Finite Group Databasebeta

← #14720698

Subgroups — #14720698

Order 2816.

958 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082180C211yesmaximal, characteristic
2#13077282C211yesmaximal, characteristic, complemented
3#13067090C211yesmaximal, characteristic, complemented
4#13067082C211yesmaximal, characteristic, complemented
5#13067077C211yesmaximal, characteristic, complemented
6#13067060C211yesmaximal, characteristic, complemented
7#13067056C211yesmaximal, characteristic, complemented
8#13067051C211yesmaximal, characteristic, complemented
9#13067038C211yesmaximal, characteristic, complemented
10#13067030C211yesmaximal, characteristic, complemented
11#13067025C211yesmaximal, characteristic, complemented
12#13067008C211yesmaximal, characteristic, complemented
13#13067004C211yesmaximal, characteristic, complemented
14#13066999C211yesmaximal, characteristic, complemented
15C11×#2965C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17#10623359—21no—
18#10623115C411yescharacteristic
19#10623112—21no—
20#10623110C411yescharacteristic
21#10623094C411yescharacteristic
22#10623089—21no—
23#10623087—21no—
24#10623087—21no—
25#10623082C411yescharacteristic
26#10623081C411yescharacteristic
27#10623081C411yescharacteristic
28#10623072C411yescharacteristic
29#10623072C411yescharacteristic
30#10623059—21no—
31#10623059—21no—
32D11×#117—21no—
33#10623010C2211yescharacteristic
34#10623010C2211yescharacteristic
35C4×#4339C2211yescharacteristic
36C4×#4339C2211yescharacteristic
37C2×C4×D44C2211yescharacteristic
38#10623001C2211yescharacteristic
39C11×#446—21no—
40C11×#436—21no—
41C11×#435—21no—
42C11×#435—21no—
43C11×#431C2211yescharacteristic
44C11×#431C2211yescharacteristic, complemented
45C11×#431C2211yescharacteristic, complemented
46C4×C11×M16C2211yescharacteristic
47C4×C11×M16C2211yescharacteristic, complemented
48C2×C4×C8×C11C2211yescharacteristic, complemented
49#10622847—21no—
50#10622613—21no—
51#10622613—21no—
52#10622610—21no—
53#10622539C2211yescharacteristic
54#10622539C2211yescharacteristic, complemented
55#10622538C2211yescharacteristic
56#10622538C2211yescharacteristic, complemented
57#10622537C2211yescharacteristic, complemented
58C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
59#10622097C2211yescharacteristic
60#10622097C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622097C2211yescharacteristic
64#10622097C2211yescharacteristic
65#10622097C2211yescharacteristic
66#10622097C2211yescharacteristic
67#10622094C2211yescharacteristic, complemented
68#10622094C2211yescharacteristic, complemented
69#10622094C2211yescharacteristic, complemented
70#10622094C2211yescharacteristic, complemented
71#10622094C2211yescharacteristic, complemented
72#10622094C2211yescharacteristic, complemented
73#10622094C2211yescharacteristic, complemented
74#10622094C2211yescharacteristic, complemented
75C2×C11×#41D411yescharacteristic
76C2×#4339C2×C411yescharacteristic
77C2×#4339C2×C411yescharacteristic
78C22×D44C2×C411yescharacteristic
79C22×C4×D11—21no—
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#66999—21no—
98#66999—21no—
99#66991—21no—
100#66991—21no—
101#66990—21no—
102#66990—21no—
103#66988—21no—
104#66988—21no—
105#66983C2×C411yescharacteristic
106#66983C2×C411yescharacteristic
107#66982—21no—
108#66982—21no—
109C4×C22⋊D11—21no—
110C4×C22⋊D11—21no—
111C4×C22⋊D11—21no—
112C4×C22⋊D11—21no—
113C4×C22⋊D11—21no—
114C4×C22⋊D11—21no—
115C2×(C2×D11)⋊C4—21no—
116#66979—21no—
117#66979C2×C411yescharacteristic
118#66979C2×C411yescharacteristic
119C2×C4⋊Dic11C2×C411yescharacteristic
120#66977—21no—
121#66977C2×C411yescharacteristic
122#66977C2×C411yescharacteristic
123#66977C2×C411yescharacteristic
124#66977C2×C411yescharacteristic
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#66945—21no—
134#66945—21no—
135C4⋊C4×D11—21no—
136C4⋊C4×D11—21no—
137#66942—21no—
138#66942—21no—
139#66938—21no—
140#66938—21no—
141#66937—21no—
142#66937—21no—
143#66936—21no—
144#66936—21no—
145C22⋊C4×D11—21no—
146C22⋊C4×D11—21no—
147#66932—21no—
148#66932—21no—
149#66930—21no—
150#66930—21no—
151#66929—21no—
152#66929—21no—
153#66928C2×C411yescharacteristic
154#66928C2×C411yescharacteristic
155C4×D44—21no—
156C4×D44—21no—
157C4×D44C2×C411yescharacteristic
158C4×D44C2×C411yescharacteristic
159C4×D44C2×C411yescharacteristic
160C4×D44C2×C411yescharacteristic
161C4×D44C2311yescharacteristic
162C4×D44C2311yescharacteristic
163#66925—21no—
164#66925—21no—
165#66925—21no—
166#66925—21no—
167C42×D11—21no—
168C42×D11—21no—
169#66923—21no—
170#66923C2×C411yescharacteristic
171#66923C2×C411yescharacteristic
172#66922C2×C411yescharacteristic
173#66922C2×C411yescharacteristic
174C4×Dic22—21no—
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#17513—111nomaximal, Sylow
207C23×D11—21no—
208C11×#41—41no—
209C11×#41—41no—
210C2×Q8×C11C22⋊C411yescharacteristic
211C2×D4×C11C22⋊C411yescharacteristic
212C2×D4×C11C22⋊C411yescharacteristic
213C2×D4×C11C22⋊C411yescharacteristic
214C22×C4×C11C22×C411yescharacteristic
215C22×C4×C11C22×C411yescharacteristic
216C22×C4×C11C22×C411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C2×C22⋊D11—21no—
224C2×C22⋊D11—21no—
225C2×C22⋊D11—21no—
226C2×C22⋊D11—21no—
227C22×Dic11—21no—
228#4339—22no—
229#4339—22no—
230#4339—41no—
231#4339—41no—
232C2×D44—22no—
233C2×D44—21no—
234C2×D44—41no—
235C2×D44C22×C411yescharacteristic
236C2×D44C22×C411yescharacteristic
237C2×C4×D11—21no—
238C2×C4×D11—21no—
239C2×C4×D11—21no—
240C2×C4×D11—21no—
241C2×C4×D11—21no—
242C2×C4×D11—21no—
243C2×C4×D11—21no—
244C2×C4×D11—21no—
245C2×C4×D11—42no—
246C2×C4×D11—42no—
247C2×Dic22—21no—
248C2×Dic22C22×C411yescharacteristic
249C2×Dic22C22×C411yescharacteristic
250C11×M16—42no—
251C11×M16—42no—
252C2×C8×C11—21no—
253C2×C8×C11—21no—
254C2×C8×C11—21no—
255C2×C8×C11—21no—
256C2×C8×C11—42no—
257C11×C4⋊C4C22⋊C411yescharacteristic
258C11×C4⋊C4C22⋊C411yescharacteristic
259C11×C4⋊C4C22⋊C411yescharacteristic
260C11×C4⋊C4C22⋊C411yescharacteristic
261C11×C4⋊C4C22⋊C411yescharacteristic
262C11×C4⋊C4C22⋊C411yescharacteristic
263C11×C22⋊C4C22⋊C411yescharacteristic
264C11×C22⋊C4C22⋊C411yescharacteristic
265C11×C22⋊C4C22⋊C411yescharacteristic
266C11×C22⋊C4C22⋊C411yescharacteristic
267C11×C22⋊C4C22⋊C411yescharacteristic
268C11×C22⋊C4C22⋊C411yescharacteristic
269C42×C11C22×C411yescharacteristic
270C42×C11C22×C411yescharacteristic
271C42×C11C22×C411yescharacteristic
272C42×C11C2×D411yescharacteristic
273C42×C11C2×D411yescharacteristic
274C42×C11C2×D411yescharacteristic
275C42×C11C2×D411yescharacteristic
276C42×C11C2×D411yescharacteristic
277C42×C11C2×D411yescharacteristic
278C42×C11C2411yescharacteristic
279C22⋊Dic11—21no—
280C22⋊Dic11—21no—
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⋊Dic11—21no—
300C4⋊Dic11—21no—
301C4⋊Dic11C22×C411yescharacteristic
302C4⋊Dic11C22×C411yescharacteristic
303C4⋊Dic11C22×C411yescharacteristic
304C4⋊Dic11C22×C411yescharacteristic
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—
315Dic11⋊C4—21no—
316Dic11⋊C4—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#3475—111no—
330#2965D1111yescharacteristic, complemented
331#2925—111no—
332#1497—111no—
333#1495—111no—
334#1494—111no—
335#1490—111no—
336#1489—111no—
337#1488—111no—
338#1485—111no—
339#1483—111no—
340#1482—111no—
341#1478—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—
349C22×D11—42no—
350C22×D11—42no—
351C22×D11—81no—
352Q8×C11—41no—
353D4×C11—41no—
354D4×C11—41no—
355D4×C11—41no—
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—21no—
366C2×C4×C11—21no—
367C2×C4×C11—21no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
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×C11C2×C22⋊C411yescharacteristic
378C2×C4×C11C2×C22⋊C411yescharacteristic
379C2×C4×C11C2×C22⋊C411yescharacteristic
380C2×C4×C11C23×C411yescharacteristic
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C22×D411yescharacteristic
383C22⋊D11—42no—
384C22⋊D11—42no—
385C22⋊D11—81no—
386C22⋊D11—81no—
387C2×Dic11—21no—
388C2×Dic11—21no—
389C2×Dic11—21no—
390C2×Dic11—21no—
391C2×Dic11—21no—
392C2×Dic11—21no—
393C2×Dic11—42no—
394D44—21no—
395D44—21no—
396D44—21no—
397D44—42no—
398D44#13112yes—
399C4×D11—42no—
400C4×D11—42no—
401C4×D11—42no—
402C4×D11—42no—
403C4×D11—41no—
404C4×D11—41no—
405C4×D11—41no—
406C4×D11—41no—
407C4×D11—81no—
408C4×D11—81no—
409Dic22—21no—
410Dic22—21no—
411Dic22—21no—
412Dic22—21no—
413Dic22—81no—
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#556—111no—
423#555—111no—
424#554—111no—
425#553—221no—
426#552—111no—
427#552—111no—
428#552—221no—
429#551—221no—
430#551—221no—
431#547—111no—
432#546—111no—
433#546—111no—
434#533—111no—
435#529—111no—
436#529—111no—
437#529—221no—
438#529—221no—
439#525—221no—
440C4×#41—111no—
441C4×#41—111no—
442C4×#41C2×D1111yescharacteristic
443C2×C4×D4—111no—
444C2×#117—221no—
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, complemented
457#431C2×D1111yescharacteristic, complemented
458#423—111no—
459C2×C4⋊C8—111no—
460#408—221no—
461#405—221no—
462C4×M16C2×D1111yescharacteristic
463C4×M16C2×D1111yescharacteristic, complemented
464C2×C4×C8C2×D1111yescharacteristic, complemented
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—22no—
492C2×D11—41no—
493C2×D11—41no—
494C2×D11—41no—
495C2×D11—41no—
496C2×D11—41no—
497C2×D11—84no—
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×C11—21no—
508C4×C11C2×#13111yescharacteristic
509C4×C11#56811yescharacteristic
510C4×C11#57511yescharacteristic
511C4×C11#57511yescharacteristic
512Dic11—41no—
513Dic11—41no—
514Dic11—41no—
515Dic11—41no—
516Dic11—41no—
517Dic11—41no—
518C2×#41—111no—
519C2×#41—111no—
520C2×#41D4411yescharacteristic
521C22×D4—111no—
522C23×C4—221no—
523C2×M16—21no—
524C2×M16—21no—
525C2×M16—221no—
526C22×C8—21no—
527C22×C8—221no—
528C4⋊Q8—111no—
529C4⋊Q8—111no—
530#126—221no—
531#126—221no—
532#126—221no—
533#126—221no—
534#126—221no—
535#126—221no—
536#125—111no—
537#125—111no—
538#125—221no—
539#125—221no—
540#125—221no—
541#124—111no—
542#124—111no—
543#124—221no—
544#124—221no—
545#123—221no—
546#123—221no—
547#123—221no—
548#123—221no—
549#123—221no—
550#123—221no—
551#123—221no—
552#123—221no—
553C22⋊Q8—111no—
554C22⋊Q8—111no—
555C22⋊Q8—111no—
556C22⋊Q8—111no—
557C22⋊Q8—221no—
558C22⋊Q8—221no—
559C22⋊Q8—221no—
560C22⋊Q8—221no—
561C22⋊Q8—221no—
562#121—111no—
563#121—111no—
564#121—221no—
565#121—221no—
566#121—221no—
567#121—221no—
568#120—221no—
569#120—221no—
570C4×Q8—111no—
571C4×Q8—111no—
572C4×Q8—111no—
573C4×Q8—111no—
574C4×Q8—221no—
575C4×Q8C4×D1111yescharacteristic
576C4×Q8C22⋊D1111yescharacteristic
577C4×D4—111no—
578C4×D4—111no—
579C4×D4—111no—
580C4×D4—111no—
581C4×D4—111no—
582C4×D4—111no—
583C4×D4—221no—
584C4×D4—221no—
585C4×D4—221no—
586C4×D4—221no—
587C4×D4—221no—
588C4×D4—221no—
589C4×D4—221no—
590C4×D4—221no—
591C4×D4C4×D1111yescharacteristic
592C4×D4C4×D1111yescharacteristic
593C4×D4C4×D1111yescharacteristic
594C4×D4C22⋊D1111yescharacteristic
595C4×D4C22⋊D1111yescharacteristic
596C4×D4C22⋊D1111yescharacteristic
597#117—111no—
598#117—111no—
599#117—221no—
600#117—221no—
601#117—221no—
602#117—221no—
603#117—221no—
604#117—221no—
605#117—221no—
606#117—221no—
607#117—221no—
608#117D4411yescharacteristic
609#117D4411yescharacteristic
610#117D4411yescharacteristic
611C2×C4⋊C4—111no—
612C2×C4⋊C4—221no—
613C2×C4⋊C4—221no—
614C2×C22⋊C4—221no—
615C2×C22⋊C4—221no—
616C2×C22⋊C4—221no—
617C2×C42—221no—
618C2×C42—221no—
619C2×C42C22×D1111yescharacteristic
620C2×C42C22×D1111yescharacteristic
621C2×C42C22×D1111yescharacteristic
622C4⋊C8—21no—
623C4⋊C8—21no—
624C4⋊C8—21no—
625C4⋊C8—111no—
626C4⋊C8—111no—
627C4⋊C8—111no—
628C4⋊C8—111no—
629C4⋊C8—221no—
630C4⋊C8—221no—
631C22⋊C8—21no—
632C22⋊C8—21no—
633C22⋊C8—21no—
634C22⋊C8—221no—
635C22⋊C8—221no—
636C22⋊C8—221no—
637C22⋊C8—221no—
638#97—21no—
639#97—21no—
640#97—221no—
641#97—221no—
642C4×C8—21no—
643C4×C8—221no—
644C4×C8—221no—
645C4×C8C22×D1111yescharacteristic
646C4×C8C22×D1111yescharacteristic
647C4×C8C22×D1111yescharacteristic
648C4×C8C22×D1111yescharacteristic
649C2×C11—41no—
650C2×C11—41no—
651C2×C11—41no—
652C2×C11#288011yescharacteristic
653C2×C11#289611yescharacteristic
654C2×C11#290111yescharacteristic
655D11—42no—
656D11—81no—
657C24—221no—
658#41—41no—
659#41—41no—
660#41—222no—
661#41—222no—
662#41—441no—
663#41—441no—
664C2×Q8—111no—
665C2×Q8—111no—
666C2×Q8—221no—
667C2×Q8(C2×D11)⋊C411yescharacteristic
668C2×D4—111no—
669C2×D4—111no—
670C2×D4—222no—
671C2×D4—221no—
672C2×D4—221no—
673C2×D4—221no—
674C2×D4—221no—
675C2×D4—221no—
676C2×D4—441no—
677C2×D4(C2×D11)⋊C411yescharacteristic
678C2×D4(C2×D11)⋊C411yescharacteristic
679C2×D4(C2×D11)⋊C411yescharacteristic
680C22×C4—221no—
681C22×C4—221no—
682C22×C4—221no—
683C22×C4—221no—
684C22×C4—221no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—221no—
688C22×C4—221no—
689C22×C4—442no—
690C22×C4—442no—
691C22×C4C2×C4×D1111yescharacteristic
692C22×C4C2×C4×D1111yescharacteristic
693C22×C4C2×C4×D1111yescharacteristic
694C22×C4C2×D4411yescharacteristic
695C22×C4C2×D4411yescharacteristic
696C22×C4C2×D4411yescharacteristic
697C22×C4C2×C22⋊D1111yescharacteristic
698C22×C4C2×C22⋊D1111yescharacteristic
699C22×C4C2×C22⋊D1111yescharacteristic
700M16—42no—
701M16—42no—
702M16—442no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—42no—
708C2×C8—221no—
709C2×C8—221no—
710C2×C8—221no—
711C2×C8—221no—
712C2×C8—442no—
713C4⋊C4—111no—
714C4⋊C4—111no—
715C4⋊C4—111no—
716C4⋊C4—111no—
717C4⋊C4—221no—
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—221no—
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
738C4⋊C4(C2×D11)⋊C411yescharacteristic
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—221no—
755C22⋊C4—221no—
756C22⋊C4—221no—
757C22⋊C4(C2×D11)⋊C411yescharacteristic
758C22⋊C4(C2×D11)⋊C411yescharacteristic
759C22⋊C4(C2×D11)⋊C411yescharacteristic
760C22⋊C4(C2×D11)⋊C411yescharacteristic
761C22⋊C4(C2×D11)⋊C411yescharacteristic
762C22⋊C4(C2×D11)⋊C411yescharacteristic
763C42—221no—
764C42—221no—
765C42—221no—
766C42—221no—
767C42—221no—
768C42—221no—
769C42C2×C4×D1111yescharacteristic
770C42C2×C4×D1111yescharacteristic
771C42C2×C4×D1111yescharacteristic
772C42C2×D4411yescharacteristic
773C42C2×D4411yescharacteristic
774C42C2×D4411yescharacteristic
775C42C2×C22⋊D1111yescharacteristic
776C42C2×C22⋊D1111yescharacteristic
777C42C2×C22⋊D1111yescharacteristic
778C42C23×D1111yescharacteristic
779C11#1751311yescharacteristic, complemented, Sylow
780C23—221no—
781C23—221no—
782C23—442no—
783C23—442no—
784C23—881no—
785C23C2×(C2×D11)⋊C411yescharacteristic
786C23C2×(C2×D11)⋊C411yescharacteristic
787C23C2×(C2×D11)⋊C411yescharacteristic
788Q8—41no—
789Q8—221no—
790Q8—221no—
791Q8—221no—
792Q8—221no—
793Q8—881no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—112no—
798D4—221no—
799D4—221no—
800D4—221no—
801D4—442no—
802D4—442no—
803D4—442no—
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—442no—
831C2×C4—442no—
832C2×C4—441no—
833C2×C4—441no—
834C2×C4—441no—
835C2×C4—441no—
836C2×C4—881no—
837C2×C4—881no—
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×C4C2×(C2×D11)⋊C411yescharacteristic
847C2×C4C22×C4×D1111yescharacteristic
848C2×C4C22×D4411yescharacteristic
849C2×C4C22×C22⋊D1111yescharacteristic
850C8—22no—
851C8—41no—
852C8—41no—
853C8—41no—
854C8—441no—
855C8—441no—
856C8—441no—
857C8—441no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—222no—
868C22—441no—
869C22—441no—
870C22—441no—
871C22—441no—
872C22—441no—
873C22—884no—
874C22C22×(C2×D11)⋊C411yescharacteristic
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—441no—
886C4—441no—
887C4—441no—
888C4—441no—
889C4—441no—
890C4—441no—
891C4#1062327911yescharacteristic
892C4#1062327911yescharacteristic
893C4D11×#13111yescharacteristic
894C4#1062328111yescharacteristic
895C2—41no—
896C2—41no—
897C2—41no—
898C2—442no—
899C2—881no—
900C2#1307706311yescharacteristic
901C2#1307713611yescharacteristic
902C2#1307716411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2965C2
socleC22×C11C22×C22⋊C4
prime radical#13082180C2
cosocleC42×C11C24
hypercenter#2965D11
hypocenterC11#17513
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. #13067090C2semidirect
4. #13067082C2semidirect
5. #13067077C2semidirect
6. #13067060C2semidirect
7. #13067056C2semidirect
8. #13067051C2semidirect
9. #13067038C2semidirect
10. #13067030C2semidirect
11. #13067025C2semidirect
12. #13067008C2semidirect
13. #13067004C2semidirect
14. #13066999C2semidirect
15. C11×#2965C2semidirect
44. C11×#431C22semidirect
45. C11×#431C22semidirect
47. C4×C11×M16C22semidirect
48. C2×C4×C8×C11C22semidirect
54. #10622539C22semidirect
56. #10622538C22semidirect
57. #10622537C22semidirect
58. C2×C4⋊(C11⋊C8)C22semidirect
67. #10622094C22semidirect
68. #10622094C22semidirect
69. #10622094C22semidirect
70. #10622094C22semidirect
71. #10622094C22semidirect
72. #10622094C22semidirect
73. #10622094C22semidirect
74. #10622094C22semidirect
330. #2965D11semidirect
456. #431C2×D11semidirect
457. #431C2×D11semidirect
463. C4×M16C2×D11semidirect
464. C2×C4×C8C2×D11semidirect
779. C11#17513semidirect

Maximal subgroups

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

subgroupindex
#130821802
#130772822
#130670902
#130670822
#130670772
#130670602
#130670562
#130670512
#130670382
#130670302
#130670252
#130670082
#130670042
#130669992
C11×#29652
#1751311