Finite Group Databasebeta

← D11×#3063 #15621012

Subgroups — D11×#3063 #15621012

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 1362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#137C211yesmaximal, characteristic, complemented
2C2×D11×#131C211yesmaximal, characteristic, complemented
3D11×#537C211yesmaximal, characteristic
4D11×#536C211yesmaximal, characteristic, complemented
5#13078310C211yesmaximal, characteristic, complemented
6#13078309C211yesmaximal, characteristic, complemented
7#13078308C211yesmaximal, characteristic, complemented
8#13078307C211yesmaximal, characteristic, complemented
9#13078306C212yesmaximal, complemented
10#13078305C211yesmaximal, characteristic, complemented
11#13078304C212yesmaximal, complemented
12#13078303C211yesmaximal, characteristic, complemented
13#13078302C212yesmaximal, complemented
14#13078301C211yesmaximal, characteristic, complemented
15#13078300C212yesmaximal, complemented
16D11×#470C212yesmaximal, complemented
17D11×#468C212yesmaximal, complemented
18D11×#467C212yesmaximal, complemented
19D11×#465C212yesmaximal, complemented
20D11×#428C211yesmaximal, characteristic, complemented
21D11×#416C211yesmaximal, characteristic, complemented
22C2×D11×#103C211yesmaximal, characteristic, complemented
23C11×#3063C211yesmaximal, characteristic, complemented
24C2×#41×D11C2211yescharacteristic
25C2×#41×D11C2211yescharacteristic
26C22×Q8×D11C2211yescharacteristic
27C2×C11×#137C2211yescharacteristic, complemented
28C2×C11×#131C2211yescharacteristic, complemented
29C11×#537C2211yescharacteristic
30C11×#536C2211yescharacteristic, complemented
31#10623364C2211yescharacteristic
32#10623364C2211yescharacteristic
33#10623356C2211yescharacteristic, complemented
34C2×#67004C2211yescharacteristic, complemented
35C2×#67001C2211yescharacteristic, complemented
36#10623347C2211yescharacteristic, complemented
37C2×#66995C2211yescharacteristic, complemented
38D11×#137—28no—
39C2×#66971C2212yescomplemented
40C2×Q16×D11C2212yes—
41C2×#66968C2212yescomplemented
42C2×SD16×D11C2212yes—
43D11×#131—28no—
44C2×#66962C2211yescharacteristic, complemented
45C2×#66960C2211yescharacteristic, complemented
46C2×#66960C2212yescomplemented
47C2×M16×D11C2212yes—
48C2×M16×D11C2211yescharacteristic
49C2×#66954C2212yescomplemented
50C2×#66954C2211yescharacteristic, complemented
51C22×C8×D11C2211yescharacteristic
52C22×C8×D11C2212yes—
53#10623255—21no—
54D11×C4⋊Q8—21no—
55#10623206—21no—
56D11×#124—21no—
57D11×#123—22no—
58#10623179—22no—
59#10623160—21no—
60#10623160C2212yes—
61#10623159C2212yescomplemented
62#10623159C2212yescomplemented
63D11×C22⋊Q8—21no—
64D11×C22⋊Q8C2212yes—
65D11×C22⋊Q8C2212yes—
66D11×C22⋊Q8C2212yes—
67#10623139—21no—
68#10623139C2212yes—
69D11×#121—21no—
70D11×#121—22no—
71D11×#121C2212yes—
72#10623128—22no—
73#10623057C2211yescharacteristic, complemented
74D11×#117C2211yescharacteristic
75#10623041C2211yescharacteristic
76C2×C4⋊C4×D11C2211yescharacteristic
77C11×#470C2212yescomplemented
78C11×#468C2212yescomplemented
79C11×#467C2212yescomplemented
80C11×#465C2212yescomplemented
81C11×#428C2211yescharacteristic, complemented
82C11×#416C2211yescharacteristic, complemented
83C2×C11×#103C2211yescharacteristic, complemented
84#10622846C2211yescharacteristic, complemented
85C2×#66899C2211yescharacteristic, complemented
86#10622802C2212yescomplemented
87#10622801C2212yescomplemented
88#10622787C2212yescomplemented
89#10622784C2212yescomplemented
90#10622750C2212yescomplemented
91#10622747C2212yescomplemented
92#10622734C2211yescharacteristic, complemented
93#10622729C2212yescomplemented
94#10622727C2212yescomplemented
95#10622726C2211yescharacteristic, complemented
96C2×#66880C2211yescharacteristic, complemented
97#10622665C2212yescomplemented
98#10622665C2212yescomplemented
99#10622664C2212yescomplemented
100#10622664C2212yescomplemented
101#10622662C2212yescomplemented
102#10622661C2212yescomplemented
103#10622655C2212yescomplemented
104#10622654C2212yescomplemented
105#10622615C2211yescharacteristic, complemented
106#10622608C2211yescharacteristic, complemented
107C2×#66874C2211yescharacteristic, complemented
108#10622577C2211yescharacteristic, complemented
109#10622500C2212yescomplemented
110#10622499C2212yescomplemented
111#10622494C2212yescomplemented
112D11×#107C2212yes—
113#10622481C2212yescomplemented
114#10622477C2212yescomplemented
115#10622474C2212yescomplemented
116D11×#106C2212yes—
117#10622429C2212yescomplemented
118#10622429C2212yescomplemented
119#10622426C2212yescomplemented
120#10622426C2212yescomplemented
121#10622425C2212yescomplemented
122#10622420C2212yescomplemented
123#10622417C2211yescharacteristic, complemented
124#10622417C2211yescharacteristic, complemented
125D11×#103C2212yes—
126D11×#103C2212yes—
127D11×#103C2211yescharacteristic
128D11×#103C2211yescharacteristic
129D11×#103C2212yescomplemented
130D11×#103C2212yescomplemented
131#10622393C2212yescomplemented
132#10622391C2212yescomplemented
133#10622385C2211yescharacteristic, complemented
134#10622385C2211yescharacteristic, complemented
135D11×#102C2211yescharacteristic
136D11×#102C2211yescharacteristic
137C2×C11×#41C2311yescharacteristic
138C2×C11×#41C2311yescharacteristic
139C22×Q8×C11C2311yescharacteristic
140#41×D11—24no—
141#41×D11—24no—
142#41×D11—24no—
143#41×D11—24no—
144C2×#4343D411yescharacteristic
145C2×#4343C2311yescharacteristic
146C2×Q8×D11—21no—
147C2×Q8×D11—21no—
148C2×Q8×D11—24no—
149C2×Q8×D11—24no—
150C2×Q8×D11D411yescharacteristic
151C2×Q8×D11C2312yes—
152C2×Q8×D11C2312yes—
153C2×Q8×D11C2311yescharacteristic
154C2×#4341—21no—
155C2×#4341D412yes—
156C2×#4341D411yescharacteristic
157C2×#4341C2311yescharacteristic
158C2×D4×D11—21no—
159C2×D4×D11—22no—
160C2×D4×D11D412yes—
161C2×D4×D11D411yescharacteristic
162C2×D4×D11C2311yescharacteristic
163C2×#4339—21no—
164C2×#4339C2311yescharacteristic
165C2×#4339C2312yes—
166C2×#4339C2311yescharacteristic
167C22×C4×D11—21no—
168C22×C4×D11—21no—
169C22×C4×D11—21no—
170C22×C4×D11C2312yes—
171C22×C4×D11C2311yescharacteristic
172C22×Dic22—21no—
173C22×Dic22C2311yescharacteristic
174C11×#137—24no—
175C2×C11×Q16C2312yes—
176C2×C11×SD16C2312yes—
177C11×#131—24no—
178C2×C11×M16C2312yes—
179C2×C11×M16C2311yescharacteristic
180C22×C8×C11C2311yescharacteristic
181C22×C8×C11C2312yes—
182C11×C4⋊Q8—21no—
183C11×#124—21no—
184C11×#123—22no—
185C11×C22⋊Q8—21no—
186C11×C22⋊Q8C2312yes—
187C11×C22⋊Q8C2312yes—
188C11×C22⋊Q8C2312yes—
189C11×#121—22no—
190C11×#121—21no—
191C11×#121C2312yes—
192C11×#117C2311yescharacteristic
193C2×C11×C4⋊C4C2311yescharacteristic
194#67004—24no—
195#67001—24no—
196#67000—21no—
197#66999—21no—
198#66999C2312yes—
199#66999C2312yes—
200#66999C2312yes—
201#66997—21no—
202#66997—21no—
203C2×#4326C2312yes—
204C2×#4326C2312yes—
205#66995—24no—
206C2×#4325C2312yes—
207#66992—22no—
208#66992—22no—
209#66992—22no—
210#66992—22no—
211#66991—21no—
212#66991—22no—
213#66991C2312yes—
214#66989—21no—
215#66988—22no—
216C2×#4324C2312yes—
217#66983—22no—
218#66983—21no—
219#66983C2312yes—
220#66982—22no—
221#66979C2311yescharacteristic
222C2×C4⋊Dic11C2311yescharacteristic
223#66977—21no—
224#66977C2312yes—
225#66977C2312yes—
226#66977C2312yes—
227C2×Dic11⋊C4—21no—
228C2×#4318C2312yes—
229C2×#4318C2311yescharacteristic
230C22×C11⋊C8C2311yescharacteristic
231C22×C11⋊C8C2312yes—
232#66971—28no—
233Q16×D11—28no—
234#66968—28no—
235SD16×D11—28no—
236#66962—24no—
237#66960—24no—
238#66960—28no—
239M16×D11—28no—
240M16×D11D418yescomplemented
241C2×Dic44C2312yes—
242C2×#4314C2312yes—
243#66954—24no—
244#66954—28no—
245C2×#4313C2312yes—
246C2×#4313C2312yes—
247C2×#4313C2312yes—
248C2×C8×D11—24no—
249C2×C8×D11—28no—
250C2×C8×D11C2312yes—
251C2×C8×D11C2311yescharacteristic
252C2×C8×D11C2311yescharacteristic
253C2×C8×D11C2312yes—
254C2×C8×D11C2311yescharacteristic
255C2×C8×D11C2311yescharacteristic
256C2×C8×D11C2312yes—
257#66950—21no—
258#66950C2312yes—
259#66950C2312yes—
260#66950C2312yes—
261#66949—22no—
262#66949—22no—
263#66949—22no—
264#66949—22no—
265#66948—21no—
266#66948—22no—
267#66948C2312yes—
268#66947—22no—
269#66947—22no—
270#66945C2311yescharacteristic
271#66945C2311yescharacteristic
272C4⋊C4×D11—22no—
273C4⋊C4×D11—22no—
274C4⋊C4×D11—21no—
275C4⋊C4×D11—21no—
276C4⋊C4×D11—22no—
277C4⋊C4×D11C2311yescharacteristic
278C4⋊C4×D11C2312yes—
279C4⋊C4×D11C2312yes—
280C4⋊C4×D11C2311yescharacteristic
281#66941—22no—
282#66941—22no—
283#66939—22no—
284#66938—22no—
285#66938—22no—
286#66937—22no—
287#66937—22no—
288#66937—22no—
289#66937—22no—
290#66936—22no—
291#66936—22no—
292C22⋊C4×D11—21no—
293C22⋊C4×D11—22no—
294C22⋊C4×D11—22no—
295C22⋊C4×D11—22no—
296C22⋊C4×D11—22no—
297#66931—22no—
298#66931—22no—
299#66931—22no—
300#66931—22no—
301#66930—21no—
302#66928—21no—
303#66925—21no—
304C42×D11—21no—
305#66922—21no—
306C11×#107C2312yes—
307C11×#106C2312yes—
308C11×#103C2312yes—
309C11×#103C2312yes—
310C11×#103C2311yescharacteristic
311C11×#103C2311yescharacteristic
312C11×#102C2311yescharacteristic
313C11×#102C2311yescharacteristic
314#66899C2312yes—
315#66899C2312yes—
316#66899C2311yescharacteristic
317#66899C2311yescharacteristic
318#66896C2311yescharacteristic
319#66896C2311yescharacteristic
320#66885C2311yescharacteristic
321#66885C2311yescharacteristic
322#66882C2312yes—
323#66881C2312yes—
324#66880C2311yescharacteristic
325#66880C2311yescharacteristic
326#66880C2312yes—
327#66880C2312yes—
328#66874C2312yes—
329#66874C2311yescharacteristic
330#66874C2312yes—
331#66874C2311yescharacteristic
332#66873C2311yescharacteristic
333#66873C2311yescharacteristic
334#66872C2312yes—
335#66872C2312yes—
336#66871C2312yes—
337#66871C2312yes—
338C2×#3063—111nomaximal, Sylow
339C23×D11—21no—
340C23×D11C2×D412yes—
341C23×D11C2×D411yescharacteristic
342C11×#41—22no—
343C11×#41—22no—
344C11×#41—22no—
345C11×#41—22no—
346C2×Q8×C11—21no—
347C2×Q8×C11—22no—
348C2×Q8×C11—22no—
349C2×Q8×C11C2×D411yescharacteristic
350C2×Q8×C11C2412yes—
351C2×Q8×C11C2411yescharacteristic
352C2×D4×C11—21no—
353C2×D4×C11—22no—
354C2×D4×C11C2×D412yes—
355C2×D4×C11C2×D411yescharacteristic
356C2×D4×C11C2411yescharacteristic
357C22×C4×C11—21no—
358C22×C4×C11—21no—
359C22×C4×C11—21no—
360C22×C4×C11C2412yes—
361C22×C4×C11C2411yescharacteristic
362C2×C22⋊D11—21no—
363C2×C22⋊D11—21no—
364C2×C22⋊D11—22no—
365C2×C22⋊D11—21no—
366C2×C22⋊D11—22no—
367C2×C22⋊D11C2×D412yes—
368C2×C22⋊D11C2×D412yes—
369C2×C22⋊D11C2×D412yes—
370C22×Dic11—21no—
371C22×Dic11—21no—
372C22×Dic11—21no—
373C22×Dic11C2×D412yes—
374C22×Dic11C2×D411yescharacteristic
375#4343—24no—
376#4343—22no—
377#4343—22no—
378Q8×D11—24no—
379Q8×D11—24no—
380Q8×D11—24no—
381Q8×D11—22no—
382Q8×D11—24no—
383Q8×D11—24no—
384Q8×D11—22no—
385Q8×D11—44no—
386Q8×D11—44no—
387#4341—28no—
388#4341—24no—
389#4341—22no—
390#4341—22no—
391#4341—44no—
392D4×D11—24no—
393D4×D11—28no—
394D4×D11—22no—
395D4×D11—22no—
396D4×D11—44no—
397D4×D11—84no—
398#4339—24no—
399#4339—24no—
400#4339—22no—
401#4339—22no—
402#4339—22no—
403#4339—22no—
404#4339—44no—
405C2×D44—21no—
406C2×D44—22no—
407C2×D44C2×D411yescharacteristic
408C2×D44C2×D412yes—
409C2×D44C2411yescharacteristic
410C2×C4×D11—24no—
411C2×C4×D11—24no—
412C2×C4×D11—21no—
413C2×C4×D11—21no—
414C2×C4×D11—21no—
415C2×C4×D11—22no—
416C2×C4×D11—21no—
417C2×C4×D11—22no—
418C2×C4×D11—22no—
419C2×C4×D11—22no—
420C2×C4×D11—21no—
421C2×C4×D11—44no—
422C2×C4×D11—44no—
423C2×C4×D11—82no—
424C2×C4×D11C2×D414yes—
425C2×C4×D11C2×D412yes—
426C2×C4×D11C2×D412yes—
427C2×C4×D11C2×D411yescharacteristic
428C2×C4×D11C2×D411yescharacteristic
429C2×C4×D11#4114yes—
430C2×C4×D11C2412yes—
431C2×C4×D11C2411yescharacteristic
432C2×C4×D11C2411yescharacteristic
433C2×Dic22—22no—
434C2×Dic22—21no—
435C2×Dic22—22no—
436C2×Dic22—22no—
437C2×Dic22—21no—
438C2×Dic22—22no—
439C2×Dic22—44no—
440C2×Dic22C2×D411yescharacteristic
441C2×Dic22C2×D412yes—
442C2×Dic22C2412yes—
443C2×Dic22C2411yescharacteristic
444C11×Q16—24no—
445C11×SD16—24no—
446C11×M16—24no—
447C11×M16C2×D414yescomplemented
448C2×C8×C11—24no—
449C2×C8×C11—22no—
450C2×C8×C11C2411yescharacteristic
451C2×C8×C11C2411yescharacteristic
452C2×C8×C11C2412yes—
453C11×C4⋊C4—22no—
454C11×C4⋊C4—22no—
455C11×C4⋊C4—21no—
456C11×C4⋊C4—22no—
457C11×C4⋊C4C2411yescharacteristic
458C11×C4⋊C4C2412yes—
459C11×C4⋊C4C2411yescharacteristic
460C11×C22⋊C4—21no—
461C11×C22⋊C4—22no—
462C11×C22⋊C4—22no—
463C11×C22⋊C4—22no—
464C11×C22⋊C4—22no—
465C42×C11—21no—
466C22⋊Dic11—22no—
467C22⋊Dic11—21no—
468C22⋊Dic11—22no—
469C22⋊Dic11—22no—
470C22⋊Dic11—22no—
471#4326—24no—
472#4326—24no—
473#4325—24no—
474#4324—24no—
475(C2×D11)⋊C4—22no—
476(C2×D11)⋊C4—21no—
477(C2×D11)⋊C4—21no—
478(C2×D11)⋊C4—22no—
479(C2×D11)⋊C4—22no—
480(C2×D11)⋊C4—22no—
481(C2×D11)⋊C4—22no—
482(C2×D11)⋊C4—22no—
483(C2×D11)⋊C4—22no—
484(C2×D11)⋊C4—22no—
485C4⋊Dic11—22no—
486C4⋊Dic11—22no—
487C4⋊Dic11—22no—
488C4⋊Dic11—21no—
489C4⋊Dic11C2411yescharacteristic
490C4⋊Dic11C2412yes—
491C4⋊Dic11C2411yescharacteristic
492Dic11⋊C4—21no—
493Dic11⋊C4—21no—
494Dic11⋊C4—22no—
495Dic11⋊C4—22no—
496Dic11⋊C4—22no—
497Dic11⋊C4—22no—
498Dic11⋊C4—22no—
499Dic11⋊C4—22no—
500Dic11⋊C4—22no—
501Dic11⋊C4—22no—
502C4×Dic11—21no—
503C4×Dic11—21no—
504C4×Dic11—21no—
505#4318—24no—
506#4318C2×D414yescomplemented
507C2×C11⋊C8—24no—
508C2×C11⋊C8—22no—
509C2×C11⋊C8C2411yescharacteristic
510C2×C11⋊C8C2411yescharacteristic
511C2×C11⋊C8C2412yes—
512Dic44—24no—
513#4314—24no—
514#4313—24no—
515#4313—24no—
516#4313C2×D418yescomplemented
517C8×D11—22no—
518C8×D11—22no—
519C8×D11—22no—
520C8×D11—22no—
521C8×D11—24no—
522C8×D11—24no—
523C8×D11C2×D418yes—
524C22×#137—111no—
525C22×#131—111no—
526C2×#537—111no—
527C2×#536—111no—
528#3063—112no—
529#3063—112no—
530#3063—112no—
531#3063—112no—
532#3063—111no—
533#3063—111no—
534#3063—111no—
535#3063—111no—
536#3063—111no—
537#3063—111no—
538#3063—111no—
539#3063D1111yescharacteristic, direct product factor
540C2×#470—112no—
541C2×#468—112no—
542C2×#467—112no—
543C2×#465—112no—
544C2×#428—111no—
545C2×#416—111no—
546C22×#103—111no—
547C23×C11—21no—
548C23×C11C22×D412yes—
549C23×C11C22×D411yescharacteristic
550C22×D11—22no—
551C22×D11—22no—
552C22×D11—24no—
553C22×D11—24no—
554C22×D11—24no—
555C22×D11—21no—
556C22×D11—42no—
557C22×D11—42no—
558C22×D11—42no—
559C22×D11#12114yes—
560C22×D11C22×D412yes—
561C22×D11C22×D411yescharacteristic
562C22×D11C22×D411yescharacteristic
563Q8×C11—22no—
564Q8×C11—22no—
565Q8×C11—21no—
566Q8×C11—22no—
567Q8×C11—21no—
568Q8×C11—42no—
569D4×C11—24no—
570D4×C11—22no—
571D4×C11—21no—
572D4×C11—21no—
573D4×C11—42no—
574D4×C11—82no—
575C2×C4×C11—22no—
576C2×C4×C11—22no—
577C2×C4×C11—21no—
578C2×C4×C11—21no—
579C2×C4×C11—22no—
580C2×C4×C11—22no—
581C2×C4×C11—21no—
582C2×C4×C11—42no—
583C2×C4×C11—42no—
584C2×C4×C11—81no—
585C2×C4×C11C22×D412yes—
586C2×C4×C11C22×D411yescharacteristic
587C2×C4×C11C22×D412yes—
588C2×C4×C11C2×#4112yes—
589C2×C4×C11C2511yescharacteristic
590C22⋊D11—24no—
591C22⋊D11—24no—
592C22⋊D11—24no—
593C22⋊D11—42no—
594C22⋊D11—42no—
595C22⋊D11—42no—
596C22⋊D11—82no—
597C22⋊D11—82no—
598C2×Dic11—24no—
599C2×Dic11—21no—
600C2×Dic11—21no—
601C2×Dic11—22no—
602C2×Dic11—22no—
603C2×Dic11—21no—
604C2×Dic11—42no—
605C2×Dic11—42no—
606C2×Dic11—81no—
607C2×Dic11#12114yes—
608C2×Dic11C22×D412yes—
609C2×Dic11C22×D411yescharacteristic
610C2×Dic11C22×D411yescharacteristic
611D44—24no—
612D44—22no—
613D44—21no—
614D44—21no—
615D44—42no—
616D44—82no—
617C4×D11—24no—
618C4×D11—22no—
619C4×D11—22no—
620C4×D11—24no—
621C4×D11—42no—
622C4×D11—44no—
623C4×D11—44no—
624C4×D11—42no—
625C4×D11—44no—
626C4×D11—42no—
627C4×D11—42no—
628C4×D11—42no—
629C4×D11—82no—
630C4×D11#12114yes—
631C4×D11#12114yes—
632C4×D11C22×D412yes—
633C4×D11C22×D412yes—
634C4×D11C2×#4112yes—
635C4×D11C2×#4112yes—
636Dic22—22no—
637Dic22—24no—
638Dic22—22no—
639Dic22—21no—
640Dic22—22no—
641Dic22—21no—
642Dic22—42no—
643Dic22—44no—
644Dic22—44no—
645Dic22—42no—
646C8×C11—21no—
647C8×C11—21no—
648C8×C11C22×D414yes—
649C11⋊C8—21no—
650C11⋊C8—21no—
651C11⋊C8C22×D414yes—
652C22×#41—111no—
653C22×#41—111no—
654C23×Q8—111no—
655C2×#137—111no—
656C2×#137—111no—
657C2×#137—112no—
658C2×#137—112no—
659C2×#137—111no—
660C2×#137—228no—
661C2×#137C2×D1111yescharacteristic, complemented
662C22×Q16—112no—
663C22×SD16—112no—
664C2×#131—111no—
665C2×#131—111no—
666C2×#131—112no—
667C2×#131—112no—
668C2×#131—111no—
669C2×#131—228no—
670C2×#131C2×D1111yescharacteristic, complemented
671C22×M16—111no—
672C22×M16—112no—
673C23×C8—111no—
674C23×C8—112no—
675#537—111no—
676#537—111no—
677#537—112no—
678#537—112no—
679#537—111no—
680#537—222no—
681#537—221no—
682#537—221no—
683#537C2×D1111yescharacteristic
684#536—111no—
685#536—111no—
686#536—112no—
687#536—112no—
688#536—111no—
689#536—222no—
690#536—221no—
691#536—221no—
692#536C2×D1111yescharacteristic, complemented
693C2×C4⋊Q8—221no—
694C2×#124—221no—
695C2×#123—222no—
696C2×C22⋊Q8—112no—
697C2×C22⋊Q8—112no—
698C2×C22⋊Q8—112no—
699C2×C22⋊Q8—221no—
700C2×#121—112no—
701C2×#121—222no—
702C2×#121—221no—
703C2×#117—111no—
704C22×C4⋊C4—111no—
705#470—112no—
706#470—112no—
707#470—112no—
708#470—112no—
709#470—112no—
710#470—112no—
711#470—112no—
712#470C2×D1112yescomplemented
713#468—112no—
714#468—112no—
715#468—112no—
716#468—112no—
717#468—112no—
718#468—112no—
719#468—112no—
720#468C2×D1112yescomplemented
721#467—112no—
722#467—112no—
723#467—112no—
724#467—112no—
725#467—112no—
726#467—112no—
727#467—112no—
728#467C2×D1112yescomplemented
729#465—112no—
730#465—112no—
731#465—112no—
732#465—112no—
733#465—112no—
734#465—112no—
735#465—112no—
736#465C2×D1112yescomplemented
737#428—111no—
738#428—111no—
739#428—111no—
740#428—112no—
741#428—112no—
742#428C2×D1111yescharacteristic, complemented
743C2×#107—112no—
744C2×#106—112no—
745#416—111no—
746#416—111no—
747#416—111no—
748#416—111no—
749#416—111no—
750#416—111no—
751#416—111no—
752#416C2×D1111yescharacteristic, complemented
753C2×#103—111no—
754C2×#103—111no—
755C2×#103—111no—
756C2×#103—112no—
757C2×#103—112no—
758C2×#103—112no—
759C2×#103—112no—
760C2×#103—111no—
761C2×#103—111no—
762C2×#103C2×D1111yescharacteristic, complemented
763C2×#102—111no—
764C2×#102—111no—
765C22×C11—21no—
766C22×C11—21no—
767C22×C11—22no—
768C22×C11—22no—
769C22×C11—22no—
770C22×C11—41no—
771C22×C11—41no—
772C22×C11—41no—
773C22×C11C2×#12112yes—
774C22×C11C23×D411yescharacteristic
775C2×D11—21no—
776C2×D11—21no—
777C2×D11—28no—
778C2×D11—22no—
779C2×D11—22no—
780C2×D11—22no—
781C2×D11—48no—
782C2×D11—41no—
783C2×D11—41no—
784C2×D11—41no—
785C2×D11—84no—
786C2×D11C2×#12112yes—
787C2×D11C2×#12112yes—
788C2×D11#57712yes—
789C2×D11#57812yes—
790C4×C11—22no—
791C4×C11—41no—
792C4×C11—42no—
793C4×C11—42no—
794C4×C11—41no—
795C4×C11—41no—
796C4×C11C2×#12112yes—
797C4×C11C23×D411yescharacteristic
798C4×C11C22×#4111yescharacteristic
799Dic11—22no—
800Dic11—42no—
801Dic11—41no—
802Dic11—42no—
803Dic11—41no—
804Dic11—41no—
805Dic11C2×#12112yes—
806Dic11C2×#12112yes—
807C2×#41—111no—
808C2×#41—112no—
809C2×#41—111no—
810C2×#41—112no—
811C2×#41—111no—
812C2×#41—111no—
813C2×#41—111no—
814C2×#41—111no—
815C2×#41—221no—
816C2×#41—221no—
817C2×#41—224no—
818C2×#41—224no—
819C2×#41—224no—
820C2×#41—224no—
821C2×#41C22×D1111yescharacteristic
822C2×#41C22×D1111yescharacteristic
823C22×Q8—111no—
824C22×Q8—112no—
825C22×Q8—111no—
826C22×Q8—112no—
827C22×Q8—111no—
828C22×Q8—221no—
829C22×Q8—221no—
830C22×Q8—221no—
831C22×Q8—224no—
832C22×Q8—224no—
833C22×Q8C22×D1111yescharacteristic
834C22×D4—112no—
835C22×D4—111no—
836C22×D4—111no—
837C22×D4—221no—
838C22×D4—222no—
839C23×C4—111no—
840C23×C4—112no—
841C23×C4—221no—
842C23×C4—221no—
843C23×C4—221no—
844#137—24no—
845#137—228no—
846#137—228no—
847#137—224no—
848#137—224no—
849#137—224no—
850C2×Q16—112no—
851C2×Q16—112no—
852C2×Q16—112no—
853C2×Q16—228no—
854C2×Q16C22×D1112yes—
855C2×SD16—112no—
856C2×SD16—112no—
857C2×SD16—112no—
858C2×SD16—228no—
859C2×SD16C22×D1112yes—
860#131—24no—
861#131—224no—
862#131—228no—
863#131—228no—
864#131—224no—
865#131—224no—
866C2×M16—111no—
867C2×M16—118no—
868C2×M16—112no—
869C2×M16—112no—
870C2×M16—112no—
871C2×M16—112no—
872C2×M16—228no—
873C2×M16C22×D1112yes—
874C2×M16C22×D1111yescharacteristic
875C22×C8—112no—
876C22×C8—111no—
877C22×C8—112no—
878C22×C8—111no—
879C22×C8—111no—
880C22×C8—111no—
881C22×C8—111no—
882C22×C8—112no—
883C22×C8—112no—
884C22×C8—228no—
885C22×C8—224no—
886C22×C8C22×D1111yescharacteristic
887C22×C8C22×D1112yes—
888C4⋊Q8—21no—
889C4⋊Q8—221no—
890C4⋊Q8—222no—
891C4⋊Q8—222no—
892C4⋊Q8—221no—
893C4⋊Q8—221no—
894#124—21no—
895#124—221no—
896#124—222no—
897#124—222no—
898#124—221no—
899#124—221no—
900#123—22no—
901#123—222no—
902#123—222no—
903#123—222no—
904#123—222no—
905#123—222no—
906#123—222no—
907#123—222no—
908C22⋊Q8—21no—
909C22⋊Q8—112no—
910C22⋊Q8—112no—
911C22⋊Q8—112no—
912C22⋊Q8—112no—
913C22⋊Q8—112no—
914C22⋊Q8—112no—
915C22⋊Q8—112no—
916C22⋊Q8—112no—
917C22⋊Q8—112no—
918C22⋊Q8—222no—
919C22⋊Q8—222no—
920C22⋊Q8—222no—
921C22⋊Q8—222no—
922C22⋊Q8—222no—
923C22⋊Q8—222no—
924C22⋊Q8—222no—
925C22⋊Q8—222no—
926C22⋊Q8—221no—
927C22⋊Q8—221no—
928C22⋊Q8—221no—
929C22⋊Q8C22×D1112yes—
930C22⋊Q8C22×D1112yes—
931C22⋊Q8C22×D1112yes—
932#121—21no—
933#121—22no—
934#121—112no—
935#121—112no—
936#121—112no—
937#121—222no—
938#121—222no—
939#121—222no—
940#121—222no—
941#121—221no—
942#121—222no—
943#121—222no—
944#121—221no—
945#121—222no—
946#121—222no—
947#121—222no—
948#121—222no—
949#121—221no—
950#121—222no—
951#121C22×D1112yes—
952#117—111no—
953#117—111no—
954#117—111no—
955#117—221no—
956#117—221no—
957#117C22×D1111yescharacteristic
958C2×C4⋊C4—111no—
959C2×C4⋊C4—112no—
960C2×C4⋊C4—112no—
961C2×C4⋊C4—111no—
962C2×C4⋊C4—111no—
963C2×C4⋊C4—221no—
964C2×C4⋊C4—221no—
965C2×C4⋊C4—222no—
966C2×C4⋊C4—222no—
967C2×C4⋊C4—222no—
968C2×C4⋊C4—221no—
969C2×C4⋊C4C22×D1111yescharacteristic
970C2×C22⋊C4—222no—
971C2×C22⋊C4—221no—
972C2×C22⋊C4—222no—
973C2×C22⋊C4—222no—
974C2×C22⋊C4—222no—
975C2×C42—221no—
976#107—112no—
977#107—112no—
978#107—112no—
979#107C22×D1112yes—
980#106—112no—
981#106—112no—
982#106—112no—
983#106C22×D1112yes—
984#103—112no—
985#103—112no—
986#103—111no—
987#103—111no—
988#103—112no—
989#103—112no—
990#103—111no—
991#103—111no—
992#103—112no—
993#103—112no—
994#103—111no—
995#103—111no—
996#103C22×D1112yes—
997#103C22×D1112yes—
998#103C22×D1111yescharacteristic
999#103C22×D1111yescharacteristic
1000#102—111no—
1001#102—111no—
1002#102—111no—
1003#102—111no—
1004#102—111no—
1005#102—111no—
1006#102C22×D1111yescharacteristic
1007#102C22×D1111yescharacteristic
1008C2×C11—22no—
1009C2×C11—42no—
1010C2×C11—81no—
1011C2×C11C22×#12111yescharacteristic
1012C2×C11C2×#57711yescharacteristic
1013C2×C11C2×#57811yescharacteristic
1014D11—22no—
1015D11—42no—
1016D11—81no—
1017D11#306314yesdirect product factor
1018C24—111no—
1019C24—112no—
1020C24—221no—
1021#41—22no—
1022#41—22no—
1023#41—22no—
1024#41—22no—
1025#41—224no—
1026#41—224no—
1027#41—228no—
1028#41—224no—
1029#41—224no—
1030#41—222no—
1031#41—222no—
1032#41—222no—
1033#41—222no—
1034#41—222no—
1035#41—222no—
1036#41—222no—
1037#41—222no—
1038#41—444no—
1039#41—444no—
1040C2×Q8—21no—
1041C2×Q8—22no—
1042C2×Q8—22no—
1043C2×Q8—112no—
1044C2×Q8—111no—
1045C2×Q8—112no—
1046C2×Q8—111no—
1047C2×Q8—222no—
1048C2×Q8—221no—
1049C2×Q8—222no—
1050C2×Q8—224no—
1051C2×Q8—224no—
1052C2×Q8—222no—
1053C2×Q8—224no—
1054C2×Q8—224no—
1055C2×Q8—224no—
1056C2×Q8—222no—
1057C2×Q8—221no—
1058C2×Q8—222no—
1059C2×Q8—222no—
1060C2×Q8—444no—
1061C2×Q8—444no—
1062C2×Q8—444no—
1063C2×Q8D4×D1111yescharacteristic
1064C2×Q8C23×D1112yes—
1065C2×Q8C23×D1111yescharacteristic
1066C2×D4—21no—
1067C2×D4—22no—
1068C2×D4—112no—
1069C2×D4—112no—
1070C2×D4—112no—
1071C2×D4—112no—
1072C2×D4—111no—
1073C2×D4—111no—
1074C2×D4—221no—
1075C2×D4—222no—
1076C2×D4—224no—
1077C2×D4—222no—
1078C2×D4—222no—
1079C2×D4—221no—
1080C2×D4—228no—
1081C2×D4—221no—
1082C2×D4—221no—
1083C2×D4—222no—
1084C2×D4—222no—
1085C2×D4—444no—
1086C2×D4—884no—
1087C2×D4D4×D1112yes—
1088C2×D4D4×D1111yescharacteristic
1089C2×D4C23×D1111yescharacteristic
1090C22×C4—21no—
1091C22×C4—21no—
1092C22×C4—21no—
1093C22×C4—111no—
1094C22×C4—111no—
1095C22×C4—111no—
1096C22×C4—114no—
1097C22×C4—114no—
1098C22×C4—111no—
1099C22×C4—111no—
1100C22×C4—112no—
1101C22×C4—112no—
1102C22×C4—112no—
1103C22×C4—112no—
1104C22×C4—224no—
1105C22×C4—224no—
1106C22×C4—221no—
1107C22×C4—221no—
1108C22×C4—221no—
1109C22×C4—222no—
1110C22×C4—221no—
1111C22×C4—222no—
1112C22×C4—222no—
1113C22×C4—222no—
1114C22×C4—221no—
1115C22×C4—221no—
1116C22×C4—221no—
1117C22×C4—221no—
1118C22×C4—444no—
1119C22×C4—444no—
1120C22×C4—882no—
1121C22×C4C23×D1112yes—
1122C22×C4C23×D1111yescharacteristic
1123Q16—24no—
1124Q16—224no—
1125Q16—224no—
1126Q16—224no—
1127SD16—24no—
1128SD16—224no—
1129SD16—224no—
1130SD16—224no—
1131M16—24no—
1132M16—114no—
1133M16—118no—
1134M16—224no—
1135M16—224no—
1136M16—224no—
1137M16D4×D1114yescomplemented
1138C2×C8—22no—
1139C2×C8—24no—
1140C2×C8—112no—
1141C2×C8—118no—
1142C2×C8—111no—
1143C2×C8—111no—
1144C2×C8—224no—
1145C2×C8—222no—
1146C2×C8—222no—
1147C2×C8—222no—
1148C2×C8—222no—
1149C2×C8—224no—
1150C2×C8—222no—
1151C2×C8—224no—
1152C2×C8C23×D1111yescharacteristic
1153C2×C8C23×D1111yescharacteristic
1154C2×C8C23×D1112yes—
1155C4⋊C4—21no—
1156C4⋊C4—22no—
1157C4⋊C4—22no—
1158C4⋊C4—22no—
1159C4⋊C4—111no—
1160C4⋊C4—111no—
1161C4⋊C4—112no—
1162C4⋊C4—222no—
1163C4⋊C4—222no—
1164C4⋊C4—221no—
1165C4⋊C4—221no—
1166C4⋊C4—222no—
1167C4⋊C4—222no—
1168C4⋊C4—222no—
1169C4⋊C4—222no—
1170C4⋊C4—222no—
1171C4⋊C4—222no—
1172C4⋊C4—221no—
1173C4⋊C4—222no—
1174C4⋊C4—222no—
1175C4⋊C4—222no—
1176C4⋊C4C23×D1111yescharacteristic
1177C4⋊C4C23×D1111yescharacteristic
1178C4⋊C4C23×D1112yes—
1179C22⋊C4—21no—
1180C22⋊C4—22no—
1181C22⋊C4—22no—
1182C22⋊C4—22no—
1183C22⋊C4—22no—
1184C22⋊C4—222no—
1185C22⋊C4—221no—
1186C22⋊C4—221no—
1187C22⋊C4—222no—
1188C22⋊C4—222no—
1189C22⋊C4—222no—
1190C22⋊C4—222no—
1191C22⋊C4—222no—
1192C22⋊C4—222no—
1193C22⋊C4—222no—
1194C22⋊C4—221no—
1195C22⋊C4—222no—
1196C22⋊C4—222no—
1197C22⋊C4—222no—
1198C22⋊C4—222no—
1199C42—21no—
1200C42—221no—
1201C42—221no—
1202C42—221no—
1203C11C2×#306311yescharacteristic, complemented, Sylow
1204C23—21no—
1205C23—111no—
1206C23—114no—
1207C23—111no—
1208C23—112no—
1209C23—222no—
1210C23—222no—
1211C23—224no—
1212C23—224no—
1213C23—224no—
1214C23—221no—
1215C23—442no—
1216C23—442no—
1217C23—442no—
1218C23C2×D4×D1112yes—
1219C23C2×D4×D1111yescharacteristic
1220Q8—22no—
1221Q8—22no—
1222Q8—21no—
1223Q8—22no—
1224Q8—21no—
1225Q8—42no—
1226Q8—224no—
1227Q8—222no—
1228Q8—222no—
1229Q8—221no—
1230Q8—222no—
1231Q8—221no—
1232Q8—444no—
1233Q8—444no—
1234Q8—442no—
1235Q8—442no—
1236D4—24no—
1237D4—22no—
1238D4—21no—
1239D4—21no—
1240D4—42no—
1241D4—82no—
1242D4—224no—
1243D4—224no—
1244D4—224no—
1245D4—224no—
1246D4—222no—
1247D4—221no—
1248D4—221no—
1249D4—442no—
1250D4—442no—
1251D4—442no—
1252D4—442no—
1253D4—882no—
1254D4—882no—
1255D4—882no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—22no—
1261C2×C4—21no—
1262C2×C4—22no—
1263C2×C4—42no—
1264C2×C4—42no—
1265C2×C4—81no—
1266C2×C4—114no—
1267C2×C4—111no—
1268C2×C4—111no—
1269C2×C4—114no—
1270C2×C4—114no—
1271C2×C4—112no—
1272C2×C4—112no—
1273C2×C4—112no—
1274C2×C4—112no—
1275C2×C4—112no—
1276C2×C4—224no—
1277C2×C4—224no—
1278C2×C4—224no—
1279C2×C4—222no—
1280C2×C4—222no—
1281C2×C4—221no—
1282C2×C4—221no—
1283C2×C4—222no—
1284C2×C4—221no—
1285C2×C4—222no—
1286C2×C4—442no—
1287C2×C4—442no—
1288C2×C4—444no—
1289C2×C4—444no—
1290C2×C4—444no—
1291C2×C4—442no—
1292C2×C4—442no—
1293C2×C4—442no—
1294C2×C4—442no—
1295C2×C4—442no—
1296C2×C4—882no—
1297C2×C4—881no—
1298C2×C4C2×D4×D1112yes—
1299C2×C4C2×D4×D1111yescharacteristic
1300C2×C4C2×D4×D1112yes—
1301C2×C4#41×D1112yes—
1302C2×C4C24×D1111yescharacteristic
1303C8—21no—
1304C8—21no—
1305C8—114no—
1306C8—221no—
1307C8—221no—
1308C8C2×D4×D1114yes—
1309C22—21no—
1310C22—21no—
1311C22—22no—
1312C22—22no—
1313C22—22no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—112no—
1318C22—112no—
1319C22—112no—
1320C22—112no—
1321C22—228no—
1322C22—221no—
1323C22—221no—
1324C22—222no—
1325C22—222no—
1326C22—222no—
1327C22—448no—
1328C22—441no—
1329C22—441no—
1330C22—441no—
1331C22—884no—
1332C22D11×#12112yes—
1333C22C22×D4×D1111yescharacteristic
1334C4—22no—
1335C4—41no—
1336C4—42no—
1337C4—42no—
1338C4—41no—
1339C4—41no—
1340C4—112no—
1341C4—112no—
1342C4—222no—
1343C4—441no—
1344C4—442no—
1345C4—442no—
1346C4—441no—
1347C4—441no—
1348C4D11×#12112yes—
1349C4C22×D4×D1111yescharacteristic
1350C4C2×#41×D1111yescharacteristic
1351C2—22no—
1352C2—42no—
1353C2—81no—
1354C2—114no—
1355C2—222no—
1356C2—442no—
1357C2—881no—
1358C2C2×D11×#12111yescharacteristic
1359C2D11×#57711yescharacteristic
1360C2D11×#57811yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3063C2
socleC22×C11C23×D4
prime radicalD11×#537C2
hypercenter#3063D11
hypocenterC11C2×#3063
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3063

Complements

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

NH ≅ G/Ntype
1. C2×D11×#137C2semidirect
2. C2×D11×#131C2semidirect
4. D11×#536C2semidirect
5. #13078310C2semidirect
6. #13078309C2semidirect
7. #13078308C2semidirect
8. #13078307C2semidirect
9. #13078306C2semidirect
10. #13078305C2semidirect
11. #13078304C2semidirect
12. #13078303C2semidirect
13. #13078302C2semidirect
14. #13078301C2semidirect
15. #13078300C2semidirect
16. D11×#470C2semidirect
17. D11×#468C2semidirect
18. D11×#467C2semidirect
19. D11×#465C2semidirect
20. D11×#428C2semidirect
21. D11×#416C2semidirect
22. C2×D11×#103C2semidirect
23. C11×#3063C2semidirect
27. C2×C11×#137C22semidirect
28. C2×C11×#131C22semidirect
30. C11×#536C22semidirect
33. #10623356C22semidirect
34. C2×#67004C22semidirect
35. C2×#67001C22semidirect
36. #10623347C22semidirect
37. C2×#66995C22semidirect
39. C2×#66971C22semidirect
41. C2×#66968C22semidirect
44. C2×#66962C22semidirect
45. C2×#66960C22semidirect
46. C2×#66960C22semidirect
49. C2×#66954C22semidirect
50. C2×#66954C22semidirect
61. #10623159C22semidirect
62. #10623159C22semidirect
73. #10623057C22semidirect
77. C11×#470C22semidirect
78. C11×#468C22semidirect
79. C11×#467C22semidirect
80. C11×#465C22semidirect
81. C11×#428C22semidirect
82. C11×#416C22semidirect
83. C2×C11×#103C22semidirect
84. #10622846C22semidirect
85. C2×#66899C22semidirect
86. #10622802C22semidirect
87. #10622801C22semidirect
88. #10622787C22semidirect
89. #10622784C22semidirect
90. #10622750C22semidirect
91. #10622747C22semidirect
92. #10622734C22semidirect
93. #10622729C22semidirect
94. #10622727C22semidirect
95. #10622726C22semidirect
96. C2×#66880C22semidirect
97. #10622665C22semidirect
98. #10622665C22semidirect
99. #10622664C22semidirect
100. #10622664C22semidirect
101. #10622662C22semidirect
102. #10622661C22semidirect
103. #10622655C22semidirect
104. #10622654C22semidirect
105. #10622615C22semidirect
106. #10622608C22semidirect
107. C2×#66874C22semidirect
108. #10622577C22semidirect
109. #10622500C22semidirect
110. #10622499C22semidirect
111. #10622494C22semidirect
113. #10622481C22semidirect
114. #10622477C22semidirect
115. #10622474C22semidirect
117. #10622429C22semidirect
118. #10622429C22semidirect
119. #10622426C22semidirect
120. #10622426C22semidirect
121. #10622425C22semidirect
122. #10622420C22semidirect
123. #10622417C22semidirect
124. #10622417C22semidirect
129. D11×#103C22semidirect
130. D11×#103C22semidirect
131. #10622393C22semidirect
132. #10622391C22semidirect
133. #10622385C22semidirect
134. #10622385C22semidirect
240. M16×D11D4semidirect
447. C11×M16C2×D4semidirect
506. #4318C2×D4semidirect
516. #4313C2×D4semidirect
539. #3063D11direct (N × H)
661. C2×#137C2×D11semidirect
670. C2×#131C2×D11semidirect
692. #536C2×D11semidirect
712. #470C2×D11semidirect
720. #468C2×D11semidirect
728. #467C2×D11semidirect
736. #465C2×D11semidirect
742. #428C2×D11semidirect
752. #416C2×D11semidirect
762. C2×#103C2×D11semidirect
1017. D11#3063direct (N × H)
1137. M16D4×D11semidirect
1203. C11C2×#3063semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1372
C2×D11×#1312
D11×#5372
D11×#5362
#130783102
#130783092
#130783082
#130783072
#130783062
#130783052
#130783042
#130783032
#130783022
#130783012
#130783002
D11×#4702
D11×#4682
D11×#4672
D11×#4652
D11×#4282
D11×#4162
C2×D11×#1032
C11×#30632
C2×#306311