Finite Group Databasebeta

← #15649344

Subgroups — #15649344

Order 2816.

1738 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082502C211yesmaximal, characteristic, complemented
2#13081491C212yesmaximal, complemented
3#13081297C212yesmaximal, complemented
4#13081029C212yesmaximal, complemented
5#13080978C214yesmaximal, complemented
6#13080533C212yesmaximal, complemented
7#13080451C214yesmaximal, complemented
8#13079958C211yesmaximal, characteristic, complemented
9#13079953C212yesmaximal, complemented
10#13079791C212yesmaximal, complemented
11#13079757C211yesmaximal, characteristic, complemented
12#13078687C212yesmaximal, complemented
13#13078624C211yesmaximal, characteristic, complemented
14#13078404C212yesmaximal, complemented
15C2×#10622620C211yesmaximal, characteristic, complemented
16#13077727C211yesmaximal, characteristic, complemented
17C11×#3475C211yesmaximal, characteristic
18C11×#556C2211yescharacteristic
19C11×#555C2211yescharacteristic
20C11×#554C2211yescharacteristic
21C11×#553—21no—
22C11×#552—21no—
23C11×#552C2212yes—
24C11×#551—22no—
25C11×#547C2211yescharacteristic
26C11×#546C2212yes—
27C11×#533C2211yescharacteristic
28C11×#529—22no—
29C11×#529C2212yes—
30C11×#525—21no—
31C4×C11×#41C2212yes—
32C4×C11×#41C2211yescharacteristic
33C2×C4×D4×C11C2211yescharacteristic
34C2×C11×#117—21no—
35#10623356—21no—
36#10623098—21no—
37#10623098C2212yescomplemented
38#10623073—21no—
39#10623073C2212yescomplemented
40#10623072—22no—
41#10623072C2214yes—
42#10623049—22no—
43#10623047—21no—
44#10623001C2211yescharacteristic
45#10623001C2212yescomplemented
46#10623001C2212yescomplemented
47C2×#66922C2211yescharacteristic
48#10622852C2214yes—
49#10622846C2214yes—
50#10622831C2212yes—
51C2×#66896C2212yes—
52#10622704C2212yescomplemented
53#10622703C2212yescomplemented
54#10622694C2212yescomplemented
55#10622692C2212yescomplemented
56#10622677C2214yescomplemented
57#10622676C2214yescomplemented
58#10622669C2214yes—
59#10622667C2214yes—
60#10622664C2214yes—
61#10622664C2214yescomplemented
62#10622658C2214yescomplemented
63#10622656C2214yes—
64#10622654C2214yes—
65#10622648C2214yes—
66#10622644C2212yescomplemented
67C4×#4326C2214yescomplemented
68Q8×C11⋊C8C2212yescomplemented
69#10622635C2214yescomplemented
70#10622634C2212yescomplemented
71#10622633C2212yescomplemented
72#10622633C2212yescomplemented
73#10622632C2211yescharacteristic
74#10622632C2211yescharacteristic
75C4×#4324C2212yes—
76C4×#4324C2212yes—
77C4×#4324C2214yes—
78D4×C11⋊C8C2214yes—
79D4×C11⋊C8C2212yescomplemented
80#10622622C2214yes—
81#10622621C2211yescharacteristic
82#10622621C2211yescharacteristic
83#10622620C2212yes—
84#10622620C2212yes—
85#10622620C2212yes—
86#10622620C2212yes—
87#10622611C2214yescomplemented
88#10622609C2214yescomplemented
89#10622584C2212yes—
90C2×#66871C2212yes—
91#10622538C2211yescharacteristic
92#10622538C2212yescomplemented
93C2×C4⋊(C11⋊C8)C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2212yescomplemented
95C2×C11×#41D411yescharacteristic
96C2×C11×#41C2312yes—
97C22×D4×C11C2311yescharacteristic
98C23×C4×C11—21no—
99C22×Dic22—21no—
100C11×C4⋊Q8C2311yescharacteristic
101C11×C4⋊Q8C2311yescharacteristic
102C11×#126—22no—
103C11×#126—22no—
104C11×#126—22no—
105C11×#125—22no—
106C11×#125—21no—
107C11×#125C2312yes—
108C11×#124—22no—
109C11×#124C2312yes—
110C11×#123—22no—
111C11×#123—22no—
112C11×#123—22no—
113C11×#123—22no—
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8—21no—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8—22no—
118C11×C22⋊Q8C2312yes—
119C11×C22⋊Q8C2312yes—
120C11×#121—21no—
121C11×#121—21no—
122C11×#121—22no—
123C11×#121C2312yes—
124C11×#120—22no—
125C4×Q8×C11—21no—
126C4×Q8×C11D411yescharacteristic
127C4×Q8×C11C2312yes—
128C4×Q8×C11C2312yes—
129C4×Q8×C11C2311yescharacteristic
130C4×D4×C11—22no—
131C4×D4×C11—22no—
132C4×D4×C11—22no—
133C4×D4×C11—21no—
134C4×D4×C11—21no—
135C4×D4×C11D412yes—
136C4×D4×C11D411yescharacteristic
137C4×D4×C11C2311yescharacteristic
138C4×D4×C11C2311yescharacteristic
139C4×D4×C11C2311yescharacteristic
140C4×D4×C11C2311yescharacteristic
141C4×D4×C11C2312yes—
142C4×D4×C11C2312yes—
143C4×D4×C11C2311yescharacteristic
144C11×#117—21no—
145C11×#117—21no—
146C11×#117—21no—
147C11×#117—22no—
148C11×#117—22no—
149C11×#117—22no—
150C11×#117D411yescharacteristic
151C11×#117D412yes—
152C11×#117C2312yes—
153C2×C11×C4⋊C4—21no—
154C2×C11×C4⋊C4—21no—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C22⋊C4—21no—
157C2×C11×C22⋊C4—22no—
158C2×C42×C11—22no—
159C2×C42×C11C2311yescharacteristic
160C2×C42×C11C2312yes—
161#66997—22no—
162C2×#4326C2314yes—
163#66989—22no—
164#66988—24no—
165C2×#4324C2312yes—
166C2×#4324C2312yes—
167#66979—21no—
168#66979—22no—
169#66979C2314yes—
170C2×C4⋊Dic11—21no—
171C2×C4⋊Dic11C2312yes—
172#66977—21no—
173#66977—22no—
174#66977—22no—
175#66977—22no—
176#66977C2312yes—
177#66977C2314yes—
178C22×C11⋊C8C2312yes—
179C22×C11⋊C8C2314yes—
180#66942—24no—
181#66942—24no—
182#66940—22no—
183#66940—22no—
184#66932—24no—
185#66932—24no—
186#66930—24no—
187#66923—21no—
188#66923—22no—
189#66923C2314yes—
190#66922—21no—
191#66922—21no—
192#66922C2311yescharacteristic
193#66922C2312yes—
194#66922C2312yes—
195#66922C2311yescharacteristic
196C4×Dic22—21no—
197C4×Dic22—22no—
198C4×Dic22—22no—
199C4×Dic22—22no—
200C4×Dic22C2312yes—
201C4×Dic22C2314yes—
202#66899C2314yes—
203#66899C2314yes—
204#66899C2314yes—
205#66896C2314yes—
206#66896C2314yes—
207#66896C2312yes—
208#66896C2312yes—
209C22⋊(C11⋊C8)C2312yes—
210C22⋊(C11⋊C8)C2314yes—
211#66874C2312yes—
212#66874C2312yes—
213#66874C2314yes—
214#66872C2312yes—
215#66872C2312yes—
216#66872C2314yes—
217#66872C2314yes—
218#66871C2314yes—
219#66871C2314yes—
220#66871C2314yes—
221C4⋊(C11⋊C8)C2312yes—
222C4⋊(C11⋊C8)C2312yes—
223C4⋊(C11⋊C8)C2311yescharacteristic
224C4⋊(C11⋊C8)C2314yes—
225C4⋊(C11⋊C8)C2311yescharacteristic
226C4×C11⋊C8C2312yes—
227C4×C11⋊C8C2314yes—
228#62097—111nomaximal, Sylow
229C24×C11—21no—
230C11×#41—24no—
231C11×#41—24no—
232C11×#41—42no—
233C2×Q8×C11—21no—
234C2×Q8×C11C2×D411yescharacteristic
235C2×Q8×C11C2412yes—
236C2×D4×C11—22no—
237C2×D4×C11—22no—
238C2×D4×C11—22no—
239C2×D4×C11—21no—
240C2×D4×C11—41no—
241C2×D4×C11C2×D412yes—
242C2×D4×C11C2×D411yescharacteristic
243C2×D4×C11C2411yescharacteristic
244C2×D4×C11C2411yescharacteristic
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—22no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—22no—
252C22×C4×C11—44no—
253C22×C4×C11C2×D412yes—
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D412yes—
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2412yes—
259C22×Dic11—22no—
260C2×Dic22—21no—
261C2×Dic22—22no—
262C2×Dic22—22no—
263C2×Dic22—44no—
264C2×Dic22C2412yes—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—21no—
267C11×C4⋊C4—22no—
268C11×C4⋊C4—22no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—22no—
271C11×C4⋊C4—22no—
272C11×C4⋊C4—22no—
273C11×C4⋊C4—22no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4C2×D411yescharacteristic
276C11×C4⋊C4C2×D411yescharacteristic
277C11×C4⋊C4C2×D412yes—
278C11×C4⋊C4C2×D412yes—
279C11×C4⋊C4C2411yescharacteristic
280C11×C4⋊C4C2411yescharacteristic
281C11×C4⋊C4C2412yes—
282C11×C22⋊C4—22no—
283C11×C22⋊C4—22no—
284C11×C22⋊C4—22no—
285C11×C22⋊C4—21no—
286C11×C22⋊C4—22no—
287C11×C22⋊C4—22no—
288C11×C22⋊C4—21no—
289C11×C22⋊C4—21no—
290C11×C22⋊C4—21no—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4C2×D412yes—
294C11×C22⋊C4C2×D412yes—
295C11×C22⋊C4C2×D412yes—
296C42×C11—22no—
297C42×C11—22no—
298C42×C11—22no—
299C42×C11C2×D412yes—
300C42×C11C2×D411yescharacteristic
301C42×C11C2×D412yes—
302C42×C11C2×D411yescharacteristic
303C42×C11C2411yescharacteristic
304C42×C11C2412yes—
305C42×C11C2411yescharacteristic
306C22⋊Dic11—22no—
307C22⋊Dic11—24no—
308C22⋊Dic11—24no—
309#4326—44no—
310#4324—24no—
311#4324—42no—
312C4⋊Dic11—21no—
313C4⋊Dic11—21no—
314C4⋊Dic11—22no—
315C4⋊Dic11—21no—
316C4⋊Dic11—22no—
317C4⋊Dic11—22no—
318C4⋊Dic11C2414yes—
319C4⋊Dic11C2412yes—
320Dic11⋊C4—24no—
321Dic11⋊C4—22no—
322Dic11⋊C4—24no—
323Dic11⋊C4—24no—
324Dic11⋊C4—22no—
325Dic11⋊C4—24no—
326C4×Dic11—24no—
327C4×Dic11—24no—
328C4×Dic11—22no—
329C2×C11⋊C8—42no—
330C2×C11⋊C8—44no—
331C2×C11⋊C8C2412yes—
332C2×C11⋊C8C2414yes—
333C2×C11⋊C8C2412yes—
334#3509—111no—
335#3475D1111yescharacteristic
336#3381—112no—
337#3364—112no—
338#3340—112no—
339#3336—114no—
340#3302—112no—
341#3296—114no—
342#3249—111no—
343#3248—112no—
344#3233—112no—
345#3229—111no—
346#3107—112no—
347#3101—111no—
348#3076—112no—
349C2×#474—111no—
350#2988—111no—
351C23×C11—21no—
352C23×C11—21no—
353C23×C11—42no—
354C23×C11—42no—
355C23×C11—81no—
356C23×C11C22×D412yes—
357C23×C11C22×D411yescharacteristic
358Q8×C11—22no—
359Q8×C11—22no—
360Q8×C11—22no—
361Q8×C11—81no—
362D4×C11—24no—
363D4×C11—22no—
364D4×C11—21no—
365D4×C11—21no—
366D4×C11—21no—
367D4×C11—42no—
368D4×C11—44no—
369D4×C11—82no—
370D4×C112−1+412yes—
371C2×C4×C11—24no—
372C2×C4×C11—21no—
373C2×C4×C11—22no—
374C2×C4×C11—21no—
375C2×C4×C11—22no—
376C2×C4×C11—21no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—21no—
380C2×C4×C11—42no—
381C2×C4×C11—41no—
382C2×C4×C11—44no—
383C2×C4×C11—42no—
384C2×C4×C11—42no—
385C2×C4×C11—42no—
386C2×C4×C11—42no—
387C2×C4×C11—42no—
388C2×C4×C11—82no—
389C2×C4×C11#13514yes—
390C2×C4×C11C22×D412yes—
391C2×C4×C11C22×D412yes—
392C2×C4×C11C22×D412yes—
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C2511yescharacteristic
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—24no—
402C2×Dic11—44no—
403Dic22—22no—
404Dic22—22no—
405Dic22—42no—
406Dic22—44no—
407Dic22—44no—
408C11⋊C8—22no—
409C11⋊C8—22no—
410C11⋊C8—24no—
411#557—112no—
412#557—221no—
413#556—112no—
414#556—221no—
415#556C2×D1111yescharacteristic
416#555C2×D1111yescharacteristic
417#554C2×D1111yescharacteristic
418#553—21no—
419#552—21no—
420#552—114no—
421#552—222no—
422#552C2×D1112yes—
423#551—22no—
424#547C2×D1111yescharacteristic
425#546C2×D1112yes—
426#541—222no—
427#536—221no—
428#533—112no—
429#533—111no—
430#533—112no—
431#533C2×D1111yescharacteristic
432C2×C4⋊Q8—111no—
433#529—22no—
434#529C2×D1112yes—
435#525—21no—
436#519—221no—
437C4×#41C2×D1112yes—
438C4×#41C2×D1111yescharacteristic
439C2×C4×D4C2×D1111yescharacteristic
440C2×#117—21no—
441#499—114no—
442#498—112no—
443#488—114no—
444#487—112no—
445#485—114no—
446#485—114no—
447#483—114no—
448#483—112no—
449#482—114no—
450#479—114no—
451#479—114no—
452#478—114no—
453#477—112no—
454#477—112no—
455#476—111no—
456#476—111no—
457#475—112no—
458#475—112no—
459#474—112no—
460#474—112no—
461#474—112no—
462#474—112no—
463#467—114no—
464#467—114no—
465#465—114no—
466#464—114no—
467#462—112no—
468#462—112no—
469#461—111no—
470#461—111no—
471#452—114no—
472#450—112no—
473C8×Q8—112no—
474C4×Q16—114no—
475C4×SD16—112no—
476C4×SD16—112no—
477C4×SD16—114no—
478C8×D4—114no—
479C8×D4—112no—
480#431—111no—
481#431—112no—
482#427—114no—
483C2×#107—112no—
484C2×C4⋊C8—112no—
485C2×C4⋊C8—111no—
486#416—114no—
487C2×#102—112no—
488C22×C11—21no—
489C22×C11—21no—
490C22×C11—22no—
491C22×C11—22no—
492C22×C11—22no—
493C22×C11—22no—
494C22×C11—41no—
495C22×C11—41no—
496C22×C11—41no—
497C22×C11—41no—
498C22×C11—41no—
499C22×C11—84no—
500C22×C11C2×#13512yes—
501C22×C11C23×D411yescharacteristic
502C4×C11—21no—
503C4×C11—22no—
504C4×C11—21no—
505C4×C11—22no—
506C4×C11—21no—
507C4×C11—22no—
508C4×C11—42no—
509C4×C11—42no—
510C4×C11—41no—
511C4×C11—41no—
512C4×C11C2×#13512yes—
513C4×C11C2×#13512yes—
514C4×C11C2×2−1+411yescharacteristic
515C4×C11#58511yescharacteristic
516Dic11—42no—
517Dic11—42no—
518Dic11—44no—
519C2×#41C22⋊D1111yescharacteristic
520C2×#41C22×D1112yes—
521C22×Q8—221no—
522C22×D4C22×D1111yescharacteristic
523C23×C4—21no—
524C2×Q16—114no—
525C2×SD16—112no—
526C2×SD16—112no—
527C22×C8—112no—
528C22×C8—114no—
529C4⋊Q8—112no—
530C4⋊Q8—112no—
531C4⋊Q8—111no—
532C4⋊Q8—111no—
533C4⋊Q8—222no—
534C4⋊Q8—221no—
535C4⋊Q8—221no—
536C4⋊Q8C22×D1111yescharacteristic
537C4⋊Q8C22×D1111yescharacteristic
538#126—22no—
539#126—22no—
540#126—22no—
541#126—224no—
542#126—224no—
543#125—22no—
544#125—21no—
545#125—114no—
546#125—224no—
547#125—224no—
548#125—221no—
549#125—222no—
550#125C22×D1112yes—
551#124—22no—
552#124—222no—
553#124C22×D1112yes—
554#123—22no—
555#123—22no—
556#123—22no—
557#123—22no—
558#123—224no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—22no—
563C22⋊Q8—112no—
564C22⋊Q8—114no—
565C22⋊Q8—222no—
566C22⋊Q8—222no—
567C22⋊Q8—221no—
568C22⋊Q8—222no—
569C22⋊Q8C22×D1112yes—
570C22⋊Q8C22×D1112yes—
571#121—21no—
572#121—21no—
573#121—22no—
574#121C22×D1112yes—
575#120—22no—
576C4×Q8—21no—
577C4×Q8—114no—
578C4×Q8—112no—
579C4×Q8—222no—
580C4×Q8—222no—
581C4×Q8—222no—
582C4×Q8—222no—
583C4×Q8—222no—
584C4×Q8—221no—
585C4×Q8C22⋊D1111yescharacteristic
586C4×Q8C22×D1112yes—
587C4×Q8C22×D1112yes—
588C4×Q8C22×D1111yescharacteristic
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4C22⋊D1112yes—
595C4×D4C22⋊D1111yescharacteristic
596C4×D4C22×D1111yescharacteristic
597C4×D4C22×D1111yescharacteristic
598C4×D4C22×D1111yescharacteristic
599C4×D4C22×D1111yescharacteristic
600C4×D4C22×D1112yes—
601C4×D4C22×D1112yes—
602C4×D4C22×D1111yescharacteristic
603#117—21no—
604#117—21no—
605#117—21no—
606#117—22no—
607#117—22no—
608#117—22no—
609#117—114no—
610#117—221no—
611#117—222no—
612#117—224no—
613#117C22⋊D1111yescharacteristic
614#117C22⋊D1112yes—
615#117C22×D1112yes—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—112no—
619C2×C4⋊C4—221no—
620C2×C4⋊C4C22×D1111yescharacteristic
621C2×C22⋊C4—21no—
622C2×C22⋊C4—22no—
623C2×C42—22no—
624C2×C42C22×D1111yescharacteristic
625C2×C42C22×D1112yes—
626#107—114no—
627#107—114no—
628#107—114no—
629#106—112no—
630#106—114no—
631#106—114no—
632#106—112no—
633C4⋊C8—111no—
634C4⋊C8—112no—
635C4⋊C8—112no—
636C4⋊C8—114no—
637C4⋊C8—111no—
638#103—114no—
639#103—114no—
640#103—114no—
641#103—112no—
642#103—112no—
643#103—114no—
644#102—114no—
645#102—114no—
646#102—112no—
647#102—112no—
648C22⋊C8—112no—
649C22⋊C8—114no—
650C4×C8—112no—
651C4×C8—114no—
652C2×C11—22no—
653C2×C11—42no—
654C2×C11—42no—
655C2×C11—81no—
656C2×C11#348911yescharacteristic
657C2×C11C22×#13511yescharacteristic
658C2×C11#358611yescharacteristic
659C24—21no—
660#41—24no—
661#41—24no—
662#41—42no—
663C2×Q8—21no—
664C2×Q8—112no—
665C2×Q8—221no—
666C2×Q8—222no—
667C2×Q8—222no—
668C2×Q8—444no—
669C2×Q8C2×C22⋊D1111yescharacteristic
670C2×Q8C23×D1112yes—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—21no—
675C2×D4—41no—
676C2×D4C2×C22⋊D1112yes—
677C2×D4C2×C22⋊D1111yescharacteristic
678C2×D4C23×D1111yescharacteristic
679C2×D4C23×D1111yescharacteristic
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—22no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—22no—
687C22×C4—44no—
688C22×C4—222no—
689C22×C4C2×C22⋊D1112yes—
690C22×C4C2×C22⋊D1111yescharacteristic
691C22×C4C2×C22⋊D1112yes—
692C22×C4C2×C22⋊D1111yescharacteristic
693C22×C4C23×D1111yescharacteristic
694C22×C4C23×D1112yes—
695Q16—444no—
696SD16—224no—
697SD16—442no—
698C2×C8—112no—
699C2×C8—114no—
700C2×C8—112no—
701C2×C8—444no—
702C2×C8—442no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—22no—
706C4⋊C4—22no—
707C4⋊C4—21no—
708C4⋊C4—22no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—21no—
713C4⋊C4—114no—
714C4⋊C4—112no—
715C4⋊C4—222no—
716C4⋊C4—222no—
717C4⋊C4—222no—
718C4⋊C4—221no—
719C4⋊C4—224no—
720C4⋊C4—221no—
721C4⋊C4—221no—
722C4⋊C4—224no—
723C4⋊C4—224no—
724C4⋊C4—222no—
725C4⋊C4—222no—
726C4⋊C4—224no—
727C4⋊C4C2×C22⋊D1111yescharacteristic
728C4⋊C4C2×C22⋊D1111yescharacteristic
729C4⋊C4C2×C22⋊D1112yes—
730C4⋊C4C2×C22⋊D1112yes—
731C4⋊C4C23×D1112yes—
732C4⋊C4C23×D1111yescharacteristic
733C4⋊C4C23×D1111yescharacteristic
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—21no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—224no—
746C22⋊C4—222no—
747C22⋊C4—224no—
748C22⋊C4C2×C22⋊D1112yes—
749C22⋊C4C2×C22⋊D1112yes—
750C22⋊C4C2×C22⋊D1112yes—
751C42—22no—
752C42—22no—
753C42—22no—
754C42—224no—
755C42—224no—
756C42—222no—
757C42C2×C22⋊D1112yes—
758C42C2×C22⋊D1112yes—
759C42C2×C22⋊D1111yescharacteristic
760C42C2×C22⋊D1111yescharacteristic
761C42C23×D1111yescharacteristic
762C42C23×D1112yes—
763C42C23×D1111yescharacteristic
764C11#6209711yescharacteristic, complemented, Sylow
765C23—21no—
766C23—21no—
767C23—42no—
768C23—42no—
769C23—81no—
770C23C22×C22⋊D1112yes—
771C23C22×C22⋊D1111yescharacteristic
772Q8—22no—
773Q8—22no—
774Q8—22no—
775Q8—81no—
776Q8—222no—
777Q8—222no—
778Q8—442no—
779Q8—444no—
780Q8—444no—
781D4—24no—
782D4—22no—
783D4—21no—
784D4—21no—
785D4—21no—
786D4—42no—
787D4—44no—
788D4—82no—
789D4#6704312yes—
790C2×C4—24no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—21no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—82no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—224no—
811C2×C4—444no—
812C2×C4#6700314yes—
813C2×C4C22×C22⋊D1112yes—
814C2×C4C22×C22⋊D1112yes—
815C2×C4C22×C22⋊D1111yescharacteristic
816C2×C4C22×C22⋊D1111yescharacteristic
817C2×C4C22×C22⋊D1111yescharacteristic
818C2×C4C22×C22⋊D1112yes—
819C2×C4C22×C22⋊D1111yescharacteristic
820C2×C4C22×C22⋊D1111yescharacteristic
821C2×C4C24×D1111yescharacteristic
822C8—222no—
823C8—222no—
824C8—224no—
825C22—21no—
826C22—21no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—84no—
837C22C2×#6700312yes—
838C22C23×C22⋊D1111yescharacteristic
839C4—21no—
840C4—22no—
841C4—21no—
842C4—22no—
843C4—21no—
844C4—22no—
845C4—42no—
846C4—42no—
847C4—41no—
848C4—41no—
849C4—442no—
850C4—442no—
851C4—444no—
852C4C2×#6700312yes—
853C4C2×#6700312yes—
854C4C2×#6704311yescharacteristic
855C4#1062345311yescharacteristic
856C2—22no—
857C2—42no—
858C2—42no—
859C2—81no—
860C2#1308229611yescharacteristic
861C2C22×#6700311yescharacteristic
862C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC11×#3475C2
socleC22×C11C23×D4
hypercenter#3475D11
hypocenterC11#62097
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. #13082502C2semidirect
2. #13081491C2semidirect
3. #13081297C2semidirect
4. #13081029C2semidirect
5. #13080978C2semidirect
6. #13080533C2semidirect
7. #13080451C2semidirect
8. #13079958C2semidirect
9. #13079953C2semidirect
10. #13079791C2semidirect
11. #13079757C2semidirect
12. #13078687C2semidirect
13. #13078624C2semidirect
14. #13078404C2semidirect
15. C2×#10622620C2semidirect
16. #13077727C2semidirect
37. #10623098C22semidirect
39. #10623073C22semidirect
45. #10623001C22semidirect
46. #10623001C22semidirect
52. #10622704C22semidirect
53. #10622703C22semidirect
54. #10622694C22semidirect
55. #10622692C22semidirect
56. #10622677C22semidirect
57. #10622676C22semidirect
61. #10622664C22semidirect
62. #10622658C22semidirect
66. #10622644C22semidirect
67. C4×#4326C22semidirect
68. Q8×C11⋊C8C22semidirect
69. #10622635C22semidirect
70. #10622634C22semidirect
71. #10622633C22semidirect
72. #10622633C22semidirect
79. D4×C11⋊C8C22semidirect
87. #10622611C22semidirect
88. #10622609C22semidirect
92. #10622538C22semidirect
94. C2×C4⋊(C11⋊C8)C22semidirect
764. C11#62097semidirect

Maximal subgroups

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

subgroupindex
#130825022
#130814912
#130812972
#130810292
#130809782
#130805332
#130804512
#130799582
#130799532
#130797912
#130797572
#130786872
#130786242
#130784042
C2×#106226202
#130777272
C11×#34752
#6209711