Finite Group Databasebeta

← #15624850

Subgroups — #15624850

Order 2816.

2200 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082288C211yesmaximal, characteristic, complemented
2#13082277C211yesmaximal, characteristic, complemented
3#13079521C212yesmaximal, complemented
4#13079501C212yesmaximal, complemented
5#13079482C212yesmaximal, complemented
6#13079461C212yesmaximal, complemented
7#13079405C212yesmaximal, complemented
8#13079398C212yesmaximal, complemented
9#13079376C212yesmaximal, complemented
10#13079368C212yesmaximal, complemented
11#13078603C211yesmaximal, characteristic, complemented
12#13078603C211yesmaximal, characteristic, complemented
13#13078588C211yesmaximal, characteristic, complemented
14#13078577C211yesmaximal, characteristic, complemented
15#13078248C211yesmaximal, characteristic, complemented
16#13078237C211yesmaximal, characteristic, complemented
17C2×#10622727C211yesmaximal, characteristic, complemented
18#13077927C211yesmaximal, characteristic, complemented
19#13077916C211yesmaximal, characteristic, complemented
20#13077905C211yesmaximal, characteristic, complemented
21#13077896C211yesmaximal, characteristic, complemented
22C2×#10622723C211yesmaximal, characteristic, complemented
23C11×#3050C211yesmaximal, characteristic, complemented
24C2×#67043C2211yescharacteristic, complemented
25C2×#67042C2211yescharacteristic
26C22×#4339C2211yescharacteristic
27C2×C11×#135C2211yescharacteristic, complemented
28C23×C8×C11C2211yescharacteristic, complemented
29C11×#525C2211yescharacteristic
30C11×#525C2211yescharacteristic, complemented
31#10623364C2211yescharacteristic
32#10623364C2211yescharacteristic
33C2×#67004C2211yescharacteristic, complemented
34C2×#67002C2211yescharacteristic, complemented
35C2×#66983C2211yescharacteristic
36C2×#66977C2211yescharacteristic, complemented
37C22×#4318C2211yescharacteristic, complemented
38C22×#4314C2211yescharacteristic, complemented
39#10623186—22no—
40#10623185—22no—
41#10623160C2212yes—
42#10623159C2212yescomplemented
43#10623158C2212yes—
44D11×C22⋊Q8C2212yescomplemented
45#10623139C2212yescomplemented
46#10623138C2212yes—
47#10623137C2212yescomplemented
48D11×#121C2212yes—
49#10623122—22no—
50#10623121—22no—
51#10623084—21no—
52#10623083—21no—
53#10623083—21no—
54#10623082—21no—
55#10623081—21no—
56#10623081—21no—
57D4×D44—21no—
58D4×Dic22—21no—
59#10623057C2211yescharacteristic
60#10623056C2211yescharacteristic
61#10623054C2211yescharacteristic
62#10623054C2211yescharacteristic, complemented
63C11×#467C2211yescharacteristic, complemented
64C11×#467C2211yescharacteristic, complemented
65C11×#466C2211yescharacteristic, complemented
66C11×#466C2211yescharacteristic, complemented
67C11×#465C2211yescharacteristic, complemented
68C11×#465C2211yescharacteristic, complemented
69C11×#465C2211yescharacteristic, complemented
70C11×#465C2211yescharacteristic, complemented
71C11×#427C2211yescharacteristic, complemented
72C11×#416C2211yescharacteristic, complemented
73C11×#416C2211yescharacteristic, complemented
74#10622845C2211yescharacteristic, complemented
75#10622845C2211yescharacteristic, complemented
76#10622800C2212yescomplemented
77#10622799C2212yescomplemented
78#10622786C2212yescomplemented
79#10622785C2212yescomplemented
80#10622783C2212yescomplemented
81#10622782C2212yescomplemented
82#10622771C2212yescomplemented
83#10622769C2212yescomplemented
84#10622727C2212yescomplemented
85#10622727C2212yescomplemented
86#10622727C2212yescomplemented
87#10622727C2212yescomplemented
88C2×#66885C2211yescharacteristic, complemented
89#10622723C2211yescharacteristic
90#10622723C2211yescharacteristic
91#10622723C2211yescharacteristic, complemented
92#10622723C2211yescharacteristic, complemented
93#10622723C2212yescomplemented
94#10622723C2212yescomplemented
95C2×(C2×D11)⋊C8C2212yescomplemented
96C2×(C2×D11)⋊C8C2212yescomplemented
97C2×#66881C2211yescharacteristic, complemented
98C2×#66880C2211yescharacteristic, complemented
99#10622665C2212yescomplemented
100#10622664C2212yescomplemented
101#10622662C2212yescomplemented
102#10622661C2212yescomplemented
103#10622655C2212yescomplemented
104#10622654C2212yescomplemented
105#10622652C2212yescomplemented
106#10622651C2212yescomplemented
107#10622617C2211yescharacteristic, complemented
108#10622614C2211yescharacteristic, complemented
109#10622608C2211yescharacteristic, complemented
110#10622608C2211yescharacteristic, complemented
111#10622501C2212yescomplemented
112#10622498C2212yescomplemented
113#10622497C2212yescomplemented
114#10622495C2212yescomplemented
115#10622480C2212yescomplemented
116#10622479C2212yescomplemented
117#10622476C2212yescomplemented
118#10622475C2212yescomplemented
119#10622428C2212yescomplemented
120#10622428C2212yescomplemented
121#10622423C2212yescomplemented
122#10622423C2212yescomplemented
123#10622419C2212yescomplemented
124#10622419C2212yescomplemented
125#10622418C2212yescomplemented
126#10622418C2212yescomplemented
127#10622394C2212yescomplemented
128#10622394C2212yescomplemented
129#10622392C2212yescomplemented
130#10622392C2212yescomplemented
131#10622390C2212yescomplemented
132#10622390C2212yescomplemented
133#10622389C2212yescomplemented
134#10622389C2212yescomplemented
135C2×C11×#41C2311yescharacteristic
136C2×C11×#41C2311yescharacteristic
137C23×C4×C11C2311yescharacteristic
138C22×C22⋊D11—21no—
139C22×C22⋊D11D412yes—
140#67043—42no—
141#67043—42no—
142#67042—42no—
143#67042—42no—
144C2×#4343C2312yes—
145C2×Q8×D11C2312yes—
146C2×#4341—22no—
147C2×#4341C2312yes—
148C2×D4×D11—22no—
149C2×D4×D11—22no—
150C2×D4×D11C2312yes—
151C2×#4339—21no—
152C2×#4339—21no—
153C2×#4339—42no—
154C2×#4339—42no—
155C2×#4339D411yescharacteristic
156C2×#4339D411yescharacteristic
157C2×#4339D412yes—
158C2×#4339C2311yescharacteristic
159C2×#4339C2311yescharacteristic
160C2×#4339C2312yes—
161C22×D44—21no—
162C22×D44D411yescharacteristic
163C22×D44C2311yescharacteristic
164C22×C4×D11C2312yes—
165C22×Dic22—21no—
166C22×Dic22D411yescharacteristic
167C22×Dic22C2311yescharacteristic
168C11×#135—42no—
169C2×C11×Q16C2311yescharacteristic
170C2×C11×SD16C2311yescharacteristic
171C2×C11×SD16C2311yescharacteristic
172C2×C11×D8C2311yescharacteristic
173C22×C8×C11—42no—
174C22×C8×C11C2311yescharacteristic
175C22×C8×C11C2311yescharacteristic
176C22×C8×C11C2311yescharacteristic
177C22×C8×C11C2311yescharacteristic
178C22×C8×C11C2311yescharacteristic
179C22×C8×C11C2311yescharacteristic
180C11×#123—21no—
181C11×#123—21no—
182C11×C22⋊Q8C2311yescharacteristic
183C11×C22⋊Q8C2311yescharacteristic
184C11×C22⋊Q8C2311yescharacteristic
185C11×C22⋊Q8C2311yescharacteristic
186C11×#121C2311yescharacteristic
187C11×#121C2311yescharacteristic
188C11×#121C2311yescharacteristic
189C11×#121C2311yescharacteristic
190C11×#120—21no—
191C11×#120—21no—
192C4×D4×C11—21no—
193C4×D4×C11—21no—
194C4×D4×C11—21no—
195C4×D4×C11—21no—
196C11×#117C2311yescharacteristic
197C11×#117C2311yescharacteristic
198C2×C22⋊Dic11—21no—
199#67004—42no—
200#67002—42no—
201#66999C2312yes—
202#66999C2312yes—
203C2×#4326C2312yes—
204C2×#4325C2312yes—
205#66993—22no—
206#66992—22no—
207#66992—22no—
208#66992—22no—
209#66992—22no—
210#66991—22no—
211#66991C2312yes—
212#66991C2312yes—
213#66990—22no—
214#66990—22no—
215D4×Dic11—22no—
216C2×#4324C2312yes—
217C2×#4323C2312yes—
218#66983—21no—
219#66983—21no—
220#66983—21no—
221#66983—21no—
222#66983C2312yes—
223#66983C2312yes—
224C2×(C2×D11)⋊C4—21no—
225C2×C4⋊Dic11C2311yescharacteristic
226C2×C4⋊Dic11C2311yescharacteristic
227#66977—21no—
228#66977—21no—
229#66977—21no—
230#66977—21no—
231#66977C2312yes—
232#66977C2312yes—
233C2×Dic11⋊C4—21no—
234C2×#4318—42no—
235C2×#4318C2311yescharacteristic
236C2×#4318C2311yescharacteristic
237C2×#4318C2312yes—
238C22×C11⋊C8C2312yes—
239C2×#4314—42no—
240C2×#4314C2312yes—
241C2×#4314C2312yes—
242#66950C2312yes—
243#66950C2312yes—
244#66949—22no—
245#66949—22no—
246#66948—22no—
247#66948C2312yes—
248#66948C2312yes—
249#66947—22no—
250#66947—22no—
251#66946—22no—
252#66945C2312yes—
253#66945C2312yes—
254C4⋊C4×D11—22no—
255C4⋊C4×D11C2312yes—
256C4⋊C4×D11C2312yes—
257#66941—22no—
258#66939—22no—
259#66938—22no—
260#66938—22no—
261#66937—22no—
262#66937—22no—
263#66937—22no—
264#66937—22no—
265#66936—22no—
266#66936—22no—
267#66935—22no—
268#66935—22no—
269#66935—22no—
270(C22⋊D11)⋊C4—22no—
271(C22⋊D11)⋊C4—22no—
272(C22⋊D11)⋊C4—22no—
273(C22⋊D11)⋊C4—22no—
274C22⋊C4×D11—22no—
275C22⋊C4×D11—22no—
276#66931—22no—
277#66931—22no—
278#66928—21no—
279#66928—21no—
280#66927—21no—
281C4×D44—21no—
282C4×D44—21no—
283#66922—21no—
284C4×Dic22—21no—
285C4×Dic22—21no—
286C11×#107C2311yescharacteristic
287C11×#107C2311yescharacteristic
288C11×#106C2311yescharacteristic
289C11×#106C2311yescharacteristic
290C11×#103C2311yescharacteristic
291C11×#103C2311yescharacteristic
292C11×#103C2311yescharacteristic
293C11×#103C2311yescharacteristic
294C11×#102C2311yescharacteristic
295C11×#102C2311yescharacteristic
296C11×#102C2311yescharacteristic
297C11×#102C2311yescharacteristic
298#66899C2312yes—
299#66899C2312yes—
300#66896C2312yes—
301#66896C2312yes—
302#66885C2312yes—
303#66885C2312yes—
304(C2×D11)⋊C8C2312yes—
305(C2×D11)⋊C8C2312yes—
306(C2×D11)⋊C8C2312yes—
307(C2×D11)⋊C8C2312yes—
308(C2×D11)⋊C8C2312yes—
309(C2×D11)⋊C8C2312yes—
310(C2×D11)⋊C8C2312yes—
311(C2×D11)⋊C8C2312yes—
312#66881C2312yes—
313#66881C2312yes—
314#66880C2312yes—
315#66880C2312yes—
316#66874C2312yes—
317#66874C2312yes—
318#66873C2312yes—
319#66873C2312yes—
320#66872C2312yes—
321#66872C2312yes—
322#66871C2312yes—
323#66871C2312yes—
324#60769—111nomaximal, Sylow
325C24×C11C2×D411yescharacteristic
326C23×D11—21no—
327C23×D11—22no—
328C23×D11C2×D412yes—
329C11×#41—22no—
330C11×#41—22no—
331C11×#41—22no—
332C11×#41—22no—
333C2×Q8×C11C2411yescharacteristic
334C2×Q8×C11C2411yescharacteristic
335C2×D4×C11—21no—
336C2×D4×C11—21no—
337C2×D4×C11—21no—
338C2×D4×C11—21no—
339C2×D4×C11—21no—
340C2×D4×C11—21no—
341C2×D4×C11C2411yescharacteristic
342C2×D4×C11C2411yescharacteristic
343C22×C4×C11—22no—
344C22×C4×C11—22no—
345C22×C4×C11—21no—
346C22×C4×C11—21no—
347C22×C4×C11C2×D411yescharacteristic
348C22×C4×C11C2×D411yescharacteristic
349C22×C4×C11C2×D411yescharacteristic
350C22×C4×C11C2411yescharacteristic
351C22×C4×C11C2411yescharacteristic
352C22×C4×C11C2411yescharacteristic
353C2×C22⋊D11—22no—
354C2×C22⋊D11—22no—
355C2×C22⋊D11—22no—
356C2×C22⋊D11—22no—
357C2×C22⋊D11—22no—
358C2×C22⋊D11—22no—
359C2×C22⋊D11—44no—
360C2×C22⋊D11—82no—
361C2×C22⋊D11C2×D412yes—
362C2×C22⋊D11C2×D412yes—
363C2×C22⋊D11C2×D412yes—
364C2×C22⋊D11C2×D412yes—
365C22×Dic11—22no—
366C22×Dic11—21no—
367C22×Dic11—21no—
368C22×Dic11—21no—
369C22×Dic11C2×D412yes—
370#4343—42no—
371#4343—42no—
372Q8×D11—42no—
373Q8×D11—42no—
374#4341—42no—
375#4341—42no—
376#4341—48no—
377D4×D11—42no—
378D4×D11—42no—
379D4×D11—48no—
380D4×D11—84no—
381#4339—22no—
382#4339—22no—
383#4339—22no—
384#4339—22no—
385#4339—42no—
386#4339—42no—
387#4339—42no—
388#4339—42no—
389#4339—44no—
390#4339—44no—
391#4339—44no—
392C2×D44—22no—
393C2×D44—22no—
394C2×D44—22no—
395C2×D44—21no—
396C2×D44—22no—
397C2×D44—22no—
398C2×D44—42no—
399C2×D44—44no—
400C2×D44C2×D411yescharacteristic
401C2×D44C2×D411yescharacteristic
402C2×D44C2×D412yes—
403C2×D44C2412yes—
404C2×C4×D11—22no—
405C2×C4×D11—22no—
406C2×C4×D11—22no—
407C2×C4×D11—22no—
408C2×C4×D11—42no—
409C2×C4×D11—42no—
410C2×C4×D11C2×D412yes—
411C2×C4×D11C2×D412yes—
412C2×C4×D11C2412yes—
413C2×C4×D11C2412yes—
414C2×Dic22—22no—
415C2×Dic22—21no—
416C2×Dic22—22no—
417C2×Dic22—22no—
418C2×Dic22—42no—
419C2×Dic22—44no—
420C2×Dic22C2×D411yescharacteristic
421C2×Dic22C2×D411yescharacteristic
422C2×Dic22C2×D412yes—
423C2×Dic22C2412yes—
424C11×Q16—41no—
425C11×SD16—41no—
426C11×SD16—41no—
427C11×D8—41no—
428C2×C8×C11—22no—
429C2×C8×C11—22no—
430C2×C8×C11—41no—
431C2×C8×C11—41no—
432C2×C8×C11—41no—
433C2×C8×C11—41no—
434C2×C8×C11C2411yescharacteristic
435C2×C8×C11C2411yescharacteristic
436C2×C8×C11C2411yescharacteristic
437C2×C8×C11C2411yescharacteristic
438C11×C4⋊C4—21no—
439C11×C4⋊C4—21no—
440C11×C4⋊C4—21no—
441C11×C4⋊C4—21no—
442C11×C4⋊C4C2411yescharacteristic
443C11×C4⋊C4C2411yescharacteristic
444C11×C4⋊C4C2411yescharacteristic
445C11×C4⋊C4C2411yescharacteristic
446C11×C22⋊C4—21no—
447C11×C22⋊C4—21no—
448C11×C22⋊C4—21no—
449C11×C22⋊C4—21no—
450C11×C22⋊C4—21no—
451C11×C22⋊C4—21no—
452C11×C22⋊C4—21no—
453C11×C22⋊C4—21no—
454C11×C22⋊C4—21no—
455C11×C22⋊C4—21no—
456C42×C11—21no—
457C42×C11—21no—
458C22⋊Dic11—22no—
459C22⋊Dic11—22no—
460C22⋊Dic11—22no—
461C22⋊Dic11—22no—
462#4326—42no—
463#4325—42no—
464#4324—42no—
465#4323—42no—
466(C2×D11)⋊C4—22no—
467(C2×D11)⋊C4—22no—
468(C2×D11)⋊C4—22no—
469(C2×D11)⋊C4—22no—
470(C2×D11)⋊C4—22no—
471(C2×D11)⋊C4—22no—
472(C2×D11)⋊C4—22no—
473(C2×D11)⋊C4—22no—
474(C2×D11)⋊C4—22no—
475(C2×D11)⋊C4—22no—
476C4⋊Dic11—22no—
477C4⋊Dic11—22no—
478C4⋊Dic11—21no—
479C4⋊Dic11—21no—
480C4⋊Dic11C2412yes—
481C4⋊Dic11C2412yes—
482Dic11⋊C4—22no—
483Dic11⋊C4—22no—
484Dic11⋊C4—22no—
485Dic11⋊C4—22no—
486Dic11⋊C4—22no—
487Dic11⋊C4—22no—
488C4×Dic11—22no—
489C4×Dic11—22no—
490#4318—22no—
491#4318—22no—
492#4318—42no—
493C2×C11⋊C8—42no—
494C2×C11⋊C8C2412yes—
495C2×C11⋊C8C2412yes—
496#4314—42no—
497#4314—42no—
498#3489—111no—
499#3488—111no—
500#3204—112no—
501#3201—112no—
502#3200—112no—
503#3198—112no—
504#3191—112no—
505#3190—112no—
506#3188—112no—
507#3187—112no—
508#3099—111no—
509#3099—111no—
510#3097—111no—
511#3096—111no—
512#3056—111no—
513#3055—111no—
514#3050D1111yescharacteristic, complemented
515C2×#465—111no—
516#3013—111no—
517#3012—111no—
518#3010—111no—
519#3009—111no—
520C2×#408—111no—
521C23×C11—22no—
522C23×C11—22no—
523C23×C11—21no—
524C23×C11—21no—
525C23×C11—41no—
526C23×C11C22×D411yescharacteristic
527C23×C11C22×D411yescharacteristic
528C23×C11C22×D411yescharacteristic
529C22×D11—24no—
530C22×D11—22no—
531C22×D11—42no—
532C22×D11—42no—
533C22×D11—44no—
534C22×D11—42no—
535C22×D11—82no—
536C22×D11—82no—
537C22×D11—81no—
538C22×D11—81no—
539C22×D11C22×D412yes—
540C22×D11C22×D412yes—
541Q8×C11—21no—
542Q8×C11—21no—
543Q8×C11—21no—
544Q8×C11—21no—
545D4×C11—21no—
546D4×C11—21no—
547D4×C11—21no—
548D4×C11—21no—
549D4×C11—42no—
550D4×C11—42no—
551D4×C11—42no—
552D4×C11—42no—
553D4×C11—81no—
554D4×C11—81no—
555C2×C4×C11—22no—
556C2×C4×C11—22no—
557C2×C4×C11—22no—
558C2×C4×C11—21no—
559C2×C4×C11—21no—
560C2×C4×C11—21no—
561C2×C4×C11—21no—
562C2×C4×C11—21no—
563C2×C4×C11—21no—
564C2×C4×C11—21no—
565C2×C4×C11—21no—
566C2×C4×C11—21no—
567C2×C4×C11—21no—
568C2×C4×C11—42no—
569C2×C4×C11—42no—
570C2×C4×C11C22×D411yescharacteristic
571C2×C4×C11C22×D411yescharacteristic
572C2×C4×C11C22×D411yescharacteristic
573C2×C4×C11H(5,𝔽2)12yes—
574C2×C4×C11H(5,𝔽2)12yes—
575C2×C4×C11C2511yescharacteristic
576C22⋊D11—24no—
577C22⋊D11—24no—
578C22⋊D11—42no—
579C22⋊D11—42no—
580C22⋊D11—44no—
581C22⋊D11—44no—
582C22⋊D11—44no—
583C22⋊D11—82no—
584C22⋊D11—82no—
585C22⋊D11—82no—
586C2×Dic11—22no—
587C2×Dic11—22no—
588C2×Dic11—22no—
589C2×Dic11—42no—
590C2×Dic11—44no—
591C2×Dic11—42no—
592C2×Dic11—81no—
593C2×Dic11—81no—
594C2×Dic11C22×D412yes—
595C2×Dic11C22×D412yes—
596D44—22no—
597D44—22no—
598D44—22no—
599D44—22no—
600D44—42no—
601D44—44no—
602D44—42no—
603D44—82no—
604D44—82no—
605C4×D11—22no—
606C4×D11—22no—
607C4×D11—22no—
608C4×D11—22no—
609C4×D11—42no—
610C4×D11—42no—
611C4×D11—44no—
612C4×D11—44no—
613C4×D11—82no—
614C4×D11—82no—
615Dic22—22no—
616Dic22—22no—
617Dic22—22no—
618Dic22—22no—
619Dic22—42no—
620Dic22—44no—
621Dic22—42no—
622C8×C11—21no—
623C8×C11—21no—
624C8×C11—21no—
625C8×C11—21no—
626C11⋊C8—22no—
627C11⋊C8—22no—
628C2×2−1+4—111no—
629C2×H(5,𝔽2)—111no—
630C22×#41—111no—
631C2×#137—111no—
632C2×AGL(1,ℤ/8)—111no—
633C2×#135C2×D1111yescharacteristic, complemented
634C22×SD16—111no—
635C22×M16—111no—
636C23×C8C2×D1111yescharacteristic, complemented
637#550—221no—
638D4×Q8—221no—
639#548—221no—
640#548—221no—
641#547—221no—
642#547—222no—
643#546—221no—
644#546—221no—
645#546—222no—
646#546—222no—
647D42—221no—
648D42—222no—
649#537—111no—
650#537—111no—
651#537—112no—
652#537—112no—
653#536—112no—
654#536—111no—
655#535—112no—
656#535—111no—
657#525—112no—
658#525—112no—
659#525C2×D1111yescharacteristic
660#525C2×D1111yescharacteristic, complemented
661C2×C22⋊Q8—111no—
662C2×C22⋊Q8—112no—
663C2×#121—111no—
664C2×#121—112no—
665#520—111no—
666#520—111no—
667#485—112no—
668#485—112no—
669#485—112no—
670#485—112no—
671#484—112no—
672#483—112no—
673#483—112no—
674#483—112no—
675#482—112no—
676#482—112no—
677#482—112no—
678#482—112no—
679#481—112no—
680#481—112no—
681#481—112no—
682#480—112no—
683#470—112no—
684#469—112no—
685#468—112no—
686#468—112no—
687#467—112no—
688#467C2×D1111yescharacteristic, complemented
689#467C2×D1111yescharacteristic, complemented
690#466—112no—
691#466C2×D1111yescharacteristic, complemented
692#466C2×D1111yescharacteristic, complemented
693#465—112no—
694#465—112no—
695#465—112no—
696#465—112no—
697#465—112no—
698#465—112no—
699#465C2×D1111yescharacteristic, complemented
700#465C2×D1111yescharacteristic, complemented
701#465C2×D1111yescharacteristic, complemented
702#465C2×D1111yescharacteristic, complemented
703#452—112no—
704#452—112no—
705#452—112no—
706#452—112no—
707#451—112no—
708#450—112no—
709#450—112no—
710#450—112no—
711#449—112no—
712#449—112no—
713#449—112no—
714#449—112no—
715#448—112no—
716#448—112no—
717#448—112no—
718#447—112no—
719#428—111no—
720#428—111no—
721#427C2×D1111yescharacteristic, complemented
722C2×#106—111no—
723#419—111no—
724#418—111no—
725#417—111no—
726#417—111no—
727#416C2×D1111yescharacteristic, complemented
728#416C2×D1111yescharacteristic, complemented
729C2×#103—111no—
730C2×#102—111no—
731#408—111no—
732#408—111no—
733#408—111no—
734#408—111no—
735#408—112no—
736#408—112no—
737C2×C22⋊C8—112no—
738C2×C22⋊C8—112no—
739C22×C11—21no—
740C22×C11—21no—
741C22×C11—21no—
742C22×C11—21no—
743C22×C11—21no—
744C22×C11—21no—
745C22×C11—21no—
746C22×C11—44no—
747C22×C11—41no—
748C22×C11—41no—
749C22×C11—41no—
750C22×C11—41no—
751C22×C11—41no—
752C22×C11—41no—
753C22×C11#53412yes—
754C22×C11#57712yes—
755C22×C11C23×D411yescharacteristic
756C2×D11—22no—
757C2×D11—22no—
758C2×D11—22no—
759C2×D11—22no—
760C2×D11—22no—
761C2×D11—22no—
762C2×D11—42no—
763C2×D11—42no—
764C2×D11—42no—
765C2×D11—84no—
766C2×D11—164no—
767C2×D11—162no—
768C4×C11—21no—
769C4×C11—21no—
770C4×C11—41no—
771C4×C11—41no—
772C4×C11—41no—
773C4×C11—41no—
774C4×C11—41no—
775C4×C11—41no—
776C4×C11#53412yes—
777C4×C11C2×H(5,𝔽2)11yescharacteristic
778C4×C11C2×H(5,𝔽2)11yescharacteristic
779Dic11—22no—
780Dic11—22no—
781Dic11—42no—
782Dic11—42no—
783Dic11—42no—
7842−1+4—442no—
7852−1+4—442no—
786H(5,𝔽2)—442no—
787H(5,𝔽2)—442no—
788C2×#41—112no—
789C2×#41—111no—
790C2×#41—111no—
791C2×#41—111no—
792C2×#41—111no—
793C2×#41—112no—
794C2×#41—112no—
795C2×#41—112no—
796C2×#41—221no—
797C2×#41—221no—
798C2×#41—222no—
799C2×#41—442no—
800C2×#41—442no—
801C2×#41C22×D1111yescharacteristic
802C2×#41C22×D1111yescharacteristic
803C22×Q8—111no—
804C22×Q8—112no—
805C22×Q8—111no—
806C22×Q8—221no—
807C22×D4—112no—
808C22×D4—112no—
809C22×D4—111no—
810C22×D4—111no—
811C22×D4—221no—
812C22×D4—222no—
813C22×D4—222no—
814C22×D4—221no—
815C23×C4—112no—
816C23×C4C22×D1111yescharacteristic
817#137—442no—
818AGL(1,ℤ/8)—442no—
819#135—42no—
820C2×Q16—112no—
821C2×Q16C22×D1111yescharacteristic
822C2×SD16—112no—
823C2×SD16—112no—
824C2×SD16—112no—
825C2×SD16—112no—
826C2×SD16—442no—
827C2×SD16C22×D1111yescharacteristic
828C2×SD16C22×D1111yescharacteristic
829C2×D8—112no—
830C2×D8C22×D1111yescharacteristic
831C2×M16—111no—
832C2×M16—111no—
833C2×M16—112no—
834C2×M16—442no—
835C22×C8—42no—
836C22×C8—112no—
837C22×C8C22×D1111yescharacteristic
838C22×C8C22×D1111yescharacteristic
839C22×C8C22×D1111yescharacteristic
840C22×C8C22×D1111yescharacteristic
841C22×C8C22×D1111yescharacteristic
842C22×C8C22×D1111yescharacteristic
843C4⋊Q8—221no—
844C4⋊Q8—222no—
845#127—221no—
846#127—222no—
847#124—221no—
848#124—221no—
849#124—222no—
850#124—222no—
851#123—21no—
852#123—21no—
853#123—222no—
854#123—222no—
855#123—222no—
856#123—222no—
857#123—222no—
858C22⋊Q8—112no—
859C22⋊Q8—112no—
860C22⋊Q8—112no—
861C22⋊Q8—112no—
862C22⋊Q8—112no—
863C22⋊Q8—112no—
864C22⋊Q8—222no—
865C22⋊Q8—222no—
866C22⋊Q8—222no—
867C22⋊Q8—222no—
868C22⋊Q8—221no—
869C22⋊Q8—221no—
870C22⋊Q8—221no—
871C22⋊Q8—221no—
872C22⋊Q8C22×D1111yescharacteristic
873C22⋊Q8C22×D1111yescharacteristic
874C22⋊Q8C22×D1111yescharacteristic
875C22⋊Q8C22×D1111yescharacteristic
876#121—112no—
877#121—112no—
878#121—112no—
879#121—112no—
880#121—112no—
881#121—112no—
882#121—222no—
883#121—222no—
884#121—222no—
885#121—222no—
886#121—222no—
887#121—221no—
888#121—221no—
889#121—222no—
890#121—222no—
891#121—222no—
892#121—222no—
893#121—222no—
894#121—221no—
895#121—221no—
896#121C22×D1111yescharacteristic
897#121C22×D1111yescharacteristic
898#121C22×D1111yescharacteristic
899#121C22×D1111yescharacteristic
900#120—21no—
901#120—21no—
902#120—222no—
903#120—222no—
904#120—222no—
905#120—222no—
906#120—222no—
907C4×Q8—221no—
908C4×Q8—221no—
909C4×D4—21no—
910C4×D4—21no—
911C4×D4—21no—
912C4×D4—21no—
913C4×D4—221no—
914C4×D4—221no—
915C4×D4—222no—
916C4×D4—222no—
917C4×D4—222no—
918C4×D4—222no—
919C4×D4—222no—
920C4×D4—222no—
921#117—112no—
922#117—112no—
923#117C22×D1111yescharacteristic
924#117C22×D1111yescharacteristic
925C2×C4⋊C4—111no—
926C2×C4⋊C4—111no—
927C2×C4⋊C4—112no—
928C2×C4⋊C4—112no—
929C2×C4⋊C4—222no—
930C2×C4⋊C4—221no—
931C2×C22⋊C4—222no—
932C2×C22⋊C4—222no—
933C2×C22⋊C4—221no—
934C2×C22⋊C4—221no—
935#107—112no—
936#107—112no—
937#107C22×D1111yescharacteristic
938#107C22×D1111yescharacteristic
939#106—112no—
940#106—112no—
941#106—112no—
942#106—112no—
943#106C22×D1111yescharacteristic
944#106C22×D1111yescharacteristic
945#103—112no—
946#103—112no—
947#103—112no—
948#103—112no—
949#103—112no—
950#103—112no—
951#103C22×D1111yescharacteristic
952#103C22×D1111yescharacteristic
953#103C22×D1111yescharacteristic
954#103C22×D1111yescharacteristic
955#102—112no—
956#102—112no—
957#102—112no—
958#102—112no—
959#102—112no—
960#102—112no—
961#102C22×D1111yescharacteristic
962#102C22×D1111yescharacteristic
963#102C22×D1111yescharacteristic
964#102C22×D1111yescharacteristic
965C22⋊C8—112no—
966C22⋊C8—112no—
967C22⋊C8—112no—
968C22⋊C8—112no—
969C22⋊C8—112no—
970C22⋊C8—112no—
971C22⋊C8—112no—
972C22⋊C8—112no—
973C2×C11—22no—
974C2×C11—22no—
975C2×C11—41no—
976C2×C11—81no—
977C2×C11—81no—
978C2×C11C2×#53411yescharacteristic
979C2×C11C2×#57711yescharacteristic
980C2×C11#358411yescharacteristic
981D11—42no—
982D11—42no—
983D11—82no—
984C24—112no—
985C24—222no—
986C24—221no—
987C24D4×D1111yescharacteristic
988#41—22no—
989#41—22no—
990#41—22no—
991#41—22no—
992#41—222no—
993#41—222no—
994#41—222no—
995#41—222no—
996#41—442no—
997#41—442no—
998#41—444no—
999#41—442no—
1000#41—442no—
1001#41—444no—
1002#41—444no—
1003#41—442no—
1004#41—442no—
1005#41—442no—
1006#41—442no—
1007#41—448no—
1008C2×Q8—111no—
1009C2×Q8—111no—
1010C2×Q8—112no—
1011C2×Q8—112no—
1012C2×Q8—222no—
1013C2×Q8—221no—
1014C2×Q8—222no—
1015C2×Q8—222no—
1016C2×Q8—442no—
1017C2×Q8—444no—
1018C2×Q8—442no—
1019C2×Q8—442no—
1020C2×Q8C23×D1111yescharacteristic
1021C2×Q8C23×D1111yescharacteristic
1022C2×D4—21no—
1023C2×D4—21no—
1024C2×D4—21no—
1025C2×D4—21no—
1026C2×D4—21no—
1027C2×D4—21no—
1028C2×D4—112no—
1029C2×D4—112no—
1030C2×D4—112no—
1031C2×D4—112no—
1032C2×D4—111no—
1033C2×D4—111no—
1034C2×D4—112no—
1035C2×D4—112no—
1036C2×D4—222no—
1037C2×D4—222no—
1038C2×D4—222no—
1039C2×D4—222no—
1040C2×D4—222no—
1041C2×D4—222no—
1042C2×D4—222no—
1043C2×D4—222no—
1044C2×D4—222no—
1045C2×D4—221no—
1046C2×D4—222no—
1047C2×D4—222no—
1048C2×D4—442no—
1049C2×D4—444no—
1050C2×D4—442no—
1051C2×D4—442no—
1052C2×D4—448no—
1053C2×D4—444no—
1054C2×D4—884no—
1055C2×D4—882no—
1056C2×D4C23×D1111yescharacteristic
1057C2×D4C23×D1111yescharacteristic
1058C22×C4—22no—
1059C22×C4—22no—
1060C22×C4—21no—
1061C22×C4—21no—
1062C22×C4—112no—
1063C22×C4—112no—
1064C22×C4—112no—
1065C22×C4—112no—
1066C22×C4—112no—
1067C22×C4—222no—
1068C22×C4—222no—
1069C22×C4—222no—
1070C22×C4—222no—
1071C22×C4—222no—
1072C22×C4—221no—
1073C22×C4—221no—
1074C22×C4—221no—
1075C22×C4—442no—
1076C22×C4—442no—
1077C22×C4D4×D1111yescharacteristic
1078C22×C4D4×D1111yescharacteristic
1079C22×C4D4×D1111yescharacteristic
1080C22×C4C23×D1111yescharacteristic
1081C22×C4C23×D1111yescharacteristic
1082C22×C4C23×D1111yescharacteristic
1083Q16—41no—
1084Q16—442no—
1085SD16—41no—
1086SD16—41no—
1087SD16—442no—
1088SD16—442no—
1089SD16—442no—
1090SD16—442no—
1091D8—41no—
1092D8—442no—
1093M16—222no—
1094M16—222no—
1095M16—442no—
1096C2×C8—22no—
1097C2×C8—22no—
1098C2×C8—41no—
1099C2×C8—41no—
1100C2×C8—41no—
1101C2×C8—41no—
1102C2×C8—112no—
1103C2×C8—112no—
1104C2×C8—442no—
1105C2×C8C23×D1111yescharacteristic
1106C2×C8C23×D1111yescharacteristic
1107C2×C8C23×D1111yescharacteristic
1108C2×C8C23×D1111yescharacteristic
1109C4⋊C4—21no—
1110C4⋊C4—21no—
1111C4⋊C4—21no—
1112C4⋊C4—21no—
1113C4⋊C4—112no—
1114C4⋊C4—112no—
1115C4⋊C4—222no—
1116C4⋊C4—222no—
1117C4⋊C4—222no—
1118C4⋊C4—222no—
1119C4⋊C4—222no—
1120C4⋊C4—222no—
1121C4⋊C4—221no—
1122C4⋊C4—221no—
1123C4⋊C4—222no—
1124C4⋊C4—222no—
1125C4⋊C4C23×D1111yescharacteristic
1126C4⋊C4C23×D1111yescharacteristic
1127C4⋊C4C23×D1111yescharacteristic
1128C4⋊C4C23×D1111yescharacteristic
1129C22⋊C4—21no—
1130C22⋊C4—21no—
1131C22⋊C4—21no—
1132C22⋊C4—21no—
1133C22⋊C4—21no—
1134C22⋊C4—21no—
1135C22⋊C4—21no—
1136C22⋊C4—21no—
1137C22⋊C4—21no—
1138C22⋊C4—21no—
1139C22⋊C4—222no—
1140C22⋊C4—222no—
1141C22⋊C4—222no—
1142C22⋊C4—222no—
1143C22⋊C4—222no—
1144C22⋊C4—222no—
1145C22⋊C4—222no—
1146C22⋊C4—222no—
1147C22⋊C4—222no—
1148C22⋊C4—222no—
1149C22⋊C4—222no—
1150C22⋊C4—222no—
1151C22⋊C4—222no—
1152C22⋊C4—222no—
1153C42—21no—
1154C42—21no—
1155C42—222no—
1156C42—222no—
1157C11#6076911yescharacteristic, complemented, Sylow
1158C23—22no—
1159C23—22no—
1160C23—21no—
1161C23—21no—
1162C23—41no—
1163C23—112no—
1164C23—112no—
1165C23—224no—
1166C23—222no—
1167C23—442no—
1168C23—442no—
1169C23—444no—
1170C23—442no—
1171C23—881no—
1172C23—881no—
1173C23—882no—
1174C23—882no—
1175C23C2×D4×D1111yescharacteristic
1176C23C2×D4×D1111yescharacteristic
1177C23C2×D4×D1111yescharacteristic
1178Q8—21no—
1179Q8—21no—
1180Q8—21no—
1181Q8—21no—
1182Q8—222no—
1183Q8—222no—
1184Q8—222no—
1185Q8—222no—
1186Q8—442no—
1187Q8—444no—
1188Q8—442no—
1189D4—21no—
1190D4—21no—
1191D4—21no—
1192D4—21no—
1193D4—42no—
1194D4—42no—
1195D4—42no—
1196D4—42no—
1197D4—81no—
1198D4—81no—
1199D4—224no—
1200D4—224no—
1201D4—222no—
1202D4—222no—
1203D4—222no—
1204D4—222no—
1205D4—442no—
1206D4—444no—
1207D4—442no—
1208D4—442no—
1209D4—444no—
1210D4—444no—
1211D4—444no—
1212D4—442no—
1213D4—882no—
1214D4—882no—
1215D4—882no—
1216D4—882no—
1217D4—882no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—112no—
1234C2×C4—112no—
1235C2×C4—222no—
1236C2×C4—222no—
1237C2×C4—222no—
1238C2×C4—222no—
1239C2×C4—222no—
1240C2×C4—222no—
1241C2×C4—222no—
1242C2×C4—442no—
1243C2×C4—442no—
1244C2×C4—444no—
1245C2×C4—444no—
1246C2×C4—442no—
1247C2×C4—444no—
1248C2×C4—442no—
1249C2×C4—882no—
1250C2×C4—882no—
1251C2×C4—881no—
1252C2×C4—881no—
1253C2×C4C2×D4×D1111yescharacteristic
1254C2×C4C2×D4×D1111yescharacteristic
1255C2×C4C2×D4×D1111yescharacteristic
1256C2×C4#6703712yes—
1257C2×C4#6704212yes—
1258C2×C4C24×D1111yescharacteristic
1259C8—21no—
1260C8—21no—
1261C8—21no—
1262C8—21no—
1263C8—222no—
1264C8—222no—
1265C22—21no—
1266C22—21no—
1267C22—21no—
1268C22—21no—
1269C22—21no—
1270C22—21no—
1271C22—21no—
1272C22—44no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—222no—
1280C22—222no—
1281C22—222no—
1282C22—222no—
1283C22—222no—
1284C22—222no—
1285C22—442no—
1286C22—442no—
1287C22—442no—
1288C22—884no—
1289C22—1762no—
1290C22—1764no—
1291C22#1062313612yes—
1292C22#1062330112yes—
1293C22C22×D4×D1111yescharacteristic
1294C4—21no—
1295C4—21no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—222no—
1303C4—222no—
1304C4—442no—
1305C4—442no—
1306C4—442no—
1307C4#1062313612yes—
1308C4C2×#6703711yescharacteristic
1309C4C2×#6704211yescharacteristic
1310C2—22no—
1311C2—22no—
1312C2—41no—
1313C2—81no—
1314C2—81no—
1315C2—442no—
1316C2—442no—
1317C2—882no—
1318C2C2×#1062313611yescharacteristic
1319C2C2×#1062330111yescharacteristic
1320C2#1308338511yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3050C2
socleC22×C11C23×D4
hypercenter#3050D11
hypocenterC11#60769
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. #13082288C2semidirect
2. #13082277C2semidirect
3. #13079521C2semidirect
4. #13079501C2semidirect
5. #13079482C2semidirect
6. #13079461C2semidirect
7. #13079405C2semidirect
8. #13079398C2semidirect
9. #13079376C2semidirect
10. #13079368C2semidirect
11. #13078603C2semidirect
12. #13078603C2semidirect
13. #13078588C2semidirect
14. #13078577C2semidirect
15. #13078248C2semidirect
16. #13078237C2semidirect
17. C2×#10622727C2semidirect
18. #13077927C2semidirect
19. #13077916C2semidirect
20. #13077905C2semidirect
21. #13077896C2semidirect
22. C2×#10622723C2semidirect
23. C11×#3050C2semidirect
24. C2×#67043C22semidirect
27. C2×C11×#135C22semidirect
28. C23×C8×C11C22semidirect
30. C11×#525C22semidirect
33. C2×#67004C22semidirect
34. C2×#67002C22semidirect
36. C2×#66977C22semidirect
37. C22×#4318C22semidirect
38. C22×#4314C22semidirect
42. #10623159C22semidirect
44. D11×C22⋊Q8C22semidirect
45. #10623139C22semidirect
47. #10623137C22semidirect
62. #10623054C22semidirect
63. C11×#467C22semidirect
64. C11×#467C22semidirect
65. C11×#466C22semidirect
66. C11×#466C22semidirect
67. C11×#465C22semidirect
68. C11×#465C22semidirect
69. C11×#465C22semidirect
70. C11×#465C22semidirect
71. C11×#427C22semidirect
72. C11×#416C22semidirect
73. C11×#416C22semidirect
74. #10622845C22semidirect
75. #10622845C22semidirect
76. #10622800C22semidirect
77. #10622799C22semidirect
78. #10622786C22semidirect
79. #10622785C22semidirect
80. #10622783C22semidirect
81. #10622782C22semidirect
82. #10622771C22semidirect
83. #10622769C22semidirect
84. #10622727C22semidirect
85. #10622727C22semidirect
86. #10622727C22semidirect
87. #10622727C22semidirect
88. C2×#66885C22semidirect
91. #10622723C22semidirect
92. #10622723C22semidirect
93. #10622723C22semidirect
94. #10622723C22semidirect
95. C2×(C2×D11)⋊C8C22semidirect
96. C2×(C2×D11)⋊C8C22semidirect
97. C2×#66881C22semidirect
98. C2×#66880C22semidirect
99. #10622665C22semidirect
100. #10622664C22semidirect
101. #10622662C22semidirect
102. #10622661C22semidirect
103. #10622655C22semidirect
104. #10622654C22semidirect
105. #10622652C22semidirect
106. #10622651C22semidirect
107. #10622617C22semidirect
108. #10622614C22semidirect
109. #10622608C22semidirect
110. #10622608C22semidirect
111. #10622501C22semidirect
112. #10622498C22semidirect
113. #10622497C22semidirect
114. #10622495C22semidirect
115. #10622480C22semidirect
116. #10622479C22semidirect
117. #10622476C22semidirect
118. #10622475C22semidirect
119. #10622428C22semidirect
120. #10622428C22semidirect
121. #10622423C22semidirect
122. #10622423C22semidirect
123. #10622419C22semidirect
124. #10622419C22semidirect
125. #10622418C22semidirect
126. #10622418C22semidirect
127. #10622394C22semidirect
128. #10622394C22semidirect
129. #10622392C22semidirect
130. #10622392C22semidirect
131. #10622390C22semidirect
132. #10622390C22semidirect
133. #10622389C22semidirect
134. #10622389C22semidirect
514. #3050D11semidirect
633. C2×#135C2×D11semidirect
636. C23×C8C2×D11semidirect
660. #525C2×D11semidirect
688. #467C2×D11semidirect
689. #467C2×D11semidirect
691. #466C2×D11semidirect
692. #466C2×D11semidirect
699. #465C2×D11semidirect
700. #465C2×D11semidirect
701. #465C2×D11semidirect
702. #465C2×D11semidirect
721. #427C2×D11semidirect
727. #416C2×D11semidirect
728. #416C2×D11semidirect
1157. C11#60769semidirect

Maximal subgroups

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

subgroupindex
#130822882
#130822772
#130795212
#130795012
#130794822
#130794612
#130794052
#130793982
#130793762
#130793682
#130786032
#130785882
#130785772
#130782482
#130782372
C2×#106227272
#130779272
#130779162
#130779052
#130778962
C2×#106227232
C11×#30502
#6076911