Finite Group Databasebeta

← #15622513

Subgroups — #15622513

Order 2816.

2274 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082353C211yesmaximal, characteristic, complemented
2C2×#10623052C211yesmaximal, characteristic, complemented
3#13078855C214yesmaximal, complemented
4#13078803C214yesmaximal, complemented
5#13078757C212yesmaximal, complemented
6#13078704C212yesmaximal, complemented
7#13078666C212yesmaximal, complemented
8#13078613C212yesmaximal, complemented
9#13078556C211yesmaximal, characteristic, complemented
10#13078450C212yesmaximal, complemented
11#13078122C212yesmaximal, complemented
12#13077842C211yesmaximal, characteristic, complemented
13C2×#10622345C211yesmaximal, characteristic, complemented
14#13077467C212yesmaximal, complemented
15#13077451C212yesmaximal, complemented
16#13077270C211yesmaximal, characteristic, complemented
17C11×#3091C211yesmaximal, characteristic, complemented
18C23×D44C2211yescharacteristic
19C11×#525C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21#10623361C2211yescharacteristic, complemented
22#10623358C2211yescharacteristic, complemented
23C2×#67002C2212yes—
24C2×#66983C2211yescharacteristic
25C2×#66979C2211yescharacteristic
26C22×D88C2212yes—
27#10623189—22no—
28#10623174C2212yescomplemented
29#10623155C2212yescomplemented
30#10623150C2212yescomplemented
31#10623127C2212yescomplemented
32#10623122—22no—
33#10623096—21no—
34#10623096—21no—
35#10623094—21no—
36#10623086—21no—
37#10623052—21no—
38#10623052—21no—
39#10623052—22no—
40#10623052C2212yes—
41#10623052C2212yes—
42#10623052C2214yescomplemented
43#10623052C2211yescharacteristic, complemented
44#10623050C2211yescharacteristic, complemented
45C2×#66946C2212yescomplemented
46C2×#66946C2212yescomplemented
47C2×C22⋊C4×D11—22no—
48C2×C4×D44—21no—
49C2×C4×D44—21no—
50C11×#485C2212yescomplemented
51C11×#484C2211yescharacteristic, complemented
52C11×#483C2211yescharacteristic, complemented
53C11×#482C2212yescomplemented
54C11×#481C2211yescharacteristic, complemented
55C11×#480C2211yescharacteristic, complemented
56C11×#427C2212yescomplemented
57C11×#416C2212yescomplemented
58C2×C11×C22⋊C8C2211yescharacteristic
59#10622820C2211yescharacteristic
60C2×#66885C2212yes—
61#10622715C2212yescomplemented
62#10622714C2212yescomplemented
63#10622659C2212yescomplemented
64#10622659C2212yescomplemented
65#10622649C2212yescomplemented
66#10622649C2212yescomplemented
67#10622616C2214yescomplemented
68#10622614C2212yes—
69#10622614C2212yescomplemented
70#10622608C2212yescomplemented
71#10622581C2212yescomplemented
72#10622580C2212yescomplemented
73#10622504C2214yescomplemented
74#10622503C2214yescomplemented
75#10622485C2214yescomplemented
76#10622485C2214yescomplemented
77#10622484C2214yescomplemented
78#10622483C2214yescomplemented
79#10622482C2214yescomplemented
80#10622482C2214yescomplemented
81#10622432C2214yescomplemented
82#10622432C2214yescomplemented
83#10622430C2214yescomplemented
84#10622401C2214yescomplemented
85#10622399C2214yescomplemented
86#10622399C2214yescomplemented
87#10622398C2214yescomplemented
88#10622369C2214yescomplemented
89#10622345C2214yes—
90#10622345C2212yes—
91#10622345C2212yes—
92#10622333C2214yescomplemented
93#10622332C2212yescomplemented
94#10622331C2212yescomplemented
95C24×D11—21no—
96C2×C11×#41C2311yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C22×C22⋊D11—21no—
99C2×#4341—22no—
100C22×D44—21no—
101C22×D44—21no—
102C22×D44—21no—
103C22×D44—28no—
104C22×D44C2311yescharacteristic
105C22×D44C2312yes—
106C22×D44C2312yes—
107C22×D44C2312yes—
108C22×C4×D11—22no—
109C22×C4×D11—22no—
110C22×C8×C11C2312yes—
111C11×#123—21no—
112C11×C22⋊Q8C2311yescharacteristic
113C11×C22⋊Q8C2311yescharacteristic
114C11×#121C2311yescharacteristic
115C11×#121C2311yescharacteristic
116C11×#120—21no—
117C4×D4×C11—21no—
118C4×D4×C11—21no—
119C11×#117—21no—
120C11×#117—21no—
121C11×#117C2311yescharacteristic
122C11×#117C2312yes—
123C11×#117C2312yes—
124C2×C11×C4⋊C4C2311yescharacteristic
125C2×C11×C4⋊C4C2311yescharacteristic
126C2×C11×C22⋊C4—21no—
127C2×C42×C11—21no—
128C2×C22⋊Dic11D412yes—
129#67002—28no—
130#67000C2312yescomplemented
131Q8×Dic11C2312yescomplemented
132C2×#4325C2314yes—
133#66993C2312yescomplemented
134#66992—22no—
135#66992—22no—
136#66991—22no—
137#66990—22no—
138D4×Dic11—22no—
139D4×Dic11C2312yescomplemented
140C2×#4323C2314yes—
141#66983—21no—
142#66983—21no—
143#66983—21no—
144#66983—21no—
145#66983C2312yes—
146#66983C2312yes—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4—22no—
149C2×(C2×D11)⋊C4—22no—
150#66979—21no—
151#66979D411yescharacteristic
152#66979D411yescharacteristic
153#66979D412yes—
154#66979C2311yescharacteristic
155#66979C2311yescharacteristic
156#66979C2312yes—
157C2×C4⋊Dic11—21no—
158C2×C4⋊Dic11D411yescharacteristic
159C2×C4⋊Dic11D411yescharacteristic
160C2×C4⋊Dic11C2311yescharacteristic
161C2×C4×Dic11C2312yes—
162C2×#4318C2312yes—
163C2×D88—28no—
164C2×D88C2314yes—
165C2×D88C2314yes—
166#66951—22no—
167#66951—22no—
168#66950—22no—
169#66946—22no—
170#66946—22no—
171#66946—22no—
172#66946—22no—
173#66946C2314yes—
174#66946C2314yes—
175#66946C2314yes—
176#66946C2314yes—
177#66946C2312yescomplemented
178#66946C2312yescomplemented
179#66945—22no—
180#66943C2312yescomplemented
181#66941C2312yescomplemented
182#66939—22no—
183#66939—22no—
184#66938—22no—
185#66938—22no—
186#66936—22no—
187#66936—22no—
188(C22⋊D11)⋊C4—22no—
189(C22⋊D11)⋊C4—22no—
190C22⋊C4×D11—24no—
191C22⋊C4×D11—24no—
192C22⋊C4×D11—24no—
193C22⋊C4×D11—24no—
194C22⋊C4×D11—22no—
195#66931—22no—
196C4×D44—22no—
197C4×D44—22no—
198C4×D44—22no—
199C4×D44—22no—
200C4×D44—24no—
201C4×D44—24no—
202C4×D44—21no—
203C4×D44—21no—
204#66923—21no—
205#66922—21no—
206C11×#107C2312yescomplemented
207C11×#107C2312yescomplemented
208C11×#106C2312yescomplemented
209C11×#106C2312yescomplemented
210C11×#103C2312yescomplemented
211C11×#103C2312yescomplemented
212C11×#102C2312yescomplemented
213C11×#102C2312yescomplemented
214C11×C22⋊C8C2311yescharacteristic
215C11×C22⋊C8C2311yescharacteristic
216C11×C22⋊C8C2312yes—
217C22⋊(C11⋊C8)C2312yes—
218C22⋊(C11⋊C8)C2312yes—
219#66885C2314yes—
220#66885C2314yes—
221#66879C2314yescomplemented
222Dic11⋊C8C2314yescomplemented
223Dic11⋊C8C2314yescomplemented
224C8×Dic11C2314yescomplemented
225#66873C2314yes—
226#66873C2314yes—
227#66873C2314yescomplemented
228#66873C2314yescomplemented
229#66872C2314yescomplemented
230#66871C2314yescomplemented
231#60578—111nomaximal, Sylow
232C24×C11C2×D411yescharacteristic
233C23×D11—22no—
234C23×D11—28no—
235C23×D11—22no—
236C23×D11—22no—
237C23×D11—21no—
238C23×D11—82no—
239C23×D11—82no—
240C11×#41—24no—
241C2×Q8×C11C2411yescharacteristic
242C2×D4×C11—21no—
243C2×D4×C11—21no—
244C2×D4×C11—21no—
245C2×D4×C11C2411yescharacteristic
246C22×C4×C11—24no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2411yescharacteristic
255C22×C4×C11C2411yescharacteristic
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×Dic11C2×D412yes—
264C22×Dic11C2×D412yes—
265#4341—84no—
266C2×D44—28no—
267C2×D44—28no—
268C2×D44—28no—
269C2×D44—28no—
270C2×D44—28no—
271C2×D44—22no—
272C2×D44—22no—
273C2×D44—22no—
274C2×D44—21no—
275C2×D44—24no—
276C2×D44—24no—
277C2×D44#4118yescomplemented
278C2×D44C2412yes—
279C2×D44C2414yes—
280C2×C4×D11—24no—
281C2×C4×D11—24no—
282C2×C4×D11—24no—
283C2×C4×D11—24no—
284C2×C4×D11—22no—
285C2×C4×D11—22no—
286C2×C4×D11—84no—
287C2×C4×D11—84no—
288C2×Dic22—22no—
289C2×C8×C11—24no—
290C2×C8×C11C2412yes—
291C2×C8×C11C2412yes—
292C11×C4⋊C4—21no—
293C11×C4⋊C4—21no—
294C11×C4⋊C4—21no—
295C11×C4⋊C4—21no—
296C11×C4⋊C4C2412yes—
297C11×C4⋊C4C2412yes—
298C11×C4⋊C4C2411yescharacteristic
299C11×C4⋊C4C2411yescharacteristic
300C11×C22⋊C4—21no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—22no—
303C11×C22⋊C4—21no—
304C11×C22⋊C4—21no—
305C11×C22⋊C4—21no—
306C11×C22⋊C4—21no—
307C42×C11—21no—
308C42×C11—22no—
309C42×C11—22no—
310C22⋊Dic11—22no—
311C22⋊Dic11C2×D412yes—
312C22⋊Dic11C2×D412yes—
313C22⋊Dic11C2×D412yes—
314C22⋊Dic11C2×D412yes—
315#4325—28no—
316#4323—28no—
317(C2×D11)⋊C4—24no—
318(C2×D11)⋊C4—24no—
319(C2×D11)⋊C4—24no—
320(C2×D11)⋊C4—24no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—22no—
327C4⋊Dic11—22no—
328C4⋊Dic11—22no—
329C4⋊Dic11—21no—
330C4⋊Dic11C2×D411yescharacteristic
331C4⋊Dic11C2×D411yescharacteristic
332C4⋊Dic11C2×D411yescharacteristic
333C4⋊Dic11C2×D411yescharacteristic
334C4⋊Dic11C2×D412yes—
335C4⋊Dic11C2×D412yes—
336C4⋊Dic11C2412yes—
337Dic11⋊C4—22no—
338Dic11⋊C4—22no—
339C4×Dic11—22no—
340C4×Dic11C2×D412yes—
341C4×Dic11C2×D412yes—
342C4×Dic11C2412yes—
343C4×Dic11C2412yes—
344#4318—24no—
345C2×C11⋊C8C2414yes—
346D88—28no—
347D88—28no—
348#3494—111no—
349C2×#518—111no—
350#3122—114no—
351#3118—114no—
352#3114—112no—
353#3109—112no—
354#3105—112no—
355#3100—112no—
356#3094—111no—
357#3091D1111yescharacteristic, complemented
358#3081—112no—
359#3041—112no—
360#3003—111no—
361C2×#447—111no—
362#2948—112no—
363#2946—112no—
364#2924—111no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—21no—
368C23×C11—41no—
369C23×C11C22×D411yescharacteristic
370C23×C11C22×D411yescharacteristic
371C23×C11C22×D411yescharacteristic
372C22×D11—28no—
373C22×D11—24no—
374C22×D11—28no—
375C22×D11—28no—
376C22×D11—22no—
377C22×D11—44no—
378C22×D11—44no—
379C22×D11—42no—
380C22×D11—82no—
381C22×D11—82no—
382C22×D11—82no—
383C22×D11—82no—
384C22×D11—816no—
385C22×D11—81no—
386C22×D11—81no—
387Q8×C11—22no—
388D4×C11—22no—
389D4×C11—42no—
390D4×C11—42no—
391D4×C11—81no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
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×C11C2×#4114yes—
409C2×C4×C11C2511yescharacteristic
410C22⋊D11—44no—
411C22⋊D11—82no—
412C22⋊D11—82no—
413C22⋊D11—82no—
414C2×Dic11—24no—
415C2×Dic11—22no—
416C2×Dic11—42no—
417C2×Dic11—82no—
418C2×Dic11—81no—
419C2×Dic11C22×D412yes—
420C2×Dic11C22×D412yes—
421C2×Dic11C22×D412yes—
422C2×Dic11C22×D412yes—
423D44—28no—
424D44—28no—
425D44—28no—
426D44—24no—
427D44—24no—
428D44—42no—
429D44C2×#4118yes—
430C4×D11—82no—
431C4×D11—84no—
432C4×D11—84no—
433C4×D11—84no—
434C4×D11—84no—
435C4×D11—82no—
436Dic22—82no—
437C8×C11—22no—
438C8×C11—22no—
439C11⋊C8—24no—
440C23×D4—111no—
441C2×AGL(1,ℤ/8)—112no—
442C22×D8—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#518—112no—
459#518—114no—
460#518—112no—
461#518—111no—
462#518—222no—
463#518—221no—
464#518—221no—
465C2×C4×D4—112no—
466C2×C4×D4—112no—
467C2×C4×D4—221no—
468C2×C4×D4—221no—
469C2×#117—111no—
470C2×#117C2×D1111yescharacteristic
471C22×C22⋊C4—222no—
472#485C2×D1112yescomplemented
473#484C2×D1111yescharacteristic, complemented
474#483C2×D1111yescharacteristic, complemented
475#482—114no—
476#482C2×D1112yescomplemented
477#481—112no—
478#481C2×D1111yescharacteristic, complemented
479#480—112no—
480#480C2×D1111yescharacteristic, complemented
481#478—114no—
482#478—114no—
483#476—114no—
484#474—114no—
485#463—114no—
486#463—114no—
487#459—114no—
488#459—114no—
489#450—112no—
490#450—112no—
491#447—112no—
492#447—112no—
493#447—112no—
494#447—112no—
495#447—114no—
496#442—114no—
497#442—114no—
498#442—114no—
499#440—114no—
500C4×SD16—114no—
501C4×D8—114no—
502C4×D8—114no—
503C4×D8—114no—
504#433—114no—
505#432—112no—
506#431—112no—
507#428—112no—
508#427C2×D1112yescomplemented
509#424—112no—
510#418—112no—
511#418—112no—
512#416C2×D1112yescomplemented
513C2×#102—112no—
514#407—111no—
515C2×C22⋊C8C2×D1111yescharacteristic
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#57612yes—
530C22×C11C23×D411yescharacteristic
531C2×D11—28no—
532C2×D11—416no—
533C2×D11—44no—
534C2×D11—44no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—88no—
539C2×D11—88no—
540C2×D11—162no—
541C4×C11—21no—
542C4×C11—21no—
543C4×C11—42no—
544C4×C11—41no—
545C4×C11—41no—
546C4×C11—42no—
547C4×C11—41no—
548C4×C11#52512yes—
549C4×C11C22×#4112yes—
550Dic11—22no—
551Dic11—22no—
552Dic11—22no—
553Dic11—22no—
554Dic11—42no—
555C25—221no—
556C2×#41—222no—
557C2×#41C22×D1111yescharacteristic
558C22×D4—112no—
559C22×D4—112no—
560C22×D4—112no—
561C22×D4—111no—
562C22×D4—228no—
563C22×D4—221no—
564C22×D4—221no—
565C22×D4—221no—
566C22×D4—221no—
567C23×C4—222no—
568C23×C4—222no—
569C23×C4C22×D1111yescharacteristic
570AGL(1,ℤ/8)—228no—
571C2×SD16—114no—
572C2×D8—114no—
573C2×D8—114no—
574C2×D8—114no—
575C2×D8—228no—
576C2×M16—112no—
577C22×C8C22×D1112yes—
578C4⋊Q8—112no—
579C4⋊Q8—221no—
580#127—112no—
581#126—222no—
582#126—222no—
583#125—112no—
584#125—221no—
585#124—112no—
586#124—222no—
587#124—222no—
588#123—21no—
589#123—222no—
590#123—222no—
591#123—222no—
592#123—222no—
593C22⋊Q8—222no—
594C22⋊Q8—222no—
595C22⋊Q8C22×D1111yescharacteristic
596C22⋊Q8C22×D1111yescharacteristic
597#121—112no—
598#121—112no—
599#121—222no—
600#121—222no—
601#121—221no—
602#121—221no—
603#121—222no—
604#121—221no—
605#121—221no—
606#121C22×D1111yescharacteristic
607#121C22×D1111yescharacteristic
608#120—21no—
609#120—222no—
610C4×Q8—112no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—112no—
614C4×D4—114no—
615C4×D4—114no—
616C4×D4—114no—
617C4×D4—114no—
618C4×D4—112no—
619C4×D4—112no—
620C4×D4—222no—
621C4×D4—222no—
622C4×D4—222no—
623C4×D4—222no—
624C4×D4—224no—
625C4×D4—224no—
626C4×D4—221no—
627C4×D4—221no—
628C4×D4—222no—
629C4×D4—222no—
630C4×D4—222no—
631C4×D4—222no—
632C4×D4—222no—
633C4×D4—222no—
634C4×D4—222no—
635#117—21no—
636#117—21no—
637#117—112no—
638#117—111no—
639#117—111no—
640#117—111no—
641#117—111no—
642#117—112no—
643#117—222no—
644#117—221no—
645#117C22×D1112yes—
646#117C22×D1112yes—
647#117C22×D1111yescharacteristic
648C2×C4⋊C4—111no—
649C2×C4⋊C4—111no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—221no—
652C2×C4⋊C4C22×D1111yescharacteristic
653C2×C4⋊C4C22×D1111yescharacteristic
654C2×C22⋊C4—21no—
655C2×C22⋊C4—112no—
656C2×C22⋊C4—224no—
657C2×C22⋊C4—224no—
658C2×C22⋊C4—224no—
659C2×C22⋊C4—224no—
660C2×C22⋊C4—222no—
661C2×C22⋊C4—222no—
662C2×C22⋊C4—222no—
663C2×C22⋊C4—221no—
664C2×C42—21no—
665C2×C42—112no—
666#107—114no—
667#107C22×D1112yescomplemented
668#107C22×D1112yescomplemented
669#106—114no—
670#106C22×D1112yescomplemented
671#106C22×D1112yescomplemented
672C4⋊C8—114no—
673C4⋊C8—114no—
674#103C22×D1112yescomplemented
675#103C22×D1112yescomplemented
676#102—114no—
677#102—114no—
678#102—114no—
679#102—114no—
680#102—114no—
681#102—114no—
682#102C22×D1112yescomplemented
683#102C22×D1112yescomplemented
684C22⋊C8—112no—
685C22⋊C8—112no—
686C22⋊C8C22×D1111yescharacteristic
687C22⋊C8C22×D1111yescharacteristic
688C22⋊C8C22×D1112yes—
689#97—114no—
690C4×C8—114no—
691C2×C11—22no—
692C2×C11—22no—
693C2×C11—41no—
694C2×C11—81no—
695C2×C11C2×#52511yescharacteristic
696C2×C11C2×#57611yescharacteristic
697C2×C11#358511yescharacteristic
698D11—48no—
699D11—82no—
700C24—228no—
701C24—222no—
702C24—222no—
703C24—222no—
704C24—221no—
705C24—882no—
706C24—882no—
707C24D4×D1111yescharacteristic
708#41—24no—
709#41—884no—
710C2×Q8—222no—
711C2×Q8C23×D1111yescharacteristic
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—118no—
716C2×D4—114no—
717C2×D4—112no—
718C2×D4—228no—
719C2×D4—228no—
720C2×D4—228no—
721C2×D4—228no—
722C2×D4—228no—
723C2×D4—222no—
724C2×D4—222no—
725C2×D4—222no—
726C2×D4—222no—
727C2×D4—222no—
728C2×D4—222no—
729C2×D4—222no—
730C2×D4—221no—
731C2×D4—224no—
732C2×D4—224no—
733C2×D4—882no—
734C2×D4C23×D1111yescharacteristic
735C22×C4—24no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—224no—
742C22×C4—224no—
743C22×C4—224no—
744C22×C4—224no—
745C22×C4—222no—
746C22×C4—222no—
747C22×C4—222no—
748C22×C4—221no—
749C22×C4—884no—
750C22×C4—884no—
751C22×C4D4×D1111yescharacteristic
752C22×C4D4×D1111yescharacteristic
753C22×C4D4×D1111yescharacteristic
754C22×C4C23×D1111yescharacteristic
755C22×C4C23×D1111yescharacteristic
756C22×C4C23×D1111yescharacteristic
757SD16—228no—
758D8—228no—
759D8—228no—
760D8—228no—
761M16—224no—
762C2×C8—24no—
763C2×C8—114no—
764C2×C8C23×D1112yes—
765C2×C8C23×D1112yes—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—111no—
771C4⋊C4—111no—
772C4⋊C4—111no—
773C4⋊C4—111no—
774C4⋊C4—112no—
775C4⋊C4—112no—
776C4⋊C4—112no—
777C4⋊C4—222no—
778C4⋊C4—222no—
779C4⋊C4—222no—
780C4⋊C4—222no—
781C4⋊C4—221no—
782C4⋊C4C23×D1111yescharacteristic
783C4⋊C4C23×D1111yescharacteristic
784C4⋊C4C23×D1112yes—
785C4⋊C4C23×D1112yes—
786C22⋊C4—22no—
787C22⋊C4—22no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—112no—
794C22⋊C4—112no—
795C22⋊C4—112no—
796C22⋊C4—112no—
797C22⋊C4—224no—
798C22⋊C4—224no—
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—22no—
809C42—22no—
810C42—21no—
811C42—112no—
812C42—112no—
813C42—112no—
814C42—112no—
815C42—222no—
816C11#6057811yescharacteristic, complemented, Sylow
817C23—22no—
818C23—22no—
819C23—21no—
820C23—41no—
821C23—228no—
822C23—228no—
823C23—224no—
824C23—228no—
825C23—222no—
826C23—444no—
827C23—444no—
828C23—442no—
829C23—882no—
830C23—882no—
831C23—882no—
832C23—882no—
833C23—881no—
834C23—881no—
835C23—8816no—
836C23C2×D4×D1111yescharacteristic
837C23C2×D4×D1111yescharacteristic
838C23C2×D4×D1111yescharacteristic
839Q8—22no—
840Q8—882no—
841D4—22no—
842D4—42no—
843D4—42no—
844D4—81no—
845D4—118no—
846D4—228no—
847D4—228no—
848D4—228no—
849D4—224no—
850D4—224no—
851D4—444no—
852D4—442no—
853D4—882no—
854D4—882no—
855D4—882no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—112no—
870C2×C4—112no—
871C2×C4—112no—
872C2×C4—112no—
873C2×C4—224no—
874C2×C4—222no—
875C2×C4—442no—
876C2×C4—884no—
877C2×C4—884no—
878C2×C4—884no—
879C2×C4—884no—
880C2×C4—882no—
881C2×C4—882no—
882C2×C4—882no—
883C2×C4—881no—
884C2×C4C2×D4×D1111yescharacteristic
885C2×C4C2×D4×D1111yescharacteristic
886C2×C4C2×D4×D1111yescharacteristic
887C2×C4#41×D1114yes—
888C2×C4C24×D1111yescharacteristic
889C8—22no—
890C8—22no—
891C8—224no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—44no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—228no—
904C22—4416no—
905C22—444no—
906C22—444no—
907C22—442no—
908C22—442no—
909C22—442no—
910C22—888no—
911C22—888no—
912C22—1762no—
913C22#1062318712yes—
914C22#1062330012yes—
915C22C22×D4×D1111yescharacteristic
916C4—21no—
917C4—21no—
918C4—42no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—41no—
923C4—222no—
924C4—222no—
925C4—222no—
926C4—222no—
927C4—442no—
928C4#1062318712yes—
929C4C2×#41×D1112yes—
930C2—22no—
931C2—22no—
932C2—41no—
933C2—81no—
934C2—448no—
935C2—882no—
936C2C2×#1062318711yescharacteristic
937C2C2×#1062330011yescharacteristic
938C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3091C2
socleC22×C11C23×D4
hypercenter#3091D11
hypocenterC11#60578
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3091

Complements

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

NH ≅ G/Ntype
1. #13082353C2semidirect
2. C2×#10623052C2semidirect
3. #13078855C2semidirect
4. #13078803C2semidirect
5. #13078757C2semidirect
6. #13078704C2semidirect
7. #13078666C2semidirect
8. #13078613C2semidirect
9. #13078556C2semidirect
10. #13078450C2semidirect
11. #13078122C2semidirect
12. #13077842C2semidirect
13. C2×#10622345C2semidirect
14. #13077467C2semidirect
15. #13077451C2semidirect
16. #13077270C2semidirect
17. C11×#3091C2semidirect
21. #10623361C22semidirect
22. #10623358C22semidirect
28. #10623174C22semidirect
29. #10623155C22semidirect
30. #10623150C22semidirect
31. #10623127C22semidirect
42. #10623052C22semidirect
43. #10623052C22semidirect
44. #10623050C22semidirect
45. C2×#66946C22semidirect
46. C2×#66946C22semidirect
50. C11×#485C22semidirect
51. C11×#484C22semidirect
52. C11×#483C22semidirect
53. C11×#482C22semidirect
54. C11×#481C22semidirect
55. C11×#480C22semidirect
56. C11×#427C22semidirect
57. C11×#416C22semidirect
61. #10622715C22semidirect
62. #10622714C22semidirect
63. #10622659C22semidirect
64. #10622659C22semidirect
65. #10622649C22semidirect
66. #10622649C22semidirect
67. #10622616C22semidirect
69. #10622614C22semidirect
70. #10622608C22semidirect
71. #10622581C22semidirect
72. #10622580C22semidirect
73. #10622504C22semidirect
74. #10622503C22semidirect
75. #10622485C22semidirect
76. #10622485C22semidirect
77. #10622484C22semidirect
78. #10622483C22semidirect
79. #10622482C22semidirect
80. #10622482C22semidirect
81. #10622432C22semidirect
82. #10622432C22semidirect
83. #10622430C22semidirect
84. #10622401C22semidirect
85. #10622399C22semidirect
86. #10622399C22semidirect
87. #10622398C22semidirect
88. #10622369C22semidirect
92. #10622333C22semidirect
93. #10622332C22semidirect
94. #10622331C22semidirect
130. #67000C23semidirect
131. Q8×Dic11C23semidirect
133. #66993C23semidirect
139. D4×Dic11C23semidirect
177. #66946C23semidirect
178. #66946C23semidirect
180. #66943C23semidirect
181. #66941C23semidirect
206. C11×#107C23semidirect
207. C11×#107C23semidirect
208. C11×#106C23semidirect
209. C11×#106C23semidirect
210. C11×#103C23semidirect
211. C11×#103C23semidirect
212. C11×#102C23semidirect
213. C11×#102C23semidirect
221. #66879C23semidirect
222. Dic11⋊C8C23semidirect
223. Dic11⋊C8C23semidirect
224. C8×Dic11C23semidirect
227. #66873C23semidirect
228. #66873C23semidirect
229. #66872C23semidirect
230. #66871C23semidirect
277. C2×D44#41semidirect
357. #3091D11semidirect
472. #485C2×D11semidirect
473. #484C2×D11semidirect
474. #483C2×D11semidirect
476. #482C2×D11semidirect
478. #481C2×D11semidirect
480. #480C2×D11semidirect
508. #427C2×D11semidirect
512. #416C2×D11semidirect
667. #107C22×D11semidirect
668. #107C22×D11semidirect
670. #106C22×D11semidirect
671. #106C22×D11semidirect
674. #103C22×D11semidirect
675. #103C22×D11semidirect
682. #102C22×D11semidirect
683. #102C22×D11semidirect
816. C11#60578semidirect

Maximal subgroups

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

subgroupindex
#130823532
C2×#106230522
#130788552
#130788032
#130787572
#130787042
#130786662
#130786132
#130785562
#130784502
#130781222
#130778422
C2×#106223452
#130774672
#130774512
#130772702
C11×#30912
#6057811