Finite Group Databasebeta

← #15634602

Subgroups — #15634602

Order 2816.

1726 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082421C211yesmaximal, characteristic, complemented
2#13081579C214yesmaximal, complemented
3#13081544C212yesmaximal, complemented
4#13081537C214yesmaximal, complemented
5#13081526C212yesmaximal, complemented
6Q8×#4326C212yesmaximal, complemented
7#13081491C212yesmaximal, complemented
8#13079158C211yesmaximal, characteristic, complemented
9#13079150C212yesmaximal, complemented
10#13078467C212yesmaximal
11#13078452C212yesmaximal, complemented
12#13078404C211yesmaximal, characteristic
13C2×#10622704C211yesmaximal, characteristic, complemented
14#13077565C211yesmaximal, characteristic, complemented
15#13077455C212yesmaximal
16C4×#67004C211yesmaximal, characteristic
17C11×#3503C211yesmaximal, characteristic
18Q82×C11C2212yes—
19C11×#557C2212yes—
20C11×#554—22no—
21C11×#554C2212yes—
22D4×Q8×C11—22no—
23D4×Q8×C11C2212yes—
24C11×#544—22no—
25C11×#544C2212yes—
26C11×#533—21no—
27C11×#533C2211yescharacteristic
28C2×C11×C4⋊Q8—21no—
29C2×C11×C4⋊Q8C2211yescharacteristic
30C11×#520C2212yes—
31C4×C11×#41C2211yescharacteristic
32C2×#67004C2211yescharacteristic
33#10623253—21no—
34#10623252—21no—
35#10623216—22no—
36#10623154—22no—
37#10623153—22no—
38#10623098C2212yes—
39#10623098C2214yes—
40Q8×Dic22C2212yes—
41#10623050C2212yes—
42#10623047C2212yes—
43#10623001C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45#10622846C2212yes—
46#10622845C2211yescharacteristic
47#10622707C2214yes—
48#10622704C2212yes—
49#10622704C2212yes—
50#10622704C2214yes—
51#10622704C2214yes—
52#10622693C2214yes—
53#10622693C2214yes—
54#10622692C2212yes—
55#10622691C2214yes—
56#10622691C2212yes—
57#10622678C2214yes—
58#10622677C2214yes—
59#10622676C2214yes—
60#10622676C2214yes—
61#10622643C2212yes—
62#10622643C2214yes—
63C4×#4326C2212yes—
64C4×#4326C2214yes—
65#10622637C2212yes—
66#10622637C2214yes—
67Q8×C11⋊C8C2212yes—
68#10622635C2212yes—
69#10622635C2214yes—
70#10622634C2211yescharacteristic
71#10622634C2214yes—
72#10622633C2211yescharacteristic
73#10622631C2214yes—
74#10622631C2212yes—
75C4×#4324C2212yes—
76C4×#4324C2214yes—
77#10622622C2212yes—
78#10622622C2214yes—
79#10622621C2211yescharacteristic
80#10622620C2211yescharacteristic
81#10622620C2214yes—
82#10622617C2211yescharacteristic
83#10622612C2212yes—
84#10622611C2212yes—
85#10622610C2212yes—
86#10622608C2211yescharacteristic
87C2×#66874C2212yes—
88#10622577C2212yes—
89#10622577C2212yes—
90C2×#66871C2212yes—
91C2×C4⋊(C11⋊C8)C2211yescharacteristic
92C4×#4318C2211yescharacteristic
93C2×C11×#41C2311yescharacteristic
94C22×Q8×C11—22no—
95C22×Q8×C11—21no—
96C22×Dic22C2311yescharacteristic
97C11×C4⋊Q8—22no—
98C11×C4⋊Q8—22no—
99C11×C4⋊Q8—22no—
100C11×C4⋊Q8—24no—
101C11×C4⋊Q8—21no—
102C11×C4⋊Q8—21no—
103C11×C4⋊Q8D411yescharacteristic
104C11×C4⋊Q8D411yescharacteristic
105C11×C4⋊Q8C2312yes—
106C11×C4⋊Q8C2312yes—
107C11×C4⋊Q8C2314yes—
108C11×#125—22no—
109C11×#125—24no—
110C11×#125D412yes—
111C11×#125C2314yes—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—24no—
115C11×C22⋊Q8—24no—
116C11×C22⋊Q8—24no—
117C11×C22⋊Q8D412yes—
118C11×C22⋊Q8D412yes—
119C4×Q8×C11—22no—
120C4×Q8×C11—22no—
121C4×Q8×C11C2311yescharacteristic
122C4×Q8×C11C2311yescharacteristic
123C4×Q8×C11C2314yes—
124C4×Q8×C11C2312yes—
125C4×Q8×C11C2312yes—
126C4×D4×C11—21no—
127C4×D4×C11—21no—
128C4×D4×C11—24no—
129C4×D4×C11C2311yescharacteristic
130C4×D4×C11C2311yescharacteristic
131C4×D4×C11C2314yes—
132C11×#117—22no—
133C11×#117—21no—
134C11×#117C2311yescharacteristic
135C11×#117C2312yes—
136C2×C11×C4⋊C4—21no—
137C2×C11×C4⋊C4—22no—
138C2×C11×C4⋊C4—22no—
139C2×C11×C4⋊C4C2312yes—
140C2×C42×C11—21no—
141C2×C42×C11C2311yescharacteristic
142#67004Q818yescomplemented
143Q8×Dic11—22no—
144#66997—22no—
145#66997—24no—
146C2×#4326C2312yes—
147C2×#4324C2312yes—
148#66979C2312yes—
149C2×C4⋊Dic11C2311yescharacteristic
150#66977—21no—
151#66977—21no—
152C2×Dic11⋊C4—21no—
153C2×C4×Dic11—21no—
154C2×#4318C2311yescharacteristic
155C2×#4318C2311yescharacteristic
156C22×C11⋊C8C2312yes—
157#66943—22no—
158#66942—24no—
159#66942—24no—
160#66942—24no—
161#66941—22no—
162#66941—22no—
163#66941—24no—
164#66940—22no—
165#66940—22no—
166#66940—22no—
167#66940—24no—
168#66931—24no—
169#66930—24no—
170#66923C2312yes—
171#66923C2314yes—
172#66922C2311yescharacteristic
173#66922C2311yescharacteristic
174#66922C2314yes—
175C4×Dic22—21no—
176C4×Dic22—21no—
177C4×Dic22—21no—
178C4×Dic22—21no—
179C4×Dic22C2312yes—
180C4×Dic22C2312yes—
181C4×Dic22C2314yes—
182C4×Dic22C2314yes—
183#66899C2312yes—
184#66899C2312yes—
185#66899C2312yes—
186#66896C2312yes—
187#66896C2312yes—
188#66896C2312yes—
189#66874C2314yes—
190#66874C2314yes—
191#66874C2312yes—
192#66874C2312yes—
193#66872C2314yes—
194#66872C2314yes—
195#66872C2312yes—
196#66872C2312yes—
197#66872C2312yes—
198#66871C2314yes—
199#66871C2314yes—
200#66871C2314yes—
201#66871C2314yes—
202#66871C2312yes—
203#66871C2312yes—
204#66871C2312yes—
205C4⋊(C11⋊C8)C2311yescharacteristic
206C4⋊(C11⋊C8)C2311yescharacteristic
207C4⋊(C11⋊C8)C2312yes—
208C4⋊(C11⋊C8)C2314yes—
209C4⋊(C11⋊C8)C2314yes—
210#66867C2312yes—
211#66867C2314yes—
212C4×C11⋊C8C2312yes—
213C4×C11⋊C8C2314yes—
214#61384—111nomaximal, Sylow
215C11×#41—22no—
216C11×#41C2×Q814yes—
217C2×Q8×C11—22no—
218C2×Q8×C11—24no—
219C2×Q8×C11—22no—
220C2×Q8×C11—82no—
221C2×Q8×C11—84no—
222C2×Q8×C11C2×D412yes—
223C2×Q8×C11C2×D412yes—
224C2×Q8×C11C2411yescharacteristic
225C2×D4×C11—21no—
226C2×D4×C11C2411yescharacteristic
227C22×C4×C11—21no—
228C22×C4×C11—22no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—24no—
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2411yescharacteristic
235C22×Dic11—21no—
236C22×Dic11—21no—
237C2×Dic22—21no—
238C2×Dic22—21no—
239C2×Dic22—21no—
240C2×Dic22—24no—
241C2×Dic22—22no—
242C2×Dic22C2×Q814yescomplemented
243C2×Dic22C2412yes—
244C11×C4⋊C4—22no—
245C11×C4⋊C4—22no—
246C11×C4⋊C4—24no—
247C11×C4⋊C4—22no—
248C11×C4⋊C4—24no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4C2×D412yes—
254C11×C4⋊C4C2×D412yes—
255C11×C4⋊C4C2×D414yes—
256C11×C4⋊C4C2×D412yes—
257C11×C4⋊C4C2×D414yes—
258C11×C4⋊C4C2×D412yes—
259C11×C4⋊C4C2414yes—
260C11×C4⋊C4C2411yescharacteristic
261C11×C4⋊C4C2411yescharacteristic
262C11×C22⋊C4—21no—
263C11×C22⋊C4—21no—
264C11×C22⋊C4—21no—
265C11×C22⋊C4—24no—
266C11×C22⋊C4C2×D414yes—
267C42×C11—21no—
268C42×C11—21no—
269C42×C11—21no—
270C42×C11—24no—
271C42×C11C2×D411yescharacteristic
272C42×C11C2×D411yescharacteristic
273C42×C11C2411yescharacteristic
274C42×C11C2414yes—
275C42×C11C2411yescharacteristic
276C22⋊Dic11—22no—
277#4326C2×Q818yescomplemented
278#4324C2×Q818yescomplemented
279C4⋊Dic11—21no—
280C4⋊Dic11—21no—
281C4⋊Dic11—21no—
282C4⋊Dic11—24no—
283C4⋊Dic11C2412yes—
284C4⋊Dic11C2412yes—
285C4⋊Dic11C2412yes—
286Dic11⋊C4—22no—
287Dic11⋊C4—22no—
288Dic11⋊C4—22no—
289Dic11⋊C4—22no—
290Dic11⋊C4—24no—
291Dic11⋊C4—24no—
292Dic11⋊C4—24no—
293Dic11⋊C4—24no—
294C4×Dic11—22no—
295C4×Dic11—22no—
296C4×Dic11—22no—
297C4×Dic11—24no—
298C4×Dic11—24no—
299#4318—22no—
300#4318C2×Q814yescomplemented
301C2×C11⋊C8—24no—
302C2×C11⋊C8C2412yes—
303C2×C11⋊C8C2412yes—
304C2×C11⋊C8C2412yes—
305C2×C11⋊C8C2412yes—
306#3503D1111yescharacteristic
307#3502—111no—
308#3390—114no—
309#3387—112no—
310#3386—114no—
311#3385—112no—
312Q8×Q16—112no—
313#3381—112no—
314#3165—111no—
315#3164—112no—
316#3083—112no—
317#3082—112no—
318#3076—111no—
319C2×#477—111no—
320#2962—111no—
321#2947—112no—
322C4×#137—111no—
323C23×C11—21no—
324C23×C11C22×D411yescharacteristic
325Q8×C11—24no—
326Q8×C11—21no—
327Q8×C11—42no—
328Q8×C11—44no—
329Q8×C11—82no—
330Q8×C11—84no—
331Q8×C11C22×Q812yes—
332D4×C11—24no—
333D4×C11—21no—
334D4×C11C22×Q812yes—
335C2×C4×C11—21no—
336C2×C4×C11—24no—
337C2×C4×C11—22no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—24no—
341C2×C4×C11—41no—
342C2×C4×C11—42no—
343C2×C4×C11—42no—
344C2×C4×C11—84no—
345C2×C4×C11—82no—
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C22×D414yes—
348C2×C4×C11C22×D414yes—
349C2×C4×C11C22×D411yescharacteristic
350C2×C4×C11C22×D411yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11C22×Q812yes—
354C2×C4×C112−1+412yes—
355C2×C4×C11C2511yescharacteristic
356C2×Dic11—24no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—81no—
362Dic22—24no—
363Dic22—22no—
364Dic22—42no—
365Dic22—81no—
366Dic22—84no—
367Dic22C22×Q814yes—
368C11⋊C8—22no—
369C11⋊C8—22no—
370C11⋊C8—22no—
371C11⋊C8C22×Q814yes—
372C2×#137—111no—
373Q82—112no—
374Q82—221no—
375Q82C2×D1112yes—
376#557—112no—
377#557—114no—
378#557—221no—
379#557—222no—
380#557C2×D1112yes—
381#554—22no—
382#554C2×D1112yes—
383D4×Q8—22no—
384D4×Q8C2×D1112yes—
385#544—22no—
386#544—112no—
387#544—222no—
388#544C2×D1112yes—
389#533—21no—
390#533—111no—
391#533—222no—
392#533C2×D1111yescharacteristic
393C2×C4⋊Q8—21no—
394C2×C4⋊Q8C2×D1111yescharacteristic
395#520C2×D1112yes—
396#519—112no—
397C4×#41C2×D1111yescharacteristic
398C2×C4×Q8—111no—
399#501—114no—
400#501—114no—
401#501—114no—
402#500—112no—
403#500—114no—
404#499—114no—
405#498—112no—
406#479—114no—
407#479—114no—
408#479—112no—
409#479—114no—
410#478—112no—
411#478—114no—
412#477—112no—
413#477—112no—
414#477—114no—
415#477—114no—
416#477—111no—
417#477—114no—
418#476—111no—
419#475—114no—
420#475—111no—
421#474—111no—
422#474—114no—
423#446—112no—
424#446—114no—
425C8×Q8—112no—
426#441—114no—
427#441—112no—
428#440—114no—
429#440—112no—
430C4×Q16—112no—
431C4×Q16—114no—
432C4×SD16—112no—
433C4×SD16—114no—
434#428—111no—
435#428—112no—
436#428—112no—
437#427—112no—
438C2×#107—112no—
439#424—112no—
440C2×C4⋊C8—111no—
441#419—111no—
442#417—111no—
443#416—112no—
444C2×#103—112no—
445#405—112no—
446C4×M16—111no—
447C22×C11—21no—
448C22×C11—21no—
449C22×C11—22no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11D4×Q812yes—
453C22×C11C23×D411yescharacteristic
454C4×C11—21no—
455C4×C11—21no—
456C4×C11—24no—
457C4×C11—22no—
458C4×C11—21no—
459C4×C11—24no—
460C4×C11—41no—
461C4×C11—44no—
462C4×C11—41no—
463C4×C11D4×Q812yes—
464C4×C11#57812yes—
465C4×C11C23×Q811yescharacteristic
466C4×C11C2×2−1+411yescharacteristic
467Dic11—24no—
468Dic11—42no—
469Dic11—42no—
470Dic11—42no—
471C2×#41C22×D1111yescharacteristic
472C22×Q8—22no—
473C22×Q8—21no—
474C22×Q8—111no—
475#137—118no—
476C2×Q16—112no—
477C2×SD16—112no—
478C2×M16—111no—
479C2×M16—111no—
480C22×C8—112no—
481C4⋊Q8—22no—
482C4⋊Q8—22no—
483C4⋊Q8—22no—
484C4⋊Q8—24no—
485C4⋊Q8—21no—
486C4⋊Q8—21no—
487C4⋊Q8—111no—
488C4⋊Q8—111no—
489C4⋊Q8—114no—
490C4⋊Q8—222no—
491C4⋊Q8—224no—
492C4⋊Q8—222no—
493C4⋊Q8—222no—
494C4⋊Q8—224no—
495C4⋊Q8C22⋊D1111yescharacteristic
496C4⋊Q8C22⋊D1111yescharacteristic
497C4⋊Q8C22×D1112yes—
498C4⋊Q8C22×D1112yes—
499C4⋊Q8C22×D1114yes—
500#125—22no—
501#125—24no—
502#125—112no—
503#125—114no—
504#125—224no—
505#125—222no—
506#125—224no—
507#125—224no—
508#125C22⋊D1112yes—
509#125C22×D1114yes—
510C22⋊Q8—22no—
511C22⋊Q8—22no—
512C22⋊Q8—24no—
513C22⋊Q8—24no—
514C22⋊Q8—24no—
515C22⋊Q8—221no—
516C22⋊Q8—221no—
517C22⋊Q8—224no—
518C22⋊Q8C22⋊D1112yes—
519C22⋊Q8C22⋊D1112yes—
520C4×Q8—22no—
521C4×Q8—22no—
522C4×Q8—112no—
523C4×Q8—112no—
524C4×Q8—114no—
525C4×Q8—114no—
526C4×Q8—222no—
527C4×Q8—222no—
528C4×Q8—222no—
529C4×Q8—224no—
530C4×Q8—222no—
531C4×Q8—221no—
532C4×Q8—221no—
533C4×Q8—221no—
534C4×Q8—221no—
535C4×Q8C22×D1111yescharacteristic
536C4×Q8C22×D1111yescharacteristic
537C4×Q8C22×D1114yes—
538C4×Q8C22×D1112yes—
539C4×Q8C22×D1112yes—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—24no—
543C4×D4C22×D1111yescharacteristic
544C4×D4C22×D1111yescharacteristic
545C4×D4C22×D1114yes—
546#117—22no—
547#117—21no—
548#117—112no—
549#117—224no—
550#117C22×D1111yescharacteristic
551#117C22×D1112yes—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—221no—
557C2×C4⋊C4C22×D1112yes—
558C2×C42—21no—
559C2×C42—221no—
560C2×C42C22×D1111yescharacteristic
561#107—114no—
562#107—114no—
563#107—112no—
564#107—112no—
565#107—112no—
566#107—114no—
567#107—114no—
568#106—112no—
569#106—112no—
570#106—114no—
571#106—112no—
572#106—114no—
573C4⋊C8—111no—
574C4⋊C8—111no—
575C4⋊C8—112no—
576C4⋊C8—114no—
577C4⋊C8—114no—
578#103—112no—
579#103—112no—
580#103—112no—
581#103—114no—
582#103—114no—
583#103—112no—
584#103—112no—
585#102—112no—
586#102—112no—
587#102—112no—
588#97—112no—
589#97—114no—
590C4×C8—112no—
591C4×C8—114no—
592C2×C11—22no—
593C2×C11—42no—
594C2×C11C2×D4×Q811yescharacteristic
595C2×C11C2×#57811yescharacteristic
596C2×C11#358511yescharacteristic
597#41—22no—
598#41Q8×D1114yes—
599C2×Q8—22no—
600C2×Q8—24no—
601C2×Q8—22no—
602C2×Q8—82no—
603C2×Q8—84no—
604C2×Q8—114no—
605C2×Q8—112no—
606C2×Q8—222no—
607C2×Q8—221no—
608C2×Q8—221no—
609C2×Q8—221no—
610C2×Q8—224no—
611C2×Q8C2×C22⋊D1112yes—
612C2×Q8C2×C22⋊D1112yes—
613C2×Q8C23×D1111yescharacteristic
614C2×D4—21no—
615C2×D4C23×D1111yescharacteristic
616C22×C4—21no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—24no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4C2×C22⋊D1111yescharacteristic
624C22×C4C2×C22⋊D1111yescharacteristic
625C22×C4C23×D1111yescharacteristic
626Q16—118no—
627SD16—118no—
628M16—114no—
629M16—222no—
630C2×C8—112no—
631C2×C8—112no—
632C2×C8—112no—
633C2×C8—112no—
634C2×C8—224no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—24no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—112no—
645C4⋊C4—112no—
646C4⋊C4—112no—
647C4⋊C4—221no—
648C4⋊C4—222no—
649C4⋊C4—222no—
650C4⋊C4—224no—
651C4⋊C4—224no—
652C4⋊C4—222no—
653C4⋊C4—221no—
654C4⋊C4—224no—
655C4⋊C4—222no—
656C4⋊C4—224no—
657C4⋊C4—221no—
658C4⋊C4—224no—
659C4⋊C4C2×C22⋊D1112yes—
660C4⋊C4C2×C22⋊D1112yes—
661C4⋊C4C2×C22⋊D1112yes—
662C4⋊C4C2×C22⋊D1112yes—
663C4⋊C4C2×C22⋊D1114yes—
664C4⋊C4C2×C22⋊D1114yes—
665C4⋊C4C23×D1111yescharacteristic
666C4⋊C4C23×D1114yes—
667C4⋊C4C23×D1111yescharacteristic
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—24no—
672C22⋊C4—222no—
673C22⋊C4C2×C22⋊D1114yes—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—24no—
678C42—222no—
679C42—222no—
680C42—222no—
681C42—224no—
682C42—224no—
683C42C2×C22⋊D1111yescharacteristic
684C42C2×C22⋊D1111yescharacteristic
685C42C23×D1111yescharacteristic
686C42C23×D1114yes—
687C42C23×D1111yescharacteristic
688C11#6138411yescharacteristic, complemented, Sylow
689C23—21no—
690C23C22×C22⋊D1111yescharacteristic
691Q8—24no—
692Q8—21no—
693Q8—42no—
694Q8—44no—
695Q8—82no—
696Q8—84no—
697Q8—114no—
698Q8—224no—
699Q8—222no—
700Q8—442no—
701Q8—881no—
702Q8—884no—
703Q8C2×Q8×D1112yes—
704D4—24no—
705D4—21no—
706D4C2×Q8×D1112yes—
707C2×C4—21no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—24no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—84no—
717C2×C4—82no—
718C2×C4—224no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—881no—
724C2×C4C2×Q8×D1112yes—
725C2×C4#6704012yes—
726C2×C4C22×C22⋊D1114yes—
727C2×C4C22×C22⋊D1111yescharacteristic
728C2×C4C22×C22⋊D1111yescharacteristic
729C2×C4C22×C22⋊D1114yes—
730C2×C4C22×C22⋊D1111yescharacteristic
731C2×C4C22×C22⋊D1111yescharacteristic
732C2×C4C22×C22⋊D1111yescharacteristic
733C2×C4C24×D1111yescharacteristic
734C8—114no—
735C8—222no—
736C8—222no—
737C8—222no—
738C22—21no—
739C22—21no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22Q8×C22⋊D1112yes—
744C22C23×C22⋊D1111yescharacteristic
745C4—21no—
746C4—21no—
747C4—24no—
748C4—22no—
749C4—21no—
750C4—24no—
751C4—41no—
752C4—44no—
753C4—41no—
754C4—224no—
755C4—442no—
756C4—442no—
757C4—442no—
758C4Q8×C22⋊D1112yes—
759C4#1062336912yes—
760C4C22×Q8×D1111yescharacteristic
761C4C2×#6704011yescharacteristic
762C2—22no—
763C2—42no—
764C2C2×Q8×C22⋊D1111yescharacteristic
765C2C2×#1062336911yescharacteristic
766C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3503C2
socleC22×C11C23×D4
prime radicalC2×C11×#41C23
hypercenter#3503D11
hypocenterC11#61384
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #533 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #13082421C2semidirect
2. #13081579C2semidirect
3. #13081544C2semidirect
4. #13081537C2semidirect
5. #13081526C2semidirect
6. Q8×#4326C2semidirect
7. #13081491C2semidirect
8. #13079158C2semidirect
9. #13079150C2semidirect
11. #13078452C2semidirect
13. C2×#10622704C2semidirect
14. #13077565C2semidirect
142. #67004Q8semidirect
242. C2×Dic22C2×Q8semidirect
277. #4326C2×Q8semidirect
278. #4324C2×Q8semidirect
300. #4318C2×Q8semidirect
688. C11#61384semidirect

Maximal subgroups

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

subgroupindex
#130824212
#130815792
#130815442
#130815372
#130815262
Q8×#43262
#130814912
#130791582
#130791502
#130784672
#130784522
#130784042
C2×#106227042
#130775652
#130774552
C4×#670042
C11×#35032
#6138411