Finite Group Databasebeta

← #15622512

Subgroups — #15622512

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#13082351C211yesmaximal, characteristic, complemented
2C2×#10623052C211yesmaximal, characteristic, complemented
3#13078860C214yesmaximal, complemented
4#13078802C214yesmaximal, complemented
5#13078756C212yesmaximal, complemented
6#13078708C212yesmaximal, complemented
7#13078665C212yesmaximal, complemented
8#13078617C212yesmaximal, complemented
9#13078557C211yesmaximal, characteristic, complemented
10#13078531C211yesmaximal, characteristic, complemented
11#13078448C212yesmaximal, complemented
12#13078120C212yesmaximal, complemented
13#13077846C211yesmaximal, characteristic, complemented
14C2×#10622345C211yesmaximal, characteristic, complemented
15#13077469C212yesmaximal, complemented
16#13077450C212yesmaximal, complemented
17C11×#2924C211yesmaximal, characteristic, complemented
18C23×D44C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20#10623322C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C2×#66961C2212yes—
24C22×D88C2212yes—
25#10623066C2212yescomplemented
26#10623065C2212yescomplemented
27#10623063—21no—
28#10623061—21no—
29#10623058—22no—
30#10623056C2211yescharacteristic, complemented
31#10623054C2211yescharacteristic, complemented
32#10623052—22no—
33#10623052—21no—
34#10623052—21no—
35#10623052C2212yes—
36#10623052C2212yes—
37#10623052C2214yescomplemented
38#10623052C2211yescharacteristic, complemented
39#10623050C2211yescharacteristic, complemented
40#10623045—21no—
41#10623038—21no—
42C2×#66946—21no—
43C2×#66946—21no—
44#10623021—22no—
45C2×C22⋊C4×D11—22no—
46#10623010C2212yescomplemented
47#10623008C2212yescomplemented
48C2×C4×D44C2212yescomplemented
49C2×C4×D44C2212yescomplemented
50C11×#433C2214yescomplemented
51C11×#432C2212yescomplemented
52C11×#431C2212yescomplemented
53C11×#424C2212yescomplemented
54C11×#407C2211yescharacteristic
55C2×C11×C22⋊C8C2211yescharacteristic
56C11×#405C2212yescomplemented
57#10622744C2212yes—
58#10622744C2212yescomplemented
59#10622734C2212yescomplemented
60#10622726C2212yescomplemented
61C2×#66885C2212yes—
62#10622719C2212yescomplemented
63#10622460C2214yescomplemented
64#10622460C2214yescomplemented
65#10622459C2214yescomplemented
66#10622457C2214yescomplemented
67#10622457C2214yescomplemented
68#10622456C2214yescomplemented
69#10622456C2214yescomplemented
70#10622455C2214yescomplemented
71#10622350C2212yescomplemented
72#10622350C2214yescomplemented
73#10622349C2211yescharacteristic, complemented
74#10622349C2212yescomplemented
75#10622348C2211yescharacteristic, complemented
76#10622348C2212yescomplemented
77#10622345C2214yes—
78#10622345C2212yes—
79#10622345C2212yes—
80#10622345C2212yescomplemented
81#10622345C2212yescomplemented
82#10622344C2212yescomplemented
83#10622344C2212yescomplemented
84#10622336C2212yescomplemented
85#10622335C2211yescharacteristic, complemented
86#10622334C2211yescharacteristic, complemented
87#10622324C2214yescomplemented
88#10622324C2214yescomplemented
89#10622324C2214yescomplemented
90#10622323C2214yescomplemented
91C4×D88C2214yescomplemented
92C4×D88C2214yescomplemented
93C4×D88C2214yescomplemented
94C4×#4314C2214yescomplemented
95C24×D11—21no—
96C23×C4×C11C2311yescharacteristic
97C22×C22⋊D11—21no—
98C2×#4339—22no—
99C2×#4339C2311yescharacteristic
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—
110C2×C11×M16C2312yes—
111C22×C8×C11C2312yes—
112C11×#117D412yes—
113C11×#117D411yescharacteristic
114C11×#117D411yescharacteristic
115C11×#117C2311yescharacteristic
116C11×#117C2311yescharacteristic
117C11×#117C2312yes—
118C2×C11×C4⋊C4D411yescharacteristic
119C2×C11×C4⋊C4D411yescharacteristic
120C2×C11×C22⋊C4D412yes—
121C2×C42×C11C2312yes—
122#67006—21no—
123C2×C22⋊Dic11—21no—
124#66983—22no—
125#66983—21no—
126#66983—21no—
127#66983C2311yescharacteristic
128#66983C2312yes—
129#66983C2312yes—
130#66983C2311yescharacteristic
131#66982—22no—
132#66982—21no—
133C4×C22⋊D11—22no—
134C4×C22⋊D11—21no—
135C4×C22⋊D11—21no—
136C2×(C2×D11)⋊C4—22no—
137C2×(C2×D11)⋊C4—22no—
138C2×(C2×D11)⋊C4—21no—
139#66979—21no—
140#66979—21no—
141#66979C2312yes—
142#66979C2311yescharacteristic
143#66979C2312yes—
144C2×C4⋊Dic11C2311yescharacteristic
145C2×C4⋊Dic11C2311yescharacteristic
146C2×C4⋊Dic11C2311yescharacteristic
147#66977C2311yescharacteristic
148#66977C2311yescharacteristic
149C2×C4×Dic11—21no—
150#66961—28no—
151C2×D88—28no—
152C2×D88C2314yes—
153C2×D88C2314yes—
154C2×D88C2314yes—
155C2×#4314C2314yes—
156#66951—22no—
157#66949—22no—
158#66948—21no—
159#66948—21no—
160#66947—22no—
161#66947—22no—
162#66946—22no—
163#66946—22no—
164#66946—22no—
165#66946—22no—
166#66946—24no—
167#66946—24no—
168#66946—21no—
169#66946—21no—
170#66945—21no—
171C4⋊C4×D11—21no—
172#66943—21no—
173#66941—21no—
174#66938—22no—
175#66937—22no—
176#66937—22no—
177#66936—22no—
178#66935—22no—
179(C22⋊D11)⋊C4—22no—
180C22⋊C4×D11—24no—
181C22⋊C4×D11—24no—
182C22⋊C4×D11—24no—
183C22⋊C4×D11—24no—
184C22⋊C4×D11—22no—
185#66931—22no—
186#66929—22no—
187#66928—22no—
188#66928C2312yescomplemented
189#66927C2312yescomplemented
190C4×D44—22no—
191C4×D44—22no—
192C4×D44—22no—
193C4×D44—22no—
194C4×D44—22no—
195C4×D44C2314yes—
196C4×D44C2314yes—
197C4×D44C2314yes—
198C4×D44C2314yes—
199C4×D44C2312yescomplemented
200C4×D44C2312yescomplemented
201C4×D44C2312yescomplemented
202#66925—22no—
203#66923C2312yescomplemented
204#66922C2312yescomplemented
205C4×Dic22C2312yescomplemented
206C11×C4⋊C8C2314yescomplemented
207C11×C4⋊C8C2314yescomplemented
208C11×C22⋊C8C2311yescharacteristic
209C11×C22⋊C8C2311yescharacteristic
210C11×C22⋊C8C2312yes—
211C11×C22⋊C8C2312yes—
212C11×C22⋊C8C2312yes—
213C11×#97C2314yescomplemented
214C4×C8×C11C2314yescomplemented
215#66885C2314yes—
216#66885C2314yes—
217#66885C2314yes—
218#66885C2314yes—
219#66885C2312yescomplemented
220#66885C2312yescomplemented
221#66885C2314yescomplemented
222#66885C2314yescomplemented
223#66882C2314yescomplemented
224#66882C2312yescomplemented
225#66882C2312yescomplemented
226#66881C2314yescomplemented
227#66881C2312yescomplemented
228#66881C2312yescomplemented
229#66880C2312yescomplemented
230#66880C2312yescomplemented
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—
240C22×C4×C11—24no—
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D412yes—
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2411yescharacteristic
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C2×C22⋊D11—21no—
250C2×C22⋊D11—22no—
251C2×C22⋊D11—21no—
252C2×C22⋊D11—22no—
253C2×C22⋊D11—21no—
254C2×C22⋊D11—82no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258#4339—24no—
259#4339—84no—
260C2×D44—28no—
261C2×D44—28no—
262C2×D44—28no—
263C2×D44—28no—
264C2×D44—28no—
265C2×D44—22no—
266C2×D44—22no—
267C2×D44—22no—
268C2×D44—21no—
269C2×D44—22no—
270C2×D44—22no—
271C2×D44—24no—
272C2×D44—24no—
273C2×D44#4118yescomplemented
274C2×D44C2411yescharacteristic
275C2×D44C2412yes—
276C2×D44C2414yes—
277C2×C4×D11—21no—
278C2×C4×D11—22no—
279C2×C4×D11—24no—
280C2×C4×D11—24no—
281C2×C4×D11—24no—
282C2×C4×D11—24no—
283C2×C4×D11—22no—
284C2×C4×D11—22no—
285C2×C4×D11—84no—
286C2×C4×D11—84no—
287C2×Dic22—22no—
288C2×Dic22C2411yescharacteristic
289C11×M16—24no—
290C2×C8×C11—24no—
291C2×C8×C11C2412yes—
292C2×C8×C11C2412yes—
293C2×C8×C11C2414yes—
294C11×C4⋊C4C2×D411yescharacteristic
295C11×C4⋊C4C2×D411yescharacteristic
296C11×C4⋊C4C2×D411yescharacteristic
297C11×C4⋊C4C2×D411yescharacteristic
298C11×C4⋊C4C2×D412yes—
299C11×C4⋊C4C2×D412yes—
300C11×C22⋊C4C2×D412yes—
301C11×C22⋊C4C2×D412yes—
302C11×C22⋊C4C2×D412yes—
303C11×C22⋊C4C2×D412yes—
304C42×C11C2×D412yes—
305C42×C11C2×D412yes—
306C42×C11C2412yes—
307C42×C11C2412yes—
308C22⋊Dic11—21no—
309C22⋊Dic11—22no—
310C22⋊Dic11—22no—
311C22⋊Dic11—21no—
312C22⋊Dic11—21no—
313(C2×D11)⋊C4—22no—
314(C2×D11)⋊C4—22no—
315(C2×D11)⋊C4—21no—
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)⋊C4—22no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—21no—
325(C2×D11)⋊C4—22no—
326C4⋊Dic11—22no—
327C4⋊Dic11—21no—
328C4⋊Dic11—21no—
329C4⋊Dic11—21no—
330C4⋊Dic11C2412yes—
331C4⋊Dic11C2412yes—
332C4⋊Dic11C2412yes—
333C4⋊Dic11C2411yescharacteristic
334C4⋊Dic11C2411yescharacteristic
335Dic11⋊C4—22no—
336Dic11⋊C4—22no—
337Dic11⋊C4—22no—
338Dic11⋊C4—21no—
339Dic11⋊C4—21no—
340C4×Dic11—22no—
341C4×Dic11—21no—
342C4×Dic11—22no—
343C4×Dic11—22no—
344D88—28no—
345D88—28no—
346D88—28no—
347#4314—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#3091—111no—
358#3081—112no—
359#3041—112no—
360#3003—111no—
361C2×#447—111no—
362#2948—112no—
363#2946—112no—
364#2924D1111yescharacteristic, complemented
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—41no—
368C23×C11C22×D411yescharacteristic
369C23×C11C22×D411yescharacteristic
370C23×C11C22×D411yescharacteristic
371C22×D11—28no—
372C22×D11—24no—
373C22×D11—28no—
374C22×D11—28no—
375C22×D11—22no—
376C22×D11—21no—
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—
387C2×C4×C11—22no—
388C2×C4×C11—24no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—42no—
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D412yes—
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D412yes—
398C2×C4×C11C22×D412yes—
399C2×C4×C11C22×D412yes—
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C2×#4114yes—
402C2×C4×C11C2511yescharacteristic
403C22⋊D11—42no—
404C22⋊D11—42no—
405C22⋊D11—44no—
406C22⋊D11—81no—
407C22⋊D11—82no—
408C2×Dic11—21no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—21no—
412C2×Dic11—22no—
413C2×Dic11—21no—
414C2×Dic11—42no—
415C2×Dic11—42no—
416C2×Dic11—81no—
417D44—28no—
418D44—28no—
419D44—28no—
420D44—24no—
421D44—24no—
422D44—22no—
423D44—42no—
424D44—82no—
425D44—82no—
426D44C2×#4118yes—
427C4×D11—42no—
428C4×D11—82no—
429C4×D11—84no—
430C4×D11—84no—
431C4×D11—84no—
432C4×D11—84no—
433C4×D11—82no—
434C4×D11—82no—
435Dic22—22no—
436Dic22—82no—
437C8×C11—24no—
438C8×C11—22no—
439C8×C11—22no—
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#525—111no—
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#485—112no—
473#484—111no—
474#483—111no—
475#482—112no—
476#482—114no—
477#481—111no—
478#481—112no—
479#480—111no—
480#480—112no—
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—114no—
495#447—112no—
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#433C2×D1114yescomplemented
505#432C2×D1112yescomplemented
506#431C2×D1112yescomplemented
507#428—112no—
508#427—112no—
509#424C2×D1112yescomplemented
510#418—112no—
511#418—112no—
512#416—112no—
513C2×#102—112no—
514#407C2×D1111yescharacteristic
515C2×C22⋊C8C2×D1111yescharacteristic
516#405C2×D1112yescomplemented
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#52512yes—
526C22×C11#57612yes—
527C22×C11C23×D411yescharacteristic
528C2×D11—28no—
529C2×D11—416no—
530C2×D11—44no—
531C2×D11—44no—
532C2×D11—42no—
533C2×D11—41no—
534C2×D11—42no—
535C2×D11—41no—
536C2×D11—42no—
537C2×D11—41no—
538C2×D11—88no—
539C2×D11—88no—
540C2×D11—162no—
541C4×C11—22no—
542C4×C11—22no—
543C4×C11—21no—
544C4×C11—21no—
545C4×C11—22no—
546C4×C11—22no—
547C4×C11#52512yes—
548C4×C11C22×#4112yes—
549Dic11—42no—
550Dic11—41no—
551Dic11—41no—
552Dic11—41no—
553Dic11—42no—
554Dic11—42no—
555C25—221no—
556C2×#41—111no—
557C2×#41—222no—
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×M16C22×D1112yes—
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—221no—
589#123—222no—
590#123—222no—
591#123—222no—
592#123—222no—
593C22⋊Q8—111no—
594C22⋊Q8—111no—
595C22⋊Q8—222no—
596C22⋊Q8—222no—
597#121—112no—
598#121—112no—
599#121—111no—
600#121—111no—
601#121—221no—
602#121—221no—
603#121—222no—
604#121—221no—
605#121—221no—
606#121—222no—
607#121—222no—
608#120—221no—
609#120—222no—
610C4×Q8—112no—
611C4×D4—114no—
612C4×D4—114no—
613C4×D4—114no—
614C4×D4—114no—
615C4×D4—112no—
616C4×D4—112no—
617C4×D4—112no—
618C4×D4—221no—
619C4×D4—221no—
620C4×D4—222no—
621C4×D4—222no—
622C4×D4—222no—
623C4×D4—222no—
624C4×D4—222no—
625C4×D4—224no—
626C4×D4—224no—
627C4×D4—221no—
628C4×D4—221no—
629C4×D4—222no—
630C4×D4—222no—
631C4×D4—222no—
632C4×D4—222no—
633C4×D4—222no—
634C4×D4—222no—
635#117—112no—
636#117—112no—
637#117—111no—
638#117—221no—
639#117—221no—
640#117—221no—
641#117—222no—
642#117D4412yes—
643#117D4411yescharacteristic
644#117D4411yescharacteristic
645#117C22×D1111yescharacteristic
646#117C22×D1111yescharacteristic
647#117C22×D1112yes—
648C2×C4⋊C4—111no—
649C2×C4⋊C4—111no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—221no—
652C2×C4⋊C4D4411yescharacteristic
653C2×C4⋊C4D4411yescharacteristic
654C2×C22⋊C4—221no—
655C2×C22⋊C4—222no—
656C2×C22⋊C4—222no—
657C2×C22⋊C4—221no—
658C2×C22⋊C4—224no—
659C2×C22⋊C4—224no—
660C2×C22⋊C4—224no—
661C2×C22⋊C4—224no—
662C2×C22⋊C4—222no—
663C2×C22⋊C4D4412yes—
664C2×C42—221no—
665C2×C42C22×D1112yes—
666#107—112no—
667#107—112no—
668#107—114no—
669#106—112no—
670#106—112no—
671#106—114no—
672C4⋊C8C22×D1114yescomplemented
673C4⋊C8C22×D1114yescomplemented
674#103—112no—
675#103—112no—
676#102—114no—
677#102—114no—
678#102—114no—
679#102—114no—
680#102—112no—
681#102—112no—
682#102—114no—
683#102—114no—
684C22⋊C8C22×D1111yescharacteristic
685C22⋊C8C22×D1111yescharacteristic
686C22⋊C8C22×D1112yes—
687C22⋊C8C22×D1112yes—
688C22⋊C8C22×D1112yes—
689#97C22×D1114yescomplemented
690C4×C8C22×D1114yescomplemented
691C2×C11—22no—
692C2×C11—22no—
693C2×C11—41no—
694C2×C11C2×#52511yescharacteristic
695C2×C11C2×#57611yescharacteristic
696C2×C11#358511yescharacteristic
697D11—48no—
698D11—81no—
699D11—82no—
700C24—228no—
701C24—222no—
702C24—222no—
703C24—222no—
704C24—221no—
705C24—882no—
706C24—882no—
707C24C2×D4411yescharacteristic
708#41—224no—
709#41—884no—
710C2×Q8—111no—
711C2×Q8—222no—
712C2×D4—118no—
713C2×D4—114no—
714C2×D4—112no—
715C2×D4—111no—
716C2×D4—228no—
717C2×D4—228no—
718C2×D4—228no—
719C2×D4—228no—
720C2×D4—228no—
721C2×D4—221no—
722C2×D4—221no—
723C2×D4—222no—
724C2×D4—221no—
725C2×D4—222no—
726C2×D4—222no—
727C2×D4—222no—
728C2×D4—222no—
729C2×D4—221no—
730C2×D4—222no—
731C2×D4—222no—
732C2×D4—224no—
733C2×D4—224no—
734C2×D4—882no—
735C22×C4—24no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—224no—
741C22×C4—224no—
742C22×C4—224no—
743C22×C4—224no—
744C22×C4—222no—
745C22×C4—222no—
746C22×C4—222no—
747C22×C4—884no—
748C22×C4—884no—
749C22×C4C2×D4411yescharacteristic
750C22×C4C2×D4412yes—
751C22×C4C2×D4411yescharacteristic
752C22×C4C2×D4411yescharacteristic
753C22×C4C2×D4412yes—
754C22×C4C23×D1111yescharacteristic
755C22×C4C23×D1111yescharacteristic
756C22×C4C23×D1111yescharacteristic
757SD16—228no—
758D8—228no—
759D8—228no—
760D8—228no—
761M16—24no—
762C2×C8—24no—
763C2×C8C23×D1112yes—
764C2×C8C23×D1114yes—
765C2×C8C23×D1112yes—
766C4⋊C4—112no—
767C4⋊C4—111no—
768C4⋊C4—111no—
769C4⋊C4—112no—
770C4⋊C4—112no—
771C4⋊C4—221no—
772C4⋊C4—221no—
773C4⋊C4—221no—
774C4⋊C4—222no—
775C4⋊C4—221no—
776C4⋊C4—222no—
777C4⋊C4—222no—
778C4⋊C4—222no—
779C4⋊C4—221no—
780C4⋊C4C2×D4411yescharacteristic
781C4⋊C4C2×D4411yescharacteristic
782C4⋊C4C2×D4411yescharacteristic
783C4⋊C4C2×D4411yescharacteristic
784C4⋊C4C2×D4412yes—
785C4⋊C4C2×D4412yes—
786C22⋊C4—222no—
787C22⋊C4—222no—
788C22⋊C4—221no—
789C22⋊C4—221no—
790C22⋊C4—221no—
791C22⋊C4—224no—
792C22⋊C4—224no—
793C22⋊C4—224no—
794C22⋊C4—224no—
795C22⋊C4—222no—
796C22⋊C4—222no—
797C22⋊C4—222no—
798C22⋊C4—222no—
799C22⋊C4—222no—
800C22⋊C4—222no—
801C22⋊C4—221no—
802C22⋊C4—222no—
803C22⋊C4—221no—
804C22⋊C4C2×D4412yes—
805C22⋊C4C2×D4412yes—
806C22⋊C4C2×D4412yes—
807C22⋊C4C2×D4412yes—
808C42—222no—
809C42—222no—
810C42—221no—
811C42—222no—
812C42C2×D4412yes—
813C42C2×D4412yes—
814C42C23×D1112yes—
815C42C23×D1112yes—
816C11#6057811yescharacteristic, complemented, Sylow
817C23—22no—
818C23—22no—
819C23—41no—
820C23—228no—
821C23—228no—
822C23—224no—
823C23—228no—
824C23—222no—
825C23—221no—
826C23—444no—
827C23—444no—
828C23—442no—
829C23—882no—
830C23—882no—
831C23—882no—
832C23—882no—
833C23—881no—
834C23—881no—
835C23—8816no—
836C23C22×D4411yescharacteristic
837C23C22×D4411yescharacteristic
838C23C22×D4411yescharacteristic
839Q8—222no—
840Q8—882no—
841D4—118no—
842D4—228no—
843D4—228no—
844D4—228no—
845D4—224no—
846D4—224no—
847D4—222no—
848D4—444no—
849D4—442no—
850D4—442no—
851D4—442no—
852D4—882no—
853D4—882no—
854D4—882no—
855D4—881no—
856C2×C4—24no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—42no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—221no—
866C2×C4—221no—
867C2×C4—221no—
868C2×C4—222no—
869C2×C4—442no—
870C2×C4—442no—
871C2×C4—442no—
872C2×C4—884no—
873C2×C4—884no—
874C2×C4—884no—
875C2×C4—884no—
876C2×C4—882no—
877C2×C4—882no—
878C2×C4—882no—
879C2×C4—881no—
880C2×C4C22×D4411yescharacteristic
881C2×C4C22×D4412yes—
882C2×C4C22×D4411yescharacteristic
883C2×C4C22×D4412yes—
884C2×C4C22×D4412yes—
885C2×C4C22×D4412yes—
886C2×C4C22×D4411yescharacteristic
887C2×C4#41×D1114yes—
888C2×C4C24×D1111yescharacteristic
889C8—22no—
890C8—22no—
891C8—24no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—44no—
900C22—228no—
901C22—4416no—
902C22—444no—
903C22—444no—
904C22—441no—
905C22—442no—
906C22—442no—
907C22—441no—
908C22—441no—
909C22—442no—
910C22—888no—
911C22—888no—
912C22—1762no—
913C22#1062305512yes—
914C22#1062328312yes—
915C22C23×D4411yescharacteristic
916C4—21no—
917C4—21no—
918C4—22no—
919C4—22no—
920C4—22no—
921C4—22no—
922C4—441no—
923C4—442no—
924C4—441no—
925C4—442no—
926C4—442no—
927C4—441no—
928C4#1062305512yes—
929C4C2×#41×D1112yes—
930C2—22no—
931C2—22no—
932C2—41no—
933C2—448no—
934C2—882no—
935C2—881no—
936C2C2×#1062305511yescharacteristic
937C2C2×#1062328311yescharacteristic
938C2#1308339711yescharacteristic
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2924C2
socleC22×C11C23×D4
hypercenter#2924D11
hypocenterC11#60578
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
1. #13082351C2semidirect
2. C2×#10623052C2semidirect
3. #13078860C2semidirect
4. #13078802C2semidirect
5. #13078756C2semidirect
6. #13078708C2semidirect
7. #13078665C2semidirect
8. #13078617C2semidirect
9. #13078557C2semidirect
10. #13078531C2semidirect
11. #13078448C2semidirect
12. #13078120C2semidirect
13. #13077846C2semidirect
14. C2×#10622345C2semidirect
15. #13077469C2semidirect
16. #13077450C2semidirect
17. C11×#2924C2semidirect
25. #10623066C22semidirect
26. #10623065C22semidirect
30. #10623056C22semidirect
31. #10623054C22semidirect
37. #10623052C22semidirect
38. #10623052C22semidirect
39. #10623050C22semidirect
46. #10623010C22semidirect
47. #10623008C22semidirect
48. C2×C4×D44C22semidirect
49. C2×C4×D44C22semidirect
50. C11×#433C22semidirect
51. C11×#432C22semidirect
52. C11×#431C22semidirect
53. C11×#424C22semidirect
56. C11×#405C22semidirect
58. #10622744C22semidirect
59. #10622734C22semidirect
60. #10622726C22semidirect
62. #10622719C22semidirect
63. #10622460C22semidirect
64. #10622460C22semidirect
65. #10622459C22semidirect
66. #10622457C22semidirect
67. #10622457C22semidirect
68. #10622456C22semidirect
69. #10622456C22semidirect
70. #10622455C22semidirect
71. #10622350C22semidirect
72. #10622350C22semidirect
73. #10622349C22semidirect
74. #10622349C22semidirect
75. #10622348C22semidirect
76. #10622348C22semidirect
80. #10622345C22semidirect
81. #10622345C22semidirect
82. #10622344C22semidirect
83. #10622344C22semidirect
84. #10622336C22semidirect
85. #10622335C22semidirect
86. #10622334C22semidirect
87. #10622324C22semidirect
88. #10622324C22semidirect
89. #10622324C22semidirect
90. #10622323C22semidirect
91. C4×D88C22semidirect
92. C4×D88C22semidirect
93. C4×D88C22semidirect
94. C4×#4314C22semidirect
188. #66928C23semidirect
189. #66927C23semidirect
199. C4×D44C23semidirect
200. C4×D44C23semidirect
201. C4×D44C23semidirect
203. #66923C23semidirect
204. #66922C23semidirect
205. C4×Dic22C23semidirect
206. C11×C4⋊C8C23semidirect
207. C11×C4⋊C8C23semidirect
213. C11×#97C23semidirect
214. C4×C8×C11C23semidirect
219. #66885C23semidirect
220. #66885C23semidirect
221. #66885C23semidirect
222. #66885C23semidirect
223. #66882C23semidirect
224. #66882C23semidirect
225. #66882C23semidirect
226. #66881C23semidirect
227. #66881C23semidirect
228. #66881C23semidirect
229. #66880C23semidirect
230. #66880C23semidirect
273. C2×D44#41semidirect
364. #2924D11semidirect
504. #433C2×D11semidirect
505. #432C2×D11semidirect
506. #431C2×D11semidirect
509. #424C2×D11semidirect
516. #405C2×D11semidirect
672. C4⋊C8C22×D11semidirect
673. C4⋊C8C22×D11semidirect
689. #97C22×D11semidirect
690. C4×C8C22×D11semidirect
816. C11#60578semidirect

Maximal subgroups

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

subgroupindex
#130823512
C2×#106230522
#130788602
#130788022
#130787562
#130787082
#130786652
#130786172
#130785572
#130785312
#130784482
#130781202
#130778462
C2×#106223452
#130774692
#130774502
C11×#29242
#6057811