Finite Group Databasebeta

← #15624239

Subgroups — #15624239

Order 2816.

1874 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082512C211yesmaximal, characteristic, complemented
2#13079339C214yesmaximal, complemented
3#13079301C214yesmaximal, complemented
4#13079286C214yesmaximal, complemented
5#13079180C214yesmaximal, complemented
6#13079165C211yesmaximal, characteristic, complemented
7#13079084C211yesmaximal, characteristic, complemented
8#13078938C211yesmaximal, characteristic, complemented
9C2×#10622681C211yesmaximal, characteristic, complemented
10#13078309C212yesmaximal, complemented
11#13078298C212yesmaximal, complemented
12#13077455C212yesmaximal, complemented
13#13077444C212yesmaximal, complemented
14C4×#67001C211yesmaximal, characteristic, complemented
15C11×#3512C211yesmaximal, characteristic, complemented
16C11×#553—24no—
17C11×#553—22no—
18C11×#552—22no—
19C11×#541C2212yescomplemented
20C11×#540C2212yescomplemented
21C11×#537C2212yes—
22C11×#532C2211yescharacteristic
23C11×#529C2214yescomplemented
24C2×C11×#125C2211yescharacteristic
25C11×#520C2212yes—
26C4×C11×#41C2211yescharacteristic
27#10623361C2211yescharacteristic
28#10623356C2211yescharacteristic
29C2×#67004C2212yes—
30C2×#67002C2212yes—
31C2×#67001C2212yes—
32#10623099—22no—
33#10623090—22no—
34#10623087—24no—
35#10623065C2214yes—
36#10623052C2211yescharacteristic
37#10623047C2211yescharacteristic
38#10623010C2214yes—
39C2×#66928C2211yescharacteristic
40#10623001C2211yescharacteristic
41#10622846C2212yes—
42#10622846C2212yes—
43#10622699C2212yes—
44#10622694C2212yescomplemented
45#10622687C2212yes—
46#10622683C2212yescomplemented
47#10622681C2214yes—
48#10622681C2212yes—
49#10622681C2212yes—
50#10622678C2214yescomplemented
51#10622677C2214yescomplemented
52#10622672C2214yes—
53#10622669C2212yescomplemented
54#10622669C2212yescomplemented
55#10622665C2214yescomplemented
56#10622664C2214yescomplemented
57#10622662C2214yes—
58#10622661C2214yes—
59#10622655C2214yescomplemented
60#10622654C2214yescomplemented
61#10622652C2214yes—
62#10622651C2214yes—
63#10622643C2214yescomplemented
64C4×#4326C2214yescomplemented
65#10622639C2214yes—
66C4×#4325C2214yes—
67#10622631C2214yescomplemented
68C4×#4324C2214yescomplemented
69#10622627C2214yes—
70C4×#4323C2214yes—
71#10622610C2212yes—
72#10622610C2214yescomplemented
73C2×#66874C2212yes—
74C2×#66873C2212yes—
75#10622577C2212yes—
76#10622577C2212yes—
77C4×#4318C2211yescharacteristic
78C4×#4318C2212yescomplemented
79C2×C4×C11⋊C8C2211yescharacteristic
80C2×C4×C11⋊C8C2212yescomplemented
81C2×C11×#41C2312yes—
82C2×C11×#41C2311yescharacteristic
83C22×D44C2311yescharacteristic
84C22×Dic22C2311yescharacteristic
85C11×C4⋊Q8C2311yescharacteristic
86C11×#127C2311yescharacteristic
87C11×#126—24no—
88C11×#126—24no—
89C11×#125—24no—
90C11×#125—22no—
91C11×#125C2312yes—
92C11×#125C2312yes—
93C11×#124C2312yes—
94C11×#123—24no—
95C11×#123—24no—
96C11×C22⋊Q8—22no—
97C11×C22⋊Q8C2314yes—
98C11×#121—22no—
99C11×#121—24no—
100C11×#121—22no—
101C11×#121—24no—
102C11×#121C2314yes—
103C4×Q8×C11D412yes—
104C4×Q8×C11C2314yes—
105C4×D4×C11—24no—
106C4×D4×C11—24no—
107C4×D4×C11—22no—
108C4×D4×C11D414yes—
109C4×D4×C11D412yes—
110C4×D4×C11C2314yes—
111C11×#117—22no—
112C11×#117—24no—
113C11×#117C2311yescharacteristic
114C11×#117C2312yes—
115C2×C11×C4⋊C4—22no—
116C2×C11×C4⋊C4—22no—
117C2×C11×C4⋊C4C2312yes—
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2312yes—
120#67004—28no—
121#67002—28no—
122#67001—28no—
123#67000—21no—
124#66997—21no—
125C2×#4326C2314yes—
126C2×#4325C2314yes—
127#66993—21no—
128#66990—22no—
129#66989—21no—
130#66988—22no—
131C2×#4324C2314yes—
132C2×#4323C2314yes—
133#66983C2314yes—
134#66982—24no—
135C4×C22⋊D11—24no—
136C2×(C2×D11)⋊C4—22no—
137#66979C2311yescharacteristic
138#66979C2311yescharacteristic
139#66977—22no—
140#66977C2314yes—
141C2×#4318C2314yes—
142C2×#4318C2312yes—
143C22×C11⋊C8C2312yes—
144C22×C11⋊C8C2314yes—
145#66951—24no—
146#66949—24no—
147#66946—22no—
148#66940—22no—
149#66938—24no—
150#66936—24no—
151C22⋊C4×D11—22no—
152#66930—22no—
153#66929—24no—
154#66928—22no—
155#66928C2312yes—
156#66928C2312yes—
157C4×D44C2314yes—
158#66925—24no—
159#66923C2312yes—
160#66922C2312yes—
161C4×Dic22—22no—
162C4×Dic22C2314yes—
163#66899C2312yes—
164#66899C2312yes—
165#66899C2312yes—
166#66899C2312yes—
167#66896C2312yes—
168#66896C2312yes—
169#66896C2312yes—
170#66896C2312yes—
171#66874C2314yes—
172#66874C2314yes—
173#66873C2314yes—
174#66873C2314yes—
175#66872C2314yes—
176#66872C2314yes—
177#66871C2314yes—
178#66871C2314yes—
179#66867C2312yes—
180#66867C2314yes—
181C4×C11⋊C8C2311yescharacteristic
182C4×C11⋊C8C2311yescharacteristic
183C4×C11⋊C8C2312yes—
184C4×C11⋊C8C2312yes—
185C4×C11⋊C8C2314yes—
186#60724—111nomaximal, Sylow
187C23×D11—21no—
188C11×#41—24no—
189C11×#41—24no—
190C11×#41—24no—
191C2×Q8×C11C2×D411yescharacteristic
192C2×Q8×C11C2412yes—
193C2×D4×C11—22no—
194C2×D4×C11—24no—
195C2×D4×C11—22no—
196C2×D4×C11C2×D412yes—
197C2×D4×C11C2×D411yescharacteristic
198C2×D4×C11C2412yes—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—24no—
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2×D414yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2411yescharacteristic
206C2×C22⋊D11—24no—
207C22×Dic11—21no—
208C2×D44—21no—
209C2×D44—24no—
210C2×D44C2412yes—
211C2×C4×D11—24no—
212C2×Dic22—21no—
213C2×Dic22—22no—
214C2×Dic22—24no—
215C2×Dic22C2412yes—
216C11×C4⋊C4—22no—
217C11×C4⋊C4—24no—
218C11×C4⋊C4—24no—
219C11×C4⋊C4—24no—
220C11×C4⋊C4—24no—
221C11×C4⋊C4—22no—
222C11×C4⋊C4C2×D412yes—
223C11×C4⋊C4C2×D414yes—
224C11×C4⋊C4C2414yes—
225C11×C22⋊C4—24no—
226C11×C22⋊C4—22no—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—24no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4C2×D412yes—
231C11×C22⋊C4C2×D414yes—
232C42×C11—24no—
233C42×C11C2×D412yes—
234C42×C11C2×D414yes—
235C42×C11C2411yescharacteristic
236C42×C11C2412yes—
237C42×C11C2411yescharacteristic
238C22⋊Dic11—21no—
239C22⋊Dic11—21no—
240C22⋊Dic11—24no—
241#4326—28no—
242#4325—28no—
243#4324—28no—
244#4323—28no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249C4⋊Dic11—22no—
250C4⋊Dic11C2412yes—
251C4⋊Dic11C2412yes—
252Dic11⋊C4—22no—
253Dic11⋊C4—22no—
254Dic11⋊C4—24no—
255Dic11⋊C4—24no—
256C4×Dic11—21no—
257C4×Dic11—21no—
258C4×Dic11—24no—
259#4318—28no—
260#4318#4118yes—
261C2×C11⋊C8—28no—
262C2×C11⋊C8—24no—
263C2×C11⋊C8C2412yes—
264C2×C11⋊C8C2412yes—
265C2×C11⋊C8C2414yes—
266#3512D1111yescharacteristic, complemented
267#3510—111no—
268#3183—114no—
269#3179—114no—
270#3178—114no—
271#3168—114no—
272#3166—111no—
273#3153—111no—
274#3131—111no—
275C2×#488—111no—
276#3063—112no—
277#3062—112no—
278#2947—112no—
279#2946—112no—
280C4×#131—111no—
281C23×C11—22no—
282C23×C11C22×D412yes—
283C23×C11C22×D411yescharacteristic
284C22×D11—22no—
285C22×D11—42no—
286C22×D11—82no—
287Q8×C11—22no—
288Q8×C11—22no—
289Q8×C11—22no—
290D4×C11—24no—
291D4×C11—22no—
292D4×C11—22no—
293D4×C11—22no—
294D4×C11—44no—
295D4×C11—82no—
296D4×C11—84no—
297C2×C4×C11—24no—
298C2×C4×C11—22no—
299C2×C4×C11—24no—
300C2×C4×C11—44no—
301C2×C4×C11—42no—
302C2×C4×C11—44no—
303C2×C4×C11—84no—
304C2×C4×C11—82no—
305C2×C4×C11C22×D414yes—
306C2×C4×C11C22×D412yes—
307C2×C4×C11C22×D412yes—
308C2×C4×C11C22×D412yes—
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C2×#4114yes—
311C2×C4×C11C2511yescharacteristic
312C22⋊D11—84no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—42no—
317D44—24no—
318D44—42no—
319C4×D11—84no—
320Dic22—24no—
321Dic22—42no—
322Dic22—82no—
323C11⋊C8—22no—
324C11⋊C8—22no—
325C11⋊C8C2×#4118yes—
326C2×#137—112no—
327C2×AGL(1,ℤ/8)—112no—
328C2×#131—112no—
329#559—222no—
330#556—222no—
331#553—24no—
332#553—22no—
333#552—22no—
334#551—224no—
335#542—114no—
336#541C2×D1112yescomplemented
337#540C2×D1112yescomplemented
338#537C2×D1112yes—
339#536—111no—
340#535—111no—
341#533—111no—
342#532C2×D1111yescharacteristic
343#529—114no—
344#529C2×D1114yescomplemented
345C2×#125C2×D1111yescharacteristic
346C2×#124—111no—
347#520C2×D1112yes—
348#519—111no—
349#518—111no—
350C4×#41C2×D1111yescharacteristic
351#501—114no—
352#499—114no—
353#497—112no—
354#496—112no—
355#495—114no—
356#488—112no—
357#488—114no—
358#488—112no—
359#488—112no—
360#488—112no—
361#487—112no—
362#486—112no—
363#470—114no—
364#469—114no—
365#468—114no—
366#468—114no—
367#467—114no—
368#466—114no—
369#465—114no—
370#465—114no—
371#442—114no—
372#441—114no—
373#440—114no—
374#440—114no—
375C4×Q16—114no—
376C4×SD16—114no—
377C4×SD16—114no—
378C4×D8—114no—
379#428—112no—
380#428—112no—
381#416—112no—
382#416—112no—
383C2×#103—112no—
384C2×#102—112no—
385#405—114no—
386#405—112no—
387C4×M16—111no—
388C4×M16—112no—
389C2×C4×C8—111no—
390C2×C4×C8—112no—
391C22×C11—22no—
392C22×C11—24no—
393C22×C11—22no—
394C22×C11—42no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11#53212yes—
398C22×C11C23×D411yescharacteristic
399C2×D11—44no—
400C2×D11—42no—
401C2×D11—162no—
402C4×C11—22no—
403C4×C11—24no—
404C4×C11—22no—
405C4×C11—22no—
406C4×C11—44no—
407C4×C11—42no—
408C4×C11#53212yes—
409C4×C11C22×#4112yes—
410Dic11—42no—
411Dic11—42no—
412Dic11—42no—
413C2×#41C22×D1112yes—
414C2×#41C22×D1111yescharacteristic
415C22×Q8—111no—
416C22×D4—111no—
417#137—228no—
418AGL(1,ℤ/8)—228no—
419C2×Q16—114no—
420C2×SD16—114no—
421C2×SD16—114no—
422C2×D8—114no—
423#131—228no—
424C2×M16—112no—
425C2×M16—114no—
426C22×C8—112no—
427C22×C8—114no—
428C4⋊Q8—112no—
429C4⋊Q8—221no—
430C4⋊Q8C22×D1111yescharacteristic
431#127—221no—
432#127C22×D1111yescharacteristic
433#126—24no—
434#126—24no—
435#126—224no—
436#126—224no—
437#125—24no—
438#125—22no—
439#125—112no—
440#125C22×D1112yes—
441#125C22×D1112yes—
442#124—112no—
443#124—112no—
444#124—221no—
445#124—221no—
446#124—224no—
447#124—222no—
448#124C22×D1112yes—
449#123—24no—
450#123—24no—
451#123—222no—
452#123—224no—
453#123—224no—
454C22⋊Q8—22no—
455C22⋊Q8—114no—
456C22⋊Q8—222no—
457C22⋊Q8—224no—
458C22⋊Q8C22×D1114yes—
459#121—22no—
460#121—24no—
461#121—22no—
462#121—24no—
463#121—114no—
464#121C22×D1114yes—
465#120—222no—
466C4×Q8—114no—
467C4×Q8—222no—
468C4×Q8—222no—
469C4×Q8C22⋊D1112yes—
470C4×Q8C22×D1114yes—
471C4×D4—24no—
472C4×D4—24no—
473C4×D4—22no—
474C4×D4—114no—
475C4×D4—224no—
476C4×D4—222no—
477C4×D4C22⋊D1114yes—
478C4×D4C22⋊D1112yes—
479C4×D4C22×D1114yes—
480#117—22no—
481#117—24no—
482#117—111no—
483#117—111no—
484#117—222no—
485#117—224no—
486#117C22×D1111yescharacteristic
487#117C22×D1112yes—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4C22×D1112yes—
491C2×C22⋊C4—222no—
492C2×C22⋊C4—222no—
493C2×C42C22×D1111yescharacteristic
494C2×C42C22×D1112yes—
495#107—114no—
496#107—114no—
497#106—114no—
498#106—114no—
499#103—112no—
500#103—112no—
501#103—112no—
502#103—112no—
503#103—114no—
504#103—114no—
505#102—112no—
506#102—112no—
507#102—112no—
508#102—112no—
509#102—114no—
510#102—114no—
511#97—114no—
512#97—112no—
513C4×C8—111no—
514C4×C8—111no—
515C4×C8—112no—
516C4×C8—114no—
517C4×C8—112no—
518C2×C11—22no—
519C2×C11—42no—
520C2×C11—82no—
521C2×C11C2×#53211yescharacteristic
522C2×C11#358412yes—
523D11—82no—
524C24—221no—
525#41—24no—
526#41—24no—
527#41—24no—
528C2×Q8—112no—
529C2×Q8—221no—
530C2×Q8—222no—
531C2×Q8—224no—
532C2×Q8C2×C22⋊D1111yescharacteristic
533C2×Q8C23×D1112yes—
534C2×D4—22no—
535C2×D4—24no—
536C2×D4—22no—
537C2×D4—112no—
538C2×D4—224no—
539C2×D4—224no—
540C2×D4—221no—
541C2×D4C2×C22⋊D1112yes—
542C2×D4C2×C22⋊D1111yescharacteristic
543C2×D4C23×D1112yes—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—221no—
548C22×C4—224no—
549C22×C4C2×C22⋊D1112yes—
550C22×C4C2×C22⋊D1114yes—
551C22×C4C23×D1112yes—
552C22×C4C23×D1111yescharacteristic
553Q16—228no—
554SD16—228no—
555SD16—228no—
556D8—228no—
557M16—118no—
558M16—228no—
559C2×C8—114no—
560C2×C8—112no—
561C2×C8—112no—
562C2×C8—228no—
563C2×C8—224no—
564C4⋊C4—22no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—22no—
570C4⋊C4—112no—
571C4⋊C4—112no—
572C4⋊C4—222no—
573C4⋊C4—224no—
574C4⋊C4—224no—
575C4⋊C4—222no—
576C4⋊C4—222no—
577C4⋊C4C2×C22⋊D1112yes—
578C4⋊C4C2×C22⋊D1114yes—
579C4⋊C4C23×D1114yes—
580C22⋊C4—24no—
581C22⋊C4—22no—
582C22⋊C4—24no—
583C22⋊C4—24no—
584C22⋊C4—22no—
585C22⋊C4—221no—
586C22⋊C4—221no—
587C22⋊C4—224no—
588C22⋊C4—224no—
589C22⋊C4—224no—
590C22⋊C4—224no—
591C22⋊C4—224no—
592C22⋊C4C2×C22⋊D1112yes—
593C22⋊C4C2×C22⋊D1114yes—
594C42—24no—
595C42—221no—
596C42—221no—
597C42—224no—
598C42C2×C22⋊D1114yes—
599C42C2×C22⋊D1112yes—
600C42C23×D1111yescharacteristic
601C42C23×D1112yes—
602C42C23×D1111yescharacteristic
603C11#6072411yescharacteristic, complemented, Sylow
604C23—22no—
605C23—222no—
606C23—442no—
607C23—882no—
608C23C22×C22⋊D1112yes—
609C23C22×C22⋊D1111yescharacteristic
610Q8—22no—
611Q8—22no—
612Q8—22no—
613Q8—224no—
614Q8—442no—
615Q8—882no—
616D4—24no—
617D4—22no—
618D4—22no—
619D4—22no—
620D4—44no—
621D4—82no—
622D4—84no—
623D4—224no—
624D4—442no—
625D4—884no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—44no—
630C2×C4—42no—
631C2×C4—44no—
632C2×C4—84no—
633C2×C4—82no—
634C2×C4—222no—
635C2×C4—222no—
636C2×C4—222no—
637C2×C4—442no—
638C2×C4—884no—
639C2×C4#41×D1114yes—
640C2×C4C22×C22⋊D1114yes—
641C2×C4C22×C22⋊D1112yes—
642C2×C4C22×C22⋊D1112yes—
643C2×C4C22×C22⋊D1112yes—
644C2×C4C22×C22⋊D1111yescharacteristic
645C2×C4C24×D1111yescharacteristic
646C8—118no—
647C8—222no—
648C8—222no—
649C22—22no—
650C22—22no—
651C22—24no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—442no—
656C22—444no—
657C22—1762no—
658C22#1062336312yes—
659C22C23×C22⋊D1111yescharacteristic
660C4—22no—
661C4—22no—
662C4—24no—
663C4—22no—
664C4—42no—
665C4—44no—
666C4—442no—
667C4—442no—
668C4—442no—
669C4#1062336312yes—
670C4C2×#41×D1112yes—
671C2—22no—
672C2—42no—
673C2—82no—
674C2—882no—
675C2C2×#1062336311yescharacteristic
676C2#1308338712yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3512C2
socleC22×C11C23×D4
hypercenter#3512D11
hypocenterC11#60724
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3512

Complements

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

NH ≅ G/Ntype
1. #13082512C2semidirect
2. #13079339C2semidirect
3. #13079301C2semidirect
4. #13079286C2semidirect
5. #13079180C2semidirect
6. #13079165C2semidirect
7. #13079084C2semidirect
8. #13078938C2semidirect
9. C2×#10622681C2semidirect
10. #13078309C2semidirect
11. #13078298C2semidirect
12. #13077455C2semidirect
13. #13077444C2semidirect
14. C4×#67001C2semidirect
15. C11×#3512C2semidirect
19. C11×#541C22semidirect
20. C11×#540C22semidirect
23. C11×#529C22semidirect
44. #10622694C22semidirect
46. #10622683C22semidirect
50. #10622678C22semidirect
51. #10622677C22semidirect
53. #10622669C22semidirect
54. #10622669C22semidirect
55. #10622665C22semidirect
56. #10622664C22semidirect
59. #10622655C22semidirect
60. #10622654C22semidirect
63. #10622643C22semidirect
64. C4×#4326C22semidirect
67. #10622631C22semidirect
68. C4×#4324C22semidirect
72. #10622610C22semidirect
78. C4×#4318C22semidirect
80. C2×C4×C11⋊C8C22semidirect
266. #3512D11semidirect
336. #541C2×D11semidirect
337. #540C2×D11semidirect
344. #529C2×D11semidirect
603. C11#60724semidirect

Maximal subgroups

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

subgroupindex
#130825122
#130793392
#130793012
#130792862
#130791802
#130791652
#130790842
#130789382
C2×#106226812
#130783092
#130782982
#130774552
#130774442
C4×#670012
C11×#35122
#6072411