Finite Group Databasebeta

← #15622701

Subgroups — #15622701

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
2#13078893C214yesmaximal, complemented
3#13078815C214yesmaximal, complemented
4#13078787C212yesmaximal, complemented
5#13078707C212yesmaximal, complemented
6#13078663C212yesmaximal, complemented
7#13078647C212yesmaximal, complemented
8#13078539C211yesmaximal, characteristic, complemented
9C2×#10622581C211yesmaximal, characteristic, complemented
10#13078478C212yesmaximal, complemented
11#13078155C212yesmaximal, complemented
12#13077868C211yesmaximal, characteristic, complemented
13#13077834C211yesmaximal, characteristic, complemented
14#13077497C212yesmaximal, complemented
15#13077444C212yesmaximal, complemented
16#13077274C211yesmaximal, characteristic, complemented
17C2×C11×#520C211yesmaximal, characteristic, complemented
18C22×C11×#41C2211yescharacteristic
19C11×#520—21no—
20C11×#520—21no—
21C11×#520—22no—
22C11×#520C2212yes—
23C11×#520C2212yes—
24C11×#520C2214yescomplemented
25C2×C4×Q8×C11C2212yescomplemented
26C2×C4×D4×C11—22no—
27C2×C4×D4×C11C2212yescomplemented
28C2×C11×#117—21no—
29C2×C11×#117C2211yescharacteristic
30C22×C11×C4⋊C4—21no—
31C22×C11×C4⋊C4C2211yescharacteristic
32C2×#67003C2212yes—
33C2×#67002C2212yes—
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#10623010C2212yes—
49#10623008C2212yes—
50#10622852C2212yescomplemented
51#10622851C2214yes—
52#10622851C2212yescomplemented
53#10622846C2212yes—
54#10622845C2212yes—
55#10622841C2211yescharacteristic, complemented
56#10622840C2212yes—
57#10622840C2211yescharacteristic, complemented
58#10622831C2211yescharacteristic, complemented
59#10622830C2212yes—
60#10622830C2211yescharacteristic, complemented
61#10622820C2211yescharacteristic
62C2×C22⋊(C11⋊C8)C2211yescharacteristic
63#10622643C2214yescomplemented
64#10622641C2214yescomplemented
65#10622640C2214yescomplemented
66#10622639C2214yescomplemented
67C4×#4325C2214yescomplemented
68C4×#4325C2214yescomplemented
69#10622635C2214yescomplemented
70#10622633C2214yescomplemented
71C4×#4324C2214yescomplemented
72#10622629C2214yescomplemented
73#10622628C2214yescomplemented
74#10622627C2214yescomplemented
75#10622627C2214yescomplemented
76C4×#4323C2214yescomplemented
77#10622622C2214yescomplemented
78#10622621C2214yescomplemented
79#10622613C2214yescomplemented
80#10622612C2212yescomplemented
81#10622610C2212yescomplemented
82#10622584C2212yescomplemented
83#10622583C2212yescomplemented
84#10622581C2212yes—
85#10622581C2212yes—
86#10622581C2212yescomplemented
87#10622581C2214yescomplemented
88#10622580C2212yescomplemented
89#10622579C2212yescomplemented
90C2×#66873C2212yescomplemented
91#10622577C2212yescomplemented
92C2×#66872C2212yescomplemented
93#10622539C2212yescomplemented
94#10622538C2212yescomplemented
95C2×C11×#41—28no—
96C2×C11×#41—21no—
97C2×C11×#41—21no—
98C2×C11×#41C2312yes—
99C2×C11×#41C2312yes—
100C22×Q8×C11C2311yescharacteristic
101C22×D4×C11—21no—
102C22×D4×C11C2311yescharacteristic
103C23×C4×C11—21no—
104C23×C4×C11—21no—
105C23×C4×C11—22no—
106C23×C4×C11C2311yescharacteristic
107C22×C22⋊D11—21no—
108C2×#4339—22no—
109C2×#4339C2311yescharacteristic
110C22×D44C2311yescharacteristic
111C4×Q8×C11—22no—
112C4×Q8×C11—22no—
113C4×Q8×C11C2314yes—
114C4×Q8×C11C2314yes—
115C4×D4×C11—24no—
116C4×D4×C11—24no—
117C4×D4×C11—24no—
118C4×D4×C11—24no—
119C4×D4×C11—22no—
120C4×D4×C11—22no—
121C4×D4×C11C2314yes—
122C4×D4×C11C2314yes—
123C11×#117—22no—
124C11×#117—22no—
125C11×#117—24no—
126C11×#117D412yes—
127C11×#117D411yescharacteristic
128C11×#117D411yescharacteristic
129C11×#117C2311yescharacteristic
130C11×#117C2311yescharacteristic
131C11×#117C2312yes—
132C2×C11×C4⋊C4—21no—
133C2×C11×C4⋊C4—22no—
134C2×C11×C4⋊C4—21no—
135C2×C11×C4⋊C4—21no—
136C2×C11×C4⋊C4—22no—
137C2×C11×C4⋊C4—22no—
138C2×C11×C4⋊C4—24no—
139C2×C11×C4⋊C4D411yescharacteristic
140C2×C11×C4⋊C4D411yescharacteristic
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C4⋊C4C2312yes—
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C22⋊C4—22no—
145C2×C11×C22⋊C4D412yes—
146C2×C42×C11—22no—
147C2×C42×C11C2312yes—
148#67006—21no—
149#67003—28no—
150#67002—28no—
151C2×#4326C2312yes—
152C2×#4325C2314yes—
153C2×#4325C2312yes—
154C2×#4324C2312yes—
155C2×#4323C2314yes—
156C2×#4323C2312yes—
157#66983—22no—
158#66983—21no—
159#66983—21no—
160#66983C2311yescharacteristic
161#66983C2312yes—
162#66983C2312yes—
163#66983C2311yescharacteristic
164#66982—22no—
165#66982—21no—
166C4×C22⋊D11—22no—
167C4×C22⋊D11—21no—
168C4×C22⋊D11—21no—
169C2×(C2×D11)⋊C4—21no—
170#66979C2311yescharacteristic
171C2×C4⋊Dic11C2311yescharacteristic
172#66977C2311yescharacteristic
173#66977C2311yescharacteristic
174C2×#4318C2312yes—
175C22×C11⋊C8C2312yes—
176#66951—22no—
177#66949—22no—
178#66948—21no—
179#66948—21no—
180#66947—22no—
181#66947—22no—
182#66946—21no—
183#66946—21no—
184#66945—21no—
185C4⋊C4×D11—21no—
186#66943—21no—
187#66941—21no—
188#66938—22no—
189#66937—22no—
190#66937—22no—
191#66936—22no—
192#66935—22no—
193(C22⋊D11)⋊C4—22no—
194C22⋊C4×D11—22no—
195#66931—22no—
196#66929—22no—
197#66928—22no—
198#66928C2312yes—
199#66927C2312yes—
200C4×D44—22no—
201C4×D44C2312yes—
202C4×D44C2312yes—
203C4×D44C2312yes—
204#66925—22no—
205#66923C2312yes—
206#66922C2312yes—
207C4×Dic22C2312yes—
208#66899C2314yes—
209#66899C2312yes—
210#66899C2312yes—
211#66896C2314yes—
212#66896C2312yes—
213#66896C2312yes—
214C22⋊(C11⋊C8)C2311yescharacteristic
215C22⋊(C11⋊C8)C2312yes—
216C22⋊(C11⋊C8)C2311yescharacteristic
217C22⋊(C11⋊C8)C2312yes—
218C22⋊(C11⋊C8)C2312yes—
219#66874C2314yes—
220#66873C2314yes—
221#66873C2314yes—
222#66873C2314yes—
223#66872C2314yes—
224#66872C2314yes—
225#66872C2314yes—
226#66871C2314yes—
227C4⋊(C11⋊C8)C2314yes—
228C4⋊(C11⋊C8)C2314yes—
229#66867C2314yes—
230C4×C11⋊C8C2314yes—
231#60588—111nomaximal, Sylow
232C24×C11—21no—
233C24×C11C2×D411yescharacteristic
234C23×D11—21no—
235C11×#41—28no—
236C11×#41—28no—
237C11×#41—24no—
238C11×#41—24no—
239C11×#41—24no—
240C11×#41#4118yescomplemented
241C2×Q8×C11—24no—
242C2×Q8×C11—21no—
243C2×Q8×C11C2412yes—
244C2×D4×C11—28no—
245C2×D4×C11—22no—
246C2×D4×C11—22no—
247C2×D4×C11—24no—
248C2×D4×C11—21no—
249C2×D4×C11C2412yes—
250C22×C4×C11—28no—
251C22×C4×C11—21no—
252C22×C4×C11—22no—
253C22×C4×C11—22no—
254C22×C4×C11—24no—
255C22×C4×C11—22no—
256C22×C4×C11—22no—
257C22×C4×C11—22no—
258C22×C4×C11—24no—
259C22×C4×C11—24no—
260C22×C4×C11—84no—
261C22×C4×C11—82no—
262C22×C4×C11C2×D411yescharacteristic
263C22×C4×C11C2×D411yescharacteristic
264C22×C4×C11C2×D411yescharacteristic
265C22×C4×C11C2×D412yes—
266C22×C4×C11C2×D412yes—
267C22×C4×C11C2411yescharacteristic
268C22×C4×C11C2411yescharacteristic
269C22×C4×C11C2411yescharacteristic
270C2×C22⋊D11—21no—
271C2×C22⋊D11—22no—
272C2×C22⋊D11—21no—
273C2×C22⋊D11—22no—
274C2×C22⋊D11—21no—
275C2×C22⋊D11—82no—
276C22×Dic11—21no—
277#4339—24no—
278#4339—84no—
279C2×D44—21no—
280C2×D44—22no—
281C2×D44—22no—
282C2×D44—24no—
283C2×D44C2411yescharacteristic
284C2×D44C2412yes—
285C2×C4×D11—21no—
286C2×C4×D11—22no—
287C2×C4×D11—22no—
288C2×C4×D11—22no—
289C2×Dic22—22no—
290C2×Dic22C2411yescharacteristic
291C11×C4⋊C4—22no—
292C11×C4⋊C4—22no—
293C11×C4⋊C4—24no—
294C11×C4⋊C4—24no—
295C11×C4⋊C4—22no—
296C11×C4⋊C4C2×D411yescharacteristic
297C11×C4⋊C4C2×D411yescharacteristic
298C11×C4⋊C4C2×D411yescharacteristic
299C11×C4⋊C4C2×D411yescharacteristic
300C11×C4⋊C4C2×D412yes—
301C11×C4⋊C4C2×D412yes—
302C11×C4⋊C4C2414yes—
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—24no—
310C42×C11—24no—
311C42×C11C2×D412yes—
312C42×C11C2×D412yes—
313C42×C11C2412yes—
314C42×C11C2412yes—
315C22⋊Dic11—21no—
316C22⋊Dic11—21no—
317C22⋊Dic11—21no—
318#4326—24no—
319#4325—28no—
320#4325—24no—
321#4324—24no—
322#4323—28no—
323#4323—24no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—21no—
327(C2×D11)⋊C4—22no—
328(C2×D11)⋊C4—22no—
329(C2×D11)⋊C4—22no—
330(C2×D11)⋊C4—22no—
331(C2×D11)⋊C4—21no—
332(C2×D11)⋊C4—22no—
333C4⋊Dic11—22no—
334C4⋊Dic11—21no—
335C4⋊Dic11C2411yescharacteristic
336C4⋊Dic11C2412yes—
337C4⋊Dic11C2411yescharacteristic
338Dic11⋊C4—22no—
339Dic11⋊C4—22no—
340Dic11⋊C4—22no—
341Dic11⋊C4—21no—
342Dic11⋊C4—21no—
343C4×Dic11—22no—
344C4×Dic11—21no—
345#4318—24no—
346C2×C11⋊C8—24no—
347C2×C11⋊C8C2412yes—
348C2×C11⋊C8C2414yes—
349C2×C11⋊C8C2412yes—
350#3494—111no—
351C2×#520D1111yescharacteristic, complemented
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#2924—111no—
367C23×C11—24no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—41no—
372C23×C11—42no—
373C23×C11—42no—
374C23×C11C22×D411yescharacteristic
375C23×C11C22×D411yescharacteristic
376C23×C11C22×D411yescharacteristic
377C22×D11—22no—
378C22×D11—21no—
379C22×D11—42no—
380C22×D11—81no—
381C22×D11—81no—
382Q8×C11—24no—
383Q8×C11—22no—
384Q8×C11C2×#4114yes—
385D4×C11—28no—
386D4×C11—24no—
387D4×C11—28no—
388D4×C11—22no—
389D4×C11C2×#4114yes—
390C2×C4×C11—24no—
391C2×C4×C11—28no—
392C2×C4×C11—22no—
393C2×C4×C11—24no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—28no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—24no—
401C2×C4×C11—42no—
402C2×C4×C11—44no—
403C2×C4×C11—84no—
404C2×C4×C11—84no—
405C2×C4×C11—82no—
406C2×C4×C11—82no—
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—
440C22×#41C2×D1111yescharacteristic
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—21no—
458#520—21no—
459#520—22no—
460#520—111no—
461#520C2×D1112yes—
462#520C2×D1112yes—
463#520C2×D1114yescomplemented
464#518—111no—
465C2×C4×Q8C2×D1112yescomplemented
466C2×C4×D4—22no—
467C2×C4×D4C2×D1112yescomplemented
468C2×#117—21no—
469C2×#117C2×D1111yescharacteristic
470C22×C4⋊C4—21no—
471C22×C4⋊C4C2×D1111yescharacteristic
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#433—114no—
505#432—112no—
506#431—112no—
507#428—112no—
508C2×#106—112no—
509#424—112no—
510#417—112no—
511#417—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—24no—
524C22×C11—21no—
525C22×C11—44no—
526C22×C11—48no—
527C22×C11—42no—
528C22×C11—42no—
529C22×C11#52512yes—
530C22×C11#57712yes—
531C22×C11C23×D411yescharacteristic
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—24no—
543C4×C11—21no—
544C4×C11—22no—
545C4×C11—22no—
546C4×C11—44no—
547C4×C11#52512yes—
548C4×C11C22×#4112yes—
549Dic11—41no—
550Dic11—41no—
551Dic11—41no—
552Dic11—42no—
553C2×#41—28no—
554C2×#41—21no—
555C2×#41—21no—
556C2×#41—111no—
557C2×#41—222no—
558C2×#41C22×D1112yes—
559C2×#41C22×D1112yes—
560C22×Q8C22×D1111yescharacteristic
561C22×D4—21no—
562C22×D4—111no—
563C22×D4—221no—
564C22×D4C22×D1111yescharacteristic
565C23×C4—21no—
566C23×C4—21no—
567C23×C4—22no—
568C23×C4C22×D1111yescharacteristic
569AGL(1,ℤ/8)—228no—
570#135—228no—
571C2×Q16—112no—
572C2×SD16—112no—
573C2×SD16—114no—
574C2×SD16—112no—
575C2×D8—112no—
576C2×D8—114no—
577C2×M16—112no—
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—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—22no—
612C4×Q8—22no—
613C4×Q8—112no—
614C4×Q8C22×D1114yes—
615C4×Q8C22×D1114yes—
616C4×D4—24no—
617C4×D4—24no—
618C4×D4—24no—
619C4×D4—24no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—112no—
623C4×D4—112no—
624C4×D4—112no—
625C4×D4—221no—
626C4×D4—221no—
627C4×D4—222no—
628C4×D4—221no—
629C4×D4—221no—
630C4×D4—222no—
631C4×D4—222no—
632C4×D4C22×D1114yes—
633C4×D4C22×D1114yes—
634#117—22no—
635#117—22no—
636#117—24no—
637#117—111no—
638#117—221no—
639#117—222no—
640#117C22⋊D1112yes—
641#117C22⋊D1111yescharacteristic
642#117C22⋊D1111yescharacteristic
643#117C22×D1111yescharacteristic
644#117C22×D1111yescharacteristic
645#117C22×D1112yes—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—24no—
653C2×C4⋊C4—111no—
654C2×C4⋊C4—221no—
655C2×C4⋊C4C22⋊D1111yescharacteristic
656C2×C4⋊C4C22⋊D1111yescharacteristic
657C2×C4⋊C4C22×D1112yes—
658C2×C4⋊C4C22×D1112yes—
659C2×C4⋊C4C22×D1112yes—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—221no—
662C2×C22⋊C4—222no—
663C2×C22⋊C4C22⋊D1112yes—
664C2×C42—22no—
665C2×C42C22×D1112yes—
666#107—114no—
667#106—114no—
668#106—114no—
669#106—114no—
670C4⋊C8—114no—
671C4⋊C8—114no—
672#103—112no—
673#103—112no—
674#103—114no—
675#103—114no—
676#102—112no—
677#102—112no—
678#102—114no—
679#102—114no—
680#102—114no—
681#102—114no—
682C22⋊C8—111no—
683C22⋊C8—111no—
684C22⋊C8—112no—
685C22⋊C8—112no—
686C22⋊C8—112no—
687#97—114no—
688C4×C8—114no—
689C2×C11—22no—
690C2×C11—22no—
691C2×C11—41no—
692C2×C11—44no—
693C2×C11C2×#52511yescharacteristic
694C2×C11C2×#57711yescharacteristic
695C2×C11#358511yescharacteristic
696D11—81no—
697D11—82no—
698C24—21no—
699C24—221no—
700C24C2×C22⋊D1111yescharacteristic
701#41—28no—
702#41—28no—
703#41—24no—
704#41—24no—
705#41—24no—
706#41—224no—
707#41—884no—
708#41#433918yescomplemented
709C2×Q8—24no—
710C2×Q8—21no—
711C2×Q8—111no—
712C2×Q8—222no—
713C2×Q8C23×D1112yes—
714C2×D4—28no—
715C2×D4—22no—
716C2×D4—22no—
717C2×D4—24no—
718C2×D4—21no—
719C2×D4—112no—
720C2×D4—111no—
721C2×D4—221no—
722C2×D4—221no—
723C2×D4—222no—
724C2×D4—221no—
725C2×D4—222no—
726C2×D4—224no—
727C2×D4—221no—
728C2×D4—222no—
729C2×D4—222no—
730C2×D4—882no—
731C2×D4C23×D1112yes—
732C22×C4—28no—
733C22×C4—21no—
734C22×C4—24no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—84no—
743C22×C4—82no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—222no—
747C22×C4—222no—
748C22×C4—222no—
749C22×C4C2×C22⋊D1112yes—
750C22×C4C2×C22⋊D1111yescharacteristic
751C22×C4C2×C22⋊D1111yescharacteristic
752C22×C4C2×C22⋊D1111yescharacteristic
753C22×C4C2×C22⋊D1112yes—
754C22×C4C23×D1111yescharacteristic
755C22×C4C23×D1111yescharacteristic
756C22×C4C23×D1111yescharacteristic
757Q16—224no—
758SD16—224no—
759SD16—228no—
760SD16—224no—
761D8—224no—
762D8—228no—
763M16—224no—
764C2×C8—112no—
765C2×C8—114no—
766C2×C8—112no—
767C2×C8—224no—
768C4⋊C4—22no—
769C4⋊C4—22no—
770C4⋊C4—24no—
771C4⋊C4—24no—
772C4⋊C4—22no—
773C4⋊C4—112no—
774C4⋊C4—111no—
775C4⋊C4—111no—
776C4⋊C4—221no—
777C4⋊C4—222no—
778C4⋊C4—221no—
779C4⋊C4—222no—
780C4⋊C4—222no—
781C4⋊C4—222no—
782C4⋊C4—221no—
783C4⋊C4C2×C22⋊D1111yescharacteristic
784C4⋊C4C2×C22⋊D1111yescharacteristic
785C4⋊C4C2×C22⋊D1112yes—
786C4⋊C4C2×C22⋊D1111yescharacteristic
787C4⋊C4C2×C22⋊D1111yescharacteristic
788C4⋊C4C2×C22⋊D1112yes—
789C4⋊C4C23×D1114yes—
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—24no—
809C42—24no—
810C42—221no—
811C42—222no—
812C42C2×C22⋊D1112yes—
813C42C2×C22⋊D1112yes—
814C42C23×D1112yes—
815C42C23×D1112yes—
816C11#6058811yescharacteristic, complemented, Sylow
817C23—24no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—41no—
822C23—42no—
823C23—42no—
824C23—222no—
825C23—221no—
826C23—442no—
827C23—881no—
828C23—881no—
829C23C22×C22⋊D1111yescharacteristic
830C23C22×C22⋊D1111yescharacteristic
831C23C22×C22⋊D1111yescharacteristic
832Q8—24no—
833Q8—22no—
834Q8—222no—
835Q8—882no—
836Q8C2×#433914yes—
837D4—28no—
838D4—24no—
839D4—28no—
840D4—22no—
841D4—224no—
842D4—222no—
843D4—442no—
844D4—444no—
845D4—442no—
846D4—442no—
847D4—882no—
848D4—882no—
849D4—882no—
850D4—881no—
851D4C2×#433914yes—
852C2×C4—24no—
853C2×C4—28no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—28no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—24no—
863C2×C4—42no—
864C2×C4—44no—
865C2×C4—84no—
866C2×C4—84no—
867C2×C4—82no—
868C2×C4—82no—
869C2×C4—221no—
870C2×C4—221no—
871C2×C4—221no—
872C2×C4—222no—
873C2×C4—442no—
874C2×C4—882no—
875C2×C4—882no—
876C2×C4—882no—
877C2×C4—881no—
878C2×C4C2×#433914yes—
879C2×C4C22×C22⋊D1112yes—
880C2×C4C22×C22⋊D1112yes—
881C2×C4C22×C22⋊D1112yes—
882C2×C4C22×C22⋊D1111yescharacteristic
883C2×C4C22×C22⋊D1112yes—
884C2×C4C22×C22⋊D1111yescharacteristic
885C2×C4C22×C22⋊D1111yescharacteristic
886C2×C4C24×D1111yescharacteristic
887C8—222no—
888C8—222no—
889C8—224no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—24no—
896C22—21no—
897C22—21no—
898C22—44no—
899C22—48no—
900C22—42no—
901C22—42no—
902C22—441no—
903C22—442no—
904C22—442no—
905C22—441no—
906C22—441no—
907C22—442no—
908C22—1762no—
909C22#1062332212yes—
910C22#1062336812yes—
911C22C23×C22⋊D1111yescharacteristic
912C4—21no—
913C4—24no—
914C4—21no—
915C4—22no—
916C4—22no—
917C4—22no—
918C4—22no—
919C4—44no—
920C4—441no—
921C4—441no—
922C4—442no—
923C4—441no—
924C4#1062332212yes—
925C4C22×#433912yes—
926C2—22no—
927C2—22no—
928C2—41no—
929C2—44no—
930C2—882no—
931C2—881no—
932C2C2×#1062332211yescharacteristic
933C2C2×#1062336811yescharacteristic
934C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#520C2
socleC22×C11C23×D4
hypercenterC2×#520D11
hypocenterC11#60588
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #13082351C2semidirect
2. #13078893C2semidirect
3. #13078815C2semidirect
4. #13078787C2semidirect
5. #13078707C2semidirect
6. #13078663C2semidirect
7. #13078647C2semidirect
8. #13078539C2semidirect
9. C2×#10622581C2semidirect
10. #13078478C2semidirect
11. #13078155C2semidirect
12. #13077868C2semidirect
13. #13077834C2semidirect
14. #13077497C2semidirect
15. #13077444C2semidirect
16. #13077274C2semidirect
17. C2×C11×#520C2semidirect
24. C11×#520C22semidirect
25. C2×C4×Q8×C11C22semidirect
27. C2×C4×D4×C11C22semidirect
36. #10623066C22semidirect
37. #10623065C22semidirect
41. #10623056C22semidirect
42. #10623054C22semidirect
43. #10623052C22semidirect
44. #10623050C22semidirect
50. #10622852C22semidirect
52. #10622851C22semidirect
55. #10622841C22semidirect
57. #10622840C22semidirect
58. #10622831C22semidirect
60. #10622830C22semidirect
63. #10622643C22semidirect
64. #10622641C22semidirect
65. #10622640C22semidirect
66. #10622639C22semidirect
67. C4×#4325C22semidirect
68. C4×#4325C22semidirect
69. #10622635C22semidirect
70. #10622633C22semidirect
71. C4×#4324C22semidirect
72. #10622629C22semidirect
73. #10622628C22semidirect
74. #10622627C22semidirect
75. #10622627C22semidirect
76. C4×#4323C22semidirect
77. #10622622C22semidirect
78. #10622621C22semidirect
79. #10622613C22semidirect
80. #10622612C22semidirect
81. #10622610C22semidirect
82. #10622584C22semidirect
83. #10622583C22semidirect
86. #10622581C22semidirect
87. #10622581C22semidirect
88. #10622580C22semidirect
89. #10622579C22semidirect
90. C2×#66873C22semidirect
91. #10622577C22semidirect
92. C2×#66872C22semidirect
93. #10622539C22semidirect
94. #10622538C22semidirect
240. C11×#41#41semidirect
351. C2×#520D11semidirect
463. #520C2×D11semidirect
465. C2×C4×Q8C2×D11semidirect
467. C2×C4×D4C2×D11semidirect
708. #41#4339semidirect
816. C11#60588semidirect

Maximal subgroups

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

subgroupindex
#130823512
#130788932
#130788152
#130787872
#130787072
#130786632
#130786472
#130785392
C2×#106225812
#130784782
#130781552
#130778682
#130778342
#130774972
#130774442
#130772742
C2×C11×#5202
#6058811