Finite Group Databasebeta

← #15622510

Subgroups — #15622510

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
2#13078859C214yesmaximal, complemented
3#13078800C214yesmaximal, complemented
4#13078754C212yesmaximal, complemented
5#13078707C212yesmaximal, complemented
6#13078663C212yesmaximal, complemented
7#13078616C212yesmaximal, complemented
8#13078556C211yesmaximal, characteristic, complemented
9#13078529C211yesmaximal, characteristic, complemented
10#13078447C212yesmaximal, complemented
11#13078119C212yesmaximal, complemented
12#13077843C211yesmaximal, characteristic, complemented
13C2×#10622830C211yesmaximal, characteristic, complemented
14#13077466C212yesmaximal, complemented
15#13077448C212yesmaximal, complemented
16#13077274C211yesmaximal, characteristic, complemented
17C2×C11×#518C211yesmaximal, characteristic, complemented
18C23×D4×C11C2211yescharacteristic
19C11×#518—22no—
20C11×#518—21no—
21C11×#518—21no—
22C11×#518C2212yes—
23C11×#518C2212yes—
24C11×#518C2214yescomplemented
25C2×C4×D4×C11—21no—
26C2×C4×D4×C11—21no—
27C2×C4×D4×C11C2212yescomplemented
28C2×C4×D4×C11C2212yescomplemented
29C2×C11×#117C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31C22×C11×C22⋊C4—22no—
32C2×#66985C2212yes—
33C22×#4323C2212yes—
34#10623322C2211yescharacteristic
35C2×#66983C2211yescharacteristic
36#10623066C2212yescomplemented
37#10623065C2212yescomplemented
38#10623063—21no—
39#10623061—21no—
40#10623058—22no—
41#10623056C2211yescharacteristic, complemented
42#10623054C2211yescharacteristic, complemented
43#10623052C2211yescharacteristic, complemented
44#10623050C2211yescharacteristic, complemented
45#10623045—21no—
46#10623038—21no—
47#10623021—22no—
48#10623010C2212yescomplemented
49#10623008C2212yescomplemented
50#10622831C2212yescomplemented
51#10622831C2212yescomplemented
52#10622830C2214yes—
53#10622830C2212yes—
54#10622830C2212yes—
55#10622830C2212yescomplemented
56#10622830C2212yescomplemented
57#10622828C2212yes—
58C2×#66896C2212yes—
59#10622820C2211yescharacteristic
60C2×C22⋊(C11⋊C8)C2211yescharacteristic
61#10622631C2214yescomplemented
62C4×#4324C2214yescomplemented
63#10622629C2214yescomplemented
64#10622629C2214yescomplemented
65#10622628C2214yescomplemented
66#10622628C2214yescomplemented
67#10622627C2214yescomplemented
68#10622627C2214yescomplemented
69#10622627C2214yescomplemented
70C4×#4323C2214yescomplemented
71C4×#4323C2214yescomplemented
72C4×#4323C2214yescomplemented
73#10622622C2214yescomplemented
74#10622622C2214yescomplemented
75#10622621C2214yescomplemented
76#10622620C2214yescomplemented
77#10622616C2212yescomplemented
78#10622616C2214yescomplemented
79#10622615C2212yescomplemented
80#10622614C2212yescomplemented
81#10622613C2214yescomplemented
82#10622612C2212yescomplemented
83#10622611C2212yescomplemented
84#10622610C2212yescomplemented
85#10622609C2212yescomplemented
86#10622608C2212yescomplemented
87#10622584C2211yescharacteristic, complemented
88#10622583C2211yescharacteristic, complemented
89#10622581C2211yescharacteristic, complemented
90#10622581C2212yescomplemented
91#10622580C2211yescharacteristic, complemented
92#10622580C2212yescomplemented
93#10622539C2212yescomplemented
94#10622538C2212yescomplemented
95C25×C11—21no—
96C22×D4×C11—28no—
97C22×D4×C11—21no—
98C22×D4×C11—21no—
99C22×D4×C11—21no—
100C22×D4×C11C2312yes—
101C22×D4×C11C2312yes—
102C22×D4×C11C2312yes—
103C23×C4×C11—22no—
104C23×C4×C11—22no—
105C23×C4×C11C2311yescharacteristic
106C22×C22⋊D11—21no—
107C2×#4339—22no—
108C2×#4339C2311yescharacteristic
109C22×D44C2311yescharacteristic
110C4×D4×C11—22no—
111C4×D4×C11—22no—
112C4×D4×C11—22no—
113C4×D4×C11—22no—
114C4×D4×C11—24no—
115C4×D4×C11—24no—
116C4×D4×C11—22no—
117C4×D4×C11—22no—
118C4×D4×C11—22no—
119C4×D4×C11—22no—
120C4×D4×C11C2314yes—
121C4×D4×C11C2314yes—
122C4×D4×C11C2314yes—
123C4×D4×C11C2314yes—
124C11×#117—21no—
125C11×#117—21no—
126C11×#117D412yes—
127C11×#117D411yescharacteristic
128C11×#117D411yescharacteristic
129C11×#117C2312yes—
130C11×#117C2312yes—
131C11×#117C2311yescharacteristic
132C11×#117C2311yescharacteristic
133C11×#117C2312yes—
134C2×C11×C4⋊C4D411yescharacteristic
135C2×C11×C4⋊C4D411yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4—22no—
140C2×C11×C22⋊C4—22no—
141C2×C11×C22⋊C4—24no—
142C2×C11×C22⋊C4—24no—
143C2×C11×C22⋊C4—24no—
144C2×C11×C22⋊C4—24no—
145C2×C11×C22⋊C4D412yes—
146C2×C42×C11—21no—
147C2×C42×C11C2312yes—
148#67006—21no—
149C2×#4324C2314yes—
150#66985—28no—
151C2×#4323—28no—
152C2×#4323C2314yes—
153C2×#4323C2314yes—
154C2×#4323C2314yes—
155#66983—22no—
156#66983—21no—
157#66983—21no—
158#66983C2311yescharacteristic
159#66983C2312yes—
160#66983C2312yes—
161#66983C2311yescharacteristic
162#66982—22no—
163#66982—21no—
164C4×C22⋊D11—22no—
165C4×C22⋊D11—21no—
166C4×C22⋊D11—21no—
167C2×(C2×D11)⋊C4—21no—
168#66979C2311yescharacteristic
169C2×C4⋊Dic11C2311yescharacteristic
170#66977C2311yescharacteristic
171#66977C2311yescharacteristic
172C2×#4318C2312yes—
173C22×C11⋊C8C2312yes—
174#66951—22no—
175#66949—22no—
176#66948—21no—
177#66948—21no—
178#66947—22no—
179#66947—22no—
180#66946—21no—
181#66946—21no—
182#66945—21no—
183C4⋊C4×D11—21no—
184#66943—21no—
185#66941—21no—
186#66938—22no—
187#66937—22no—
188#66937—22no—
189#66936—22no—
190#66935—22no—
191(C22⋊D11)⋊C4—22no—
192C22⋊C4×D11—22no—
193#66931—22no—
194#66929—22no—
195#66928—22no—
196#66928C2312yescomplemented
197#66927C2312yescomplemented
198C4×D44—22no—
199C4×D44C2312yescomplemented
200C4×D44C2312yescomplemented
201C4×D44C2312yescomplemented
202#66925—22no—
203#66923C2312yescomplemented
204#66922C2312yescomplemented
205C4×Dic22C2312yescomplemented
206#66896C2314yes—
207#66896C2314yes—
208#66896C2314yes—
209#66896C2314yes—
210C22⋊(C11⋊C8)C2311yescharacteristic
211C22⋊(C11⋊C8)C2312yes—
212C22⋊(C11⋊C8)C2311yescharacteristic
213C22⋊(C11⋊C8)C2312yes—
214C22⋊(C11⋊C8)C2312yes—
215#66874C2312yescomplemented
216#66874C2312yescomplemented
217#66873C2314yescomplemented
218#66873C2312yescomplemented
219#66873C2314yescomplemented
220#66873C2312yescomplemented
221#66872C2314yescomplemented
222#66872C2312yescomplemented
223#66872C2312yescomplemented
224#66871C2314yescomplemented
225#66871C2312yescomplemented
226#66871C2312yescomplemented
227C4⋊(C11⋊C8)C2314yescomplemented
228C4⋊(C11⋊C8)C2314yescomplemented
229#66867C2314yescomplemented
230C4×C11⋊C8C2314yescomplemented
231#60578—111nomaximal, Sylow
232C24×C11—28no—
233C24×C11—22no—
234C24×C11—22no—
235C24×C11—22no—
236C24×C11—82no—
237C24×C11—82no—
238C24×C11C2×D411yescharacteristic
239C23×D11—21no—
240C2×D4×C11—28no—
241C2×D4×C11—28no—
242C2×D4×C11—28no—
243C2×D4×C11—28no—
244C2×D4×C11—28no—
245C2×D4×C11—22no—
246C2×D4×C11—22no—
247C2×D4×C11—22no—
248C2×D4×C11—24no—
249C2×D4×C11#4118yescomplemented
250C2×D4×C11C2414yes—
251C22×C4×C11—24no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—24no—
255C22×C4×C11—24no—
256C22×C4×C11—24no—
257C22×C4×C11—24no—
258C22×C4×C11—84no—
259C22×C4×C11—84no—
260C22×C4×C11C2×D411yescharacteristic
261C22×C4×C11C2×D411yescharacteristic
262C22×C4×C11C2×D411yescharacteristic
263C22×C4×C11C2×D412yes—
264C22×C4×C11C2×D412yes—
265C22×C4×C11C2411yescharacteristic
266C22×C4×C11C2411yescharacteristic
267C22×C4×C11C2411yescharacteristic
268C2×C22⋊D11—21no—
269C2×C22⋊D11—22no—
270C2×C22⋊D11—21no—
271C2×C22⋊D11—22no—
272C2×C22⋊D11—21no—
273C2×C22⋊D11—82no—
274C22×Dic11—21no—
275#4339—24no—
276#4339—84no—
277C2×D44—21no—
278C2×D44—22no—
279C2×D44—22no—
280C2×D44—24no—
281C2×D44C2411yescharacteristic
282C2×D44C2412yes—
283C2×C4×D11—21no—
284C2×C4×D11—22no—
285C2×C4×D11—22no—
286C2×C4×D11—22no—
287C2×Dic22—22no—
288C2×Dic22C2411yescharacteristic
289C11×C4⋊C4—21no—
290C11×C4⋊C4—21no—
291C11×C4⋊C4C2×D411yescharacteristic
292C11×C4⋊C4C2×D411yescharacteristic
293C11×C4⋊C4C2×D411yescharacteristic
294C11×C4⋊C4C2×D411yescharacteristic
295C11×C4⋊C4C2×D412yes—
296C11×C4⋊C4C2×D412yes—
297C11×C4⋊C4C2412yes—
298C11×C4⋊C4C2412yes—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—22no—
301C11×C22⋊C4—24no—
302C11×C22⋊C4—24no—
303C11×C22⋊C4—24no—
304C11×C22⋊C4—24no—
305C11×C22⋊C4C2×D412yes—
306C11×C22⋊C4C2×D412yes—
307C11×C22⋊C4C2×D412yes—
308C11×C22⋊C4C2×D412yes—
309C42×C11—22no—
310C42×C11—22no—
311C42×C11C2×D412yes—
312C42×C11C2×D412yes—
313C42×C11C2412yes—
314C42×C11C2412yes—
315C22⋊Dic11—21no—
316C22⋊Dic11—21no—
317C22⋊Dic11—21no—
318#4324—28no—
319#4323—28no—
320#4323—28no—
321#4323—28no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—21no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—22no—
327(C2×D11)⋊C4—22no—
328(C2×D11)⋊C4—22no—
329(C2×D11)⋊C4—21no—
330(C2×D11)⋊C4—22no—
331C4⋊Dic11—22no—
332C4⋊Dic11—21no—
333C4⋊Dic11C2412yes—
334C4⋊Dic11C2411yescharacteristic
335C4⋊Dic11C2411yescharacteristic
336Dic11⋊C4—22no—
337Dic11⋊C4—22no—
338Dic11⋊C4—22no—
339Dic11⋊C4—21no—
340Dic11⋊C4—21no—
341C4×Dic11—22no—
342C4×Dic11—21no—
343#4318—24no—
344C2×C11⋊C8—24no—
345C2×C11⋊C8C2412yes—
346C2×C11⋊C8C2414yes—
347C2×C11⋊C8C2412yes—
348#3494—111no—
349C2×#518D1111yescharacteristic, complemented
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#2924—111no—
365C23×C11—28no—
366C23×C11—28no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—24no—
370C23×C11—28no—
371C23×C11—41no—
372C23×C11—44no—
373C23×C11—44no—
374C23×C11—82no—
375C23×C11—82no—
376C23×C11—82no—
377C23×C11—82no—
378C23×C11—816no—
379C23×C11C22×D411yescharacteristic
380C23×C11C22×D411yescharacteristic
381C23×C11C22×D411yescharacteristic
382C22×D11—22no—
383C22×D11—21no—
384C22×D11—42no—
385C22×D11—81no—
386C22×D11—81no—
387D4×C11—28no—
388D4×C11—28no—
389D4×C11—28no—
390D4×C11—24no—
391D4×C11C2×#4118yes—
392C2×C4×C11—22no—
393C2×C4×C11—24no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—42no—
401C2×C4×C11—42no—
402C2×C4×C11—42no—
403C2×C4×C11—84no—
404C2×C4×C11—84no—
405C2×C4×C11—84no—
406C2×C4×C11—84no—
407C2×C4×C11C22×D412yes—
408C2×C4×C11C22×D412yes—
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C22×D412yes—
412C2×C4×C11C22×D412yes—
413C2×C4×C11C22×D411yescharacteristic
414C2×C4×C11C2×#4114yes—
415C2×C4×C11C2511yescharacteristic
416C22⋊D11—42no—
417C22⋊D11—42no—
418C22⋊D11—44no—
419C22⋊D11—81no—
420C22⋊D11—82no—
421C2×Dic11—21no—
422C2×Dic11—21no—
423C2×Dic11—22no—
424C2×Dic11—21no—
425C2×Dic11—81no—
426D44—24no—
427D44—22no—
428D44—42no—
429D44—82no—
430D44—82no—
431C4×D11—42no—
432C4×D11—82no—
433C4×D11—82no—
434C4×D11—82no—
435Dic22—22no—
436Dic22—82no—
437C11⋊C8—22no—
438C11⋊C8—22no—
439C11⋊C8—24no—
440C23×D4C2×D1111yescharacteristic
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—22no—
459#518—21no—
460#518—21no—
461#518—111no—
462#518C2×D1112yes—
463#518C2×D1112yes—
464#518C2×D1114yescomplemented
465C2×C4×D4—21no—
466C2×C4×D4—21no—
467C2×C4×D4C2×D1112yescomplemented
468C2×C4×D4C2×D1112yescomplemented
469C2×#117C2×D1111yescharacteristic
470C2×#117C2×D1111yescharacteristic
471C22×C22⋊C4—22no—
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#433—114no—
505#432—112no—
506#431—112no—
507#428—112no—
508#427—112no—
509#424—112no—
510#418—112no—
511#418—112no—
512#416—112no—
513C2×#102—112no—
514#407—111no—
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—28no—
524C22×C11—21no—
525C22×C11—44no—
526C22×C11—416no—
527C22×C11—44no—
528C22×C11—44no—
529C22×C11—88no—
530C22×C11—88no—
531C22×C11#52512yes—
532C22×C11#57612yes—
533C22×C11C23×D411yescharacteristic
534C2×D11—42no—
535C2×D11—41no—
536C2×D11—42no—
537C2×D11—41no—
538C2×D11—42no—
539C2×D11—41no—
540C2×D11—162no—
541C4×C11—22no—
542C4×C11—22no—
543C4×C11—21no—
544C4×C11—21no—
545C4×C11—22no—
546C4×C11—22no—
547C4×C11—42no—
548C4×C11—42no—
549C4×C11#52512yes—
550C4×C11C22×#4112yes—
551Dic11—41no—
552Dic11—41no—
553Dic11—41no—
554Dic11—42no—
555C25—21no—
556C2×#41—111no—
557C2×#41—222no—
558C22×D4—28no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—111no—
563C22×D4—221no—
564C22×D4C22×D1112yes—
565C22×D4C22×D1112yes—
566C22×D4C22×D1112yes—
567C23×C4—22no—
568C23×C4—22no—
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×C8—112no—
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—22no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—24no—
616C4×D4—24no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—112no—
622C4×D4—112no—
623C4×D4—112no—
624C4×D4—221no—
625C4×D4—221no—
626C4×D4—222no—
627C4×D4—221no—
628C4×D4—221no—
629C4×D4—222no—
630C4×D4—222no—
631C4×D4C22×D1114yes—
632C4×D4C22×D1114yes—
633C4×D4C22×D1114yes—
634C4×D4C22×D1114yes—
635#117—21no—
636#117—21no—
637#117—111no—
638#117—221no—
639#117—222no—
640#117C22⋊D1112yes—
641#117C22⋊D1111yescharacteristic
642#117C22⋊D1111yescharacteristic
643#117C22×D1112yes—
644#117C22×D1112yes—
645#117C22×D1111yescharacteristic
646#117C22×D1111yescharacteristic
647#117C22×D1112yes—
648C2×C4⋊C4—111no—
649C2×C4⋊C4—221no—
650C2×C4⋊C4C22⋊D1111yescharacteristic
651C2×C4⋊C4C22⋊D1111yescharacteristic
652C2×C4⋊C4C22×D1111yescharacteristic
653C2×C4⋊C4C22×D1111yescharacteristic
654C2×C22⋊C4—21no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—24no—
658C2×C22⋊C4—24no—
659C2×C22⋊C4—24no—
660C2×C22⋊C4—24no—
661C2×C22⋊C4—221no—
662C2×C22⋊C4—222no—
663C2×C22⋊C4C22⋊D1112yes—
664C2×C42—21no—
665C2×C42C22×D1112yes—
666#107—112no—
667#107—112no—
668#107—114no—
669#106—112no—
670#106—112no—
671#106—114no—
672C4⋊C8—114no—
673C4⋊C8—114no—
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⋊C8—111no—
685C22⋊C8—111no—
686C22⋊C8—112no—
687C22⋊C8—112no—
688C22⋊C8—112no—
689#97—114no—
690C4×C8—114no—
691C2×C11—22no—
692C2×C11—22no—
693C2×C11—41no—
694C2×C11—48no—
695C2×C11C2×#52511yescharacteristic
696C2×C11C2×#57611yescharacteristic
697C2×C11#358511yescharacteristic
698D11—81no—
699D11—82no—
700C24—28no—
701C24—22no—
702C24—22no—
703C24—22no—
704C24—82no—
705C24—82no—
706C24—221no—
707C24C2×C22⋊D1111yescharacteristic
708#41—224no—
709#41—884no—
710C2×Q8—111no—
711C2×Q8—222no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—28no—
716C2×D4—28no—
717C2×D4—24no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—112no—
722C2×D4—111no—
723C2×D4—221no—
724C2×D4—221no—
725C2×D4—222no—
726C2×D4—221no—
727C2×D4—222no—
728C2×D4—224no—
729C2×D4—221no—
730C2×D4—222no—
731C2×D4—222no—
732C2×D4—882no—
733C2×D4#433918yescomplemented
734C2×D4C23×D1114yes—
735C22×C4—24no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—84no—
743C22×C4—84no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—222no—
747C22×C4—222no—
748C22×C4—222no—
749C22×C4C2×C22⋊D1111yescharacteristic
750C22×C4C2×C22⋊D1112yes—
751C22×C4C2×C22⋊D1111yescharacteristic
752C22×C4C2×C22⋊D1111yescharacteristic
753C22×C4C2×C22⋊D1112yes—
754C22×C4C23×D1111yescharacteristic
755C22×C4C23×D1111yescharacteristic
756C22×C4C23×D1111yescharacteristic
757SD16—228no—
758D8—228no—
759D8—228no—
760D8—228no—
761M16—224no—
762C2×C8—112no—
763C2×C8—114no—
764C2×C8—112no—
765C2×C8—224no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—112no—
769C4⋊C4—111no—
770C4⋊C4—111no—
771C4⋊C4—221no—
772C4⋊C4—222no—
773C4⋊C4—221no—
774C4⋊C4—222no—
775C4⋊C4—222no—
776C4⋊C4—222no—
777C4⋊C4—221no—
778C4⋊C4C2×C22⋊D1111yescharacteristic
779C4⋊C4C2×C22⋊D1111yescharacteristic
780C4⋊C4C2×C22⋊D1111yescharacteristic
781C4⋊C4C2×C22⋊D1111yescharacteristic
782C4⋊C4C2×C22⋊D1112yes—
783C4⋊C4C2×C22⋊D1112yes—
784C4⋊C4C23×D1112yes—
785C4⋊C4C23×D1112yes—
786C22⋊C4—22no—
787C22⋊C4—22no—
788C22⋊C4—24no—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—24no—
792C22⋊C4—221no—
793C22⋊C4—221no—
794C22⋊C4—221no—
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×C22⋊D1112yes—
805C22⋊C4C2×C22⋊D1112yes—
806C22⋊C4C2×C22⋊D1112yes—
807C22⋊C4C2×C22⋊D1112yes—
808C42—22no—
809C42—22no—
810C42—221no—
811C42—222no—
812C42C2×C22⋊D1112yes—
813C42C2×C22⋊D1112yes—
814C42C23×D1112yes—
815C42C23×D1112yes—
816C11#6057811yescharacteristic, complemented, Sylow
817C23—28no—
818C23—28no—
819C23—22no—
820C23—22no—
821C23—24no—
822C23—28no—
823C23—41no—
824C23—44no—
825C23—44no—
826C23—82no—
827C23—82no—
828C23—82no—
829C23—82no—
830C23—816no—
831C23—222no—
832C23—221no—
833C23—442no—
834C23—881no—
835C23—881no—
836C23C22×C22⋊D1111yescharacteristic
837C23C22×C22⋊D1111yescharacteristic
838C23C22×C22⋊D1111yescharacteristic
839Q8—222no—
840Q8—882no—
841D4—28no—
842D4—28no—
843D4—28no—
844D4—24no—
845D4—224no—
846D4—222no—
847D4—442no—
848D4—444no—
849D4—442no—
850D4—442no—
851D4—882no—
852D4—882no—
853D4—882no—
854D4—881no—
855D4C2×#433918yes—
856C2×C4—22no—
857C2×C4—24no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—84no—
868C2×C4—84no—
869C2×C4—84no—
870C2×C4—84no—
871C2×C4—221no—
872C2×C4—221no—
873C2×C4—221no—
874C2×C4—222no—
875C2×C4—442no—
876C2×C4—882no—
877C2×C4—882no—
878C2×C4—882no—
879C2×C4—881no—
880C2×C4C2×#433914yes—
881C2×C4C22×C22⋊D1111yescharacteristic
882C2×C4C22×C22⋊D1112yes—
883C2×C4C22×C22⋊D1111yescharacteristic
884C2×C4C22×C22⋊D1112yes—
885C2×C4C22×C22⋊D1112yes—
886C2×C4C22×C22⋊D1112yes—
887C2×C4C22×C22⋊D1111yescharacteristic
888C2×C4C24×D1111yescharacteristic
889C8—222no—
890C8—222no—
891C8—224no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—28no—
898C22—21no—
899C22—21no—
900C22—44no—
901C22—416no—
902C22—44no—
903C22—44no—
904C22—88no—
905C22—88no—
906C22—441no—
907C22—442no—
908C22—442no—
909C22—441no—
910C22—441no—
911C22—442no—
912C22—1762no—
913C22#1062332212yes—
914C22#1062336612yes—
915C22C23×C22⋊D1111yescharacteristic
916C4—21no—
917C4—21no—
918C4—22no—
919C4—22no—
920C4—22no—
921C4—22no—
922C4—42no—
923C4—42no—
924C4—441no—
925C4—441no—
926C4—442no—
927C4—441no—
928C4#1062332212yes—
929C4C22×#433912yes—
930C2—22no—
931C2—22no—
932C2—41no—
933C2—48no—
934C2—882no—
935C2—881no—
936C2C2×#1062332211yescharacteristic
937C2C2×#1062336611yescharacteristic
938C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#518C2
socleC22×C11C23×D4
hypercenterC2×#518D11
hypocenterC11#60578
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
1. #13082351C2semidirect
2. #13078859C2semidirect
3. #13078800C2semidirect
4. #13078754C2semidirect
5. #13078707C2semidirect
6. #13078663C2semidirect
7. #13078616C2semidirect
8. #13078556C2semidirect
9. #13078529C2semidirect
10. #13078447C2semidirect
11. #13078119C2semidirect
12. #13077843C2semidirect
13. C2×#10622830C2semidirect
14. #13077466C2semidirect
15. #13077448C2semidirect
16. #13077274C2semidirect
17. C2×C11×#518C2semidirect
24. C11×#518C22semidirect
27. C2×C4×D4×C11C22semidirect
28. C2×C4×D4×C11C22semidirect
36. #10623066C22semidirect
37. #10623065C22semidirect
41. #10623056C22semidirect
42. #10623054C22semidirect
43. #10623052C22semidirect
44. #10623050C22semidirect
48. #10623010C22semidirect
49. #10623008C22semidirect
50. #10622831C22semidirect
51. #10622831C22semidirect
55. #10622830C22semidirect
56. #10622830C22semidirect
61. #10622631C22semidirect
62. C4×#4324C22semidirect
63. #10622629C22semidirect
64. #10622629C22semidirect
65. #10622628C22semidirect
66. #10622628C22semidirect
67. #10622627C22semidirect
68. #10622627C22semidirect
69. #10622627C22semidirect
70. C4×#4323C22semidirect
71. C4×#4323C22semidirect
72. C4×#4323C22semidirect
73. #10622622C22semidirect
74. #10622622C22semidirect
75. #10622621C22semidirect
76. #10622620C22semidirect
77. #10622616C22semidirect
78. #10622616C22semidirect
79. #10622615C22semidirect
80. #10622614C22semidirect
81. #10622613C22semidirect
82. #10622612C22semidirect
83. #10622611C22semidirect
84. #10622610C22semidirect
85. #10622609C22semidirect
86. #10622608C22semidirect
87. #10622584C22semidirect
88. #10622583C22semidirect
89. #10622581C22semidirect
90. #10622581C22semidirect
91. #10622580C22semidirect
92. #10622580C22semidirect
93. #10622539C22semidirect
94. #10622538C22semidirect
196. #66928C23semidirect
197. #66927C23semidirect
199. C4×D44C23semidirect
200. C4×D44C23semidirect
201. C4×D44C23semidirect
203. #66923C23semidirect
204. #66922C23semidirect
205. C4×Dic22C23semidirect
215. #66874C23semidirect
216. #66874C23semidirect
217. #66873C23semidirect
218. #66873C23semidirect
219. #66873C23semidirect
220. #66873C23semidirect
221. #66872C23semidirect
222. #66872C23semidirect
223. #66872C23semidirect
224. #66871C23semidirect
225. #66871C23semidirect
226. #66871C23semidirect
227. C4⋊(C11⋊C8)C23semidirect
228. C4⋊(C11⋊C8)C23semidirect
229. #66867C23semidirect
230. C4×C11⋊C8C23semidirect
249. C2×D4×C11#41semidirect
349. C2×#518D11semidirect
464. #518C2×D11semidirect
467. C2×C4×D4C2×D11semidirect
468. C2×C4×D4C2×D11semidirect
733. C2×D4#4339semidirect
816. C11#60578semidirect

Maximal subgroups

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

subgroupindex
#130823512
#130788592
#130788002
#130787542
#130787072
#130786632
#130786162
#130785562
#130785292
#130784472
#130781192
#130778432
C2×#106228302
#130774662
#130774482
#130772742
C2×C11×#5182
#6057811