Finite Group Databasebeta

← #15626529

Subgroups — #15626529

Order 2816.

1672 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082435C211yesmaximal, characteristic, complemented
2#13079893C214yesmaximal, complemented
3#13079878C214yesmaximal, complemented
4#13079834C212yesmaximal, complemented
5#13079826C212yesmaximal, complemented
6#13079791C212yesmaximal, complemented
7#13079764C212yesmaximal, complemented
8#13079150C212yesmaximal, complemented
9#13078981C212yesmaximal, complemented
10#13078590C212yesmaximal
11#13078579C212yesmaximal, complemented
12#13078431C211yesmaximal, characteristic, complemented
13#13078421C211yesmaximal, characteristic, complemented
14#13078404C211yesmaximal, characteristic, complemented
15C2×#10622634C211yesmaximal, characteristic, complemented
16#13077282C211yesmaximal, characteristic, complemented
17C11×#3461C211yesmaximal, characteristic
18C11×#544C2211yescharacteristic
19C11×#542—21no—
20C11×#542C2212yes—
21C11×#541—21no—
22C11×#541C2212yes—
23C11×#539—22no—
24C11×#537C2211yescharacteristic
25C11×#536C2211yescharacteristic
26C11×#536C2211yescharacteristic
27C11×#533—21no—
28C11×#533C2212yes—
29C11×#529—22no—
30C11×#529—21no—
31C11×#529C2212yes—
32C4×C11×#41C2211yescharacteristic
33C4×C11×#41C2211yescharacteristic
34C2×C4×Q8×C11C2211yescharacteristic
35#10623358C2212yes—
36#10623101—21no—
37Q8×Dic22—21no—
38#10623074—21no—
39#10623074—22no—
40D4×Dic22—22no—
41D4×Dic22—21no—
42#10623050C2214yes—
43#10623050C2212yes—
44#10623001C2212yes—
45#10623001C2211yescharacteristic
46C2×#66922C2212yes—
47C2×#66922C2211yescharacteristic
48#10622847C2212yes—
49#10622846C2212yes—
50#10622845C2212yes—
51#10622838C2212yes—
52C2×#66899C2212yes—
53#10622695C2214yes—
54#10622694C2214yes—
55#10622693C2214yes—
56#10622691C2214yes—
57#10622678C2214yes—
58#10622677C2214yes—
59#10622669C2214yes—
60#10622668C2214yes—
61#10622658C2214yes—
62#10622658C2214yes—
63#10622658C2214yes—
64#10622657C2214yes—
65#10622657C2214yes—
66#10622656C2214yes—
67#10622648C2214yes—
68#10622646C2214yes—
69#10622635C2212yes—
70#10622635C2214yes—
71#10622634C2212yes—
72#10622634C2212yes—
73#10622634C2212yes—
74#10622634C2214yes—
75#10622634C2212yes—
76#10622634C2211yescharacteristic
77#10622633C2211yescharacteristic
78#10622633C2212yes—
79#10622633C2212yes—
80#10622622C2212yes—
81#10622621C2211yescharacteristic
82#10622621C2212yes—
83#10622620C2212yes—
84#10622620C2211yescharacteristic
85#10622613C2214yes—
86#10622611C2212yes—
87#10622610C2212yes—
88#10622608C2212yes—
89#10622577C2212yes—
90C2×#66871C2212yes—
91#10622539C2212yes—
92#10622538C2212yes—
93#10622537C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2211yescharacteristic
95C2×C11×#41C2311yescharacteristic
96C2×C11×#41C2311yescharacteristic
97C22×Q8×C11C2311yescharacteristic
98C22×Dic22—21no—
99C22×Dic22—22no—
100C11×C4⋊Q8—21no—
101C11×C4⋊Q8—21no—
102C11×C4⋊Q8C2312yes—
103C11×C4⋊Q8C2312yes—
104C11×#126—22no—
105C11×#126—22no—
106C11×#126—22no—
107C11×#126—22no—
108C11×#125—22no—
109C11×#125—21no—
110C11×#125—22no—
111C11×#125—22no—
112C11×#125C2312yes—
113C11×#124—21no—
114C11×#124—22no—
115C11×#124C2312yes—
116C11×#123—22no—
117C11×#123—22no—
118C11×#123—22no—
119C11×#123—22no—
120C11×C22⋊Q8—21no—
121C11×C22⋊Q8—22no—
122C11×C22⋊Q8—21no—
123C11×C22⋊Q8—21no—
124C11×C22⋊Q8—22no—
125C11×C22⋊Q8—22no—
126C11×C22⋊Q8C2312yes—
127C11×C22⋊Q8C2312yes—
128C11×C22⋊Q8C2312yes—
129C11×#121—22no—
130C11×#121—21no—
131C11×#121C2312yes—
132C4×Q8×C11—21no—
133C4×Q8×C11—21no—
134C4×Q8×C11—22no—
135C4×Q8×C11D411yescharacteristic
136C4×Q8×C11D411yescharacteristic
137C4×Q8×C11C2312yes—
138C4×Q8×C11C2312yes—
139C4×Q8×C11C2311yescharacteristic
140C4×Q8×C11C2311yescharacteristic
141C4×D4×C11—21no—
142C4×D4×C11—21no—
143C4×D4×C11—22no—
144C4×D4×C11D412yes—
145C4×D4×C11D411yescharacteristic
146C4×D4×C11D411yescharacteristic
147C4×D4×C11D412yes—
148C4×D4×C11C2311yescharacteristic
149C4×D4×C11C2311yescharacteristic
150C11×#117—22no—
151C11×#117—21no—
152C11×#117—22no—
153C11×#117C2311yescharacteristic
154C11×#117C2311yescharacteristic
155C11×#117C2312yes—
156C2×C11×C4⋊C4—21no—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C42×C11—21no—
159C2×C42×C11—21no—
160C2×C42×C11C2311yescharacteristic
161C2×C42×C11C2312yes—
162Q8×Dic11—22no—
163D4×Dic11—24no—
164D4×Dic11—22no—
165#66979C2312yes—
166#66979C2314yes—
167C2×C4⋊Dic11—21no—
168C2×C4⋊Dic11—22no—
169C2×C4⋊Dic11C2312yes—
170C2×C4⋊Dic11C2314yes—
171#66977—21no—
172#66977—22no—
173#66977—21no—
174#66977—22no—
175C2×#4318C2312yes—
176C22×C11⋊C8C2312yes—
177#66943—22no—
178#66943—24no—
179#66941—24no—
180#66941—22no—
181#66931—24no—
182#66931—24no—
183#66931—24no—
184#66923C2312yes—
185#66923C2314yes—
186#66922—21no—
187#66922—22no—
188#66922—21no—
189#66922—22no—
190#66922C2311yescharacteristic
191#66922C2312yes—
192#66922C2312yes—
193#66922C2314yes—
194#66922C2311yescharacteristic
195C4×Dic22—21no—
196C4×Dic22—22no—
197C4×Dic22—21no—
198C4×Dic22—22no—
199#66899C2314yes—
200#66899C2314yes—
201#66899C2314yes—
202#66899C2314yes—
203#66899C2314yes—
204#66899C2312yes—
205#66899C2312yes—
206#66896C2314yes—
207#66896C2312yes—
208#66896C2312yes—
209C22⋊(C11⋊C8)C2314yes—
210C22⋊(C11⋊C8)C2314yes—
211#66872C2314yes—
212#66872C2314yes—
213#66872C2312yes—
214#66872C2312yes—
215#66871C2314yes—
216#66871C2314yes—
217#66871C2314yes—
218#66871C2314yes—
219#66871C2312yes—
220#66871C2312yes—
221C4⋊(C11⋊C8)C2311yescharacteristic
222C4⋊(C11⋊C8)C2311yescharacteristic
223C4⋊(C11⋊C8)C2312yes—
224C4⋊(C11⋊C8)C2312yes—
225C4⋊(C11⋊C8)C2312yes—
226#66867C2314yes—
227C4×C11⋊C8C2314yes—
228#60893—111nomaximal, Sylow
229C11×#41—22no—
230C11×#41—22no—
231C11×#41—22no—
232C11×#41—22no—
233C2×Q8×C11—21no—
234C2×Q8×C11—22no—
235C2×Q8×C11—22no—
236C2×Q8×C11—22no—
237C2×Q8×C11C2×D411yescharacteristic
238C2×Q8×C11C2412yes—
239C2×Q8×C11C2411yescharacteristic
240C2×D4×C11—21no—
241C2×D4×C11—22no—
242C2×D4×C11C2×D412yes—
243C2×D4×C11C2×D411yescharacteristic
244C2×D4×C11C2411yescharacteristic
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D412yes—
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D412yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2411yescharacteristic
256C22×Dic11—24no—
257C22×Dic11—22no—
258C2×Dic22—21no—
259C2×Dic22—21no—
260C2×Dic22—22no—
261C2×Dic22—22no—
262C2×Dic22—24no—
263C2×Dic22—82no—
264C2×Dic22—84no—
265C11×C4⋊C4—22no—
266C11×C4⋊C4—22no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—22no—
271C11×C4⋊C4—22no—
272C11×C4⋊C4—22no—
273C11×C4⋊C4—22no—
274C11×C4⋊C4—22no—
275C11×C4⋊C4—22no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4C2×D412yes—
279C11×C4⋊C4C2×D411yescharacteristic
280C11×C4⋊C4C2×D411yescharacteristic
281C11×C4⋊C4C2×D412yes—
282C11×C4⋊C4C2412yes—
283C11×C4⋊C4C2411yescharacteristic
284C11×C4⋊C4C2411yescharacteristic
285C11×C22⋊C4—22no—
286C11×C22⋊C4—22no—
287C11×C22⋊C4—21no—
288C11×C22⋊C4—22no—
289C11×C22⋊C4—21no—
290C11×C22⋊C4—21no—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—22no—
294C11×C22⋊C4C2×D412yes—
295C11×C22⋊C4C2×D412yes—
296C11×C22⋊C4C2×D412yes—
297C42×C11—22no—
298C42×C11—21no—
299C42×C11—21no—
300C42×C11—21no—
301C42×C11—22no—
302C42×C11C2×D411yescharacteristic
303C42×C11C2×D412yes—
304C42×C11C2×D411yescharacteristic
305C42×C11C2×D412yes—
306C42×C11C2412yes—
307C42×C11C2411yescharacteristic
308C42×C11C2411yescharacteristic
309C22⋊Dic11—24no—
310C22⋊Dic11—22no—
311C4⋊Dic11—21no—
312C4⋊Dic11—21no—
313C4⋊Dic11—22no—
314C4⋊Dic11—24no—
315C4⋊Dic11—22no—
316C4⋊Dic11—22no—
317C4⋊Dic11—24no—
318C4⋊Dic11C2414yes—
319C4⋊Dic11C2412yes—
320C4⋊Dic11C2412yes—
321Dic11⋊C4—22no—
322Dic11⋊C4—24no—
323Dic11⋊C4—22no—
324Dic11⋊C4—24no—
325C4×Dic11—24no—
326C4×Dic11—22no—
327#4318—24no—
328C2×C11⋊C8—24no—
329C2×C11⋊C8C2412yes—
330C2×C11⋊C8C2414yes—
331C2×C11⋊C8C2412yes—
332#3503—111no—
333#3461D1111yescharacteristic
334#3243—114no—
335#3242—114no—
336#3238—112no—
337#3237—112no—
338#3233—112no—
339#3230—112no—
340#3164—112no—
341#3137—112no—
342#3098—112no—
343#3097—112no—
344#3079—111no—
345#3078—111no—
346#3076—111no—
347C2×#477—111no—
348#2925—111no—
349C23×C11—21no—
350C23×C11C22×D412yes—
351C23×C11C22×D411yescharacteristic
352Q8×C11—22no—
353Q8×C11—22no—
354Q8×C11—22no—
355Q8×C11—21no—
356Q8×C11—21no—
357Q8×C11—42no—
358Q8×C11—82no—
359D4×C11—24no—
360D4×C11—22no—
361D4×C11—21no—
362D4×C11—21no—
363D4×C11—42no—
364D4×C11—82no—
365C2×C4×C11—22no—
366C2×C4×C11—24no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—21no—
370C2×C4×C11—22no—
371C2×C4×C11—21no—
372C2×C4×C11—21no—
373C2×C4×C11—22no—
374C2×C4×C11—41no—
375C2×C4×C11—42no—
376C2×C4×C11—42no—
377C2×C4×C11—42no—
378C2×C4×C11—42no—
379C2×C4×C11—81no—
380C2×C4×C11—81no—
381C2×C4×C11C22×D412yes—
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D412yes—
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C22×D412yes—
386C2×C4×C11C22×D411yescharacteristic
387C2×C4×C11C22×D411yescharacteristic
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C112−1+412yes—
390C2×C4×C112−1+412yes—
391C2×C4×C11C2511yescharacteristic
392C2×Dic11—22no—
393C2×Dic11—24no—
394C2×Dic11—22no—
395C2×Dic11—82no—
396C2×Dic11—84no—
397Dic22—44no—
398Dic22—42no—
399Dic22—42no—
400Dic22—82no—
401Dic22—84no—
402C11⋊C8—22no—
403C11⋊C8—22no—
404C11⋊C8—24no—
405Q82—221no—
406#557—221no—
407#554—222no—
408#554—221no—
409D4×Q8—222no—
410D4×Q8—221no—
411#544—112no—
412#544—114no—
413#544C2×D1111yescharacteristic
414#542—21no—
415#542C2×D1112yes—
416#541—21no—
417#541C2×D1112yes—
418#539—22no—
419#537C2×D1111yescharacteristic
420#536C2×D1111yescharacteristic
421#536C2×D1111yescharacteristic
422#533—21no—
423#533—111no—
424#533—112no—
425#533C2×D1112yes—
426C2×C4⋊Q8—111no—
427C2×C4⋊Q8—112no—
428#529—22no—
429#529—21no—
430#529C2×D1112yes—
431#520—112no—
432C4×#41C2×D1111yescharacteristic
433C4×#41C2×D1111yescharacteristic
434C2×C4×Q8C2×D1111yescharacteristic
435#501—114no—
436#501—114no—
437#500—114no—
438#499—114no—
439#491—114no—
440#489—114no—
441#488—114no—
442#487—114no—
443#485—114no—
444#485—114no—
445#485—114no—
446#484—114no—
447#484—114no—
448#483—114no—
449#482—114no—
450#480—114no—
451#479—112no—
452#479—114no—
453#478—112no—
454#477—112no—
455#477—112no—
456#477—114no—
457#477—111no—
458#477—112no—
459#477—112no—
460#476—111no—
461#476—112no—
462#475—111no—
463#475—112no—
464#475—112no—
465#474—111no—
466#474—112no—
467#433—114no—
468#432—112no—
469#431—112no—
470#428—112no—
471#428—112no—
472#427—112no—
473C2×#107—112no—
474#423—111no—
475C2×C4⋊C8—111no—
476#419—112no—
477#417—112no—
478#416—112no—
479C2×#103—112no—
480#408—112no—
481#405—112no—
482C22×C11—21no—
483C22×C11—21no—
484C22×C11—22no—
485C22×C11—22no—
486C22×C11—22no—
487C22×C11—41no—
488C22×C11—41no—
489C22×C11—41no—
490C22×C11#53612yes—
491C22×C11C23×D411yescharacteristic
492C4×C11—21no—
493C4×C11—21no—
494C4×C11—22no—
495C4×C11—22no—
496C4×C11—21no—
497C4×C11—22no—
498C4×C11—42no—
499C4×C11—41no—
500C4×C11—41no—
501C4×C11—42no—
502C4×C11—41no—
503C4×C11#53612yes—
504C4×C11#57812yes—
505C4×C11C2×2−1+411yescharacteristic
506C4×C11C2×2−1+411yescharacteristic
507Dic11—44no—
508Dic11—42no—
509Dic11—42no—
510C2×#41C22×D1111yescharacteristic
511C2×#41C22×D1111yescharacteristic
512C22×Q8—221no—
513C22×Q8—222no—
514C22×Q8C22×D1111yescharacteristic
515C2×M16—112no—
516C22×C8—112no—
517C4⋊Q8—21no—
518C4⋊Q8—21no—
519C4⋊Q8—112no—
520C4⋊Q8—111no—
521C4⋊Q8—112no—
522C4⋊Q8—114no—
523C4⋊Q8—111no—
524C4⋊Q8—224no—
525C4⋊Q8—222no—
526C4⋊Q8—221no—
527C4⋊Q8—222no—
528C4⋊Q8—221no—
529C4⋊Q8—222no—
530C4⋊Q8C22×D1112yes—
531C4⋊Q8C22×D1112yes—
532#126—22no—
533#126—22no—
534#126—22no—
535#126—22no—
536#125—22no—
537#125—21no—
538#125—22no—
539#125—22no—
540#125—112no—
541#125—114no—
542#125—222no—
543#125—224no—
544#125C22×D1112yes—
545#124—21no—
546#124—22no—
547#124C22×D1112yes—
548#123—22no—
549#123—22no—
550#123—22no—
551#123—22no—
552C22⋊Q8—21no—
553C22⋊Q8—22no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—22no—
557C22⋊Q8—22no—
558C22⋊Q8—221no—
559C22⋊Q8—222no—
560C22⋊Q8—221no—
561C22⋊Q8—222no—
562C22⋊Q8—224no—
563C22⋊Q8—224no—
564C22⋊Q8—224no—
565C22⋊Q8C22×D1112yes—
566C22⋊Q8C22×D1112yes—
567C22⋊Q8C22×D1112yes—
568#121—22no—
569#121—21no—
570#121C22×D1112yes—
571C4×Q8—21no—
572C4×Q8—21no—
573C4×Q8—22no—
574C4×Q8—222no—
575C4×Q8—221no—
576C4×Q8—222no—
577C4×Q8—221no—
578C4×Q8—222no—
579C4×Q8C22⋊D1111yescharacteristic
580C4×Q8C22⋊D1111yescharacteristic
581C4×Q8C22×D1112yes—
582C4×Q8C22×D1112yes—
583C4×Q8C22×D1111yescharacteristic
584C4×Q8C22×D1111yescharacteristic
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—22no—
588C4×D4—224no—
589C4×D4—222no—
590C4×D4C22⋊D1111yescharacteristic
591C4×D4C22⋊D1112yes—
592C4×D4C22⋊D1112yes—
593C4×D4C22⋊D1111yescharacteristic
594C4×D4C22×D1111yescharacteristic
595C4×D4C22×D1111yescharacteristic
596#117—22no—
597#117—21no—
598#117—22no—
599#117—112no—
600#117—114no—
601#117C22×D1111yescharacteristic
602#117C22×D1111yescharacteristic
603#117C22×D1112yes—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—112no—
606C2×C4⋊C4—114no—
607C2×C4⋊C4—221no—
608C2×C4⋊C4—222no—
609C2×C4⋊C4C22×D1111yescharacteristic
610C2×C42—21no—
611C2×C42—21no—
612C2×C42C22×D1111yescharacteristic
613C2×C42C22×D1112yes—
614#107—114no—
615#107—114no—
616#107—112no—
617#107—112no—
618#107—114no—
619#107—114no—
620#106—112no—
621#106—112no—
622#106—114no—
623#106—114no—
624C4⋊C8—111no—
625C4⋊C8—111no—
626C4⋊C8—112no—
627C4⋊C8—112no—
628C4⋊C8—112no—
629#103—114no—
630#103—114no—
631#103—112no—
632#103—112no—
633#103—114no—
634#103—114no—
635#103—114no—
636#102—112no—
637#102—112no—
638#102—114no—
639C22⋊C8—114no—
640C22⋊C8—114no—
641#97—114no—
642C4×C8—114no—
643C2×C11—22no—
644C2×C11—42no—
645C2×C11—81no—
646C2×C11C2×#53611yescharacteristic
647C2×C11C2×#57811yescharacteristic
648C2×C11#358511yescharacteristic
649#41—22no—
650#41—22no—
651#41—22no—
652#41—22no—
653C2×Q8—21no—
654C2×Q8—22no—
655C2×Q8—22no—
656C2×Q8—22no—
657C2×Q8—221no—
658C2×Q8—221no—
659C2×Q8—222no—
660C2×Q8—222no—
661C2×Q8—224no—
662C2×Q8—882no—
663C2×Q8—884no—
664C2×Q8C2×C22⋊D1111yescharacteristic
665C2×Q8C23×D1112yes—
666C2×Q8C23×D1111yescharacteristic
667C2×D4—21no—
668C2×D4—22no—
669C2×D4C2×C22⋊D1112yes—
670C2×D4C2×C22⋊D1111yescharacteristic
671C2×D4C23×D1111yescharacteristic
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—224no—
678C22×C4—222no—
679C22×C4C2×C22⋊D1111yescharacteristic
680C22×C4C2×C22⋊D1112yes—
681C22×C4C2×C22⋊D1111yescharacteristic
682C22×C4C2×C22⋊D1112yes—
683C22×C4C23×D1112yes—
684C22×C4C23×D1111yescharacteristic
685M16—224no—
686C2×C8—112no—
687C2×C8—114no—
688C2×C8—112no—
689C2×C8—224no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—22no—
703C4⋊C4—112no—
704C4⋊C4—112no—
705C4⋊C4—114no—
706C4⋊C4—224no—
707C4⋊C4—222no—
708C4⋊C4—222no—
709C4⋊C4—221no—
710C4⋊C4—222no—
711C4⋊C4—224no—
712C4⋊C4—221no—
713C4⋊C4—222no—
714C4⋊C4—224no—
715C4⋊C4—222no—
716C4⋊C4—224no—
717C4⋊C4C2×C22⋊D1111yescharacteristic
718C4⋊C4C2×C22⋊D1112yes—
719C4⋊C4C2×C22⋊D1111yescharacteristic
720C4⋊C4C2×C22⋊D1112yes—
721C4⋊C4C23×D1111yescharacteristic
722C4⋊C4C23×D1112yes—
723C4⋊C4C23×D1111yescharacteristic
724C22⋊C4—22no—
725C22⋊C4—22no—
726C22⋊C4—21no—
727C22⋊C4—22no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—224no—
734C22⋊C4—222no—
735C22⋊C4C2×C22⋊D1112yes—
736C22⋊C4C2×C22⋊D1112yes—
737C22⋊C4C2×C22⋊D1112yes—
738C42—22no—
739C42—21no—
740C42—21no—
741C42—21no—
742C42—22no—
743C42—224no—
744C42—222no—
745C42C2×C22⋊D1111yescharacteristic
746C42C2×C22⋊D1111yescharacteristic
747C42C2×C22⋊D1112yes—
748C42C2×C22⋊D1112yes—
749C42C23×D1112yes—
750C42C23×D1111yescharacteristic
751C42C23×D1111yescharacteristic
752C11#6089311yescharacteristic, complemented, Sylow
753C23—21no—
754C23C22×C22⋊D1112yes—
755C23C22×C22⋊D1111yescharacteristic
756Q8—22no—
757Q8—22no—
758Q8—22no—
759Q8—21no—
760Q8—21no—
761Q8—42no—
762Q8—82no—
763Q8—444no—
764Q8—442no—
765Q8—442no—
766Q8—882no—
767Q8—884no—
768D4—24no—
769D4—22no—
770D4—21no—
771D4—21no—
772D4—42no—
773D4—82no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—222no—
791C2×C4—224no—
792C2×C4—222no—
793C2×C4—882no—
794C2×C4—884no—
795C2×C4#6704312yes—
796C2×C4#6704312yes—
797C2×C4C22×C22⋊D1111yescharacteristic
798C2×C4C22×C22⋊D1111yescharacteristic
799C2×C4C22×C22⋊D1112yes—
800C2×C4C22×C22⋊D1111yescharacteristic
801C2×C4C22×C22⋊D1112yes—
802C2×C4C22×C22⋊D1112yes—
803C2×C4C22×C22⋊D1111yescharacteristic
804C2×C4C22×C22⋊D1111yescharacteristic
805C2×C4C24×D1111yescharacteristic
806C8—222no—
807C8—222no—
808C8—224no—
809C22—21no—
810C22—21no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22#1062335612yes—
818C22C23×C22⋊D1111yescharacteristic
819C4—21no—
820C4—21no—
821C4—22no—
822C4—22no—
823C4—21no—
824C4—22no—
825C4—42no—
826C4—41no—
827C4—41no—
828C4—42no—
829C4—41no—
830C4—444no—
831C4—442no—
832C4—442no—
833C4#1062335612yes—
834C4#1062336912yes—
835C4C2×#6704311yescharacteristic
836C4C2×#6704311yescharacteristic
837C2—22no—
838C2—42no—
839C2—81no—
840C2C2×#1062335611yescharacteristic
841C2C2×#1062336911yescharacteristic
842C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3461C2
socleC22×C11C23×D4
prime radicalC11×#537C22
hypercenter#3461D11
hypocenterC11#60893
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3461

Complements

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

NH ≅ G/Ntype
1. #13082435C2semidirect
2. #13079893C2semidirect
3. #13079878C2semidirect
4. #13079834C2semidirect
5. #13079826C2semidirect
6. #13079791C2semidirect
7. #13079764C2semidirect
8. #13079150C2semidirect
9. #13078981C2semidirect
11. #13078579C2semidirect
12. #13078431C2semidirect
13. #13078421C2semidirect
14. #13078404C2semidirect
15. C2×#10622634C2semidirect
16. #13077282C2semidirect
752. C11#60893semidirect

Maximal subgroups

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

subgroupindex
#130824352
#130798932
#130798782
#130798342
#130798262
#130797912
#130797642
#130791502
#130789812
#130785902
#130785792
#130784312
#130784212
#130784042
C2×#106226342
#130772822
C11×#34612
#6089311