Finite Group Databasebeta

← #15622704

Subgroups — #15622704

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#13082351C211yesmaximal, characteristic, complemented
2C2×#10623054C211yesmaximal, characteristic, complemented
3#13078895C214yesmaximal, complemented
4#13078817C214yesmaximal, complemented
5#13078789C212yesmaximal, complemented
6#13078708C212yesmaximal, complemented
7#13078665C212yesmaximal, complemented
8#13078648C212yesmaximal, complemented
9#13078541C211yesmaximal, characteristic, complemented
10C2×#10622348C211yesmaximal, characteristic, complemented
11#13078480C212yesmaximal, complemented
12#13078157C212yesmaximal, complemented
13#13077870C211yesmaximal, characteristic, complemented
14#13077838C211yesmaximal, characteristic, complemented
15#13077501C212yesmaximal, complemented
16#13077450C212yesmaximal, complemented
17C11×#2924C211yesmaximal, characteristic, complemented
18C22×#4339C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20#10623322C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C2×#66961C2212yes—
24C2×#66957C2212yes—
25#10623066C2212yescomplemented
26#10623065C2212yescomplemented
27#10623063—21no—
28#10623061—21no—
29#10623058—22no—
30#10623056C2211yescharacteristic, complemented
31#10623054—22no—
32#10623054—21no—
33#10623054—21no—
34#10623054C2212yes—
35#10623054C2212yes—
36#10623054C2214yescomplemented
37#10623054C2211yescharacteristic, complemented
38#10623052C2211yescharacteristic, complemented
39#10623050C2211yescharacteristic, complemented
40#10623045—21no—
41#10623038—21no—
42C2×#66945—21no—
43C2×C4⋊C4×D11—21no—
44#10623021—22no—
45C2×(C22⋊D11)⋊C4—22no—
46#10623010C2212yes—
47#10623008C2212yes—
48C2×C4×D44C2212yescomplemented
49C2×C4×Dic22C2212yescomplemented
50C11×#433C2214yescomplemented
51C11×#432C2212yescomplemented
52C11×#431C2212yescomplemented
53C11×#424C2212yescomplemented
54C11×#407C2211yescharacteristic
55C2×C11×C22⋊C8C2211yescharacteristic
56C11×#405C2212yescomplemented
57#10622746C2212yes—
58#10622746C2212yescomplemented
59#10622734C2212yescomplemented
60#10622726C2212yes—
61C2×#66885C2212yescomplemented
62C2×#66881C2212yescomplemented
63#10622464C2214yescomplemented
64#10622461C2214yescomplemented
65#10622460C2214yescomplemented
66#10622458C2214yescomplemented
67#10622457C2214yescomplemented
68#10622456C2214yescomplemented
69#10622455C2214yescomplemented
70#10622442C2214yescomplemented
71#10622352C2211yescharacteristic, complemented
72#10622351C2212yes—
73#10622351C2211yescharacteristic, complemented
74#10622349C2212yescomplemented
75#10622348C2212yes—
76#10622348C2212yes—
77#10622348C2212yescomplemented
78#10622348C2214yescomplemented
79#10622347C2214yes—
80#10622347C2212yescomplemented
81#10622346C2212yescomplemented
82#10622345C2212yes—
83#10622345C2211yescharacteristic, complemented
84#10622344C2211yescharacteristic, complemented
85#10622335C2212yescomplemented
86#10622334C2212yescomplemented
87#10622329C2214yescomplemented
88#10622324C2214yescomplemented
89#10622324C2214yescomplemented
90#10622323C2214yescomplemented
91C4×D88C2214yescomplemented
92C4×#4314C2214yescomplemented
93C4×#4314C2214yescomplemented
94C4×#4314C2214yescomplemented
95C23×C4×C11C2311yescharacteristic
96C22×C22⋊D11—21no—
97C22×C22⋊D11—21no—
98C23×Dic11—21no—
99C2×#4339—21no—
100C2×#4339—21no—
101C2×#4339—28no—
102C2×#4339—22no—
103C2×#4339C2311yescharacteristic
104C2×#4339C2312yes—
105C2×#4339C2312yes—
106C22×D44C2311yescharacteristic
107C22×D44C2311yescharacteristic
108C22×C4×D11—21no—
109C22×C4×D11—22no—
110C22×Dic22C2311yescharacteristic
111C2×C11×M16C2312yes—
112C22×C8×C11C2312yes—
113C11×#117D412yes—
114C11×#117D411yescharacteristic
115C11×#117D411yescharacteristic
116C11×#117C2311yescharacteristic
117C11×#117C2311yescharacteristic
118C11×#117C2312yes—
119C2×C11×C4⋊C4D411yescharacteristic
120C2×C11×C4⋊C4D411yescharacteristic
121C2×C11×C22⋊C4D412yes—
122C2×C42×C11C2312yes—
123#67006—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—21no—
138#66979C2311yescharacteristic
139C2×C4⋊Dic11—21no—
140C2×C4⋊Dic11—21no—
141C2×C4⋊Dic11—21no—
142C2×C4⋊Dic11C2312yes—
143C2×C4⋊Dic11C2312yes—
144C2×C4⋊Dic11C2311yescharacteristic
145C2×C4⋊Dic11C2312yes—
146#66977C2311yescharacteristic
147#66977C2311yescharacteristic
148C2×Dic11⋊C4—22no—
149C2×C4×Dic11—22no—
150#66961—28no—
151C2×Dic44C2312yes—
152#66957—28no—
153C2×D88C2312yes—
154C2×D88C2314yes—
155C2×#4314C2312yes—
156C2×#4314C2312yes—
157C2×#4314C2314yes—
158#66951—22no—
159#66949—22no—
160#66948—21no—
161#66948—21no—
162#66947—22no—
163#66947—22no—
164#66946—21no—
165#66946—21no—
166#66945—22no—
167#66945—22no—
168#66945—24no—
169#66945—21no—
170C4⋊C4×D11—22no—
171C4⋊C4×D11—22no—
172C4⋊C4×D11—24no—
173C4⋊C4×D11—21no—
174#66943—21no—
175#66941—21no—
176#66938—22no—
177#66937—22no—
178#66937—22no—
179#66936—22no—
180#66935—22no—
181(C22⋊D11)⋊C4—24no—
182(C22⋊D11)⋊C4—24no—
183(C22⋊D11)⋊C4—24no—
184(C22⋊D11)⋊C4—24no—
185(C22⋊D11)⋊C4—22no—
186C22⋊C4×D11—22no—
187#66931—22no—
188#66929—22no—
189#66928—22no—
190#66928C2312yes—
191#66927C2312yes—
192C4×D44—22no—
193C4×D44—22no—
194C4×D44—22no—
195C4×D44C2314yes—
196C4×D44C2314yes—
197C4×D44C2312yes—
198C4×D44C2312yes—
199C4×D44C2312yes—
200#66925—22no—
201#66923C2312yes—
202#66922C2312yes—
203C4×Dic22—22no—
204C4×Dic22—22no—
205C4×Dic22C2314yes—
206C4×Dic22C2314yes—
207C4×Dic22C2312yes—
208C11×C4⋊C8C2314yes—
209C11×C4⋊C8C2314yes—
210C11×C22⋊C8C2312yes—
211C11×C22⋊C8C2312yes—
212C11×C22⋊C8C2311yescharacteristic
213C11×C22⋊C8C2311yescharacteristic
214C11×C22⋊C8C2312yes—
215C11×#97C2314yes—
216C4×C8×C11C2314yes—
217#66885C2314yes—
218#66885C2314yes—
219#66885C2312yes—
220#66885C2312yes—
221#66885C2314yes—
222#66885C2314yes—
223#66882C2314yes—
224#66881C2314yes—
225#66881C2314yes—
226#66881C2314yes—
227#66880C2312yes—
228#66880C2314yes—
229#66880C2312yes—
230#66880C2314yes—
231#60588—111nomaximal, Sylow
232C24×C11C2×D411yescharacteristic
233C23×D11—21no—
234C23×D11—21no—
235C22×C4×C11—24no—
236C22×C4×C11C2×D412yes—
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D412yes—
241C22×C4×C11C2411yescharacteristic
242C22×C4×C11C2411yescharacteristic
243C22×C4×C11C2411yescharacteristic
244C2×C22⋊D11—28no—
245C2×C22⋊D11—22no—
246C2×C22⋊D11—22no—
247C2×C22⋊D11—21no—
248C2×C22⋊D11—22no—
249C2×C22⋊D11—21no—
250C2×C22⋊D11—22no—
251C2×C22⋊D11—21no—
252C2×C22⋊D11—82no—
253C22×Dic11—21no—
254C22×Dic11—22no—
255C22×Dic11—21no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—82no—
259#4339—28no—
260#4339—28no—
261#4339—24no—
262#4339—24no—
263#4339—24no—
264#4339—24no—
265#4339—84no—
266#4339#4118yescomplemented
267C2×D44—24no—
268C2×D44—21no—
269C2×D44—21no—
270C2×D44—22no—
271C2×D44—22no—
272C2×D44—24no—
273C2×D44C2411yescharacteristic
274C2×D44C2412yes—
275C2×D44C2412yes—
276C2×C4×D11—28no—
277C2×C4×D11—22no—
278C2×C4×D11—22no—
279C2×C4×D11—21no—
280C2×C4×D11—22no—
281C2×C4×D11—22no—
282C2×C4×D11—24no—
283C2×C4×D11—24no—
284C2×C4×D11—22no—
285C2×C4×D11—84no—
286C2×Dic22—24no—
287C2×Dic22—21no—
288C2×Dic22—22no—
289C2×Dic22C2411yescharacteristic
290C2×Dic22C2412yes—
291C11×M16—24no—
292C2×C8×C11—24no—
293C2×C8×C11C2414yes—
294C2×C8×C11C2412yes—
295C2×C8×C11C2412yes—
296C11×C4⋊C4C2×D411yescharacteristic
297C11×C4⋊C4C2×D411yescharacteristic
298C11×C4⋊C4C2×D411yescharacteristic
299C11×C4⋊C4C2×D412yes—
300C11×C4⋊C4C2×D411yescharacteristic
301C11×C4⋊C4C2×D412yes—
302C11×C22⋊C4C2×D412yes—
303C11×C22⋊C4C2×D412yes—
304C11×C22⋊C4C2×D412yes—
305C11×C22⋊C4C2×D412yes—
306C42×C11C2×D412yes—
307C42×C11C2×D412yes—
308C42×C11C2412yes—
309C42×C11C2412yes—
310C22⋊Dic11—21no—
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—22no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4—21no—
323(C2×D11)⋊C4—22no—
324C4⋊Dic11—22no—
325C4⋊Dic11—22no—
326C4⋊Dic11—21no—
327C4⋊Dic11—22no—
328C4⋊Dic11—22no—
329C4⋊Dic11C2412yes—
330C4⋊Dic11C2411yescharacteristic
331C4⋊Dic11C2411yescharacteristic
332C4⋊Dic11C2414yes—
333Dic11⋊C4—24no—
334Dic11⋊C4—24no—
335Dic11⋊C4—22no—
336Dic11⋊C4—22no—
337Dic11⋊C4—22no—
338Dic11⋊C4—21no—
339Dic11⋊C4—21no—
340C4×Dic11—24no—
341C4×Dic11—24no—
342C4×Dic11—22no—
343C4×Dic11—21no—
344Dic44—24no—
345D88—24no—
346D88—28no—
347#4314—24no—
348#4314—24no—
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#3092—111no—
359C2×#481—111no—
360#3084—112no—
361#3045—112no—
362#3006—111no—
363#3002—111no—
364#2952—112no—
365#2946—112no—
366#2924D1111yescharacteristic, complemented
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—41no—
370C23×C11C22×D411yescharacteristic
371C23×C11C22×D411yescharacteristic
372C23×C11C22×D411yescharacteristic
373C22×D11—24no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—21no—
377C22×D11—42no—
378C22×D11—42no—
379C22×D11—42no—
380C22×D11—81no—
381C22×D11—81no—
382C2×C4×C11—22no—
383C2×C4×C11—24no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—42no—
389C2×C4×C11C22×D412yes—
390C2×C4×C11C22×D412yes—
391C2×C4×C11C22×D412yes—
392C2×C4×C11C22×D412yes—
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C2×#4114yes—
397C2×C4×C11C2511yescharacteristic
398C22⋊D11—28no—
399C22⋊D11—28no—
400C22⋊D11—42no—
401C22⋊D11—42no—
402C22⋊D11—44no—
403C22⋊D11—81no—
404C22⋊D11—82no—
405C2×Dic11—24no—
406C2×Dic11—22no—
407C2×Dic11—21no—
408C2×Dic11—24no—
409C2×Dic11—21no—
410C2×Dic11—22no—
411C2×Dic11—21no—
412C2×Dic11—44no—
413C2×Dic11—82no—
414C2×Dic11—82no—
415C2×Dic11—81no—
416D44—24no—
417D44—22no—
418D44—24no—
419D44—22no—
420D44—42no—
421D44—82no—
422D44—82no—
423D44C2×#4114yes—
424C4×D11—28no—
425C4×D11—28no—
426C4×D11—42no—
427C4×D11—82no—
428C4×D11—84no—
429C4×D11—84no—
430C4×D11—82no—
431C4×D11—82no—
432Dic22—24no—
433Dic22—22no—
434Dic22—22no—
435Dic22—82no—
436Dic22C2×#4114yes—
437C8×C11—22no—
438C8×C11—24no—
439C8×C11—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#525—111no—
456C2×#121—111no—
457#520—112no—
458#520—114no—
459#520—112no—
460#520—111no—
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—221no—
469C2×#117C2×D1111yescharacteristic
470C22×C4⋊C4—111no—
471C22×C4⋊C4—221no—
472#484—112no—
473#483—112no—
474#481—112no—
475#481—112no—
476#481—114no—
477#481—112no—
478#480—112no—
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—112no—
495#447—111no—
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#433C2×D1114yescomplemented
505#432C2×D1112yescomplemented
506#431C2×D1112yescomplemented
507#428—112no—
508C2×#106—112no—
509#424C2×D1112yescomplemented
510#417—112no—
511#417—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#57712yes—
527C22×C11C23×D411yescharacteristic
528C2×D11—24no—
529C2×D11—48no—
530C2×D11—42no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—41no—
534C2×D11—42no—
535C2×D11—41no—
536C2×D11—42no—
537C2×D11—41no—
538C2×D11—162no—
539C4×C11—22no—
540C4×C11—22no—
541C4×C11—21no—
542C4×C11—21no—
543C4×C11—22no—
544C4×C11—22no—
545C4×C11#52512yes—
546C4×C11C22×#4112yes—
547Dic11—24no—
548Dic11—44no—
549Dic11—41no—
550Dic11—41no—
551Dic11—41no—
552Dic11—42no—
553C2×#41—112no—
554C2×#41—112no—
555C2×#41—111no—
556C2×#41—228no—
557C2×#41—221no—
558C2×#41—221no—
559C2×#41—222no—
560C22×Q8—111no—
561C22×D4—111no—
562C22×D4—111no—
563C22×D4—221no—
564C22×D4—221no—
565C23×C4—221no—
566C23×C4—221no—
567C23×C4—222no—
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×C8C22×D1112yes—
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—221no—
590#123—222no—
591#123—222no—
592#123—222no—
593#123—222no—
594C22⋊Q8—111no—
595C22⋊Q8—111no—
596C22⋊Q8—222no—
597C22⋊Q8—222no—
598#121—112no—
599#121—112no—
600#121—111no—
601#121—111no—
602#121—221no—
603#121—221no—
604#121—222no—
605#121—221no—
606#121—221no—
607#121—222no—
608#121—222no—
609#120—221no—
610#120—222no—
611C4×Q8—114no—
612C4×Q8—114no—
613C4×Q8—112no—
614C4×Q8—222no—
615C4×Q8—222no—
616C4×D4—114no—
617C4×D4—114no—
618C4×D4—112no—
619C4×D4—112no—
620C4×D4—112no—
621C4×D4—221no—
622C4×D4—221no—
623C4×D4—222no—
624C4×D4—221no—
625C4×D4—221no—
626C4×D4—224no—
627C4×D4—224no—
628C4×D4—224no—
629C4×D4—224no—
630C4×D4—222no—
631C4×D4—222no—
632C4×D4—222no—
633C4×D4—222no—
634#117—111no—
635#117—222no—
636#117—222no—
637#117—224no—
638#117—221no—
639#117—222no—
640#117D4412yes—
641#117D4411yescharacteristic
642#117D4411yescharacteristic
643#117C22×D1111yescharacteristic
644#117C22×D1111yescharacteristic
645#117C22×D1112yes—
646C2×C4⋊C4—112no—
647C2×C4⋊C4—112no—
648C2×C4⋊C4—112no—
649C2×C4⋊C4—111no—
650C2×C4⋊C4—221no—
651C2×C4⋊C4—221no—
652C2×C4⋊C4—221no—
653C2×C4⋊C4—222no—
654C2×C4⋊C4—222no—
655C2×C4⋊C4—222no—
656C2×C4⋊C4—224no—
657C2×C4⋊C4—221no—
658C2×C4⋊C4D4411yescharacteristic
659C2×C4⋊C4D4411yescharacteristic
660C2×C22⋊C4—222no—
661C2×C22⋊C4—221no—
662C2×C22⋊C4—222no—
663C2×C22⋊C4D4412yes—
664C2×C42—222no—
665C2×C42C22×D1112yes—
666#107—114no—
667#106—114no—
668#106—114no—
669#106—114no—
670C4⋊C8C22×D1114yes—
671C4⋊C8C22×D1114yes—
672#103—112no—
673#103—112no—
674#103—114no—
675#103—114no—
676#102—114no—
677#102—114no—
678#102—112no—
679#102—112no—
680#102—114no—
681#102—114no—
682C22⋊C8C22×D1111yescharacteristic
683C22⋊C8C22×D1111yescharacteristic
684C22⋊C8C22×D1112yes—
685C22⋊C8C22×D1112yes—
686C22⋊C8C22×D1112yes—
687#97C22×D1114yes—
688C4×C8C22×D1114yes—
689C2×C11—22no—
690C2×C11—22no—
691C2×C11—41no—
692C2×C11C2×#52511yescharacteristic
693C2×C11C2×#57711yescharacteristic
694C2×C11#358511yescharacteristic
695D11—44no—
696D11—81no—
697D11—82no—
698C24—221no—
699C24—221no—
700C24C2×D4411yescharacteristic
701#41—118no—
702#41—224no—
703#41—224no—
704#41—228no—
705#41—228no—
706#41—224no—
707#41—224no—
708#41—884no—
709C2×Q8—112no—
710C2×Q8—111no—
711C2×Q8—224no—
712C2×Q8—221no—
713C2×Q8—222no—
714C2×D4—112no—
715C2×D4—112no—
716C2×D4—111no—
717C2×D4—224no—
718C2×D4—228no—
719C2×D4—222no—
720C2×D4—222no—
721C2×D4—221no—
722C2×D4—221no—
723C2×D4—222no—
724C2×D4—221no—
725C2×D4—222no—
726C2×D4—221no—
727C2×D4—221no—
728C2×D4—222no—
729C2×D4—222no—
730C2×D4—224no—
731C2×D4—882no—
732C22×C4—24no—
733C22×C4—228no—
734C22×C4—221no—
735C22×C4—222no—
736C22×C4—222no—
737C22×C4—222no—
738C22×C4—221no—
739C22×C4—222no—
740C22×C4—222no—
741C22×C4—221no—
742C22×C4—222no—
743C22×C4—222no—
744C22×C4—224no—
745C22×C4—224no—
746C22×C4—222no—
747C22×C4—884no—
748C22×C4—882no—
749C22×C4C2×D4412yes—
750C22×C4C2×D4411yescharacteristic
751C22×C4C2×D4411yescharacteristic
752C22×C4C2×D4411yescharacteristic
753C22×C4C2×D4412yes—
754C22×C4C23×D1111yescharacteristic
755C22×C4C23×D1111yescharacteristic
756C22×C4C23×D1111yescharacteristic
757Q16—224no—
758SD16—224no—
759SD16—224no—
760SD16—228no—
761D8—224no—
762D8—228no—
763M16—24no—
764C2×C8—24no—
765C2×C8C23×D1112yes—
766C2×C8C23×D1114yes—
767C2×C8C23×D1112yes—
768C4⋊C4—114no—
769C4⋊C4—112no—
770C4⋊C4—111no—
771C4⋊C4—111no—
772C4⋊C4—222no—
773C4⋊C4—222no—
774C4⋊C4—222no—
775C4⋊C4—221no—
776C4⋊C4—224no—
777C4⋊C4—224no—
778C4⋊C4—222no—
779C4⋊C4—221no—
780C4⋊C4—222no—
781C4⋊C4—222no—
782C4⋊C4—222no—
783C4⋊C4—221no—
784C4⋊C4C2×D4411yescharacteristic
785C4⋊C4C2×D4411yescharacteristic
786C4⋊C4C2×D4412yes—
787C4⋊C4C2×D4411yescharacteristic
788C4⋊C4C2×D4411yescharacteristic
789C4⋊C4C2×D4412yes—
790C22⋊C4—221no—
791C22⋊C4—221no—
792C22⋊C4—221no—
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—224no—
809C42—224no—
810C42—221no—
811C42—222no—
812C42C2×D4412yes—
813C42C2×D4412yes—
814C42C23×D1112yes—
815C42C23×D1112yes—
816C11#6058811yescharacteristic, complemented, Sylow
817C23—22no—
818C23—22no—
819C23—41no—
820C23—224no—
821C23—222no—
822C23—222no—
823C23—221no—
824C23—442no—
825C23—442no—
826C23—442no—
827C23—881no—
828C23—881no—
829C23C22×D4411yescharacteristic
830C23C22×D4411yescharacteristic
831C23C22×D4411yescharacteristic
832Q8—114no—
833Q8—224no—
834Q8—222no—
835Q8—222no—
836Q8—882no—
837D4—114no—
838D4—224no—
839D4—228no—
840D4—228no—
841D4—222no—
842D4—224no—
843D4—222no—
844D4—444no—
845D4—442no—
846D4—442no—
847D4—442no—
848D4—882no—
849D4—882no—
850D4—882no—
851D4—881no—
852C2×C4—24no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—42no—
859C2×C4—228no—
860C2×C4—224no—
861C2×C4—222no—
862C2×C4—228no—
863C2×C4—221no—
864C2×C4—224no—
865C2×C4—221no—
866C2×C4—221no—
867C2×C4—222no—
868C2×C4—444no—
869C2×C4—442no—
870C2×C4—884no—
871C2×C4—884no—
872C2×C4—882no—
873C2×C4—882no—
874C2×C4—882no—
875C2×C4—882no—
876C2×C4—882no—
877C2×C4—881no—
878C2×C4C22×D4412yes—
879C2×C4C22×D4412yes—
880C2×C4C22×D4412yes—
881C2×C4C22×D4411yescharacteristic
882C2×C4C22×D4412yes—
883C2×C4C22×D4411yescharacteristic
884C2×C4C22×D4411yescharacteristic
885C2×C4#41×D1114yes—
886C2×C4C24×D1111yescharacteristic
887C8—22no—
888C8—22no—
889C8—24no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—44no—
898C22—224no—
899C22—448no—
900C22—442no—
901C22—442no—
902C22—441no—
903C22—442no—
904C22—442no—
905C22—441no—
906C22—441no—
907C22—442no—
908C22—1762no—
909C22#1062305512yes—
910C22#1062328212yes—
911C22C23×D4411yescharacteristic
912C4—21no—
913C4—21no—
914C4—22no—
915C4—22no—
916C4—22no—
917C4—22no—
918C4—224no—
919C4—441no—
920C4—444no—
921C4—441no—
922C4—442no—
923C4—441no—
924C4#1062305512yes—
925C4C2×#41×D1112yes—
926C2—22no—
927C2—22no—
928C2—41no—
929C2—444no—
930C2—882no—
931C2—881no—
932C2C2×#1062305511yescharacteristic
933C2C2×#1062328211yescharacteristic
934C2#1308339711yescharacteristic
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2924C2
socleC22×C11C23×D4
hypercenter#2924D11
hypocenterC11#60588
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×#10623054C2semidirect
3. #13078895C2semidirect
4. #13078817C2semidirect
5. #13078789C2semidirect
6. #13078708C2semidirect
7. #13078665C2semidirect
8. #13078648C2semidirect
9. #13078541C2semidirect
10. C2×#10622348C2semidirect
11. #13078480C2semidirect
12. #13078157C2semidirect
13. #13077870C2semidirect
14. #13077838C2semidirect
15. #13077501C2semidirect
16. #13077450C2semidirect
17. C11×#2924C2semidirect
25. #10623066C22semidirect
26. #10623065C22semidirect
30. #10623056C22semidirect
36. #10623054C22semidirect
37. #10623054C22semidirect
38. #10623052C22semidirect
39. #10623050C22semidirect
48. C2×C4×D44C22semidirect
49. C2×C4×Dic22C22semidirect
50. C11×#433C22semidirect
51. C11×#432C22semidirect
52. C11×#431C22semidirect
53. C11×#424C22semidirect
56. C11×#405C22semidirect
58. #10622746C22semidirect
59. #10622734C22semidirect
61. C2×#66885C22semidirect
62. C2×#66881C22semidirect
63. #10622464C22semidirect
64. #10622461C22semidirect
65. #10622460C22semidirect
66. #10622458C22semidirect
67. #10622457C22semidirect
68. #10622456C22semidirect
69. #10622455C22semidirect
70. #10622442C22semidirect
71. #10622352C22semidirect
73. #10622351C22semidirect
74. #10622349C22semidirect
77. #10622348C22semidirect
78. #10622348C22semidirect
80. #10622347C22semidirect
81. #10622346C22semidirect
83. #10622345C22semidirect
84. #10622344C22semidirect
85. #10622335C22semidirect
86. #10622334C22semidirect
87. #10622329C22semidirect
88. #10622324C22semidirect
89. #10622324C22semidirect
90. #10622323C22semidirect
91. C4×D88C22semidirect
92. C4×#4314C22semidirect
93. C4×#4314C22semidirect
94. C4×#4314C22semidirect
266. #4339#41semidirect
366. #2924D11semidirect
504. #433C2×D11semidirect
505. #432C2×D11semidirect
506. #431C2×D11semidirect
509. #424C2×D11semidirect
516. #405C2×D11semidirect
816. C11#60588semidirect

Maximal subgroups

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

subgroupindex
#130823512
C2×#106230542
#130788952
#130788172
#130787892
#130787082
#130786652
#130786482
#130785412
C2×#106223482
#130784802
#130781572
#130778702
#130778382
#130775012
#130774502
C11×#29242
#6058811