Finite Group Databasebeta

← #15638675

Subgroups — #15638675

Order 2816.

2126 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082455C211yesmaximal, characteristic, complemented
2#13080712C214yesmaximal, complemented
3#13080592C214yesmaximal, complemented
4#13080167C214yesmaximal, complemented
5#13080142C214yesmaximal, complemented
6#13079643C212yesmaximal, complemented
7#13079437C211yesmaximal, characteristic, complemented
8#13079418C211yesmaximal, characteristic, complemented
9#13079397C212yesmaximal, complemented
10#13078754C212yesmaximal, complemented
11#13077876C211yesmaximal, characteristic, complemented
12#13077868C211yesmaximal, characteristic, complemented
13#13077834C212yesmaximal, complemented
14#13077645C211yesmaximal, characteristic, complemented
15C2×C11×#547C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic, complemented
18C11×#547—22no—
19C11×#547—22no—
20C11×#547C2214yes—
21C11×#547C2214yescomplemented
22C2×C11×C4⋊Q8C2211yescharacteristic, complemented
23C2×C11×#123—21no—
24C2×C11×#123—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic, complemented
27C2×C11×#121—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic, complemented
30C22×C11×C4⋊C4—21no—
31C2×#67004C2212yescomplemented
32C2×#67003C2214yescomplemented
33C2×#67002C2212yescomplemented
34#10623335—21no—
35#10623322C2212yes—
36C2×#66983C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38#10623096C2212yescomplemented
39#10623087—22no—
40#10623083C2212yescomplemented
41#10623081C2212yescomplemented
42#10623072C2212yescomplemented
43#10623071—22no—
44#10623046—21no—
45#10623025—21no—
46#10623017—21no—
47#10623010C2212yes—
48#10622852C2214yescomplemented
49#10622852C2214yescomplemented
50#10622851C2214yescomplemented
51#10622851C2214yescomplemented
52#10622846C2214yescomplemented
53#10622845C2212yescomplemented
54#10622845C2212yescomplemented
55#10622841C2212yescomplemented
56#10622841C2212yescomplemented
57#10622840C2212yes—
58#10622840C2212yes—
59#10622831C2212yescomplemented
60#10622830C2212yes—
61#10622820C2211yescharacteristic
62#10622820C2211yescharacteristic
63C2×C22⋊(C11⋊C8)C2212yescomplemented
64#10622703C2214yescomplemented
65#10622699C2214yescomplemented
66#10622696C2214yescomplemented
67#10622695C2214yescomplemented
68#10622665C2214yescomplemented
69#10622664C2214yescomplemented
70#10622663C2212yescomplemented
71#10622662C2214yescomplemented
72#10622661C2214yescomplemented
73#10622660C2214yescomplemented
74#10622659C2212yescomplemented
75#10622658C2214yescomplemented
76#10622657C2212yescomplemented
77#10622656C2212yescomplemented
78#10622631C2214yescomplemented
79#10622629C2214yescomplemented
80#10622627C2214yescomplemented
81#10622624C2214yescomplemented
82#10622624C2214yescomplemented
83#10622622C2214yescomplemented
84#10622584C2212yescomplemented
85#10622580C2212yes—
86#10622539C2212yescomplemented
87C2×C11×#41—21no—
88C2×C11×#41—21no—
89C2×C11×#41—22no—
90C2×C11×#41—44no—
91C2×C11×#41—44no—
92C2×C11×#41C2312yes—
93C2×C11×#41C2314yes—
94C2×C11×#41C2312yes—
95C22×Q8×C11C2311yescharacteristic
96C22×Q8×C11C2311yescharacteristic
97C22×D4×C11—21no—
98C22×D4×C11—21no—
99C22×D4×C11D411yescharacteristic
100C22×D4×C11C2311yescharacteristic
101C23×C4×C11—21no—
102C23×C4×C11—21no—
103C23×C4×C11—21no—
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C22×C22⋊D11—21no—
107C2×#4339C2312yes—
108C22×D44C2311yescharacteristic
109C22×Dic22C2311yescharacteristic
110C11×C4⋊Q8—22no—
111C11×C4⋊Q8C2314yes—
112C11×#123—24no—
113C11×#123—24no—
114C11×#123—24no—
115C11×#123—24no—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8—21no—
118C11×C22⋊Q8—22no—
119C11×C22⋊Q8C2312yes—
120C11×C22⋊Q8C2312yes—
121C11×C22⋊Q8C2314yes—
122C11×#121—24no—
123C11×#121—24no—
124C4×D4×C11—22no—
125C4×D4×C11D412yes—
126C4×D4×C11D412yes—
127C4×D4×C11C2314yes—
128C4×D4×C11C2312yes—
129C4×D4×C11C2312yes—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4—21no—
132C2×C11×C4⋊C4—21no—
133C2×C11×C4⋊C4—21no—
134C2×C11×C4⋊C4—24no—
135C2×C11×C4⋊C4—24no—
136C2×C11×C4⋊C4D411yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4—21no—
140C2×C11×C22⋊C4—21no—
141C2×C11×C22⋊C4D411yescharacteristic
142C2×C11×C22⋊C4D411yescharacteristic
143C2×C42×C11C2311yescharacteristic
144#67006—22no—
145C2×C22⋊Dic11—21no—
146#67004—44no—
147#67003—48no—
148#67002—44no—
149C2×#4326C2314yes—
150C2×#4326C2314yes—
151C2×#4325C2314yes—
152C2×#4325C2314yes—
153#66992—22no—
154#66992—22no—
155#66990—22no—
156#66988—22no—
157C2×#4324C2314yes—
158C2×#4323C2314yes—
159#66983—21no—
160#66983—21no—
161#66983C2312yes—
162#66983C2312yes—
163#66983C2312yes—
164#66982—22no—
165#66982—22no—
166C4×C22⋊D11—22no—
167C4×C22⋊D11—22no—
168C4×C22⋊D11—22no—
169C2×(C2×D11)⋊C4—21no—
170#66979C2312yes—
171C2×C4⋊Dic11C2311yescharacteristic
172C2×C4⋊Dic11C2311yescharacteristic
173#66977—21no—
174#66977—21no—
175#66977C2312yes—
176#66977C2312yes—
177#66977C2312yes—
178C2×Dic11⋊C4—21no—
179C2×#4318C2312yes—
180C2×#4318C2312yes—
181C22×C11⋊C8C2314yes—
182#66951—22no—
183#66949—22no—
184#66947—22no—
185#66942—22no—
186#66938—22no—
187#66937—22no—
188#66936—22no—
189(C22⋊D11)⋊C4—22no—
190(C22⋊D11)⋊C4—22no—
191C22⋊C4×D11—22no—
192#66932—22no—
193#66930—22no—
194#66929—22no—
195#66928C2312yes—
196C4×D44C2312yes—
197#66925—22no—
198#66923C2312yes—
199C4×Dic22C2312yes—
200#66899C2314yes—
201#66899C2314yes—
202#66899C2314yes—
203#66899C2314yes—
204#66896C2314yes—
205#66896C2314yes—
206C22⋊(C11⋊C8)C2312yes—
207C22⋊(C11⋊C8)C2312yes—
208C22⋊(C11⋊C8)C2314yes—
209C22⋊(C11⋊C8)C2312yes—
210C22⋊(C11⋊C8)C2312yes—
211#66874C2314yes—
212#66873C2314yes—
213#66872C2314yes—
214#66871C2314yes—
215C4⋊(C11⋊C8)C2314yes—
216#66867C2314yes—
217#61575—111nomaximal, Sylow
218C24×C11—21no—
219C24×C11C2×D411yescharacteristic
220C24×C11C2×D411yescharacteristic
221C23×D11—21no—
222C11×#41—24no—
223C11×#41—28no—
224C11×#41—24no—
225C11×#41—44no—
226C11×#41—42no—
227C11×#41—42no—
228C11×#41—44no—
229C11×#41—44no—
230C11×#41—48no—
231C2×Q8×C11—21no—
232C2×Q8×C11—21no—
233C2×Q8×C11—42no—
234C2×Q8×C11—42no—
235C2×Q8×C11C2412yes—
236C2×Q8×C11C2412yes—
237C2×D4×C11—24no—
238C2×D4×C11—22no—
239C2×D4×C11—24no—
240C2×D4×C11—22no—
241C2×D4×C11—21no—
242C2×D4×C11—42no—
243C2×D4×C11—44no—
244C2×D4×C11—44no—
245C2×D4×C11C2×D412yes—
246C2×D4×C11C2×D412yes—
247C2×D4×C11C2412yes—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—24no—
252C22×C4×C11—24no—
253C22×C4×C11—22no—
254C22×C4×C11—22no—
255C22×C4×C11—42no—
256C22×C4×C11—42no—
257C22×C4×C11—44no—
258C22×C4×C11—44no—
259C22×C4×C11—44no—
260C22×C4×C11C2×D411yescharacteristic
261C22×C4×C11C2×D411yescharacteristic
262C22×C4×C11C2×D411yescharacteristic
263C22×C4×C11C2×D411yescharacteristic
264C22×C4×C11C2×D411yescharacteristic
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2×D412yes—
267C22×C4×C11C2411yescharacteristic
268C22×C4×C11C2412yes—
269C22×C4×C11C2411yescharacteristic
270C22×C4×C11C2411yescharacteristic
271C2×C22⋊D11—22no—
272C2×C22⋊D11—22no—
273C2×C22⋊D11—22no—
274C2×C22⋊D11—22no—
275C2×C22⋊D11—44no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279#4339—44no—
280C2×D44—21no—
281C2×D44—42no—
282C2×D44C2412yes—
283C2×C4×D11—22no—
284C2×C4×D11—22no—
285C2×Dic22—21no—
286C2×Dic22—42no—
287C2×Dic22C2412yes—
288C11×C4⋊C4—24no—
289C11×C4⋊C4—24no—
290C11×C4⋊C4—22no—
291C11×C4⋊C4—22no—
292C11×C4⋊C4—24no—
293C11×C4⋊C4—21no—
294C11×C4⋊C4C2×D412yes—
295C11×C4⋊C4C2×D412yes—
296C11×C4⋊C4C2412yes—
297C11×C22⋊C4—22no—
298C11×C22⋊C4—24no—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—24no—
301C11×C22⋊C4C2×D412yes—
302C11×C22⋊C4C2×D412yes—
303C11×C22⋊C4C2×D412yes—
304C11×C22⋊C4C2×D412yes—
305C42×C11C2×D412yes—
306C42×C11C2412yes—
307C22⋊Dic11—22no—
308C22⋊Dic11—22no—
309C22⋊Dic11—22no—
310C22⋊Dic11—22no—
311#4326—44no—
312#4326—44no—
313#4325—44no—
314#4325—44no—
315#4324—28no—
316#4323—28no—
317(C2×D11)⋊C4—22no—
318(C2×D11)⋊C4—22no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4—22no—
323C4⋊Dic11—21no—
324C4⋊Dic11—21no—
325C4⋊Dic11C2412yes—
326C4⋊Dic11C2412yes—
327Dic11⋊C4—22no—
328Dic11⋊C4—22no—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333C4×Dic11—22no—
334C4×Dic11—22no—
335#4318—42no—
336#4318—42no—
337C2×C11⋊C8—44no—
338C2×C11⋊C8C2414yes—
339C2×C11⋊C8C2414yes—
340#3505—111no—
341C2×#547D1111yescharacteristic, complemented
342#3315—114no—
343#3307—114no—
344#3269—114no—
345#3267—114no—
346#3218—112no—
347#3195—111no—
348#3193—111no—
349#3190—112no—
350#3114—112no—
351#3007—111no—
352#3006—111no—
353#3002—112no—
354#2973—111no—
355C23×C11—24no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—42no—
364C23×C11—42no—
365C23×C11C22×D411yescharacteristic
366C23×C11C22×D412yes—
367C23×C11C22×D411yescharacteristic
368C23×C11C22×D411yescharacteristic
369C22×D11—22no—
370C22×D11—42no—
371C22×D11—81no—
372C22×D11—81no—
373Q8×C11—22no—
374Q8×C11—24no—
375Q8×C11—22no—
376Q8×C11—42no—
377Q8×C11—42no—
378D4×C11—24no—
379D4×C11—22no—
380D4×C11—42no—
381D4×C11—42no—
382D4×C11—44no—
383D4×C11—44no—
384D4×C11—48no—
385D4×C11H(5,𝔽2)14yes—
386C2×C4×C11—22no—
387C2×C4×C11—24no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—42no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—44no—
401C2×C4×C11—48no—
402C2×C4×C11—44no—
403C2×C4×C11—48no—
404C2×C4×C11—42no—
405C2×C4×C11—42no—
406C2×C4×C11—42no—
407C2×C4×C11C22×D412yes—
408C2×C4×C11C22×D412yes—
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C22×D412yes—
412C2×C4×C11C22×D411yescharacteristic
413C2×C4×C11C2511yescharacteristic
414C22⋊D11—44no—
415C22⋊D11—44no—
416C22⋊D11—82no—
417C22⋊D11—82no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—42no—
422C2×Dic11—81no—
423C2×Dic11—81no—
424D44—24no—
425D44—81no—
426C4×D11—82no—
427C4×D11—82no—
428Dic22—24no—
429Dic22—81no—
430C11⋊C8—24no—
431C11⋊C8—24no—
432C22×#41C2×D1111yescharacteristic
433C22×#41C2×D1111yescharacteristic, complemented
434C2×#137—112no—
435C2×AGL(1,ℤ/8)—112no—
436C2×#135—114no—
437#553—112no—
438#553—222no—
439#552—112no—
440#551—222no—
441#548—112no—
442#547—22no—
443#547—22no—
444#547C2×D1114yes—
445#547C2×D1114yescomplemented
446#546—112no—
447#539—221no—
448#538—221no—
449#534—221no—
450C2×C4⋊Q8C2×D1111yescharacteristic, complemented
451#529—112no—
452#525—112no—
453C2×#123—21no—
454C2×#123—21no—
455C2×C22⋊Q8—111no—
456C2×C22⋊Q8C2×D1111yescharacteristic
457C2×C22⋊Q8C2×D1111yescharacteristic, complemented
458C2×#121—21no—
459C2×#121—111no—
460#518—221no—
461C2×C4×D4C2×D1111yescharacteristic
462C2×C4×D4C2×D1111yescharacteristic, complemented
463C22×C4⋊C4—21no—
464#497—114no—
465#491—114no—
466#485—114no—
467#484—112no—
468#483—112no—
469#483—112no—
470#480—112no—
471#478—114no—
472#470—114no—
473#468—114no—
474#467—114no—
475#465—114no—
476#463—114no—
477#462—114no—
478#461—114no—
479#452—114no—
480#452—114no—
481#452—114no—
482#451—112no—
483#451—112no—
484#451—112no—
485#450—112no—
486#450—112no—
487#449—114no—
488#449—114no—
489#448—112no—
490#448—112no—
491#447—112no—
492#442—114no—
493#440—114no—
494#435—114no—
495#435—114no—
496#432—112no—
497#417—112no—
498#417—112no—
499#416—114no—
500#407—111no—
501#407—111no—
502C2×C22⋊C8—112no—
503C22×C11—21no—
504C22×C11—21no—
505C22×C11—21no—
506C22×C11—21no—
507C22×C11—22no—
508C22×C11—21no—
509C22×C11—21no—
510C22×C11—22no—
511C22×C11—24no—
512C22×C11—21no—
513C22×C11—22no—
514C22×C11—21no—
515C22×C11—48no—
516C22×C11—42no—
517C22×C11—42no—
518C22×C11—82no—
519C22×C11—82no—
520C22×C11#57512yes—
521C22×C11C23×D411yescharacteristic
522C2×D11—42no—
523C2×D11—42no—
524C2×D11—42no—
525C2×D11—162no—
526C4×C11—22no—
527C4×C11—21no—
528C4×C11—22no—
529C4×C11—21no—
530C4×C11—21no—
531C4×C11—22no—
532C4×C11—42no—
533C4×C11—42no—
534C4×C11—42no—
535C4×C11C2×H(5,𝔽2)12yes—
536Dic11—42no—
537Dic11—42no—
538Dic11—42no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—22no—
542C2×#41—44no—
543C2×#41—44no—
544C2×#41—112no—
545C2×#41C22×D1112yes—
546C2×#41C22×D1114yes—
547C2×#41C22×D1112yes—
548C22×Q8—111no—
549C22×Q8C22×D1111yescharacteristic
550C22×Q8C22×D1111yescharacteristic
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—111no—
554C22×D4—221no—
555C22×D4C22⋊D1111yescharacteristic
556C22×D4C22×D1111yescharacteristic
557C23×C4—21no—
558C23×C4—21no—
559C23×C4—21no—
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1111yescharacteristic
562#137—444no—
563AGL(1,ℤ/8)—444no—
564#135—448no—
565C2×Q16—114no—
566C2×Q16—114no—
567C2×SD16—114no—
568C2×SD16—114no—
569C2×SD16—114no—
570C2×D8—114no—
571C2×M16—112no—
572C2×M16—112no—
573C22×C8—114no—
574C4⋊Q8—22no—
575C4⋊Q8C22×D1114yes—
576#126—222no—
577#126—222no—
578#126—222no—
579#125—112no—
580#125—222no—
581#124—112no—
582#124—222no—
583#123—24no—
584#123—24no—
585#123—24no—
586#123—24no—
587#123—222no—
588#123—222no—
589#123—222no—
590#123—222no—
591#123—222no—
592C22⋊Q8—21no—
593C22⋊Q8—21no—
594C22⋊Q8—22no—
595C22⋊Q8—112no—
596C22⋊Q8—112no—
597C22⋊Q8—112no—
598C22⋊Q8—221no—
599C22⋊Q8—221no—
600C22⋊Q8—222no—
601C22⋊Q8C22×D1112yes—
602C22⋊Q8C22×D1112yes—
603C22⋊Q8C22×D1114yes—
604#121—24no—
605#121—24no—
606#121—112no—
607#121—112no—
608#121—112no—
609#121—222no—
610#121—222no—
611#121—221no—
612#121—221no—
613#121—222no—
614#120—222no—
615#120—222no—
616C4×Q8—112no—
617C4×D4—22no—
618C4×D4—112no—
619C4×D4—222no—
620C4×D4—222no—
621C4×D4—222no—
622C4×D4—222no—
623C4×D4—222no—
624C4×D4C22⋊D1112yes—
625C4×D4C22⋊D1112yes—
626C4×D4C22×D1114yes—
627C4×D4C22×D1112yes—
628C4×D4C22×D1112yes—
629#117—112no—
630#117—222no—
631#117—222no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—24no—
637C2×C4⋊C4—24no—
638C2×C4⋊C4—111no—
639C2×C4⋊C4—111no—
640C2×C4⋊C4—221no—
641C2×C4⋊C4C22⋊D1111yescharacteristic
642C2×C4⋊C4C22×D1111yescharacteristic
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—221no—
647C2×C22⋊C4—221no—
648C2×C22⋊C4—222no—
649C2×C22⋊C4C22⋊D1111yescharacteristic
650C2×C22⋊C4C22⋊D1111yescharacteristic
651C2×C42C22×D1111yescharacteristic
652#107—114no—
653#106—114no—
654C4⋊C8—114no—
655#103—114no—
656#103—114no—
657#103—114no—
658#103—114no—
659#103—114no—
660#102—114no—
661#102—114no—
662#102—114no—
663C22⋊C8—112no—
664C22⋊C8—112no—
665C22⋊C8—114no—
666C22⋊C8—112no—
667C22⋊C8—112no—
668#97—114no—
669C2×C11—22no—
670C2×C11—41no—
671C2×C11—41no—
672C2×C11—42no—
673C2×C11—44no—
674C2×C11#348411yescharacteristic
675C2×C11C2×#57511yescharacteristic
676C2×C11#358611yescharacteristic
677D11—82no—
678C24—21no—
679C24—221no—
680C24C2×C22⋊D1111yescharacteristic
681C24C2×C22⋊D1111yescharacteristic
682#41—28no—
683#41—24no—
684#41—24no—
685#41—44no—
686#41—42no—
687#41—42no—
688#41—44no—
689#41—44no—
690#41—48no—
691#41—444no—
692C2×Q8—21no—
693C2×Q8—21no—
694C2×Q8—42no—
695C2×Q8—42no—
696C2×Q8—112no—
697C2×Q8—221no—
698C2×Q8—442no—
699C2×Q8C23×D1112yes—
700C2×Q8C23×D1112yes—
701C2×D4—24no—
702C2×D4—22no—
703C2×D4—24no—
704C2×D4—22no—
705C2×D4—21no—
706C2×D4—42no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—112no—
710C2×D4—222no—
711C2×D4—222no—
712C2×D4—222no—
713C2×D4—222no—
714C2×D4—221no—
715C2×D4—442no—
716C2×D4—444no—
717C2×D4C2×C22⋊D1112yes—
718C2×D4C2×C22⋊D1112yes—
719C2×D4C23×D1112yes—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—222no—
736C22×C4—222no—
737C22×C4C2×C22⋊D1111yescharacteristic
738C22×C4C2×C22⋊D1111yescharacteristic
739C22×C4C2×C22⋊D1111yescharacteristic
740C22×C4C2×C22⋊D1111yescharacteristic
741C22×C4C2×C22⋊D1111yescharacteristic
742C22×C4C2×C22⋊D1111yescharacteristic
743C22×C4C2×C22⋊D1112yes—
744C22×C4C23×D1111yescharacteristic
745C22×C4C23×D1111yescharacteristic
746C22×C4C23×D1111yescharacteristic
747C22×C4C23×D1112yes—
748Q16—444no—
749Q16—444no—
750SD16—228no—
751SD16—444no—
752SD16—444no—
753D8—228no—
754M16—442no—
755M16—442no—
756C2×C8—114no—
757C2×C8—114no—
758C2×C8—444no—
759C4⋊C4—24no—
760C4⋊C4—24no—
761C4⋊C4—22no—
762C4⋊C4—22no—
763C4⋊C4—24no—
764C4⋊C4—21no—
765C4⋊C4—112no—
766C4⋊C4—112no—
767C4⋊C4—221no—
768C4⋊C4—221no—
769C4⋊C4—222no—
770C4⋊C4—222no—
771C4⋊C4—222no—
772C4⋊C4—222no—
773C4⋊C4—222no—
774C4⋊C4—222no—
775C4⋊C4C2×C22⋊D1112yes—
776C4⋊C4C2×C22⋊D1112yes—
777C4⋊C4C23×D1112yes—
778C22⋊C4—22no—
779C22⋊C4—24no—
780C22⋊C4—22no—
781C22⋊C4—24no—
782C22⋊C4—222no—
783C22⋊C4—222no—
784C22⋊C4—222no—
785C22⋊C4—222no—
786C22⋊C4—222no—
787C22⋊C4—222no—
788C22⋊C4—222no—
789C22⋊C4—222no—
790C22⋊C4—222no—
791C22⋊C4—222no—
792C22⋊C4C2×C22⋊D1112yes—
793C22⋊C4C2×C22⋊D1112yes—
794C22⋊C4C2×C22⋊D1112yes—
795C22⋊C4C2×C22⋊D1112yes—
796C42—222no—
797C42—222no—
798C42C2×C22⋊D1112yes—
799C42C23×D1112yes—
800C11#6157511yescharacteristic, complemented, Sylow
801C23—24no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—42no—
810C23—42no—
811C23—222no—
812C23—442no—
813C23—881no—
814C23—881no—
815C23C22×C22⋊D1111yescharacteristic
816C23C22×C22⋊D1112yes—
817C23C22×C22⋊D1111yescharacteristic
818C23C22×C22⋊D1111yescharacteristic
819Q8—22no—
820Q8—24no—
821Q8—22no—
822Q8—42no—
823Q8—42no—
824Q8—224no—
825Q8—881no—
826D4—24no—
827D4—22no—
828D4—42no—
829D4—42no—
830D4—44no—
831D4—48no—
832D4—44no—
833D4—224no—
834D4—444no—
835D4—444no—
836D4—881no—
837D4—882no—
838D4—882no—
839D4#6703714yes—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—48no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—48no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—442no—
865C2×C4—882no—
866C2×C4—882no—
867C2×C4—881no—
868C2×C4—881no—
869C2×C4C22×C22⋊D1112yes—
870C2×C4C22×C22⋊D1112yes—
871C2×C4C22×C22⋊D1111yescharacteristic
872C2×C4C22×C22⋊D1112yes—
873C2×C4C22×C22⋊D1111yescharacteristic
874C2×C4C22×C22⋊D1111yescharacteristic
875C2×C4C24×D1111yescharacteristic
876C8—224no—
877C8—224no—
878C22—21no—
879C22—21no—
880C22—21no—
881C22—22no—
882C22—21no—
883C22—21no—
884C22—22no—
885C22—21no—
886C22—24no—
887C22—21no—
888C22—21no—
889C22—22no—
890C22—48no—
891C22—42no—
892C22—42no—
893C22—82no—
894C22—82no—
895C22—442no—
896C22—442no—
897C22—442no—
898C22—1762no—
899C22#1062335312yes—
900C22C23×C22⋊D1111yescharacteristic
901C4—22no—
902C4—22no—
903C4—21no—
904C4—21no—
905C4—21no—
906C4—22no—
907C4—42no—
908C4—42no—
909C4—42no—
910C4—442no—
911C4—442no—
912C4—442no—
913C4C2×#6703712yes—
914C2—22no—
915C2—41no—
916C2—41no—
917C2—42no—
918C2—44no—
919C2—882no—
920C2#1308225111yescharacteristic
921C2C2×#1062335311yescharacteristic
922C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#547C2
socleC22×C11C23×D4
hypercenterC2×#547D11
hypocenterC11#61575
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #13082455C2semidirect
2. #13080712C2semidirect
3. #13080592C2semidirect
4. #13080167C2semidirect
5. #13080142C2semidirect
6. #13079643C2semidirect
7. #13079437C2semidirect
8. #13079418C2semidirect
9. #13079397C2semidirect
10. #13078754C2semidirect
11. #13077876C2semidirect
12. #13077868C2semidirect
13. #13077834C2semidirect
14. #13077645C2semidirect
15. C2×C11×#547C2semidirect
17. C22×C11×#41C22semidirect
21. C11×#547C22semidirect
22. C2×C11×C4⋊Q8C22semidirect
26. C2×C11×C22⋊Q8C22semidirect
29. C2×C4×D4×C11C22semidirect
31. C2×#67004C22semidirect
32. C2×#67003C22semidirect
33. C2×#67002C22semidirect
38. #10623096C22semidirect
40. #10623083C22semidirect
41. #10623081C22semidirect
42. #10623072C22semidirect
48. #10622852C22semidirect
49. #10622852C22semidirect
50. #10622851C22semidirect
51. #10622851C22semidirect
52. #10622846C22semidirect
53. #10622845C22semidirect
54. #10622845C22semidirect
55. #10622841C22semidirect
56. #10622841C22semidirect
59. #10622831C22semidirect
63. C2×C22⋊(C11⋊C8)C22semidirect
64. #10622703C22semidirect
65. #10622699C22semidirect
66. #10622696C22semidirect
67. #10622695C22semidirect
68. #10622665C22semidirect
69. #10622664C22semidirect
70. #10622663C22semidirect
71. #10622662C22semidirect
72. #10622661C22semidirect
73. #10622660C22semidirect
74. #10622659C22semidirect
75. #10622658C22semidirect
76. #10622657C22semidirect
77. #10622656C22semidirect
78. #10622631C22semidirect
79. #10622629C22semidirect
80. #10622627C22semidirect
81. #10622624C22semidirect
82. #10622624C22semidirect
83. #10622622C22semidirect
84. #10622584C22semidirect
86. #10622539C22semidirect
341. C2×#547D11semidirect
433. C22×#41C2×D11semidirect
445. #547C2×D11semidirect
450. C2×C4⋊Q8C2×D11semidirect
457. C2×C22⋊Q8C2×D11semidirect
462. C2×C4×D4C2×D11semidirect
800. C11#61575semidirect

Maximal subgroups

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

subgroupindex
#130824552
#130807122
#130805922
#130801672
#130801422
#130796432
#130794372
#130794182
#130793972
#130787542
#130778762
#130778682
#130778342
#130776452
C2×C11×#5472
#6157511