Finite Group Databasebeta

← #15639295

Subgroups — #15639295

Order 2816.

2132 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082468C211yesmaximal, characteristic, complemented
2#13080899C211yesmaximal, characteristic, complemented
3#13080847C211yesmaximal, characteristic, complemented
4#13080802C212yesmaximal, complemented
5#13080772C212yesmaximal, complemented
6#13080555C211yesmaximal, characteristic, complemented
7#13080533C211yesmaximal, characteristic, complemented
8#13080372C211yesmaximal, characteristic, complemented
9#13080342C211yesmaximal, characteristic, complemented
10#13080278C211yesmaximal, characteristic, complemented
11#13080232C211yesmaximal, characteristic, complemented
12#13080172C212yesmaximal, complemented
13#13080137C212yesmaximal, complemented
14#13079627C211yesmaximal, characteristic, complemented
15#13079549C211yesmaximal, characteristic, complemented
16#13079453C212yesmaximal, complemented
17#13079404C212yesmaximal, complemented
18#13078767C211yesmaximal, characteristic, complemented
19#13078687C211yesmaximal, characteristic, complemented
20#13077858C212yesmaximal, complemented
21#13077834C212yesmaximal, complemented
22#13077651C211yesmaximal, characteristic, complemented
23D4×C11×#41C211yesmaximal, characteristic, complemented
24C22×C11×#41C2212yes—
25C11×#550C2211yescharacteristic
26D4×Q8×C11C2211yescharacteristic
27C11×#548C2212yes—
28C11×#547—21no—
29C11×#547C2211yescharacteristic
30C11×#546—22no—
31C11×#546C2212yes—
32D42×C11—21no—
33D42×C11C2211yescharacteristic
34C11×#532—21no—
35C11×#532C2211yescharacteristic
36C11×#525—22no—
37C11×#525C2212yes—
38C4×C11×#41C2211yescharacteristic
39C2×C4×D4×C11—21no—
40C2×C4×D4×C11C2211yescharacteristic
41C2×#67003C2212yescomplemented
42C2×#67003C2212yescomplemented
43C2×#66995C2212yescomplemented
44#10623336—21no—
45C2×#66985C2212yescomplemented
46#10623322C2212yescomplemented
47#10623322C2212yescomplemented
48#10623094C2212yescomplemented
49#10623090—21no—
50#10623090—21no—
51#10623089—22no—
52#10623084C2211yescharacteristic
53#10623084C2211yescharacteristic, complemented
54#10623082C2212yescomplemented
55#10623073C2211yescharacteristic
56#10623073C2211yescharacteristic, complemented
57#10623035—21no—
58#10623025—22no—
59#10623008C2211yescharacteristic, complemented
60#10623001C2211yescharacteristic, complemented
61#10622852C2211yescharacteristic
62#10622852C2211yescharacteristic
63#10622852C2212yescomplemented
64#10622852C2212yescomplemented
65#10622852C2212yescomplemented
66#10622852C2212yescomplemented
67#10622851C2212yes—
68#10622851C2212yescomplemented
69#10622851C2212yescomplemented
70#10622851C2212yescomplemented
71#10622851C2212yescomplemented
72#10622846C2212yescomplemented
73#10622846C2212yescomplemented
74#10622841C2212yescomplemented
75#10622840C2212yescomplemented
76#10622838C2212yescomplemented
77#10622831C2212yescomplemented
78#10622830C2212yescomplemented
79#10622828C2212yescomplemented
80#10622820C2212yescomplemented
81C2×C22⋊(C11⋊C8)C2212yescomplemented
82#10622703C2211yescharacteristic, complemented
83#10622703C2211yescharacteristic, complemented
84#10622698C2211yescharacteristic, complemented
85#10622694C2211yescharacteristic, complemented
86#10622688C2211yescharacteristic, complemented
87#10622688C2211yescharacteristic, complemented
88#10622686C2211yescharacteristic, complemented
89#10622683C2211yescharacteristic, complemented
90#10622673C2212yescomplemented
91#10622670C2212yescomplemented
92#10622670C2212yescomplemented
93#10622668C2212yescomplemented
94#10622665C2212yescomplemented
95#10622664C2212yescomplemented
96#10622662C2212yescomplemented
97#10622661C2212yescomplemented
98#10622660C2212yescomplemented
99#10622660C2212yescomplemented
100#10622658C2212yescomplemented
101#10622658C2212yescomplemented
102#10622655C2212yescomplemented
103#10622654C2212yescomplemented
104#10622652C2212yescomplemented
105#10622651C2212yescomplemented
106#10622650C2212yescomplemented
107#10622650C2212yescomplemented
108#10622648C2212yescomplemented
109#10622648C2212yescomplemented
110#10622644C2211yescharacteristic, complemented
111C4×#4326C2211yescharacteristic, complemented
112C4×#4326C2211yescharacteristic, complemented
113#10622640C2211yescharacteristic, complemented
114#10622639C2212yescomplemented
115#10622633C2211yescharacteristic, complemented
116#10622633C2211yescharacteristic, complemented
117#10622632C2211yescharacteristic, complemented
118C4×#4324C2211yescharacteristic, complemented
119C4×#4324C2211yescharacteristic, complemented
120#10622628C2211yescharacteristic, complemented
121#10622627C2212yescomplemented
122#10622625C2211yescharacteristic
123#10622625C2211yescharacteristic
124#10622624C2212yescomplemented
125#10622624C2212yescomplemented
126D4×C11⋊C8C2211yescharacteristic, complemented
127D4×C11⋊C8C2211yescharacteristic, complemented
128#10622620C2211yescharacteristic, complemented
129#10622620C2211yescharacteristic, complemented
130#10622616C2212yescomplemented
131#10622609C2211yescharacteristic, complemented
132#10622609C2211yescharacteristic, complemented
133#10622539C2211yescharacteristic, complemented
134#10622538C2211yescharacteristic, complemented
135C2×C11×#41—22no—
136C2×C11×#41—22no—
137C2×C11×#41—44no—
138C2×C11×#41—44no—
139C2×C11×#41C2311yescharacteristic
140C2×C11×#41C2312yes—
141C2×C11×#41C2312yes—
142C2×C11×#41C2312yes—
143C22×Q8×C11C2312yes—
144C22×D4×C11—22no—
145C22×D4×C11—21no—
146C22×D4×C11D411yescharacteristic
147C22×D4×C11C2312yes—
148C23×C4×C11—22no—
149C23×C4×C11C2312yes—
150C2×#4339—21no—
151C2×#4339C2312yes—
152C2×#4339C2312yes—
153C11×C4⋊Q8—21no—
154C11×C4⋊Q8C2311yescharacteristic
155C11×#127—21no—
156C11×#127C2311yescharacteristic
157C11×#124—22no—
158C11×#124C2312yes—
159C11×#123—22no—
160C11×#123—22no—
161C11×#123—22no—
162C11×C22⋊Q8—22no—
163C11×C22⋊Q8—22no—
164C11×C22⋊Q8C2312yes—
165C11×C22⋊Q8C2312yes—
166C11×#121—22no—
167C11×#121—21no—
168C11×#121—21no—
169C11×#121—21no—
170C11×#121—21no—
171C11×#121—22no—
172C11×#121—22no—
173C11×#121C2312yes—
174C11×#121C2312yes—
175C11×#120—22no—
176C11×#120—22no—
177C11×#120—22no—
178C4×Q8×C11C2311yescharacteristic
179C4×Q8×C11C2311yescharacteristic
180C4×D4×C11—21no—
181C4×D4×C11—22no—
182C4×D4×C11—21no—
183C4×D4×C11—21no—
184C4×D4×C11—22no—
185C4×D4×C11—21no—
186C4×D4×C11—22no—
187C4×D4×C11—21no—
188C4×D4×C11—21no—
189C4×D4×C11D412yes—
190C4×D4×C11D411yescharacteristic
191C4×D4×C11D411yescharacteristic
192C4×D4×C11C2311yescharacteristic
193C4×D4×C11C2311yescharacteristic
194C4×D4×C11C2311yescharacteristic
195C4×D4×C11C2311yescharacteristic
196C4×D4×C11C2312yes—
197C11×#117—21no—
198C11×#117C2311yescharacteristic
199C2×C11×C4⋊C4—21no—
200C2×C11×C4⋊C4D411yescharacteristic
201C2×C11×C22⋊C4—22no—
202C2×C11×C22⋊C4D412yes—
203C2×C42×C11—21no—
204C2×C42×C11C2311yescharacteristic
205#67006—22no—
206#67006—22no—
207#67003—44no—
208#67003—44no—
209C2×#4326C2311yescharacteristic
210C2×#4326C2311yescharacteristic
211C2×#4326C2312yes—
212C2×#4326C2312yes—
213#66995—44no—
214C2×#4325C2312yes—
215C2×#4325C2312yes—
216C2×#4325C2312yes—
217#66993—21no—
218#66993—21no—
219#66991—22no—
220#66991—22no—
221#66989—21no—
222#66989—21no—
223C2×#4324C2311yescharacteristic
224C2×#4324C2311yescharacteristic
225C2×#4324C2312yes—
226C2×#4324C2312yes—
227#66985—44no—
228C2×#4323C2312yes—
229C2×#4323C2312yes—
230C2×#4323C2312yes—
231#66983—21no—
232#66983C2312yes—
233#66983C2312yes—
234#66983C2312yes—
235#66982—22no—
236#66982—22no—
237C4×C22⋊D11—22no—
238C4×C22⋊D11—22no—
239C4×C22⋊D11—22no—
240C4×C22⋊D11—22no—
241#66979—21no—
242#66979C2312yes—
243#66979C2312yes—
244#66977—21no—
245#66977C2311yescharacteristic
246#66977C2311yescharacteristic
247#66977C2312yes—
248#66977C2312yes—
249C2×#4318C2312yes—
250C2×#4318C2312yes—
251C22×C11⋊C8C2312yes—
252C22×C11⋊C8C2312yes—
253#66946—21no—
254#66946—21no—
255#66945—22no—
256C4⋊C4×D11—22no—
257#66940—21no—
258#66940—21no—
259#66938—22no—
260#66938—22no—
261#66937—22no—
262#66937—22no—
263#66936—22no—
264#66936—22no—
265#66932—22no—
266#66932—22no—
267#66928—21no—
268#66927C2311yescharacteristic
269C4×D44—21no—
270C4×D44C2312yes—
271#66923—21no—
272#66922C2311yescharacteristic
273#66922C2311yescharacteristic
274#66922C2311yescharacteristic
275C4×Dic22—21no—
276C4×Dic22C2311yescharacteristic
277C4×Dic22C2311yescharacteristic
278#66899C2311yescharacteristic
279#66899C2312yes—
280#66899C2312yes—
281#66899C2312yes—
282#66899C2311yescharacteristic
283#66899C2312yes—
284#66899C2312yes—
285#66896C2311yescharacteristic
286#66896C2312yes—
287#66896C2312yes—
288#66896C2312yes—
289#66896C2311yescharacteristic
290#66896C2312yes—
291#66896C2312yes—
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—
299#66874C2311yescharacteristic
300#66874C2311yescharacteristic
301#66874C2311yescharacteristic
302#66874C2311yescharacteristic
303#66873C2312yes—
304#66873C2312yes—
305#66872C2311yescharacteristic
306#66872C2311yescharacteristic
307#66872C2312yes—
308#66871C2311yescharacteristic
309#66871C2311yescharacteristic
310#66871C2312yes—
311C4⋊(C11⋊C8)C2311yescharacteristic
312C4⋊(C11⋊C8)C2311yescharacteristic
313C4⋊(C11⋊C8)C2311yescharacteristic
314C4⋊(C11⋊C8)C2311yescharacteristic
315#66867C2312yes—
316C4×C11⋊C8C2311yescharacteristic
317C4×C11⋊C8C2311yescharacteristic
318#61608—111nomaximal, Sylow
319C24×C11—22no—
320C24×C11C2×D412yes—
321C11×#41—22no—
322C11×#41—22no—
323C11×#41—24no—
324C11×#41—24no—
325C11×#41—42no—
326C11×#41—42no—
327C11×#41—42no—
328C11×#41—42no—
329C11×#41—48no—
330C11×#41—48no—
331C2×Q8×C11—22no—
332C2×Q8×C11—24no—
333C2×Q8×C11—42no—
334C2×Q8×C11C2412yes—
335C2×Q8×C11C2411yescharacteristic
336C2×D4×C11—21no—
337C2×D4×C11—24no—
338C2×D4×C11—22no—
339C2×D4×C11—22no—
340C2×D4×C11—22no—
341C2×D4×C11—22no—
342C2×D4×C11—22no—
343C2×D4×C11—21no—
344C2×D4×C11—22no—
345C2×D4×C11—21no—
346C2×D4×C11—42no—
347C2×D4×C11—42no—
348C2×D4×C11—44no—
349C2×D4×C11—48no—
350C2×D4×C11C2×D411yescharacteristic
351C2×D4×C11C2×D411yescharacteristic
352C2×D4×C11C2×D412yes—
353C2×D4×C11C2412yes—
354C2×D4×C11C2411yescharacteristic
355C22×C4×C11—21no—
356C22×C4×C11—22no—
357C22×C4×C11—21no—
358C22×C4×C11—22no—
359C22×C4×C11—22no—
360C22×C4×C11—22no—
361C22×C4×C11—21no—
362C22×C4×C11—42no—
363C22×C4×C11—42no—
364C22×C4×C11—48no—
365C22×C4×C11C2×D411yescharacteristic
366C22×C4×C11C2×D411yescharacteristic
367C22×C4×C11C2×D412yes—
368C22×C4×C11C2×D412yes—
369C22×C4×C11C2×D412yes—
370C22×C4×C11C2411yescharacteristic
371C22×C4×C11C2412yes—
372C22×C4×C11C2412yes—
373C2×C22⋊D11—22no—
374C2×C22⋊D11—22no—
375C2×C22⋊D11—22no—
376C2×C22⋊D11—22no—
377C2×C22⋊D11—22no—
378#4339—42no—
379#4339—42no—
380#4339—42no—
381#4339—42no—
382#4339—44no—
383C2×D44—21no—
384C2×D44—21no—
385C2×D44C2412yes—
386C2×C4×D11—22no—
387C2×C4×D11—22no—
388C2×C4×D11—22no—
389C2×Dic22—21no—
390C2×Dic22—21no—
391C2×Dic22C2411yescharacteristic
392C2×Dic22C2411yescharacteristic
393C11×C4⋊C4—21no—
394C11×C4⋊C4—22no—
395C11×C4⋊C4—21no—
396C11×C4⋊C4—21no—
397C11×C4⋊C4—21no—
398C11×C4⋊C4—22no—
399C11×C4⋊C4C2×D411yescharacteristic
400C11×C4⋊C4C2×D411yescharacteristic
401C11×C4⋊C4C2×D412yes—
402C11×C4⋊C4C2411yescharacteristic
403C11×C4⋊C4C2411yescharacteristic
404C11×C22⋊C4—22no—
405C11×C22⋊C4—21no—
406C11×C22⋊C4—22no—
407C11×C22⋊C4—22no—
408C11×C22⋊C4—22no—
409C11×C22⋊C4—21no—
410C11×C22⋊C4—21no—
411C11×C22⋊C4—22no—
412C11×C22⋊C4—22no—
413C11×C22⋊C4C2×D412yes—
414C11×C22⋊C4C2×D412yes—
415C11×C22⋊C4C2×D412yes—
416C11×C22⋊C4C2×D412yes—
417C42×C11—21no—
418C42×C11—21no—
419C42×C11—21no—
420C42×C11C2×D411yescharacteristic
421C42×C11C2×D411yescharacteristic
422C42×C11C2411yescharacteristic
423C42×C11C2411yescharacteristic
424C22⋊Dic11—22no—
425C22⋊Dic11—22no—
426C22⋊Dic11—22no—
427C22⋊Dic11—22no—
428C22⋊Dic11—21no—
429C22⋊Dic11—21no—
430#4326—22no—
431#4326—22no—
432#4326—42no—
433#4326—42no—
434#4325—24no—
435#4325—42no—
436#4325—42no—
437#4324—22no—
438#4324—22no—
439#4324—42no—
440#4324—42no—
441#4323—24no—
442#4323—42no—
443#4323—42no—
444(C2×D11)⋊C4—22no—
445(C2×D11)⋊C4—22no—
446(C2×D11)⋊C4—22no—
447(C2×D11)⋊C4—22no—
448C4⋊Dic11—21no—
449C4⋊Dic11—21no—
450C4⋊Dic11—21no—
451C4⋊Dic11—21no—
452C4⋊Dic11C2411yescharacteristic
453C4⋊Dic11C2411yescharacteristic
454C4⋊Dic11C2412yes—
455Dic11⋊C4—21no—
456Dic11⋊C4—21no—
457Dic11⋊C4—21no—
458Dic11⋊C4—21no—
459Dic11⋊C4—22no—
460Dic11⋊C4—22no—
461C4×Dic11—21no—
462C4×Dic11—21no—
463C4×Dic11—22no—
464C4×Dic11—22no—
465#4318—42no—
466#4318—42no—
467C2×C11⋊C8—42no—
468C2×C11⋊C8—42no—
469C2×C11⋊C8C2411yescharacteristic
470C2×C11⋊C8C2411yescharacteristic
471C2×C11⋊C8C2411yescharacteristic
472C2×C11⋊C8C2411yescharacteristic
473C2×C11⋊C8C2412yes—
474C2×C11⋊C8C2412yes—
475#3506—111no—
476D4×#41D1111yescharacteristic, complemented
477#3328—111no—
478#3324—111no—
479#3321—112no—
480#3319—112no—
481#3304—111no—
482#3302—111no—
483#3287—111no—
484#3284—111no—
485#3278—111no—
486#3274—111no—
487#3269—112no—
488#3267—112no—
489#3216—111no—
490#3207—111no—
491#3197—112no—
492#3191—112no—
493#3115—111no—
494#3107—111no—
495#3005—112no—
496#3002—112no—
497#2974—111no—
498C23×C11—21no—
499C23×C11—22no—
500C23×C11—42no—
501C23×C11—42no—
502C23×C11—42no—
503C23×C11—44no—
504C23×C11—44no—
505C23×C11—82no—
506C23×C11C22×D412yes—
507C23×C11C22×D412yes—
508C23×C11C22×D411yescharacteristic
509C22×D11—22no—
510Q8×C11—21no—
511Q8×C11—22no—
512Q8×C11—22no—
513Q8×C11—44no—
514Q8×C11H(5,𝔽2)12yes—
515D4×C11—24no—
516D4×C11—22no—
517D4×C11—22no—
518D4×C11—21no—
519D4×C11—22no—
520D4×C11—22no—
521D4×C11—42no—
522D4×C11—44no—
523D4×C11—44no—
524D4×C11—44no—
525D4×C11—44no—
526D4×C11—44no—
527D4×C11—42no—
528D4×C11—81no—
529D4×C11—82no—
530D4×C11H(5,𝔽2)12yes—
531C2×C4×C11—24no—
532C2×C4×C11—21no—
533C2×C4×C11—22no—
534C2×C4×C11—22no—
535C2×C4×C11—22no—
536C2×C4×C11—22no—
537C2×C4×C11—22no—
538C2×C4×C11—21no—
539C2×C4×C11—21no—
540C2×C4×C11—21no—
541C2×C4×C11—21no—
542C2×C4×C11—22no—
543C2×C4×C11—42no—
544C2×C4×C11—42no—
545C2×C4×C11—42no—
546C2×C4×C11—41no—
547C2×C4×C11—44no—
548C2×C4×C11—44no—
549C2×C4×C11—44no—
550C2×C4×C11—44no—
551C2×C4×C11—42no—
552C2×C4×C11—81no—
553C2×C4×C11C22×D412yes—
554C2×C4×C11C22×D412yes—
555C2×C4×C11C22×D411yescharacteristic
556C2×C4×C11C22×D411yescharacteristic
557C2×C4×C11C22×D411yescharacteristic
558C2×C4×C11C22×D411yescharacteristic
559C2×C4×C11C22×D411yescharacteristic
560C2×C4×C11C2511yescharacteristic
561C22⋊D11—44no—
562C22⋊D11—82no—
563C22⋊D11—82no—
564C22⋊D11—82no—
565C22⋊D11—82no—
566C2×Dic11—21no—
567C2×Dic11—21no—
568C2×Dic11—22no—
569C2×Dic11—21no—
570C2×Dic11—21no—
571D44—22no—
572D44—22no—
573D44—42no—
574D44—81no—
575C4×D11—44no—
576C4×D11—82no—
577C4×D11—82no—
578Dic22—21no—
579Dic22—21no—
580Dic22—21no—
581Dic22—21no—
582Dic22—42no—
583Dic22—81no—
584C11⋊C8—21no—
585C11⋊C8—21no—
586C11⋊C8—22no—
587C11⋊C8—22no—
588C11⋊C8—21no—
589C11⋊C8—21no—
590C22×#41C2×D1112yes—
591C2×#137—112no—
592C2×AGL(1,ℤ/8)—112no—
593C2×#135—112no—
594C2×#135—112no—
595#559—221no—
596#559—221no—
597#556—111no—
598#556—111no—
599#555—112no—
600#553—222no—
601#550—111no—
602#550—111no—
603#550C2×D1111yescharacteristic
604D4×Q8C2×D1111yescharacteristic
605#548C2×D1112yes—
606#547—21no—
607#547—112no—
608#547C2×D1111yescharacteristic
609#546—22no—
610#546C2×D1112yes—
611D42—21no—
612D42C2×D1111yescharacteristic
613#538—222no—
614#535—221no—
615#533—111no—
616#532—21no—
617#532—111no—
618#532C2×D1111yescharacteristic
619#525—22no—
620#525—112no—
621#525—112no—
622#525C2×D1112yes—
623#520—221no—
624C4×#41C2×D1111yescharacteristic
625C2×C4×D4—21no—
626C2×C4×D4C2×D1111yescharacteristic
627#497—112no—
628#493—111no—
629#492—111no—
630#489—112no—
631#487—111no—
632#486—111no—
633#485—112no—
634#485—112no—
635#485—111no—
636#485—111no—
637#482—112no—
638#482—112no—
639#482—112no—
640#475—111no—
641#475—111no—
642#474—111no—
643#474—111no—
644#470—112no—
645#469—112no—
646#468—112no—
647#468—112no—
648#467—112no—
649#466—112no—
650#465—112no—
651#465—112no—
652#463—112no—
653#463—112no—
654#462—111no—
655#462—111no—
656#462—111no—
657#461—111no—
658#460—111no—
659#460—111no—
660#460—111no—
661#459—111no—
662#452—111no—
663#452—111no—
664#452—112no—
665#452—112no—
666#452—112no—
667#452—112no—
668#452—112no—
669#452—112no—
670#451—112no—
671#450—112no—
672#449—112no—
673#449—112no—
674#449—112no—
675#449—112no—
676#449—112no—
677#449—112no—
678#449—112no—
679#448—112no—
680#447—112no—
681#442—112no—
682#440—112no—
683C4×Q16—111no—
684C4×Q16—111no—
685C4×SD16—111no—
686C4×SD16—111no—
687#436—111no—
688#436—111no—
689#435—112no—
690#435—112no—
691C8×D4—111no—
692C8×D4—111no—
693#432—111no—
694#431—111no—
695#419—112no—
696#418—112no—
697#416—112no—
698#416—112no—
699#407—112no—
700C2×C22⋊C8—112no—
701C22×C11—21no—
702C22×C11—22no—
703C22×C11—22no—
704C22×C11—22no—
705C22×C11—21no—
706C22×C11—22no—
707C22×C11—22no—
708C22×C11—21no—
709C22×C11—22no—
710C22×C11—22no—
711C22×C11—41no—
712C22×C11—41no—
713C22×C11—42no—
714C22×C11—42no—
715C22×C11—42no—
716C22×C11—84no—
717C22×C11—88no—
718C22×C11C23×D411yescharacteristic
719C2×D11—42no—
720C2×D11—42no—
721C2×D11—42no—
722C4×C11—21no—
723C4×C11—21no—
724C4×C11—21no—
725C4×C11—22no—
726C4×C11—22no—
727C4×C11—22no—
728C4×C11—21no—
729C4×C11—41no—
730C4×C11—42no—
731C4×C11—41no—
732C4×C11#57512yes—
733C4×C11C2×H(5,𝔽2)11yescharacteristic
734C4×C11C2×H(5,𝔽2)11yescharacteristic
735Dic11—41no—
736Dic11—41no—
737Dic11—41no—
738Dic11—41no—
739Dic11—42no—
740C2×#41—22no—
741C2×#41—22no—
742C2×#41—44no—
743C2×#41—44no—
744C2×#41—112no—
745C2×#41—112no—
746C2×#41—221no—
747C2×#41C22×D1111yescharacteristic
748C2×#41C22×D1112yes—
749C2×#41C22×D1112yes—
750C2×#41C22×D1112yes—
751C22×Q8C22×D1112yes—
752C22×D4—22no—
753C22×D4—21no—
754C22×D4C22⋊D1111yescharacteristic
755C22×D4C22×D1112yes—
756C23×C4—22no—
757C23×C4C22×D1112yes—
758#137—444no—
759AGL(1,ℤ/8)—444no—
760#135—444no—
761#135—444no—
762C2×Q16—111no—
763C2×Q16—111no—
764C2×Q16—112no—
765C2×Q16—112no—
766C2×SD16—112no—
767C2×SD16—111no—
768C2×SD16—111no—
769C2×SD16—112no—
770C2×SD16—112no—
771C2×SD16—112no—
772C2×SD16—112no—
773C2×D8—112no—
774C2×D8—112no—
775C2×D8—112no—
776C2×M16—112no—
777C2×M16—112no—
778C22×C8—112no—
779C22×C8—112no—
780C4⋊Q8—21no—
781C4⋊Q8—111no—
782C4⋊Q8—111no—
783C4⋊Q8—111no—
784C4⋊Q8C22×D1111yescharacteristic
785#127—21no—
786#127—111no—
787#127—221no—
788#127—221no—
789#127C22×D1111yescharacteristic
790#126—222no—
791#126—222no—
792#125—221no—
793#124—22no—
794#124—221no—
795#124—221no—
796#124—222no—
797#124—222no—
798#124—221no—
799#124C22×D1112yes—
800#123—22no—
801#123—22no—
802#123—22no—
803#123—222no—
804#123—222no—
805#123—222no—
806#123—222no—
807C22⋊Q8—22no—
808C22⋊Q8—22no—
809C22⋊Q8—111no—
810C22⋊Q8—111no—
811C22⋊Q8—112no—
812C22⋊Q8—112no—
813C22⋊Q8—221no—
814C22⋊Q8C22×D1112yes—
815C22⋊Q8C22×D1112yes—
816#121—22no—
817#121—21no—
818#121—21no—
819#121—21no—
820#121—21no—
821#121—22no—
822#121—22no—
823#121—112no—
824#121—112no—
825#121—112no—
826#121—222no—
827#121—222no—
828#121—221no—
829#121—222no—
830#121—222no—
831#121C22×D1112yes—
832#121C22×D1112yes—
833#120—22no—
834#120—22no—
835#120—22no—
836#120—222no—
837#120—222no—
838C4×Q8—111no—
839C4×Q8—111no—
840C4×Q8—221no—
841C4×Q8—221no—
842C4×Q8—221no—
843C4×Q8C22×D1111yescharacteristic
844C4×Q8C22×D1111yescharacteristic
845C4×D4—21no—
846C4×D4—22no—
847C4×D4—21no—
848C4×D4—21no—
849C4×D4—22no—
850C4×D4—21no—
851C4×D4—22no—
852C4×D4—21no—
853C4×D4—21no—
854C4×D4—112no—
855C4×D4—222no—
856C4×D4—222no—
857C4×D4—222no—
858C4×D4—222no—
859C4×D4—221no—
860C4×D4—221no—
861C4×D4—221no—
862C4×D4C22⋊D1111yescharacteristic
863C4×D4C22⋊D1112yes—
864C4×D4C22⋊D1111yescharacteristic
865C4×D4C22×D1111yescharacteristic
866C4×D4C22×D1111yescharacteristic
867C4×D4C22×D1111yescharacteristic
868C4×D4C22×D1112yes—
869C4×D4C22×D1111yescharacteristic
870#117—21no—
871#117—112no—
872#117—112no—
873#117—221no—
874#117—222no—
875#117C22×D1111yescharacteristic
876C2×C4⋊C4—21no—
877C2×C4⋊C4—222no—
878C2×C4⋊C4C22⋊D1111yescharacteristic
879C2×C22⋊C4—22no—
880C2×C22⋊C4C22⋊D1112yes—
881C2×C42—21no—
882C2×C42C22×D1111yescharacteristic
883#107—111no—
884#107—111no—
885#107—112no—
886#106—111no—
887#106—111no—
888#106—112no—
889C4⋊C8—111no—
890C4⋊C8—111no—
891C4⋊C8—111no—
892C4⋊C8—111no—
893#103—111no—
894#103—112no—
895#103—112no—
896#103—112no—
897#103—111no—
898#103—112no—
899#103—112no—
900#103—111no—
901#103—111no—
902#103—111no—
903#103—111no—
904#102—111no—
905#102—112no—
906#102—112no—
907#102—112no—
908#102—111no—
909#102—112no—
910#102—112no—
911#102—112no—
912#102—112no—
913C22⋊C8—111no—
914C22⋊C8—112no—
915C22⋊C8—112no—
916C22⋊C8—112no—
917C22⋊C8—111no—
918C22⋊C8—112no—
919C22⋊C8—112no—
920#97—112no—
921C4×C8—111no—
922C4×C8—111no—
923C2×C11—42no—
924C2×C11—41no—
925C2×C11—42no—
926C2×C11—42no—
927C2×C11—82no—
928C2×C11#348411yescharacteristic
929C2×C11C2×#57511yescharacteristic
930C2×C11#358411yescharacteristic
931D11—82no—
932C24—22no—
933C24C2×C22⋊D1112yes—
934#41—22no—
935#41—22no—
936#41—24no—
937#41—24no—
938#41—42no—
939#41—42no—
940#41—42no—
941#41—42no—
942#41—48no—
943#41—48no—
944#41—444no—
945#41—442no—
946#41—442no—
947#41—442no—
948#41—442no—
949C2×Q8—22no—
950C2×Q8—24no—
951C2×Q8—42no—
952C2×Q8—111no—
953C2×Q8—111no—
954C2×Q8—221no—
955C2×Q8—221no—
956C2×Q8C23×D1112yes—
957C2×Q8C23×D1111yescharacteristic
958C2×D4—21no—
959C2×D4—24no—
960C2×D4—22no—
961C2×D4—22no—
962C2×D4—22no—
963C2×D4—22no—
964C2×D4—22no—
965C2×D4—21no—
966C2×D4—22no—
967C2×D4—21no—
968C2×D4—42no—
969C2×D4—42no—
970C2×D4—48no—
971C2×D4—44no—
972C2×D4—112no—
973C2×D4—222no—
974C2×D4—222no—
975C2×D4—222no—
976C2×D4—222no—
977C2×D4—222no—
978C2×D4—221no—
979C2×D4—221no—
980C2×D4C2×C22⋊D1111yescharacteristic
981C2×D4C2×C22⋊D1111yescharacteristic
982C2×D4C2×C22⋊D1112yes—
983C2×D4C23×D1112yes—
984C2×D4C23×D1111yescharacteristic
985C22×C4—21no—
986C22×C4—22no—
987C22×C4—21no—
988C22×C4—22no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—21no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—48no—
995C22×C4—222no—
996C22×C4—222no—
997C22×C4—222no—
998C22×C4C2×C22⋊D1111yescharacteristic
999C22×C4C2×C22⋊D1111yescharacteristic
1000C22×C4C2×C22⋊D1112yes—
1001C22×C4C2×C22⋊D1112yes—
1002C22×C4C2×C22⋊D1112yes—
1003C22×C4C23×D1111yescharacteristic
1004C22×C4C23×D1112yes—
1005C22×C4C23×D1112yes—
1006Q16—222no—
1007Q16—222no—
1008Q16—442no—
1009Q16—442no—
1010SD16—224no—
1011SD16—222no—
1012SD16—222no—
1013SD16—442no—
1014SD16—442no—
1015SD16—442no—
1016SD16—442no—
1017D8—224no—
1018D8—442no—
1019D8—442no—
1020M16—442no—
1021M16—442no—
1022C2×C8—111no—
1023C2×C8—111no—
1024C2×C8—111no—
1025C2×C8—111no—
1026C2×C8—112no—
1027C2×C8—112no—
1028C2×C8—442no—
1029C2×C8—442no—
1030C4⋊C4—21no—
1031C4⋊C4—22no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—22no—
1036C4⋊C4—112no—
1037C4⋊C4—111no—
1038C4⋊C4—111no—
1039C4⋊C4—221no—
1040C4⋊C4—222no—
1041C4⋊C4—222no—
1042C4⋊C4—221no—
1043C4⋊C4—221no—
1044C4⋊C4—221no—
1045C4⋊C4—221no—
1046C4⋊C4—221no—
1047C4⋊C4—221no—
1048C4⋊C4—221no—
1049C4⋊C4C2×C22⋊D1111yescharacteristic
1050C4⋊C4C2×C22⋊D1112yes—
1051C4⋊C4C2×C22⋊D1111yescharacteristic
1052C4⋊C4C23×D1111yescharacteristic
1053C4⋊C4C23×D1111yescharacteristic
1054C22⋊C4—22no—
1055C22⋊C4—21no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—21no—
1060C22⋊C4—21no—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—222no—
1064C22⋊C4—222no—
1065C22⋊C4—221no—
1066C22⋊C4—221no—
1067C22⋊C4—222no—
1068C22⋊C4—222no—
1069C22⋊C4—222no—
1070C22⋊C4—222no—
1071C22⋊C4—222no—
1072C22⋊C4—222no—
1073C22⋊C4C2×C22⋊D1112yes—
1074C22⋊C4C2×C22⋊D1112yes—
1075C22⋊C4C2×C22⋊D1112yes—
1076C22⋊C4C2×C22⋊D1112yes—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—222no—
1081C42—222no—
1082C42—221no—
1083C42—221no—
1084C42C2×C22⋊D1111yescharacteristic
1085C42C2×C22⋊D1111yescharacteristic
1086C42C23×D1111yescharacteristic
1087C42C23×D1111yescharacteristic
1088C11#6160811yescharacteristic, complemented, Sylow
1089C23—21no—
1090C23—22no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—44no—
1095C23—44no—
1096C23—82no—
1097C23—222no—
1098C23C22×C22⋊D1112yes—
1099C23C22×C22⋊D1112yes—
1100C23C22×C22⋊D1111yescharacteristic
1101Q8—21no—
1102Q8—22no—
1103Q8—22no—
1104Q8—44no—
1105Q8—221no—
1106Q8—221no—
1107Q8—221no—
1108Q8—221no—
1109Q8—442no—
1110Q8—881no—
1111Q8#6703712yes—
1112D4—24no—
1113D4—22no—
1114D4—22no—
1115D4—21no—
1116D4—22no—
1117D4—22no—
1118D4—42no—
1119D4—44no—
1120D4—44no—
1121D4—44no—
1122D4—44no—
1123D4—44no—
1124D4—42no—
1125D4—81no—
1126D4—82no—
1127D4—222no—
1128D4—222no—
1129D4—444no—
1130D4—442no—
1131D4—881no—
1132D4—882no—
1133D4—882no—
1134D4—882no—
1135D4—882no—
1136D4#6703712yes—
1137C2×C4—24no—
1138C2×C4—21no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—22no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—41no—
1153C2×C4—44no—
1154C2×C4—44no—
1155C2×C4—44no—
1156C2×C4—44no—
1157C2×C4—42no—
1158C2×C4—81no—
1159C2×C4—221no—
1160C2×C4—221no—
1161C2×C4—222no—
1162C2×C4—221no—
1163C2×C4—221no—
1164C2×C4—444no—
1165C2×C4—882no—
1166C2×C4—882no—
1167C2×C4C22×C22⋊D1111yescharacteristic
1168C2×C4C22×C22⋊D1111yescharacteristic
1169C2×C4C22×C22⋊D1112yes—
1170C2×C4C22×C22⋊D1112yes—
1171C2×C4C22×C22⋊D1111yescharacteristic
1172C2×C4C22×C22⋊D1111yescharacteristic
1173C2×C4C22×C22⋊D1111yescharacteristic
1174C2×C4C24×D1111yescharacteristic
1175C8—221no—
1176C8—221no—
1177C8—222no—
1178C8—222no—
1179C8—221no—
1180C8—221no—
1181C22—22no—
1182C22—21no—
1183C22—22no—
1184C22—22no—
1185C22—21no—
1186C22—22no—
1187C22—22no—
1188C22—21no—
1189C22—22no—
1190C22—22no—
1191C22—41no—
1192C22—41no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—84no—
1197C22—88no—
1198C22—442no—
1199C22—442no—
1200C22—442no—
1201C22C23×C22⋊D1111yescharacteristic
1202C4—21no—
1203C4—22no—
1204C4—22no—
1205C4—22no—
1206C4—21no—
1207C4—21no—
1208C4—21no—
1209C4—42no—
1210C4—41no—
1211C4—41no—
1212C4—441no—
1213C4—441no—
1214C4—442no—
1215C4—441no—
1216C4—441no—
1217C4#1062335312yes—
1218C4C2×#6703711yescharacteristic
1219C4C2×#6703711yescharacteristic
1220C2—42no—
1221C2—41no—
1222C2—42no—
1223C2—42no—
1224C2—82no—
1225C2—882no—
1226C2#1308225111yescharacteristic
1227C2C2×#1062335311yescharacteristic
1228C2#1308338711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingD4×C11×#41C2
socleC22×C11C23×D4
hypercenterD4×#41D11
hypocenterC11#61608
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. #13082468C2semidirect
2. #13080899C2semidirect
3. #13080847C2semidirect
4. #13080802C2semidirect
5. #13080772C2semidirect
6. #13080555C2semidirect
7. #13080533C2semidirect
8. #13080372C2semidirect
9. #13080342C2semidirect
10. #13080278C2semidirect
11. #13080232C2semidirect
12. #13080172C2semidirect
13. #13080137C2semidirect
14. #13079627C2semidirect
15. #13079549C2semidirect
16. #13079453C2semidirect
17. #13079404C2semidirect
18. #13078767C2semidirect
19. #13078687C2semidirect
20. #13077858C2semidirect
21. #13077834C2semidirect
22. #13077651C2semidirect
23. D4×C11×#41C2semidirect
41. C2×#67003C22semidirect
42. C2×#67003C22semidirect
43. C2×#66995C22semidirect
45. C2×#66985C22semidirect
46. #10623322C22semidirect
47. #10623322C22semidirect
48. #10623094C22semidirect
53. #10623084C22semidirect
54. #10623082C22semidirect
56. #10623073C22semidirect
59. #10623008C22semidirect
60. #10623001C22semidirect
63. #10622852C22semidirect
64. #10622852C22semidirect
65. #10622852C22semidirect
66. #10622852C22semidirect
68. #10622851C22semidirect
69. #10622851C22semidirect
70. #10622851C22semidirect
71. #10622851C22semidirect
72. #10622846C22semidirect
73. #10622846C22semidirect
74. #10622841C22semidirect
75. #10622840C22semidirect
76. #10622838C22semidirect
77. #10622831C22semidirect
78. #10622830C22semidirect
79. #10622828C22semidirect
80. #10622820C22semidirect
81. C2×C22⋊(C11⋊C8)C22semidirect
82. #10622703C22semidirect
83. #10622703C22semidirect
84. #10622698C22semidirect
85. #10622694C22semidirect
86. #10622688C22semidirect
87. #10622688C22semidirect
88. #10622686C22semidirect
89. #10622683C22semidirect
90. #10622673C22semidirect
91. #10622670C22semidirect
92. #10622670C22semidirect
93. #10622668C22semidirect
94. #10622665C22semidirect
95. #10622664C22semidirect
96. #10622662C22semidirect
97. #10622661C22semidirect
98. #10622660C22semidirect
99. #10622660C22semidirect
100. #10622658C22semidirect
101. #10622658C22semidirect
102. #10622655C22semidirect
103. #10622654C22semidirect
104. #10622652C22semidirect
105. #10622651C22semidirect
106. #10622650C22semidirect
107. #10622650C22semidirect
108. #10622648C22semidirect
109. #10622648C22semidirect
110. #10622644C22semidirect
111. C4×#4326C22semidirect
112. C4×#4326C22semidirect
113. #10622640C22semidirect
114. #10622639C22semidirect
115. #10622633C22semidirect
116. #10622633C22semidirect
117. #10622632C22semidirect
118. C4×#4324C22semidirect
119. C4×#4324C22semidirect
120. #10622628C22semidirect
121. #10622627C22semidirect
124. #10622624C22semidirect
125. #10622624C22semidirect
126. D4×C11⋊C8C22semidirect
127. D4×C11⋊C8C22semidirect
128. #10622620C22semidirect
129. #10622620C22semidirect
130. #10622616C22semidirect
131. #10622609C22semidirect
132. #10622609C22semidirect
133. #10622539C22semidirect
134. #10622538C22semidirect
476. D4×#41D11semidirect
1088. C11#61608semidirect

Maximal subgroups

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

subgroupindex
#130824682
#130808992
#130808472
#130808022
#130807722
#130805552
#130805332
#130803722
#130803422
#130802782
#130802322
#130801722
#130801372
#130796272
#130795492
#130794532
#130794042
#130787672
#130786872
#130778582
#130778342
#130776512
D4×C11×#412
#6160811