Finite Group Databasebeta

← #15633931

Subgroups — #15633931

Order 2816.

1852 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082492C211yesmaximal, characteristic, complemented
2#13082440C211yesmaximal, characteristic, complemented
3#13081387C214yesmaximal, complemented
4#13081372C214yesmaximal, complemented
5#13081348C214yesmaximal, complemented
6#13081326C214yesmaximal, complemented
7#13078973C212yesmaximal, complemented
8C2×#10622680C211yesmaximal, characteristic, complemented
9#13078445C212yesmaximal, complemented
10#13078154C212yesmaximal, complemented
11#13078097C211yesmaximal, characteristic, complemented
12#13077553C211yesmaximal, characteristic, complemented
13#13077446C212yesmaximal, complemented
14#13077414C211yesmaximal, characteristic, complemented
15C11×#3080C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18#10623361C2212yes—
19C2×#67003C2211yescharacteristic
20C2×#66961C2212yes—
21#10623221C2214yescomplemented
22#10623220—22no—
23#10623219—21no—
24D11×#125—21no—
25#10623216C2214yescomplemented
26#10623116C2214yes—
27#10623084C2214yes—
28#10623081—24no—
29#10623066—21no—
30#10623066—21no—
31#10623052C2212yes—
32#10623042—24no—
33#10623035C2212yes—
34#10623031C2212yes—
35#10623008—22no—
36C2×#66927C2211yescharacteristic
37C4×#4339C2211yescharacteristic
38#10623001C2211yescharacteristic
39C11×#479C2214yescomplemented
40C11×#478C2214yescomplemented
41C11×#428C2212yes—
42C11×#423C2211yescharacteristic
43C11×#417C2212yes—
44#10622846C2211yescharacteristic
45#10622744C2212yes—
46#10622735C2212yes—
47#10622732C2212yes—
48#10622680C2214yes—
49#10622680C2214yes—
50#10622643C2212yescomplemented
51#10622639C2212yescomplemented
52#10622631C2212yescomplemented
53#10622627C2212yescomplemented
54#10622615C2211yescharacteristic
55#10622611C2211yescharacteristic
56C2×#66873C2212yes—
57C2×#66873C2212yes—
58C2×#66867C2211yescharacteristic
59#10622504C2214yescomplemented
60#10622503C2214yescomplemented
61#10622502C2214yescomplemented
62#10622485C2214yescomplemented
63#10622484C2214yescomplemented
64#10622483C2214yescomplemented
65#10622482C2214yescomplemented
66#10622465C2214yescomplemented
67#10622461C2214yes—
68#10622456C2214yes—
69#10622441C2214yescomplemented
70#10622441C2214yescomplemented
71#10622432C2214yescomplemented
72#10622413C2214yescomplemented
73#10622411C2214yescomplemented
74#10622408C2214yescomplemented
75#10622399C2214yescomplemented
76#10622377C2214yescomplemented
77#10622375C2214yescomplemented
78#10622373C2214yescomplemented
79C2×C11×#41C2311yescharacteristic
80C2×#4339—24no—
81C2×#4339C2311yescharacteristic
82C22×D44—22no—
83C22×D44C2312yes—
84C2×C11×M16C2312yes—
85C11×#125—21no—
86C11×#125—21no—
87C11×#125C2314yes—
88C4×Q8×C11C2312yes—
89C4×D4×C11—22no—
90C4×D4×C11C2312yes—
91C11×#117—21no—
92C11×#117C2311yescharacteristic
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4C2312yes—
95C2×C42×C11—21no—
96C2×C42×C11C2311yescharacteristic
97#67003—24no—
98#67000C2314yes—
99C2×#4326C2311yescharacteristic
100C2×#4325C2311yescharacteristic
101#66993C2314yes—
102#66990—24no—
103C2×#4324C2311yescharacteristic
104C2×#4323C2311yescharacteristic
105#66983—22no—
106#66983—22no—
107#66983—24no—
108C4×C22⋊D11—22no—
109C4×C22⋊D11—24no—
110#66979C2311yescharacteristic
111#66979C2312yes—
112#66977—24no—
113#66977D414yes—
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116#66961—28no—
117C2×D88C2314yes—
118C2×#4314C2314yes—
119#66950—24no—
120#66949—24no—
121#66949—24no—
122#66947—24no—
123#66947—24no—
124#66946C2314yes—
125#66946C2314yes—
126#66946C2314yes—
127#66945—22no—
128C4⋊C4×D11—22no—
129C4⋊C4×D11—24no—
130#66943—22no—
131#66943C2314yes—
132#66942—24no—
133#66942—24no—
134#66941—24no—
135#66941—22no—
136#66941C2314yes—
137#66940—24no—
138#66940C2314yes—
139#66937—24no—
140#66937—24no—
141C22⋊C4×D11—24no—
142#66928—24no—
143#66927—21no—
144#66927—21no—
145#66927C2314yes—
146C4×D44—22no—
147C4×D44—22no—
148C4×D44—24no—
149C4×D44C2312yes—
150#66925—21no—
151C42×D11—21no—
152#66923D411yescharacteristic
153#66923D411yescharacteristic
154#66922D412yes—
155C4×Dic22C2312yes—
156C4×Dic22C2314yes—
157C11×#107C2314yes—
158C11×#106C2314yes—
159C11×C4⋊C8C2314yes—
160C11×#103C2314yes—
161C11×#102C2314yes—
162#66899C2312yes—
163#66896C2312yes—
164#66885C2314yes—
165#66885C2314yes—
166#66879C2314yes—
167Dic11⋊C8C2314yes—
168Dic11⋊C8C2314yes—
169C8×Dic11C2314yes—
170#66874C2312yes—
171#66873C2314yes—
172#66873C2312yes—
173#66873C2314yes—
174#66873C2314yes—
175#66873C2314yes—
176#66872C2312yes—
177#66871C2312yes—
178#66867C2312yes—
179#66867C2312yes—
180#61337—111nomaximal, Sylow
181C23×D11—22no—
182C11×#41—22no—
183C11×#41—22no—
184C2×Q8×C11C2411yescharacteristic
185C2×D4×C11—21no—
186C2×D4×C11C2411yescharacteristic
187C22×C4×C11—22no—
188C22×C4×C11—21no—
189C22×C4×C11—22no—
190C22×C4×C11C2×D412yes—
191C22×C4×C11C2411yescharacteristic
192C2×C22⋊D11—24no—
193C2×C22⋊D11—24no—
194C2×C22⋊D11—21no—
195#4339—22no—
196#4339—88no—
197#4339#4114yescomplemented
198C2×D44—22no—
199C2×D44—24no—
200C2×D44—24no—
201C2×D44—24no—
202C2×D44—24no—
203C2×D44—84no—
204C2×D44C2414yes—
205C2×D44C2411yescharacteristic
206C2×C4×D11—24no—
207C2×C4×D11—24no—
208C2×C4×D11—24no—
209C2×C4×D11—21no—
210C2×C4×D11—22no—
211C2×Dic22—24no—
212C2×Dic22C2×D414yes—
213C2×Dic22C2411yescharacteristic
214C11×M16—24no—
215C2×C8×C11C2414yes—
216C11×C4⋊C4—24no—
217C11×C4⋊C4—24no—
218C11×C4⋊C4—22no—
219C11×C4⋊C4—22no—
220C11×C4⋊C4C2412yes—
221C11×C4⋊C4C2414yes—
222C11×C22⋊C4—21no—
223C11×C22⋊C4—22no—
224C42×C11—21no—
225C42×C11—22no—
226C42×C11C2×D411yescharacteristic
227C42×C11C2×D411yescharacteristic
228C42×C11C2412yes—
229C22⋊Dic11—21no—
230C22⋊Dic11C2×D414yes—
231#4326—22no—
232#4325—22no—
233#4324—22no—
234#4323—22no—
235(C2×D11)⋊C4—24no—
236(C2×D11)⋊C4—24no—
237(C2×D11)⋊C4—24no—
238(C2×D11)⋊C4—24no—
239(C2×D11)⋊C4—24no—
240(C2×D11)⋊C4—22no—
241C4⋊Dic11—24no—
242C4⋊Dic11C2×D414yes—
243C4⋊Dic11C2×D412yes—
244C4⋊Dic11C2×D412yes—
245C4⋊Dic11C2412yes—
246Dic11⋊C4—24no—
247Dic11⋊C4—24no—
248Dic11⋊C4—24no—
249Dic11⋊C4—22no—
250Dic11⋊C4C2×D414yes—
251Dic11⋊C4C2×D414yes—
252C4×Dic11—24no—
253C4×Dic11—22no—
254C4×Dic11—21no—
255C4×Dic11C2414yes—
256C2×C11⋊C8—22no—
257C2×C11⋊C8—22no—
258C2×C11⋊C8C2411yescharacteristic
259C2×C11⋊C8C2411yescharacteristic
260C2×C11⋊C8C2412yes—
261D88—28no—
262#4314—28no—
263#3508—111no—
264#3504—111no—
265#3371—114no—
266#3370—114no—
267#3368—114no—
268#3366—114no—
269#3136—112no—
270C2×#490—111no—
271#3081—112no—
272#3080D1111yescharacteristic, complemented
273#3045—112no—
274#3038—111no—
275#2961—111no—
276#2946—112no—
277#2943—111no—
278C23×C11—21no—
279C23×C11C22×D411yescharacteristic
280C22×D11—21no—
281C22×D11—24no—
282C22×D11—44no—
283C22×D11—82no—
284C22×D11—82no—
285Q8×C11—21no—
286Q8×C11—21no—
287D4×C11—21no—
288D4×C11—21no—
289D4×C11—42no—
290C2×C4×C11—24no—
291C2×C4×C11—21no—
292C2×C4×C11—22no—
293C2×C4×C11—42no—
294C2×C4×C11—44no—
295C2×C4×C11—42no—
296C2×C4×C11—82no—
297C2×C4×C11C22×D412yes—
298C2×C4×C11C22×D412yes—
299C2×C4×C11C22×D411yescharacteristic
300C2×C4×C11C2×#4112yes—
301C2×C4×C112−1+412yes—
302C2×C4×C11C2511yescharacteristic
303C22⋊D11—24no—
304C22⋊D11—84no—
305C22⋊D11—84no—
306C2×Dic11—21no—
307C2×Dic11—22no—
308C2×Dic11C22×D414yes—
309C2×Dic11C22×D414yes—
310D44—24no—
311D44—21no—
312D44—24no—
313D44—48no—
314D44—44no—
315D44—84no—
316D44C2×#4112yes—
317C4×D11—24no—
318C4×D11—84no—
319C4×D11—84no—
320C4×D11—84no—
321C4×D11—82no—
322Dic22—21no—
323Dic22—44no—
324Dic22—84no—
325Dic22C2×#4112yes—
326C8×C11—24no—
327C11⋊C8—21no—
328C11⋊C8—21no—
329C11⋊C8—22no—
330C2×AGL(1,ℤ/8)—112no—
331C2×#135—111no—
332#559—114no—
333#557—114no—
334#554—114no—
335#554—224no—
336#550—114no—
337#546—224no—
338#544—112no—
339#544—222no—
340#540—221no—
341#540—221no—
342#535—112no—
343#533—111no—
344#533—221no—
345#532—222no—
346C2×#127—111no—
347C2×#125—221no—
348C2×#125C2×D1111yescharacteristic
349#520—112no—
350#518—112no—
351C4×#41—111no—
352C4×#41C2×D1111yescharacteristic
353#490—114no—
354#490—114no—
355#490—114no—
356#489—114no—
357#488—114no—
358#486—114no—
359#479C2×D1114yescomplemented
360#478—114no—
361#478—114no—
362#478C2×D1114yescomplemented
363#476—114no—
364#474—114no—
365#464—114no—
366#463—114no—
367#460—114no—
368#460—114no—
369#459—114no—
370#459—114no—
371#446—114no—
372#446—114no—
373#442—112no—
374#442—114no—
375#441—112no—
376#440—112no—
377#440—112no—
378#440—114no—
379C4×SD16—114no—
380C4×D8—114no—
381#428C2×D1112yes—
382#427—111no—
383#424—112no—
384#423C2×D1111yescharacteristic
385#418—112no—
386#417C2×D1112yes—
387#416—111no—
388#416—111no—
389C2×#102—112no—
390C2×#102—112no—
391#405—112no—
392C2×#97—111no—
393C22×C11—22no—
394C22×C11—42no—
395C22×C11—41no—
396C22×C11#54812yes—
397C22×C11C23×D411yescharacteristic
398C2×D11—22no—
399C2×D11—42no—
400C2×D11—44no—
401C2×D11—44no—
402C2×D11—44no—
403C2×D11—164no—
404C4×C11—22no—
405C4×C11—22no—
406C4×C11—42no—
407C4×C11—44no—
408C4×C11—41no—
409C4×C11#54812yes—
410C4×C11C22×#4111yescharacteristic
411C4×C11C2×2−1+411yescharacteristic
412Dic11—24no—
413Dic11—24no—
414Dic11—22no—
415Dic11—42no—
416C2×#41—111no—
417C2×#41—224no—
418C2×#41C22×D1111yescharacteristic
419C22×D4—112no—
420C22×D4—222no—
421AGL(1,ℤ/8)—228no—
422#135—224no—
423C2×Q16—111no—
424C2×SD16—111no—
425C2×SD16—111no—
426C2×SD16—114no—
427C2×D8—111no—
428C2×D8—114no—
429C2×M16C22×D1112yes—
430C22×C8—111no—
431C22×C8—111no—
432C4⋊Q8—114no—
433C4⋊Q8—112no—
434C4⋊Q8—222no—
435C4⋊Q8—224no—
436#127—114no—
437#127—114no—
438#127—221no—
439#127—221no—
440#125—21no—
441#125—21no—
442#125—114no—
443#125—111no—
444#125—111no—
445#125—222no—
446#125—224no—
447#125—224no—
448#125C22×D1114yes—
449#124—114no—
450#124—224no—
451#123—224no—
452#123—224no—
453C22⋊Q8—114no—
454C22⋊Q8—224no—
455C22⋊Q8—224no—
456C22⋊Q8—224no—
457C22⋊Q8—224no—
458#121—224no—
459#121—224no—
460#121—222no—
461#121—222no—
462#121—224no—
463#120—224no—
464C4×Q8—114no—
465C4×Q8—114no—
466C4×Q8—112no—
467C4×Q8—224no—
468C4×Q8C22×D1112yes—
469C4×D4—22no—
470C4×D4—114no—
471C4×D4—114no—
472C4×D4—114no—
473C4×D4—112no—
474C4×D4—222no—
475C4×D4—222no—
476C4×D4—224no—
477C4×D4—224no—
478C4×D4—222no—
479C4×D4C22×D1112yes—
480#117—21no—
481#117—112no—
482#117—111no—
483#117—222no—
484#117—221no—
485#117C22×D1111yescharacteristic
486C2×C4⋊C4—22no—
487C2×C4⋊C4—222no—
488C2×C4⋊C4—224no—
489C2×C4⋊C4C22×D1112yes—
490C2×C22⋊C4—224no—
491C2×C42—21no—
492C2×C42—221no—
493C2×C42C22×D1111yescharacteristic
494#107—112no—
495#107C22×D1114yes—
496#106—112no—
497#106C22×D1114yes—
498C4⋊C8—114no—
499C4⋊C8—114no—
500C4⋊C8C22×D1114yes—
501#103—112no—
502#103—112no—
503#103C22×D1114yes—
504#102—112no—
505#102—114no—
506#102—114no—
507#102—114no—
508#102—114no—
509#102—114no—
510#102—114no—
511#102—112no—
512#102C22×D1114yes—
513#97—114no—
514#97—112no—
515#97—112no—
516C4×C8—114no—
517C2×C11—22no—
518C2×C11—81no—
519C2×C11C2×#54811yescharacteristic
520C2×C11#358512yes—
521D11—42no—
522D11—84no—
523C24—222no—
524#41—22no—
525#41—22no—
526#41—114no—
527#41—222no—
528#41—888no—
529C2×Q8—114no—
530C2×Q8—111no—
531C2×Q8—224no—
532C2×Q8C23×D1111yescharacteristic
533C2×D4—21no—
534C2×D4—111no—
535C2×D4—114no—
536C2×D4—224no—
537C2×D4—224no—
538C2×D4—221no—
539C2×D4—222no—
540C2×D4—224no—
541C2×D4—224no—
542C2×D4—224no—
543C2×D4—224no—
544C2×D4—884no—
545C2×D4C23×D1111yescharacteristic
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—224no—
550C22×C4—224no—
551C22×C4—224no—
552C22×C4—221no—
553C22×C4—222no—
554C22×C4D4×D1112yes—
555C22×C4C23×D1111yescharacteristic
556Q16—222no—
557SD16—228no—
558SD16—222no—
559SD16—222no—
560D8—228no—
561D8—222no—
562M16—24no—
563C2×C8—112no—
564C2×C8—111no—
565C2×C8—111no—
566C2×C8—222no—
567C2×C8—222no—
568C2×C8C23×D1114yes—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—112no—
574C4⋊C4—114no—
575C4⋊C4—112no—
576C4⋊C4—114no—
577C4⋊C4—114no—
578C4⋊C4—112no—
579C4⋊C4—224no—
580C4⋊C4—224no—
581C4⋊C4—224no—
582C4⋊C4—224no—
583C4⋊C4—222no—
584C4⋊C4C23×D1114yes—
585C4⋊C4C23×D1112yes—
586C22⋊C4—21no—
587C22⋊C4—22no—
588C22⋊C4—114no—
589C22⋊C4—224no—
590C22⋊C4—224no—
591C22⋊C4—224no—
592C22⋊C4—224no—
593C22⋊C4—224no—
594C22⋊C4—221no—
595C22⋊C4—222no—
596C42—21no—
597C42—22no—
598C42—114no—
599C42—224no—
600C42—221no—
601C42—222no—
602C42D4×D1111yescharacteristic
603C42D4×D1111yescharacteristic
604C42C23×D1112yes—
605C11#6133711yescharacteristic, complemented, Sylow
606C23—21no—
607C23—221no—
608C23—224no—
609C23—444no—
610C23—882no—
611C23—882no—
612C23C2×D4×D1111yescharacteristic
613Q8—21no—
614Q8—21no—
615Q8—112no—
616Q8—221no—
617Q8—444no—
618Q8—884no—
619D4—21no—
620D4—21no—
621D4—42no—
622D4—112no—
623D4—224no—
624D4—221no—
625D4—224no—
626D4—224no—
627D4—448no—
628D4—444no—
629D4—884no—
630D4—884no—
631D4—884no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—24no—
635C2×C4—42no—
636C2×C4—44no—
637C2×C4—42no—
638C2×C4—82no—
639C2×C4—114no—
640C2×C4—114no—
641C2×C4—221no—
642C2×C4—224no—
643C2×C4—222no—
644C2×C4—882no—
645C2×C4—884no—
646C2×C4—884no—
647C2×C4—884no—
648C2×C4C2×D4×D1112yes—
649C2×C4C2×D4×D1112yes—
650C2×C4C2×D4×D1111yescharacteristic
651C2×C4#6704012yes—
652C2×C4#41×D1112yes—
653C2×C4C24×D1111yescharacteristic
654C8—24no—
655C8—222no—
656C8—221no—
657C8—221no—
658C22—22no—
659C22—42no—
660C22—41no—
661C22—222no—
662C22—442no—
663C22—444no—
664C22—444no—
665C22—444no—
666C22—1764no—
667C22#1062316412yes—
668C22C22×D4×D1111yescharacteristic
669C4—22no—
670C4—22no—
671C4—42no—
672C4—44no—
673C4—41no—
674C4—224no—
675C4—224no—
676C4—222no—
677C4—442no—
678C4#1062316412yes—
679C4C2×#6704011yescharacteristic
680C4C2×#41×D1111yescharacteristic
681C2—22no—
682C2—81no—
683C2—442no—
684C2—884no—
685C2C2×#1062316411yescharacteristic
686C2#1308339312yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3080C2
socleC22×C11C23×D4
hypercenter#3080D11
hypocenterC11#61337
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3080

Complements

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

NH ≅ G/Ntype
1. #13082492C2semidirect
2. #13082440C2semidirect
3. #13081387C2semidirect
4. #13081372C2semidirect
5. #13081348C2semidirect
6. #13081326C2semidirect
7. #13078973C2semidirect
8. C2×#10622680C2semidirect
9. #13078445C2semidirect
10. #13078154C2semidirect
11. #13078097C2semidirect
12. #13077553C2semidirect
13. #13077446C2semidirect
14. #13077414C2semidirect
15. C11×#3080C2semidirect
21. #10623221C22semidirect
25. #10623216C22semidirect
39. C11×#479C22semidirect
40. C11×#478C22semidirect
50. #10622643C22semidirect
51. #10622639C22semidirect
52. #10622631C22semidirect
53. #10622627C22semidirect
59. #10622504C22semidirect
60. #10622503C22semidirect
61. #10622502C22semidirect
62. #10622485C22semidirect
63. #10622484C22semidirect
64. #10622483C22semidirect
65. #10622482C22semidirect
66. #10622465C22semidirect
69. #10622441C22semidirect
70. #10622441C22semidirect
71. #10622432C22semidirect
72. #10622413C22semidirect
73. #10622411C22semidirect
74. #10622408C22semidirect
75. #10622399C22semidirect
76. #10622377C22semidirect
77. #10622375C22semidirect
78. #10622373C22semidirect
197. #4339#41semidirect
272. #3080D11semidirect
359. #479C2×D11semidirect
362. #478C2×D11semidirect
605. C11#61337semidirect

Maximal subgroups

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

subgroupindex
#130824922
#130824402
#130813872
#130813722
#130813482
#130813262
#130789732
C2×#106226802
#130784452
#130781542
#130780972
#130775532
#130774462
#130774142
C11×#30802
#6133711