Finite Group Databasebeta

← #14781253

Subgroups — #14781253

Order 2816.

1610 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
1C2×#10623359C211yesmaximal, characteristic
2C2×#10622719C211yesmaximal, characteristic, complemented
3C2×#10622846C211yesmaximal, characteristic, complemented
4C22×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
5#13070995C211yesmaximal, characteristic, complemented
6#13069818C212yesmaximal, complemented
7#13069811C212yesmaximal, complemented
8#13069804C212yesmaximal, complemented
9#13069797C212yesmaximal, complemented
10#13068332C211yesmaximal, characteristic, complemented
11C2×C11×#416C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16#10623359—24no—
17#10623359—24no—
18C2×#66999C2212yes—
19C2×#66991C2212yes—
20C2×#66990—21no—
21C2×#66988—21no—
22C2×C4×C22⋊D11—22no—
23C2×#66979C2211yescharacteristic
24C2×#66979C2211yescharacteristic
25C23×C11⋊C8C2211yescharacteristic
26C11×#416—24no—
27C2×C11×#103C2211yescharacteristic, complemented
28C2×C11×#103C2211yescharacteristic, complemented
29C2×C11×#102C2211yescharacteristic, complemented
30C2×C11×#102C2211yescharacteristic, complemented
31#10622846—24no—
32C2×#66899C2212yescomplemented
33C2×#66896C2212yescomplemented
34C2×(C2×D11)⋊C8—24no—
35C2×(C2×D11)⋊C8C2212yes—
36C2×(C2×D11)⋊C8C2212yes—
37#10622719—24no—
38C2×#66882C2212yescomplemented
39C2×#66881C2212yescomplemented
40#10622600C2212yes—
41#10622600C2212yes—
42#10622568—21no—
43#10622556—21no—
44C4×(C2×D11)⋊C4—22no—
45#10622167C2212yescomplemented
46#10622167C2212yescomplemented
47C24×D11D411yescharacteristic
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41—22no—
53C2×C11×#41D414yes—
54C22×Q8×C11C2311yescharacteristic
55C22×D4×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—22no—
60C23×Dic11D411yescharacteristic
61C22×C4×D11—22no—
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×C4×D11—22no—
65C22×C4×D11—22no—
66C22×C4×D11—22no—
67C22×C4×D11D412yes—
68C22×C4×D11C2312yes—
69C22×C8×C11—22no—
70C22×C8×C11—22no—
71C22×C8×C11D414yescomplemented
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×#117—22no—
75C11×#117—22no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C42×C11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—21no—
83#66999—24no—
84#66999—24no—
85#66991—24no—
86#66991—24no—
87#66990—28no—
88#66988—28no—
89C4×C22⋊D11—216no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93#66979—22no—
94#66979—22no—
95#66979—22no—
96#66979D414yes—
97C2×C4⋊Dic11C2312yes—
98C2×C4⋊Dic11C2312yes—
99C2×Dic11⋊C4—22no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C22×C11⋊C8—22no—
103C22×C11⋊C8—22no—
104C22×C11⋊C8—22no—
105C22×C11⋊C8C2312yes—
106C11×#103—22no—
107C11×#103—22no—
108C11×#102—22no—
109C11×#102—22no—
110#66899—24no—
111#66896—24no—
112C11⋊#95—22no—
113C11⋊#95—22no—
114(C2×D11)⋊C8—24no—
115(C2×D11)⋊C8—24no—
116#66882—24no—
117#66881—24no—
118#23479—111nomaximal, Sylow
119C24×C11—21no—
120C24×C11C2×D411yescharacteristic
121C23×D11—22no—
122C23×D11—24no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—42no—
126C23×D11C2×D412yes—
127C11×#41—28no—
128C11×#41—28no—
129C11×#41—44no—
130C11×#41—44no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11C2×D412yes—
137C2×D4×C11—24no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—42no—
144C2×D4×C11—42no—
145C2×D4×C11C2×D412yes—
146C22×C4×C11—21no—
147C22×C4×C11—24no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11#4112yes—
157C22×C4×C11#4112yes—
158C22×C4×C11#4112yes—
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—28no—
161C2×C22⋊D11—44no—
162C2×C22⋊D11—44no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11C2×D412yes—
169C2×C4×D11—24no—
170C2×C4×D11—24no—
171C2×C4×D11—24no—
172C2×C4×D11—22no—
173C2×C4×D11—22no—
174C2×C4×D11—22no—
175C2×C4×D11—22no—
176C2×C4×D11—22no—
177C2×C4×D11—22no—
178C2×C4×D11—44no—
179C2×C4×D11—44no—
180C2×C4×D11—44no—
181C2×C4×D11—44no—
182C2×C8×C11—28no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11C2×D412yes—
188C2×C8×C11C2×D412yes—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C22⋊C4—42no—
194C42×C11—42no—
195C22⋊Dic11—28no—
196C22⋊Dic11—24no—
197C22⋊Dic11—42no—
198(C2×D11)⋊C4—28no—
199(C2×D11)⋊C4—44no—
200(C2×D11)⋊C4—44no—
201C4⋊Dic11—22no—
202C4⋊Dic11—22no—
203C4⋊Dic11—22no—
204C4⋊Dic11C2×D414yes—
205Dic11⋊C4—28no—
206C4×Dic11—24no—
207C4×Dic11—42no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8—22no—
210C2×C11⋊C8—22no—
211C2×C11⋊C8—44no—
212C2×#525—111no—
213C2×#427—111no—
214C2×#416—111no—
215C2×#416D1111yescharacteristic, complemented
216C22×C22⋊C8—111no—
217#2280—111no—
218#2036—112no—
219#2035—112no—
220#2034—112no—
221#2033—112no—
222#1735—111no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11#12012yes—
231C23×C11#12112yes—
232C23×C11#12312yes—
233C23×C11C22×D411yescharacteristic
234C22×D11—28no—
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—48no—
242C22×D11—48no—
243C22×D11—44no—
244C22×D11—44no—
245C22×D11#13514yes—
246Q8×C11—22no—
247Q8×C11—22no—
248Q8×C11—41no—
249Q8×C11—41no—
250D4×C11—22no—
251D4×C11—22no—
252D4×C11—48no—
253D4×C11—41no—
254D4×C11—41no—
255C2×C4×C11—22no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—48no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11#12012yes—
264C2×C4×C11#12114yes—
265C2×C4×C11#12112yes—
266C2×C4×C11#12114yes—
267C2×C4×C11#12312yes—
268C2×C4×C11#12314yes—
269C2×C4×C11#12414yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C22⋊D11—416no—
277C2×Dic11—24no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—44no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C4×D11—42no—
288C4×D11—42no—
289C4×D11—42no—
290C4×D11—42no—
291C4×D11—48no—
292C8×C11—22no—
293C8×C11—22no—
294C11⋊C8—42no—
295C22×#41C2×D1111yescharacteristic
296C24×C4—111no—
297C23×C8—111no—
298C23×C8C2×D1111yescharacteristic
299#525—224no—
300#525—224no—
301C2×#123—221no—
302C2×C22⋊Q8—112no—
303C2×#121—112no—
304C2×#120—221no—
305C2×C4×D4—222no—
306C2×#117—111no—
307C2×#117—111no—
308C2×#117C2×D1111yescharacteristic
309#427—224no—
310C2×#107—112no—
311C2×#106—112no—
312#416—24no—
313#416—224no—
314C2×#103—112no—
315C2×#103C2×D1111yescharacteristic, complemented
316C2×#103C2×D1111yescharacteristic, complemented
317C2×#102—112no—
318C2×#102C2×D1111yescharacteristic, complemented
319C2×#102C2×D1111yescharacteristic, complemented
320C2×C22⋊C8—112no—
321C2×C22⋊C8—112no—
322C2×C22⋊C8—224no—
323#381—221no—
324#380—112no—
325#380—112no—
326#379—221no—
327C4×C22⋊C4—222no—
328#340—112no—
329#340—112no—
330C22×C11—24no—
331C22×C11—24no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—42no—
335C22×C11—44no—
336C22×C11—82no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11#39414yes—
340C22×C11C2×#12011yescharacteristic
341C22×C11C2×#12111yescharacteristic
342C22×C11C2×#12311yescharacteristic
343C22×C11C2×#13512yes—
344C22×C11#57512yes—
345C2×D11—24no—
346C2×D11—24no—
347C2×D11—24no—
348C2×D11—416no—
349C2×D11—42no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—42no—
353C4×C11—42no—
354C4×C11—81no—
355C4×C11—81no—
356C4×C11#39414yes—
357C4×C11C2×#12111yescharacteristic
358C4×C11C2×#12111yescharacteristic
359C4×C11C2×#12311yescharacteristic
360C4×C11C2×#12411yescharacteristic
361Dic11—42no—
362Dic11—44no—
363Dic11—82no—
364C25—111no—
365C2×#41—22no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—22no—
369C2×#41—22no—
370C2×#41D4414yes—
371C22×Q8C22×D1111yescharacteristic
372C22×D4—21no—
373C22×D4—222no—
374C22×D4C22×D1111yescharacteristic
375C23×C4—21no—
376C23×C4—111no—
377C23×C4—112no—
378C23×C4—112no—
379C23×C4—222no—
380C23×C4—222no—
381C23×C4—222no—
382C23×C4—222no—
383C23×C4—222no—
384C23×C4—222no—
385C23×C4C22×D1111yescharacteristic
386C22×C8—22no—
387C22×C8—22no—
388C22×C8—112no—
389C22×C8—222no—
390C22×C8—222no—
391C22×C8—222no—
392C22×C8C22⋊D1114yescomplemented
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395#123—228no—
396C22⋊Q8—224no—
397C22⋊Q8—224no—
398#121—224no—
399#121—224no—
400#120—228no—
401C4×D4—2216no—
402#117—22no—
403#117—22no—
404#117—114no—
405#117—222no—
406#117—222no—
407#117—222no—
408C2×C4⋊C4—112no—
409C2×C4⋊C4—112no—
410C2×C4⋊C4—222no—
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—222no—
415C2×C22⋊C4—222no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—222no—
418C2×C22⋊C4—222no—
419C2×C22⋊C4—221no—
420C2×C42—21no—
421C2×C42—221no—
422C2×C42—221no—
423#107—224no—
424#106—224no—
425#103—22no—
426#103—22no—
427#103—224no—
428#102—22no—
429#102—22no—
430#102—224no—
431C22⋊C8—224no—
432C22⋊C8—224no—
433#95—222no—
434#95—222no—
435C2×C11—24no—
436C2×C11—82no—
437C2×C11C2×#39411yescharacteristic
438C2×C11#300212yes—
439C2×C11#305011yescharacteristic
440C2×C11#305411yescharacteristic
441C2×C11#309112yes—
442D11—44no—
443C24—21no—
444C24—112no—
445C24—224no—
446C24—222no—
447C24—222no—
448C24—222no—
449C24—442no—
450C24D4×D1111yescharacteristic
451#41—28no—
452#41—28no—
453#41—44no—
454#41—44no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8C2×D4412yes—
461C2×D4—24no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—228no—
470C2×D4—444no—
471C2×D4—444no—
472C2×D4C2×D4412yes—
473C22×C4—21no—
474C22×C4—24no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—112no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—224no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—444no—
495C22×C4—444no—
496C22×C4—444no—
497C22×C4—444no—
498C22×C4C2×D4412yes—
499C22×C4#433912yes—
500C22×C4D4×D1112yes—
501C22×C4D4×D1111yescharacteristic
502C22×C4#434112yes—
503C22×C4#434112yes—
504C22×C4C2×C22⋊D1112yes—
505C22×C4C23×D1111yescharacteristic
506C2×C8—28no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—222no—
512C2×C8—222no—
513C2×C8—222no—
514C2×C8—444no—
515C2×C8C2×C22⋊D1112yes—
516C2×C8C2×C22⋊D1112yes—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—114no—
522C4⋊C4—228no—
523C4⋊C4—222no—
524C4⋊C4—222no—
525C4⋊C4—222no—
526C22⋊C4—42no—
527C22⋊C4—228no—
528C22⋊C4—228no—
529C22⋊C4—224no—
530C22⋊C4—444no—
531C22⋊C4—444no—
532C22⋊C4—442no—
533C42—42no—
534C42—224no—
535C42—442no—
536C11#2347911yescharacteristic, complemented, Sylow
537C23—22no—
538C23—22no—
539C23—22no—
540C23—41no—
541C23—42no—
542C23—42no—
543C23—41no—
544C23—114no—
545C23—228no—
546C23—222no—
547C23—222no—
548C23—222no—
549C23—222no—
550C23—222no—
551C23—222no—
552C23—448no—
553C23—448no—
554C23—444no—
555C23—444no—
556C23#6693512yes—
557C23#6693612yes—
558C23#6699112yes—
559C23C2×D4×D1111yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—41no—
563Q8—41no—
564D4—22no—
565D4—22no—
566D4—48no—
567D4—41no—
568D4—41no—
569D4—4416no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—48no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—224no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—444no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—448no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4#6693512yes—
594C2×C4#6693612yes—
595C2×C4#6693814yes—
596C2×C4#6693914yes—
597C2×C4#6698314yes—
598C2×C4#6699112yes—
599C2×C4#6699214yes—
600C2×C4C22×D4411yescharacteristic
601C2×C4C2×#433911yescharacteristic
602C2×C4C2×D4×D1111yescharacteristic
603C2×C4C2×#434111yescharacteristic
604C2×C4C2×#434111yescharacteristic
605C2×C4C22×C22⋊D1111yescharacteristic
606C8—22no—
607C8—22no—
608C8—442no—
609C22—24no—
610C22—22no—
611C22—22no—
612C22—24no—
613C22—44no—
614C22—42no—
615C22—81no—
616C22—81no—
617C22—82no—
618C22—224no—
619C22—224no—
620C22—224no—
621C22—4416no—
622C22—442no—
623C22—442no—
624C22—442no—
625C22—442no—
626C22#1062257414yes—
627C22C2×#6693511yescharacteristic
628C22C2×#6693611yescharacteristic
629C22D11×#13512yes—
630C22#1062329912yes—
631C22C2×#6699111yescharacteristic
632C4—42no—
633C4—81no—
634C4—81no—
635C4—444no—
636C4—442no—
637C4—882no—
638C4#1062257414yes—
639C4C2×#6693811yescharacteristic
640C4C2×#6693911yescharacteristic
641C4C2×#6698311yescharacteristic
642C4C2×#6699211yescharacteristic
643C2—24no—
644C2—82no—
645C2—444no—
646C2C2×#1062257411yescharacteristic
647C2#1307783612yes—
648C2#1307819311yescharacteristic
649C2#1307822111yescharacteristic
650C2#1307852712yes—
subgroupG/H
centerC22×C4D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC2×#10623359C2
hypercenterC2×#416D11
hypocenterC11#23479
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#10622719C2semidirect
3. C2×#10622846C2semidirect
4. C22×(C2×D11)⋊C8C2semidirect
5. #13070995C2semidirect
6. #13069818C2semidirect
7. #13069811C2semidirect
8. #13069804C2semidirect
9. #13069797C2semidirect
10. #13068332C2semidirect
11. C2×C11×#416C2semidirect
27. C2×C11×#103C22semidirect
28. C2×C11×#103C22semidirect
29. C2×C11×#102C22semidirect
30. C2×C11×#102C22semidirect
32. C2×#66899C22semidirect
33. C2×#66896C22semidirect
38. C2×#66882C22semidirect
39. C2×#66881C22semidirect
45. #10622167C22semidirect
46. #10622167C22semidirect
71. C22×C8×C11D4semidirect
215. C2×#416D11semidirect
315. C2×#103C2×D11semidirect
316. C2×#103C2×D11semidirect
318. C2×#102C2×D11semidirect
319. C2×#102C2×D11semidirect
392. C22×C8C22⋊D11semidirect
536. C11#23479semidirect

Maximal subgroups

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

subgroupindex
C2×#106233592
C2×#106227192
C2×#106228462
C22×(C2×D11)⋊C82
#130709952
#130698182
#130698112
#130698042
#130697972
#130683322
C2×C11×#4162
#2347911