Finite Group Databasebeta

← #15634924

Subgroups — #15634924

Order 2816.

2078 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082493C211yesmaximal, characteristic, complemented
2#13081658C214yesmaximal, complemented
3#13081654C214yesmaximal, complemented
4#13081624C214yesmaximal, complemented
5#13081588C214yesmaximal, complemented
6#13079099C212yesmaximal, complemented
7C2×#10622686C211yesmaximal, characteristic, complemented
8#13078119C212yesmaximal, complemented
9#13078115C212yesmaximal, complemented
10#13078096C211yesmaximal, characteristic, complemented
11#13078092C211yesmaximal, characteristic, complemented
12#13077551C211yesmaximal, characteristic, complemented
13#13077466C212yesmaximal, complemented
14C4×#67003C211yesmaximal, characteristic, complemented
15C11×#3508C211yesmaximal, characteristic, complemented
16C11×#559C2214yescomplemented
17C11×#550C2214yescomplemented
18C11×#546—24no—
19C11×#540—22no—
20C11×#535C2212yes—
21C11×#533C2211yescharacteristic
22C11×#532—22no—
23C2×C11×#127C2211yescharacteristic
24C11×#518C2212yes—
25C4×C11×#41C2211yescharacteristic
26C2×#67003C2211yescharacteristic
27C2×#67002C2212yes—
28C2×#66985C2212yes—
29C22×#4323C2212yes—
30C22×#4323C2212yes—
31#10623256—22no—
32#10623229—22no—
33#10623161—24no—
34#10623116C2214yescomplemented
35#10623108C2214yescomplemented
36#10623056C2212yes—
37#10623052C2212yes—
38C2×#66927C2211yescharacteristic
39C4×#4339C2211yescharacteristic
40#10622846C2211yescharacteristic
41#10622828C2212yes—
42#10622688C2214yescomplemented
43#10622687C2214yescomplemented
44#10622686C2214yes—
45#10622686C2214yes—
46#10622686C2214yescomplemented
47#10622685C2214yescomplemented
48#10622685C2218yescomplemented
49#10622672C2214yescomplemented
50#10622671C2214yescomplemented
51#10622670C2218yescomplemented
52C4×#4326C2212yescomplemented
53#10622640C2214yescomplemented
54C4×#4325C2212yescomplemented
55#10622637C2214yescomplemented
56Q8×C11⋊C8C2214yescomplemented
57C4×#4324C2212yescomplemented
58#10622629C2218yescomplemented
59#10622628C2218yescomplemented
60#10622628C2214yescomplemented
61#10622627C2218yescomplemented
62C4×#4323C2218yescomplemented
63C4×#4323C2212yescomplemented
64#10622615C2211yescharacteristic
65#10622614C2212yes—
66#10622612C2212yes—
67#10622611C2211yescharacteristic
68#10622610C2212yes—
69#10622537C2211yescharacteristic
70C2×C4×C11⋊C8C2211yescharacteristic
71C2×C11×#41—24no—
72C2×C11×#41C2311yescharacteristic
73C22×D4×C11—22no—
74C22×D4×C11C2312yes—
75C2×#4343—24no—
76C2×#4339C2311yescharacteristic
77C22×D44—22no—
78C22×D44C2312yes—
79C11×C4⋊Q8D412yes—
80C11×#127—21no—
81C11×#127—21no—
82C11×#127C2314yes—
83C11×#127C2314yes—
84C11×#125D412yes—
85C11×#124—24no—
86C11×#124C2314yes—
87C11×#123—28no—
88C11×C22⋊Q8D414yes—
89C11×#121—24no—
90C11×#121—24no—
91C11×#121—28no—
92C11×#120—24no—
93C4×Q8×C11C2312yes—
94C4×Q8×C11C2314yes—
95C4×D4×C11—22no—
96C4×D4×C11—24no—
97C4×D4×C11—24no—
98C4×D4×C11C2312yes—
99C4×D4×C11C2318yes—
100C11×#117—21no—
101C11×#117C2311yescharacteristic
102C11×#117C2312yes—
103C2×C11×C22⋊C4—24no—
104C2×C42×C11—21no—
105C2×C42×C11C2311yescharacteristic
106#67003—24no—
107#67002—44no—
108#67000—24no—
109C2×#4326C2311yescharacteristic
110C2×#4325C2311yescharacteristic
111C2×#4325C2314yes—
112C2×#4324C2311yescharacteristic
113C2×#4324C2314yes—
114#66985—44no—
115C2×#4323—28no—
116C2×#4323—44no—
117C2×#4323C2314yes—
118C2×#4323C2314yes—
119C2×#4323C2311yescharacteristic
120C2×#4323C2318yes—
121C2×#4323C2314yes—
122C2×#4323C2314yes—
123C4×C22⋊D11—22no—
124#66979C2311yescharacteristic
125C2×#4318C2312yes—
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128#66948—24no—
129#66948—24no—
130#66948—28no—
131#66947—28no—
132#66946—24no—
133#66946—24no—
134#66935—24no—
135C22⋊C4×D11—24no—
136#66928C2314yes—
137#66927—21no—
138#66927—21no—
139#66927C2314yes—
140#66927C2314yes—
141C4×D44C2312yes—
142C4×D44C2318yes—
143#66925—21no—
144C42×D11—21no—
145C4×Dic22C2312yes—
146#66899C2312yes—
147#66896C2318yes—
148#66896C2312yes—
149#66874C2312yes—
150#66873C2318yes—
151#66873C2312yes—
152#66872C2312yes—
153#66871C2312yes—
154C4⋊(C11⋊C8)C2314yes—
155C4⋊(C11⋊C8)C2318yes—
156#66867C2314yes—
157C4×C11⋊C8C2312yes—
158C4×C11⋊C8C2312yes—
159C4×C11⋊C8C2314yes—
160#61409—111nomaximal, Sylow
161C24×C11—22no—
162C23×D11—22no—
163C11×#41—22no—
164C11×#41—22no—
165C11×#41—88no—
166C2×Q8×C11C2×D414yes—
167C2×Q8×C11C2411yescharacteristic
168C2×D4×C11—21no—
169C2×D4×C11—22no—
170C2×D4×C11—24no—
171C2×D4×C11—28no—
172C2×D4×C11—24no—
173C2×D4×C11—24no—
174C2×D4×C11—24no—
175C2×D4×C11—84no—
176C2×D4×C11C2414yes—
177C2×D4×C11C2411yescharacteristic
178C22×C4×C11—21no—
179C22×C4×C11—22no—
180C22×C4×C11—28no—
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2411yescharacteristic
183C2×C22⋊D11—21no—
184#4343—88no—
185#4339—22no—
186#4339—22no—
187C2×D44—22no—
188C2×D44—24no—
189C2×D44—24no—
190C2×D44—28no—
191C2×D44—24no—
192C2×D44—24no—
193C2×D44—84no—
194C2×D44C2411yescharacteristic
195C2×D44C2414yes—
196C2×C4×D11—21no—
197C2×C4×D11—22no—
198C2×C4×D11—28no—
199C2×Dic22C2411yescharacteristic
200C11×C4⋊C4—22no—
201C11×C4⋊C4C2×D414yes—
202C11×C4⋊C4C2×D414yes—
203C11×C4⋊C4C2×D418yes—
204C11×C4⋊C4C2412yes—
205C11×C22⋊C4—21no—
206C11×C22⋊C4—28no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—28no—
209C11×C22⋊C4C2×D414yes—
210C42×C11—21no—
211C42×C11—22no—
212C42×C11C2×D411yescharacteristic
213C42×C11C2×D411yescharacteristic
214C42×C11C2412yes—
215C42×C11C2414yes—
216C22⋊Dic11—21no—
217#4326—22no—
218#4325—22no—
219#4325—44no—
220#4324—22no—
221#4324—44no—
222#4323—28no—
223#4323—28no—
224#4323—22no—
225#4323—48no—
226#4323—44no—
227#4323—44no—
228(C2×D11)⋊C4—22no—
229(C2×D11)⋊C4—28no—
230(C2×D11)⋊C4—28no—
231C4⋊Dic11C2412yes—
232Dic11⋊C4—22no—
233C4×Dic11—22no—
234C4×Dic11—21no—
235#4318—24no—
236C2×C11⋊C8—22no—
237C2×C11⋊C8#4114yescomplemented
238C2×C11⋊C8C2412yes—
239C2×C11⋊C8C2414yes—
240C2×C11⋊C8C2411yescharacteristic
241C2×C11⋊C8C2411yescharacteristic
242#3508—111no—
243#3508D1111yescharacteristic, complemented
244#3399—114no—
245#3399—114no—
246#3396—114no—
247#3391—114no—
248#3155—112no—
249C2×#493—111no—
250#3041—112no—
251#3041—112no—
252#3038—111no—
253#3038—111no—
254#2960—111no—
255#2948—112no—
256C4×#135—111no—
257C23×C11—24no—
258C23×C11—21no—
259C23×C11—44no—
260C23×C11—84no—
261C23×C11C22×D411yescharacteristic
262C22×D11—24no—
263C22×D11—21no—
264C22×D11—44no—
265C22×D11—84no—
266Q8×C11—28no—
267Q8×C11—21no—
268Q8×C11—21no—
269D4×C11—24no—
270D4×C11—21no—
271D4×C11—21no—
272D4×C11—24no—
273D4×C11—42no—
274D4×C11—44no—
275D4×C11—48no—
276D4×C11—84no—
277D4×C11—88no—
278C2×C4×C11—24no—
279C2×C4×C11—21no—
280C2×C4×C11—22no—
281C2×C4×C11—42no—
282C2×C4×C11—44no—
283C2×C4×C11—88no—
284C2×C4×C11C22×D412yes—
285C2×C4×C11C22×D418yes—
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C22×D412yes—
288C2×C4×C11C2×#4112yes—
289C2×C4×C11H(5,𝔽2)12yes—
290C2×C4×C11C2511yescharacteristic
291C22⋊D11—42no—
292C2×Dic11—21no—
293C2×Dic11—22no—
294D44—24no—
295D44—21no—
296D44—21no—
297D44—24no—
298D44—44no—
299D44—48no—
300D44—84no—
301D44—88no—
302C4×D11—42no—
303C4×D11—44no—
304C4×D11—88no—
305Dic22—21no—
306Dic22—21no—
307C11⋊C8—22no—
308C11⋊C8—24no—
309C11⋊C8C2×#4112yes—
310C11⋊C8C2×#4112yes—
311C2×AGL(1,ℤ/8)—112no—
312C2×AGL(1,ℤ/8)—112no—
313C2×#135—111no—
314C22×D8—112no—
315C22×D8—112no—
316#559—114no—
317#559C2×D1114yescomplemented
318#550—114no—
319#550C2×D1114yescomplemented
320#546—24no—
321#546—224no—
322#540—22no—
323#540—222no—
324#535—112no—
325#535C2×D1112yes—
326#533C2×D1111yescharacteristic
327#532—22no—
328#532—222no—
329C2×#127—111no—
330C2×#127C2×D1111yescharacteristic
331#518—112no—
332#518C2×D1112yes—
333C4×#41—111no—
334C4×#41C2×D1111yescharacteristic
335#496—114no—
336#496—114no—
337#495—114no—
338#493—114no—
339#493—114no—
340#493—114no—
341#463—118no—
342#463—118no—
343#460—114no—
344#460—114no—
345#459—114no—
346#459—118no—
347#459—114no—
348#459—118no—
349#446—114no—
350C8×Q8—114no—
351#442—118no—
352C4×Q16—112no—
353C4×SD16—112no—
354C4×SD16—112no—
355C4×D8—112no—
356C4×D8—118no—
357#427—111no—
358#424—112no—
359#423—111no—
360#418—112no—
361#418—112no—
362#416—111no—
363#416—111no—
364#405—112no—
365C2×C4×C8—111no—
366C22×C11—22no—
367C22×C11—41no—
368C22×C11—44no—
369C22×C11—42no—
370C22×C11—48no—
371C22×C11—164no—
372C22×C11#55012yes—
373C22×C11C23×D411yescharacteristic
374C2×D11—44no—
375C2×D11—41no—
376C2×D11—48no—
377C2×D11—42no—
378C2×D11—164no—
379C4×C11—22no—
380C4×C11—28no—
381C4×C11—41no—
382C4×C11—42no—
383C4×C11#55012yes—
384C4×C11#57614yes—
385C4×C11C22×#4111yescharacteristic
386C4×C11C2×H(5,𝔽2)11yescharacteristic
387Dic11—41no—
388Dic11—42no—
389C2×#41—24no—
390C2×#41—111no—
391C2×#41—224no—
392C2×#41C22×D1111yescharacteristic
393C22×D4—22no—
394C22×D4—112no—
395C22×D4—222no—
396C22×D4C22×D1112yes—
397AGL(1,ℤ/8)—444no—
398AGL(1,ℤ/8)—444no—
399#135—224no—
400C2×Q16—111no—
401C2×SD16—111no—
402C2×SD16—111no—
403C2×SD16—114no—
404C2×SD16—114no—
405C2×D8—114no—
406C2×D8—114no—
407C2×D8—111no—
408C2×D8—118no—
409C2×D8—114no—
410C2×D8—114no—
411C2×D8—228no—
412C2×D8—444no—
413C2×M16—112no—
414C22×C8—111no—
415C22×C8—111no—
416C4⋊Q8C22⋊D1112yes—
417#127—21no—
418#127—21no—
419#127—114no—
420#127—114no—
421#127—221no—
422#127—221no—
423#127C22×D1114yes—
424#127C22×D1114yes—
425#125C22⋊D1112yes—
426#124—24no—
427#124—114no—
428#124—224no—
429#124C22×D1114yes—
430#123—28no—
431#123—228no—
432C22⋊Q8C22⋊D1114yes—
433#121—24no—
434#121—24no—
435#121—28no—
436#121—224no—
437#121—224no—
438#121—228no—
439#120—24no—
440#120—224no—
441C4×Q8—112no—
442C4×Q8C22×D1112yes—
443C4×Q8C22×D1114yes—
444C4×D4—22no—
445C4×D4—24no—
446C4×D4—24no—
447C4×D4—112no—
448C4×D4—118no—
449C4×D4—222no—
450C4×D4—224no—
451C4×D4—224no—
452C4×D4C22×D1112yes—
453C4×D4C22×D1118yes—
454#117—21no—
455#117—111no—
456#117—221no—
457#117C22×D1111yescharacteristic
458#117C22×D1112yes—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—224no—
461C2×C42—21no—
462C2×C42—221no—
463C2×C42C22×D1111yescharacteristic
464#107—112no—
465#106—112no—
466C4⋊C8—114no—
467C4⋊C8—118no—
468#103—112no—
469#103—112no—
470#102—112no—
471#102—118no—
472#102—112no—
473#102—118no—
474#97—114no—
475C4×C8—112no—
476C4×C8—112no—
477C4×C8—114no—
478C2×C11—22no—
479C2×C11—81no—
480C2×C11—84no—
481C2×C11C2×#55011yescharacteristic
482C2×C11C2×#57612yes—
483D11—81no—
484D11—84no—
485C24—22no—
486C24—222no—
487#41—22no—
488#41—22no—
489#41—88no—
490#41—222no—
491#41—222no—
492#41—888no—
493C2×Q8—111no—
494C2×Q8C2×C22⋊D1114yes—
495C2×Q8C23×D1111yescharacteristic
496C2×D4—21no—
497C2×D4—24no—
498C2×D4—24no—
499C2×D4—22no—
500C2×D4—24no—
501C2×D4—28no—
502C2×D4—24no—
503C2×D4—84no—
504C2×D4—114no—
505C2×D4—111no—
506C2×D4—221no—
507C2×D4—224no—
508C2×D4—224no—
509C2×D4—222no—
510C2×D4—224no—
511C2×D4—228no—
512C2×D4—224no—
513C2×D4—884no—
514C2×D4C23×D1114yes—
515C2×D4C23×D1111yescharacteristic
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—28no—
519C22×C4—221no—
520C22×C4—222no—
521C22×C4—228no—
522C22×C4C2×C22⋊D1112yes—
523C22×C4C23×D1111yescharacteristic
524Q16—222no—
525SD16—222no—
526SD16—222no—
527SD16—444no—
528SD16—444no—
529D8—228no—
530D8—228no—
531D8—222no—
532D8—448no—
533D8—444no—
534D8—444no—
535M16—224no—
536C2×C8—114no—
537C2×C8—111no—
538C2×C8—111no—
539C2×C8—112no—
540C2×C8—114no—
541C2×C8—222no—
542C4⋊C4—22no—
543C4⋊C4—112no—
544C4⋊C4—222no—
545C4⋊C4C2×C22⋊D1114yes—
546C4⋊C4C2×C22⋊D1114yes—
547C4⋊C4C2×C22⋊D1118yes—
548C4⋊C4C23×D1112yes—
549C22⋊C4—21no—
550C22⋊C4—28no—
551C22⋊C4—22no—
552C22⋊C4—28no—
553C22⋊C4—221no—
554C22⋊C4—228no—
555C22⋊C4—222no—
556C22⋊C4—228no—
557C22⋊C4C2×C22⋊D1114yes—
558C42—21no—
559C42—22no—
560C42—221no—
561C42—222no—
562C42C2×C22⋊D1111yescharacteristic
563C42C2×C22⋊D1111yescharacteristic
564C42C23×D1112yes—
565C42C23×D1114yes—
566C11#6140911yescharacteristic, complemented, Sylow
567C23—24no—
568C23—21no—
569C23—44no—
570C23—84no—
571C23—224no—
572C23—221no—
573C23—444no—
574C23—884no—
575C23C22×C22⋊D1111yescharacteristic
576Q8—28no—
577Q8—21no—
578Q8—21no—
579Q8—221no—
580Q8—221no—
581D4—24no—
582D4—21no—
583D4—21no—
584D4—24no—
585D4—42no—
586D4—44no—
587D4—48no—
588D4—84no—
589D4—88no—
590D4—224no—
591D4—221no—
592D4—221no—
593D4—224no—
594D4—442no—
595D4—444no—
596D4—448no—
597D4—884no—
598D4—888no—
599C2×C4—24no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—42no—
603C2×C4—44no—
604C2×C4—88no—
605C2×C4—221no—
606C2×C4—222no—
607C2×C4—442no—
608C2×C4—444no—
609C2×C4—888no—
610C2×C4#41×D1112yes—
611C2×C4#6704212yes—
612C2×C4C22×C22⋊D1112yes—
613C2×C4C22×C22⋊D1118yes—
614C2×C4C22×C22⋊D1111yescharacteristic
615C2×C4C22×C22⋊D1112yes—
616C2×C4C24×D1111yescharacteristic
617C8—112no—
618C8—112no—
619C8—222no—
620C8—224no—
621C22—22no—
622C22—42no—
623C22—48no—
624C22—41no—
625C22—44no—
626C22—164no—
627C22—442no—
628C22—448no—
629C22—441no—
630C22—444no—
631C22—1764no—
632C22#1062336512yes—
633C22C23×C22⋊D1111yescharacteristic
634C4—22no—
635C4—28no—
636C4—42no—
637C4—41no—
638C4—442no—
639C4—441no—
640C4#1062336512yes—
641C4#1062336614yes—
642C4C2×#41×D1111yescharacteristic
643C4C2×#6704211yescharacteristic
644C2—22no—
645C2—84no—
646C2—81no—
647C2—884no—
648C2—881no—
649C2C2×#1062336511yescharacteristic
650C2C2×#1062336612yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3508C2
socleC22×C11C23×D4
hypercenter#3508D11
hypocenterC11#61409
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #533 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #13082493C2semidirect
2. #13081658C2semidirect
3. #13081654C2semidirect
4. #13081624C2semidirect
5. #13081588C2semidirect
6. #13079099C2semidirect
7. C2×#10622686C2semidirect
8. #13078119C2semidirect
9. #13078115C2semidirect
10. #13078096C2semidirect
11. #13078092C2semidirect
12. #13077551C2semidirect
13. #13077466C2semidirect
14. C4×#67003C2semidirect
15. C11×#3508C2semidirect
16. C11×#559C22semidirect
17. C11×#550C22semidirect
34. #10623116C22semidirect
35. #10623108C22semidirect
42. #10622688C22semidirect
43. #10622687C22semidirect
46. #10622686C22semidirect
47. #10622685C22semidirect
48. #10622685C22semidirect
49. #10622672C22semidirect
50. #10622671C22semidirect
51. #10622670C22semidirect
52. C4×#4326C22semidirect
53. #10622640C22semidirect
54. C4×#4325C22semidirect
55. #10622637C22semidirect
56. Q8×C11⋊C8C22semidirect
57. C4×#4324C22semidirect
58. #10622629C22semidirect
59. #10622628C22semidirect
60. #10622628C22semidirect
61. #10622627C22semidirect
62. C4×#4323C22semidirect
63. C4×#4323C22semidirect
237. C2×C11⋊C8#41semidirect
243. #3508D11semidirect
317. #559C2×D11semidirect
319. #550C2×D11semidirect
566. C11#61409semidirect

Maximal subgroups

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

subgroupindex
#130824932
#130816582
#130816542
#130816242
#130815882
#130790992
C2×#106226862
#130781192
#130781152
#130780962
#130780922
#130775512
#130774662
C4×#670032
C11×#35082
#6140911