Finite Group Databasebeta

← #15624901

Subgroups — #15624901

Order 2816.

2186 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#13082281C211yesmaximal, characteristic, complemented
3#13079512C212yesmaximal, complemented
4#13079491C212yesmaximal, complemented
5#13079482C212yesmaximal, complemented
6#13079461C212yesmaximal, complemented
7#13079452C212yesmaximal, complemented
8#13079441C212yesmaximal, complemented
9#13079425C212yesmaximal, complemented
10#13079417C212yesmaximal, complemented
11#13078598C211yesmaximal, characteristic, complemented
12#13078593C211yesmaximal, characteristic, complemented
13#13078587C211yesmaximal, characteristic, complemented
14#13078572C211yesmaximal, characteristic, complemented
15#13078246C211yesmaximal, characteristic, complemented
16#13078222C211yesmaximal, characteristic, complemented
17C2×#10622655C211yesmaximal, characteristic, complemented
18#13077933C211yesmaximal, characteristic, complemented
19#13077919C211yesmaximal, characteristic, complemented
20#13077901C211yesmaximal, characteristic, complemented
21#13077894C211yesmaximal, characteristic, complemented
22#13077060C211yesmaximal, characteristic, complemented
23C11×#3055C211yesmaximal, characteristic, complemented
24C2×#67043C2211yescharacteristic, complemented
25C2×#67037C2211yescharacteristic
26C22×#4339C2211yescharacteristic
27C2×C11×AGL(1,ℤ/8)C2211yescharacteristic, complemented
28C22×C11×M16C2211yescharacteristic, complemented
29C11×#525C2211yescharacteristic, complemented
30C2×C11×#121C2211yescharacteristic
31#10623364C2211yescharacteristic
32C2×#67003C2211yescharacteristic, complemented
33#10623336C2211yescharacteristic
34D4×C22⋊D11—22no—
35C22×#4324C2211yescharacteristic, complemented
36#10623322C2211yescharacteristic
37C2×#66977C2211yescharacteristic, complemented
38C22×#4318C2211yescharacteristic, complemented
39C2×#66962C2211yescharacteristic, complemented
40#10623186—22no—
41#10623159C2212yescomplemented
42D11×C22⋊Q8C2212yescomplemented
43#10623143—21no—
44#10623140—21no—
45#10623139C2212yes—
46#10623139C2212yescomplemented
47#10623138C2212yes—
48#10623137C2212yes—
49#10623137C2212yescomplemented
50D11×#121C2212yes—
51#10623130—21no—
52#10623129—21no—
53#10623122—22no—
54#10623083—21no—
55#10623082—21no—
56#10623081—21no—
57D4×Dic22—21no—
58#10623057C2211yescharacteristic
59#10623054C2211yescharacteristic, complemented
60#10623041C2211yescharacteristic
61#10623035C2211yescharacteristic
62#10623021—22no—
63C11×#469C2212yescomplemented
64C11×#468C2212yescomplemented
65C11×#466C2212yescomplemented
66C11×#465C2212yescomplemented
67C11×#428C2211yescharacteristic, complemented
68C11×#418C2211yescharacteristic, complemented
69C11×#417C2211yescharacteristic, complemented
70#10622846C2211yescharacteristic, complemented
71C2×#66896C2211yescharacteristic, complemented
72#10622786C2212yescomplemented
73#10622783C2212yescomplemented
74#10622783C2212yescomplemented
75#10622782C2212yescomplemented
76#10622771C2212yescomplemented
77#10622771C2212yescomplemented
78#10622771C2212yescomplemented
79#10622769C2212yescomplemented
80#10622750C2212yescomplemented
81#10622747C2212yescomplemented
82#10622746C2211yescharacteristic, complemented
83#10622742C2211yescharacteristic
84#10622742C2211yescharacteristic
85#10622742C2211yescharacteristic, complemented
86#10622742C2211yescharacteristic, complemented
87#10622739C2212yescomplemented
88#10622739C2212yescomplemented
89#10622734C2211yescharacteristic, complemented
90#10622733C2211yescharacteristic, complemented
91#10622729C2212yescomplemented
92#10622727C2212yescomplemented
93#10622723C2212yescomplemented
94#10622723C2212yescomplemented
95#10622665C2211yescharacteristic, complemented
96#10622665C2211yescharacteristic, complemented
97#10622662C2211yescharacteristic, complemented
98#10622662C2211yescharacteristic, complemented
99#10622655C2212yescomplemented
100#10622655C2212yescomplemented
101#10622655C2211yescharacteristic, complemented
102#10622655C2212yescomplemented
103#10622655C2212yescomplemented
104#10622655C2211yescharacteristic, complemented
105#10622652C2211yescharacteristic, complemented
106#10622652C2211yescharacteristic, complemented
107#10622615C2211yescharacteristic, complemented
108#10622611C2211yescharacteristic, complemented
109C2×#66874C2211yescharacteristic, complemented
110C2×#66871C2211yescharacteristic, complemented
111#10622501C2212yescomplemented
112#10622497C2212yescomplemented
113#10622497C2212yescomplemented
114#10622495C2212yescomplemented
115#10622480C2212yescomplemented
116#10622480C2212yescomplemented
117#10622479C2212yescomplemented
118#10622475C2212yescomplemented
119#10622428C2212yescomplemented
120#10622422C2212yescomplemented
121#10622421C2212yescomplemented
122#10622419C2212yescomplemented
123#10622397C2212yescomplemented
124#10622396C2212yescomplemented
125#10622396C2212yescomplemented
126#10622396C2212yescomplemented
127#10622394C2212yescomplemented
128#10622392C2212yescomplemented
129#10622392C2212yescomplemented
130#10622390C2212yescomplemented
131#10622389C2212yescomplemented
132#10622389C2212yescomplemented
133#10622387C2212yescomplemented
134#10622387C2212yescomplemented
135C2×C11×#41C2311yescharacteristic
136C22×D4×C11—21no—
137C22×D4×C11C2311yescharacteristic
138C23×C4×C11C2311yescharacteristic
139C22×C22⋊D11—22no—
140C22×C22⋊D11D412yes—
141#67043—42no—
142#67043—42no—
143C2×Q8×D11C2312yes—
144#67037—42no—
145#67037—42no—
146C2×#4341—22no—
147C2×#4341—21no—
148C2×#4341C2312yes—
149C2×#4341C2312yes—
150C2×D4×D11—22no—
151C2×D4×D11—21no—
152C2×D4×D11C2312yes—
153C2×#4339—21no—
154C2×#4339—42no—
155C2×#4339—42no—
156C2×#4339D412yes—
157C2×#4339D411yescharacteristic
158C2×#4339D411yescharacteristic
159C2×#4339C2311yescharacteristic
160C2×#4339C2311yescharacteristic
161C2×#4339C2312yes—
162C2×#4339C2311yescharacteristic
163C22×D44D411yescharacteristic
164C22×C4×D11C2312yes—
165C22×Dic22—21no—
166C22×Dic22D411yescharacteristic
167C22×Dic22C2311yescharacteristic
168C11×AGL(1,ℤ/8)—42no—
169C2×C11×SD16C2312yes—
170C2×C11×D8C2312yes—
171C2×C11×M16—42no—
172C2×C11×M16C2311yescharacteristic
173C2×C11×M16C2311yescharacteristic
174C2×C11×M16C2312yes—
175C22×C8×C11C2312yes—
176C11×#123—21no—
177C11×C22⋊Q8C2311yescharacteristic
178C11×C22⋊Q8C2311yescharacteristic
179C11×#121—21no—
180C11×#121—21no—
181C11×#121C2312yes—
182C11×#121C2312yes—
183C11×#121C2311yescharacteristic
184C11×#121C2311yescharacteristic
185C11×#120—21no—
186C4×D4×C11—21no—
187C4×D4×C11—21no—
188C11×#117C2311yescharacteristic
189C2×C11×C4⋊C4C2311yescharacteristic
190C2×C11×C22⋊C4—21no—
191#67006—21no—
192#67006—22no—
193C2×C22⋊Dic11—21no—
194#67003—42no—
195#66999C2312yes—
196C2×#4326C2311yescharacteristic
197C2×#4325C2311yescharacteristic
198#66993—22no—
199#66993—21no—
200#66992—22no—
201#66992—22no—
202#66992—22no—
203#66992—22no—
204#66991—22no—
205#66991—22no—
206#66991C2312yes—
207#66991C2312yes—
208#66991C2312yes—
209#66990—22no—
210#66990—22no—
211#66990—22no—
212#66989—21no—
213D4×Dic11—22no—
214D4×Dic11—22no—
215C2×#4324—42no—
216C2×#4324C2311yescharacteristic
217C2×#4324C2312yes—
218C2×#4324C2312yes—
219C2×#4323C2311yescharacteristic
220#66983—22no—
221#66983—21no—
222#66983C2311yescharacteristic
223#66983C2311yescharacteristic
224#66982—21no—
225C4×C22⋊D11—21no—
226C4×C22⋊D11—21no—
227C4×C22⋊D11—22no—
228#66979C2311yescharacteristic
229C2×C4⋊Dic11C2311yescharacteristic
230#66977—21no—
231#66977—21no—
232#66977—21no—
233#66977C2312yes—
234#66977C2311yescharacteristic
235#66977C2312yes—
236#66977C2311yescharacteristic
237C2×Dic11⋊C4—21no—
238C2×#4318—42no—
239C2×#4318C2311yescharacteristic
240C2×#4318C2311yescharacteristic
241C2×#4318C2311yescharacteristic
242C2×#4318C2311yescharacteristic
243C22×C11⋊C8C2311yescharacteristic
244C22×C11⋊C8C2311yescharacteristic
245#66962—42no—
246C2×Dic44C2312yes—
247C2×#4314C2312yes—
248#66950—21no—
249#66950C2312yes—
250#66950C2312yes—
251#66950C2312yes—
252#66949—22no—
253#66948—21no—
254#66948C2312yes—
255#66947—22no—
256#66946—21no—
257#66945C2312yes—
258#66945C2312yes—
259C4⋊C4×D11—22no—
260C4⋊C4×D11C2312yes—
261C4⋊C4×D11C2312yes—
262#66941—22no—
263#66940—21no—
264#66939—22no—
265#66938—22no—
266#66938—22no—
267#66937—22no—
268#66937—22no—
269#66937—22no—
270#66936—22no—
271#66936—22no—
272#66936—22no—
273#66935—22no—
274(C22⋊D11)⋊C4—22no—
275(C22⋊D11)⋊C4—22no—
276(C22⋊D11)⋊C4—22no—
277C22⋊C4×D11—22no—
278C22⋊C4×D11—22no—
279#66931—22no—
280#66931—22no—
281#66931—22no—
282#66928—21no—
283C4×D44—21no—
284#66922—21no—
285C4×Dic22—21no—
286C11×#107C2312yes—
287C11×#106C2312yes—
288C11×#103C2312yes—
289C11×#102C2312yes—
290C11×#102C2312yes—
291C11×#102C2312yes—
292#66899C2311yescharacteristic
293#66899C2311yescharacteristic
294#66896C2312yes—
295#66896C2311yescharacteristic
296#66896C2311yescharacteristic
297#66896C2312yes—
298#66885C2312yes—
299(C2×D11)⋊C8C2312yes—
300(C2×D11)⋊C8C2312yes—
301(C2×D11)⋊C8C2312yes—
302(C2×D11)⋊C8C2312yes—
303(C2×D11)⋊C8C2312yes—
304(C2×D11)⋊C8C2312yes—
305(C2×D11)⋊C8C2312yes—
306(C2×D11)⋊C8C2312yes—
307#66882C2312yes—
308#66881C2312yes—
309#66880C2312yes—
310#66880C2312yes—
311#66880C2312yes—
312#66874C2312yes—
313#66874C2311yescharacteristic
314#66874C2312yes—
315#66874C2311yescharacteristic
316#66873C2311yescharacteristic
317#66873C2311yescharacteristic
318#66872C2311yescharacteristic
319#66872C2311yescharacteristic
320#66871C2312yes—
321#66871C2311yescharacteristic
322#66871C2312yes—
323#66871C2311yescharacteristic
324#60772—111nomaximal, Sylow
325C24×C11—21no—
326C24×C11C2×D411yescharacteristic
327C23×D11—22no—
328C23×D11C2×D412yes—
329C11×#41—22no—
330C11×#41—22no—
331C2×Q8×C11C2411yescharacteristic
332C2×D4×C11—21no—
333C2×D4×C11—22no—
334C2×D4×C11—21no—
335C2×D4×C11—22no—
336C2×D4×C11—21no—
337C2×D4×C11—21no—
338C2×D4×C11—22no—
339C2×D4×C11—22no—
340C2×D4×C11—82no—
341C2×D4×C11C2411yescharacteristic
342C2×D4×C11C2412yes—
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—21no—
355C2×C22⋊D11—21no—
356C2×C22⋊D11—21no—
357C2×C22⋊D11—22no—
358C2×C22⋊D11—22no—
359C2×C22⋊D11—22no—
360C2×C22⋊D11—22no—
361C2×C22⋊D11—22no—
362C2×C22⋊D11—44no—
363C2×C22⋊D11—48no—
364C2×C22⋊D11C2×D412yes—
365C2×C22⋊D11C2×D412yes—
366C2×C22⋊D11C2×D412yes—
367C2×C22⋊D11C2×D412yes—
368C22×Dic11—22no—
369C22×Dic11—22no—
370C22×Dic11—21no—
371C22×Dic11—21no—
372C22×Dic11C2×D412yes—
373Q8×D11—42no—
374Q8×D11—42no—
375#4341—42no—
376#4341—42no—
377#4341—42no—
378#4341—42no—
379#4341—44no—
380#4341—48no—
381D4×D11—42no—
382D4×D11—42no—
383D4×D11—44no—
384D4×D11—84no—
385#4339—22no—
386#4339—22no—
387#4339—22no—
388#4339—22no—
389#4339—22no—
390#4339—22no—
391#4339—42no—
392#4339—42no—
393#4339—42no—
394#4339—42no—
395#4339—44no—
396#4339—44no—
397C2×D44—22no—
398C2×D44—42no—
399C2×D44C2×D411yescharacteristic
400C2×D44C2×D411yescharacteristic
401C2×D44C2×D412yes—
402C2×D44C2411yescharacteristic
403C2×C4×D11—22no—
404C2×C4×D11—22no—
405C2×C4×D11—22no—
406C2×C4×D11—21no—
407C2×C4×D11—42no—
408C2×C4×D11—42no—
409C2×C4×D11C2×D412yes—
410C2×C4×D11C2×D412yes—
411C2×C4×D11C2412yes—
412C2×C4×D11C2412yes—
413C2×Dic22—22no—
414C2×Dic22—21no—
415C2×Dic22—22no—
416C2×Dic22—22no—
417C2×Dic22—42no—
418C2×Dic22—44no—
419C2×Dic22C2×D411yescharacteristic
420C2×Dic22C2×D411yescharacteristic
421C2×Dic22C2×D412yes—
422C2×Dic22C2412yes—
423C2×Dic22C2411yescharacteristic
424C11×SD16—42no—
425C11×D8—42no—
426C11×M16—22no—
427C11×M16—22no—
428C11×M16—42no—
429C2×C8×C11—42no—
430C2×C8×C11C2412yes—
431C2×C8×C11C2412yes—
432C11×C4⋊C4—21no—
433C11×C4⋊C4—21no—
434C11×C4⋊C4—21no—
435C11×C4⋊C4C2412yes—
436C11×C4⋊C4C2411yescharacteristic
437C11×C4⋊C4C2411yescharacteristic
438C11×C22⋊C4—21no—
439C11×C22⋊C4—21no—
440C11×C22⋊C4—21no—
441C11×C22⋊C4—21no—
442C11×C22⋊C4—22no—
443C11×C22⋊C4—22no—
444C11×C22⋊C4—21no—
445C42×C11—21no—
446C22⋊Dic11—22no—
447C22⋊Dic11—22no—
448C22⋊Dic11—22no—
449C22⋊Dic11—22no—
450C22⋊Dic11—22no—
451C22⋊Dic11—21no—
452C22⋊Dic11—21no—
453C22⋊Dic11—21no—
454#4326—41no—
455#4325—41no—
456#4324—42no—
457#4324—42no—
458#4324—41no—
459#4323—41no—
460(C2×D11)⋊C4—22no—
461(C2×D11)⋊C4—22no—
462(C2×D11)⋊C4—22no—
463(C2×D11)⋊C4—22no—
464(C2×D11)⋊C4—22no—
465(C2×D11)⋊C4—22no—
466(C2×D11)⋊C4—22no—
467(C2×D11)⋊C4—21no—
468(C2×D11)⋊C4—21no—
469C4⋊Dic11—22no—
470C4⋊Dic11—22no—
471C4⋊Dic11—22no—
472C4⋊Dic11—21no—
473C4⋊Dic11C2412yes—
474C4⋊Dic11C2411yescharacteristic
475C4⋊Dic11C2411yescharacteristic
476Dic11⋊C4—22no—
477Dic11⋊C4—22no—
478Dic11⋊C4—22no—
479Dic11⋊C4—21no—
480Dic11⋊C4—22no—
481Dic11⋊C4—21no—
482Dic11⋊C4—22no—
483C4×Dic11—22no—
484C4×Dic11—22no—
485C4×Dic11—21no—
486#4318—41no—
487#4318—41no—
488#4318—41no—
489#4318—41no—
490C2×C11⋊C8—22no—
491C2×C11⋊C8—22no—
492C2×C11⋊C8C2411yescharacteristic
493C2×C11⋊C8C2411yescharacteristic
494C2×C11⋊C8C2411yescharacteristic
495C2×C11⋊C8C2411yescharacteristic
496Dic44—42no—
497#4314—42no—
498#3489—111no—
499#3488—111no—
500#3203—112no—
501#3201—112no—
502#3200—112no—
503#3198—112no—
504#3197—112no—
505#3196—112no—
506#3194—112no—
507#3193—112no—
508#3098—111no—
509#3098—111no—
510#3097—111no—
511#3096—111no—
512#3056—111no—
513#3055D1111yescharacteristic, complemented
514#3054—111no—
515C2×#468—111no—
516#3013—111no—
517#3012—111no—
518#3010—111no—
519#3009—111no—
520#2879—111no—
521C23×C11—22no—
522C23×C11—21no—
523C23×C11—22no—
524C23×C11—41no—
525C23×C11—41no—
526C23×C11—42no—
527C23×C11—81no—
528C23×C11—81no—
529C23×C11C22×D411yescharacteristic
530C23×C11C22×D411yescharacteristic
531C23×C11C22×D411yescharacteristic
532C22×D11—21no—
533C22×D11—42no—
534C22×D11—42no—
535C22×D11—42no—
536C22×D11—44no—
537C22×D11—82no—
538C22×D11—82no—
539C22×D11C22×D412yes—
540C22×D11C22×D412yes—
541Q8×C11—21no—
542Q8×C11—21no—
543D4×C11—21no—
544D4×C11—22no—
545D4×C11—21no—
546D4×C11—22no—
547D4×C11—44no—
548D4×C11—42no—
549D4×C11—42no—
550D4×C11—42no—
551D4×C11—81no—
552D4×C11—82no—
553C2×C4×C11—22no—
554C2×C4×C11—22no—
555C2×C4×C11—22no—
556C2×C4×C11—21no—
557C2×C4×C11—21no—
558C2×C4×C11—21no—
559C2×C4×C11—21no—
560C2×C4×C11—21no—
561C2×C4×C11—22no—
562C2×C4×C11—21no—
563C2×C4×C11—21no—
564C2×C4×C11—42no—
565C2×C4×C11—81no—
566C2×C4×C11C22×D411yescharacteristic
567C2×C4×C11C22×D411yescharacteristic
568C2×C4×C11C22×D411yescharacteristic
569C2×C4×C11H(5,𝔽2)12yes—
570C2×C4×C11H(5,𝔽2)12yes—
571C2×C4×C11C2511yescharacteristic
572C22⋊D11—24no—
573C22⋊D11—24no—
574C22⋊D11—42no—
575C22⋊D11—42no—
576C22⋊D11—44no—
577C22⋊D11—44no—
578C22⋊D11—44no—
579C22⋊D11—42no—
580C22⋊D11—42no—
581C22⋊D11—82no—
582C22⋊D11—82no—
583C22⋊D11—82no—
584C22⋊D11—81no—
585C2×Dic11—21no—
586C2×Dic11—22no—
587C2×Dic11—21no—
588C2×Dic11—22no—
589C2×Dic11—21no—
590C2×Dic11—42no—
591C2×Dic11—44no—
592C2×Dic11—44no—
593C2×Dic11—42no—
594C2×Dic11—81no—
595C2×Dic11C22×D412yes—
596C2×Dic11C22×D412yes—
597D44—22no—
598D44—22no—
599D44—21no—
600D44—21no—
601D44—42no—
602D44—82no—
603C4×D11—22no—
604C4×D11—22no—
605C4×D11—22no—
606C4×D11—22no—
607C4×D11—42no—
608C4×D11—42no—
609C4×D11—44no—
610C4×D11—42no—
611C4×D11—82no—
612C4×D11—82no—
613Dic22—22no—
614Dic22—22no—
615Dic22—22no—
616Dic22—21no—
617Dic22—22no—
618Dic22—21no—
619Dic22—42no—
620Dic22—44no—
621Dic22—42no—
622C8×C11—22no—
623C8×C11—22no—
624C11⋊C8—21no—
625C11⋊C8—21no—
626C11⋊C8—21no—
627C11⋊C8—21no—
628C2×2−1+4—111no—
629C2×H(5,𝔽2)—111no—
630C22×#41—111no—
631C2×#137—111no—
632C2×AGL(1,ℤ/8)C2×D1111yescharacteristic, complemented
633C2×#135—111no—
634C22×SD16—111no—
635C22×M16—111no—
636C22×M16C2×D1111yescharacteristic, complemented
637#550—221no—
638D4×Q8—221no—
639#548—221no—
640#548—221no—
641#547—221no—
642#547—222no—
643#546—222no—
644#546—221no—
645#546—222no—
646#546—221no—
647D42—221no—
648D42—222no—
649#537—111no—
650#537—112no—
651#537—112no—
652#537—111no—
653#536—112no—
654#536—111no—
655#535—111no—
656#535—112no—
657#525—111no—
658#525—112no—
659#525—112no—
660#525C2×D1111yescharacteristic, complemented
661C2×C22⋊Q8—111no—
662C2×C22⋊Q8—112no—
663C2×#121—112no—
664C2×#121C2×D1111yescharacteristic
665#520—111no—
666#520—111no—
667#485—112no—
668#485—112no—
669#485—112no—
670#485—112no—
671#484—112no—
672#484—112no—
673#484—112no—
674#483—112no—
675#482—112no—
676#482—112no—
677#482—112no—
678#482—112no—
679#481—112no—
680#480—112no—
681#480—112no—
682#480—112no—
683#470—112no—
684#470—111no—
685#470—111no—
686#469—111no—
687#469—111no—
688#469C2×D1112yescomplemented
689#468—112no—
690#468—111no—
691#468—111no—
692#468—112no—
693#468—112no—
694#468—111no—
695#468—112no—
696#468—112no—
697#468—111no—
698#468C2×D1112yescomplemented
699#467—112no—
700#466C2×D1112yescomplemented
701#465—112no—
702#465C2×D1112yescomplemented
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#428C2×D1111yescharacteristic, complemented
721#427—111no—
722C2×#107—111no—
723#419—111no—
724#418C2×D1111yescharacteristic, complemented
725#417—111no—
726#417C2×D1111yescharacteristic, complemented
727#416—111no—
728#416—111no—
729C2×#103—111no—
730C2×#102—111no—
731#408—111no—
732#408—111no—
733#408—111no—
734#408—111no—
735#408—112no—
736#408—112no—
737#407—112no—
738#407—112no—
739C22×C11—21no—
740C22×C11—21no—
741C22×C11—21no—
742C22×C11—21no—
743C22×C11—21no—
744C22×C11—21no—
745C22×C11—21no—
746C22×C11—21no—
747C22×C11—42no—
748C22×C11—41no—
749C22×C11—41no—
750C22×C11—42no—
751C22×C11—41no—
752C22×C11—42no—
753C22×C11—82no—
754C22×C11—162no—
755C22×C11#53412yes—
756C22×C11C23×D411yescharacteristic
757C2×D11—22no—
758C2×D11—22no—
759C2×D11—22no—
760C2×D11—22no—
761C2×D11—22no—
762C2×D11—22no—
763C2×D11—41no—
764C2×D11—41no—
765C2×D11—41no—
766C2×D11—84no—
767C2×D11—164no—
768C4×C11—21no—
769C4×C11—21no—
770C4×C11—42no—
771C4×C11—41no—
772C4×C11—41no—
773C4×C11—41no—
774C4×C11#53412yes—
775C4×C11C2×H(5,𝔽2)11yescharacteristic
776C4×C11C2×H(5,𝔽2)11yescharacteristic
777Dic11—22no—
778Dic11—22no—
779Dic11—41no—
780Dic11—42no—
781Dic11—41no—
782Dic11—42no—
783Dic11—41no—
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—111no—
797C2×#41—221no—
798C2×#41—222no—
799C2×#41—221no—
800C2×#41—442no—
801C2×#41—442no—
802C2×#41C22×D1111yescharacteristic
803C22×Q8—111no—
804C22×Q8—112no—
805C22×Q8—111no—
806C22×Q8—221no—
807C22×D4—21no—
808C22×D4—112no—
809C22×D4—112no—
810C22×D4—111no—
811C22×D4—221no—
812C22×D4—222no—
813C22×D4—222no—
814C22×D4C22×D1111yescharacteristic
815C23×C4—112no—
816C23×C4C22×D1111yescharacteristic
817#137—442no—
818AGL(1,ℤ/8)—42no—
819#135—442no—
820C2×Q16—111no—
821C2×Q16—112no—
822C2×SD16—111no—
823C2×SD16—112no—
824C2×SD16—112no—
825C2×SD16—111no—
826C2×SD16—112no—
827C2×SD16—442no—
828C2×SD16C22×D1112yes—
829C2×D8—111no—
830C2×D8C22×D1112yes—
831C2×M16—42no—
832C2×M16—111no—
833C2×M16—111no—
834C2×M16—111no—
835C2×M16—111no—
836C2×M16—442no—
837C2×M16C22×D1111yescharacteristic
838C2×M16C22×D1111yescharacteristic
839C2×M16C22×D1112yes—
840C22×C8—111no—
841C22×C8—111no—
842C22×C8C22×D1112yes—
843C4⋊Q8—221no—
844C4⋊Q8—222no—
845#127—222no—
846#127—221no—
847#124—221no—
848#124—222no—
849#124—222no—
850#124—221no—
851#123—21no—
852#123—222no—
853#123—222no—
854#123—222no—
855#123—222no—
856#123—222no—
857#123—221no—
858C22⋊Q8—112no—
859C22⋊Q8—112no—
860C22⋊Q8—112no—
861C22⋊Q8—111no—
862C22⋊Q8—111no—
863C22⋊Q8—112no—
864C22⋊Q8—112no—
865C22⋊Q8—112no—
866C22⋊Q8—222no—
867C22⋊Q8—222no—
868C22⋊Q8—222no—
869C22⋊Q8—222no—
870C22⋊Q8—221no—
871C22⋊Q8—221no—
872C22⋊Q8—221no—
873C22⋊Q8—221no—
874C22⋊Q8C22×D1111yescharacteristic
875C22⋊Q8C22×D1111yescharacteristic
876#121—21no—
877#121—21no—
878#121—112no—
879#121—112no—
880#121—112no—
881#121—111no—
882#121—111no—
883#121—112no—
884#121—222no—
885#121—222no—
886#121—222no—
887#121—221no—
888#121—222no—
889#121—221no—
890#121—222no—
891#121—222no—
892#121—222no—
893#121—222no—
894#121—222no—
895#121—222no—
896#121C22×D1112yes—
897#121C22×D1112yes—
898#121C22×D1111yescharacteristic
899#121C22×D1111yescharacteristic
900#120—21no—
901#120—222no—
902#120—222no—
903#120—222no—
904#120—222no—
905#120—222no—
906#120—221no—
907C4×Q8—221no—
908C4×Q8—221no—
909C4×D4—21no—
910C4×D4—21no—
911C4×D4—221no—
912C4×D4—222no—
913C4×D4—222no—
914C4×D4—222no—
915C4×D4—221no—
916C4×D4—222no—
917C4×D4—222no—
918C4×D4—222no—
919C4×D4—221no—
920C4×D4—221no—
921#117—111no—
922#117—112no—
923#117—112no—
924#117C22×D1111yescharacteristic
925C2×C4⋊C4—111no—
926C2×C4⋊C4—112no—
927C2×C4⋊C4—112no—
928C2×C4⋊C4—222no—
929C2×C4⋊C4—221no—
930C2×C4⋊C4C22×D1111yescharacteristic
931C2×C22⋊C4—21no—
932C2×C22⋊C4—222no—
933C2×C22⋊C4—222no—
934C2×C22⋊C4—221no—
935#107—112no—
936#107—112no—
937#107—112no—
938#107—111no—
939#107—111no—
940#107C22×D1112yes—
941#106—112no—
942#106—111no—
943#106—111no—
944#106C22×D1112yes—
945#103—111no—
946#103—111no—
947#103—112no—
948#103—112no—
949#103—112no—
950#103—112no—
951#103—112no—
952#103—111no—
953#103—111no—
954#103C22×D1112yes—
955#102—112no—
956#102—112no—
957#102—111no—
958#102—111no—
959#102—112no—
960#102—111no—
961#102—111no—
962#102C22×D1112yes—
963#102C22×D1112yes—
964#102C22×D1112yes—
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—41no—
975C2×C11—41no—
976C2×C11—82no—
977C2×C11—81no—
978C2×C11C2×#53411yescharacteristic
979C2×C11#358511yescharacteristic
980C2×C11#358611yescharacteristic
981D11—42no—
982D11—42no—
983D11—81no—
984C24—21no—
985C24—112no—
986C24—222no—
987C24D4×D1111yescharacteristic
988#41—22no—
989#41—22no—
990#41—222no—
991#41—222no—
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—442no—
1003#41—442no—
1004#41—442no—
1005#41—442no—
1006#41—448no—
1007#41—444no—
1008C2×Q8—111no—
1009C2×Q8—111no—
1010C2×Q8—112no—
1011C2×Q8—112no—
1012C2×Q8—111no—
1013C2×Q8—222no—
1014C2×Q8—221no—
1015C2×Q8—222no—
1016C2×Q8—222no—
1017C2×Q8—442no—
1018C2×Q8—444no—
1019C2×Q8—442no—
1020C2×Q8—442no—
1021C2×Q8C23×D1111yescharacteristic
1022C2×D4—21no—
1023C2×D4—22no—
1024C2×D4—21no—
1025C2×D4—21no—
1026C2×D4—22no—
1027C2×D4—21no—
1028C2×D4—22no—
1029C2×D4—22no—
1030C2×D4—82no—
1031C2×D4—112no—
1032C2×D4—112no—
1033C2×D4—112no—
1034C2×D4—112no—
1035C2×D4—111no—
1036C2×D4—111no—
1037C2×D4—112no—
1038C2×D4—111no—
1039C2×D4—222no—
1040C2×D4—222no—
1041C2×D4—222no—
1042C2×D4—222no—
1043C2×D4—221no—
1044C2×D4—221no—
1045C2×D4—222no—
1046C2×D4—222no—
1047C2×D4—222no—
1048C2×D4—221no—
1049C2×D4—442no—
1050C2×D4—442no—
1051C2×D4—442no—
1052C2×D4—444no—
1053C2×D4—444no—
1054C2×D4—448no—
1055C2×D4—884no—
1056C2×D4C23×D1111yescharacteristic
1057C2×D4C23×D1112yes—
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—442no—
1084Q16—441no—
1085SD16—42no—
1086SD16—442no—
1087SD16—442no—
1088SD16—442no—
1089SD16—441no—
1090SD16—441no—
1091D8—42no—
1092D8—441no—
1093M16—22no—
1094M16—22no—
1095M16—42no—
1096M16—441no—
1097M16—441no—
1098M16—441no—
1099M16—441no—
1100C2×C8—42no—
1101C2×C8—111no—
1102C2×C8—111no—
1103C2×C8—111no—
1104C2×C8—111no—
1105C2×C8—222no—
1106C2×C8—222no—
1107C2×C8C23×D1112yes—
1108C2×C8C23×D1112yes—
1109C4⋊C4—21no—
1110C4⋊C4—21no—
1111C4⋊C4—21no—
1112C4⋊C4—112no—
1113C4⋊C4—111no—
1114C4⋊C4—111no—
1115C4⋊C4—222no—
1116C4⋊C4—222no—
1117C4⋊C4—222no—
1118C4⋊C4—222no—
1119C4⋊C4—222no—
1120C4⋊C4—222no—
1121C4⋊C4—221no—
1122C4⋊C4—222no—
1123C4⋊C4—222no—
1124C4⋊C4—221no—
1125C4⋊C4—221no—
1126C4⋊C4C23×D1111yescharacteristic
1127C4⋊C4C23×D1111yescharacteristic
1128C4⋊C4C23×D1112yes—
1129C22⋊C4—21no—
1130C22⋊C4—21no—
1131C22⋊C4—21no—
1132C22⋊C4—22no—
1133C22⋊C4—22no—
1134C22⋊C4—21no—
1135C22⋊C4—21no—
1136C22⋊C4—222no—
1137C22⋊C4—222no—
1138C22⋊C4—222no—
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—221no—
1149C22⋊C4—221no—
1150C22⋊C4—221no—
1151C22⋊C4—221no—
1152C22⋊C4—221no—
1153C42—21no—
1154C42—222no—
1155C42—222no—
1156C42—221no—
1157C11#6077211yescharacteristic, complemented, Sylow
1158C23—22no—
1159C23—21no—
1160C23—22no—
1161C23—41no—
1162C23—41no—
1163C23—42no—
1164C23—81no—
1165C23—81no—
1166C23—112no—
1167C23—112no—
1168C23—221no—
1169C23—442no—
1170C23—442no—
1171C23—442no—
1172C23—444no—
1173C23—882no—
1174C23—882no—
1175C23C2×D4×D1111yescharacteristic
1176C23C2×D4×D1111yescharacteristic
1177C23C2×D4×D1111yescharacteristic
1178Q8—21no—
1179Q8—21no—
1180Q8—222no—
1181Q8—222no—
1182Q8—222no—
1183Q8—221no—
1184Q8—222no—
1185Q8—221no—
1186Q8—442no—
1187Q8—444no—
1188Q8—442no—
1189D4—21no—
1190D4—22no—
1191D4—21no—
1192D4—22no—
1193D4—42no—
1194D4—44no—
1195D4—42no—
1196D4—42no—
1197D4—81no—
1198D4—82no—
1199D4—224no—
1200D4—224no—
1201D4—222no—
1202D4—222no—
1203D4—221no—
1204D4—221no—
1205D4—442no—
1206D4—442no—
1207D4—442no—
1208D4—444no—
1209D4—442no—
1210D4—444no—
1211D4—444no—
1212D4—442no—
1213D4—882no—
1214D4—881no—
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—22no—
1228C2×C4—21no—
1229C2×C4—42no—
1230C2×C4—81no—
1231C2×C4—112no—
1232C2×C4—112no—
1233C2×C4—222no—
1234C2×C4—222no—
1235C2×C4—222no—
1236C2×C4—222no—
1237C2×C4—221no—
1238C2×C4—222no—
1239C2×C4—221no—
1240C2×C4—221no—
1241C2×C4—222no—
1242C2×C4—442no—
1243C2×C4—442no—
1244C2×C4—444no—
1245C2×C4—442no—
1246C2×C4—444no—
1247C2×C4—444no—
1248C2×C4—442no—
1249C2×C4—442no—
1250C2×C4—882no—
1251C2×C4—882no—
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—22no—
1260C8—22no—
1261C8—221no—
1262C8—221no—
1263C8—221no—
1264C8—221no—
1265C22—21no—
1266C22—21no—
1267C22—21no—
1268C22—21no—
1269C22—21no—
1270C22—21no—
1271C22—21no—
1272C22—21no—
1273C22—42no—
1274C22—41no—
1275C22—41no—
1276C22—42no—
1277C22—41no—
1278C22—42no—
1279C22—82no—
1280C22—162no—
1281C22—222no—
1282C22—222no—
1283C22—222no—
1284C22—222no—
1285C22—222no—
1286C22—222no—
1287C22—441no—
1288C22—441no—
1289C22—441no—
1290C22—884no—
1291C22—1764no—
1292C22#1062313612yes—
1293C22C22×D4×D1111yescharacteristic
1294C4—21no—
1295C4—21no—
1296C4—42no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—222no—
1301C4—222no—
1302C4—441no—
1303C4—442no—
1304C4—441no—
1305C4—441no—
1306C4—442no—
1307C4#1062313612yes—
1308C4C2×#6703711yescharacteristic
1309C4C2×#6704211yescharacteristic
1310C2—22no—
1311C2—41no—
1312C2—41no—
1313C2—82no—
1314C2—81no—
1315C2—442no—
1316C2—442no—
1317C2—881no—
1318C2C2×#1062313611yescharacteristic
1319C2#1308339211yescharacteristic
1320C2#1308340011yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3055C2
socleC22×C11C23×D4
hypercenter#3055D11
hypocenterC11#60772
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3055

Complements

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

NH ≅ G/Ntype
1. #13082288C2semidirect
2. #13082281C2semidirect
3. #13079512C2semidirect
4. #13079491C2semidirect
5. #13079482C2semidirect
6. #13079461C2semidirect
7. #13079452C2semidirect
8. #13079441C2semidirect
9. #13079425C2semidirect
10. #13079417C2semidirect
11. #13078598C2semidirect
12. #13078593C2semidirect
13. #13078587C2semidirect
14. #13078572C2semidirect
15. #13078246C2semidirect
16. #13078222C2semidirect
17. C2×#10622655C2semidirect
18. #13077933C2semidirect
19. #13077919C2semidirect
20. #13077901C2semidirect
21. #13077894C2semidirect
22. #13077060C2semidirect
23. C11×#3055C2semidirect
24. C2×#67043C22semidirect
27. C2×C11×AGL(1,ℤ/8)C22semidirect
28. C22×C11×M16C22semidirect
29. C11×#525C22semidirect
32. C2×#67003C22semidirect
35. C22×#4324C22semidirect
37. C2×#66977C22semidirect
38. C22×#4318C22semidirect
39. C2×#66962C22semidirect
41. #10623159C22semidirect
42. D11×C22⋊Q8C22semidirect
46. #10623139C22semidirect
49. #10623137C22semidirect
59. #10623054C22semidirect
63. C11×#469C22semidirect
64. C11×#468C22semidirect
65. C11×#466C22semidirect
66. C11×#465C22semidirect
67. C11×#428C22semidirect
68. C11×#418C22semidirect
69. C11×#417C22semidirect
70. #10622846C22semidirect
71. C2×#66896C22semidirect
72. #10622786C22semidirect
73. #10622783C22semidirect
74. #10622783C22semidirect
75. #10622782C22semidirect
76. #10622771C22semidirect
77. #10622771C22semidirect
78. #10622771C22semidirect
79. #10622769C22semidirect
80. #10622750C22semidirect
81. #10622747C22semidirect
82. #10622746C22semidirect
85. #10622742C22semidirect
86. #10622742C22semidirect
87. #10622739C22semidirect
88. #10622739C22semidirect
89. #10622734C22semidirect
90. #10622733C22semidirect
91. #10622729C22semidirect
92. #10622727C22semidirect
93. #10622723C22semidirect
94. #10622723C22semidirect
95. #10622665C22semidirect
96. #10622665C22semidirect
97. #10622662C22semidirect
98. #10622662C22semidirect
99. #10622655C22semidirect
100. #10622655C22semidirect
101. #10622655C22semidirect
102. #10622655C22semidirect
103. #10622655C22semidirect
104. #10622655C22semidirect
105. #10622652C22semidirect
106. #10622652C22semidirect
107. #10622615C22semidirect
108. #10622611C22semidirect
109. C2×#66874C22semidirect
110. C2×#66871C22semidirect
111. #10622501C22semidirect
112. #10622497C22semidirect
113. #10622497C22semidirect
114. #10622495C22semidirect
115. #10622480C22semidirect
116. #10622480C22semidirect
117. #10622479C22semidirect
118. #10622475C22semidirect
119. #10622428C22semidirect
120. #10622422C22semidirect
121. #10622421C22semidirect
122. #10622419C22semidirect
123. #10622397C22semidirect
124. #10622396C22semidirect
125. #10622396C22semidirect
126. #10622396C22semidirect
127. #10622394C22semidirect
128. #10622392C22semidirect
129. #10622392C22semidirect
130. #10622390C22semidirect
131. #10622389C22semidirect
132. #10622389C22semidirect
133. #10622387C22semidirect
134. #10622387C22semidirect
513. #3055D11semidirect
632. C2×AGL(1,ℤ/8)C2×D11semidirect
636. C22×M16C2×D11semidirect
660. #525C2×D11semidirect
688. #469C2×D11semidirect
698. #468C2×D11semidirect
700. #466C2×D11semidirect
702. #465C2×D11semidirect
720. #428C2×D11semidirect
724. #418C2×D11semidirect
726. #417C2×D11semidirect
1157. C11#60772semidirect

Maximal subgroups

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

subgroupindex
#130822882
#130822812
#130795122
#130794912
#130794822
#130794612
#130794522
#130794412
#130794252
#130794172
#130785982
#130785932
#130785872
#130785722
#130782462
#130782222
C2×#106226552
#130779332
#130779192
#130779012
#130778942
#130770602
C11×#30552
#6077211