Finite Group Databasebeta

← #15622247

Subgroups — #15622247

Order 2816.

2218 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082005C211yesmaximal, characteristic, complemented
2C2×#10623076C211yesmaximal, characteristic, complemented
3#13078866C214yesmaximal, complemented
4#13078857C214yesmaximal, complemented
5#13078799C214yesmaximal, complemented
6#13078797C214yesmaximal, complemented
7#13078546C212yesmaximal, complemented
8#13078415C211yesmaximal, characteristic, complemented
9#13078413C211yesmaximal, characteristic, complemented
10#13078076C211yesmaximal, characteristic, complemented
11#13077841C212yesmaximal, complemented
12#13077429C212yesmaximal, complemented
13AGL(1,ℤ/8)×Dic11C212yesmaximal, complemented
14#13077253C211yesmaximal, characteristic, complemented
15C11×#3036C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C2×C11×AGL(1,ℤ/8)C2212yes—
18C11×#532C2211yescharacteristic, complemented
19C2×C4×D4×C11C2211yescharacteristic
20#10623359C2212yes—
21#41×Dic11C2212yescomplemented
22C2×#67002C2212yes—
23C2×D4×Dic11C2211yescharacteristic
24C2×C4×C22⋊D11—21no—
25C22×(C2×D11)⋊C4—21no—
26#10623262C2212yescomplemented
27#10623250C2212yescomplemented
28#10623213C2212yescomplemented
29#10623213C2212yescomplemented
30#10623148—21no—
31#10623148—21no—
32#10623133—21no—
33#10623133—21no—
34#10623076—22no—
35#10623076—22no—
36#10623076C2214yes—
37#10623076C2214yes—
38#10623069—22no—
39#10623069—22no—
40C2×#66946C2211yescharacteristic
41C2×#66945C2211yescharacteristic
42C2×(C22⋊D11)⋊C4—21no—
43C2×C22⋊C4×D11—21no—
44C2×C4×D44C2211yescharacteristic
45C2×#66925C2211yescharacteristic
46#10623001C2211yescharacteristic, complemented
47C11×#463C2214yescomplemented
48C11×#461C2212yescomplemented
49C11×#459C2212yescomplemented
50C11×#423C2211yescharacteristic, complemented
51C11×#417C2212yescomplemented
52#10622845C2212yescomplemented
53#10622828C2212yes—
54#10622782C2214yes—
55#10622782C2214yes—
56#10622777C2214yescomplemented
57SD16×Dic11C2214yescomplemented
58#10622769C2214yes—
59#10622769C2214yes—
60#10622765C2214yescomplemented
61D8×Dic11C2214yescomplemented
62#10622744C2212yes—
63#10622739C2212yes—
64#10622734C2212yescomplemented
65M16×Dic11C2212yescomplemented
66#10622696C2212yescomplemented
67#10622685C2212yescomplemented
68#10622670C2214yescomplemented
69#10622622C2214yescomplemented
70#10622621C2212yescomplemented
71#10622620C2212yescomplemented
72#10622577C2212yescomplemented
73#10622537C2211yescharacteristic, complemented
74#10622460C2214yescomplemented
75#10622459C2212yescomplemented
76#10622455C2212yescomplemented
77#10622453C2214yescomplemented
78#10622453C2214yescomplemented
79#10622430C2214yescomplemented
80#10622428C2214yescomplemented
81#10622427C2214yescomplemented
82#10622401C2214yescomplemented
83#10622398C2214yescomplemented
84#10622397C2214yescomplemented
85#10622392C2214yescomplemented
86#10622369C2214yescomplemented
87C24×D11—21no—
88C2×C11×#41C2312yes—
89C22×D4×C11C2311yescharacteristic
90C23×C4×C11—21no—
91C22×C22⋊D11—21no—
92C23×Dic11—21no—
93C2×D4×D11—24no—
94C2×D4×D11—24no—
95C2×D4×D11—22no—
96C2×D4×D11C2314yes—
97C22×D44C2311yescharacteristic
98C22×C4×D11—21no—
99C22×C4×D11—21no—
100C22×C4×D11C2311yescharacteristic
101C11×AGL(1,ℤ/8)—28no—
102C2×C11×SD16C2314yes—
103C2×C11×D8C2314yes—
104C2×C11×M16C2312yes—
105C11×C4⋊Q8C2311yescharacteristic, complemented
106C11×#127C2311yescharacteristic, complemented
107C11×#124C2312yescomplemented
108C11×#121—21no—
109C11×#121—21no—
110C4×D4×C11—21no—
111C4×D4×C11—21no—
112C4×D4×C11—21no—
113C4×D4×C11—21no—
114C4×D4×C11C2312yes—
115C4×D4×C11C2312yes—
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C22⋊C4—21no—
118C2×C42×C11C2311yescharacteristic
119C2×C22⋊Dic11—21no—
120#67002—28no—
121#66999C2312yes—
122#66999C2312yes—
123Q8×Dic11C2312yescomplemented
124Q8×Dic11C2312yescomplemented
125C2×#4325C2314yes—
126#66992—22no—
127#66992—22no—
128#66991C2312yes—
129#66991C2312yes—
130#66990—22no—
131#66988—22no—
132#66988—22no—
133#66988—22no—
134D4×Dic11—22no—
135D4×Dic11—22no—
136D4×Dic11—22no—
137D4×Dic11C2314yes—
138D4×Dic11C2312yescomplemented
139D4×Dic11C2312yescomplemented
140C2×#4323C2314yes—
141C4×C22⋊D11—22no—
142C4×C22⋊D11—22no—
143C4×C22⋊D11—24no—
144C4×C22⋊D11—24no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4—24no—
149C2×(C2×D11)⋊C4—24no—
150C2×(C2×D11)⋊C4D411yescharacteristic
151C2×(C2×D11)⋊C4D411yescharacteristic
152#66979—22no—
153#66979C2312yes—
154C2×C4⋊Dic11C2311yescharacteristic
155#66977—21no—
156#66977—21no—
157C2×Dic11⋊C4D411yescharacteristic
158C2×Dic11⋊C4D411yescharacteristic
159C2×C4×Dic11—21no—
160C2×C4×Dic11—22no—
161C2×C4×Dic11C2311yescharacteristic
162C2×#4318C2312yes—
163#66951—22no—
164#66951—22no—
165#66946—22no—
166#66946C2314yes—
167#66945—22no—
168#66945C2314yes—
169#66942—22no—
170#66942—22no—
171#66939—22no—
172#66939—22no—
173#66938—22no—
174#66938—22no—
175(C22⋊D11)⋊C4—24no—
176(C22⋊D11)⋊C4—24no—
177C22⋊C4×D11—24no—
178C22⋊C4×D11—24no—
179#66932—22no—
180#66932—22no—
181#66931—22no—
182#66931—22no—
183C4×D44—21no—
184C4×D44—21no—
185C4×D44C2312yes—
186C4×D44C2312yes—
187#66925D412yes—
188#66925D412yes—
189#66925C2312yes—
190#66925C2312yes—
191#66923C2312yescomplemented
192#66922C2311yescharacteristic, complemented
193#66922C2311yescharacteristic, complemented
194C4×Dic22—21no—
195C4×Dic22—21no—
196C11×C4⋊C8C2312yescomplemented
197C11×C4⋊C8C2312yescomplemented
198C11×#103C2314yescomplemented
199C11×#102C2314yescomplemented
200#66899C2314yescomplemented
201#66896C2314yes—
202#66896C2314yes—
203#66896C2314yescomplemented
204#66885C2314yes—
205#66885C2314yes—
206(C2×D11)⋊C8C2314yes—
207(C2×D11)⋊C8C2314yes—
208#66882C2314yescomplemented
209#66881C2314yescomplemented
210#66879C2314yescomplemented
211C8×Dic11C2314yescomplemented
212#66872C2314yescomplemented
213#66871C2314yescomplemented
214C4⋊(C11⋊C8)C2312yescomplemented
215C4⋊(C11⋊C8)C2312yescomplemented
216#60564—111nomaximal, Sylow
217C24×C11—21no—
218C23×D11—21no—
219C23×D11—28no—
220C23×D11—24no—
221C23×D11—82no—
222C23×D11—82no—
223C23×D11C2×D411yescharacteristic
224C11×#41—24no—
225C11×#41—24no—
226C2×Q8×C11C2412yes—
227C2×D4×C11—22no—
228C2×D4×C11—21no—
229C2×D4×C11—21no—
230C2×D4×C11—21no—
231C2×D4×C11—22no—
232C2×D4×C11#4114yes—
233C2×D4×C11C2412yes—
234C2×D4×C11C2412yes—
235C22×C4×C11—21no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11—82no—
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2411yescharacteristic
243C2×C22⋊D11—28no—
244C2×C22⋊D11—24no—
245C2×C22⋊D11—22no—
246C2×C22⋊D11—22no—
247C22×Dic11—22no—
248C22×Dic11—22no—
249C22×Dic11—24no—
250C22×Dic11—21no—
251C22×Dic11—82no—
252C22×Dic11C2×D411yescharacteristic
253C22×Dic11C2×D411yescharacteristic
254C22×Dic11C2×D411yescharacteristic
255D4×D11—216no—
256D4×D11—28no—
257D4×D11—28no—
258C2×D44—21no—
259C2×D44—22no—
260C2×D44#4114yes—
261C2×D44C2412yes—
262C2×C4×D11—24no—
263C2×C4×D11—22no—
264C2×C4×D11—22no—
265C2×C4×D11—22no—
266C2×C4×D11—22no—
267C2×C4×D11—82no—
268C2×C4×D11—82no—
269C2×C4×D11C2×D412yes—
270C2×C4×D11C2412yes—
271C2×Dic22—21no—
272C2×Dic22—21no—
273C11×SD16—28no—
274C11×D8—28no—
275C11×M16—24no—
276C2×C8×C11C2414yes—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4C2412yes—
281C11×C22⋊C4—22no—
282C11×C22⋊C4—22no—
283C11×C22⋊C4—22no—
284C11×C22⋊C4—22no—
285C42×C11C2×D411yescharacteristic
286C42×C11C2×D411yescharacteristic
287C42×C11C2411yescharacteristic
288C42×C11C2411yescharacteristic
289C22⋊Dic11—22no—
290C22⋊Dic11—22no—
291C22⋊Dic11—22no—
292C22⋊Dic11—22no—
293C22⋊Dic11—24no—
294C22⋊Dic11—22no—
295#4325—28no—
296#4323—28no—
297(C2×D11)⋊C4—24no—
298(C2×D11)⋊C4—24no—
299(C2×D11)⋊C4—22no—
300(C2×D11)⋊C4—22no—
301(C2×D11)⋊C4—22no—
302(C2×D11)⋊C4—22no—
303(C2×D11)⋊C4C2×D412yes—
304(C2×D11)⋊C4C2×D412yes—
305(C2×D11)⋊C4C2×D412yes—
306(C2×D11)⋊C4C2×D412yes—
307C4⋊Dic11—22no—
308C4⋊Dic11—22no—
309C4⋊Dic11—21no—
310C4⋊Dic11—21no—
311C4⋊Dic11—21no—
312C4⋊Dic11C2412yes—
313C4⋊Dic11C2412yes—
314C4⋊Dic11C2412yes—
315Dic11⋊C4—22no—
316Dic11⋊C4—22no—
317Dic11⋊C4—22no—
318Dic11⋊C4—22no—
319Dic11⋊C4C2×D412yes—
320Dic11⋊C4C2×D412yes—
321Dic11⋊C4C2×D412yes—
322Dic11⋊C4C2×D412yes—
323C4×Dic11—22no—
324C4×Dic11—22no—
325C4×Dic11—24no—
326C4×Dic11—22no—
327C4×Dic11C2×D412yes—
328C4×Dic11C2412yes—
329#4318—24no—
330C2×C11⋊C8C2414yes—
331#3455—111no—
332C2×#518—111no—
333#3123—114no—
334#3122—114no—
335#3118—114no—
336#3118—114no—
337#3093—112no—
338#3077—111no—
339#3077—111no—
340#3036—111no—
341#3036D1111yescharacteristic, complemented
342#3003—112no—
343C4×AGL(1,ℤ/8)—112no—
344C4×AGL(1,ℤ/8)—112no—
345#2921—111no—
346C23×C11—24no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—42no—
350C23×C11—42no—
351C23×C11C22×D411yescharacteristic
352C22×D11—22no—
353C22×D11—24no—
354C22×D11—22no—
355C22×D11—216no—
356C22×D11—41no—
357C22×D11—41no—
358C22×D11—42no—
359C22×D11—42no—
360C22×D11—84no—
361C22×D11—84no—
362C22×D11—816no—
363C22×D11C22×D412yes—
364Q8×C11—22no—
365Q8×C11—22no—
366D4×C11—24no—
367D4×C11—22no—
368D4×C11—22no—
369D4×C11—22no—
370D4×C11—44no—
371D4×C11—81no—
372D4×C11—81no—
373D4×C11C2×#4114yes—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—42no—
379C2×C4×C11—44no—
380C2×C4×C11—82no—
381C2×C4×C11—82no—
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C22×D411yescharacteristic
386C2×C4×C11C22×D411yescharacteristic
387C2×C4×C11C2×#4112yes—
388C2×C4×C11C2×#4112yes—
389C2×C4×C11C2511yescharacteristic
390C22⋊D11—216no—
391C22⋊D11—82no—
392C22⋊D11—82no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—41no—
398C2×Dic11—41no—
399C2×Dic11—42no—
400C2×Dic11—82no—
401C2×Dic11—82no—
402C2×Dic11—84no—
403C2×Dic11C22×D412yes—
404C2×Dic11C22×D412yes—
405C2×Dic11C22×D412yes—
406D44—24no—
407D44—22no—
408D44C2×#4114yes—
409C4×D11—24no—
410C4×D11—22no—
411C4×D11—22no—
412C4×D11—84no—
413C4×D11—82no—
414C4×D11—82no—
415Dic22—81no—
416Dic22—81no—
417C8×C11—24no—
418C11⋊C8—24no—
419C23×D4—111no—
420C2×AGL(1,ℤ/8)—112no—
421C2×AGL(1,ℤ/8)C2×D1112yes—
422#542—112no—
423#542—112no—
424#541—112no—
425#540—112no—
426#539—221no—
427#539—221no—
428#538—221no—
429#538—221no—
430#533—111no—
431#532C2×D1111yescharacteristic, complemented
432#529—222no—
433#529—222no—
434#525—112no—
435#518—114no—
436#518—114no—
437#518—222no—
438#518—222no—
439C4×#41—112no—
440C2×C4×D4—111no—
441C2×C4×D4—111no—
442C2×C4×D4—111no—
443C2×C4×D4—221no—
444C2×C4×D4—221no—
445C2×C4×D4C2×D1111yescharacteristic
446C2×#117—111no—
447C2×#117—111no—
448C22×C22⋊C4—221no—
449C22×C22⋊C4—221no—
450#485—114no—
451#485—114no—
452#482—114no—
453#482—114no—
454#478—114no—
455#478—114no—
456#476—112no—
457#476—112no—
458#474—112no—
459#474—112no—
460#463—114no—
461#463C2×D1114yescomplemented
462#461—112no—
463#461C2×D1112yescomplemented
464#459—112no—
465#459C2×D1112yescomplemented
466#450—114no—
467#450—114no—
468#447—114no—
469#447—114no—
470#442—114no—
471#442—114no—
472#440—114no—
473#440—114no—
474C4×SD16—114no—
475C4×SD16—114no—
476C4×D8—114no—
477C4×D8—114no—
478#433—114no—
479#433—114no—
480#428—112no—
481#428—112no—
482#423—111no—
483#423C2×D1111yescharacteristic, complemented
484#418—112no—
485#418—112no—
486#417—112no—
487#417C2×D1112yescomplemented
488#407—112no—
489C4×M16—112no—
490C22×C11—21no—
491C22×C11—21no—
492C22×C11—24no—
493C22×C11—48no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11#52512yes—
500C22×C11C23×D411yescharacteristic
501C2×D11—22no—
502C2×D11—22no—
503C2×D11—22no—
504C2×D11—24no—
505C2×D11—48no—
506C2×D11—44no—
507C2×D11—42no—
508C2×D11—42no—
509C2×D11—816no—
510C4×C11—21no—
511C4×C11—21no—
512C4×C11—21no—
513C4×C11—21no—
514C4×C11—42no—
515C4×C11—42no—
516C4×C11#52512yes—
517C4×C11C22×#4111yescharacteristic
518C4×C11C22×#4111yescharacteristic
519Dic11—22no—
520Dic11—22no—
521Dic11—22no—
522Dic11—42no—
523Dic11—42no—
524Dic11—42no—
525C25—221no—
526C2×#41C22×D1112yes—
527C22×D4—114no—
528C22×D4—111no—
529C22×D4—222no—
530C22×D4—221no—
531C22×D4—224no—
532C22×D4—224no—
533C22×D4C22×D1111yescharacteristic
534C23×C4—21no—
535C23×C4—111no—
536C23×C4—221no—
537C23×C4—221no—
538C23×C4—221no—
539AGL(1,ℤ/8)—28no—
540AGL(1,ℤ/8)—228no—
541C2×SD16—114no—
542C2×SD16C22×D1114yes—
543C2×D8—114no—
544C2×D8C22×D1114yes—
545C2×M16—112no—
546C2×M16C22×D1112yes—
547C4⋊Q8—111no—
548C4⋊Q8—111no—
549C4⋊Q8C22×D1111yescharacteristic, complemented
550#127C22×D1111yescharacteristic, complemented
551#126—222no—
552#126—222no—
553#126—222no—
554#126—222no—
555#125—112no—
556#125—222no—
557#125—222no—
558#124—222no—
559#124—222no—
560#124C22×D1112yescomplemented
561#123—222no—
562#123—222no—
563#123—222no—
564#123—222no—
565#123—222no—
566C22⋊Q8—112no—
567C22⋊Q8—112no—
568C22⋊Q8—222no—
569C22⋊Q8—222no—
570C22⋊Q8—221no—
571C22⋊Q8—221no—
572#121—21no—
573#121—21no—
574#121—112no—
575#121—112no—
576#121—222no—
577#121—222no—
578#120—222no—
579C4×Q8—112no—
580C4×Q8—112no—
581C4×Q8—221no—
582C4×Q8—221no—
583C4×D4—21no—
584C4×D4—21no—
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—114no—
588C4×D4—112no—
589C4×D4—112no—
590C4×D4—114no—
591C4×D4—112no—
592C4×D4—112no—
593C4×D4—222no—
594C4×D4—222no—
595C4×D4—224no—
596C4×D4—224no—
597C4×D4—224no—
598C4×D4—224no—
599C4×D4—222no—
600C4×D4—222no—
601C4×D4—222no—
602C4×D4—222no—
603C4×D4—221no—
604C4×D4—221no—
605C4×D4C22×D1112yes—
606C4×D4C22×D1112yes—
607#117—112no—
608#117—112no—
609#117—112no—
610#117—112no—
611#117—112no—
612#117—114no—
613#117—222no—
614#117—222no—
615C2×C4⋊C4—111no—
616C2×C4⋊C4—111no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4C22×D1111yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—111no—
621C2×C22⋊C4—111no—
622C2×C22⋊C4—224no—
623C2×C22⋊C4—224no—
624C2×C22⋊C4—224no—
625C2×C22⋊C4—224no—
626C2×C22⋊C4—221no—
627C2×C22⋊C4—221no—
628C2×C22⋊C4—221no—
629C2×C22⋊C4—221no—
630C2×C42—111no—
631C2×C42—222no—
632C2×C42—221no—
633C2×C42C22×D1111yescharacteristic
634#107—114no—
635#107—114no—
636#106—114no—
637#106—114no—
638C4⋊C8—112no—
639C4⋊C8—112no—
640C4⋊C8C22×D1112yescomplemented
641C4⋊C8C22×D1112yescomplemented
642#103—114no—
643#103C22×D1114yescomplemented
644#102—114no—
645#102—114no—
646#102—114no—
647#102—114no—
648#102—114no—
649#102C22×D1114yescomplemented
650C22⋊C8—114no—
651C22⋊C8—114no—
652#97—114no—
653C4×C8—114no—
654C2×C11—22no—
655C2×C11—44no—
656C2×C11—82no—
657C2×C11C2×#52511yescharacteristic
658C2×C11#358511yescharacteristic
659C2×C11#358511yescharacteristic
660D11—42no—
661D11—44no—
662C24—21no—
663C24—111no—
664C24—224no—
665C24—228no—
666C24—221no—
667C24—882no—
668C24—882no—
669#41—24no—
670#41—24no—
671C2×Q8—221no—
672C2×Q8—221no—
673C2×Q8C23×D1112yes—
674C2×D4—22no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—22no—
679C2×D4—114no—
680C2×D4—112no—
681C2×D4—224no—
682C2×D4—228no—
683C2×D4—2216no—
684C2×D4—228no—
685C2×D4—228no—
686C2×D4—222no—
687C2×D4—222no—
688C2×D4—221no—
689C2×D4—222no—
690C2×D4#434114yes—
691C2×D4C23×D1112yes—
692C2×D4C23×D1112yes—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—82no—
698C22×C4—111no—
699C22×C4—111no—
700C22×C4—111no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—224no—
704C22×C4—222no—
705C22×C4—222no—
706C22×C4—224no—
707C22×C4—222no—
708C22×C4—222no—
709C22×C4—221no—
710C22×C4—222no—
711C22×C4—222no—
712C22×C4—882no—
713C22×C4—882no—
714C22×C4—882no—
715C22×C4D4×D1111yescharacteristic
716C22×C4D4×D1111yescharacteristic
717C22×C4C23×D1111yescharacteristic
718SD16—28no—
719SD16—228no—
720D8—28no—
721D8—228no—
722M16—24no—
723M16—224no—
724C2×C8—114no—
725C2×C8C23×D1114yes—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—112no—
730C4⋊C4—112no—
731C4⋊C4—112no—
732C4⋊C4—112no—
733C4⋊C4—112no—
734C4⋊C4—112no—
735C4⋊C4—112no—
736C4⋊C4—222no—
737C4⋊C4—222no—
738C4⋊C4—222no—
739C4⋊C4—222no—
740C4⋊C4—221no—
741C4⋊C4—222no—
742C4⋊C4—222no—
743C4⋊C4—221no—
744C4⋊C4—221no—
745C4⋊C4C23×D1112yes—
746C22⋊C4—22no—
747C22⋊C4—22no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—112no—
751C22⋊C4—112no—
752C22⋊C4—112no—
753C22⋊C4—112no—
754C22⋊C4—224no—
755C22⋊C4—224no—
756C22⋊C4—222no—
757C22⋊C4—222no—
758C22⋊C4—224no—
759C22⋊C4—222no—
760C22⋊C4—222no—
761C22⋊C4—222no—
762C22⋊C4—222no—
763C22⋊C4—222no—
764C22⋊C4—222no—
765C22⋊C4—222no—
766C42—112no—
767C42—112no—
768C42—224no—
769C42—222no—
770C42—222no—
771C42—222no—
772C42D4×D1111yescharacteristic
773C42D4×D1111yescharacteristic
774C42C23×D1111yescharacteristic
775C42C23×D1111yescharacteristic
776C11#6056411yescharacteristic, complemented, Sylow
777C23—24no—
778C23—22no—
779C23—22no—
780C23—42no—
781C23—42no—
782C23—112no—
783C23—2216no—
784C23—222no—
785C23—224no—
786C23—222no—
787C23—441no—
788C23—441no—
789C23—442no—
790C23—442no—
791C23—884no—
792C23—884no—
793C23—8816no—
794C23C2×D4×D1111yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—881no—
798Q8—881no—
799D4—24no—
800D4—22no—
801D4—22no—
802D4—22no—
803D4—44no—
804D4—81no—
805D4—81no—
806D4—114no—
807D4—2216no—
808D4—224no—
809D4—222no—
810D4—882no—
811D4—882no—
812D4C2×#434114yes—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—82no—
820C2×C4—82no—
821C2×C4—112no—
822C2×C4—112no—
823C2×C4—112no—
824C2×C4—222no—
825C2×C4—224no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—441no—
832C2×C4—441no—
833C2×C4—442no—
834C2×C4—882no—
835C2×C4—882no—
836C2×C4—884no—
837C2×C4—884no—
838C2×C4—882no—
839C2×C4—882no—
840C2×C4C2×D4×D1111yescharacteristic
841C2×C4C2×D4×D1111yescharacteristic
842C2×C4C2×D4×D1111yescharacteristic
843C2×C4C2×D4×D1111yescharacteristic
844C2×C4C2×D4×D1111yescharacteristic
845C2×C4C2×#434112yes—
846C2×C4#41×D1112yes—
847C2×C4C24×D1111yescharacteristic
848C8—24no—
849C8—224no—
850C22—21no—
851C22—21no—
852C22—24no—
853C22—48no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—222no—
860C22—222no—
861C22—224no—
862C22—222no—
863C22—444no—
864C22—448no—
865C22—442no—
866C22—442no—
867C22—8816no—
868C22#1062313712yes—
869C22C22×D4×D1111yescharacteristic
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—42no—
875C4—42no—
876C4—222no—
877C4—222no—
878C4—222no—
879C4—442no—
880C4—442no—
881C4—442no—
882C4#1062313712yes—
883C4C22×#434111yescharacteristic
884C4C2×#41×D1111yescharacteristic
885C2—22no—
886C2—44no—
887C2—82no—
888C2—442no—
889C2—444no—
890C2C2×#1062313711yescharacteristic
891C2#1308339211yescharacteristic
892C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3036C2
socleC22×C11C23×D4
hypercenter#3036D11
hypocenterC11#60564
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #13082005C2semidirect
2. C2×#10623076C2semidirect
3. #13078866C2semidirect
4. #13078857C2semidirect
5. #13078799C2semidirect
6. #13078797C2semidirect
7. #13078546C2semidirect
8. #13078415C2semidirect
9. #13078413C2semidirect
10. #13078076C2semidirect
11. #13077841C2semidirect
12. #13077429C2semidirect
13. AGL(1,ℤ/8)×Dic11C2semidirect
14. #13077253C2semidirect
15. C11×#3036C2semidirect
18. C11×#532C22semidirect
21. #41×Dic11C22semidirect
26. #10623262C22semidirect
27. #10623250C22semidirect
28. #10623213C22semidirect
29. #10623213C22semidirect
46. #10623001C22semidirect
47. C11×#463C22semidirect
48. C11×#461C22semidirect
49. C11×#459C22semidirect
50. C11×#423C22semidirect
51. C11×#417C22semidirect
52. #10622845C22semidirect
56. #10622777C22semidirect
57. SD16×Dic11C22semidirect
60. #10622765C22semidirect
61. D8×Dic11C22semidirect
64. #10622734C22semidirect
65. M16×Dic11C22semidirect
66. #10622696C22semidirect
67. #10622685C22semidirect
68. #10622670C22semidirect
69. #10622622C22semidirect
70. #10622621C22semidirect
71. #10622620C22semidirect
72. #10622577C22semidirect
73. #10622537C22semidirect
74. #10622460C22semidirect
75. #10622459C22semidirect
76. #10622455C22semidirect
77. #10622453C22semidirect
78. #10622453C22semidirect
79. #10622430C22semidirect
80. #10622428C22semidirect
81. #10622427C22semidirect
82. #10622401C22semidirect
83. #10622398C22semidirect
84. #10622397C22semidirect
85. #10622392C22semidirect
86. #10622369C22semidirect
105. C11×C4⋊Q8C23semidirect
106. C11×#127C23semidirect
107. C11×#124C23semidirect
123. Q8×Dic11C23semidirect
124. Q8×Dic11C23semidirect
138. D4×Dic11C23semidirect
139. D4×Dic11C23semidirect
191. #66923C23semidirect
192. #66922C23semidirect
193. #66922C23semidirect
196. C11×C4⋊C8C23semidirect
197. C11×C4⋊C8C23semidirect
198. C11×#103C23semidirect
199. C11×#102C23semidirect
200. #66899C23semidirect
203. #66896C23semidirect
208. #66882C23semidirect
209. #66881C23semidirect
210. #66879C23semidirect
211. C8×Dic11C23semidirect
212. #66872C23semidirect
213. #66871C23semidirect
214. C4⋊(C11⋊C8)C23semidirect
215. C4⋊(C11⋊C8)C23semidirect
341. #3036D11semidirect
431. #532C2×D11semidirect
461. #463C2×D11semidirect
463. #461C2×D11semidirect
465. #459C2×D11semidirect
483. #423C2×D11semidirect
487. #417C2×D11semidirect
549. C4⋊Q8C22×D11semidirect
550. #127C22×D11semidirect
560. #124C22×D11semidirect
640. C4⋊C8C22×D11semidirect
641. C4⋊C8C22×D11semidirect
643. #103C22×D11semidirect
649. #102C22×D11semidirect
776. C11#60564semidirect

Maximal subgroups

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

subgroupindex
#130820052
C2×#106230762
#130788662
#130788572
#130787992
#130787972
#130785462
#130784152
#130784132
#130780762
#130778412
#130774292
AGL(1,ℤ/8)×Dic112
#130772532
C11×#30362
#6056411