Finite Group Databasebeta

← #15622697

Subgroups — #15622697

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082353C211yesmaximal, characteristic, complemented
2C2×#10623035C211yesmaximal, characteristic, complemented
3#13078888C214yesmaximal, complemented
4#13078818C214yesmaximal, complemented
5#13078790C212yesmaximal, complemented
6#13078704C212yesmaximal, complemented
7#13078666C212yesmaximal, complemented
8#13078644C212yesmaximal, complemented
9C2×#10622581C211yesmaximal, characteristic, complemented
10#13078477C212yesmaximal, complemented
11#13078154C212yesmaximal, complemented
12#13077870C211yesmaximal, characteristic, complemented
13#13077832C211yesmaximal, characteristic, complemented
14#13077495C212yesmaximal, complemented
15#13077446C212yesmaximal, complemented
16#13077276C211yesmaximal, characteristic, complemented
17C11×#3092C211yesmaximal, characteristic, complemented
18C22×#4339C2211yescharacteristic
19C11×#525C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21#10623361C2211yescharacteristic, complemented
22#10623358C2211yescharacteristic, complemented
23C2×#67003C2212yes—
24C2×#66983C2211yescharacteristic
25C2×C4×C22⋊D11—22no—
26C2×#66979C2211yescharacteristic
27C2×#66961C2212yes—
28#10623189—22no—
29#10623174C2212yescomplemented
30#10623155C2212yes—
31#10623150C2212yescomplemented
32#10623127C2212yes—
33#10623122—22no—
34#10623096—21no—
35#10623096—21no—
36#10623094—21no—
37#10623086—21no—
38#10623052C2211yescharacteristic, complemented
39#10623050C2211yescharacteristic, complemented
40#10623035—21no—
41#10623035—21no—
42#10623035—22no—
43#10623035C2212yes—
44#10623035C2212yes—
45#10623035C2214yescomplemented
46C2×#66946C2212yescomplemented
47C2×#66945—21no—
48C2×C4⋊C4×D11—21no—
49C2×#66940C2212yescomplemented
50C11×#484C2212yescomplemented
51C11×#483C2212yescomplemented
52C11×#481C2212yescomplemented
53C11×#480C2212yescomplemented
54C11×#428C2212yescomplemented
55C11×#417C2212yescomplemented
56C11×#407C2211yescharacteristic
57C2×C22⋊(C11⋊C8)C2211yescharacteristic
58#10622746C2212yes—
59#10622735C2212yescomplemented
60#10622732C2212yescomplemented
61#10622663C2211yescharacteristic, complemented
62#10622660C2212yescomplemented
63#10622659C2211yescharacteristic, complemented
64#10622653C2211yescharacteristic, complemented
65#10622650C2212yescomplemented
66#10622649C2211yescharacteristic, complemented
67#10622615C2212yes—
68#10622581C2212yes—
69#10622581C2212yes—
70#10622581C2214yescomplemented
71C2×#66873C2212yescomplemented
72C2×#66872C2212yescomplemented
73#10622504C2214yescomplemented
74#10622502C2214yescomplemented
75#10622490C2214yescomplemented
76#10622485C2214yescomplemented
77#10622483C2214yescomplemented
78#10622482C2214yescomplemented
79#10622467C2214yescomplemented
80#10622465C2214yescomplemented
81#10622432C2214yescomplemented
82#10622411C2214yescomplemented
83#10622402C2214yescomplemented
84#10622401C2214yescomplemented
85#10622399C2214yescomplemented
86#10622398C2214yescomplemented
87#10622375C2214yescomplemented
88#10622371C2214yescomplemented
89#10622351C2212yes—
90#10622347C2214yes—
91#10622345C2212yes—
92#10622333C2214yescomplemented
93#10622332C2212yescomplemented
94#10622331C2212yescomplemented
95C2×C11×#41C2311yescharacteristic
96C23×C4×C11—21no—
97C23×C4×C11C2311yescharacteristic
98C22×C22⋊D11—21no—
99C22×C22⋊D11—21no—
100C2×#4341—22no—
101C2×#4339—21no—
102C2×#4339—21no—
103C2×#4339—28no—
104C2×#4339C2312yes—
105C2×#4339C2312yes—
106C22×D44C2311yescharacteristic
107C22×D44C2311yescharacteristic
108C22×C4×D11—21no—
109C22×C4×D11—22no—
110C22×Dic22C2311yescharacteristic
111C2×C11×M16C2312yes—
112C11×#123—21no—
113C11×C22⋊Q8C2311yescharacteristic
114C11×C22⋊Q8C2311yescharacteristic
115C11×#121C2311yescharacteristic
116C11×#121C2311yescharacteristic
117C11×#120—21no—
118C4×D4×C11—21no—
119C4×D4×C11—21no—
120C11×#117C2311yescharacteristic
121C2×C11×C4⋊C4—21no—
122C2×C11×C4⋊C4—21no—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4C2312yes—
125C2×C11×C4⋊C4C2312yes—
126C2×C11×C4⋊C4C2312yes—
127C2×C22⋊Dic11D412yes—
128#67003—28no—
129#67000C2312yes—
130Q8×Dic11C2312yes—
131C2×#4326C2312yes—
132C2×#4325C2312yes—
133#66993C2312yes—
134#66992—22no—
135#66992—22no—
136#66991—22no—
137#66990—22no—
138D4×Dic11—22no—
139D4×Dic11C2312yes—
140C2×#4324C2312yes—
141C2×#4323C2312yes—
142#66983—21no—
143#66983—21no—
144#66983—21no—
145#66983—21no—
146#66983C2312yes—
147#66983C2312yes—
148C4×C22⋊D11—24no—
149C4×C22⋊D11—24no—
150C4×C22⋊D11—24no—
151C4×C22⋊D11—24no—
152C2×(C2×D11)⋊C4—21no—
153C2×(C2×D11)⋊C4—22no—
154#66979—21no—
155#66979D411yescharacteristic
156#66979D411yescharacteristic
157#66979D412yes—
158#66979C2311yescharacteristic
159#66979C2311yescharacteristic
160#66979C2312yes—
161C2×C4⋊Dic11—21no—
162C2×C4⋊Dic11D411yescharacteristic
163C2×C4⋊Dic11D411yescharacteristic
164C2×C4⋊Dic11C2311yescharacteristic
165C2×Dic11⋊C4—22no—
166C2×C4×Dic11—22no—
167C2×C4×Dic11C2312yes—
168C22×C11⋊C8C2312yes—
169#66961—28no—
170C2×D88C2314yes—
171C2×#4314C2314yes—
172#66951—22no—
173#66951—22no—
174#66950—22no—
175#66946—22no—
176#66946—22no—
177#66946C2312yes—
178#66946C2314yes—
179#66946C2314yes—
180#66946C2312yes—
181#66945—22no—
182#66945—22no—
183#66945—24no—
184#66945—22no—
185C4⋊C4×D11—22no—
186C4⋊C4×D11—22no—
187C4⋊C4×D11—24no—
188#66943C2312yes—
189#66941C2312yes—
190#66940—22no—
191#66940—22no—
192#66940C2314yes—
193#66940C2314yes—
194#66939—22no—
195#66939—22no—
196#66938—22no—
197#66938—22no—
198#66936—22no—
199#66936—22no—
200(C22⋊D11)⋊C4—22no—
201(C22⋊D11)⋊C4—22no—
202C22⋊C4×D11—22no—
203#66931—22no—
204C4×D44—21no—
205C4×D44—21no—
206#66923—21no—
207#66922—21no—
208C11×#107C2314yes—
209C11×#106C2314yes—
210C11×#103C2314yes—
211C11×#102C2314yes—
212C11×C22⋊C8C2312yes—
213C11×C22⋊C8C2312yes—
214C22⋊(C11⋊C8)C2311yescharacteristic
215C22⋊(C11⋊C8)C2311yescharacteristic
216C22⋊(C11⋊C8)C2312yes—
217#66885C2314yes—
218#66880C2314yes—
219#66879C2314yes—
220Dic11⋊C8C2314yes—
221Dic11⋊C8C2314yes—
222C8×Dic11C2314yes—
223#66874C2312yes—
224#66874C2312yes—
225#66873C2314yes—
226#66873C2312yes—
227#66873C2314yes—
228#66873C2312yes—
229#66872C2314yes—
230#66872C2314yes—
231#60588—111nomaximal, Sylow
232C24×C11C2×D411yescharacteristic
233C23×D11—21no—
234C23×D11—21no—
235C11×#41—24no—
236C2×Q8×C11C2411yescharacteristic
237C2×D4×C11—21no—
238C2×D4×C11—21no—
239C2×D4×C11—21no—
240C2×D4×C11C2411yescharacteristic
241C22×C4×C11—24no—
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—21no—
246C22×C4×C11—82no—
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C2×C22⋊D11—28no—
254C2×C22⋊D11—22no—
255C2×C22⋊D11—22no—
256C2×C22⋊D11—22no—
257C2×C22⋊D11—22no—
258C2×C22⋊D11—22no—
259C2×C22⋊D11—22no—
260C2×C22⋊D11—82no—
261C22×Dic11—22no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11C2×D412yes—
265C22×Dic11C2×D412yes—
266#4341—84no—
267#4339—28no—
268#4339—28no—
269#4339—24no—
270#4339—24no—
271#4339—24no—
272#4339#4118yescomplemented
273C2×D44—24no—
274C2×D44—21no—
275C2×D44—21no—
276C2×D44—24no—
277C2×D44C2412yes—
278C2×D44C2412yes—
279C2×C4×D11—28no—
280C2×C4×D11—22no—
281C2×C4×D11—22no—
282C2×C4×D11—24no—
283C2×C4×D11—24no—
284C2×C4×D11—22no—
285C2×C4×D11—22no—
286C2×C4×D11—84no—
287C2×Dic22—24no—
288C2×Dic22—22no—
289C2×Dic22—21no—
290C2×Dic22C2412yes—
291C11×M16—24no—
292C2×C8×C11C2414yes—
293C11×C4⋊C4—22no—
294C11×C4⋊C4—22no—
295C11×C4⋊C4—22no—
296C11×C4⋊C4—21no—
297C11×C4⋊C4—21no—
298C11×C4⋊C4C2414yes—
299C11×C4⋊C4C2411yescharacteristic
300C11×C4⋊C4C2411yescharacteristic
301C11×C22⋊C4—21no—
302C11×C22⋊C4—21no—
303C11×C22⋊C4—21no—
304C11×C22⋊C4—21no—
305C11×C22⋊C4—21no—
306C42×C11—21no—
307C22⋊Dic11—22no—
308C22⋊Dic11C2×D412yes—
309C22⋊Dic11C2×D412yes—
310C22⋊Dic11C2×D412yes—
311C22⋊Dic11C2×D412yes—
312#4326—24no—
313#4325—24no—
314#4324—24no—
315#4323—24no—
316(C2×D11)⋊C4—22no—
317(C2×D11)⋊C4—22no—
318(C2×D11)⋊C4—22no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—24no—
321(C2×D11)⋊C4—24no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—22no—
324C4⋊Dic11—22no—
325C4⋊Dic11—22no—
326C4⋊Dic11—21no—
327C4⋊Dic11C2×D411yescharacteristic
328C4⋊Dic11C2×D411yescharacteristic
329C4⋊Dic11C2×D411yescharacteristic
330C4⋊Dic11C2×D411yescharacteristic
331C4⋊Dic11C2×D412yes—
332C4⋊Dic11C2×D412yes—
333C4⋊Dic11C2412yes—
334Dic11⋊C4—22no—
335Dic11⋊C4—22no—
336Dic11⋊C4—24no—
337Dic11⋊C4—24no—
338C4×Dic11—22no—
339C4×Dic11—24no—
340C4×Dic11—24no—
341C4×Dic11C2×D412yes—
342C4×Dic11C2×D412yes—
343C4×Dic11C2412yes—
344C4×Dic11C2412yes—
345C2×C11⋊C8—24no—
346C2×C11⋊C8C2412yes—
347C2×C11⋊C8C2412yes—
348D88—28no—
349#4314—28no—
350#3494—111no—
351C2×#520—111no—
352#3125—114no—
353#3119—114no—
354#3117—112no—
355#3109—112no—
356#3105—112no—
357#3103—112no—
358#3092D1111yescharacteristic, complemented
359C2×#481—111no—
360#3084—112no—
361#3045—112no—
362#3006—111no—
363#3002—111no—
364#2952—112no—
365#2946—112no—
366#2924—111no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—21no—
370C23×C11—41no—
371C23×C11C22×D411yescharacteristic
372C23×C11C22×D411yescharacteristic
373C23×C11C22×D411yescharacteristic
374C22×D11—24no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—42no—
378C22×D11—42no—
379C22×D11—42no—
380C22×D11—81no—
381C22×D11—81no—
382Q8×C11—22no—
383D4×C11—22no—
384D4×C11—42no—
385D4×C11—42no—
386D4×C11—81no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—24no—
393C2×C4×C11—21no—
394C2×C4×C11—21no—
395C2×C4×C11—21no—
396C2×C4×C11—44no—
397C2×C4×C11—42no—
398C2×C4×C11—82no—
399C2×C4×C11—82no—
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C2×#4114yes—
404C2×C4×C11C2511yescharacteristic
405C22⋊D11—28no—
406C22⋊D11—28no—
407C22⋊D11—44no—
408C22⋊D11—82no—
409C22⋊D11—82no—
410C22⋊D11—82no—
411C2×Dic11—24no—
412C2×Dic11—24no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—42no—
416C2×Dic11—82no—
417C2×Dic11—81no—
418C2×Dic11C22×D412yes—
419C2×Dic11C22×D412yes—
420C2×Dic11C22×D412yes—
421C2×Dic11C22×D412yes—
422D44—24no—
423D44—22no—
424D44—24no—
425D44—42no—
426D44C2×#4114yes—
427C4×D11—28no—
428C4×D11—28no—
429C4×D11—82no—
430C4×D11—84no—
431C4×D11—84no—
432C4×D11—82no—
433Dic22—24no—
434Dic22—22no—
435Dic22—82no—
436Dic22C2×#4114yes—
437C8×C11—24no—
438C11⋊C8—22no—
439C11⋊C8—22no—
440C22×#41—111no—
441C2×AGL(1,ℤ/8)—112no—
442C2×#135—112no—
443#555—221no—
444#553—221no—
445#553—221no—
446#551—222no—
447#547—221no—
448#546—222no—
449#544—111no—
450#542—112no—
451#540—112no—
452#535—111no—
453#532—112no—
454#529—112no—
455#525C2×D1111yescharacteristic
456C2×#121—111no—
457#520—111no—
458#520—112no—
459#520—114no—
460#520—112no—
461#520—222no—
462#520—221no—
463#520—221no—
464#518—111no—
465C2×C4×Q8—112no—
466C2×C4×D4—112no—
467C2×C4×D4—222no—
468C2×#117—111no—
469C2×#117—221no—
470C22×C4⋊C4—221no—
471C22×C4⋊C4C2×D1111yescharacteristic
472#484C2×D1112yescomplemented
473#483C2×D1112yescomplemented
474#481—112no—
475#481—112no—
476#481—114no—
477#481C2×D1112yescomplemented
478#480C2×D1112yescomplemented
479#479—114no—
480#478—114no—
481#476—114no—
482#475—114no—
483#464—114no—
484#463—114no—
485#460—114no—
486#459—114no—
487#452—112no—
488#451—111no—
489#450—111no—
490#449—112no—
491#449—114no—
492#448—111no—
493#448—112no—
494#447—111no—
495#447—112no—
496#442—114no—
497#442—114no—
498#441—114no—
499#440—114no—
500C4×SD16—114no—
501C4×SD16—114no—
502C4×SD16—114no—
503C4×D8—114no—
504#433—114no—
505#432—112no—
506#431—112no—
507#428C2×D1112yescomplemented
508C2×#106—112no—
509#424—112no—
510#417—112no—
511#417C2×D1112yescomplemented
512#416—112no—
513C2×#102—112no—
514#407C2×D1111yescharacteristic
515C2×C22⋊C8—111no—
516#405—112no—
517C22×C11—21no—
518C22×C11—21no—
519C22×C11—21no—
520C22×C11—21no—
521C22×C11—21no—
522C22×C11—21no—
523C22×C11—21no—
524C22×C11—44no—
525C22×C11—41no—
526C22×C11—41no—
527C22×C11—41no—
528C22×C11#52512yes—
529C22×C11#57712yes—
530C22×C11C23×D411yescharacteristic
531C2×D11—24no—
532C2×D11—48no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—162no—
539C4×C11—21no—
540C4×C11—21no—
541C4×C11—44no—
542C4×C11—41no—
543C4×C11—41no—
544C4×C11—41no—
545C4×C11#52512yes—
546C4×C11C22×#4112yes—
547Dic11—22no—
548Dic11—22no—
549Dic11—24no—
550Dic11—22no—
551Dic11—22no—
552Dic11—42no—
553C2×#41—112no—
554C2×#41—112no—
555C2×#41—228no—
556C2×#41—222no—
557C2×#41—221no—
558C2×#41—221no—
559C2×#41C22×D1111yescharacteristic
560C22×Q8—111no—
561C22×D4—111no—
562C22×D4—111no—
563C22×D4—221no—
564C22×D4—221no—
565C23×C4—21no—
566C23×C4—222no—
567C23×C4—221no—
568C23×C4C22×D1111yescharacteristic
569AGL(1,ℤ/8)—228no—
570#135—228no—
571C2×Q16—112no—
572C2×SD16—112no—
573C2×SD16—112no—
574C2×SD16—114no—
575C2×D8—112no—
576C2×D8—114no—
577C2×M16C22×D1112yes—
578C22×C8—112no—
579C4⋊Q8—112no—
580C4⋊Q8—221no—
581#127—112no—
582#126—222no—
583#126—222no—
584#125—112no—
585#125—221no—
586#124—112no—
587#124—222no—
588#124—222no—
589#123—21no—
590#123—222no—
591#123—222no—
592#123—222no—
593#123—222no—
594C22⋊Q8—222no—
595C22⋊Q8—222no—
596C22⋊Q8C22×D1111yescharacteristic
597C22⋊Q8C22×D1111yescharacteristic
598#121—112no—
599#121—112no—
600#121—222no—
601#121—222no—
602#121—221no—
603#121—221no—
604#121—222no—
605#121—221no—
606#121—221no—
607#121C22×D1111yescharacteristic
608#121C22×D1111yescharacteristic
609#120—21no—
610#120—222no—
611C4×Q8—112no—
612C4×Q8—114no—
613C4×Q8—114no—
614C4×Q8—222no—
615C4×Q8—222no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—112no—
619C4×D4—114no—
620C4×D4—114no—
621C4×D4—112no—
622C4×D4—112no—
623C4×D4—221no—
624C4×D4—221no—
625C4×D4—222no—
626C4×D4—222no—
627C4×D4—222no—
628C4×D4—222no—
629C4×D4—224no—
630C4×D4—224no—
631C4×D4—224no—
632C4×D4—224no—
633C4×D4—222no—
634#117—112no—
635#117—111no—
636#117—111no—
637#117—111no—
638#117—111no—
639#117—112no—
640#117—222no—
641#117—222no—
642#117—222no—
643#117—224no—
644#117—221no—
645#117C22×D1111yescharacteristic
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—111no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—111no—
652C2×C4⋊C4—222no—
653C2×C4⋊C4—222no—
654C2×C4⋊C4—224no—
655C2×C4⋊C4—221no—
656C2×C4⋊C4—222no—
657C2×C4⋊C4C22×D1112yes—
658C2×C4⋊C4C22×D1112yes—
659C2×C4⋊C4C22×D1112yes—
660C2×C22⋊C4—112no—
661C2×C22⋊C4—222no—
662C2×C22⋊C4—222no—
663C2×C22⋊C4—221no—
664C2×C42—112no—
665C2×C42—222no—
666#107C22×D1114yes—
667#106—114no—
668#106—114no—
669#106C22×D1114yes—
670C4⋊C8—114no—
671C4⋊C8—114no—
672#103—114no—
673#103—112no—
674#103—112no—
675#103C22×D1114yes—
676#102—114no—
677#102—114no—
678#102—114no—
679#102—112no—
680#102—112no—
681#102C22×D1114yes—
682C22⋊C8—111no—
683C22⋊C8—111no—
684C22⋊C8—112no—
685C22⋊C8C22×D1112yes—
686C22⋊C8C22×D1112yes—
687#97—114no—
688C4×C8—114no—
689C2×C11—22no—
690C2×C11—22no—
691C2×C11—41no—
692C2×C11—81no—
693C2×C11C2×#52511yescharacteristic
694C2×C11C2×#57711yescharacteristic
695C2×C11#358511yescharacteristic
696D11—44no—
697D11—82no—
698C24—221no—
699C24—221no—
700C24D4×D1111yescharacteristic
701#41—24no—
702#41—118no—
703#41—224no—
704#41—224no—
705#41—228no—
706#41—228no—
707#41—224no—
708#41—884no—
709C2×Q8—112no—
710C2×Q8—222no—
711C2×Q8—224no—
712C2×Q8—221no—
713C2×Q8C23×D1111yescharacteristic
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—112no—
718C2×D4—112no—
719C2×D4—224no—
720C2×D4—222no—
721C2×D4—222no—
722C2×D4—228no—
723C2×D4—222no—
724C2×D4—222no—
725C2×D4—222no—
726C2×D4—222no—
727C2×D4—221no—
728C2×D4—221no—
729C2×D4—224no—
730C2×D4—882no—
731C2×D4C23×D1111yescharacteristic
732C22×C4—24no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—21no—
737C22×C4—82no—
738C22×C4—112no—
739C22×C4—112no—
740C22×C4—222no—
741C22×C4—222no—
742C22×C4—224no—
743C22×C4—224no—
744C22×C4—228no—
745C22×C4—222no—
746C22×C4—221no—
747C22×C4—222no—
748C22×C4—222no—
749C22×C4—221no—
750C22×C4—884no—
751C22×C4D4×D1111yescharacteristic
752C22×C4D4×D1111yescharacteristic
753C22×C4D4×D1111yescharacteristic
754C22×C4C23×D1111yescharacteristic
755C22×C4C23×D1111yescharacteristic
756C22×C4C23×D1111yescharacteristic
757Q16—224no—
758SD16—228no—
759SD16—224no—
760SD16—224no—
761D8—228no—
762D8—224no—
763M16—24no—
764C2×C8—112no—
765C2×C8—112no—
766C2×C8—224no—
767C2×C8C23×D1114yes—
768C4⋊C4—22no—
769C4⋊C4—22no—
770C4⋊C4—22no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—111no—
774C4⋊C4—111no—
775C4⋊C4—112no—
776C4⋊C4—111no—
777C4⋊C4—111no—
778C4⋊C4—112no—
779C4⋊C4—112no—
780C4⋊C4—224no—
781C4⋊C4—224no—
782C4⋊C4—222no—
783C4⋊C4—222no—
784C4⋊C4—222no—
785C4⋊C4—222no—
786C4⋊C4—221no—
787C4⋊C4C23×D1114yes—
788C4⋊C4C23×D1111yescharacteristic
789C4⋊C4C23×D1111yescharacteristic
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—112no—
796C22⋊C4—112no—
797C22⋊C4—112no—
798C22⋊C4—112no—
799C22⋊C4—224no—
800C22⋊C4—224no—
801C22⋊C4—222no—
802C22⋊C4—222no—
803C22⋊C4—222no—
804C22⋊C4—222no—
805C22⋊C4—222no—
806C22⋊C4—222no—
807C22⋊C4—222no—
808C42—21no—
809C42—112no—
810C42—112no—
811C42—112no—
812C42—112no—
813C42—224no—
814C42—224no—
815C42—222no—
816C11#6058811yescharacteristic, complemented, Sylow
817C23—22no—
818C23—22no—
819C23—21no—
820C23—41no—
821C23—224no—
822C23—222no—
823C23—222no—
824C23—442no—
825C23—442no—
826C23—442no—
827C23—881no—
828C23—881no—
829C23C2×D4×D1111yescharacteristic
830C23C2×D4×D1111yescharacteristic
831C23C2×D4×D1111yescharacteristic
832Q8—22no—
833Q8—114no—
834Q8—224no—
835Q8—222no—
836Q8—882no—
837D4—22no—
838D4—42no—
839D4—42no—
840D4—81no—
841D4—114no—
842D4—224no—
843D4—228no—
844D4—228no—
845D4—222no—
846D4—224no—
847D4—444no—
848D4—442no—
849D4—882no—
850D4—882no—
851D4—882no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—24no—
861C2×C4—44no—
862C2×C4—42no—
863C2×C4—82no—
864C2×C4—82no—
865C2×C4—112no—
866C2×C4—112no—
867C2×C4—112no—
868C2×C4—112no—
869C2×C4—228no—
870C2×C4—224no—
871C2×C4—224no—
872C2×C4—222no—
873C2×C4—228no—
874C2×C4—222no—
875C2×C4—442no—
876C2×C4—884no—
877C2×C4—884no—
878C2×C4—882no—
879C2×C4—882no—
880C2×C4—882no—
881C2×C4—881no—
882C2×C4C2×D4×D1111yescharacteristic
883C2×C4C2×D4×D1111yescharacteristic
884C2×C4C2×D4×D1111yescharacteristic
885C2×C4#41×D1114yes—
886C2×C4C24×D1111yescharacteristic
887C8—24no—
888C8—222no—
889C8—222no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—44no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—224no—
902C22—448no—
903C22—442no—
904C22—442no—
905C22—442no—
906C22—442no—
907C22—442no—
908C22—1762no—
909C22#1062318712yes—
910C22#1062330912yes—
911C22C22×D4×D1111yescharacteristic
912C4—21no—
913C4—21no—
914C4—44no—
915C4—41no—
916C4—41no—
917C4—41no—
918C4—222no—
919C4—222no—
920C4—222no—
921C4—222no—
922C4—224no—
923C4—442no—
924C4#1062318712yes—
925C4C2×#41×D1112yes—
926C2—22no—
927C2—22no—
928C2—41no—
929C2—81no—
930C2—444no—
931C2—882no—
932C2C2×#1062318711yescharacteristic
933C2C2×#1062330911yescharacteristic
934C2#1308339211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3092C2
socleC22×C11C23×D4
hypercenter#3092D11
hypocenterC11#60588
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3092

Complements

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

NH ≅ G/Ntype
1. #13082353C2semidirect
2. C2×#10623035C2semidirect
3. #13078888C2semidirect
4. #13078818C2semidirect
5. #13078790C2semidirect
6. #13078704C2semidirect
7. #13078666C2semidirect
8. #13078644C2semidirect
9. C2×#10622581C2semidirect
10. #13078477C2semidirect
11. #13078154C2semidirect
12. #13077870C2semidirect
13. #13077832C2semidirect
14. #13077495C2semidirect
15. #13077446C2semidirect
16. #13077276C2semidirect
17. C11×#3092C2semidirect
21. #10623361C22semidirect
22. #10623358C22semidirect
29. #10623174C22semidirect
31. #10623150C22semidirect
38. #10623052C22semidirect
39. #10623050C22semidirect
45. #10623035C22semidirect
46. C2×#66946C22semidirect
49. C2×#66940C22semidirect
50. C11×#484C22semidirect
51. C11×#483C22semidirect
52. C11×#481C22semidirect
53. C11×#480C22semidirect
54. C11×#428C22semidirect
55. C11×#417C22semidirect
59. #10622735C22semidirect
60. #10622732C22semidirect
61. #10622663C22semidirect
62. #10622660C22semidirect
63. #10622659C22semidirect
64. #10622653C22semidirect
65. #10622650C22semidirect
66. #10622649C22semidirect
70. #10622581C22semidirect
71. C2×#66873C22semidirect
72. C2×#66872C22semidirect
73. #10622504C22semidirect
74. #10622502C22semidirect
75. #10622490C22semidirect
76. #10622485C22semidirect
77. #10622483C22semidirect
78. #10622482C22semidirect
79. #10622467C22semidirect
80. #10622465C22semidirect
81. #10622432C22semidirect
82. #10622411C22semidirect
83. #10622402C22semidirect
84. #10622401C22semidirect
85. #10622399C22semidirect
86. #10622398C22semidirect
87. #10622375C22semidirect
88. #10622371C22semidirect
92. #10622333C22semidirect
93. #10622332C22semidirect
94. #10622331C22semidirect
272. #4339#41semidirect
358. #3092D11semidirect
472. #484C2×D11semidirect
473. #483C2×D11semidirect
477. #481C2×D11semidirect
478. #480C2×D11semidirect
507. #428C2×D11semidirect
511. #417C2×D11semidirect
816. C11#60588semidirect

Maximal subgroups

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

subgroupindex
#130823532
C2×#106230352
#130788882
#130788182
#130787902
#130787042
#130786662
#130786442
C2×#106225812
#130784772
#130781542
#130778702
#130778322
#130774952
#130774462
#130772762
C11×#30922
#6058811