Finite Group Databasebeta

← #15626512

Subgroups — #15626512

Order 2816.

1736 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082435C211yesmaximal, characteristic, complemented
2#13079908C214yesmaximal, complemented
3#13079863C214yesmaximal, complemented
4#13079834C212yesmaximal, complemented
5#13079810C212yesmaximal, complemented
6#13079791C212yesmaximal, complemented
7#13079741C212yesmaximal, complemented
8#13079142C212yesmaximal, complemented
9#13078970C212yesmaximal, complemented
10#13078601C212yesmaximal, complemented
11#13078568C212yesmaximal, complemented
12#13078431C211yesmaximal, characteristic, complemented
13#13078413C211yesmaximal, characteristic, complemented
14#13078404C211yesmaximal, characteristic, complemented
15C2×#10622621C211yesmaximal, characteristic, complemented
16#13077282C211yesmaximal, characteristic, complemented
17C11×#3460C211yesmaximal, characteristic
18C11×#544C2211yescharacteristic
19C11×#542—21no—
20C11×#542C2212yes—
21C11×#540—21no—
22C11×#540C2212yes—
23C11×#538—22no—
24C11×#537C2211yescharacteristic
25C11×#535C2211yescharacteristic
26C11×#535C2211yescharacteristic
27C11×#532—21no—
28C11×#532C2212yes—
29C11×#529—21no—
30C11×#529C2212yes—
31C11×#525—22no—
32C4×C11×#41C2211yescharacteristic
33C4×C11×#41C2211yescharacteristic
34C2×C4×D4×C11C2211yescharacteristic
35#10623358C2212yes—
36#10623101—21no—
37Q8×Dic22—21no—
38#10623074—21no—
39#10623074—22no—
40D4×Dic22—21no—
41D4×Dic22—22no—
42#10623050C2212yes—
43#10623050C2214yescomplemented
44#10623001C2211yescharacteristic
45#10623001C2212yescomplemented
46C2×#66922C2211yescharacteristic
47C2×#66922C2212yescomplemented
48#10622847C2212yes—
49#10622846C2212yes—
50#10622845C2212yes—
51#10622828C2212yes—
52C2×#66896C2212yes—
53#10622693C2214yescomplemented
54#10622692C2214yescomplemented
55#10622684C2214yes—
56#10622683C2214yes—
57#10622678C2214yescomplemented
58#10622677C2214yescomplemented
59#10622669C2214yes—
60#10622668C2214yes—
61#10622658C2214yescomplemented
62#10622656C2214yescomplemented
63#10622648C2214yes—
64#10622648C2214yes—
65#10622648C2214yescomplemented
66#10622647C2214yes—
67#10622647C2214yescomplemented
68#10622646C2214yes—
69#10622635C2212yescomplemented
70#10622634C2211yescharacteristic, complemented
71#10622634C2212yescomplemented
72#10622633C2212yescomplemented
73#10622633C2211yescharacteristic, complemented
74#10622622C2214yes—
75#10622622C2212yescomplemented
76#10622621C2212yes—
77#10622621C2212yes—
78#10622621C2214yes—
79#10622621C2212yes—
80#10622621C2212yescomplemented
81#10622621C2211yescharacteristic, complemented
82#10622620C2212yes—
83#10622620C2211yescharacteristic, complemented
84#10622620C2212yescomplemented
85#10622613C2214yescomplemented
86#10622611C2212yes—
87#10622610C2212yes—
88#10622608C2212yes—
89#10622577C2212yes—
90C2×#66872C2212yes—
91#10622539C2212yescomplemented
92#10622538C2212yescomplemented
93#10622537C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2211yescharacteristic
95C2×C11×#41—22no—
96C2×C11×#41C2311yescharacteristic
97C2×C11×#41C2311yescharacteristic
98C22×D4×C11C2311yescharacteristic
99C23×C4×C11—21no—
100C22×Dic22—21no—
101C22×Dic22—22no—
102C11×C4⋊Q8—21no—
103C11×C4⋊Q8C2312yes—
104C11×#127—21no—
105C11×#127C2312yes—
106C11×#126—22no—
107C11×#126—22no—
108C11×#125—21no—
109C11×#125C2312yes—
110C11×#124—21no—
111C11×#124—22no—
112C11×#124—22no—
113C11×#124C2312yes—
114C11×#123—22no—
115C11×#123—22no—
116C11×#123—22no—
117C11×#123—22no—
118C11×C22⋊Q8—21no—
119C11×C22⋊Q8—22no—
120C11×C22⋊Q8—22no—
121C11×C22⋊Q8C2312yes—
122C11×#121—22no—
123C11×#121—21no—
124C11×#121—22no—
125C11×#121—21no—
126C11×#121—21no—
127C11×#121—22no—
128C11×#121—22no—
129C11×#121C2312yes—
130C11×#121C2312yes—
131C11×#121C2312yes—
132C11×#120—22no—
133C11×#120—22no—
134C4×Q8×C11D411yescharacteristic
135C4×Q8×C11D411yescharacteristic
136C4×Q8×C11C2311yescharacteristic
137C4×Q8×C11C2311yescharacteristic
138C4×D4×C11—21no—
139C4×D4×C11—21no—
140C4×D4×C11—22no—
141C4×D4×C11—21no—
142C4×D4×C11—21no—
143C4×D4×C11—22no—
144C4×D4×C11D412yes—
145C4×D4×C11D411yescharacteristic
146C4×D4×C11D412yes—
147C4×D4×C11D411yescharacteristic
148C4×D4×C11C2312yes—
149C4×D4×C11C2312yes—
150C4×D4×C11C2311yescharacteristic
151C4×D4×C11C2311yescharacteristic
152C11×#117—21no—
153C11×#117—22no—
154C11×#117C2311yescharacteristic
155C11×#117C2311yescharacteristic
156C11×#117C2312yes—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C22⋊C4—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—21no—
173#66977—22no—
174#66977—22no—
175C2×#4318C2312yes—
176C22×C11⋊C8C2312yes—
177#66943—22no—
178#66943—24no—
179#66941—22no—
180#66941—24no—
181#66931—24no—
182#66931—24no—
183#66931—24no—
184#66923C2312yes—
185#66923C2314yes—
186#66922—21no—
187#66922—21no—
188#66922—22no—
189#66922—22no—
190#66922C2312yes—
191#66922C2312yes—
192#66922C2311yescharacteristic
193#66922C2314yes—
194#66922C2311yescharacteristic
195C4×Dic22—21no—
196C4×Dic22—21no—
197C4×Dic22—22no—
198C4×Dic22—22no—
199#66899C2314yes—
200#66899C2312yes—
201#66899C2312yes—
202#66896C2314yes—
203#66896C2314yes—
204#66896C2314yes—
205#66896C2314yes—
206#66896C2314yes—
207#66896C2312yes—
208#66896C2312yes—
209C22⋊(C11⋊C8)C2314yes—
210C22⋊(C11⋊C8)C2314yes—
211#66872C2314yes—
212#66872C2314yes—
213#66872C2314yes—
214#66872C2314yes—
215#66872C2312yes—
216#66872C2312yes—
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#60892—111nomaximal, Sylow
229C24×C11—21no—
230C11×#41—22no—
231C11×#41—22no—
232C11×#41—22no—
233C11×#41—22no—
234C11×#41—84no—
235C2×Q8×C11—22no—
236C2×Q8×C11C2×D411yescharacteristic
237C2×Q8×C11C2411yescharacteristic
238C2×D4×C11—21no—
239C2×D4×C11—22no—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—21no—
243C2×D4×C11—22no—
244C2×D4×C11—22no—
245C2×D4×C11—22no—
246C2×D4×C11—22no—
247C2×D4×C11C2×D412yes—
248C2×D4×C11C2×D411yescharacteristic
249C2×D4×C11C2412yes—
250C2×D4×C11C2411yescharacteristic
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—22no—
255C22×C4×C11—21no—
256C22×C4×C11—22no—
257C22×C4×C11—82no—
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2×D412yes—
260C22×C4×C11C2×D411yescharacteristic
261C22×C4×C11C2×D412yes—
262C22×C4×C11C2412yes—
263C22×C4×C11C2411yescharacteristic
264C22×Dic11—24no—
265C22×Dic11—22no—
266C2×Dic22—21no—
267C2×Dic22—21no—
268C2×Dic22—22no—
269C2×Dic22—22no—
270C2×Dic22—24no—
271C2×Dic22—82no—
272C2×Dic22—84no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4—22no—
279C11×C4⋊C4—22no—
280C11×C4⋊C4C2×D411yescharacteristic
281C11×C4⋊C4C2×D412yes—
282C11×C4⋊C4C2×D411yescharacteristic
283C11×C4⋊C4C2×D412yes—
284C11×C4⋊C4C2411yescharacteristic
285C11×C4⋊C4C2412yes—
286C11×C4⋊C4C2411yescharacteristic
287C11×C22⋊C4—21no—
288C11×C22⋊C4—22no—
289C11×C22⋊C4—22no—
290C11×C22⋊C4—22no—
291C11×C22⋊C4—21no—
292C11×C22⋊C4—21no—
293C11×C22⋊C4—22no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—22no—
296C11×C22⋊C4—22no—
297C11×C22⋊C4—22no—
298C11×C22⋊C4C2×D412yes—
299C11×C22⋊C4C2×D412yes—
300C11×C22⋊C4C2×D412yes—
301C42×C11—21no—
302C42×C11—21no—
303C42×C11—21no—
304C42×C11C2×D411yescharacteristic
305C42×C11C2×D412yes—
306C42×C11C2×D411yescharacteristic
307C42×C11C2×D412yes—
308C42×C11C2412yes—
309C42×C11C2411yescharacteristic
310C42×C11C2411yescharacteristic
311C22⋊Dic11—24no—
312C22⋊Dic11—22no—
313C4⋊Dic11—21no—
314C4⋊Dic11—21no—
315C4⋊Dic11—22no—
316C4⋊Dic11—24no—
317C4⋊Dic11—22no—
318C4⋊Dic11—22no—
319C4⋊Dic11—24no—
320C4⋊Dic11C2412yes—
321C4⋊Dic11C2414yes—
322C4⋊Dic11C2412yes—
323Dic11⋊C4—22no—
324Dic11⋊C4—24no—
325Dic11⋊C4—22no—
326Dic11⋊C4—24no—
327C4×Dic11—24no—
328C4×Dic11—22no—
329#4318—24no—
330C2×C11⋊C8—24no—
331C2×C11⋊C8C2412yes—
332C2×C11⋊C8C2414yes—
333C2×C11⋊C8C2412yes—
334#3503—111no—
335#3460D1111yescharacteristic
336#3244—114no—
337#3241—114no—
338#3238—112no—
339#3235—112no—
340#3233—112no—
341#3227—112no—
342#3163—112no—
343#3136—112no—
344#3099—112no—
345#3096—112no—
346#3079—111no—
347#3077—111no—
348#3076—111no—
349C2×#476—111no—
350#2925—111no—
351C23×C11—22no—
352C23×C11—21no—
353C23×C11—42no—
354C23×C11—81no—
355C23×C11—81no—
356C23×C11C22×D412yes—
357C23×C11C22×D411yescharacteristic
358Q8×C11—22no—
359Q8×C11—21no—
360Q8×C11—21no—
361Q8×C11—82no—
362D4×C11—24no—
363D4×C11—22no—
364D4×C11—22no—
365D4×C11—22no—
366D4×C11—21no—
367D4×C11—21no—
368D4×C11—42no—
369D4×C11—42no—
370D4×C11—82no—
371D4×C11—82no—
372D4×C11—82no—
373D4×C11—82no—
374D4×C11—82no—
375C2×C4×C11—22no—
376C2×C4×C11—24no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—22no—
383C2×C4×C11—41no—
384C2×C4×C11—42no—
385C2×C4×C11—42no—
386C2×C4×C11—44no—
387C2×C4×C11—42no—
388C2×C4×C11—81no—
389C2×C4×C11—82no—
390C2×C4×C11—81no—
391C2×C4×C11C22×D412yes—
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C22×D412yes—
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D412yes—
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C112−1+412yes—
400C2×C4×C112−1+412yes—
401C2×C4×C11C2511yescharacteristic
402C2×Dic11—22no—
403C2×Dic11—24no—
404C2×Dic11—22no—
405C2×Dic11—82no—
406C2×Dic11—84no—
407Dic22—42no—
408Dic22—44no—
409Dic22—42no—
410Dic22—82no—
411Dic22—84no—
412C11⋊C8—22no—
413C11⋊C8—22no—
414C11⋊C8—24no—
415Q82—221no—
416#557—221no—
417#554—222no—
418#554—221no—
419D4×Q8—222no—
420D4×Q8—221no—
421#544—112no—
422#544—114no—
423#544C2×D1111yescharacteristic
424#542—21no—
425#542C2×D1112yes—
426#540—21no—
427#540C2×D1112yes—
428#538—22no—
429#537C2×D1111yescharacteristic
430#535C2×D1111yescharacteristic
431#535C2×D1111yescharacteristic
432#533—111no—
433#533—112no—
434#532—21no—
435#532C2×D1112yes—
436C2×C4⋊Q8—111no—
437C2×C4⋊Q8—112no—
438#529—21no—
439#529C2×D1112yes—
440#525—22no—
441#520—112no—
442C4×#41C2×D1111yescharacteristic
443C4×#41C2×D1111yescharacteristic
444C2×C4×D4C2×D1111yescharacteristic
445#501—114no—
446#501—114no—
447#499—114no—
448#498—114no—
449#490—114no—
450#489—114no—
451#488—114no—
452#486—114no—
453#485—114no—
454#483—114no—
455#482—114no—
456#482—114no—
457#482—114no—
458#481—114no—
459#481—114no—
460#480—114no—
461#479—112no—
462#478—112no—
463#478—114no—
464#477—111no—
465#477—112no—
466#476—111no—
467#476—112no—
468#476—112no—
469#476—112no—
470#476—112no—
471#476—114no—
472#475—111no—
473#475—112no—
474#474—111no—
475#474—112no—
476#474—112no—
477#433—114no—
478#432—112no—
479#431—112no—
480#428—112no—
481#428—112no—
482#427—112no—
483C2×#106—112no—
484#423—111no—
485C2×C4⋊C8—111no—
486#418—112no—
487#417—112no—
488#416—112no—
489C2×#102—112no—
490#408—112no—
491#405—112no—
492C22×C11—21no—
493C22×C11—21no—
494C22×C11—22no—
495C22×C11—22no—
496C22×C11—22no—
497C22×C11—41no—
498C22×C11—42no—
499C22×C11—41no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—41no—
503C22×C11—84no—
504C22×C11#53612yes—
505C22×C11C23×D411yescharacteristic
506C4×C11—21no—
507C4×C11—21no—
508C4×C11—22no—
509C4×C11—22no—
510C4×C11—21no—
511C4×C11—22no—
512C4×C11—41no—
513C4×C11—41no—
514C4×C11—42no—
515C4×C11—41no—
516C4×C11#53612yes—
517C4×C11#57712yes—
518C4×C11C2×2−1+411yescharacteristic
519C4×C11C2×2−1+411yescharacteristic
520Dic11—44no—
521Dic11—42no—
522Dic11—42no—
523C2×#41—22no—
524C2×#41C22×D1111yescharacteristic
525C2×#41C22×D1111yescharacteristic
526C22×Q8—221no—
527C22×Q8—222no—
528C22×D4C22×D1111yescharacteristic
529C23×C4—21no—
530C2×M16—112no—
531C22×C8—112no—
532C4⋊Q8—21no—
533C4⋊Q8—112no—
534C4⋊Q8—111no—
535C4⋊Q8—112no—
536C4⋊Q8—114no—
537C4⋊Q8—111no—
538C4⋊Q8—222no—
539C4⋊Q8—224no—
540C4⋊Q8—221no—
541C4⋊Q8—222no—
542C4⋊Q8—221no—
543C4⋊Q8—222no—
544C4⋊Q8C22×D1112yes—
545#127—21no—
546#127C22×D1112yes—
547#126—22no—
548#126—22no—
549#125—21no—
550#125—112no—
551#125—114no—
552#125—222no—
553#125—224no—
554#125C22×D1112yes—
555#124—21no—
556#124—22no—
557#124—22no—
558#124C22×D1112yes—
559#123—22no—
560#123—22no—
561#123—22no—
562#123—22no—
563C22⋊Q8—21no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566C22⋊Q8—221no—
567C22⋊Q8—222no—
568C22⋊Q8—221no—
569C22⋊Q8—222no—
570C22⋊Q8—224no—
571C22⋊Q8—224no—
572C22⋊Q8—224no—
573C22⋊Q8C22×D1112yes—
574#121—22no—
575#121—21no—
576#121—22no—
577#121—21no—
578#121—21no—
579#121—22no—
580#121—22no—
581#121C22×D1112yes—
582#121C22×D1112yes—
583#121C22×D1112yes—
584#120—22no—
585#120—22no—
586C4×Q8—222no—
587C4×Q8—221no—
588C4×Q8—222no—
589C4×Q8—221no—
590C4×Q8—222no—
591C4×Q8C22⋊D1111yescharacteristic
592C4×Q8C22⋊D1111yescharacteristic
593C4×Q8C22×D1111yescharacteristic
594C4×Q8C22×D1111yescharacteristic
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—22no—
598C4×D4—21no—
599C4×D4—21no—
600C4×D4—22no—
601C4×D4—224no—
602C4×D4—222no—
603C4×D4C22⋊D1112yes—
604C4×D4C22⋊D1111yescharacteristic
605C4×D4C22⋊D1112yes—
606C4×D4C22⋊D1111yescharacteristic
607C4×D4C22×D1112yes—
608C4×D4C22×D1112yes—
609C4×D4C22×D1111yescharacteristic
610C4×D4C22×D1111yescharacteristic
611#117—21no—
612#117—22no—
613#117—112no—
614#117—114no—
615#117C22×D1111yescharacteristic
616#117C22×D1111yescharacteristic
617#117C22×D1112yes—
618C2×C4⋊C4—112no—
619C2×C4⋊C4—114no—
620C2×C4⋊C4—221no—
621C2×C4⋊C4—222no—
622C2×C4⋊C4C22×D1111yescharacteristic
623C2×C22⋊C4—21no—
624C2×C42—21no—
625C2×C42C22×D1111yescharacteristic
626C2×C42C22×D1112yes—
627#107—112no—
628#107—112no—
629#107—114no—
630#107—114no—
631#106—114no—
632#106—114no—
633#106—112no—
634#106—112no—
635#106—114no—
636#106—114no—
637C4⋊C8—111no—
638C4⋊C8—111no—
639C4⋊C8—112no—
640C4⋊C8—112no—
641C4⋊C8—112no—
642#103—112no—
643#103—112no—
644#103—114no—
645#102—114no—
646#102—114no—
647#102—112no—
648#102—112no—
649#102—114no—
650#102—114no—
651#102—114no—
652C22⋊C8—114no—
653C22⋊C8—114no—
654#97—114no—
655C4×C8—114no—
656C2×C11—22no—
657C2×C11—42no—
658C2×C11—81no—
659C2×C11—82no—
660C2×C11C2×#53611yescharacteristic
661C2×C11C2×#57711yescharacteristic
662C2×C11#358511yescharacteristic
663C24—21no—
664#41—22no—
665#41—22no—
666#41—22no—
667#41—22no—
668#41—84no—
669C2×Q8—22no—
670C2×Q8—221no—
671C2×Q8—221no—
672C2×Q8—222no—
673C2×Q8—222no—
674C2×Q8—224no—
675C2×Q8—882no—
676C2×Q8—884no—
677C2×Q8C2×C22⋊D1111yescharacteristic
678C2×Q8C23×D1111yescharacteristic
679C2×D4—21no—
680C2×D4—22no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—22no—
685C2×D4—21no—
686C2×D4—22no—
687C2×D4—22no—
688C2×D4C2×C22⋊D1112yes—
689C2×D4C2×C22⋊D1111yescharacteristic
690C2×D4C23×D1112yes—
691C2×D4C23×D1111yescharacteristic
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—82no—
699C22×C4—224no—
700C22×C4—222no—
701C22×C4C2×C22⋊D1111yescharacteristic
702C22×C4C2×C22⋊D1112yes—
703C22×C4C2×C22⋊D1111yescharacteristic
704C22×C4C2×C22⋊D1112yes—
705C22×C4C23×D1112yes—
706C22×C4C23×D1111yescharacteristic
707M16—224no—
708C2×C8—112no—
709C2×C8—114no—
710C2×C8—112no—
711C2×C8—224no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—22no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—114no—
720C4⋊C4—112no—
721C4⋊C4—112no—
722C4⋊C4—224no—
723C4⋊C4—222no—
724C4⋊C4—222no—
725C4⋊C4—221no—
726C4⋊C4—222no—
727C4⋊C4—224no—
728C4⋊C4—221no—
729C4⋊C4—222no—
730C4⋊C4—224no—
731C4⋊C4—222no—
732C4⋊C4—224no—
733C4⋊C4C2×C22⋊D1111yescharacteristic
734C4⋊C4C2×C22⋊D1111yescharacteristic
735C4⋊C4C2×C22⋊D1112yes—
736C4⋊C4C2×C22⋊D1112yes—
737C4⋊C4C23×D1112yes—
738C4⋊C4C23×D1111yescharacteristic
739C4⋊C4C23×D1111yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—22no—
747C22⋊C4—22no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—22no—
751C22⋊C4—224no—
752C22⋊C4—222no—
753C22⋊C4C2×C22⋊D1112yes—
754C22⋊C4C2×C22⋊D1112yes—
755C22⋊C4C2×C22⋊D1112yes—
756C42—21no—
757C42—21no—
758C42—21no—
759C42—224no—
760C42—222no—
761C42C2×C22⋊D1111yescharacteristic
762C42C2×C22⋊D1112yes—
763C42C2×C22⋊D1111yescharacteristic
764C42C2×C22⋊D1112yes—
765C42C23×D1112yes—
766C42C23×D1111yescharacteristic
767C42C23×D1111yescharacteristic
768C11#6089211yescharacteristic, complemented, Sylow
769C23—22no—
770C23—21no—
771C23—42no—
772C23—81no—
773C23—81no—
774C23C22×C22⋊D1112yes—
775C23C22×C22⋊D1111yescharacteristic
776Q8—22no—
777Q8—21no—
778Q8—21no—
779Q8—82no—
780Q8—444no—
781Q8—442no—
782Q8—442no—
783Q8—882no—
784Q8—884no—
785D4—24no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—21no—
790D4—21no—
791D4—42no—
792D4—42no—
793D4—82no—
794D4—82no—
795D4—82no—
796D4—82no—
797D4—82no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—44no—
810C2×C4—42no—
811C2×C4—81no—
812C2×C4—82no—
813C2×C4—81no—
814C2×C4—222no—
815C2×C4—224no—
816C2×C4—222no—
817C2×C4—882no—
818C2×C4—884no—
819C2×C4#6704312yes—
820C2×C4#6704312yes—
821C2×C4C22×C22⋊D1111yescharacteristic
822C2×C4C22×C22⋊D1112yes—
823C2×C4C22×C22⋊D1111yescharacteristic
824C2×C4C22×C22⋊D1112yes—
825C2×C4C22×C22⋊D1111yescharacteristic
826C2×C4C22×C22⋊D1112yes—
827C2×C4C22×C22⋊D1111yescharacteristic
828C2×C4C22×C22⋊D1111yescharacteristic
829C2×C4C24×D1111yescharacteristic
830C8—222no—
831C8—222no—
832C8—224no—
833C22—21no—
834C22—21no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—42no—
842C22—42no—
843C22—41no—
844C22—84no—
845C22#1062335612yes—
846C22C23×C22⋊D1111yescharacteristic
847C4—21no—
848C4—21no—
849C4—22no—
850C4—22no—
851C4—21no—
852C4—22no—
853C4—41no—
854C4—41no—
855C4—42no—
856C4—41no—
857C4—444no—
858C4—442no—
859C4—442no—
860C4#1062335612yes—
861C4#1062336712yes—
862C4C2×#6704311yescharacteristic
863C4C2×#6704311yescharacteristic
864C2—22no—
865C2—42no—
866C2—82no—
867C2—81no—
868C2C2×#1062335611yescharacteristic
869C2C2×#1062336711yescharacteristic
870C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC11×#3460C2
socleC22×C11C23×D4
hypercenter#3460D11
hypocenterC11#60892
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3460

Complements

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

NH ≅ G/Ntype
1. #13082435C2semidirect
2. #13079908C2semidirect
3. #13079863C2semidirect
4. #13079834C2semidirect
5. #13079810C2semidirect
6. #13079791C2semidirect
7. #13079741C2semidirect
8. #13079142C2semidirect
9. #13078970C2semidirect
10. #13078601C2semidirect
11. #13078568C2semidirect
12. #13078431C2semidirect
13. #13078413C2semidirect
14. #13078404C2semidirect
15. C2×#10622621C2semidirect
16. #13077282C2semidirect
43. #10623050C22semidirect
45. #10623001C22semidirect
47. C2×#66922C22semidirect
53. #10622693C22semidirect
54. #10622692C22semidirect
57. #10622678C22semidirect
58. #10622677C22semidirect
61. #10622658C22semidirect
62. #10622656C22semidirect
65. #10622648C22semidirect
67. #10622647C22semidirect
69. #10622635C22semidirect
70. #10622634C22semidirect
71. #10622634C22semidirect
72. #10622633C22semidirect
73. #10622633C22semidirect
75. #10622622C22semidirect
80. #10622621C22semidirect
81. #10622621C22semidirect
83. #10622620C22semidirect
84. #10622620C22semidirect
85. #10622613C22semidirect
91. #10622539C22semidirect
92. #10622538C22semidirect
768. C11#60892semidirect

Maximal subgroups

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

subgroupindex
#130824352
#130799082
#130798632
#130798342
#130798102
#130797912
#130797412
#130791422
#130789702
#130786012
#130785682
#130784312
#130784132
#130784042
C2×#106226212
#130772822
C11×#34602
#6089211