Finite Group Databasebeta

← #15638479

Subgroups — #15638479

Order 2816.

2282 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082450C211yesmaximal, characteristic, complemented
2C2×#10623161C211yesmaximal, characteristic, complemented
3#13080472C214yesmaximal, complemented
4#13080449C214yesmaximal, complemented
5#13080320C214yesmaximal, complemented
6#13080294C214yesmaximal, complemented
7#13079580C212yesmaximal, complemented
8#13079388C211yesmaximal, characteristic, complemented
9#13079380C212yesmaximal, complemented
10#13078660C212yesmaximal, complemented
11#13077833C212yesmaximal, complemented
12C2×#10622344C211yesmaximal, characteristic, complemented
13C2×#10622649C211yesmaximal, characteristic, complemented
14#13077638C211yesmaximal, characteristic, complemented
15C11×#3187C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic, complemented
17C23×D44C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×#67000C2211yescharacteristic, complemented
21#10623337C2212yescomplemented
22#10623335—21no—
23#10623329—21no—
24C22×#4323C2212yescomplemented
25C2×C4×C22⋊D11C2211yescharacteristic
26C2×#66977C2211yescharacteristic
27C2×#66969C2214yescomplemented
28C22×#4314C2212yescomplemented
29#10623161—22no—
30#10623161—22no—
31#10623161C2214yes—
32#10623161C2214yescomplemented
33#10623149C2212yescomplemented
34#10623148—21no—
35#10623137C2212yescomplemented
36#10623133—21no—
37#10623132—22no—
38#10623131C2212yescomplemented
39#10623129C2212yescomplemented
40#10623044C2212yescomplemented
41C2×#66948—21no—
42C2×#66948C2211yescharacteristic, complemented
43C2×#66947—21no—
44C2×#66946C2211yescharacteristic, complemented
45#10623026—22no—
46C2×#66935—21no—
47C2×C22⋊C4×D11—21no—
48C11×#483C2212yescomplemented
49C11×#481C2212yescomplemented
50C11×#465C2214yescomplemented
51C11×#450C2212yescomplemented
52C11×#448C2212yescomplemented
53C2×C11×C22⋊C8C2211yescharacteristic
54#10622841C2212yescomplemented
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56#10622785C2214yescomplemented
57#10622781C2214yescomplemented
58#10622778C2214yescomplemented
59C2×#66885C2212yescomplemented
60C8×C22⋊D11C2214yescomplemented
61#10622664C2214yescomplemented
62#10622663C2212yescomplemented
63#10622657C2212yescomplemented
64#10622649C2212yes—
65#10622649C2212yes—
66#10622649C2214yescomplemented
67#10622583C2212yescomplemented
68C2×#66873C2212yescomplemented
69#10622484C2214yescomplemented
70#10622479C2214yescomplemented
71#10622477C2214yescomplemented
72#10622465C2214yescomplemented
73#10622423C2214yescomplemented
74#10622417C2214yescomplemented
75#10622413C2214yescomplemented
76#10622411C2214yescomplemented
77#10622400C2214yescomplemented
78#10622394C2214yescomplemented
79#10622388C2214yescomplemented
80#10622369C2214yescomplemented
81#10622344C2212yescomplemented
82#10622344C2212yescomplemented
83#10622344C2214yescomplemented
84(C22⋊D11)⋊C8C2214yescomplemented
85D11×C22⋊C8C2212yescomplemented
86#10622331C2212yescomplemented
87C24×D11—21no—
88C22×Q8×C11C2311yescharacteristic
89C22×D4×C11—21no—
90C22×D4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C22×C22⋊D11D411yescharacteristic
93C2×#4343—22no—
94C2×#4343—44no—
95C2×#4343C2314yes—
96C2×#4341C2312yescomplemented
97C22×D44—21no—
98C22×D44—21no—
99C22×D44—21no—
100C22×D44—21no—
101C22×D44—21no—
102C22×D44—44no—
103C22×D44C2311yescharacteristic
104C22×D44C2312yes—
105C22×D44C2312yes—
106C22×D44C2311yescharacteristic
107C22×C4×D11—21no—
108C22×C4×D11—21no—
109C22×C4×D11C2311yescharacteristic
110C22×Dic22C2311yescharacteristic
111C2×C11×SD16C2314yescomplemented
112C22×C8×C11C2312yes—
113C11×C22⋊Q8—21no—
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8C2312yes—
116C11×C22⋊Q8C2312yes—
117C11×#121—21no—
118C11×#121—21no—
119C11×#121C2312yes—
120C11×#121C2312yes—
121C2×C11×C4⋊C4—21no—
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4—21no—
126#67006—22no—
127C2×C22⋊Dic11—21no—
128C2×C22⋊Dic11—22no—
129C2×C22⋊Dic11D411yescharacteristic
130#67000—22no—
131#67000C2314yes—
132C2×#4326C2314yescomplemented
133#66992—22no—
134#66992—22no—
135#66992—22no—
136#66991C2312yescomplemented
137#66990—22no—
138#66989C2312yescomplemented
139#66988—22no—
140#66988—22no—
141D4×Dic11—22no—
142D4×Dic11—22no—
143D4×Dic11—22no—
144D4×Dic11—22no—
145D4×Dic11C2312yescomplemented
146C2×#4323—44no—
147C2×#4323C2314yes—
148C2×#4323C2314yes—
149#66982—22no—
150C4×C22⋊D11D412yes—
151C4×C22⋊D11D412yes—
152C4×C22⋊D11C2312yes—
153C4×C22⋊D11C2312yes—
154C2×(C2×D11)⋊C4—21no—
155C2×(C2×D11)⋊C4—21no—
156C2×(C2×D11)⋊C4—21no—
157C2×(C2×D11)⋊C4—21no—
158C2×(C2×D11)⋊C4D411yescharacteristic
159#66979—22no—
160C2×C4⋊Dic11C2311yescharacteristic
161#66977—21no—
162#66977—21no—
163#66977C2312yes—
164#66977C2312yes—
165C2×Dic11⋊C4—21no—
166C2×Dic11⋊C4D411yescharacteristic
167C2×C4×Dic11C2311yescharacteristic
168C22×C11⋊C8C2312yes—
169#66969—48no—
170C2×#4314—44no—
171C2×#4314C2314yes—
172C2×#4314C2314yes—
173C2×C8×D11C2314yescomplemented
174#66951—22no—
175#66950C2312yescomplemented
176#66948—22no—
177#66948—24no—
178#66948—24no—
179#66948C2314yes—
180#66947—24no—
181#66947—24no—
182#66946—22no—
183#66946C2314yes—
184#66945C2312yescomplemented
185#66943C2312yescomplemented
186#66942—22no—
187#66940C2312yescomplemented
188#66939—22no—
189#66938—22no—
190#66936—22no—
191#66935—24no—
192#66935—24no—
193(C22⋊D11)⋊C4—22no—
194C22⋊C4×D11—24no—
195C22⋊C4×D11—24no—
196#66932—22no—
197#66932—22no—
198#66931—22no—
199#66930—22no—
200C11×#106C2314yescomplemented
201C11×#103C2314yescomplemented
202C11×#102C2314yescomplemented
203C11×C22⋊C8C2312yes—
204C11×C22⋊C8C2312yes—
205#66899C2314yescomplemented
206C22⋊(C11⋊C8)C2312yes—
207C22⋊(C11⋊C8)C2312yes—
208#66885C2314yes—
209#66885C2314yes—
210(C2×D11)⋊C8C2314yescomplemented
211Dic11⋊C8C2314yescomplemented
212C8×Dic11C2314yescomplemented
213#66874C2314yescomplemented
214#66873C2314yes—
215#66873C2314yes—
216#66871C2314yescomplemented
217#61561—111nomaximal, Sylow
218C24×C11—21no—
219C24×C11C2×D411yescharacteristic
220C23×D11—21no—
221C23×D11—21no—
222C23×D11—22no—
223C23×D11—22no—
224C23×D11—44no—
225C23×D11—44no—
226C23×D11—82no—
227C23×D11C2×D411yescharacteristic
228C2×Q8×C11—21no—
229C2×Q8×C11—42no—
230C2×Q8×C11C2412yes—
231C2×D4×C11—22no—
232C2×D4×C11—22no—
233C2×D4×C11—21no—
234C2×D4×C11—42no—
235C2×D4×C11—44no—
236C2×D4×C11C2412yes—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—42no—
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2411yescharacteristic
245C22×C4×C11C2411yescharacteristic
246C22×C4×C11C2411yescharacteristic
247C2×C22⋊D11—24no—
248C2×C22⋊D11—22no—
249C2×C22⋊D11—22no—
250C2×C22⋊D11C2×D412yes—
251C2×C22⋊D11C2×D412yes—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11C2×D411yescharacteristic
257C22×Dic11C2×D411yescharacteristic
258C22×Dic11C2×D411yescharacteristic
259#4343—28no—
260#4343—44no—
261#4343—48no—
262#4341—44no—
263C2×D44—24no—
264C2×D44—24no—
265C2×D44—24no—
266C2×D44—24no—
267C2×D44—24no—
268C2×D44—21no—
269C2×D44—22no—
270C2×D44—22no—
271C2×D44—21no—
272C2×D44—42no—
273C2×D44—42no—
274C2×D44—42no—
275C2×D44—44no—
276C2×D44—44no—
277C2×D44—44no—
278C2×D44—44no—
279C2×D44—82no—
280C2×D44C2412yes—
281C2×D44C2412yes—
282C2×C4×D11—24no—
283C2×C4×D11—24no—
284C2×C4×D11—42no—
285C2×C4×D11—44no—
286C2×C4×D11—82no—
287C2×C4×D11C2×D412yes—
288C2×C4×D11C2412yes—
289C2×Dic22—21no—
290C2×Dic22—42no—
291C2×Dic22C2412yes—
292C11×SD16—44no—
293C2×C8×C11—42no—
294C2×C8×C11C2414yes—
295C11×C4⋊C4—21no—
296C11×C4⋊C4—21no—
297C11×C4⋊C4—22no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4C2412yes—
300C11×C4⋊C4C2412yes—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—22no—
303C11×C22⋊C4—22no—
304C11×C22⋊C4—22no—
305C22⋊Dic11—22no—
306C22⋊Dic11—22no—
307C22⋊Dic11—22no—
308C22⋊Dic11—22no—
309C22⋊Dic11—22no—
310C22⋊Dic11—22no—
311C22⋊Dic11C2×D412yes—
312C22⋊Dic11C2×D412yes—
313#4326—44no—
314#4323—28no—
315#4323—44no—
316(C2×D11)⋊C4—24no—
317(C2×D11)⋊C4—24no—
318(C2×D11)⋊C4—24no—
319(C2×D11)⋊C4—24no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4C2×D412yes—
323(C2×D11)⋊C4C2×D412yes—
324C4⋊Dic11—22no—
325C4⋊Dic11—22no—
326C4⋊Dic11—21no—
327C4⋊Dic11C2412yes—
328Dic11⋊C4—22no—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331Dic11⋊C4—22no—
332Dic11⋊C4C2×D412yes—
333Dic11⋊C4C2×D412yes—
334C4×Dic11—22no—
335C4×Dic11—22no—
336C4×Dic11C2×D412yes—
337C4×Dic11C2412yes—
338C2×C11⋊C8—42no—
339C2×C11⋊C8C2414yes—
340#4314—28no—
341#4314—44no—
342C8×D11—44no—
343#3505—111no—
344C2×#546—111no—
345#3297—114no—
346#3296—114no—
347#3282—114no—
348#3280—114no—
349#3211—112no—
350#3189—111no—
351#3188—112no—
352#3187D1111yescharacteristic, complemented
353#3105—112no—
354#3002—112no—
355C2×#450—111no—
356C2×#447—111no—
357#2972—111no—
358C23×C11—22no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—42no—
362C23×C11—81no—
363C23×C11—81no—
364C23×C11#13514yescomplemented
365C23×C11C22×D411yescharacteristic
366C23×C11C22×D411yescharacteristic
367C23×C11C22×D411yescharacteristic
368C22×D11—24no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—41no—
373C22×D11—41no—
374C22×D11—44no—
375C22×D11—44no—
376C22×D11—42no—
377C22×D11—42no—
378C22×D11—42no—
379C22×D11—42no—
380C22×D11—44no—
381C22×D11—44no—
382C22×D11—42no—
383C22×D11—82no—
384C22×D11—82no—
385C22×D11—816no—
386C22×D11C22×D412yes—
387Q8×C11—24no—
388Q8×C11—42no—
389D4×C11—24no—
390D4×C11—44no—
391D4×C11—44no—
392D4×C11—81no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—42no—
403C2×C4×C11—42no—
404C2×C4×C11—42no—
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C2511yescharacteristic
409C22⋊D11—24no—
410C22⋊D11—24no—
411C22⋊D11—82no—
412C22⋊D11—82no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C2×Dic11—82no—
419C2×Dic11—82no—
420C2×Dic11—81no—
421C2×Dic11—81no—
422C2×Dic11C22×D412yes—
423C2×Dic11C22×D412yes—
424C2×Dic11C22×D412yes—
425D44—24no—
426D44—22no—
427D44—22no—
428D44—22no—
429D44—44no—
430D44—44no—
431D44—42no—
432D44—48no—
433D44—84no—
434D44H(5,𝔽2)14yes—
435C4×D11—24no—
436C4×D11—42no—
437C4×D11—48no—
438C4×D11—84no—
439Dic22—24no—
440Dic22—81no—
441C8×C11—24no—
442C11⋊C8—24no—
443C22×#41—111no—
444C23×D4—111no—
445C2×#135—114no—
446C22×SD16—112no—
447C22×D8—112no—
448#553—112no—
449#553—222no—
450#552—112no—
451#551—222no—
452#548—112no—
453#546—112no—
454#546—114no—
455#546—114no—
456#546—222no—
457#546—222no—
458#539—221no—
459#538—221no—
460#534—221no—
461#529—112no—
462C2×#124—111no—
463#525—112no—
464C2×#123—221no—
465C2×C22⋊Q8—111no—
466C2×C22⋊Q8C2×D1111yescharacteristic
467C2×#121—111no—
468C2×#121—221no—
469C2×#121C2×D1111yescharacteristic
470C2×#120—221no—
471#518—221no—
472C2×C4×D4—111no—
473C2×C4×D4—111no—
474C22×C22⋊C4—221no—
475#495—114no—
476#488—114no—
477#484—112no—
478#484—112no—
479#483C2×D1112yescomplemented
480#482—114no—
481#481C2×D1112yescomplemented
482#478—114no—
483#467—114no—
484#466—114no—
485#465—114no—
486#465C2×D1114yescomplemented
487#464—114no—
488#463—114no—
489#463—114no—
490#452—114no—
491#451—112no—
492#451—112no—
493#450—112no—
494#450—112no—
495#450—114no—
496#450C2×D1112yescomplemented
497#449—114no—
498#449—114no—
499#448C2×D1112yescomplemented
500#447—112no—
501#447—112no—
502#447—114no—
503C4×SD16—114no—
504C4×D8—114no—
505C8×D4—114no—
506C8×D4—114no—
507#431—112no—
508#416—114no—
509C2×#102—112no—
510C2×#102—112no—
511C2×C22⋊C8—111no—
512C2×C22⋊C8—112no—
513C2×C22⋊C8C2×D1111yescharacteristic
514C22×C11—21no—
515C22×C11—21no—
516C22×C11—21no—
517C22×C11—21no—
518C22×C11—21no—
519C22×C11—21no—
520C22×C11—44no—
521C22×C11—42no—
522C22×C11—42no—
523C22×C11—42no—
524C22×C11—162no—
525C22×C11C2×#13512yes—
526C22×C11C2×#13512yes—
527C22×C11C2×#13512yes—
528C22×C11C23×D411yescharacteristic
529C2×D11—22no—
530C2×D11—24no—
531C2×D11—22no—
532C2×D11—22no—
533C2×D11—48no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—82no—
540C2×D11—88no—
541C2×D11—88no—
542C2×D11—84no—
543C4×C11—21no—
544C4×C11—21no—
545C4×C11—21no—
546C4×C11—42no—
547C4×C11—42no—
548C4×C11—42no—
549C4×C11C2×H(5,𝔽2)12yes—
550Dic11—22no—
551Dic11—22no—
552Dic11—22no—
553Dic11—42no—
554Dic11—42no—
555C25—221no—
556C2×#41—114no—
557C2×#41—112no—
558C2×#41—222no—
559C2×#41—444no—
560C22×Q8—111no—
561C22×Q8C22×D1111yescharacteristic
562C22×D4—21no—
563C22×D4—111no—
564C22×D4—111no—
565C22×D4—112no—
566C22×D4—112no—
567C22×D4—111no—
568C22×D4—221no—
569C22×D4—221no—
570C22×D4—221no—
571C22×D4—221no—
572C22×D4—221no—
573C22×D4—444no—
574C22×D4C22×D1111yescharacteristic
575C23×C4—111no—
576C23×C4—221no—
577C23×C4—221no—
578C23×C4C22×D1111yescharacteristic
579#135—448no—
580C2×Q16—114no—
581C2×SD16—114no—
582C2×SD16—114no—
583C2×SD16—444no—
584C2×SD16C22×D1114yescomplemented
585C2×D8—114no—
586C2×D8—114no—
587C2×D8—444no—
588C22×C8—112no—
589C22×C8—114no—
590C22×C8C22×D1112yes—
591#126—222no—
592#126—222no—
593#126—222no—
594#125—112no—
595#125—222no—
596#124—114no—
597#124—112no—
598#124—222no—
599#124—222no—
600#123—222no—
601#123—222no—
602#123—224no—
603#123—224no—
604#123—222no—
605#123—222no—
606#123—222no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—112no—
610C22⋊Q8—112no—
611C22⋊Q8—112no—
612C22⋊Q8—222no—
613C22⋊Q8—221no—
614C22⋊Q8—221no—
615C22⋊Q8C22×D1112yes—
616C22⋊Q8C22×D1112yes—
617#121—21no—
618#121—21no—
619#121—112no—
620#121—114no—
621#121—224no—
622#121—224no—
623#121—222no—
624#121—222no—
625#121—222no—
626#121—222no—
627#121C22×D1112yes—
628#121C22×D1112yes—
629#120—224no—
630#120—224no—
631#120—222no—
632#120—222no—
633C4×Q8—112no—
634C4×D4—112no—
635C4×D4—112no—
636C4×D4—112no—
637C4×D4—112no—
638C4×D4—112no—
639C4×D4—114no—
640C4×D4—222no—
641C4×D4—222no—
642C4×D4—222no—
643C4×D4—222no—
644C4×D4—222no—
645C4×D4—222no—
646#117—112no—
647#117—222no—
648#117—222no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—111no—
652C2×C4⋊C4—221no—
653C2×C4⋊C4C22×D1111yescharacteristic
654C2×C4⋊C4C22×D1111yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—111no—
658C2×C22⋊C4—111no—
659C2×C22⋊C4—224no—
660C2×C22⋊C4—224no—
661C2×C22⋊C4—222no—
662C2×C22⋊C4—221no—
663C2×C22⋊C4—221no—
664C2×C22⋊C4—221no—
665C2×C22⋊C4—221no—
666C2×C22⋊C4—221no—
667C2×C42—111no—
668#107—114no—
669#106C22×D1114yescomplemented
670C4⋊C8—114no—
671#103—114no—
672#103—114no—
673#103C22×D1114yescomplemented
674#102—114no—
675#102—114no—
676#102—114no—
677#102—114no—
678#102C22×D1114yescomplemented
679C22⋊C8—112no—
680C22⋊C8—112no—
681C22⋊C8—114no—
682C22⋊C8C22×D1112yes—
683C22⋊C8C22×D1112yes—
684C4×C8—114no—
685C2×C11—22no—
686C2×C11—22no—
687C2×C11—22no—
688C2×C11—82no—
689C2×C11#348411yescharacteristic
690C2×C11C22×#13511yescharacteristic
691C2×C11#358511yescharacteristic
692D11—42no—
693D11—44no—
694D11—82no—
695C24—21no—
696C24—111no—
697C24—221no—
698C24—221no—
699C24—222no—
700C24—222no—
701C24—444no—
702C24—444no—
703C24—882no—
704C24D4×D1111yescharacteristic
705#41—228no—
706#41—444no—
707#41—444no—
708#41—448no—
709C2×Q8—21no—
710C2×Q8—42no—
711C2×Q8—112no—
712C2×Q8—221no—
713C2×Q8—442no—
714C2×Q8C23×D1112yes—
715C2×D4—22no—
716C2×D4—22no—
717C2×D4—21no—
718C2×D4—42no—
719C2×D4—44no—
720C2×D4—112no—
721C2×D4—112no—
722C2×D4—112no—
723C2×D4—112no—
724C2×D4—224no—
725C2×D4—224no—
726C2×D4—224no—
727C2×D4—224no—
728C2×D4—224no—
729C2×D4—224no—
730C2×D4—222no—
731C2×D4—222no—
732C2×D4—221no—
733C2×D4—222no—
734C2×D4—222no—
735C2×D4—221no—
736C2×D4—442no—
737C2×D4—442no—
738C2×D4—442no—
739C2×D4—444no—
740C2×D4—444no—
741C2×D4—444no—
742C2×D4—444no—
743C2×D4—882no—
744C2×D4C23×D1112yes—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—42no—
749C22×C4—111no—
750C22×C4—111no—
751C22×C4—111no—
752C22×C4—112no—
753C22×C4—112no—
754C22×C4—224no—
755C22×C4—224no—
756C22×C4—222no—
757C22×C4—222no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4—442no—
761C22×C4—444no—
762C22×C4—882no—
763C22×C4D4×D1111yescharacteristic
764C22×C4D4×D1111yescharacteristic
765C22×C4D4×D1111yescharacteristic
766C22×C4C23×D1111yescharacteristic
767C22×C4C23×D1111yescharacteristic
768C22×C4C23×D1111yescharacteristic
769Q16—444no—
770SD16—44no—
771SD16—228no—
772SD16—444no—
773D8—228no—
774D8—444no—
775C2×C8—42no—
776C2×C8—114no—
777C2×C8—444no—
778C2×C8—442no—
779C2×C8C23×D1114yes—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—112no—
785C4⋊C4—112no—
786C4⋊C4—112no—
787C4⋊C4—222no—
788C4⋊C4—222no—
789C4⋊C4—222no—
790C4⋊C4—222no—
791C4⋊C4—221no—
792C4⋊C4—222no—
793C4⋊C4—222no—
794C4⋊C4C23×D1112yes—
795C4⋊C4C23×D1112yes—
796C22⋊C4—22no—
797C22⋊C4—22no—
798C22⋊C4—22no—
799C22⋊C4—22no—
800C22⋊C4—112no—
801C22⋊C4—112no—
802C22⋊C4—112no—
803C22⋊C4—112no—
804C22⋊C4—224no—
805C22⋊C4—224no—
806C22⋊C4—224no—
807C22⋊C4—224no—
808C22⋊C4—222no—
809C22⋊C4—222no—
810C22⋊C4—222no—
811C22⋊C4—222no—
812C22⋊C4—222no—
813C22⋊C4—222no—
814C22⋊C4—222no—
815C22⋊C4—222no—
816C42—112no—
817C42—112no—
818C42—222no—
819C42—222no—
820C11#6156111yescharacteristic, complemented, Sylow
821C23—22no—
822C23—41no—
823C23—41no—
824C23—42no—
825C23—81no—
826C23—81no—
827C23—112no—
828C23—224no—
829C23—222no—
830C23—222no—
831C23—222no—
832C23—441no—
833C23—441no—
834C23—444no—
835C23—444no—
836C23—442no—
837C23—442no—
838C23—442no—
839C23—442no—
840C23—444no—
841C23—444no—
842C23—442no—
843C23—882no—
844C23—882no—
845C23—8816no—
846C23#6696914yescomplemented
847C23C2×D4×D1111yescharacteristic
848C23C2×D4×D1111yescharacteristic
849C23C2×D4×D1111yescharacteristic
850Q8—24no—
851Q8—42no—
852Q8—224no—
853Q8—881no—
854D4—24no—
855D4—44no—
856D4—44no—
857D4—81no—
858D4—114no—
859D4—224no—
860D4—224no—
861D4—224no—
862D4—222no—
863D4—222no—
864D4—222no—
865D4—444no—
866D4—444no—
867D4—442no—
868D4—448no—
869D4—884no—
870D4—882no—
871D4—882no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—112no—
885C2×C4—112no—
886C2×C4—112no—
887C2×C4—222no—
888C2×C4—224no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—442no—
892C2×C4—448no—
893C2×C4—441no—
894C2×C4—441no—
895C2×C4—884no—
896C2×C4—882no—
897C2×C4—882no—
898C2×C4—881no—
899C2×C4—881no—
900C2×C4C2×D4×D1111yescharacteristic
901C2×C4C2×D4×D1111yescharacteristic
902C2×C4C2×D4×D1111yescharacteristic
903C2×C4C24×D1111yescharacteristic
904C8—24no—
905C8—224no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—21no—
912C22—44no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—162no—
917C22—222no—
918C22—222no—
919C22—224no—
920C22—222no—
921C22—448no—
922C22—442no—
923C22—442no—
924C22—442no—
925C22—442no—
926C22—442no—
927C22—882no—
928C22—888no—
929C22—888no—
930C22—884no—
931C22C2×#6696912yes—
932C22C2×#6696912yes—
933C22C2×#6696912yes—
934C22C22×D4×D1111yescharacteristic
935C4—21no—
936C4—21no—
937C4—21no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4—222no—
942C4—222no—
943C4—222no—
944C4—442no—
945C4—442no—
946C4D11×H(5,𝔽2)12yes—
947C2—22no—
948C2—22no—
949C2—22no—
950C2—82no—
951C2—442no—
952C2—444no—
953C2—882no—
954C2#1308224811yescharacteristic
955C2C22×#6696911yescharacteristic
956C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3187C2
socleC22×C11C23×D4
hypercenter#3187D11
hypocenterC11#61561
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3187

Complements

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

NH ≅ G/Ntype
1. #13082450C2semidirect
2. C2×#10623161C2semidirect
3. #13080472C2semidirect
4. #13080449C2semidirect
5. #13080320C2semidirect
6. #13080294C2semidirect
7. #13079580C2semidirect
8. #13079388C2semidirect
9. #13079380C2semidirect
10. #13078660C2semidirect
11. #13077833C2semidirect
12. C2×#10622344C2semidirect
13. C2×#10622649C2semidirect
14. #13077638C2semidirect
15. C11×#3187C2semidirect
16. C22×#4343C22semidirect
20. C2×#67000C22semidirect
21. #10623337C22semidirect
24. C22×#4323C22semidirect
27. C2×#66969C22semidirect
28. C22×#4314C22semidirect
32. #10623161C22semidirect
33. #10623149C22semidirect
35. #10623137C22semidirect
38. #10623131C22semidirect
39. #10623129C22semidirect
40. #10623044C22semidirect
42. C2×#66948C22semidirect
44. C2×#66946C22semidirect
48. C11×#483C22semidirect
49. C11×#481C22semidirect
50. C11×#465C22semidirect
51. C11×#450C22semidirect
52. C11×#448C22semidirect
54. #10622841C22semidirect
56. #10622785C22semidirect
57. #10622781C22semidirect
58. #10622778C22semidirect
59. C2×#66885C22semidirect
60. C8×C22⋊D11C22semidirect
61. #10622664C22semidirect
62. #10622663C22semidirect
63. #10622657C22semidirect
66. #10622649C22semidirect
67. #10622583C22semidirect
68. C2×#66873C22semidirect
69. #10622484C22semidirect
70. #10622479C22semidirect
71. #10622477C22semidirect
72. #10622465C22semidirect
73. #10622423C22semidirect
74. #10622417C22semidirect
75. #10622413C22semidirect
76. #10622411C22semidirect
77. #10622400C22semidirect
78. #10622394C22semidirect
79. #10622388C22semidirect
80. #10622369C22semidirect
81. #10622344C22semidirect
82. #10622344C22semidirect
83. #10622344C22semidirect
84. (C22⋊D11)⋊C8C22semidirect
85. D11×C22⋊C8C22semidirect
86. #10622331C22semidirect
96. C2×#4341C23semidirect
111. C2×C11×SD16C23semidirect
132. C2×#4326C23semidirect
136. #66991C23semidirect
138. #66989C23semidirect
145. D4×Dic11C23semidirect
173. C2×C8×D11C23semidirect
175. #66950C23semidirect
184. #66945C23semidirect
185. #66943C23semidirect
187. #66940C23semidirect
200. C11×#106C23semidirect
201. C11×#103C23semidirect
202. C11×#102C23semidirect
205. #66899C23semidirect
210. (C2×D11)⋊C8C23semidirect
211. Dic11⋊C8C23semidirect
212. C8×Dic11C23semidirect
213. #66874C23semidirect
216. #66871C23semidirect
352. #3187D11semidirect
364. C23×C11#135semidirect
479. #483C2×D11semidirect
481. #481C2×D11semidirect
486. #465C2×D11semidirect
496. #450C2×D11semidirect
499. #448C2×D11semidirect
584. C2×SD16C22×D11semidirect
669. #106C22×D11semidirect
673. #103C22×D11semidirect
678. #102C22×D11semidirect
820. C11#61561semidirect
846. C23#66969semidirect

Maximal subgroups

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

subgroupindex
#130824502
C2×#106231612
#130804722
#130804492
#130803202
#130802942
#130795802
#130793882
#130793802
#130786602
#130778332
C2×#106223442
C2×#106226492
#130776382
C11×#31872
#6156111