Finite Group Databasebeta

← #15638720

Subgroups — #15638720

Order 2816.

2114 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082468C211yesmaximal, characteristic, complemented
2#13080802C214yesmaximal, complemented
3#13080682C214yesmaximal, complemented
4#13080202C214yesmaximal, complemented
5#13080172C214yesmaximal, complemented
6#13079619C211yesmaximal, characteristic, complemented
7#13079603C211yesmaximal, characteristic, complemented
8#13079430C212yesmaximal, complemented
9#13079397C212yesmaximal, complemented
10#13078746C211yesmaximal, characteristic, complemented
11#13078738C211yesmaximal, characteristic, complemented
12#13077850C212yesmaximal, complemented
13#13077834C212yesmaximal, complemented
14#13077645C211yesmaximal, characteristic, complemented
15C2×C11×#548C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×Q8×C11C2211yescharacteristic
18C11×#548—22no—
19C11×#548—22no—
20C11×#548C2214yes—
21C11×#548C2214yes—
22C2×C11×#124—21no—
23C2×C11×#124C2211yescharacteristic
24C2×C11×C22⋊Q8—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×#121—21no—
27C2×C11×#121C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×D4×C11—21no—
30C2×C4×D4×C11C2211yescharacteristic
31C2×#67003C2214yescomplemented
32C2×#66995C2214yescomplemented
33#10623336—21no—
34#10623322C2212yes—
35#10623322C2212yes—
36#10623094C2212yescomplemented
37#10623090—22no—
38#10623089—22no—
39#10623084C2212yescomplemented
40#10623082C2212yescomplemented
41#10623073C2212yescomplemented
42#10623035—21no—
43#10623025—21no—
44#10623025—21no—
45#10623008C2211yescharacteristic
46#10623001C2211yescharacteristic
47#10622852C2214yescomplemented
48#10622851C2214yescomplemented
49#10622846C2214yescomplemented
50#10622841C2212yes—
51#10622841C2212yes—
52#10622841C2214yescomplemented
53#10622840C2212yes—
54#10622840C2212yes—
55#10622840C2214yescomplemented
56#10622838C2214yescomplemented
57#10622831C2212yes—
58#10622830C2212yes—
59#10622820C2212yes—
60C2×C22⋊(C11⋊C8)C2212yes—
61#10622673C2212yescomplemented
62#10622671C2212yescomplemented
63#10622670C2214yescomplemented
64#10622668C2212yescomplemented
65#10622668C2212yescomplemented
66#10622667C2214yescomplemented
67#10622664C2214yescomplemented
68#10622661C2214yescomplemented
69#10622660C2214yescomplemented
70#10622658C2214yescomplemented
71#10622655C2214yescomplemented
72#10622652C2214yescomplemented
73#10622650C2214yescomplemented
74#10622648C2214yescomplemented
75#10622644C2212yescomplemented
76#10622643C2214yescomplemented
77#10622640C2212yescomplemented
78#10622639C2214yescomplemented
79#10622634C2212yescomplemented
80#10622633C2212yescomplemented
81#10622624C2214yescomplemented
82#10622624C2214yescomplemented
83#10622584C2212yes—
84#10622580C2212yes—
85#10622539C2211yescharacteristic
86#10622539C2211yescharacteristic
87C2×C11×#41—22no—
88C2×C11×#41—44no—
89C2×C11×#41C2314yes—
90C22×Q8×C11—21no—
91C22×Q8×C11—22no—
92C22×Q8×C11—44no—
93C22×Q8×C11C2311yescharacteristic
94C22×Q8×C11C2314yes—
95C22×Q8×C11C2311yescharacteristic
96C22×D4×C11—21no—
97C22×D4×C11—21no—
98C22×D4×C11D411yescharacteristic
99C22×D4×C11C2311yescharacteristic
100C23×C4×C11—21no—
101C23×C4×C11—21no—
102C23×C4×C11C2311yescharacteristic
103C23×C4×C11C2311yescharacteristic
104C2×#4339—21no—
105C2×#4339C2312yes—
106C2×#4339C2312yes—
107C11×#124—24no—
108C11×#124—24no—
109C11×#124—21no—
110C11×#124—21no—
111C11×#124C2312yes—
112C11×#124C2312yes—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—24no—
115C11×C22⋊Q8—24no—
116C11×C22⋊Q8C2314yes—
117C11×#121—24no—
118C11×#121—24no—
119C11×#121—22no—
120C11×#121C2314yes—
121C4×Q8×C11—21no—
122C4×Q8×C11—21no—
123C4×Q8×C11C2312yes—
124C4×Q8×C11C2312yes—
125C4×D4×C11—24no—
126C4×D4×C11—24no—
127C4×D4×C11D412yes—
128C4×D4×C11D412yes—
129C4×D4×C11C2312yes—
130C4×D4×C11C2312yes—
131C2×C11×C4⋊C4—21no—
132C2×C11×C4⋊C4—21no—
133C2×C11×C4⋊C4D411yescharacteristic
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4—21no—
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4D411yescharacteristic
140C2×C11×C22⋊C4D411yescharacteristic
141C2×C42×C11—21no—
142C2×C42×C11C2311yescharacteristic
143#67006—22no—
144#67006—22no—
145#67003—48no—
146C2×#4326C2314yes—
147C2×#4326C2314yes—
148#66995—48no—
149C2×#4325C2314yes—
150C2×#4325C2314yes—
151#66993—22no—
152#66991—22no—
153#66991—22no—
154#66989—22no—
155C2×#4324C2314yes—
156C2×#4323C2314yes—
157#66983—21no—
158#66983C2312yes—
159#66983C2312yes—
160#66983C2312yes—
161#66982—22no—
162#66982—22no—
163C4×C22⋊D11—22no—
164C4×C22⋊D11—22no—
165C4×C22⋊D11—22no—
166C4×C22⋊D11—22no—
167#66979—21no—
168#66979C2312yes—
169#66979C2312yes—
170#66977—21no—
171#66977C2312yes—
172#66977C2312yes—
173#66977C2312yes—
174C2×#4318C2314yes—
175C22×C11⋊C8C2314yes—
176#66946—22no—
177#66945—22no—
178C4⋊C4×D11—22no—
179#66940—22no—
180#66938—22no—
181#66938—22no—
182#66937—22no—
183#66937—22no—
184#66936—22no—
185#66936—22no—
186#66932—22no—
187#66932—22no—
188#66928—21no—
189#66927C2311yescharacteristic
190C4×D44—21no—
191C4×D44C2312yes—
192#66923—21no—
193#66922C2311yescharacteristic
194#66922C2311yescharacteristic
195#66922C2311yescharacteristic
196C4×Dic22—21no—
197C4×Dic22C2312yes—
198#66899C2314yes—
199#66899C2314yes—
200#66899C2314yes—
201#66899C2314yes—
202#66896C2314yes—
203#66896C2314yes—
204C22⋊(C11⋊C8)C2312yes—
205C22⋊(C11⋊C8)C2312yes—
206C22⋊(C11⋊C8)C2314yes—
207C22⋊(C11⋊C8)C2314yes—
208#66874C2314yes—
209#66873C2314yes—
210#66872C2314yes—
211#66871C2314yes—
212C4⋊(C11⋊C8)C2312yes—
213C4⋊(C11⋊C8)C2312yes—
214#66867C2312yes—
215#66867C2312yes—
216#61578—111nomaximal, Sylow
217C24×C11—21no—
218C24×C11C2×D411yescharacteristic
219C24×C11C2×D411yescharacteristic
220C11×#41—28no—
221C11×#41—44no—
222C11×#41—48no—
223C2×Q8×C11—24no—
224C2×Q8×C11—21no—
225C2×Q8×C11—24no—
226C2×Q8×C11—21no—
227C2×Q8×C11—28no—
228C2×Q8×C11—44no—
229C2×Q8×C11—42no—
230C2×Q8×C11—44no—
231C2×Q8×C11—48no—
232C2×Q8×C11C2412yes—
233C2×Q8×C11C2412yes—
234C2×D4×C11—24no—
235C2×D4×C11—24no—
236C2×D4×C11—21no—
237C2×D4×C11—42no—
238C2×D4×C11—42no—
239C2×D4×C11—44no—
240C2×D4×C11—44no—
241C2×D4×C11C2×D412yes—
242C2×D4×C11C2×D412yes—
243C2×D4×C11C2412yes—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—24no—
248C22×C4×C11—24no—
249C22×C4×C11—42no—
250C22×C4×C11—42no—
251C22×C4×C11—44no—
252C22×C4×C11—44no—
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D412yes—
258C22×C4×C11C2×D412yes—
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2412yes—
261C22×C4×C11C2412yes—
262C2×C22⋊D11—22no—
263C2×C22⋊D11—22no—
264C2×C22⋊D11—22no—
265C2×C22⋊D11—22no—
266C2×C22⋊D11—22no—
267#4339—44no—
268#4339—44no—
269#4339—44no—
270C2×D44—21no—
271C2×D44—21no—
272C2×D44C2412yes—
273C2×C4×D11—22no—
274C2×C4×D11—22no—
275C2×C4×D11—22no—
276C2×Dic22—21no—
277C2×Dic22—21no—
278C2×Dic22C2412yes—
279C11×C4⋊C4—24no—
280C11×C4⋊C4—22no—
281C11×C4⋊C4—22no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4C2×D412yes—
284C11×C4⋊C4C2×D412yes—
285C11×C4⋊C4C2412yes—
286C11×C22⋊C4—24no—
287C11×C22⋊C4—22no—
288C11×C22⋊C4—22no—
289C11×C22⋊C4—22no—
290C11×C22⋊C4—22no—
291C11×C22⋊C4—24no—
292C11×C22⋊C4C2×D412yes—
293C11×C22⋊C4C2×D412yes—
294C11×C22⋊C4C2×D412yes—
295C11×C22⋊C4C2×D412yes—
296C42×C11—22no—
297C42×C11—22no—
298C42×C11C2×D411yescharacteristic
299C42×C11C2×D411yescharacteristic
300C42×C11C2411yescharacteristic
301C42×C11C2411yescharacteristic
302C22⋊Dic11—22no—
303C22⋊Dic11—22no—
304C22⋊Dic11—22no—
305C22⋊Dic11—22no—
306C22⋊Dic11—22no—
307#4326—28no—
308#4326—44no—
309#4325—28no—
310#4325—44no—
311#4324—44no—
312#4323—44no—
313(C2×D11)⋊C4—22no—
314(C2×D11)⋊C4—22no—
315(C2×D11)⋊C4—22no—
316(C2×D11)⋊C4—22no—
317C4⋊Dic11—21no—
318C4⋊Dic11—21no—
319C4⋊Dic11—21no—
320C4⋊Dic11—21no—
321C4⋊Dic11C2412yes—
322C4⋊Dic11C2412yes—
323Dic11⋊C4—22no—
324Dic11⋊C4—22no—
325Dic11⋊C4—22no—
326Dic11⋊C4—22no—
327C4×Dic11—22no—
328C4×Dic11—22no—
329C4×Dic11—22no—
330#4318—44no—
331C2×C11⋊C8—44no—
332C2×C11⋊C8C2414yes—
333C2×C11⋊C8C2414yes—
334#3506—111no—
335C2×#548D1111yescharacteristic, complemented
336#3321—114no—
337#3313—114no—
338#3271—114no—
339#3269—114no—
340#3215—111no—
341#3213—111no—
342#3194—112no—
343#3190—112no—
344#3113—111no—
345#3112—111no—
346#3004—112no—
347#3002—112no—
348#2973—111no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—42no—
357C23×C11—42no—
358C23×C11—42no—
359C23×C11C22×D412yes—
360C23×C11C22×D412yes—
361C23×C11C22×D411yescharacteristic
362C22×D11—22no—
363Q8×C11—24no—
364Q8×C11—22no—
365Q8×C11—24no—
366Q8×C11—48no—
367Q8×C11—42no—
368Q8×C11H(5,𝔽2)14yes—
369D4×C11—24no—
370D4×C11—42no—
371D4×C11—42no—
372D4×C11—48no—
373D4×C11—42no—
374D4×C11—48no—
375C2×C4×C11—24no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—24no—
379C2×C4×C11—24no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—41no—
384C2×C4×C11—42no—
385C2×C4×C11—41no—
386C2×C4×C11—42no—
387C2×C4×C11—41no—
388C2×C4×C11—48no—
389C2×C4×C11—48no—
390C2×C4×C11—42no—
391C2×C4×C11—42no—
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C22×D412yes—
394C2×C4×C11C22×D412yes—
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C2511yescharacteristic
400C22⋊D11—44no—
401C22⋊D11—82no—
402C22⋊D11—82no—
403C22⋊D11—82no—
404C22⋊D11—82no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408D44—24no—
409D44—42no—
410D44—81no—
411C4×D11—44no—
412C4×D11—82no—
413C4×D11—82no—
414Dic22—24no—
415Dic22—42no—
416Dic22—81no—
417C11⋊C8—24no—
418C11⋊C8—24no—
419C22×#41C2×D1111yescharacteristic
420C23×Q8C2×D1111yescharacteristic
421C2×#137—114no—
422C2×#135—114no—
423#559—222no—
424#556—112no—
425#555—112no—
426#553—222no—
427#550—112no—
428#548—22no—
429#548—22no—
430#548C2×D1114yes—
431#548C2×D1114yes—
432#547—112no—
433#538—221no—
434#538—221no—
435#535—221no—
436#533—111no—
437#532—111no—
438C2×#124—21no—
439C2×#124C2×D1111yescharacteristic
440#525—112no—
441#525—112no—
442C2×C22⋊Q8—21no—
443C2×C22⋊Q8C2×D1111yescharacteristic
444C2×#121—21no—
445C2×#121C2×D1111yescharacteristic
446#520—221no—
447C2×C4×Q8C2×D1111yescharacteristic
448C2×C4×D4—21no—
449C2×C4×D4C2×D1111yescharacteristic
450#497—112no—
451#496—112no—
452#489—112no—
453#489—112no—
454#485—114no—
455#483—112no—
456#482—114no—
457#480—112no—
458#477—112no—
459#475—112no—
460#469—114no—
461#468—114no—
462#467—114no—
463#465—114no—
464#464—114no—
465#463—114no—
466#462—112no—
467#460—112no—
468#452—114no—
469#452—114no—
470#451—112no—
471#451—112no—
472#451—114no—
473#450—112no—
474#449—114no—
475#449—114no—
476#448—112no—
477#448—112no—
478#448—114no—
479#447—112no—
480#441—114no—
481#440—114no—
482#435—114no—
483#435—114no—
484#432—111no—
485#432—111no—
486#419—114no—
487#416—114no—
488#407—112no—
489C2×C22⋊C8—112no—
490C22×C11—21no—
491C22×C11—21no—
492C22×C11—22no—
493C22×C11—22no—
494C22×C11—22no—
495C22×C11—22no—
496C22×C11—22no—
497C22×C11—22no—
498C22×C11—44no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—82no—
503C22×C11—84no—
504C22×C11#57512yes—
505C22×C11C23×D411yescharacteristic
506C2×D11—42no—
507C2×D11—42no—
508C2×D11—42no—
509C4×C11—21no—
510C4×C11—21no—
511C4×C11—24no—
512C4×C11—22no—
513C4×C11—21no—
514C4×C11—22no—
515C4×C11—21no—
516C4×C11—21no—
517C4×C11—42no—
518C4×C11—42no—
519C4×C11C2×H(5,𝔽2)12yes—
520Dic11—42no—
521Dic11—42no—
522Dic11—42no—
523C2×#41—22no—
524C2×#41—44no—
525C2×#41—112no—
526C2×#41—112no—
527C2×#41—221no—
528C2×#41C22×D1114yes—
529C22×Q8—21no—
530C22×Q8—22no—
531C22×Q8—44no—
532C22×Q8C22×D1111yescharacteristic
533C22×Q8C22×D1114yes—
534C22×Q8C22×D1111yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4C22⋊D1111yescharacteristic
538C22×D4C22×D1111yescharacteristic
539C23×C4—21no—
540C23×C4—21no—
541C23×C4C22×D1111yescharacteristic
542C23×C4C22×D1111yescharacteristic
543#137—448no—
544#135—448no—
545C2×Q16—114no—
546C2×Q16—114no—
547C2×SD16—114no—
548C2×SD16—114no—
549C2×SD16—114no—
550C2×D8—114no—
551C2×M16—114no—
552C22×C8—114no—
553C4⋊Q8—111no—
554C4⋊Q8—111no—
555C4⋊Q8—111no—
556#127—111no—
557#127—222no—
558#126—222no—
559#126—222no—
560#125—221no—
561#124—24no—
562#124—24no—
563#124—21no—
564#124—21no—
565#124—222no—
566#124—222no—
567#124—222no—
568#124—221no—
569#124C22×D1112yes—
570#124C22×D1112yes—
571#123—222no—
572#123—222no—
573#123—222no—
574#123—222no—
575C22⋊Q8—22no—
576C22⋊Q8—24no—
577C22⋊Q8—24no—
578C22⋊Q8—112no—
579C22⋊Q8—112no—
580C22⋊Q8—112no—
581C22⋊Q8—221no—
582C22⋊Q8C22×D1114yes—
583#121—24no—
584#121—24no—
585#121—22no—
586#121—112no—
587#121—112no—
588#121—112no—
589#121—222no—
590#121—222no—
591#121—221no—
592#121—222no—
593#121—222no—
594#121C22×D1114yes—
595#120—222no—
596#120—222no—
597C4×Q8—21no—
598C4×Q8—21no—
599C4×Q8—112no—
600C4×Q8—222no—
601C4×Q8—221no—
602C4×Q8C22×D1112yes—
603C4×Q8C22×D1112yes—
604C4×D4—24no—
605C4×D4—24no—
606C4×D4—112no—
607C4×D4—222no—
608C4×D4—222no—
609C4×D4—222no—
610C4×D4—222no—
611C4×D4—222no—
612C4×D4—221no—
613C4×D4C22⋊D1112yes—
614C4×D4C22⋊D1112yes—
615C4×D4C22×D1112yes—
616C4×D4C22×D1112yes—
617#117—112no—
618#117—112no—
619#117—221no—
620#117—222no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—222no—
624C2×C4⋊C4C22⋊D1111yescharacteristic
625C2×C4⋊C4C22×D1111yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4C22⋊D1111yescharacteristic
631C2×C22⋊C4C22⋊D1111yescharacteristic
632C2×C42—21no—
633C2×C42C22×D1111yescharacteristic
634#107—114no—
635#106—114no—
636C4⋊C8—112no—
637C4⋊C8—112no—
638#103—114no—
639#103—114no—
640#103—114no—
641#103—114no—
642#103—114no—
643#102—114no—
644#102—114no—
645#102—114no—
646C22⋊C8—112no—
647C22⋊C8—112no—
648C22⋊C8—114no—
649C22⋊C8—114no—
650#97—112no—
651#97—112no—
652C2×C11—22no—
653C2×C11—42no—
654C2×C11—42no—
655C2×C11—82no—
656C2×C11#348411yescharacteristic
657C2×C11C2×#57511yescharacteristic
658C2×C11#358611yescharacteristic
659D11—82no—
660C24—21no—
661C24C2×C22⋊D1111yescharacteristic
662C24C2×C22⋊D1111yescharacteristic
663#41—28no—
664#41—44no—
665#41—48no—
666#41—444no—
667#41—444no—
668#41—444no—
669C2×Q8—24no—
670C2×Q8—21no—
671C2×Q8—24no—
672C2×Q8—21no—
673C2×Q8—28no—
674C2×Q8—44no—
675C2×Q8—42no—
676C2×Q8—44no—
677C2×Q8—48no—
678C2×Q8—112no—
679C2×Q8—221no—
680C2×Q8—221no—
681C2×Q8C23×D1112yes—
682C2×Q8C23×D1112yes—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—21no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—112no—
691C2×D4—222no—
692C2×D4—222no—
693C2×D4—222no—
694C2×D4—222no—
695C2×D4—222no—
696C2×D4—221no—
697C2×D4—221no—
698C2×D4C2×C22⋊D1112yes—
699C2×D4C2×C22⋊D1112yes—
700C2×D4C23×D1112yes—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—42no—
707C22×C4—42no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—222no—
711C22×C4—222no—
712C22×C4—222no—
713C22×C4C2×C22⋊D1111yescharacteristic
714C22×C4C2×C22⋊D1111yescharacteristic
715C22×C4C2×C22⋊D1111yescharacteristic
716C22×C4C2×C22⋊D1111yescharacteristic
717C22×C4C2×C22⋊D1112yes—
718C22×C4C2×C22⋊D1112yes—
719C22×C4C23×D1111yescharacteristic
720C22×C4C23×D1112yes—
721C22×C4C23×D1112yes—
722Q16—228no—
723Q16—444no—
724SD16—228no—
725SD16—444no—
726SD16—444no—
727D8—444no—
728M16—444no—
729C2×C8—114no—
730C2×C8—114no—
731C2×C8—444no—
732C4⋊C4—24no—
733C4⋊C4—22no—
734C4⋊C4—22no—
735C4⋊C4—21no—
736C4⋊C4—112no—
737C4⋊C4—112no—
738C4⋊C4—221no—
739C4⋊C4—222no—
740C4⋊C4—222no—
741C4⋊C4—221no—
742C4⋊C4—222no—
743C4⋊C4—221no—
744C4⋊C4—222no—
745C4⋊C4—221no—
746C4⋊C4C2×C22⋊D1112yes—
747C4⋊C4C2×C22⋊D1112yes—
748C4⋊C4C23×D1112yes—
749C22⋊C4—24no—
750C22⋊C4—22no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—22no—
754C22⋊C4—24no—
755C22⋊C4—222no—
756C22⋊C4—222no—
757C22⋊C4—222no—
758C22⋊C4—222no—
759C22⋊C4—222no—
760C22⋊C4—222no—
761C22⋊C4—222no—
762C22⋊C4—222no—
763C22⋊C4—222no—
764C22⋊C4C2×C22⋊D1112yes—
765C22⋊C4C2×C22⋊D1112yes—
766C22⋊C4C2×C22⋊D1112yes—
767C22⋊C4C2×C22⋊D1112yes—
768C42—22no—
769C42—22no—
770C42—222no—
771C42—222no—
772C42—222no—
773C42C2×C22⋊D1111yescharacteristic
774C42C2×C22⋊D1111yescharacteristic
775C42C23×D1111yescharacteristic
776C42C23×D1111yescharacteristic
777C11#6157811yescharacteristic, complemented, Sylow
778C23—22no—
779C23—22no—
780C23—22no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—222no—
789C23C22×C22⋊D1112yes—
790C23C22×C22⋊D1112yes—
791C23C22×C22⋊D1111yescharacteristic
792Q8—24no—
793Q8—22no—
794Q8—24no—
795Q8—48no—
796Q8—42no—
797Q8—224no—
798Q8—442no—
799Q8—881no—
800Q8#6703714yes—
801D4—24no—
802D4—42no—
803D4—42no—
804D4—48no—
805D4—42no—
806D4—48no—
807D4—224no—
808D4—442no—
809D4—444no—
810D4—881no—
811D4—882no—
812D4—882no—
813D4—882no—
814D4—882no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—41no—
828C2×C4—48no—
829C2×C4—48no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—444no—
836C2×C4—882no—
837C2×C4—882no—
838C2×C4C22×C22⋊D1111yescharacteristic
839C2×C4C22×C22⋊D1111yescharacteristic
840C2×C4C22×C22⋊D1111yescharacteristic
841C2×C4C22×C22⋊D1112yes—
842C2×C4C22×C22⋊D1112yes—
843C2×C4C22×C22⋊D1111yescharacteristic
844C2×C4C22×C22⋊D1111yescharacteristic
845C2×C4C24×D1111yescharacteristic
846C8—224no—
847C8—224no—
848C22—21no—
849C22—21no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—44no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—82no—
861C22—84no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22#1062335312yes—
866C22C23×C22⋊D1111yescharacteristic
867C4—21no—
868C4—21no—
869C4—24no—
870C4—22no—
871C4—21no—
872C4—22no—
873C4—21no—
874C4—21no—
875C4—42no—
876C4—42no—
877C4—442no—
878C4—442no—
879C4—442no—
880C4C2×#6703712yes—
881C2—22no—
882C2—42no—
883C2—42no—
884C2—82no—
885C2—882no—
886C2#1308225111yescharacteristic
887C2C2×#1062335311yescharacteristic
888C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#548C2
socleC22×C11C23×D4
hypercenterC2×#548D11
hypocenterC11#61578
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #13082468C2semidirect
2. #13080802C2semidirect
3. #13080682C2semidirect
4. #13080202C2semidirect
5. #13080172C2semidirect
6. #13079619C2semidirect
7. #13079603C2semidirect
8. #13079430C2semidirect
9. #13079397C2semidirect
10. #13078746C2semidirect
11. #13078738C2semidirect
12. #13077850C2semidirect
13. #13077834C2semidirect
14. #13077645C2semidirect
15. C2×C11×#548C2semidirect
31. C2×#67003C22semidirect
32. C2×#66995C22semidirect
36. #10623094C22semidirect
39. #10623084C22semidirect
40. #10623082C22semidirect
41. #10623073C22semidirect
47. #10622852C22semidirect
48. #10622851C22semidirect
49. #10622846C22semidirect
52. #10622841C22semidirect
55. #10622840C22semidirect
56. #10622838C22semidirect
61. #10622673C22semidirect
62. #10622671C22semidirect
63. #10622670C22semidirect
64. #10622668C22semidirect
65. #10622668C22semidirect
66. #10622667C22semidirect
67. #10622664C22semidirect
68. #10622661C22semidirect
69. #10622660C22semidirect
70. #10622658C22semidirect
71. #10622655C22semidirect
72. #10622652C22semidirect
73. #10622650C22semidirect
74. #10622648C22semidirect
75. #10622644C22semidirect
76. #10622643C22semidirect
77. #10622640C22semidirect
78. #10622639C22semidirect
79. #10622634C22semidirect
80. #10622633C22semidirect
81. #10622624C22semidirect
82. #10622624C22semidirect
335. C2×#548D11semidirect
777. C11#61578semidirect

Maximal subgroups

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

subgroupindex
#130824682
#130808022
#130806822
#130802022
#130801722
#130796192
#130796032
#130794302
#130793972
#130787462
#130787382
#130778502
#130778342
#130776452
C2×C11×#5482
#6157811