Finite Group Databasebeta

← #15624911

Subgroups — #15624911

Order 2816.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082296C211yesmaximal, characteristic, complemented
2#13079522C212yesmaximal, complemented
3#13079507C212yesmaximal, complemented
4#13079498C212yesmaximal, complemented
5#13079492C212yesmaximal, complemented
6#13079453C212yesmaximal, complemented
7#13079446C212yesmaximal, complemented
8#13079442C212yesmaximal, complemented
9#13079437C212yesmaximal, complemented
10#13078605C211yesmaximal, characteristic, complemented
11#13078601C211yesmaximal, characteristic, complemented
12#13078585C211yesmaximal, characteristic, complemented
13#13078579C211yesmaximal, characteristic, complemented
14#13078248C211yesmaximal, characteristic, complemented
15#13078242C211yesmaximal, characteristic, complemented
16#13078222C211yesmaximal, characteristic, complemented
17C2×#10622665C211yesmaximal, characteristic, complemented
18#13077931C211yesmaximal, characteristic, complemented
19#13077928C211yesmaximal, characteristic, complemented
20#13077911C211yesmaximal, characteristic, complemented
21#13077909C211yesmaximal, characteristic, complemented
22#13077061C211yesmaximal, characteristic, complemented
23C11×#3489C211yesmaximal, characteristic, complemented
24C2×C11×2−1+4C2211yescharacteristic
25C22×C11×#41C2211yescharacteristic
26C2×#67043C2211yescharacteristic
27D4×Q8×C11—21no—
28C11×#548—21no—
29C11×#547—22no—
30C11×#547—21no—
31C11×#546—22no—
32C11×#546—21no—
33C11×#537C2211yescharacteristic
34C11×#537C2212yes—
35C11×#536C2211yescharacteristic
36C11×#536C2212yes—
37C11×#525C2212yes—
38C11×#525C2211yescharacteristic
39C2×C11×C22⋊Q8C2212yes—
40C2×C11×C22⋊Q8C2211yescharacteristic
41C11×#520C2211yescharacteristic
42#10623364C2211yescharacteristic
43#10623364C2212yes—
44#10623362—21no—
45#10623358C2211yescharacteristic
46#10623356C2211yescharacteristic
47#10623356C2212yes—
48#10623355—22no—
49#10623355—21no—
50C2×#67004C2211yescharacteristic, complemented
51C2×#67003C2211yescharacteristic, complemented
52Q8×C22⋊D11—21no—
53C22×#4326C2211yescharacteristic, complemented
54C2×#66995C2211yescharacteristic, complemented
55#10623337—21no—
56#10623337—22no—
57#10623322C2212yes—
58#10623322C2211yescharacteristic
59C2×#66977C2212yes—
60C2×#66977C2211yescharacteristic
61C22×#4318C2211yescharacteristic
62C22×#4318C2211yescharacteristic
63#10622852C2212yescomplemented
64#10622852C2212yescomplemented
65#10622852C2212yescomplemented
66#10622851C2212yescomplemented
67#10622847C2211yescharacteristic
68#10622847C2211yescharacteristic
69#10622847C2211yescharacteristic
70#10622847C2211yescharacteristic
71#10622847C2212yes—
72#10622847C2212yes—
73#10622846C2211yescharacteristic, complemented
74#10622845C2211yescharacteristic, complemented
75#10622841C2212yescomplemented
76#10622841C2212yescomplemented
77#10622841C2212yescomplemented
78#10622840C2212yescomplemented
79#10622838C2211yescharacteristic, complemented
80C2×#66899C2211yescharacteristic, complemented
81#10622820C2212yes—
82#10622820C2212yes—
83#10622665C2211yescharacteristic
84#10622665C2212yes—
85#10622665C2212yes—
86#10622665C2212yes—
87#10622665C2212yes—
88#10622665C2212yescomplemented
89#10622665C2212yescomplemented
90#10622665C2211yescharacteristic, complemented
91#10622664C2212yescomplemented
92#10622664C2212yescomplemented
93#10622663C2212yescomplemented
94#10622663C2212yescomplemented
95#10622663C2212yescomplemented
96#10622662C2211yescharacteristic
97#10622662C2212yes—
98#10622662C2211yescharacteristic, complemented
99#10622661C2212yescomplemented
100#10622660C2212yescomplemented
101#10622660C2212yescomplemented
102#10622660C2212yescomplemented
103#10622658C2212yescomplemented
104#10622658C2212yescomplemented
105#10622658C2212yescomplemented
106#10622657C2212yescomplemented
107#10622656C2212yescomplemented
108#10622656C2212yescomplemented
109#10622655C2211yescharacteristic
110#10622655C2212yes—
111#10622655C2211yescharacteristic, complemented
112#10622654C2212yescomplemented
113#10622653C2212yescomplemented
114#10622652C2211yescharacteristic
115#10622652C2211yescharacteristic, complemented
116#10622650C2212yescomplemented
117#10622648C2212yescomplemented
118#10622647C2212yescomplemented
119#10622617C2211yescharacteristic, complemented
120#10622616C2212yescomplemented
121#10622615C2211yescharacteristic, complemented
122#10622611C2211yescharacteristic, complemented
123#10622609C2212yescomplemented
124#10622609C2212yescomplemented
125#10622609C2212yescomplemented
126#10622608C2211yescharacteristic, complemented
127#10622584C2212yescomplemented
128#10622584C2212yescomplemented
129#10622583C2212yescomplemented
130C2×#66874C2211yescharacteristic, complemented
131#10622581C2212yescomplemented
132#10622579C2211yescharacteristic, complemented
133#10622577C2211yescharacteristic, complemented
134C2×#66872C2211yescharacteristic, complemented
135C11×2−1+4—42no—
136C11×2−1+4—42no—
137C2×C11×#41—22no—
138C2×C11×#41—21no—
139C2×C11×#41—42no—
140C2×C11×#41—42no—
141C2×C11×#41D412yes—
142C2×C11×#41D411yescharacteristic
143C2×C11×#41D411yescharacteristic
144C2×C11×#41C2311yescharacteristic
145C2×C11×#41C2312yes—
146C2×C11×#41C2311yescharacteristic
147C2×C11×#41C2311yescharacteristic
148C2×C11×#41C2312yes—
149C22×Q8×C11—21no—
150C22×Q8×C11D411yescharacteristic
151C22×Q8×C11C2311yescharacteristic
152C22×Q8×C11C2312yes—
153C22×D4×C11D411yescharacteristic
154C22×D4×C11D412yes—
155C23×C4×C11C2311yescharacteristic
156C23×C4×C11C2312yes—
157#67043—42no—
158#67043—42no—
159C2×Q8×D11—21no—
160C2×#4341—22no—
161C2×#4341—21no—
162C2×#4339C2311yescharacteristic
163C2×#4339C2312yes—
164C22×Dic22C2311yescharacteristic
165C22×Dic22C2312yes—
166C11×C4⋊Q8—21no—
167C11×C4⋊Q8—22no—
168C11×#124—21no—
169C11×#124—22no—
170C11×#123—22no—
171C11×#123—22no—
172C11×#123—22no—
173C11×#123—21no—
174C11×#123—22no—
175C11×C22⋊Q8—21no—
176C11×C22⋊Q8—22no—
177C11×C22⋊Q8—21no—
178C11×C22⋊Q8—22no—
179C11×C22⋊Q8—21no—
180C11×C22⋊Q8—22no—
181C11×C22⋊Q8C2311yescharacteristic
182C11×C22⋊Q8C2312yes—
183C11×C22⋊Q8C2312yes—
184C11×C22⋊Q8C2312yes—
185C11×C22⋊Q8C2312yes—
186C11×C22⋊Q8C2312yes—
187C11×C22⋊Q8C2311yescharacteristic
188C11×#121—22no—
189C11×#121—22no—
190C11×#121—22no—
191C11×#121—21no—
192C11×#121—22no—
193C11×#121C2311yescharacteristic
194C11×#121C2312yes—
195C11×#121C2311yescharacteristic
196C11×#120—21no—
197C11×#120—22no—
198C4×Q8×C11—21no—
199C4×D4×C11—22no—
200C4×D4×C11—21no—
201C4×D4×C11—21no—
202C4×D4×C11—22no—
203C4×D4×C11—21no—
204C4×D4×C11—22no—
205C11×#117C2311yescharacteristic
206C11×#117C2312yes—
207C2×C11×C4⋊C4—21no—
208C2×C11×C4⋊C4—22no—
209C2×C11×C4⋊C4C2311yescharacteristic
210C2×C11×C4⋊C4C2312yes—
211C2×C11×C22⋊C4—21no—
212C2×C11×C22⋊C4—22no—
213#67006—21no—
214#67006—22no—
215C2×C22⋊Dic11—21no—
216C2×C22⋊Dic11—22no—
217#67004—42no—
218#67003—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—
228C2×#4326C2311yescharacteristic
229C2×#4326C2312yes—
230#66995—42no—
231C2×#4325C2312yes—
232C2×#4325C2311yescharacteristic
233#66992—22no—
234#66992—22no—
235#66992—22no—
236#66991—21no—
237#66991—22no—
238#66989—21no—
239#66989—22no—
240#66988—22no—
241#66988—22no—
242#66988—22no—
243D4×Dic11—22no—
244D4×Dic11—21no—
245C2×#4324C2311yescharacteristic
246C2×#4324C2312yes—
247C2×#4323C2311yescharacteristic
248#66983C2311yescharacteristic
249#66983C2312yes—
250#66983C2311yescharacteristic
251#66982—21no—
252#66982—22no—
253C4×C22⋊D11—21no—
254C4×C22⋊D11—22no—
255C4×C22⋊D11—21no—
256C4×C22⋊D11—22no—
257#66979C2311yescharacteristic
258#66979C2312yes—
259C2×C4⋊Dic11C2311yescharacteristic
260C2×C4⋊Dic11C2312yes—
261#66977—21no—
262#66977—22no—
263#66977—21no—
264#66977—22no—
265#66977C2311yescharacteristic
266#66977C2312yes—
267#66977C2312yes—
268#66977C2312yes—
269#66977C2312yes—
270#66977C2312yes—
271#66977C2311yescharacteristic
272C2×Dic11⋊C4—21no—
273C2×Dic11⋊C4—22no—
274C2×#4318—42no—
275C2×#4318—42no—
276C2×#4318C2311yescharacteristic
277C2×#4318C2311yescharacteristic
278C2×#4318C2311yescharacteristic
279C2×#4318C2311yescharacteristic
280C2×#4318C2312yes—
281C2×#4318C2311yescharacteristic
282C2×#4318C2311yescharacteristic
283C22×C11⋊C8C2311yescharacteristic
284C22×C11⋊C8C2311yescharacteristic
285C22×C11⋊C8C2312yes—
286#66899C2312yes—
287#66899C2312yes—
288#66899C2312yes—
289#66899C2312yes—
290#66899C2312yes—
291#66899C2311yescharacteristic
292#66899C2311yescharacteristic
293#66896C2312yes—
294#66896C2311yescharacteristic
295#66896C2311yescharacteristic
296C22⋊(C11⋊C8)C2312yes—
297C22⋊(C11⋊C8)C2312yes—
298C22⋊(C11⋊C8)C2312yes—
299C22⋊(C11⋊C8)C2312yes—
300C22⋊(C11⋊C8)C2312yes—
301C22⋊(C11⋊C8)C2312yes—
302C22⋊(C11⋊C8)C2312yes—
303C22⋊(C11⋊C8)C2312yes—
304#66874C2312yes—
305#66874C2312yes—
306#66874C2312yes—
307#66874C2312yes—
308#66874C2311yescharacteristic
309#66874C2311yescharacteristic
310#66874C2312yes—
311#66873C2312yes—
312#66873C2311yescharacteristic
313#66873C2311yescharacteristic
314#66872C2312yes—
315#66872C2312yes—
316#66872C2312yes—
317#66872C2312yes—
318#66872C2311yescharacteristic
319#66872C2311yescharacteristic
320#66871C2312yes—
321#66871C2311yescharacteristic
322#66871C2312yes—
323#66871C2311yescharacteristic
324#60773—111nomaximal, Sylow
325C24×C11C2×D411yescharacteristic
326C24×C11C2×D412yes—
327C11×#41—22no—
328C11×#41—22no—
329C11×#41—22no—
330C11×#41—22no—
331C11×#41—22no—
332C11×#41—22no—
333C11×#41—42no—
334C11×#41—42no—
335C11×#41—44no—
336C11×#41—42no—
337C11×#41—42no—
338C11×#41—42no—
339C11×#41—42no—
340C11×#41—48no—
341C11×#41—44no—
342C2×Q8×C11—22no—
343C2×Q8×C11—21no—
344C2×Q8×C11—22no—
345C2×Q8×C11—22no—
346C2×Q8×C11—42no—
347C2×Q8×C11—42no—
348C2×Q8×C11—42no—
349C2×Q8×C11—44no—
350C2×Q8×C11C2×D411yescharacteristic
351C2×Q8×C11C2×D411yescharacteristic
352C2×Q8×C11C2×D412yes—
353C2×Q8×C11C2412yes—
354C2×Q8×C11C2411yescharacteristic
355C2×D4×C11—21no—
356C2×D4×C11—22no—
357C2×D4×C11—21no—
358C2×D4×C11—21no—
359C2×D4×C11—22no—
360C2×D4×C11—42no—
361C2×D4×C11—44no—
362C2×D4×C11C2×D412yes—
363C2×D4×C11C2×D411yescharacteristic
364C2×D4×C11C2×D412yes—
365C2×D4×C11C2×D411yescharacteristic
366C2×D4×C11C2×D412yes—
367C2×D4×C11C2×D412yes—
368C2×D4×C11C2×D412yes—
369C2×D4×C11C2411yescharacteristic
370C22×C4×C11—22no—
371C22×C4×C11—22no—
372C22×C4×C11—22no—
373C22×C4×C11—21no—
374C22×C4×C11—22no—
375C22×C4×C11—21no—
376C22×C4×C11—22no—
377C22×C4×C11—21no—
378C22×C4×C11—42no—
379C22×C4×C11—42no—
380C22×C4×C11C2×D411yescharacteristic
381C22×C4×C11C2×D411yescharacteristic
382C22×C4×C11C2×D411yescharacteristic
383C22×C4×C11C2×D412yes—
384C22×C4×C11C2×D412yes—
385C22×C4×C11C2×D412yes—
386C22×C4×C11C2412yes—
387C22×C4×C11C2412yes—
388C22×C4×C11C2411yescharacteristic
389C22×C4×C11C2411yescharacteristic
390C22×C4×C11C2411yescharacteristic
391C2×C22⋊D11—21no—
392C2×C22⋊D11—22no—
393C2×C22⋊D11—21no—
394C2×C22⋊D11—21no—
395C2×C22⋊D11—22no—
396C22×Dic11—22no—
397C22×Dic11—21no—
398C22×Dic11—22no—
399C22×Dic11—21no—
400Q8×D11—44no—
401#4341—48no—
402#4341—44no—
403#4339—22no—
404#4339—22no—
405#4339—42no—
406#4339—42no—
407C2×D44C2411yescharacteristic
408C2×C4×D11—22no—
409C2×C4×D11—21no—
410C2×Dic22—22no—
411C2×Dic22—21no—
412C2×Dic22—22no—
413C2×Dic22—22no—
414C2×Dic22—42no—
415C2×Dic22—42no—
416C2×Dic22C2412yes—
417C2×Dic22C2411yescharacteristic
418C11×C4⋊C4—22no—
419C11×C4⋊C4—21no—
420C11×C4⋊C4—22no—
421C11×C4⋊C4—22no—
422C11×C4⋊C4—22no—
423C11×C4⋊C4—22no—
424C11×C4⋊C4—21no—
425C11×C4⋊C4—22no—
426C11×C4⋊C4—21no—
427C11×C4⋊C4C2411yescharacteristic
428C11×C4⋊C4C2412yes—
429C11×C4⋊C4C2411yescharacteristic
430C11×C22⋊C4—22no—
431C11×C22⋊C4—21no—
432C11×C22⋊C4—22no—
433C11×C22⋊C4—22no—
434C11×C22⋊C4—22no—
435C11×C22⋊C4—22no—
436C11×C22⋊C4—21no—
437C11×C22⋊C4—21no—
438C11×C22⋊C4—22no—
439C11×C22⋊C4—21no—
440C11×C22⋊C4—22no—
441C11×C22⋊C4—21no—
442C42×C11—22no—
443C42×C11—21no—
444C22⋊Dic11—22no—
445C22⋊Dic11—21no—
446C22⋊Dic11—22no—
447C22⋊Dic11—22no—
448C22⋊Dic11—22no—
449C22⋊Dic11—21no—
450C22⋊Dic11—22no—
451C22⋊Dic11—22no—
452C22⋊Dic11—21no—
453#4326—42no—
454#4326—42no—
455#4326—42no—
456#4326—41no—
457#4326—42no—
458#4325—42no—
459#4325—41no—
460#4324—41no—
461#4324—42no—
462#4323—41no—
463(C2×D11)⋊C4—21no—
464(C2×D11)⋊C4—22no—
465(C2×D11)⋊C4—21no—
466C4⋊Dic11—22no—
467C4⋊Dic11—21no—
468C4⋊Dic11C2411yescharacteristic
469C4⋊Dic11C2412yes—
470C4⋊Dic11C2411yescharacteristic
471Dic11⋊C4—22no—
472Dic11⋊C4—21no—
473Dic11⋊C4—22no—
474Dic11⋊C4—22no—
475Dic11⋊C4—22no—
476Dic11⋊C4—22no—
477Dic11⋊C4—21no—
478C4×Dic11—22no—
479C4×Dic11—21no—
480#4318—22no—
481#4318—22no—
482#4318—41no—
483#4318—41no—
484#4318—42no—
485#4318—41no—
486#4318—41no—
487C2×C11⋊C8—22no—
488C2×C11⋊C8—22no—
489C2×C11⋊C8—42no—
490C2×C11⋊C8C2411yescharacteristic
491C2×C11⋊C8C2412yes—
492C2×C11⋊C8C2412yes—
493C2×C11⋊C8C2411yescharacteristic
494C2×C11⋊C8C2411yescharacteristic
495C2×C11⋊C8C2411yescharacteristic
496#3489—111no—
497#3489D1111yescharacteristic, complemented
498#3204—112no—
499#3202—112no—
500#3201—112no—
501#3201—112no—
502#3197—112no—
503#3196—112no—
504#3196—112no—
505#3195—112no—
506#3099—111no—
507#3099—111no—
508#3097—111no—
509#3097—111no—
510#3056—111no—
511#3056—111no—
512#3054—111no—
513C2×#470—111no—
514#3013—111no—
515#3013—111no—
516#3011—111no—
517#3011—111no—
518#2879—111no—
519C23×C11—22no—
520C23×C11—21no—
521C23×C11—42no—
522C23×C11—41no—
523C23×C11—41no—
524C23×C11—42no—
525C23×C11—42no—
526C23×C11C22×D411yescharacteristic
527C23×C11C22×D411yescharacteristic
528C23×C11C22×D412yes—
529C23×C11C22×D412yes—
530C23×C11C22×D411yescharacteristic
531C22×D11—21no—
532Q8×C11—22no—
533Q8×C11—22no—
534Q8×C11—22no—
535Q8×C11—21no—
536Q8×C11—22no—
537Q8×C11—21no—
538Q8×C11—42no—
539Q8×C11—44no—
540Q8×C11—42no—
541D4×C11—24no—
542D4×C11—24no—
543D4×C11—22no—
544D4×C11—22no—
545D4×C11—21no—
546D4×C11—21no—
547D4×C11—42no—
548D4×C11—42no—
549D4×C11—42no—
550D4×C11—42no—
551D4×C11—44no—
552D4×C11—42no—
553D4×C11—81no—
554D4×C11—82no—
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—22no—
563C2×C4×C11—22no—
564C2×C4×C11—22no—
565C2×C4×C11—22no—
566C2×C4×C11—21no—
567C2×C4×C11—22no—
568C2×C4×C11—21no—
569C2×C4×C11—22no—
570C2×C4×C11—21no—
571C2×C4×C11—42no—
572C2×C4×C11—42no—
573C2×C4×C11—42no—
574C2×C4×C11—44no—
575C2×C4×C11—44no—
576C2×C4×C11—42no—
577C2×C4×C11—42no—
578C2×C4×C11—81no—
579C2×C4×C11—82no—
580C2×C4×C11C22×D412yes—
581C2×C4×C11C22×D412yes—
582C2×C4×C11C22×D411yescharacteristic
583C2×C4×C11C22×D411yescharacteristic
584C2×C4×C11C22×D411yescharacteristic
585C2×C4×C11H(5,𝔽2)12yes—
586C2×C4×C11H(5,𝔽2)12yes—
587C2×C4×C11C2511yescharacteristic
588C22⋊D11—44no—
589C22⋊D11—42no—
590C22⋊D11—42no—
591C22⋊D11—81no—
592C22⋊D11—82no—
593C2×Dic11—21no—
594C2×Dic11—22no—
595C2×Dic11—21no—
596C2×Dic11—22no—
597C2×Dic11—21no—
598C2×Dic11—44no—
599C2×Dic11—42no—
600C2×Dic11—81no—
601C2×Dic11—82no—
602D44—21no—
603D44—21no—
604C4×D11—44no—
605C4×D11—42no—
606Dic22—22no—
607Dic22—21no—
608Dic22—22no—
609Dic22—21no—
610Dic22—44no—
611Dic22—42no—
612C11⋊C8—21no—
613C11⋊C8—21no—
614C11⋊C8—21no—
615C11⋊C8—21no—
616C11⋊C8—22no—
617C11⋊C8—22no—
618C2×2−1+4—111no—
619C2×2−1+4C2×D1111yescharacteristic
620C22×#41C2×D1111yescharacteristic
621C2×#137—111no—
622C2×#137—111no—
623C2×#135—111no—
624C22×Q16—111no—
625C22×M16—111no—
626C22×M16—111no—
627D4×Q8—21no—
628D4×Q8—221no—
629#548—21no—
630#548—221no—
631#547—22no—
632#547—21no—
633#547—222no—
634#547—221no—
635#546—22no—
636#546—21no—
637#546—222no—
638#546—221no—
639#537—111no—
640#537—112no—
641#537C2×D1111yescharacteristic
642#537C2×D1112yes—
643#536—111no—
644#536—112no—
645#536C2×D1111yescharacteristic
646#536C2×D1112yes—
647#525—112no—
648#525—111no—
649#525C2×D1112yes—
650#525C2×D1111yescharacteristic
651C2×C22⋊Q8—112no—
652C2×C22⋊Q8—111no—
653C2×C22⋊Q8C2×D1112yes—
654C2×C22⋊Q8C2×D1111yescharacteristic
655#520—111no—
656#520C2×D1111yescharacteristic
657#485—112no—
658#485—112no—
659#485—112no—
660#485—112no—
661#485—112no—
662#485—112no—
663#484—112no—
664#484—112no—
665#483—112no—
666#483—112no—
667#483—112no—
668#483—112no—
669#482—112no—
670#482—112no—
671#481—112no—
672#481—112no—
673#470—111no—
674#470—112no—
675#470—112no—
676#470—112no—
677#470—112no—
678#470—112no—
679#470—111no—
680#470—112no—
681#469—111no—
682#469—111no—
683#468—111no—
684#468—112no—
685#468—111no—
686#468—111no—
687#468—112no—
688#468—111no—
689#467—112no—
690#467—112no—
691#465—112no—
692#465—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#451—112no—
702#451—112no—
703#451—112no—
704#451—112no—
705#449—112no—
706#449—112no—
707#448—112no—
708#448—112no—
709#428—111no—
710#428—111no—
711#427—111no—
712C2×#106—111no—
713#419—111no—
714#419—111no—
715#417—111no—
716#417—111no—
717#416—111no—
718#416—111no—
719C2×#103—111no—
720C2×#103—111no—
721#408—111no—
722#408—111no—
723#408—111no—
724#408—111no—
725#408—112no—
726#408—112no—
727#407—112no—
728#407—112no—
729C22×C11—21no—
730C22×C11—21no—
731C22×C11—22no—
732C22×C11—21no—
733C22×C11—21no—
734C22×C11—22no—
735C22×C11—21no—
736C22×C11—22no—
737C22×C11—21no—
738C22×C11—22no—
739C22×C11—21no—
740C22×C11—21no—
741C22×C11—22no—
742C22×C11—22no—
743C22×C11—41no—
744C22×C11—41no—
745C22×C11—41no—
746C22×C11—82no—
747C22×C11—84no—
748C22×C11#53412yes—
749C22×C11C23×D411yescharacteristic
750C2×D11—41no—
751C2×D11—41no—
752C2×D11—41no—
753C4×C11—21no—
754C4×C11—21no—
755C4×C11—22no—
756C4×C11—22no—
757C4×C11—42no—
758C4×C11—41no—
759C4×C11—41no—
760C4×C11—42no—
761C4×C11—41no—
762C4×C11#53412yes—
763C4×C11C2×H(5,𝔽2)11yescharacteristic
764C4×C11C2×H(5,𝔽2)11yescharacteristic
765Dic11—42no—
766Dic11—41no—
767Dic11—41no—
768Dic11—42no—
769Dic11—41no—
7702−1+4—42no—
7712−1+4—42no—
7722−1+4—442no—
7732−1+4—442no—
774C2×#41—22no—
775C2×#41—21no—
776C2×#41—42no—
777C2×#41—42no—
778C2×#41—111no—
779C2×#41—112no—
780C2×#41—222no—
781C2×#41—221no—
782C2×#41C22⋊D1112yes—
783C2×#41C22⋊D1111yescharacteristic
784C2×#41C22⋊D1111yescharacteristic
785C2×#41C22×D1111yescharacteristic
786C2×#41C22×D1112yes—
787C2×#41C22×D1111yescharacteristic
788C2×#41C22×D1111yescharacteristic
789C2×#41C22×D1112yes—
790C22×Q8—21no—
791C22×Q8—111no—
792C22×Q8—112no—
793C22×Q8—221no—
794C22×Q8C22⋊D1111yescharacteristic
795C22×Q8C22×D1111yescharacteristic
796C22×Q8C22×D1112yes—
797C22×D4C22⋊D1111yescharacteristic
798C22×D4C22⋊D1112yes—
799C23×C4C22×D1111yescharacteristic
800C23×C4C22×D1112yes—
801#137—442no—
802#137—442no—
803#135—442no—
804C2×Q16—112no—
805C2×Q16—112no—
806C2×Q16—111no—
807C2×Q16—112no—
808C2×Q16—112no—
809C2×Q16—442no—
810C2×SD16—111no—
811C2×SD16—112no—
812C2×SD16—111no—
813C2×SD16—112no—
814C2×D8—111no—
815C2×M16—111no—
816C2×M16—111no—
817C2×M16—111no—
818C2×M16—112no—
819C2×M16—111no—
820C2×M16—111no—
821C2×M16—111no—
822C2×M16—442no—
823C2×M16—442no—
824C22×C8—111no—
825C22×C8—111no—
826C22×C8—112no—
827C4⋊Q8—21no—
828C4⋊Q8—22no—
829C4⋊Q8—221no—
830C4⋊Q8—222no—
831#124—21no—
832#124—22no—
833#124—221no—
834#124—222no—
835#123—22no—
836#123—22no—
837#123—22no—
838#123—21no—
839#123—22no—
840#123—222no—
841#123—222no—
842#123—222no—
843#123—221no—
844#123—222no—
845C22⋊Q8—21no—
846C22⋊Q8—22no—
847C22⋊Q8—21no—
848C22⋊Q8—22no—
849C22⋊Q8—21no—
850C22⋊Q8—22no—
851C22⋊Q8—111no—
852C22⋊Q8—112no—
853C22⋊Q8—112no—
854C22⋊Q8—112no—
855C22⋊Q8—112no—
856C22⋊Q8—112no—
857C22⋊Q8—111no—
858C22⋊Q8—221no—
859C22⋊Q8—222no—
860C22⋊Q8—221no—
861C22⋊Q8—222no—
862C22⋊Q8—221no—
863C22⋊Q8—222no—
864C22⋊Q8C22×D1111yescharacteristic
865C22⋊Q8C22×D1112yes—
866C22⋊Q8C22×D1112yes—
867C22⋊Q8C22×D1112yes—
868C22⋊Q8C22×D1112yes—
869C22⋊Q8C22×D1112yes—
870C22⋊Q8C22×D1111yescharacteristic
871#121—22no—
872#121—22no—
873#121—22no—
874#121—21no—
875#121—22no—
876#121—111no—
877#121—112no—
878#121—111no—
879#121—222no—
880#121—222no—
881#121—222no—
882#121—221no—
883#121—222no—
884#121C22×D1111yescharacteristic
885#121C22×D1112yes—
886#121C22×D1111yescharacteristic
887#120—21no—
888#120—22no—
889#120—221no—
890#120—222no—
891C4×Q8—21no—
892C4×Q8—221no—
893C4×D4—22no—
894C4×D4—21no—
895C4×D4—21no—
896C4×D4—22no—
897C4×D4—21no—
898C4×D4—22no—
899C4×D4—222no—
900C4×D4—221no—
901C4×D4—221no—
902C4×D4—222no—
903C4×D4—221no—
904C4×D4—222no—
905#117—111no—
906#117—112no—
907#117C22×D1111yescharacteristic
908#117C22×D1112yes—
909C2×C4⋊C4—21no—
910C2×C4⋊C4—22no—
911C2×C4⋊C4—111no—
912C2×C4⋊C4—112no—
913C2×C4⋊C4—221no—
914C2×C4⋊C4—222no—
915C2×C4⋊C4C22×D1111yescharacteristic
916C2×C4⋊C4C22×D1112yes—
917C2×C22⋊C4—21no—
918C2×C22⋊C4—22no—
919C2×C22⋊C4—221no—
920C2×C22⋊C4—222no—
921#107—111no—
922#107—111no—
923#107—112no—
924#107—112no—
925#106—112no—
926#106—112no—
927#106—111no—
928#106—111no—
929#106—112no—
930#106—112no—
931#103—112no—
932#103—112no—
933#103—111no—
934#103—111no—
935#103—112no—
936#103—112no—
937#103—112no—
938#103—112no—
939#103—112no—
940#103—111no—
941#103—111no—
942#103—112no—
943#103—112no—
944#103—112no—
945#102—111no—
946#102—111no—
947#102—112no—
948#102—111no—
949#102—111no—
950#102—112no—
951C22⋊C8—112no—
952C22⋊C8—112no—
953C22⋊C8—112no—
954C22⋊C8—112no—
955C22⋊C8—112no—
956C22⋊C8—112no—
957C22⋊C8—112no—
958C22⋊C8—112no—
959C2×C11—22no—
960C2×C11—42no—
961C2×C11—42no—
962C2×C11—41no—
963C2×C11—41no—
964C2×C11—81no—
965C2×C11C2×#53411yescharacteristic
966C2×C11#358611yescharacteristic
967C2×C11#358611yescharacteristic
968D11—81no—
969C24C2×C22⋊D1111yescharacteristic
970C24C2×C22⋊D1112yes—
971#41—22no—
972#41—22no—
973#41—22no—
974#41—22no—
975#41—22no—
976#41—22no—
977#41—42no—
978#41—42no—
979#41—44no—
980#41—42no—
981#41—42no—
982#41—42no—
983#41—42no—
984#41—48no—
985#41—44no—
986#41—222no—
987#41—222no—
988#41—442no—
989#41—442no—
990#41—448no—
991#41—444no—
992C2×Q8—22no—
993C2×Q8—21no—
994C2×Q8—22no—
995C2×Q8—22no—
996C2×Q8—42no—
997C2×Q8—42no—
998C2×Q8—42no—
999C2×Q8—44no—
1000C2×Q8—112no—
1001C2×Q8—111no—
1002C2×Q8—222no—
1003C2×Q8—221no—
1004C2×Q8—222no—
1005C2×Q8—222no—
1006C2×Q8—442no—
1007C2×Q8—442no—
1008C2×Q8—444no—
1009C2×Q8C2×C22⋊D1111yescharacteristic
1010C2×Q8C2×C22⋊D1111yescharacteristic
1011C2×Q8C2×C22⋊D1112yes—
1012C2×Q8C23×D1112yes—
1013C2×Q8C23×D1111yescharacteristic
1014C2×D4—21no—
1015C2×D4—22no—
1016C2×D4—21no—
1017C2×D4—21no—
1018C2×D4—22no—
1019C2×D4—42no—
1020C2×D4—44no—
1021C2×D4—111no—
1022C2×D4—221no—
1023C2×D4—222no—
1024C2×D4—221no—
1025C2×D4—221no—
1026C2×D4—222no—
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×D1111yescharacteristic
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—21no—
1039C22×C4—22no—
1040C22×C4—21no—
1041C22×C4—22no—
1042C22×C4—21no—
1043C22×C4—42no—
1044C22×C4—42no—
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×D1112yes—
1059C22×C4C23×D1111yescharacteristic
1060C22×C4C23×D1111yescharacteristic
1061C22×C4C23×D1111yescharacteristic
1062Q16—442no—
1063Q16—442no—
1064Q16—441no—
1065Q16—442no—
1066Q16—442no—
1067SD16—441no—
1068SD16—442no—
1069SD16—441no—
1070SD16—442no—
1071D8—441no—
1072M16—222no—
1073M16—222no—
1074M16—441no—
1075M16—441no—
1076M16—441no—
1077M16—441no—
1078M16—442no—
1079C2×C8—111no—
1080C2×C8—111no—
1081C2×C8—112no—
1082C2×C8—112no—
1083C2×C8—111no—
1084C2×C8—111no—
1085C2×C8—222no—
1086C2×C8—222no—
1087C2×C8—442no—
1088C4⋊C4—22no—
1089C4⋊C4—21no—
1090C4⋊C4—22no—
1091C4⋊C4—22no—
1092C4⋊C4—22no—
1093C4⋊C4—22no—
1094C4⋊C4—21no—
1095C4⋊C4—22no—
1096C4⋊C4—21no—
1097C4⋊C4—111no—
1098C4⋊C4—112no—
1099C4⋊C4—111no—
1100C4⋊C4—222no—
1101C4⋊C4—221no—
1102C4⋊C4—222no—
1103C4⋊C4—221no—
1104C4⋊C4—222no—
1105C4⋊C4—222no—
1106C4⋊C4—222no—
1107C4⋊C4—222no—
1108C4⋊C4—221no—
1109C4⋊C4C23×D1111yescharacteristic
1110C4⋊C4C23×D1112yes—
1111C4⋊C4C23×D1111yescharacteristic
1112C22⋊C4—22no—
1113C22⋊C4—21no—
1114C22⋊C4—22no—
1115C22⋊C4—22no—
1116C22⋊C4—22no—
1117C22⋊C4—22no—
1118C22⋊C4—21no—
1119C22⋊C4—21no—
1120C22⋊C4—22no—
1121C22⋊C4—21no—
1122C22⋊C4—22no—
1123C22⋊C4—21no—
1124C22⋊C4—222no—
1125C22⋊C4—221no—
1126C22⋊C4—222no—
1127C22⋊C4—222no—
1128C22⋊C4—222no—
1129C22⋊C4—222no—
1130C22⋊C4—221no—
1131C22⋊C4—221no—
1132C22⋊C4—222no—
1133C22⋊C4—221no—
1134C22⋊C4—222no—
1135C22⋊C4—221no—
1136C42—22no—
1137C42—21no—
1138C42—222no—
1139C42—221no—
1140C11#6077311yescharacteristic, complemented, Sylow
1141C23—22no—
1142C23—21no—
1143C23—42no—
1144C23—41no—
1145C23—41no—
1146C23—42no—
1147C23—42no—
1148C23—221no—
1149C23C22×C22⋊D1111yescharacteristic
1150C23C22×C22⋊D1111yescharacteristic
1151C23C22×C22⋊D1112yes—
1152C23C22×C22⋊D1112yes—
1153C23C22×C22⋊D1111yescharacteristic
1154Q8—22no—
1155Q8—22no—
1156Q8—22no—
1157Q8—21no—
1158Q8—22no—
1159Q8—21no—
1160Q8—42no—
1161Q8—44no—
1162Q8—42no—
1163Q8—222no—
1164Q8—221no—
1165Q8—222no—
1166Q8—221no—
1167Q8—444no—
1168Q8—442no—
1169D4—24no—
1170D4—24no—
1171D4—22no—
1172D4—22no—
1173D4—21no—
1174D4—21no—
1175D4—42no—
1176D4—42no—
1177D4—42no—
1178D4—42no—
1179D4—44no—
1180D4—42no—
1181D4—81no—
1182D4—82no—
1183D4—221no—
1184D4—221no—
1185D4—444no—
1186D4—442no—
1187D4—442no—
1188D4—881no—
1189D4—882no—
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—22no—
1200C2×C4—22no—
1201C2×C4—21no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—21no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—44no—
1210C2×C4—44no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—81no—
1214C2×C4—82no—
1215C2×C4—221no—
1216C2×C4—222no—
1217C2×C4—221no—
1218C2×C4—222no—
1219C2×C4—221no—
1220C2×C4—444no—
1221C2×C4—444no—
1222C2×C4—442no—
1223C2×C4—442no—
1224C2×C4—881no—
1225C2×C4—882no—
1226C2×C4#6703712yes—
1227C2×C4#6703712yes—
1228C2×C4C22×C22⋊D1112yes—
1229C2×C4C22×C22⋊D1112yes—
1230C2×C4C22×C22⋊D1111yescharacteristic
1231C2×C4C22×C22⋊D1111yescharacteristic
1232C2×C4C22×C22⋊D1111yescharacteristic
1233C2×C4C24×D1111yescharacteristic
1234C8—221no—
1235C8—221no—
1236C8—221no—
1237C8—221no—
1238C8—222no—
1239C8—222no—
1240C22—21no—
1241C22—21no—
1242C22—22no—
1243C22—21no—
1244C22—22no—
1245C22—21no—
1246C22—22no—
1247C22—21no—
1248C22—21no—
1249C22—22no—
1250C22—21no—
1251C22—21no—
1252C22—22no—
1253C22—22no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—82no—
1258C22—84no—
1259C22—441no—
1260C22—441no—
1261C22—441no—
1262C22#1062333512yes—
1263C22C23×C22⋊D1111yescharacteristic
1264C4—21no—
1265C4—21no—
1266C4—22no—
1267C4—22no—
1268C4—42no—
1269C4—41no—
1270C4—41no—
1271C4—42no—
1272C4—41no—
1273C4—441no—
1274C4—442no—
1275C4—441no—
1276C4—442no—
1277C4—441no—
1278C4#1062333512yes—
1279C4C2×#6703711yescharacteristic
1280C4C2×#6703711yescharacteristic
1281C2—22no—
1282C2—41no—
1283C2—42no—
1284C2—42no—
1285C2—41no—
1286C2—81no—
1287C2—881no—
1288C2C2×#1062333511yescharacteristic
1289C2#1308340211yescharacteristic
1290C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3489C2
socleC22×C11C23×D4
hypercenter#3489D11
hypocenterC11#60773
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. #13082296C2semidirect
2. #13079522C2semidirect
3. #13079507C2semidirect
4. #13079498C2semidirect
5. #13079492C2semidirect
6. #13079453C2semidirect
7. #13079446C2semidirect
8. #13079442C2semidirect
9. #13079437C2semidirect
10. #13078605C2semidirect
11. #13078601C2semidirect
12. #13078585C2semidirect
13. #13078579C2semidirect
14. #13078248C2semidirect
15. #13078242C2semidirect
16. #13078222C2semidirect
17. C2×#10622665C2semidirect
18. #13077931C2semidirect
19. #13077928C2semidirect
20. #13077911C2semidirect
21. #13077909C2semidirect
22. #13077061C2semidirect
23. C11×#3489C2semidirect
50. C2×#67004C22semidirect
51. C2×#67003C22semidirect
53. C22×#4326C22semidirect
54. C2×#66995C22semidirect
63. #10622852C22semidirect
64. #10622852C22semidirect
65. #10622852C22semidirect
66. #10622851C22semidirect
73. #10622846C22semidirect
74. #10622845C22semidirect
75. #10622841C22semidirect
76. #10622841C22semidirect
77. #10622841C22semidirect
78. #10622840C22semidirect
79. #10622838C22semidirect
80. C2×#66899C22semidirect
88. #10622665C22semidirect
89. #10622665C22semidirect
90. #10622665C22semidirect
91. #10622664C22semidirect
92. #10622664C22semidirect
93. #10622663C22semidirect
94. #10622663C22semidirect
95. #10622663C22semidirect
98. #10622662C22semidirect
99. #10622661C22semidirect
100. #10622660C22semidirect
101. #10622660C22semidirect
102. #10622660C22semidirect
103. #10622658C22semidirect
104. #10622658C22semidirect
105. #10622658C22semidirect
106. #10622657C22semidirect
107. #10622656C22semidirect
108. #10622656C22semidirect
111. #10622655C22semidirect
112. #10622654C22semidirect
113. #10622653C22semidirect
115. #10622652C22semidirect
116. #10622650C22semidirect
117. #10622648C22semidirect
118. #10622647C22semidirect
119. #10622617C22semidirect
120. #10622616C22semidirect
121. #10622615C22semidirect
122. #10622611C22semidirect
123. #10622609C22semidirect
124. #10622609C22semidirect
125. #10622609C22semidirect
126. #10622608C22semidirect
127. #10622584C22semidirect
128. #10622584C22semidirect
129. #10622583C22semidirect
130. C2×#66874C22semidirect
131. #10622581C22semidirect
132. #10622579C22semidirect
133. #10622577C22semidirect
134. C2×#66872C22semidirect
497. #3489D11semidirect
1140. C11#60773semidirect

Maximal subgroups

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

subgroupindex
#130822962
#130795222
#130795072
#130794982
#130794922
#130794532
#130794462
#130794422
#130794372
#130786052
#130786012
#130785852
#130785792
#130782482
#130782422
#130782222
C2×#106226652
#130779312
#130779282
#130779112
#130779092
#130770612
C11×#34892
#6077311