Finite Group Databasebeta

← #15624695

Subgroups — #15624695

Order 2816.

2140 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082296C211yesmaximal, characteristic, complemented
2#13079522C212yesmaximal, complemented
3#13079513C212yesmaximal, complemented
4#13079492C212yesmaximal, complemented
5#13079492C212yesmaximal, complemented
6#13079453C212yesmaximal, complemented
7#13079442C212yesmaximal, complemented
8#13079404C212yesmaximal, complemented
9#13079393C212yesmaximal, complemented
10#13078579C211yesmaximal, characteristic, complemented
11#13078568C211yesmaximal, characteristic, complemented
12#13078564C211yesmaximal, characteristic, complemented
13#13078529C211yesmaximal, characteristic, complemented
14#13078303C211yesmaximal, characteristic, complemented
15#13078292C211yesmaximal, characteristic, complemented
16#13078268C211yesmaximal, characteristic, complemented
17#13078252C211yesmaximal, characteristic, complemented
18#13077909C211yesmaximal, characteristic, complemented
19#13077900C211yesmaximal, characteristic, complemented
20#13077858C211yesmaximal, characteristic, complemented
21C2×#10622852C211yesmaximal, characteristic, complemented
22#13077065C211yesmaximal, characteristic, complemented
23C11×#3449C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic
25C22×C11×#41C2211yescharacteristic
26C2×#67043C2211yescharacteristic
27C11×#537C2212yes—
28C11×#537C2212yes—
29C11×#536—21no—
30C11×#536C2211yescharacteristic
31C11×#536C2211yescharacteristic
32C11×#535—21no—
33C11×#535C2211yescharacteristic
34C11×#535C2211yescharacteristic
35C11×#534—22no—
36C11×#532—21no—
37C11×#532—21no—
38C11×#525—22no—
39C11×#525C2212yes—
40C11×#525C2212yes—
41C2×C11×#117C2211yescharacteristic
42#10623364C2211yescharacteristic
43#10623364C2212yescomplemented
44#10623362—21no—
45#10623358C2211yescharacteristic
46#10623356C2211yescharacteristic
47#10623356C2212yescomplemented
48#10623355—22no—
49#10623355—21no—
50C2×#67001C2211yescharacteristic
51C2×#67001C2211yescharacteristic
52Q8×C22⋊D11—21no—
53C22×#4326C2211yescharacteristic, complemented
54C2×#66995C2211yescharacteristic, complemented
55#10623337—21no—
56#10623337—22no—
57C22×#4324C2211yescharacteristic, complemented
58C2×#66985C2211yescharacteristic, complemented
59#10623322C2211yescharacteristic
60#10623322C2212yescomplemented
61C2×#66977C2211yescharacteristic
62C2×#66977C2212yescomplemented
63#10622852C2212yes—
64#10622852C2212yes—
65#10622852C2212yes—
66#10622852C2212yescomplemented
67#10622852C2212yescomplemented
68#10622852C2212yescomplemented
69#10622851C2212yes—
70#10622851C2212yescomplemented
71#10622847C2211yescharacteristic
72#10622847C2211yescharacteristic
73#10622847C2212yescomplemented
74#10622847C2212yescomplemented
75#10622838C2211yescharacteristic, complemented
76C2×#66899C2211yescharacteristic, complemented
77#10622828C2211yescharacteristic, complemented
78C2×#66896C2211yescharacteristic, complemented
79#10622820C2211yescharacteristic
80#10622820C2212yescomplemented
81C2×C22⋊(C11⋊C8)C2211yescharacteristic
82C2×C22⋊(C11⋊C8)C2212yescomplemented
83#10622665C2212yescomplemented
84#10622665C2212yescomplemented
85#10622665C2212yescomplemented
86#10622664C2212yescomplemented
87#10622664C2212yescomplemented
88#10622664C2212yescomplemented
89#10622663C2212yescomplemented
90#10622663C2212yescomplemented
91#10622662C2212yescomplemented
92#10622661C2212yescomplemented
93#10622660C2212yescomplemented
94#10622660C2212yescomplemented
95#10622658C2212yescomplemented
96#10622658C2212yescomplemented
97#10622657C2212yescomplemented
98#10622656C2212yescomplemented
99#10622655C2212yescomplemented
100#10622655C2212yescomplemented
101#10622655C2212yescomplemented
102#10622654C2212yescomplemented
103#10622654C2212yescomplemented
104#10622654C2212yescomplemented
105#10622653C2212yescomplemented
106#10622653C2212yescomplemented
107#10622652C2212yescomplemented
108#10622651C2212yescomplemented
109#10622650C2212yescomplemented
110#10622650C2212yescomplemented
111#10622648C2212yescomplemented
112#10622648C2212yescomplemented
113#10622647C2212yescomplemented
114#10622646C2212yescomplemented
115#10622617C2211yescharacteristic, complemented
116#10622617C2211yescharacteristic, complemented
117#10622616C2211yescharacteristic, complemented
118#10622616C2211yescharacteristic, complemented
119#10622615C2211yescharacteristic, complemented
120#10622615C2211yescharacteristic, complemented
121#10622611C2211yescharacteristic, complemented
122#10622611C2211yescharacteristic, complemented
123#10622609C2211yescharacteristic, complemented
124#10622609C2211yescharacteristic, complemented
125#10622609C2212yescomplemented
126#10622609C2212yescomplemented
127#10622608C2211yescharacteristic, complemented
128#10622608C2211yescharacteristic, complemented
129#10622584C2211yescharacteristic, complemented
130#10622584C2212yescomplemented
131#10622583C2211yescharacteristic, complemented
132#10622583C2212yescomplemented
133#10622581C2211yescharacteristic, complemented
134#10622580C2211yescharacteristic, complemented
135C2×C11×#41—21no—
136C2×C11×#41—21no—
137C2×C11×#41—42no—
138C2×C11×#41—42no—
139C2×C11×#41—42no—
140C2×C11×#41—42no—
141C2×C11×#41D412yes—
142C2×C11×#41D411yescharacteristic
143C2×C11×#41D411yescharacteristic
144C2×C11×#41C2312yes—
145C2×C11×#41C2312yes—
146C2×C11×#41C2311yescharacteristic
147C2×C11×#41C2311yescharacteristic
148C2×C11×#41C2312yes—
149C22×Q8×C11D411yescharacteristic
150C22×Q8×C11C2311yescharacteristic
151C22×D4×C11—21no—
152C22×D4×C11D412yes—
153C22×D4×C11D411yescharacteristic
154C22×D4×C11C2311yescharacteristic
155C23×C4×C11—21no—
156C23×C4×C11C2311yescharacteristic
157C23×C4×C11C2312yes—
158#67043—42no—
159#67043—42no—
160C2×Q8×D11—21no—
161C2×#4341—22no—
162C2×#4341—21no—
163C2×#4339C2311yescharacteristic
164C2×#4339C2312yes—
165C22×Dic22C2311yescharacteristic
166C22×Dic22C2312yes—
167C11×C4⋊Q8—21no—
168C11×C4⋊Q8—21no—
169C11×#127—21no—
170C11×#127—21no—
171C11×#124—21no—
172C11×#124—21no—
173C11×#124—21no—
174C11×#124—21no—
175C11×#123—22no—
176C11×#123—22no—
177C11×#123—22no—
178C11×#123—22no—
179C11×C22⋊Q8—22no—
180C11×C22⋊Q8—22no—
181C11×C22⋊Q8C2312yes—
182C11×C22⋊Q8C2312yes—
183C11×C22⋊Q8C2312yes—
184C11×C22⋊Q8C2312yes—
185C11×#121—22no—
186C11×#121—22no—
187C11×#121—22no—
188C11×#121—22no—
189C11×#121—22no—
190C11×#121—22no—
191C11×#121C2312yes—
192C11×#121C2312yes—
193C11×#121C2312yes—
194C11×#121C2312yes—
195C11×#120—22no—
196C11×#120—22no—
197C11×#120—22no—
198C11×#120—22no—
199C4×D4×C11—22no—
200C4×D4×C11—22no—
201C4×D4×C11—22no—
202C4×D4×C11—22no—
203C11×#117—21no—
204C11×#117—21no—
205C11×#117C2311yescharacteristic
206C11×#117C2311yescharacteristic
207C11×#117C2311yescharacteristic
208C11×#117C2311yescharacteristic
209C2×C11×C4⋊C4C2311yescharacteristic
210C2×C11×C4⋊C4C2311yescharacteristic
211C2×C11×C22⋊C4—21no—
212C2×C42×C11—21no—
213#67006—21no—
214#67006—22no—
215C2×C22⋊Dic11—21no—
216C2×C22⋊Dic11—22no—
217#67001—42no—
218#67001—42no—
219#66999—21no—
220#66999—22no—
221Q8×Dic11—21no—
222#66997—21no—
223#66997—22no—
224C2×#4326—42no—
225C2×#4326C2312yes—
226C2×#4326C2312yes—
227C2×#4326C2312yes—
228#66995—42no—
229C2×#4325C2312yes—
230#66992—22no—
231#66992—22no—
232#66992—22no—
233#66991—21no—
234#66991—22no—
235#66989—21no—
236#66989—22no—
237#66988—22no—
238#66988—22no—
239#66988—22no—
240D4×Dic11—22no—
241D4×Dic11—21no—
242C2×#4324—42no—
243C2×#4324C2312yes—
244C2×#4324C2312yes—
245C2×#4324C2312yes—
246#66985—42no—
247C2×#4323C2312yes—
248#66983C2311yescharacteristic
249#66983C2311yescharacteristic
250#66983C2312yes—
251#66982—21no—
252#66982—22no—
253C4×C22⋊D11—21no—
254C4×C22⋊D11—21no—
255C4×C22⋊D11—22no—
256C4×C22⋊D11—22no—
257#66979C2311yescharacteristic
258#66979C2312yes—
259C2×C4⋊Dic11C2311yescharacteristic
260C2×C4⋊Dic11C2312yes—
261#66977—21no—
262#66977—21no—
263#66977—22no—
264#66977—22no—
265#66977C2312yes—
266#66977C2312yes—
267#66977C2311yescharacteristic
268#66977C2312yes—
269#66977C2312yes—
270#66977C2311yescharacteristic
271#66977C2312yes—
272C2×Dic11⋊C4—21no—
273C2×Dic11⋊C4—22no—
274C2×#4318C2311yescharacteristic
275C2×#4318C2311yescharacteristic
276C2×#4318C2312yes—
277C2×#4318C2312yes—
278C22×C11⋊C8C2311yescharacteristic
279C22×C11⋊C8C2311yescharacteristic
280C22×C11⋊C8C2312yes—
281C22×C11⋊C8C2312yes—
282#66899C2312yes—
283#66899C2312yes—
284#66899C2312yes—
285#66899C2312yes—
286#66896C2312yes—
287#66896C2312yes—
288#66896C2312yes—
289#66896C2312yes—
290C22⋊(C11⋊C8)C2311yescharacteristic
291C22⋊(C11⋊C8)C2311yescharacteristic
292C22⋊(C11⋊C8)C2311yescharacteristic
293C22⋊(C11⋊C8)C2311yescharacteristic
294C22⋊(C11⋊C8)C2312yes—
295C22⋊(C11⋊C8)C2312yes—
296C22⋊(C11⋊C8)C2312yes—
297C22⋊(C11⋊C8)C2312yes—
298C22⋊(C11⋊C8)C2312yes—
299C22⋊(C11⋊C8)C2312yes—
300#66874C2311yescharacteristic
301#66874C2311yescharacteristic
302#66874C2312yes—
303#66874C2312yes—
304#66874C2311yescharacteristic
305#66874C2311yescharacteristic
306#66874C2312yes—
307#66874C2312yes—
308#66873C2311yescharacteristic
309#66873C2311yescharacteristic
310#66873C2311yescharacteristic
311#66873C2311yescharacteristic
312#66872C2311yescharacteristic
313#66872C2311yescharacteristic
314#66872C2312yes—
315#66872C2312yes—
316#66872C2311yescharacteristic
317#66872C2311yescharacteristic
318#66871C2311yescharacteristic
319#66871C2311yescharacteristic
320#66871C2312yes—
321#66871C2312yes—
322#66871C2311yescharacteristic
323#66871C2311yescharacteristic
324#60761—111nomaximal, Sylow
325C24×C11—21no—
326C24×C11C2×D411yescharacteristic
327C24×C11C2×D412yes—
328C11×#41—22no—
329C11×#41—22no—
330C11×#41—22no—
331C11×#41—22no—
332C11×#41—42no—
333C11×#41—42no—
334C11×#41—44no—
335C11×#41—42no—
336C11×#41—42no—
337C11×#41—42no—
338C11×#41—42no—
339C11×#41—42no—
340C11×#41—42no—
341C11×#41—44no—
342C11×#41—44no—
343C2×Q8×C11—21no—
344C2×Q8×C11—22no—
345C2×Q8×C11—22no—
346C2×Q8×C11—42no—
347C2×Q8×C11C2×D411yescharacteristic
348C2×Q8×C11C2×D411yescharacteristic
349C2×Q8×C11C2×D412yes—
350C2×Q8×C11C2412yes—
351C2×D4×C11—22no—
352C2×D4×C11—22no—
353C2×D4×C11—22no—
354C2×D4×C11—22no—
355C2×D4×C11—22no—
356C2×D4×C11—22no—
357C2×D4×C11—21no—
358C2×D4×C11—22no—
359C2×D4×C11—22no—
360C2×D4×C11—42no—
361C2×D4×C11—44no—
362C2×D4×C11—44no—
363C2×D4×C11C2×D412yes—
364C2×D4×C11C2×D411yescharacteristic
365C2×D4×C11C2×D412yes—
366C2×D4×C11C2×D411yescharacteristic
367C2×D4×C11C2×D412yes—
368C2×D4×C11C2×D412yes—
369C2×D4×C11C2×D412yes—
370C2×D4×C11C2412yes—
371C22×C4×C11—22no—
372C22×C4×C11—22no—
373C22×C4×C11—21no—
374C22×C4×C11—21no—
375C22×C4×C11—21no—
376C22×C4×C11—22no—
377C22×C4×C11—22no—
378C22×C4×C11—42no—
379C22×C4×C11—42no—
380C22×C4×C11—44no—
381C22×C4×C11C2×D411yescharacteristic
382C22×C4×C11C2×D411yescharacteristic
383C22×C4×C11C2×D411yescharacteristic
384C22×C4×C11C2×D412yes—
385C22×C4×C11C2×D412yes—
386C22×C4×C11C2×D412yes—
387C22×C4×C11C2411yescharacteristic
388C22×C4×C11C2411yescharacteristic
389C22×C4×C11C2412yes—
390C22×C4×C11C2412yes—
391C22×C4×C11C2411yescharacteristic
392C2×C22⋊D11—21no—
393C2×C22⋊D11—22no—
394C2×C22⋊D11—21no—
395C2×C22⋊D11—22no—
396C2×C22⋊D11—21no—
397C22×Dic11—22no—
398C22×Dic11—21no—
399C22×Dic11—22no—
400C22×Dic11—21no—
401Q8×D11—44no—
402#4341—48no—
403#4341—44no—
404#4339—22no—
405#4339—22no—
406#4339—42no—
407#4339—42no—
408C2×D44C2411yescharacteristic
409C2×C4×D11—22no—
410C2×C4×D11—21no—
411C2×Dic22—22no—
412C2×Dic22—21no—
413C2×Dic22—22no—
414C2×Dic22—22no—
415C2×Dic22—42no—
416C2×Dic22—42no—
417C2×Dic22C2412yes—
418C2×Dic22C2411yescharacteristic
419C11×C4⋊C4—21no—
420C11×C4⋊C4—21no—
421C11×C4⋊C4—22no—
422C11×C4⋊C4—22no—
423C11×C4⋊C4—22no—
424C11×C4⋊C4—22no—
425C11×C4⋊C4C2411yescharacteristic
426C11×C4⋊C4C2411yescharacteristic
427C11×C4⋊C4C2411yescharacteristic
428C11×C4⋊C4C2411yescharacteristic
429C11×C22⋊C4—21no—
430C11×C22⋊C4—21no—
431C11×C22⋊C4—21no—
432C11×C22⋊C4—21no—
433C11×C22⋊C4—22no—
434C11×C22⋊C4—22no—
435C11×C22⋊C4—22no—
436C11×C22⋊C4—22no—
437C11×C22⋊C4—22no—
438C11×C22⋊C4—22no—
439C11×C22⋊C4—22no—
440C11×C22⋊C4—22no—
441C42×C11—21no—
442C42×C11—21no—
443C42×C11—21no—
444C42×C11—21no—
445C22⋊Dic11—22no—
446C22⋊Dic11—21no—
447C22⋊Dic11—22no—
448C22⋊Dic11—22no—
449C22⋊Dic11—22no—
450C22⋊Dic11—22no—
451C22⋊Dic11—21no—
452C22⋊Dic11—22no—
453C22⋊Dic11—21no—
454#4326—42no—
455#4326—42no—
456#4326—42no—
457#4325—42no—
458#4324—42no—
459#4324—42no—
460#4324—42no—
461#4323—42no—
462(C2×D11)⋊C4—21no—
463(C2×D11)⋊C4—22no—
464(C2×D11)⋊C4—21no—
465C4⋊Dic11—22no—
466C4⋊Dic11—21no—
467C4⋊Dic11C2411yescharacteristic
468C4⋊Dic11C2412yes—
469C4⋊Dic11C2411yescharacteristic
470Dic11⋊C4—22no—
471Dic11⋊C4—21no—
472Dic11⋊C4—22no—
473Dic11⋊C4—22no—
474Dic11⋊C4—22no—
475Dic11⋊C4—22no—
476Dic11⋊C4—21no—
477C4×Dic11—22no—
478C4×Dic11—21no—
479#4318—22no—
480#4318—22no—
481#4318—42no—
482#4318—42no—
483C2×C11⋊C8—22no—
484C2×C11⋊C8—22no—
485C2×C11⋊C8—42no—
486C2×C11⋊C8—42no—
487C2×C11⋊C8C2411yescharacteristic
488C2×C11⋊C8C2411yescharacteristic
489C2×C11⋊C8C2412yes—
490C2×C11⋊C8C2412yes—
491C2×C11⋊C8C2411yescharacteristic
492C2×C11⋊C8C2411yescharacteristic
493#3489—111no—
494#3449D1111yescharacteristic, complemented
495#3204—112no—
496#3203—112no—
497#3201—112no—
498#3201—112no—
499#3197—112no—
500#3196—112no—
501#3191—112no—
502#3190—112no—
503#3097—111no—
504#3096—111no—
505#3095—111no—
506#3091—111no—
507#3063—111no—
508#3062—111no—
509#3059—111no—
510#3057—111no—
511#3011—111no—
512#3010—111no—
513#3005—111no—
514C2×#452—111no—
515#2880—111no—
516C23×C11—22no—
517C23×C11—22no—
518C23×C11—42no—
519C23×C11—41no—
520C23×C11—41no—
521C23×C11—42no—
522C23×C11—42no—
523C23×C11—42no—
524C23×C11—81no—
525C23×C11—81no—
526C23×C11C22×D411yescharacteristic
527C23×C11C22×D412yes—
528C23×C11C22×D411yescharacteristic
529C23×C11C22×D412yes—
530C23×C11C22×D411yescharacteristic
531C22×D11—21no—
532Q8×C11—22no—
533Q8×C11—22no—
534Q8×C11—22no—
535Q8×C11—22no—
536Q8×C11—42no—
537Q8×C11—42no—
538D4×C11—24no—
539D4×C11—24no—
540D4×C11—22no—
541D4×C11—22no—
542D4×C11—22no—
543D4×C11—22no—
544D4×C11—42no—
545D4×C11—42no—
546D4×C11—42no—
547D4×C11—44no—
548D4×C11—44no—
549D4×C11—42no—
550D4×C11—82no—
551D4×C11—82no—
552D4×C11—82no—
553D4×C11—82no—
554C2×C4×C11—22no—
555C2×C4×C11—22no—
556C2×C4×C11—22no—
557C2×C4×C11—22no—
558C2×C4×C11—22no—
559C2×C4×C11—22no—
560C2×C4×C11—22no—
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—21no—
569C2×C4×C11—22no—
570C2×C4×C11—42no—
571C2×C4×C11—42no—
572C2×C4×C11—42no—
573C2×C4×C11—44no—
574C2×C4×C11—44no—
575C2×C4×C11—42no—
576C2×C4×C11—81no—
577C2×C4×C11—81no—
578C2×C4×C11C22×D412yes—
579C2×C4×C11C22×D411yescharacteristic
580C2×C4×C11C22×D412yes—
581C2×C4×C11C22×D411yescharacteristic
582C2×C4×C11C22×D411yescharacteristic
583C2×C4×C11H(5,𝔽2)12yes—
584C2×C4×C11H(5,𝔽2)12yes—
585C2×C4×C11C2511yescharacteristic
586C22⋊D11—44no—
587C22⋊D11—42no—
588C22⋊D11—42no—
589C22⋊D11—81no—
590C22⋊D11—82no—
591C2×Dic11—21no—
592C2×Dic11—22no—
593C2×Dic11—21no—
594C2×Dic11—22no—
595C2×Dic11—21no—
596C2×Dic11—44no—
597C2×Dic11—42no—
598C2×Dic11—81no—
599C2×Dic11—82no—
600D44—21no—
601D44—21no—
602C4×D11—44no—
603C4×D11—42no—
604Dic22—22no—
605Dic22—21no—
606Dic22—22no—
607Dic22—21no—
608Dic22—44no—
609Dic22—42no—
610C11⋊C8—21no—
611C11⋊C8—21no—
612C11⋊C8—21no—
613C11⋊C8—21no—
614C11⋊C8—22no—
615C11⋊C8—22no—
616C2×2−1+4—111no—
617C22×#41C2×D1111yescharacteristic
618C22×#41C2×D1111yescharacteristic
619C2×#137—111no—
620C2×AGL(1,ℤ/8)—111no—
621C22×Q16—111no—
622C22×SD16—111no—
623C2×#131—111no—
624C2×#131—111no—
625D4×Q8—221no—
626#548—221no—
627#547—222no—
628#547—221no—
629#546—222no—
630#546—221no—
631#537—112no—
632#537—111no—
633#537C2×D1112yes—
634#537C2×D1112yes—
635#536—21no—
636#536—111no—
637#536—112no—
638#536C2×D1111yescharacteristic
639#536C2×D1111yescharacteristic
640#535—21no—
641#535C2×D1111yescharacteristic
642#535C2×D1111yescharacteristic
643#534—22no—
644#532—21no—
645#532—21no—
646#525—22no—
647#525—111no—
648#525—112no—
649#525C2×D1112yes—
650#525C2×D1112yes—
651C2×C22⋊Q8—111no—
652C2×C22⋊Q8—112no—
653#520—111no—
654C2×#117C2×D1111yescharacteristic
655#485—112no—
656#485—112no—
657#485—111no—
658#485—111no—
659#485—112no—
660#485—112no—
661#484—112no—
662#484—111no—
663#484—112no—
664#483—112no—
665#483—111no—
666#483—112no—
667#482—112no—
668#482—112no—
669#482—111no—
670#482—111no—
671#481—112no—
672#481—111no—
673#480—112no—
674#480—111no—
675#470—112no—
676#470—112no—
677#470—112no—
678#469—112no—
679#468—112no—
680#468—112no—
681#468—112no—
682#468—112no—
683#467—112no—
684#467—112no—
685#467—112no—
686#466—112no—
687#465—112no—
688#465—112no—
689#465—112no—
690#465—112no—
691#452—112no—
692#452—112no—
693#452—112no—
694#452—112no—
695#452—112no—
696#452—112no—
697#452—112no—
698#452—112no—
699#451—112no—
700#451—112no—
701#449—112no—
702#449—112no—
703#449—112no—
704#449—112no—
705#448—112no—
706#448—112no—
707#428—111no—
708#428—111no—
709#427—111no—
710#427—111no—
711#419—111no—
712#419—111no—
713#419—111no—
714#418—111no—
715#416—111no—
716#416—111no—
717C2×#103—111no—
718C2×#102—111no—
719#408—111no—
720#408—111no—
721#408—112no—
722#408—112no—
723#407—111no—
724#407—112no—
725C2×C22⋊C8—111no—
726C2×C22⋊C8—112no—
727C22×C11—21no—
728C22×C11—21no—
729C22×C11—21no—
730C22×C11—22no—
731C22×C11—22no—
732C22×C11—21no—
733C22×C11—21no—
734C22×C11—22no—
735C22×C11—22no—
736C22×C11—21no—
737C22×C11—21no—
738C22×C11—21no—
739C22×C11—22no—
740C22×C11—22no—
741C22×C11—42no—
742C22×C11—42no—
743C22×C11—42no—
744C22×C11—82no—
745C22×C11—84no—
746C22×C11—84no—
747C22×C11#53412yes—
748C22×C11C23×D411yescharacteristic
749C2×D11—41no—
750C2×D11—41no—
751C2×D11—41no—
752C4×C11—21no—
753C4×C11—21no—
754C4×C11—22no—
755C4×C11—22no—
756C4×C11—41no—
757C4×C11—41no—
758C4×C11—41no—
759C4×C11—41no—
760C4×C11—42no—
761C4×C11#53412yes—
762C4×C11C2×H(5,𝔽2)11yescharacteristic
763C4×C11C2×H(5,𝔽2)11yescharacteristic
764Dic11—42no—
765Dic11—41no—
766Dic11—41no—
767Dic11—42no—
768Dic11—41no—
7692−1+4—442no—
7702−1+4—442no—
771C2×#41—21no—
772C2×#41—21no—
773C2×#41—42no—
774C2×#41—42no—
775C2×#41—42no—
776C2×#41—42no—
777C2×#41—111no—
778C2×#41—112no—
779C2×#41—222no—
780C2×#41—221no—
781C2×#41C22⋊D1112yes—
782C2×#41C22⋊D1111yescharacteristic
783C2×#41C22⋊D1111yescharacteristic
784C2×#41C22×D1112yes—
785C2×#41C22×D1112yes—
786C2×#41C22×D1111yescharacteristic
787C2×#41C22×D1111yescharacteristic
788C2×#41C22×D1112yes—
789C22×Q8—111no—
790C22×Q8—112no—
791C22×Q8—221no—
792C22×Q8C22⋊D1111yescharacteristic
793C22×Q8C22×D1111yescharacteristic
794C22×D4—21no—
795C22×D4C22⋊D1112yes—
796C22×D4C22⋊D1111yescharacteristic
797C22×D4C22×D1111yescharacteristic
798C23×C4—21no—
799C23×C4C22×D1111yescharacteristic
800C23×C4C22×D1112yes—
801#137—442no—
802AGL(1,ℤ/8)—442no—
803C2×Q16—112no—
804C2×Q16—112no—
805C2×Q16—112no—
806C2×Q16—442no—
807C2×SD16—112no—
808C2×SD16—112no—
809C2×SD16—112no—
810C2×SD16—112no—
811C2×SD16—442no—
812C2×D8—112no—
813#131—442no—
814#131—442no—
815C2×M16—111no—
816C2×M16—111no—
817C2×M16—112no—
818C2×M16—112no—
819C22×C8—111no—
820C22×C8—111no—
821C22×C8—112no—
822C22×C8—112no—
823C4⋊Q8—21no—
824C4⋊Q8—21no—
825C4⋊Q8—221no—
826C4⋊Q8—222no—
827#127—21no—
828#127—21no—
829#124—21no—
830#124—21no—
831#124—21no—
832#124—21no—
833#124—221no—
834#124—222no—
835#123—22no—
836#123—22no—
837#123—22no—
838#123—22no—
839#123—222no—
840#123—222no—
841#123—222no—
842#123—221no—
843#123—222no—
844C22⋊Q8—22no—
845C22⋊Q8—22no—
846C22⋊Q8—112no—
847C22⋊Q8—111no—
848C22⋊Q8—112no—
849C22⋊Q8—112no—
850C22⋊Q8—112no—
851C22⋊Q8—111no—
852C22⋊Q8—112no—
853C22⋊Q8—221no—
854C22⋊Q8—222no—
855C22⋊Q8—221no—
856C22⋊Q8—222no—
857C22⋊Q8—221no—
858C22⋊Q8—222no—
859C22⋊Q8C22×D1112yes—
860C22⋊Q8C22×D1112yes—
861C22⋊Q8C22×D1112yes—
862C22⋊Q8C22×D1112yes—
863#121—22no—
864#121—22no—
865#121—22no—
866#121—22no—
867#121—22no—
868#121—22no—
869#121—111no—
870#121—111no—
871#121—112no—
872#121—222no—
873#121—222no—
874#121—222no—
875#121—221no—
876#121—222no—
877#121C22×D1112yes—
878#121C22×D1112yes—
879#121C22×D1112yes—
880#121C22×D1112yes—
881#120—22no—
882#120—22no—
883#120—22no—
884#120—22no—
885#120—221no—
886#120—222no—
887C4×Q8—221no—
888C4×D4—22no—
889C4×D4—22no—
890C4×D4—22no—
891C4×D4—22no—
892C4×D4—222no—
893C4×D4—221no—
894C4×D4—221no—
895C4×D4—222no—
896C4×D4—221no—
897C4×D4—222no—
898#117—21no—
899#117—21no—
900#117—111no—
901#117—112no—
902#117C22×D1111yescharacteristic
903#117C22×D1111yescharacteristic
904#117C22×D1111yescharacteristic
905#117C22×D1111yescharacteristic
906C2×C4⋊C4—111no—
907C2×C4⋊C4—112no—
908C2×C4⋊C4—221no—
909C2×C4⋊C4—222no—
910C2×C4⋊C4C22×D1111yescharacteristic
911C2×C4⋊C4C22×D1111yescharacteristic
912C2×C22⋊C4—21no—
913C2×C22⋊C4—221no—
914C2×C22⋊C4—222no—
915C2×C42—21no—
916#107—111no—
917#107—111no—
918#107—111no—
919#107—111no—
920#107—112no—
921#107—112no—
922#106—111no—
923#106—111no—
924#106—111no—
925#106—111no—
926#106—112no—
927#106—112no—
928#103—112no—
929#103—112no—
930#103—112no—
931#103—112no—
932#103—111no—
933#103—111no—
934#103—111no—
935#103—111no—
936#103—112no—
937#103—112no—
938#103—112no—
939#103—112no—
940#102—112no—
941#102—112no—
942#102—112no—
943#102—112no—
944#102—111no—
945#102—111no—
946#102—111no—
947#102—111no—
948C22⋊C8—111no—
949C22⋊C8—112no—
950C22⋊C8—111no—
951C22⋊C8—112no—
952C22⋊C8—112no—
953C22⋊C8—111no—
954C22⋊C8—111no—
955C22⋊C8—112no—
956C22⋊C8—112no—
957C22⋊C8—112no—
958C2×C11—22no—
959C2×C11—41no—
960C2×C11—42no—
961C2×C11—42no—
962C2×C11—41no—
963C2×C11—82no—
964C2×C11C2×#53411yescharacteristic
965C2×C11#358411yescharacteristic
966C2×C11#358611yescharacteristic
967D11—81no—
968C24—21no—
969C24C2×C22⋊D1111yescharacteristic
970C24C2×C22⋊D1112yes—
971#41—22no—
972#41—22no—
973#41—22no—
974#41—22no—
975#41—42no—
976#41—42no—
977#41—44no—
978#41—42no—
979#41—42no—
980#41—42no—
981#41—42no—
982#41—42no—
983#41—42no—
984#41—44no—
985#41—44no—
986#41—222no—
987#41—222no—
988#41—442no—
989#41—442no—
990#41—448no—
991#41—444no—
992C2×Q8—21no—
993C2×Q8—22no—
994C2×Q8—22no—
995C2×Q8—42no—
996C2×Q8—112no—
997C2×Q8—111no—
998C2×Q8—222no—
999C2×Q8—221no—
1000C2×Q8—222no—
1001C2×Q8—222no—
1002C2×Q8—442no—
1003C2×Q8—442no—
1004C2×Q8—444no—
1005C2×Q8C2×C22⋊D1111yescharacteristic
1006C2×Q8C2×C22⋊D1111yescharacteristic
1007C2×Q8C2×C22⋊D1112yes—
1008C2×Q8C23×D1112yes—
1009C2×D4—22no—
1010C2×D4—22no—
1011C2×D4—22no—
1012C2×D4—22no—
1013C2×D4—22no—
1014C2×D4—22no—
1015C2×D4—22no—
1016C2×D4—22no—
1017C2×D4—21no—
1018C2×D4—42no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—111no—
1022C2×D4—221no—
1023C2×D4—222no—
1024C2×D4—221no—
1025C2×D4—222no—
1026C2×D4—221no—
1027C2×D4C2×C22⋊D1112yes—
1028C2×D4C2×C22⋊D1111yescharacteristic
1029C2×D4C2×C22⋊D1112yes—
1030C2×D4C2×C22⋊D1111yescharacteristic
1031C2×D4C2×C22⋊D1112yes—
1032C2×D4C2×C22⋊D1112yes—
1033C2×D4C2×C22⋊D1112yes—
1034C2×D4C23×D1112yes—
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—21no—
1038C22×C4—21no—
1039C22×C4—21no—
1040C22×C4—22no—
1041C22×C4—22no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—44no—
1045C22×C4—222no—
1046C22×C4—221no—
1047C22×C4—222no—
1048C22×C4—221no—
1049C22×C4—222no—
1050C22×C4—221no—
1051C22×C4C2×C22⋊D1111yescharacteristic
1052C22×C4C2×C22⋊D1111yescharacteristic
1053C22×C4C2×C22⋊D1111yescharacteristic
1054C22×C4C2×C22⋊D1112yes—
1055C22×C4C2×C22⋊D1112yes—
1056C22×C4C2×C22⋊D1112yes—
1057C22×C4C23×D1112yes—
1058C22×C4C23×D1111yescharacteristic
1059C22×C4C23×D1111yescharacteristic
1060C22×C4C23×D1112yes—
1061C22×C4C23×D1111yescharacteristic
1062Q16—442no—
1063Q16—442no—
1064Q16—442no—
1065SD16—442no—
1066SD16—442no—
1067SD16—442no—
1068SD16—442no—
1069D8—442no—
1070M16—222no—
1071M16—222no—
1072M16—442no—
1073M16—442no—
1074C2×C8—111no—
1075C2×C8—111no—
1076C2×C8—112no—
1077C2×C8—111no—
1078C2×C8—111no—
1079C2×C8—112no—
1080C2×C8—222no—
1081C2×C8—222no—
1082C2×C8—442no—
1083C2×C8—442no—
1084C4⋊C4—21no—
1085C4⋊C4—21no—
1086C4⋊C4—22no—
1087C4⋊C4—22no—
1088C4⋊C4—22no—
1089C4⋊C4—22no—
1090C4⋊C4—112no—
1091C4⋊C4—111no—
1092C4⋊C4—111no—
1093C4⋊C4—222no—
1094C4⋊C4—221no—
1095C4⋊C4—222no—
1096C4⋊C4—221no—
1097C4⋊C4—222no—
1098C4⋊C4—222no—
1099C4⋊C4—222no—
1100C4⋊C4—222no—
1101C4⋊C4—221no—
1102C4⋊C4C23×D1111yescharacteristic
1103C4⋊C4C23×D1111yescharacteristic
1104C4⋊C4C23×D1111yescharacteristic
1105C4⋊C4C23×D1111yescharacteristic
1106C22⋊C4—21no—
1107C22⋊C4—21no—
1108C22⋊C4—21no—
1109C22⋊C4—21no—
1110C22⋊C4—22no—
1111C22⋊C4—22no—
1112C22⋊C4—22no—
1113C22⋊C4—22no—
1114C22⋊C4—22no—
1115C22⋊C4—22no—
1116C22⋊C4—22no—
1117C22⋊C4—22no—
1118C22⋊C4—222no—
1119C22⋊C4—221no—
1120C22⋊C4—222no—
1121C22⋊C4—222no—
1122C22⋊C4—222no—
1123C22⋊C4—222no—
1124C22⋊C4—221no—
1125C22⋊C4—222no—
1126C22⋊C4—221no—
1127C22⋊C4—221no—
1128C22⋊C4—222no—
1129C22⋊C4—221no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—222no—
1135C42—221no—
1136C11#6076111yescharacteristic, complemented, Sylow
1137C23—22no—
1138C23—22no—
1139C23—42no—
1140C23—41no—
1141C23—41no—
1142C23—42no—
1143C23—42no—
1144C23—42no—
1145C23—81no—
1146C23—81no—
1147C23—221no—
1148C23C22×C22⋊D1111yescharacteristic
1149C23C22×C22⋊D1112yes—
1150C23C22×C22⋊D1112yes—
1151C23C22×C22⋊D1111yescharacteristic
1152C23C22×C22⋊D1111yescharacteristic
1153Q8—22no—
1154Q8—22no—
1155Q8—22no—
1156Q8—22no—
1157Q8—42no—
1158Q8—42no—
1159Q8—222no—
1160Q8—221no—
1161Q8—222no—
1162Q8—221no—
1163Q8—444no—
1164Q8—442no—
1165D4—24no—
1166D4—24no—
1167D4—22no—
1168D4—22no—
1169D4—22no—
1170D4—22no—
1171D4—42no—
1172D4—42no—
1173D4—42no—
1174D4—44no—
1175D4—44no—
1176D4—42no—
1177D4—82no—
1178D4—82no—
1179D4—82no—
1180D4—82no—
1181D4—221no—
1182D4—221no—
1183D4—444no—
1184D4—442no—
1185D4—442no—
1186D4—881no—
1187D4—882no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—22no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—44no—
1208C2×C4—44no—
1209C2×C4—42no—
1210C2×C4—81no—
1211C2×C4—81no—
1212C2×C4—221no—
1213C2×C4—222no—
1214C2×C4—221no—
1215C2×C4—222no—
1216C2×C4—221no—
1217C2×C4—444no—
1218C2×C4—444no—
1219C2×C4—442no—
1220C2×C4—442no—
1221C2×C4—881no—
1222C2×C4—882no—
1223C2×C4#6703712yes—
1224C2×C4#6703712yes—
1225C2×C4C22×C22⋊D1111yescharacteristic
1226C2×C4C22×C22⋊D1112yes—
1227C2×C4C22×C22⋊D1112yes—
1228C2×C4C22×C22⋊D1111yescharacteristic
1229C2×C4C22×C22⋊D1111yescharacteristic
1230C2×C4C24×D1111yescharacteristic
1231C8—221no—
1232C8—221no—
1233C8—221no—
1234C8—221no—
1235C8—222no—
1236C8—222no—
1237C22—21no—
1238C22—21no—
1239C22—21no—
1240C22—22no—
1241C22—22no—
1242C22—21no—
1243C22—21no—
1244C22—21no—
1245C22—22no—
1246C22—22no—
1247C22—21no—
1248C22—22no—
1249C22—22no—
1250C22—21no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—82no—
1255C22—84no—
1256C22—84no—
1257C22—441no—
1258C22—441no—
1259C22—441no—
1260C22#1062333512yes—
1261C22C23×C22⋊D1111yescharacteristic
1262C4—21no—
1263C4—21no—
1264C4—22no—
1265C4—22no—
1266C4—41no—
1267C4—41no—
1268C4—42no—
1269C4—41no—
1270C4—41no—
1271C4—441no—
1272C4—442no—
1273C4—441no—
1274C4—442no—
1275C4—441no—
1276C4#1062333512yes—
1277C4C2×#6703711yescharacteristic
1278C4C2×#6703711yescharacteristic
1279C2—22no—
1280C2—41no—
1281C2—41no—
1282C2—42no—
1283C2—42no—
1284C2—82no—
1285C2—881no—
1286C2C2×#1062333511yescharacteristic
1287C2#1308338711yescharacteristic
1288C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3449C2
socleC22×C11C23×D4
hypercenter#3449D11
hypocenterC11#60761
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. #13082296C2semidirect
2. #13079522C2semidirect
3. #13079513C2semidirect
4. #13079492C2semidirect
5. #13079492C2semidirect
6. #13079453C2semidirect
7. #13079442C2semidirect
8. #13079404C2semidirect
9. #13079393C2semidirect
10. #13078579C2semidirect
11. #13078568C2semidirect
12. #13078564C2semidirect
13. #13078529C2semidirect
14. #13078303C2semidirect
15. #13078292C2semidirect
16. #13078268C2semidirect
17. #13078252C2semidirect
18. #13077909C2semidirect
19. #13077900C2semidirect
20. #13077858C2semidirect
21. C2×#10622852C2semidirect
22. #13077065C2semidirect
23. C11×#3449C2semidirect
43. #10623364C22semidirect
47. #10623356C22semidirect
53. C22×#4326C22semidirect
54. C2×#66995C22semidirect
57. C22×#4324C22semidirect
58. C2×#66985C22semidirect
60. #10623322C22semidirect
62. C2×#66977C22semidirect
66. #10622852C22semidirect
67. #10622852C22semidirect
68. #10622852C22semidirect
70. #10622851C22semidirect
73. #10622847C22semidirect
74. #10622847C22semidirect
75. #10622838C22semidirect
76. C2×#66899C22semidirect
77. #10622828C22semidirect
78. C2×#66896C22semidirect
80. #10622820C22semidirect
82. C2×C22⋊(C11⋊C8)C22semidirect
83. #10622665C22semidirect
84. #10622665C22semidirect
85. #10622665C22semidirect
86. #10622664C22semidirect
87. #10622664C22semidirect
88. #10622664C22semidirect
89. #10622663C22semidirect
90. #10622663C22semidirect
91. #10622662C22semidirect
92. #10622661C22semidirect
93. #10622660C22semidirect
94. #10622660C22semidirect
95. #10622658C22semidirect
96. #10622658C22semidirect
97. #10622657C22semidirect
98. #10622656C22semidirect
99. #10622655C22semidirect
100. #10622655C22semidirect
101. #10622655C22semidirect
102. #10622654C22semidirect
103. #10622654C22semidirect
104. #10622654C22semidirect
105. #10622653C22semidirect
106. #10622653C22semidirect
107. #10622652C22semidirect
108. #10622651C22semidirect
109. #10622650C22semidirect
110. #10622650C22semidirect
111. #10622648C22semidirect
112. #10622648C22semidirect
113. #10622647C22semidirect
114. #10622646C22semidirect
115. #10622617C22semidirect
116. #10622617C22semidirect
117. #10622616C22semidirect
118. #10622616C22semidirect
119. #10622615C22semidirect
120. #10622615C22semidirect
121. #10622611C22semidirect
122. #10622611C22semidirect
123. #10622609C22semidirect
124. #10622609C22semidirect
125. #10622609C22semidirect
126. #10622609C22semidirect
127. #10622608C22semidirect
128. #10622608C22semidirect
129. #10622584C22semidirect
130. #10622584C22semidirect
131. #10622583C22semidirect
132. #10622583C22semidirect
133. #10622581C22semidirect
134. #10622580C22semidirect
494. #3449D11semidirect
1136. C11#60761semidirect

Maximal subgroups

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

subgroupindex
#130822962
#130795222
#130795132
#130794922
#130794532
#130794422
#130794042
#130793932
#130785792
#130785682
#130785642
#130785292
#130783032
#130782922
#130782682
#130782522
#130779092
#130779002
#130778582
C2×#106228522
#130770652
C11×#34492
#6076111