Finite Group Databasebeta

← #15625758

Subgroups — #15625758

Order 2816.

2072 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082032C211yesmaximal, characteristic, complemented
2#13079725C214yesmaximal, complemented
3#13079677C214yesmaximal, complemented
4#13079643C212yesmaximal, complemented
5#13079611C212yesmaximal, complemented
6#13079592C212yesmaximal, complemented
7#13079541C212yesmaximal, complemented
8#13079094C212yesmaximal, complemented
9#13078981C212yesmaximal, complemented
10#13078099C211yesmaximal, characteristic, complemented
11#13078076C211yesmaximal, characteristic, complemented
12#13078065C211yesmaximal, characteristic, complemented
13C2×#10622696C211yesmaximal, characteristic, complemented
14#13077931C212yesmaximal, complemented
15#13077902C212yesmaximal, complemented
16#13077282C211yesmaximal, characteristic, complemented
17C11×#3499C211yesmaximal, characteristic, complemented
18C2×C11×2−1+4C2212yes—
19D4×Q8×C11—21no—
20D4×Q8×C11—21no—
21C11×#547—22no—
22C11×#547—22no—
23C11×#547—21no—
24C11×#547—21no—
25C11×#536C2212yes—
26C11×#536C2214yescomplemented
27C11×#532C2211yescharacteristic
28C11×#532C2212yescomplemented
29C2×C11×C4⋊Q8C2211yescharacteristic
30C2×C11×C4⋊Q8C2212yescomplemented
31C4×C11×#41C2211yescharacteristic
32#10623364C2211yescharacteristic
33#10623361C2211yescharacteristic
34C2×#67003C2212yes—
35C2×#67002C2212yes—
36C2×#66995C2212yes—
37C22×#4325C2212yes—
38#10623113—21no—
39#10623111—21no—
40#10623093—21no—
41#10623091—22no—
42#10623079—21no—
43#10623078—22no—
44#10623066C2212yes—
45#10623065C2212yes—
46#10623056C2211yescharacteristic
47#10623050C2211yescharacteristic
48#10623010C2212yes—
49#10623008C2212yes—
50C4×#4339C2211yescharacteristic
51C2×C4×D44C2211yescharacteristic
52#10622852C2214yescomplemented
53#10622851C2214yes—
54#10622851C2214yes—
55#10622851C2214yescomplemented
56#10622847C2212yes—
57#10622846C2212yes—
58#10622845C2212yes—
59#10622841C2214yescomplemented
60#10622840C2214yes—
61#10622840C2214yes—
62#10622840C2214yescomplemented
63#10622838C2212yes—
64C2×#66899C2212yes—
65#10622703C2212yescomplemented
66#10622703C2211yescharacteristic, complemented
67#10622703C2212yescomplemented
68#10622699C2214yes—
69#10622698C2214yes—
70#10622696C2212yes—
71#10622696C2212yes—
72#10622696C2214yes—
73#10622696C2212yes—
74#10622696C2211yescharacteristic, complemented
75#10622696C2212yescomplemented
76#10622696C2212yescomplemented
77#10622695C2214yescomplemented
78#10622694C2214yescomplemented
79#10622688C2211yescharacteristic, complemented
80#10622685C2212yes—
81#10622685C2211yescharacteristic, complemented
82#10622672C2214yes—
83#10622671C2214yes—
84#10622670C2214yes—
85#10622670C2212yescomplemented
86#10622669C2214yescomplemented
87#10622668C2214yescomplemented
88#10622667C2212yescomplemented
89#10622613C2214yescomplemented
90#10622610C2212yes—
91#10622539C2212yescomplemented
92#10622538C2212yescomplemented
93#10622537C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2211yescharacteristic
95C11×2−1+4—44no—
96C11×2−1+4—44no—
97C2×C11×#41—24no—
98C2×C11×#41—22no—
99C2×C11×#41C2312yes—
100C2×C11×#41C2314yes—
101C2×C11×#41C2311yescharacteristic
102C22×Q8×C11—22no—
103C22×Q8×C11C2312yes—
104C22×Q8×C11C2314yes—
105C2×#4339—22no—
106C2×#4339C2311yescharacteristic
107C22×D44C2311yescharacteristic
108C22×C4×D11—21no—
109C11×C4⋊Q8—21no—
110C11×C4⋊Q8—21no—
111C11×C4⋊Q8—22no—
112C11×C4⋊Q8—22no—
113C11×C4⋊Q8C2312yes—
114C11×C4⋊Q8C2312yes—
115C11×C4⋊Q8C2311yescharacteristic
116C11×C4⋊Q8C2314yes—
117C11×#127C2311yescharacteristic
118C11×#124C2312yes—
119C11×#124C2314yes—
120C11×#123—24no—
121C11×#123—24no—
122C11×#123—24no—
123C11×C22⋊Q8—22no—
124C11×C22⋊Q8—22no—
125C11×C22⋊Q8—24no—
126C11×C22⋊Q8—24no—
127C11×#121—21no—
128C11×#121—21no—
129C11×#121—22no—
130C11×#121—22no—
131C4×Q8×C11D411yescharacteristic
132C4×Q8×C11D411yescharacteristic
133C4×D4×C11—21no—
134C4×D4×C11—21no—
135C4×D4×C11—22no—
136C4×D4×C11—22no—
137C4×D4×C11D412yes—
138C4×D4×C11D411yescharacteristic
139C4×D4×C11D412yes—
140C4×D4×C11D411yescharacteristic
141C11×#117C2311yescharacteristic
142C11×#117C2312yes—
143C2×C11×C4⋊C4—21no—
144C2×C11×C4⋊C4—21no—
145C2×C11×C4⋊C4—22no—
146C2×C11×C4⋊C4—22no—
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2312yes—
149#67003—44no—
150#67002—44no—
151#67000—21no—
152#66999—21no—
153C2×#4326C2314yes—
154C2×#4326C2312yes—
155#66995—44no—
156C2×#4325—44no—
157C2×#4325C2314yes—
158C2×#4325C2314yes—
159C2×#4325C2314yes—
160C2×#4325C2314yes—
161C2×#4325C2312yes—
162#66993—21no—
163#66992—22no—
164#66991—21no—
165#66990—22no—
166C2×#4324C2312yes—
167C2×#4323C2314yes—
168C2×#4323C2312yes—
169#66983—22no—
170#66983C2312yes—
171#66983C2312yes—
172#66983C2312yes—
173#66982—22no—
174C4×C22⋊D11—21no—
175C4×C22⋊D11—21no—
176C4×C22⋊D11—22no—
177C2×(C2×D11)⋊C4—21no—
178#66979C2311yescharacteristic
179C2×C4⋊Dic11C2311yescharacteristic
180#66977C2312yes—
181C2×#4318C2312yes—
182C22×C11⋊C8C2312yes—
183#66951—22no—
184#66949—22no—
185#66948—21no—
186#66948—21no—
187#66947—22no—
188#66947—22no—
189#66943—21no—
190#66941—21no—
191#66938—22no—
192#66937—22no—
193#66937—22no—
194#66936—22no—
195#66935—22no—
196#66931—22no—
197#66929—22no—
198#66928—22no—
199#66928C2312yes—
200#66927C2312yes—
201C4×D44—21no—
202C4×D44—21no—
203C4×D44—22no—
204C4×D44C2312yes—
205C4×D44C2312yes—
206C4×D44C2311yescharacteristic
207C4×D44C2311yescharacteristic
208#66925—21no—
209#66925—22no—
210C42×D11—21no—
211#66923C2312yes—
212#66922C2312yes—
213C4×Dic22C2311yescharacteristic
214C4×Dic22C2311yescharacteristic
215#66899C2314yes—
216#66899C2314yes—
217#66899C2314yes—
218#66899C2314yes—
219#66899C2312yes—
220#66899C2312yes—
221#66899C2314yes—
222#66896C2314yes—
223#66896C2312yes—
224#66896C2312yes—
225C22⋊(C11⋊C8)C2314yes—
226C22⋊(C11⋊C8)C2314yes—
227C4⋊(C11⋊C8)C2311yescharacteristic
228C4⋊(C11⋊C8)C2311yescharacteristic
229C4⋊(C11⋊C8)C2312yes—
230C4⋊(C11⋊C8)C2312yes—
231C4⋊(C11⋊C8)C2312yes—
232#66867C2314yes—
233C4×C11⋊C8C2314yes—
234#60836—111nomaximal, Sylow
235C23×D11—21no—
236C11×#41—22no—
237C11×#41—22no—
238C11×#41—24no—
239C11×#41—24no—
240C11×#41—44no—
241C11×#41—44no—
242C11×#41—416no—
243C11×#41—48no—
244C2×Q8×C11—24no—
245C2×Q8×C11—22no—
246C2×Q8×C11—24no—
247C2×Q8×C11—24no—
248C2×Q8×C11—44no—
249C2×Q8×C11—44no—
250C2×Q8×C11—48no—
251C2×Q8×C11C2×D411yescharacteristic
252C2×Q8×C11C2414yes—
253C2×Q8×C11C2412yes—
254C2×D4×C11—24no—
255C2×D4×C11—22no—
256C2×D4×C11—21no—
257C2×D4×C11—21no—
258C2×D4×C11C2×D412yes—
259C2×D4×C11C2×D411yescharacteristic
260C2×D4×C11C2412yes—
261C22×C4×C11—24no—
262C22×C4×C11—22no—
263C22×C4×C11—24no—
264C22×C4×C11—22no—
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2×D412yes—
267C22×C4×C11C2×D411yescharacteristic
268C22×C4×C11C2×D412yes—
269C22×C4×C11C2412yes—
270C22×C4×C11C2411yescharacteristic
271C2×C22⋊D11—21no—
272C2×C22⋊D11—22no—
273C2×C22⋊D11—22no—
274C2×C22⋊D11—22no—
275C22×Dic11—21no—
276#4339—22no—
277#4339—22no—
278#4339—84no—
279C2×D44—21no—
280C2×D44—22no—
281C2×D44—22no—
282C2×D44—22no—
283C2×D44—22no—
284C2×D44C2411yescharacteristic
285C2×D44C2412yes—
286C2×C4×D11—21no—
287C2×C4×D11—21no—
288C2×C4×D11—22no—
289C2×C4×D11—21no—
290C2×C4×D11—22no—
291C2×C4×D11—82no—
292C2×Dic22—22no—
293C2×Dic22C2411yescharacteristic
294C11×C4⋊C4—22no—
295C11×C4⋊C4—21no—
296C11×C4⋊C4—22no—
297C11×C4⋊C4—21no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4—24no—
300C11×C4⋊C4—24no—
301C11×C4⋊C4—22no—
302C11×C4⋊C4C2×D411yescharacteristic
303C11×C4⋊C4C2×D411yescharacteristic
304C11×C4⋊C4C2×D412yes—
305C11×C4⋊C4C2×D412yes—
306C11×C22⋊C4—22no—
307C11×C22⋊C4—24no—
308C11×C22⋊C4—24no—
309C11×C22⋊C4—22no—
310C11×C22⋊C4C2×D412yes—
311C11×C22⋊C4C2×D412yes—
312C11×C22⋊C4C2×D412yes—
313C42×C11C2×D411yescharacteristic
314C42×C11C2×D412yes—
315C42×C11C2×D411yescharacteristic
316C42×C11C2×D412yes—
317C42×C11C2412yes—
318C42×C11C2411yescharacteristic
319C42×C11C2411yescharacteristic
320C22⋊Dic11—21no—
321C22⋊Dic11—22no—
322#4326—44no—
323#4326—42no—
324#4325—44no—
325#4325—44no—
326#4325—44no—
327#4325—44no—
328#4325—42no—
329#4324—42no—
330#4323—44no—
331#4323—42no—
332(C2×D11)⋊C4—21no—
333(C2×D11)⋊C4—21no—
334(C2×D11)⋊C4—22no—
335(C2×D11)⋊C4—22no—
336(C2×D11)⋊C4—22no—
337(C2×D11)⋊C4—22no—
338(C2×D11)⋊C4—22no—
339(C2×D11)⋊C4—22no—
340(C2×D11)⋊C4—22no—
341C4⋊Dic11—22no—
342C4⋊Dic11—21no—
343C4⋊Dic11C2411yescharacteristic
344C4⋊Dic11C2411yescharacteristic
345C4⋊Dic11C2412yes—
346Dic11⋊C4—21no—
347Dic11⋊C4—21no—
348Dic11⋊C4—22no—
349Dic11⋊C4—22no—
350Dic11⋊C4—22no—
351C4×Dic11—21no—
352C4×Dic11—21no—
353C4×Dic11—21no—
354#4318—24no—
355C2×C11⋊C8—24no—
356C2×C11⋊C8C2412yes—
357C2×C11⋊C8C2414yes—
358C2×C11⋊C8C2412yes—
359#3499D1111yescharacteristic, complemented
360#3460—111no—
361#3225—114no—
362#3221—114no—
363#3218—112no—
364#3214—112no—
365#3212—112no—
366#3206—112no—
367#3154—112no—
368#3137—112no—
369#3039—111no—
370#3036—111no—
371#3035—111no—
372C2×#461—111no—
373#3013—112no—
374#3010—112no—
375#2925—111no—
376C23×C11—22no—
377C23×C11C22×D412yes—
378C23×C11C22×D411yescharacteristic
379C22×D11—22no—
380C22×D11—21no—
381C22×D11—42no—
382C22×D11—81no—
383C22×D11—81no—
384Q8×C11—22no—
385Q8×C11—24no—
386Q8×C11—22no—
387Q8×C11—24no—
388Q8×C11—22no—
389Q8×C11—48no—
390Q8×C11—44no—
391D4×C11—24no—
392D4×C11—22no—
393D4×C11—22no—
394D4×C11—22no—
395D4×C11—42no—
396D4×C11—48no—
397D4×C11—44no—
398D4×C11—42no—
399C2×C4×C11—22no—
400C2×C4×C11—24no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—24no—
404C2×C4×C11—22no—
405C2×C4×C11—41no—
406C2×C4×C11—42no—
407C2×C4×C11—48no—
408C2×C4×C11—48no—
409C2×C4×C11—44no—
410C2×C4×C11—44no—
411C2×C4×C11C22×D411yescharacteristic
412C2×C4×C11C22×D412yes—
413C2×C4×C11C22×D411yescharacteristic
414C2×C4×C11C22×D412yes—
415C2×C4×C11C22×D412yes—
416C2×C4×C11C22×D411yescharacteristic
417C2×C4×C11C22×D411yescharacteristic
418C2×C4×C11C22×D411yescharacteristic
419C2×C4×C11H(5,𝔽2)12yes—
420C2×C4×C11H(5,𝔽2)12yes—
421C2×C4×C11C2511yescharacteristic
422C22⋊D11—42no—
423C22⋊D11—82no—
424C22⋊D11—82no—
425C22⋊D11—82no—
426C2×Dic11—21no—
427C2×Dic11—21no—
428C2×Dic11—21no—
429C2×Dic11—22no—
430C2×Dic11—81no—
431D44—22no—
432D44—21no—
433D44—22no—
434D44—21no—
435D44—42no—
436D44—82no—
437D44—82no—
438C4×D11—42no—
439C4×D11—44no—
440C4×D11—42no—
441C4×D11—81no—
442C4×D11—82no—
443Dic22—21no—
444Dic22—21no—
445Dic22—82no—
446C11⋊C8—22no—
447C11⋊C8—22no—
448C11⋊C8—24no—
449C2×2−1+4C2×D1112yes—
450C2×#137—112no—
451C2×AGL(1,ℤ/8)—112no—
452C2×#135—112no—
453C22×SD16—112no—
454D4×Q8—21no—
455D4×Q8—21no—
456#547—22no—
457#547—22no—
458#547—21no—
459#547—21no—
460#544—111no—
461#542—112no—
462#542—221no—
463#540—112no—
464#540—221no—
465#538—222no—
466#537—111no—
467#536C2×D1112yes—
468#536C2×D1114yescomplemented
469#535—111no—
470#535—111no—
471#532—112no—
472#532—221no—
473#532C2×D1111yescharacteristic
474#532C2×D1112yescomplemented
475C2×C4⋊Q8C2×D1111yescharacteristic
476C2×C4⋊Q8C2×D1112yescomplemented
477#529—112no—
478#529—221no—
479#525—222no—
480C4×#41—111no—
481C4×#41C2×D1111yescharacteristic
482C2×C4×D4—111no—
483#497—114no—
484#496—114no—
485#495—114no—
486#492—114no—
487#491—114no—
488#489—114no—
489#488—114no—
490#487—114no—
491#464—112no—
492#463—112no—
493#463—114no—
494#462—112no—
495#462—111no—
496#462—112no—
497#461—111no—
498#461—112no—
499#461—112no—
500#461—112no—
501#461—112no—
502#461—112no—
503#461—114no—
504#460—111no—
505#459—112no—
506#459—111no—
507#452—114no—
508#451—114no—
509#449—114no—
510#449—114no—
511#449—114no—
512#448—114no—
513#448—114no—
514#448—114no—
515#433—114no—
516#432—112no—
517#431—112no—
518#423—111no—
519C2×C4⋊C8—111no—
520#419—112no—
521#417—112no—
522#416—112no—
523C2×#103—112no—
524#408—112no—
525#405—112no—
526C22×C11—21no—
527C22×C11—21no—
528C22×C11—22no—
529C22×C11—22no—
530C22×C11—22no—
531C22×C11—42no—
532C22×C11—42no—
533C22×C11—42no—
534C22×C11#53512yes—
535C22×C11C23×D411yescharacteristic
536C2×D11—42no—
537C2×D11—41no—
538C2×D11—42no—
539C2×D11—41no—
540C2×D11—42no—
541C2×D11—41no—
542C2×D11—84no—
543C4×C11—21no—
544C4×C11—21no—
545C4×C11—22no—
546C4×C11—22no—
547C4×C11—22no—
548C4×C11—21no—
549C4×C11—44no—
550C4×C11—42no—
551C4×C11#53512yes—
552C4×C11#57712yes—
553C4×C11C2×H(5,𝔽2)11yescharacteristic
554C4×C11C2×H(5,𝔽2)11yescharacteristic
555Dic11—41no—
556Dic11—41no—
557Dic11—41no—
558Dic11—42no—
5592−1+4—44no—
5602−1+4—44no—
561C2×#41—24no—
562C2×#41—22no—
563C2×#41—111no—
564C2×#41—222no—
565C2×#41C22×D1112yes—
566C2×#41C22×D1114yes—
567C2×#41C22×D1111yescharacteristic
568C22×Q8—22no—
569C22×Q8C22×D1112yes—
570C22×Q8C22×D1114yes—
571C22×D4—111no—
572C23×C4—221no—
573#137—444no—
574AGL(1,ℤ/8)—444no—
575#135—444no—
576C2×Q16—112no—
577C2×Q16—114no—
578C2×SD16—114no—
579C2×SD16—114no—
580C2×SD16—112no—
581C2×SD16—114no—
582C2×SD16—114no—
583C2×SD16—112no—
584C2×SD16—444no—
585C2×D8—112no—
586C2×D8—114no—
587C2×M16—112no—
588C22×C8—112no—
589C4⋊Q8—21no—
590C4⋊Q8—21no—
591C4⋊Q8—22no—
592C4⋊Q8—22no—
593C4⋊Q8—112no—
594C4⋊Q8—221no—
595C4⋊Q8C22×D1112yes—
596C4⋊Q8C22×D1112yes—
597C4⋊Q8C22×D1111yescharacteristic
598C4⋊Q8C22×D1114yes—
599#127—112no—
600#127—221no—
601#127C22×D1111yescharacteristic
602#126—222no—
603#126—222no—
604#125—112no—
605#125—221no—
606#124—112no—
607#124—221no—
608#124—222no—
609#124—222no—
610#124C22×D1112yes—
611#124C22×D1114yes—
612#123—24no—
613#123—24no—
614#123—24no—
615#123—222no—
616#123—222no—
617#123—222no—
618#123—222no—
619C22⋊Q8—22no—
620C22⋊Q8—22no—
621C22⋊Q8—24no—
622C22⋊Q8—24no—
623C22⋊Q8—112no—
624C22⋊Q8—221no—
625C22⋊Q8—222no—
626C22⋊Q8—222no—
627#121—21no—
628#121—21no—
629#121—22no—
630#121—22no—
631#121—112no—
632#121—112no—
633#121—112no—
634#121—222no—
635#121—221no—
636#121—222no—
637#121—221no—
638#121—221no—
639#121—222no—
640#121—222no—
641#120—222no—
642#120—222no—
643C4×Q8—111no—
644C4×Q8—111no—
645C4×Q8C22⋊D1111yescharacteristic
646C4×Q8C22⋊D1111yescharacteristic
647C4×D4—21no—
648C4×D4—21no—
649C4×D4—22no—
650C4×D4—22no—
651C4×D4—112no—
652C4×D4—112no—
653C4×D4—111no—
654C4×D4—111no—
655C4×D4—221no—
656C4×D4—221no—
657C4×D4—222no—
658C4×D4—221no—
659C4×D4—221no—
660C4×D4—222no—
661C4×D4C22⋊D1112yes—
662C4×D4C22⋊D1111yescharacteristic
663C4×D4C22⋊D1112yes—
664C4×D4C22⋊D1111yescharacteristic
665#117—111no—
666#117—221no—
667#117—222no—
668#117C22×D1111yescharacteristic
669#117C22×D1112yes—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—111no—
675C2×C22⋊C4—221no—
676C2×C42—221no—
677C2×C42C22×D1111yescharacteristic
678C2×C42C22×D1112yes—
679C4⋊C8—111no—
680C4⋊C8—111no—
681C4⋊C8—112no—
682C4⋊C8—112no—
683C4⋊C8—112no—
684#103—114no—
685#103—114no—
686#103—112no—
687#103—112no—
688#103—114no—
689#103—114no—
690#103—114no—
691#102—112no—
692#102—112no—
693#102—114no—
694C22⋊C8—114no—
695C22⋊C8—114no—
696#97—114no—
697C4×C8—114no—
698C2×C11—22no—
699C2×C11—42no—
700C2×C11—82no—
701C2×C11C2×#53511yescharacteristic
702C2×C11C2×#57711yescharacteristic
703C2×C11#358611yescharacteristic
704D11—81no—
705D11—82no—
706C24—221no—
707#41—22no—
708#41—22no—
709#41—24no—
710#41—24no—
711#41—44no—
712#41—44no—
713#41—416no—
714#41—48no—
715#41—222no—
716#41—222no—
717#41—884no—
718C2×Q8—24no—
719C2×Q8—22no—
720C2×Q8—24no—
721C2×Q8—24no—
722C2×Q8—44no—
723C2×Q8—44no—
724C2×Q8—48no—
725C2×Q8—111no—
726C2×Q8—222no—
727C2×Q8C2×C22⋊D1111yescharacteristic
728C2×Q8C23×D1114yes—
729C2×Q8C23×D1112yes—
730C2×D4—24no—
731C2×D4—22no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—112no—
735C2×D4—111no—
736C2×D4—221no—
737C2×D4—222no—
738C2×D4—222no—
739C2×D4—222no—
740C2×D4—222no—
741C2×D4—222no—
742C2×D4—221no—
743C2×D4—222no—
744C2×D4—222no—
745C2×D4C2×C22⋊D1112yes—
746C2×D4C2×C22⋊D1111yescharacteristic
747C2×D4C23×D1112yes—
748C22×C4—24no—
749C22×C4—22no—
750C22×C4—24no—
751C22×C4—22no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—222no—
756C22×C4—221no—
757C22×C4—222no—
758C22×C4—882no—
759C22×C4C2×C22⋊D1111yescharacteristic
760C22×C4C2×C22⋊D1112yes—
761C22×C4C2×C22⋊D1111yescharacteristic
762C22×C4C2×C22⋊D1112yes—
763C22×C4C23×D1112yes—
764C22×C4C23×D1111yescharacteristic
765Q16—442no—
766Q16—444no—
767SD16—442no—
768SD16—444no—
769SD16—444no—
770SD16—442no—
771SD16—444no—
772SD16—444no—
773D8—442no—
774D8—444no—
775M16—224no—
776C2×C8—112no—
777C2×C8—114no—
778C2×C8—112no—
779C2×C8—224no—
780C4⋊C4—22no—
781C4⋊C4—21no—
782C4⋊C4—22no—
783C4⋊C4—21no—
784C4⋊C4—22no—
785C4⋊C4—24no—
786C4⋊C4—22no—
787C4⋊C4—24no—
788C4⋊C4—112no—
789C4⋊C4—111no—
790C4⋊C4—111no—
791C4⋊C4—221no—
792C4⋊C4—221no—
793C4⋊C4—221no—
794C4⋊C4—222no—
795C4⋊C4—222no—
796C4⋊C4—222no—
797C4⋊C4—222no—
798C4⋊C4C2×C22⋊D1111yescharacteristic
799C4⋊C4C2×C22⋊D1111yescharacteristic
800C4⋊C4C2×C22⋊D1112yes—
801C4⋊C4C2×C22⋊D1112yes—
802C22⋊C4—22no—
803C22⋊C4—24no—
804C22⋊C4—22no—
805C22⋊C4—24no—
806C22⋊C4—221no—
807C22⋊C4—222no—
808C22⋊C4—222no—
809C22⋊C4—222no—
810C22⋊C4—221no—
811C22⋊C4—221no—
812C22⋊C4—222no—
813C22⋊C4—222no—
814C22⋊C4—222no—
815C22⋊C4—222no—
816C22⋊C4—222no—
817C22⋊C4C2×C22⋊D1112yes—
818C22⋊C4C2×C22⋊D1112yes—
819C22⋊C4C2×C22⋊D1112yes—
820C42—221no—
821C42—221no—
822C42—221no—
823C42C2×C22⋊D1111yescharacteristic
824C42C2×C22⋊D1111yescharacteristic
825C42C2×C22⋊D1112yes—
826C42C2×C22⋊D1112yes—
827C42C23×D1112yes—
828C42C23×D1111yescharacteristic
829C42C23×D1111yescharacteristic
830C11#6083611yescharacteristic, complemented, Sylow
831C23—22no—
832C23—222no—
833C23—221no—
834C23—442no—
835C23—881no—
836C23—881no—
837C23C22×C22⋊D1112yes—
838C23C22×C22⋊D1111yescharacteristic
839Q8—22no—
840Q8—24no—
841Q8—22no—
842Q8—24no—
843Q8—22no—
844Q8—48no—
845Q8—44no—
846Q8—221no—
847Q8—221no—
848Q8—882no—
849D4—24no—
850D4—22no—
851D4—22no—
852D4—22no—
853D4—42no—
854D4—48no—
855D4—44no—
856D4—42no—
857D4—222no—
858D4—221no—
859D4—222no—
860D4—221no—
861D4—442no—
862D4—442no—
863D4—882no—
864D4—882no—
865D4—882no—
866D4—882no—
867D4—882no—
868C2×C4—22no—
869C2×C4—24no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—24no—
873C2×C4—22no—
874C2×C4—41no—
875C2×C4—42no—
876C2×C4—48no—
877C2×C4—48no—
878C2×C4—44no—
879C2×C4—44no—
880C2×C4—221no—
881C2×C4—221no—
882C2×C4—221no—
883C2×C4—222no—
884C2×C4—442no—
885C2×C4—444no—
886C2×C4—442no—
887C2×C4—882no—
888C2×C4—881no—
889C2×C4—881no—
890C2×C4#6703712yes—
891C2×C4#6703712yes—
892C2×C4C22×C22⋊D1111yescharacteristic
893C2×C4C22×C22⋊D1111yescharacteristic
894C2×C4C22×C22⋊D1112yes—
895C2×C4C22×C22⋊D1112yes—
896C2×C4C22×C22⋊D1111yescharacteristic
897C2×C4C22×C22⋊D1112yes—
898C2×C4C22×C22⋊D1111yescharacteristic
899C2×C4C22×C22⋊D1111yescharacteristic
900C2×C4C24×D1111yescharacteristic
901C8—222no—
902C8—222no—
903C8—224no—
904C22—21no—
905C22—21no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—441no—
913C22—442no—
914C22—441no—
915C22—442no—
916C22—442no—
917C22—441no—
918C22—884no—
919C22#1062333612yes—
920C22C23×C22⋊D1111yescharacteristic
921C4—21no—
922C4—21no—
923C4—22no—
924C4—22no—
925C4—21no—
926C4—22no—
927C4—44no—
928C4—42no—
929C4—441no—
930C4—441no—
931C4—442no—
932C4—441no—
933C4#1062333612yes—
934C4#1062336812yes—
935C4C2×#6703711yescharacteristic
936C4C2×#6703711yescharacteristic
937C2—22no—
938C2—42no—
939C2—82no—
940C2—882no—
941C2—881no—
942C2C2×#1062333611yescharacteristic
943C2C2×#1062336811yescharacteristic
944C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3499C2
socleC22×C11C23×D4
hypercenter#3499D11
hypocenterC11#60836
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. #13082032C2semidirect
2. #13079725C2semidirect
3. #13079677C2semidirect
4. #13079643C2semidirect
5. #13079611C2semidirect
6. #13079592C2semidirect
7. #13079541C2semidirect
8. #13079094C2semidirect
9. #13078981C2semidirect
10. #13078099C2semidirect
11. #13078076C2semidirect
12. #13078065C2semidirect
13. C2×#10622696C2semidirect
14. #13077931C2semidirect
15. #13077902C2semidirect
16. #13077282C2semidirect
17. C11×#3499C2semidirect
26. C11×#536C22semidirect
28. C11×#532C22semidirect
30. C2×C11×C4⋊Q8C22semidirect
52. #10622852C22semidirect
55. #10622851C22semidirect
59. #10622841C22semidirect
62. #10622840C22semidirect
65. #10622703C22semidirect
66. #10622703C22semidirect
67. #10622703C22semidirect
74. #10622696C22semidirect
75. #10622696C22semidirect
76. #10622696C22semidirect
77. #10622695C22semidirect
78. #10622694C22semidirect
79. #10622688C22semidirect
81. #10622685C22semidirect
85. #10622670C22semidirect
86. #10622669C22semidirect
87. #10622668C22semidirect
88. #10622667C22semidirect
89. #10622613C22semidirect
91. #10622539C22semidirect
92. #10622538C22semidirect
359. #3499D11semidirect
468. #536C2×D11semidirect
474. #532C2×D11semidirect
476. C2×C4⋊Q8C2×D11semidirect
830. C11#60836semidirect

Maximal subgroups

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

subgroupindex
#130820322
#130797252
#130796772
#130796432
#130796112
#130795922
#130795412
#130790942
#130789812
#130780992
#130780762
#130780652
C2×#106226962
#130779312
#130779022
#130772822
C11×#34992
#6083611