Finite Group Databasebeta

← #15662067

Subgroups — #15662067

Order 2816.

7190 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082727C214yesmaximal, complemented
2#13082717C214yesmaximal, complemented
3#13082627C214yesmaximal, complemented
4#13082616C214yesmaximal, complemented
5#13082461C216yesmaximal, complemented
6#13082422C211yesmaximal, characteristic, complemented
7#13082383C211yesmaximal, characteristic, complemented
8#13082329C216yesmaximal, complemented
9#13082275C211yesmaximal, characteristic, complemented
10#13082271C211yesmaximal, characteristic, complemented
11#13082242C214yesmaximal, complemented
12#13082233C214yesmaximal, complemented
13#13082214C214yesmaximal, complemented
14#13082211C214yesmaximal, complemented
15#13082032C216yesmaximal, complemented
16#13081909C216yesmaximal, complemented
17C4×#67040C211yesmaximal, characteristic, complemented
18C2×C4×#4343C211yesmaximal, characteristic, complemented
19C4×C11×2−1+4C211yesmaximal, characteristic, complemented
20C2×C11×2−1+4C2211yescharacteristic
21C2×#67040C2211yescharacteristic
22C22×#4343C2211yescharacteristic
23C11×#520C2216yes—
24C11×#520C2214yescomplemented
25C11×#519C2211yescharacteristic
26C11×#519C2214yescomplemented
27C4×C11×#41C2216yes—
28C4×C11×#41C2214yescomplemented
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×Q8×C11C2214yescomplemented
31#10623365C2214yes—
32#10623365C2214yes—
33#10623365C2214yescomplemented
34#10623364C2216yes—
35#10623363C2216yes—
36#10623362C2214yescomplemented
37#10623361C2216yes—
38#10623359C2216yes—
39#10623348C2214yes—
40#10623348C2214yes—
41#10623348C2214yescomplemented
42Q8×C22⋊D11C2214yescomplemented
43#10623343C2211yescharacteristic
44C2×Q8×Dic11C2211yescharacteristic
45#10623116C22112yescomplemented
46#10623115C22112yescomplemented
47#10623113C22112yescomplemented
48#10623112C22112yescomplemented
49#10623111C2216yescomplemented
50#10623111C2216yescomplemented
51#10623111C22112yescomplemented
52#10623109C2216yescomplemented
53#10623109C2216yescomplemented
54#10623108C2214yes—
55#10623108C2214yes—
56#10623107C2214yes—
57#10623107C2214yes—
58#10623105C2214yescomplemented
59C4×#4343C2214yes—
60C4×#4343C2214yes—
61C4×#4343C2214yes—
62C4×#4343C2214yes—
63C4×#4343C2214yescomplemented
64#10623103C2214yescomplemented
65C4×Q8×D11C2214yescomplemented
66#10623101C2214yescomplemented
67#10623100C2214yescomplemented
68#10623100C2214yescomplemented
69#10623099C22112yescomplemented
70Q8×Dic22C2214yescomplemented
71#10623094C22112yescomplemented
72#10623093C22112yescomplemented
73#10623091C22124yes—
74#10623090C22112yescomplemented
75#10623089C22112yescomplemented
76#10623088C2216yescomplemented
77#10623088C2216yescomplemented
78#10623084C22112yescomplemented
79#10623079C2216yescomplemented
80#10623079C2216yescomplemented
81#10623079C22112yescomplemented
82#10623078C22112yes—
83#10623078C22112yes—
84#10623069C2214yes—
85#10623069C22112yes—
86#10623066C22112yescomplemented
87#10623065C22112yescomplemented
88#10623064C22112yescomplemented
89#10623063C22112yescomplemented
90#10623063C22112yescomplemented
91#10623061C22112yescomplemented
92#10623059C22112yescomplemented
93#10623059C22112yescomplemented
94#10623056C2216yes—
95#10623055C2216yes—
96#10623050C2216yes—
97#10623048C2216yes—
98#10623045C22112yescomplemented
99#10623045C22112yescomplemented
100#10623044C22112yescomplemented
101#10623038C22112yescomplemented
102#10623035C2216yes—
103C2×#66946C2213yes—
104C2×#66945C2213yes—
105#10623010C22112yescomplemented
106#10623008C22112yescomplemented
107C4×#4339C2216yes—
108C4×#4339C22112yescomplemented
109C4×#4339C22112yescomplemented
110C2×C4×D44C2213yes—
111C2×C42×D11C2213yes—
112C11×2−1+4—28no—
113C2×C11×#41C2316yes—
114C2×C11×#41C2314yes—
115C22×Q8×C11C2314yes—
116C22×Q8×C11C2311yescharacteristic
117#67040—28no—
118C2×#4343—28no—
119C2×#4343C2314yes—
120C2×#4343C2314yes—
121C2×#4343C2314yes—
122C2×Q8×D11C2314yes—
123C2×#4339C2316yes—
124C2×#4339C23112yes—
125C2×#4339C23112yes—
126C22×D44C2313yes—
127C22×C4×D11C2313yes—
128C22×C4×D11C2313yes—
129C22×C4×D11C2313yes—
130C4×Q8×C11C2314yes—
131C4×Q8×C11C23112yes—
132C4×Q8×C11C2314yes—
133C4×Q8×C11C2314yes—
134C4×Q8×C11C2314yes—
135C4×Q8×C11C2316yes—
136C4×Q8×C11C2316yes—
137C4×D4×C11C2314yes—
138C4×D4×C11C23112yes—
139C4×D4×C11C2316yes—
140C4×D4×C11C2316yes—
141C4×D4×C11C23112yes—
142C11×#117C2316yes—
143C11×#117C23112yes—
144C11×#117C23112yes—
145C2×C11×C4⋊C4C2313yes—
146C2×C11×C4⋊C4C23112yes—
147C2×C42×C11C2313yes—
148C2×C42×C11C23112yes—
149#67000C23112yes—
150#67000C2316yes—
151#66999C23112yes—
152#66999C2316yes—
153#66999C2316yes—
154Q8×Dic11C2314yes—
155Q8×Dic11C2314yes—
156Q8×Dic11C2314yes—
157Q8×Dic11C2314yes—
158#66997C2316yes—
159#66993C2316yes—
160#66993C23112yes—
161#66992C2314yes—
162#66992C23112yes—
163#66991C2316yes—
164#66991C2316yes—
165#66991C23112yes—
166#66990C23112yes—
167#66989C2316yes—
168#66988C2314yes—
169#66983C23124yes—
170#66983C23112yes—
171#66983C23112yes—
172#66983C23112yes—
173#66982C23124yes—
174C4×C22⋊D11C2314yes—
175C4×C22⋊D11C23112yes—
176C4×C22⋊D11C2314yes—
177C4×C22⋊D11C23112yes—
178C4×C22⋊D11C23112yes—
179C4×C22⋊D11C23112yes—
180C4×C22⋊D11C23112yes—
181C4×C22⋊D11C23112yes—
182C4×C22⋊D11C23112yes—
183C4×C22⋊D11C23112yes—
184C2×(C2×D11)⋊C4C2316yes—
185#66979C2316yes—
186#66979C2314yes—
187#66979C23112yes—
188C2×C4⋊Dic11C2313yes—
189#66977C23112yes—
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2313yes—
192C2×C4×Dic11C2313yes—
193#66951C23124yes—
194#66951C23112yes—
195#66951C2314yes—
196#66950C2316yes—
197#66950C2316yes—
198#66949C23112yes—
199#66949C23112yes—
200#66948C23112yes—
201#66948C2316yes—
202#66948C2316yes—
203#66948C23112yes—
204#66947C23124yes—
205#66947C23112yes—
206#66947C23112yes—
207#66946C23112yes—
208#66946C23112yes—
209#66946C23112yes—
210#66945C23112yes—
211#66945C23112yes—
212#66945C23112yes—
213C4⋊C4×D11C23112yes—
214#66943C23112yes—
215#66943C2316yes—
216#66943C2316yes—
217#66942C23112yes—
218#66942C2314yes—
219#66941C2316yes—
220#66941C2316yes—
221#66941C23112yes—
222#66940C23112yes—
223#66939C2314yes—
224#66938C2314yes—
225#66938C23112yes—
226#66938C23124yes—
227#66937C23112yes—
228#66937C23112yes—
229#66937C23124yes—
230#66936C23112yes—
231#66936C23112yes—
232#66935C23112yes—
233#66932C2314yes—
234#66932C23112yes—
235#66931C2314yes—
236#66931C23112yes—
237#66929C23124yes—
238#66928C23124yes—
239#66928C23112yes—
240#66927C23112yes—
241C4×D44C23112yes—
242C4×D44C23112yes—
243C4×D44C2316yes—
244C4×D44C2316yes—
245C4×D44C23112yes—
246C4×D44C23112yes—
247C4×D44C23112yes—
248C4×D44C23112yes—
249#66925C23112yes—
250#66925C2314yes—
251#66925C23112yes—
252#66925C23112yes—
253#66925C23112yes—
254C42×D11C2316yes—
255C42×D11C2316yes—
256C42×D11C2316yes—
257C42×D11C2316yes—
258C42×D11C23112yes—
259#66923C23112yes—
260#66922C23112yes—
261C4×Dic22C2316yes—
262C4×Dic22C2316yes—
263C4×Dic22C2314yes—
264C4×Dic22C23112yes—
265C4×Dic22C23112yes—
266C4×Dic22C23112yes—
267#62793—111nomaximal, Sylow
268C23×D11C2413yes—
269C11×#41—216no—
270C11×#41—224no—
271C2×Q8×C11—216no—
272C2×Q8×C11#4118yescomplemented
273C2×Q8×C11C2416yes—
274C2×Q8×C11C2414yes—
275C2×D4×C11C2414yes—
276C2×D4×C11C2416yes—
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C24112yes—
279C22×C4×C11C2414yes—
280C22×C4×C11C2413yes—
281C22×C4×C11C24112yes—
282C22×C4×C11C2413yes—
283C2×C22⋊D11C2414yes—
284C2×C22⋊D11C2414yes—
285C2×C22⋊D11C24112yes—
286C2×C22⋊D11C24112yes—
287C2×C22⋊D11C24112yes—
288C22×Dic11C2411yescharacteristic
289C22×Dic11C2411yescharacteristic
290C22×Dic11C2413yes—
291#4343—216no—
292#4343—216no—
293#4343—216no—
294Q8×D11—216no—
295#4339—224no—
296#4339—424no—
297#4339—424no—
298C2×D44—212no—
299C2×D44C2416yes—
300C2×D44C24112yes—
301C2×D44C24112yes—
302C2×D44C24112yes—
303C2×C4×D11—212no—
304C2×C4×D11—46no—
305C2×C4×D11—46no—
306C2×C4×D11C2414yes—
307C2×C4×D11C2416yes—
308C2×C4×D11C2416yes—
309C2×C4×D11C2416yes—
310C2×C4×D11C2416yes—
311C2×C4×D11C24112yes—
312C2×C4×D11C2416yes—
313C2×C4×D11C2416yes—
314C2×C4×D11C24112yes—
315C2×Dic22C2414yes—
316C2×Dic22C2416yes—
317C2×Dic22C24112yes—
318C11×C4⋊C4C24112yes—
319C11×C4⋊C4C2416yes—
320C11×C4⋊C4C2416yes—
321C11×C4⋊C4C2414yes—
322C11×C4⋊C4C24112yes—
323C11×C22⋊C4C2414yes—
324C11×C22⋊C4C2414yes—
325C11×C22⋊C4C24112yes—
326C42×C11C24112yes—
327C42×C11C2416yes—
328C42×C11C2416yes—
329C42×C11C2414yes—
330C42×C11C24112yes—
331C22⋊Dic11C2414yes—
332C22⋊Dic11C2414yes—
333C22⋊Dic11C2414yes—
334C22⋊Dic11C24112yes—
335C22⋊Dic11C2414yes—
336(C2×D11)⋊C4C2414yes—
337(C2×D11)⋊C4C2414yes—
338(C2×D11)⋊C4C2414yes—
339(C2×D11)⋊C4C2414yes—
340(C2×D11)⋊C4C24112yes—
341(C2×D11)⋊C4C24112yes—
342(C2×D11)⋊C4C24112yes—
343(C2×D11)⋊C4C24112yes—
344(C2×D11)⋊C4C24112yes—
345(C2×D11)⋊C4C24112yes—
346(C2×D11)⋊C4C24124yes—
347C4⋊Dic11C2414yes—
348C4⋊Dic11C2414yes—
349C4⋊Dic11C24112yes—
350C4⋊Dic11C2416yes—
351C4⋊Dic11C2416yes—
352C4⋊Dic11C2414yes—
353C4⋊Dic11C24112yes—
354Dic11⋊C4C2414yes—
355Dic11⋊C4C2414yes—
356Dic11⋊C4C2414yes—
357Dic11⋊C4C2414yes—
358Dic11⋊C4C24112yes—
359Dic11⋊C4C24112yes—
360Dic11⋊C4C2414yes—
361Dic11⋊C4C2414yes—
362Dic11⋊C4C24112yes—
363Dic11⋊C4C24112yes—
364C4×Dic11C2411yescharacteristic
365C4×Dic11C2414yes—
366C4×Dic11C2416yes—
367C4×Dic11C2416yes—
368C4×Dic11C2416yes—
369C4×Dic11C24112yes—
370C4×Dic11C24112yes—
371C4×Dic11C2411yescharacteristic
372C4×Dic11C2411yescharacteristic
373C4×Dic11C2411yescharacteristic
374C4×Dic11C2416yes—
375#3524—114no—
376#3524—114no—
377#3518—114no—
378#3517—114no—
379#3506—116no—
380#3502—111no—
381#3497—111no—
382#3493—116no—
383#3487—111no—
384#3487—111no—
385#3483—114no—
386#3482—114no—
387#3480—114no—
388#3480—114no—
389#3460—116no—
390#3444—116no—
391C4×2−1+4—111no—
392C4×2−1+4D1111yescharacteristic, complemented
393C2×C4×#41—111no—
394C23×C11C2514yes—
395C23×C11C2511yescharacteristic
396C22×D11—26no—
397C22×D11—43no—
398C22×D11—43no—
399C22×D11C2516yes—
400C22×D11C2514yes—
401Q8×C11—212no—
402Q8×C11C2×#41116yes—
403D4×C11—28no—
404D4×C11—212no—
405C2×C4×C11—224no—
406C2×C4×C11—22no—
407C2×C4×C11—28no—
408C2×C4×C11—43no—
409C2×C4×C11—412no—
410C2×C4×C11C2×#41112yes—
411C2×C4×C11C2516yes—
412C2×C4×C11C2511yescharacteristic
413C2×C4×C11C2514yes—
414C2×C4×C11C2514yes—
415C2×C4×C11C2514yes—
416C2×C4×C11C2516yes—
417C2×C4×C11C2511yescharacteristic
418C22⋊D11—28no—
419C22⋊D11—28no—
420C22⋊D11—412no—
421C22⋊D11—412no—
422C22⋊D11—412no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—43no—
426C2×Dic11C2511yescharacteristic
427C2×Dic11C2511yescharacteristic
428C2×Dic11C2511yescharacteristic
429C2×Dic11C2514yes—
430C2×Dic11C2514yes—
431C2×Dic11C2514yes—
432C2×Dic11C2516yes—
433C2×Dic11C2511yescharacteristic
434D44—224no—
435D44—212no—
436D44—412no—
437D44—412no—
438C4×D11—212no—
439C4×D11—212no—
440C4×D11—224no—
441C4×D11—212no—
442C4×D11—28no—
443C4×D11—212no—
444C4×D11—46no—
445C4×D11—46no—
446C4×D11—412no—
447Dic22—212no—
448Dic22—28no—
449Dic22—412no—
450C2×2−1+4—111no—
451C2×2−1+4C2×D1111yescharacteristic
452C22×#41—111no—
453#559—1112no—
454#559—1112no—
455Q82—114no—
456#557—114no—
457#557—114no—
458#557—114no—
459#556—1112no—
460#556—1112no—
461#556—1112no—
462#555—1112no—
463#555—1112no—
464#555—1112no—
465#553—1112no—
466#553—1112no—
467#553—1112no—
468#553—1112no—
469#552—1112no—
470#552—1112no—
471#550—114no—
472#550—114no—
473#550—114no—
474#550—114no—
475#550—114no—
476#550—1112no—
477D4×Q8—114no—
478#548—114no—
479#548—114no—
480#548—114no—
481#548—114no—
482#548—114no—
483#548—114no—
484#547—1112no—
485#544—116no—
486#542—1112no—
487#542—1112no—
488#540—1112no—
489#540—1112no—
490#538—1124no—
491#537—116no—
492#535—116no—
493#535—116no—
494#533—116no—
495#533—116no—
496#533—116no—
497#532—116no—
498#532—116no—
499#532—116no—
500#532—1112no—
501#532—1112no—
502#529—116no—
503#529—116no—
504#529—1112no—
505#529—114no—
506#529—1112no—
507#529—116no—
508#529—116no—
509#529—1112no—
510#529—1112no—
511#529—1112no—
512#525—116no—
513#525—1112no—
514#525—1112no—
515#525—116no—
516#520—114no—
517#520—116no—
518#520C2×D1116yes—
519#520C2×D1114yescomplemented
520#519—111no—
521#519—114no—
522#519C2×D1111yescharacteristic
523#519C2×D1114yescomplemented
524C4×#41—114no—
525C4×#41—114no—
526C4×#41—114no—
527C4×#41—114no—
528C4×#41—114no—
529C4×#41—116no—
530C4×#41—1112no—
531C4×#41—1112no—
532C4×#41C2×D1116yes—
533C4×#41C2×D1114yescomplemented
534C2×C4×Q8—111no—
535C2×C4×Q8—114no—
536C2×C4×Q8C2×D1111yescharacteristic
537C2×C4×Q8C2×D1114yescomplemented
538C2×C4×D4—113no—
539C2×C4×D4—113no—
540C2×#117—113no—
541C22×C42—113no—
542C22×C11—21no—
543C22×C11—21no—
544C22×C11—24no—
545C22×C11—24no—
546C22×C11—24no—
547C22×C11C22×#4112yes—
548C22×C11C2611yescharacteristic
549C2×D11—26no—
550C2×D11—24no—
551C2×D11—26no—
552C2×D11—26no—
553C2×D11—24no—
554C2×D11—24no—
555C2×D11—412no—
556C4×C11—24no—
557C4×C11—24no—
558C4×C11—21no—
559C4×C11—24no—
560C4×C11—26no—
561C4×C11C22×#41112yes—
562C4×C11#58512yes—
563Dic11—24no—
564Dic11—21no—
565Dic11—21no—
566Dic11—24no—
567Dic11—24no—
568Dic11—26no—
569Dic11—21no—
570Dic11#58512yes—
5712−1+4—28no—
5722−1+4—228no—
573C2×#41—114no—
574C2×#41—114no—
575C2×#41—114no—
576C2×#41—116no—
577C2×#41—1112no—
578C2×#41—1112no—
579C2×#41—228no—
580C2×#41C22×D1116yes—
581C2×#41C22×D1114yes—
582C22×Q8—114no—
583C22×Q8C22×D1114yes—
584C22×Q8C22×D1111yescharacteristic
585C22×D4—113no—
586C23×C4—113no—
587C23×C4—113no—
588C23×C4—113no—
589C4⋊Q8—116no—
590C4⋊Q8—116no—
591C4⋊Q8—116no—
592C4⋊Q8—1112no—
593C4⋊Q8—1112no—
594#127—116no—
595#127—1112no—
596#127—1112no—
597#126—114no—
598#126—1112no—
599#126—1124no—
600#126—114no—
601#126—1112no—
602#126—1124no—
603#125—114no—
604#125—1112no—
605#125—116no—
606#125—116no—
607#125—1112no—
608#125—1112no—
609#124—116no—
610#124—1112no—
611#124—116no—
612#124—114no—
613#124—1112no—
614#124—1124no—
615#124—1112no—
616#124—1124no—
617#123—114no—
618#123—1124no—
619#123—1112no—
620#123—1112no—
621#123—1124no—
622#123—114no—
623#123—1112no—
624#123—1112no—
625C22⋊Q8—116no—
626C22⋊Q8—116no—
627C22⋊Q8—1112no—
628C22⋊Q8—1112no—
629C22⋊Q8—1112no—
630C22⋊Q8—1112no—
631C22⋊Q8—116no—
632C22⋊Q8—116no—
633C22⋊Q8—114no—
634C22⋊Q8—1112no—
635#121—114no—
636#121—1112no—
637#121—116no—
638#121—116no—
639#121—1112no—
640#121—1112no—
641#121—1112no—
642#121—1112no—
643#121—1124no—
644#121—116no—
645#121—116no—
646#121—1112no—
647#121—1112no—
648#121—1112no—
649#121—1112no—
650#121—1124no—
651#120—1112no—
652#120—1112no—
653C4×Q8—114no—
654C4×Q8—114no—
655C4×Q8—114no—
656C4×Q8—114no—
657C4×Q8—1112no—
658C4×Q8—116no—
659C4×Q8—114no—
660C4×Q8—116no—
661C4×Q8—1112no—
662C4×Q8—1112no—
663C4×Q8—1112no—
664C4×Q8C22×D1114yes—
665C4×Q8C22×D1114yes—
666C4×Q8C22×D1116yes—
667C4×Q8C22×D1114yes—
668C4×Q8C22×D11112yes—
669C4×Q8C22×D1116yes—
670C4×Q8C22×D1114yes—
671C4×D4—114no—
672C4×D4—114no—
673C4×D4—1112no—
674C4×D4—1112no—
675C4×D4—1112no—
676C4×D4—1112no—
677C4×D4—1112no—
678C4×D4—1112no—
679C4×D4—1112no—
680C4×D4—1112no—
681C4×D4—1112no—
682C4×D4—1112no—
683C4×D4—1112no—
684C4×D4—1112no—
685C4×D4—1112no—
686C4×D4—116no—
687C4×D4—116no—
688C4×D4—1112no—
689C4×D4—1112no—
690C4×D4—1112no—
691C4×D4—1112no—
692C4×D4C22×D1114yes—
693C4×D4C22×D1116yes—
694C4×D4C22×D11112yes—
695C4×D4C22×D1116yes—
696C4×D4C22×D11112yes—
697#117—114no—
698#117—116no—
699#117—1112no—
700#117—1112no—
701#117—1112no—
702#117—1112no—
703#117—114no—
704#117—1112no—
705#117—1112no—
706#117—1112no—
707#117—1112no—
708#117C22×D1116yes—
709#117C22×D11112yes—
710#117C22×D11112yes—
711C2×C4⋊C4—113no—
712C2×C4⋊C4—1112no—
713C2×C4⋊C4C22×D1113yes—
714C2×C4⋊C4C22×D11112yes—
715C2×C22⋊C4—116no—
716C2×C42—113no—
717C2×C42—113no—
718C2×C42—111no—
719C2×C42—1112no—
720C2×C42—116no—
721C2×C42—116no—
722C2×C42—116no—
723C2×C42—116no—
724C2×C42C22×D1113yes—
725C2×C42C22×D11112yes—
726C2×C11—22no—
727C2×C11—44no—
728C2×C11C23×#4111yescharacteristic
729C2×C11C2×#58511yescharacteristic
730C2×C11C2×#58511yescharacteristic
731D11—44no—
732D11—46no—
733C24—113no—
734#41—216no—
735#41—224no—
736#41—2216no—
737#41—2216no—
738#41—2216no—
739#41—2224no—
740#41—4424no—
741#41—4424no—
742C2×Q8—216no—
743C2×Q8—116no—
744C2×Q8—114no—
745C2×Q8—1112no—
746C2×Q8—2216no—
747C2×Q8#433918yescomplemented
748C2×Q8C23×D1116yes—
749C2×Q8C23×D1114yes—
750C2×D4—114no—
751C2×D4—114no—
752C2×D4—1112no—
753C2×D4—1112no—
754C2×D4—1112no—
755C2×D4—1112no—
756C2×D4—116no—
757C2×D4—1112no—
758C2×D4—1112no—
759C2×D4—2212no—
760C2×D4C23×D1114yes—
761C2×D4C23×D1116yes—
762C22×C4—111no—
763C22×C4—111no—
764C22×C4—113no—
765C22×C4—116no—
766C22×C4—116no—
767C22×C4—116no—
768C22×C4—1112no—
769C22×C4—114no—
770C22×C4—116no—
771C22×C4—116no—
772C22×C4—116no—
773C22×C4—1112no—
774C22×C4—2212no—
775C22×C4—446no—
776C22×C4—446no—
777C22×C4C23×D11112yes—
778C22×C4C23×D1111yescharacteristic
779C22×C4C23×D1114yes—
780C22×C4C23×D1113yes—
781C22×C4C23×D11112yes—
782C22×C4C23×D1113yes—
783C4⋊C4—116no—
784C4⋊C4—1112no—
785C4⋊C4—1112no—
786C4⋊C4—114no—
787C4⋊C4—114no—
788C4⋊C4—114no—
789C4⋊C4—114no—
790C4⋊C4—116no—
791C4⋊C4—114no—
792C4⋊C4—114no—
793C4⋊C4—114no—
794C4⋊C4—114no—
795C4⋊C4—114no—
796C4⋊C4—1112no—
797C4⋊C4—1112no—
798C4⋊C4—1112no—
799C4⋊C4—1112no—
800C4⋊C4C23×D11112yes—
801C4⋊C4C23×D1116yes—
802C4⋊C4C23×D11112yes—
803C4⋊C4C23×D1116yes—
804C4⋊C4C23×D1114yes—
805C22⋊C4—114no—
806C22⋊C4—114no—
807C22⋊C4—114no—
808C22⋊C4—114no—
809C22⋊C4—1112no—
810C22⋊C4—1124no—
811C22⋊C4—114no—
812C22⋊C4—114no—
813C22⋊C4—1112no—
814C22⋊C4—114no—
815C22⋊C4—114no—
816C22⋊C4—1112no—
817C22⋊C4—1112no—
818C22⋊C4—1112no—
819C22⋊C4—1112no—
820C22⋊C4—1112no—
821C22⋊C4C23×D1114yes—
822C22⋊C4C23×D1114yes—
823C22⋊C4C23×D11112yes—
824C42—111no—
825C42—111no—
826C42—116no—
827C42—116no—
828C42—116no—
829C42—116no—
830C42—1112no—
831C42—1112no—
832C42—111no—
833C42—111no—
834C42—114no—
835C42C23×D1116yes—
836C42C23×D11112yes—
837C42C23×D11112yes—
838C42C23×D1116yes—
839C42C23×D1114yes—
840C11#6279311yescharacteristic, complemented, Sylow
841C23—116no—
842C23—114no—
843C23—226no—
844C23—443no—
845C23—443no—
846C23C24×D1114yes—
847C23C24×D1111yescharacteristic
848Q8—212no—
849Q8—228no—
850Q8—2212no—
851Q8—4412no—
852Q8C2×#4339116yes—
853D4—28no—
854D4—212no—
855D4—228no—
856D4—228no—
857D4—2224no—
858D4—2212no—
859D4—4412no—
860D4—4412no—
861D4—4412no—
862D4—4412no—
863D4—4412no—
864C2×C4—224no—
865C2×C4—22no—
866C2×C4—28no—
867C2×C4—43no—
868C2×C4—412no—
869C2×C4—111no—
870C2×C4—111no—
871C2×C4—111no—
872C2×C4—111no—
873C2×C4—114no—
874C2×C4—114no—
875C2×C4—116no—
876C2×C4—114no—
877C2×C4—2212no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—2212no—
881C2×C4—2212no—
882C2×C4—2224no—
883C2×C4—2212no—
884C2×C4—228no—
885C2×C4—446no—
886C2×C4—446no—
887C2×C4—4412no—
888C2×C4—443no—
889C2×C4C2×#4339112yes—
890C2×C4C24×D1116yes—
891C2×C4C24×D1111yescharacteristic
892C2×C4C24×D1114yes—
893C2×C4C24×D1114yes—
894C2×C4C24×D1114yes—
895C2×C4C24×D1116yes—
896C2×C4C24×D1111yescharacteristic
897C22—21no—
898C22—21no—
899C22—24no—
900C22—24no—
901C22—24no—
902C22—224no—
903C22—226no—
904C22—226no—
905C22—224no—
906C22—226no—
907C22—224no—
908C22—4412no—
909C22C22×#433912yes—
910C22C25×D1111yescharacteristic
911C4—24no—
912C4—26no—
913C4—24no—
914C4—21no—
915C4—24no—
916C4—112no—
917C4—221no—
918C4—221no—
919C4—224no—
920C4—221no—
921C4—224no—
922C4—226no—
923C4—224no—
924C4C22×#4339112yes—
925C4#1062345712yes—
926C2—22no—
927C2—44no—
928C2—446no—
929C2—444no—
930C2C23×#433911yescharacteristic
931C2D11×#58511yescharacteristic
932C2C2×#1062345711yescharacteristic
subgroupG/H
centerC2×C4C24×D11
commutator, socle, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC4×C11×2−1+4C2
hypercenterC4×2−1+4D11
hypocenterC11#62793
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. #13082727C2semidirect
2. #13082717C2semidirect
3. #13082627C2semidirect
4. #13082616C2semidirect
5. #13082461C2semidirect
6. #13082422C2semidirect
7. #13082383C2semidirect
8. #13082329C2semidirect
9. #13082275C2semidirect
10. #13082271C2semidirect
11. #13082242C2semidirect
12. #13082233C2semidirect
13. #13082214C2semidirect
14. #13082211C2semidirect
15. #13082032C2semidirect
16. #13081909C2semidirect
17. C4×#67040C2semidirect
18. C2×C4×#4343C2semidirect
19. C4×C11×2−1+4C2semidirect
24. C11×#520C22semidirect
26. C11×#519C22semidirect
28. C4×C11×#41C22semidirect
30. C2×C4×Q8×C11C22semidirect
33. #10623365C22semidirect
36. #10623362C22semidirect
41. #10623348C22semidirect
42. Q8×C22⋊D11C22semidirect
45. #10623116C22semidirect
46. #10623115C22semidirect
47. #10623113C22semidirect
48. #10623112C22semidirect
49. #10623111C22semidirect
50. #10623111C22semidirect
51. #10623111C22semidirect
52. #10623109C22semidirect
53. #10623109C22semidirect
58. #10623105C22semidirect
63. C4×#4343C22semidirect
64. #10623103C22semidirect
65. C4×Q8×D11C22semidirect
66. #10623101C22semidirect
67. #10623100C22semidirect
68. #10623100C22semidirect
69. #10623099C22semidirect
70. Q8×Dic22C22semidirect
71. #10623094C22semidirect
72. #10623093C22semidirect
74. #10623090C22semidirect
75. #10623089C22semidirect
76. #10623088C22semidirect
77. #10623088C22semidirect
78. #10623084C22semidirect
79. #10623079C22semidirect
80. #10623079C22semidirect
81. #10623079C22semidirect
86. #10623066C22semidirect
87. #10623065C22semidirect
88. #10623064C22semidirect
89. #10623063C22semidirect
90. #10623063C22semidirect
91. #10623061C22semidirect
92. #10623059C22semidirect
93. #10623059C22semidirect
98. #10623045C22semidirect
99. #10623045C22semidirect
100. #10623044C22semidirect
101. #10623038C22semidirect
105. #10623010C22semidirect
106. #10623008C22semidirect
108. C4×#4339C22semidirect
109. C4×#4339C22semidirect
272. C2×Q8×C11#41semidirect
392. C4×2−1+4D11semidirect
519. #520C2×D11semidirect
523. #519C2×D11semidirect
533. C4×#41C2×D11semidirect
537. C2×C4×Q8C2×D11semidirect
747. C2×Q8#4339semidirect
840. C11#62793semidirect

Maximal subgroups

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

subgroupindex
#130827272
#130827172
#130826272
#130826162
#130824612
#130824222
#130823832
#130823292
#130822752
#130822712
#130822422
#130822332
#130822142
#130822112
#130820322
#130819092
C4×#670402
C2×C4×#43432
C4×C11×2−1+42
#6279311