complemented
10#13067030C211yesmaximal, characteristic, complemented
11#13067025C211yesmaximal, characteristic, complemented
12#13067012C211yesmaximal, characteristic, complemented
13#13067004C211yesmaximal, characteristic, complemented
14#13066999C211yesmaximal, characteristic, complemented
15C11×#2965C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17#10623363—21no—
18#10623116C411yescharacteristic
19#10623099—21no—
20#10623098C411yescharacteristic
21#10623096C411yescharacteristic
22#10623096C411yescharacteristic
23#10623090—21no—
24#10623084C411yescharacteristic
25#10623083C411yescharacteristic
26#10623083C411yescharacteristic
27#10623073C411yescharacteristic
28#10623071—21no—
29#10623071—21no—
30#10623059—21no—
31#10623059—21no—
32#10623053—21no—
33#10623010C2211yescharacteristic
34#10623010C2211yescharacteristic
35#10623008C2211yescharacteristic
36C4×#4339C2211yescharacteristic
37C4×#4339C2211yescharacteristic
38C2×C4×Dic22C2211yescharacteristic
39C11×#446—21no—
40C11×#436—21no—
41C11×#435—21no—
42C11×#435—21no—
43C11×#431C2211yescharacteristic
44C11×#431C2211yescharacteristic
45C11×#431C2211yescharacteristic
46C4×C11×M16C2211yescharacteristic
47C4×C11×M16C2211yescharacteristic
48C2×C4×C8×C11C2211yescharacteristic
49#10622847—21no—
50#10622613—21no—
51#10622613—21no—
52#10622610—21no—
53#10622539C2211yescharacteristic
54#10622539C2211yescharacteristic
55#10622538C2211yescharacteristic
56#10622538C2211yescharacteristic
57#10622537C2211yescharacteristic
58C2×C4⋊(C11⋊C8)C2211yescharacteristic
59#10622097C2211yescharacteristic
60#10622097C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622097C2211yescharacteristic
64#10622097C2211yescharacteristic
65#10622097C2211yescharacteristic
66#10622097C2211yescharacteristic
67#10622094C2211yescharacteristic
68#10622094C2211yescharacteristic
69#10622094C2211yescharacteristic
70#10622094C2211yescharacteristic
71#10622094C2211yescharacteristic
72#10622094C2211yescharacteristic
73#10622094C2211yescharacteristic
74#10622094C2211yescharacteristic
75C2×C11×#41D411yescharacteristic
76C2×#4339—21no—
77C2×#4339C2×C411yescharacteristic
78C2×#4339C2×C411yescharacteristic
79C22×Dic22C2×C411yescharacteristic
80C2×C11×M16—21no—
81C2×C11×M16—21no—
82C22×C8×C11—21no—
83C4×Q8×C11C2×C411yescharacteristic
84C4×Q8×C11D411yescharacteristic
85C4×D4×C11C2×C411yescharacteristic
86C4×D4×C11C2×C411yescharacteristic
87C4×D4×C11C2×C411yescharacteristic
88C4×D4×C11D411yescharacteristic
89C4×D4×C11D411yescharacteristic
90C4×D4×C11D411yescharacteristic
91C11×#117D411yescharacteristic
92C11×#117D411yescharacteristic
93C11×#117D411yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97#67000—21no—
98#66997—21no—
99#66993—21no—
100#66992—21no—
101#66992—21no—
102#66992—21no—
103#66992—21no—
104#66989—21no—
105#66983—21no—
106#66983C2×C411yescharacteristic
107#66983C2×C411yescharacteristic
108#66983C2×C411yescharacteristic
109#66983C2×C411yescharacteristic
110#66982—21no—
111#66982—21no—
112C4×C22⋊D11—21no—
113C4×C22⋊D11—21no—
114C4×C22⋊D11—21no—
115C4×C22⋊D11—21no—
116C4×C22⋊D11—21no—
117C4×C22⋊D11—21no—
118#66979C2×C411yescharacteristic
119#66979C2×C411yescharacteristic
120C2×C4⋊Dic11C2×C411yescharacteristic
121#66977C2×C411yescharacteristic
122#66977C2×C411yescharacteristic
123C2×Dic11⋊C4—21no—
124C2×C4×Dic11—21no—
125C2×#4318—21no—
126C22×C11⋊C8—21no—
127#66951—21no—
128#66951—21no—
129#66949—21no—
130#66949—21no—
131#66947—21no—
132#66947—21no—
133#66946—21no—
134#66946—21no—
135#66942—21no—
136#66942—21no—
137#66940—21no—
138#66940—21no—
139#66938—21no—
140#66938—21no—
141#66937—21no—
142#66937—21no—
143#66936—21no—
144#66936—21no—
145(C22⋊D11)⋊C4—21no—
146(C22⋊D11)⋊C4—21no—
147(C22⋊D11)⋊C4—21no—
148(C22⋊D11)⋊C4—21no—
149#66932—21no—
150#66932—21no—
151#66929—21no—
152#66929—21no—
153#66928—21no—
154#66928C2×C411yescharacteristic
155#66928C2×C411yescharacteristic
156#66927C2×C411yescharacteristic
157C4×D44—21no—
158C4×D44C2×C411yescharacteristic
159C4×D44C2×C411yescharacteristic
160C4×D44C2311yescharacteristic
161C4×D44C2311yescharacteristic
162#66925—21no—
163#66925—21no—
164#66925—21no—
165#66925—21no—
166C42×D11—21no—
167C42×D11—21no—
168#66923C2×C411yescharacteristic
169#66923C2×C411yescharacteristic
170#66922C2×C411yescharacteristic
171C4×Dic22—21no—
172C4×Dic22—21no—
173C4×Dic22C2×C411yescharacteristic
174C4×Dic22C2×C411yescharacteristic
175C4×Dic22C2×C411yescharacteristic
176C4×Dic22C2×C411yescharacteristic
177C4×Dic22C2311yescharacteristic
178C4×Dic22C2311yescharacteristic
179C11×C4⋊C8—21no—
180C11×C4⋊C8—21no—
181C11×C4⋊C8—21no—
182C11×C22⋊C8—21no—
183C11×C22⋊C8—21no—
184C11×C22⋊C8—21no—
185C11×#97—21no—
186C11×#97—21no—
187C4×C8×C11—21no—
188C4×C8×C11C2311yescharacteristic
189C4×C8×C11C2311yescharacteristic
190C4×C8×C11C2311yescharacteristic
191C4×C8×C11C2311yescharacteristic
192C22⋊(C11⋊C8)—21no—
193C22⋊(C11⋊C8)—21no—
194C22⋊(C11⋊C8)—21no—
195C22⋊(C11⋊C8)—21no—
196C4⋊(C11⋊C8)—21no—
197C4⋊(C11⋊C8)—21no—
198C4⋊(C11⋊C8)C2311yescharacteristic
199C4⋊(C11⋊C8)C2311yescharacteristic
200C4⋊(C11⋊C8)C2311yescharacteristic
201C4⋊(C11⋊C8)C2311yescharacteristic
202#66867—21no—
203#66867—21no—
204C4×C11⋊C8—21no—
205C4×C11⋊C8—21no—
206#17516—111nomaximal, Sylow
207C11×#41—41no—
208C11×#41—41no—
209C2×Q8×C11C22⋊C411yescharacteristic
210C2×D4×C11C22⋊C411yescharacteristic
211C2×D4×C11C22⋊C411yescharacteristic
212C2×D4×C11C22⋊C411yescharacteristic
213C22×C4×C11C22×C411yescharacteristic
214C22×C4×C11C22×C411yescharacteristic
215C22×C4×C11C22×C411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C2×C22⋊D11—21no—
223C2×C22⋊D11—21no—
224C2×C22⋊D11—21no—
225C2×C22⋊D11—21no—
226C2×C22⋊D11—21no—
227C2×C22⋊D11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230#4339—22no—
231#4339—22no—
232#4339—41no—
233#4339—41no—
234#4339—42no—
235#4339—42no—
236C2×D44—21no—
237C2×D44—21no—
238C2×D44C22×C411yescharacteristic
239C2×D44C22×C411yescharacteristic
240C2×C4×D11—21no—
241C2×C4×D11—21no—
242C2×C4×D11—21no—
243C2×C4×D11—21no—
244C2×C4×D11—21no—
245C2×C4×D11—21no—
246C2×Dic22—22no—
247C2×Dic22—21no—
248C2×Dic22—21no—
249C2×Dic22—41no—
250C2×Dic22C22×C411yescharacteristic
251C2×Dic22C22×C411yescharacteristic
252C11×M16—42no—
253C11×M16—42no—
254C2×C8×C11—21no—
255C2×C8×C11—21no—
256C2×C8×C11—21no—
257C2×C8×C11—21no—
258C2×C8×C11—42no—
259C11×C4⋊C4C22⋊C411yescharacteristic
260C11×C4⋊C4C22⋊C411yescharacteristic
261C11×C4⋊C4C22⋊C411yescharacteristic
262C11×C4⋊C4C22⋊C411yescharacteristic
263C11×C4⋊C4C22⋊C411yescharacteristic
264C11×C4⋊C4C22⋊C411yescharacteristic
265C11×C22⋊C4C22⋊C411yescharacteristic
266C11×C22⋊C4C22⋊C411yescharacteristic
267C11×C22⋊C4C22⋊C411yescharacteristic
268C11×C22⋊C4C22⋊C411yescharacteristic
269C11×C22⋊C4C22⋊C411yescharacteristic
270C11×C22⋊C4C22⋊C411yescharacteristic
271C42×C11C22×C411yescharacteristic
272C42×C11C22×C411yescharacteristic
273C42×C11C22×C411yescharacteristic
274C42×C11C2×D411yescharacteristic
275C42×C11C2×D411yescharacteristic
276C42×C11C2×D411yescharacteristic
277C42×C11C2×D411yescharacteristic
278C42×C11C2×D411yescharacteristic
279C42×C11C2×D411yescharacteristic
280C42×C11C2411yescharacteristic
281C22⋊Dic11—21no—
282C22⋊Dic11—21no—
283C22⋊Dic11—21no—
284C22⋊Dic11—21no—
285(C2×D11)⋊C4—21no—
286(C2×D11)⋊C4—21no—
287(C2×D11)⋊C4—21no—
288(C2×D11)⋊C4—21no—
289(C2×D11)⋊C4—21no—
290(C2×D11)⋊C4—21no—
291(C2×D11)⋊C4—21no—
292(C2×D11)⋊C4—21no—
293(C2×D11)⋊C4—21no—
294(C2×D11)⋊C4—21no—
295(C2×D11)⋊C4—21no—
296(C2×D11)⋊C4—21no—
297C4⋊Dic11—21no—
298C4⋊Dic11—21no—
299C4⋊Dic11C22×C411yescharacteristic
300C4⋊Dic11C22×C411yescharacteristic
301C4⋊Dic11C22×C411yescharacteristic
302C4⋊Dic11C22×C411yescharacteristic
303Dic11⋊C4—21no—
304Dic11⋊C4—21no—
305Dic11⋊C4—21no—
306Dic11⋊C4—21no—
307Dic11⋊C4—21no—
308Dic11⋊C4—21no—
309Dic11⋊C4—21no—
310Dic11⋊C4—21no—
311Dic11⋊C4—21no—
312Dic11⋊C4—21no—
313Dic11⋊C4—21no—
314Dic11⋊C4—21no—
315C4×Dic11—21no—
316C4×Dic11—21no—
317C4×Dic11—21no—
318C4×Dic11—21no—
319C4×Dic11—21no—
320C4×Dic11—21no—
321C4×Dic11—21no—
322C4×Dic11—21no—
323#4318—42no—
324C2×C11⋊C8—21no—
325C2×C11⋊C8—21no—
326C2×C11⋊C8—21no—
327C2×C11⋊C8—21no—
328C2×C11⋊C8—42no—
329#3480—111no—
330#2965D1111yescharacteristic, complemented
331#2925—111no—
332#1496—111no—
333#1495—111no—
334#1494—111no—
335#1491—111no—
336#1489—111no—
337#1488—111no—
338#1484—111no—
339#1483—111no—
340#1482—111no—
341#1479—111no—
342#1477—111no—
343#1476—111no—
344C23×C11C2×C22⋊C411yescharacteristic
345C23×C11C2×C22⋊C411yescharacteristic
346C23×C11C2×C22⋊C411yescharacteristic
347C22×D11—21no—
348C22×D11—21no—
349Q8×C11—41no—
350D4×C11—41no—
351D4×C11—41no—
352D4×C11—41no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—21no—
359C2×C4×C11—21no—
360C2×C4×C11—21no—
361C2×C4×C11—21no—
362C2×C4×C11—21no—
363C2×C4×C11—21no—
364C2×C4×C11—21no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11C2×C22⋊C411yescharacteristic
369C2×C4×C11C2×C22⋊C411yescharacteristic
370C2×C4×C11C2×C22⋊C411yescharacteristic
371C2×C4×C11C2×C22⋊C411yescharacteristic
372C2×C4×C11C2×C22⋊C411yescharacteristic
373C2×C4×C11C2×C22⋊C411yescharacteristic
374C2×C4×C11C2×C22⋊C411yescharacteristic
375C2×C4×C11C2×C22⋊C411yescharacteristic
376C2×C4×C11C2×C22⋊C411yescharacteristic
377C2×C4×C11C23×C411yescharacteristic
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C22⋊D11—42no—
381C22⋊D11—42no—
382C22⋊D11—42no—
383C22⋊D11—42no—
384C22⋊D11—81no—
385C22⋊D11—81no—
386C2×Dic11—21no—
387C2×Dic11—21no—
388C2×Dic11—21no—
389C2×Dic11—21no—
390C2×Dic11—21no—
391C2×Dic11—21no—
392C2×Dic11—42no—
393C2×Dic11—81no—
394D44—21no—
395D44—21no—
396D44—21no—
397D44—21no—
398D44—42no—
399D44—81no—
400C4×D11—42no—
401C4×D11—42no—
402C4×D11—41no—
403C4×D11—41no—
404C4×D11—41no—
405C4×D11—41no—
406C4×D11—81no—
407C4×D11—81no—
408Dic22—21no—
409Dic22—21no—
410Dic22—21no—
411Dic22—42no—
412Dic22—42no—
413Dic22#13112yes—
414C8×C11—22no—
415C8×C11—41no—
416C8×C11—41no—
417C8×C11—41no—
418C11⋊C8—41no—
419C11⋊C8—41no—
420C11⋊C8—41no—
421C11⋊C8—41no—
422#559—111no—
423#559—221no—
424#557—111no—
425#556—111no—
426#556—221no—
427#553—111no—
428#553—111no—
429#553—221no—
430#553—221no—
431#550—111no—
432#548—111no—
433#548—111no—
434#532—111no—
435#532—221no—
436#529—111no—
437#529—111no—
438#529—221no—
439#529—221no—
440C4×#41—111no—
441C4×#41—111no—
442C4×#41—221no—
443C4×#41C2×D1111yescharacteristic
444C2×C4×Q8—111no—
445#446—21no—
446#436—21no—
447#435—21no—
448#435—21no—
449#433—221no—
450#433—221no—
451#432—111no—
452#432—111no—
453#431—111no—
454#431—111no—
455#431C2×D1111yescharacteristic
456#431C2×D1111yescharacteristic
457#431C2×D1111yescharacteristic
458#423—111no—
459C2×C4⋊C8—111no—
460#408—221no—
461#405—221no—
462C4×M16C2×D1111yescharacteristic
463C4×M16C2×D1111yescharacteristic
464C2×C4×C8C2×D1111yescharacteristic
465Q8⋊C8—111no—
466Q8⋊C8—111no—
467Q8⋊C8—111no—
468Q8⋊C8—111no—
469Q8⋊C8—111no—
470Q8⋊C8—111no—
471Q8⋊C8—111no—
472Q8⋊C8—111no—
473D4⋊C8—111no—
474D4⋊C8—111no—
475D4⋊C8—111no—
476D4⋊C8—111no—
477D4⋊C8—111no—
478D4⋊C8—111no—
479D4⋊C8—111no—
480D4⋊C8—111no—
481C22×C11—21no—
482C22×C11—21no—
483C22×C11—21no—
484C22×C11—21no—
485C22×C11—21no—
486C22×C11—21no—
487C22×C11—21no—
488C22×C11—21no—
489C22×C11—21no—
490C22×C11C22×C22⋊C411yescharacteristic
491C2×D11—41no—
492C2×D11—41no—
493C2×D11—41no—
494C2×D11—41no—
495C2×D11—41no—
496C2×D11—41no—
497C4×C11—21no—
498C4×C11—21no—
499C4×C11—21no—
500C4×C11—21no—
501C4×C11—21no—
502C4×C11—21no—
503C4×C11—21no—
504C4×C11—21no—
505C4×C11—21no—
506C4×C11—21no—
507C4×C11C2×#13111yescharacteristic
508C4×C11#56811yescharacteristic
509C4×C11#57511yescharacteristic
510C4×C11#57511yescharacteristic
511Dic11—22no—
512Dic11—41no—
513Dic11—41no—
514Dic11—41no—
515Dic11—41no—
516Dic11—41no—
517C2×#41—111no—
518C2×#41—111no—
519C2×#41—221no—
520C2×#41D4411yescharacteristic
521C22×Q8—111no—
522C2×M16—21no—
523C2×M16—21no—
524C2×M16—221no—
525C22×C8—21no—
526C22×C8—221no—
527C4⋊Q8—111no—
528C4⋊Q8—221no—
529#127—111no—
530#127—221no—
531#126—221no—
532#126—221no—
533#126—221no—
534#126—221no—
535#126—221no—
536#126—221no—
537#125—111no—
538#125—111no—
539#125—221no—
540#125—221no—
541#124—111no—
542#124—111no—
543#124—221no—
544#124—221no—
545#124—221no—
546#124—221no—
547#124—221no—
548#123—221no—
549#123—221no—
550#123—221no—
551#123—221no—
552#123—221no—
553#123—221no—
554C22⋊Q8—111no—
555C22⋊Q8—111no—
556C22⋊Q8—221no—
557C22⋊Q8—221no—
558#121—111no—
559#121—111no—
560#121—111no—
561#121—111no—
562#121—221no—
563#121—221no—
564#121—221no—
565#121—221no—
566#121—221no—
567#121—221no—
568#121—221no—
569C4×Q8—111no—
570C4×Q8—111no—
571C4×Q8—111no—
572C4×Q8—111no—
573C4×Q8—111no—
574C4×Q8—111no—
575C4×Q8—221no—
576C4×Q8—221no—
577C4×Q8—221no—
578C4×Q8—221no—
579C4×Q8C4×D1111yescharacteristic
580C4×Q8C22⋊D1111yescharacteristic
581C4×D4—111no—
582C4×D4—111no—
583C4×D4—111no—
584C4×D4—111no—
585C4×D4—221no—
586C4×D4—221no—
587C4×D4—221no—
588C4×D4—221no—
589C4×D4—221no—
590C4×D4—221no—
591C4×D4—221no—
592C4×D4—221no—
593C4×D4—221no—
594C4×D4—221no—
595C4×D4—221no—
596C4×D4—221no—
597C4×D4—221no—
598C4×D4C4×D1111yescharacteristic
599C4×D4C4×D1111yescharacteristic
600C4×D4C4×D1111yescharacteristic
601C4×D4C22⋊D1111yescharacteristic
602C4×D4C22⋊D1111yescharacteristic
603C4×D4C22⋊D1111yescharacteristic
604#117—111no—
605#117—111no—
606#117—221no—
607#117—221no—
608#117—221no—
609#117—221no—
610#117D4411yescharacteristic
611#117D4411yescharacteristic
612#117D4411yescharacteristic
613C2×C4⋊C4—111no—
614C2×C4⋊C4—221no—
615C2×C42—221no—
616C2×C42—221no—
617C2×C42—221no—
618C2×C42C22×D1111yescharacteristic
619C2×C42C22×D1111yescharacteristic
620C2×C42C22×D1111yescharacteristic
621C4⋊C8—21no—
622C4⋊C8—21no—
623C4⋊C8—21no—
624C4⋊C8—111no—
625C4⋊C8—111no—
626C4⋊C8—111no—
627C4⋊C8—111no—
628C4⋊C8—221no—
629C4⋊C8—221no—
630C22⋊C8—21no—
631C22⋊C8—21no—
632C22⋊C8—21no—
633C22⋊C8—221no—
634C22⋊C8—221no—
635C22⋊C8—221no—
636C22⋊C8—221no—
637#97—21no—
638#97—21no—
639#97—221no—
640#97—221no—
641C4×C8—21no—
642C4×C8—221no—
643C4×C8—221no—
644C4×C8C22×D1111yescharacteristic
645C4×C8C22×D1111yescharacteristic
646C4×C8C22×D1111yescharacteristic
647C4×C8C22×D1111yescharacteristic
648C2×C11—41no—
649C2×C11—41no—
650C2×C11—41no—
651C2×C11#288011yescharacteristic
652C2×C11#289611yescharacteristic
653C2×C11#290111yescharacteristic
654D11—81no—
655D11—81no—
656#41—41no—
657#41—41no—
658#41—222no—
659#41—222no—
660#41—441no—
661#41—441no—
662#41—442no—
663#41—442no—
664C2×Q8—111no—
665C2×Q8—111no—
666C2×Q8—222no—
667C2×Q8—221no—
668C2×Q8—221no—
669C2×Q8—441no—
670C2×Q8(C2×D11)⋊C411yescharacteristic
671C2×D4—111no—
672C2×D4—111no—
673C2×D4—221no—
674C2×D4—221no—
675C2×D4—221no—
676C2×D4—221no—
677C2×D4—221no—
678C2×D4—221no—
679C2×D4—221no—
680C2×D4—221no—
681C2×D4(C2×D11)⋊C411yescharacteristic
682C2×D4(C2×D11)⋊C411yescharacteristic
683C2×D4(C2×D11)⋊C411yescharacteristic
684C22×C4—221no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—221no—
688C22×C4—221no—
689C22×C4—221no—
690C22×C4—221no—
691C22×C4—221no—
692C22×C4C2×C4×D1111yescharacteristic
693C22×C4C2×C4×D1111yescharacteristic
694C22×C4C2×C4×D1111yescharacteristic
695C22×C4C2×D4411yescharacteristic
696C22×C4C2×D4411yescharacteristic
697C22×C4C2×D4411yescharacteristic
698C22×C4C2×C22⋊D1111yescharacteristic
699C22×C4C2×C22⋊D1111yescharacteristic
700C22×C4C2×C22⋊D1111yescharacteristic
701M16—42no—
702M16—42no—
703M16—442no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—42no—
709C2×C8—221no—
710C2×C8—221no—
711C2×C8—221no—
712C2×C8—221no—
713C2×C8—442no—
714C4⋊C4—111no—
715C4⋊C4—111no—
716C4⋊C4—111no—
717C4⋊C4—111no—
718C4⋊C4—221no—
719C4⋊C4—221no—
720C4⋊C4—221no—
721C4⋊C4—221no—
722C4⋊C4—221no—
723C4⋊C4—221no—
724C4⋊C4—221no—
725C4⋊C4—221no—
726C4⋊C4—221no—
727C4⋊C4—221no—
728C4⋊C4—221no—
729C4⋊C4—221no—
730C4⋊C4—221no—
731C4⋊C4—221no—
732C4⋊C4(C2×D11)⋊C411yescharacteristic
733C4⋊C4(C2×D11)⋊C411yescharacteristic
734C4⋊C4(C2×D11)⋊C411yescharacteristic
735C4⋊C4(C2×D11)⋊C411yescharacteristic
736C4⋊C4(C2×D11)⋊C411yescharacteristic
737C4⋊C4(C2×D11)⋊C411yescharacteristic
738C22⋊C4—221no—
739C22⋊C4—221no—
740C22⋊C4—221no—
741C22⋊C4—221no—
742C22⋊C4—221no—
743C22⋊C4—221no—
744C22⋊C4—221no—
745C22⋊C4—221no—
746C22⋊C4—221no—
747C22⋊C4—221no—
748C22⋊C4—221no—
749C22⋊C4—221no—
750C22⋊C4—221no—
751C22⋊C4—221no—
752C22⋊C4—221no—
753C22⋊C4—221no—
754C22⋊C4(C2×D11)⋊C411yescharacteristic
755C22⋊C4(C2×D11)⋊C411yescharacteristic
756C22⋊C4(C2×D11)⋊C411yescharacteristic
757C22⋊C4(C2×D11)⋊C411yescharacteristic
758C22⋊C4(C2×D11)⋊C411yescharacteristic
759C22⋊C4(C2×D11)⋊C411yescharacteristic
760C42—221no—
761C42—221no—
762C42—221no—
763C42—221no—
764C42—221no—
765C42—221no—
766C42—221no—
767C42—221no—
768C42C2×C4×D1111yescharacteristic
769C42C2×C4×D1111yescharacteristic
770C42C2×C4×D1111yescharacteristic
771C42C2×D4411yescharacteristic
772C42C2×D4411yescharacteristic
773C42C2×D4411yescharacteristic
774C42C2×C22⋊D1111yescharacteristic
775C42C2×C22⋊D1111yescharacteristic
776C42C2×C22⋊D1111yescharacteristic
777C42C23×D1111yescharacteristic
778C11#1751611yescharacteristic, complemented, Sylow
779C23—221no—
780C23—221no—
781C23C2×(C2×D11)⋊C411yescharacteristic
782C23C2×(C2×D11)⋊C411yescharacteristic
783C23C2×(C2×D11)⋊C411yescharacteristic
784Q8—41no—
785Q8—112no—
786Q8—221no—
787Q8—221no—
788Q8—221no—
789Q8—442no—
790Q8—442no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—221no—
795D4—221no—
796D4—221no—
797D4—221no—
798D4—442no—
799D4—442no—
800D4—442no—
801D4—442no—
802D4—442no—
803D4—881no—
804D4—881no—
805D4—881no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—221no—
822C2×C4—221no—
823C2×C4—221no—
824C2×C4—221no—
825C2×C4—221no—
826C2×C4—221no—
827C2×C4—442no—
828C2×C4—442no—
829C2×C4—442no—
830C2×C4—441no—
831C2×C4—441no—
832C2×C4—441no—
833C2×C4—441no—
834C2×C4—881no—
835C2×C4—881no—
836C2×C4—881no—
837C2×C4C2×(C2×D11)⋊C411yescharacteristic
838C2×C4C2×(C2×D11)⋊C411yescharacteristic
839C2×C4C2×(C2×D11)⋊C411yescharacteristic
840C2×C4C2×(C2×D11)⋊C411yescharacteristic
841C2×C4C2×(C2×D11)⋊C411yescharacteristic
842C2×C4C2×(C2×D11)⋊C411yescharacteristic
843C2×C4C2×(C2×D11)⋊C411yescharacteristic
844C2×C4C2×(C2×D11)⋊C411yescharacteristic
845C2×C4C2×(C2×D11)⋊C411yescharacteristic
846C2×C4C22×C4×D1111yescharacteristic
847C2×C4C22×D4411yescharacteristic
848C2×C4C22×C22⋊D1111yescharacteristic
849C8—22no—
850C8—41no—
851C8—41no—
852C8—41no—
853C8—441no—
854C8—441no—
855C8—441no—
856C8—441no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—441no—
867C22—441no—
868C22—441no—
869C22—441no—
870C22—441no—
871C22—441no—
872C22C22×(C2×D11)⋊C411yescharacteristic
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—222no—
884C4—441no—
885C4—441no—
886C4—441no—
887C4—441no—
888C4—441no—
889C4#1062327911yescharacteristic
890C4#1062327911yescharacteristic
891C4D11×#13111yescharacteristic
892C4#1062328111yescharacteristic
893C2—41no—
894C2—41no—
895C2—41no—
896C2—881no—
897C2—881no—
898C2#1307706311yescharacteristic
899C2#1307713611yescharacteristic
900C2#1307716411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2965C2
socleC22×C11C22×C22⋊C4
prime radical#13082209C2
cosocleC42×C11C24
hypercenter#2965D11
hypocenterC11#17516
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2965

Complements

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

NH ≅ G/Ntype
2. #13077282C2semidirect
3. #13067086C2semidirect
4. #13067082C2semidirect
5. #13067077C2semidirect
6. #13067064C2semidirect
7. #13067056C2semidirect
8. #13067051C2semidirect
9. #13067034C2semidirect
10. #13067030C2semidirect
11. #13067025C2semidirect
12. #13067012C2semidirect
13. #13067004C2semidirect
14. #13066999C2semidirect
15. C11×#2965C2semidirect
330. #2965D11semidirect
778. C11#17516semidirect

Maximal subgroups

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

subgroupindex
#130822092
#130772822
#130670862
#130670822
#130670772
#130670642
#130670562
#130670512
#130670342
#130670302
#130670252
#130670122
#130670042
#130669992
C11×#29652
#1751611