Finite Group Databasebeta

← #14760613

Subgroups — #14760613

Order 2816.

914 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078222C211yesmaximal, characteristic
2C2×#10622436C211yesmaximal, characteristic, complemented
3#13077311C211yesmaximal, characteristic, complemented
4#13077306C211yesmaximal, characteristic, complemented
5C2×#10622610C211yesmaximal, characteristic, complemented
6#13069501C211yesmaximal, characteristic, complemented
7#13069363C211yesmaximal, characteristic, complemented
8#13069321C211yesmaximal, characteristic, complemented
9#13069317C211yesmaximal, characteristic, complemented
10#13069064C211yesmaximal, characteristic, complemented
11#13068656C211yesmaximal, characteristic, complemented
12#13068499C211yesmaximal, characteristic, complemented
13#13068461C211yesmaximal, characteristic, complemented
14#13068457C211yesmaximal, characteristic, complemented
15C11×#1897C211yesmaximal, characteristic, complemented
16C11×#525C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×#67003C2211yescharacteristic
19C2×#67001C2211yescharacteristic
20#10623322C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C2×#66960C2211yescharacteristic
24C2×C11×#104C2211yescharacteristic
25C2×C11×#104C2211yescharacteristic
26C11×#407C2211yescharacteristic
27#10622847C2211yescharacteristic
28#10622846C2211yescharacteristic
29#10622820C2211yescharacteristic
30#10622742C2211yescharacteristic
31C2×#66886C2211yescharacteristic
32C2×#66886C2211yescharacteristic
33#10622735C2211yescharacteristic
34#10622732C2211yescharacteristic
35#10622665C412yescomplemented
36#10622662C412yescomplemented
37#10622655C412yescomplemented
38#10622652C412yescomplemented
39#10622624—22no—
40D4×C11⋊C8—22no—
41#10622615C2211yescharacteristic
42#10622612C2211yescharacteristic
43#10622611C2211yescharacteristic
44#10622610—24no—
45#10622610C2211yescharacteristic
46C2×#66869C2211yescharacteristic
47C2×#66869C2211yescharacteristic
48C2×#66867C2211yescharacteristic
49C2×#66867C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51C2×C4×C11⋊C8C2211yescharacteristic
52#10622436—24no—
53#10622343—22no—
54(C22⋊D11)⋊C8—22no—
55C11×#339C2211yescharacteristic
56C11×#339C2211yescharacteristic
57#10622196C2211yescharacteristic
58#10622196C2211yescharacteristic
59#10622161C2211yescharacteristic
60#10622161C2211yescharacteristic
61C2×C11×#41C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C2×#4339C2311yescharacteristic
64C2×C11×M16C2311yescharacteristic
65C2×C11×M16C2311yescharacteristic
66C11×#123—21no—
67C11×C22⋊Q8C2×C412yes—
68C11×#121C2×C412yes—
69C11×#120—21no—
70C4×D4×C11—22no—
71C11×#117—22no—
72C11×#117—22no—
73C11×#117C2311yescharacteristic
74C2×C11×C4⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78#67006—21no—
79#67003—22no—
80#67003—22no—
81#67001—22no—
82#67001—22no—
83C2×#4326C2×C411yescharacteristic
84C2×#4325C2×C411yescharacteristic
85C2×#4324C2×C411yescharacteristic
86C2×#4323C2×C411yescharacteristic
87#66983C2×C412yes—
88#66982—21no—
89C4×C22⋊D11—22no—
90#66979C2311yescharacteristic
91#66977C2×C412yes—
92C2×#4318—22no—
93C2×#4318—21no—
94C2×#4318—22no—
95C2×#4318C2×C412yes—
96C2×#4318C2×C412yes—
97C2×#4318C2311yescharacteristic
98C2×#4318C2311yescharacteristic
99C22×C11⋊C8—22no—
100C22×C11⋊C8—22no—
101C22×C11⋊C8—21no—
102C22×C11⋊C8D412yes—
103C22×C11⋊C8D412yes—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108#66960—22no—
109#66960—22no—
110C2×#4313—21no—
111C2×C8×D11—21no—
112C11×#104—22no—
113C11×#104—22no—
114C11×C22⋊C8—22no—
115#66899C2×C412yes—
116#66896C2×C412yes—
117C22⋊(C11⋊C8)—22no—
118C22⋊(C11⋊C8)—22no—
119#66886—22no—
120#66886—22no—
121(C2×D11)⋊C8—22no—
122#66879—21no—
123Dic11⋊C8—22no—
124C8×Dic11—21no—
125#66874C2×C412yes—
126#66873C2×C412yes—
127#66872C2×C412yes—
128#66871C2×C412yes—
129#66869—22no—
130#66869—22no—
131C4⋊(C11⋊C8)—22no—
132#66867—22no—
133#66867—21no—
134#66867D414yescomplemented
135C4×C11⋊C8—22no—
136C4×C11⋊C8—22no—
137C4×C11⋊C8—21no—
138#21550—111nomaximal, Sylow
139C24×C11#4111yescharacteristic
140C11×#41—21no—
141C11×#41—21no—
142C11×#41—21no—
143C11×#41—21no—
144C2×Q8×C11C22×C411yescharacteristic
145C2×D4×C11—22no—
146C2×D4×C11—21no—
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11#4111yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C2×C22⋊D11—22no—
160C2×C22⋊D11—21no—
161#4339—21no—
162#4339—21no—
163#4339—21no—
164#4339—21no—
165C2×D44C22×C411yescharacteristic
166C2×C4×D11—21no—
167C2×Dic22C22×C411yescharacteristic
168C11×M16—21no—
169C11×M16—21no—
170C11×M16—21no—
171C11×M16—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4C22×C412yes—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—22no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11C2×D412yes—
185C42×C11#4112yes—
186C22⋊Dic11—22no—
187C22⋊Dic11—21no—
188#4326—22no—
189#4325—22no—
190#4324—22no—
191#4323—22no—
192(C2×D11)⋊C4—22no—
193C4⋊Dic11C22×C412yes—
194Dic11⋊C4—22no—
195C4×Dic11—21no—
196#4318—24no—
197#4318—24no—
198#4318—21no—
199#4318—21no—
200#4318—21no—
201#4318—21no—
202#4318—42no—
203C2×C11⋊C8—24no—
204C2×C11⋊C8—24no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—42no—
212C2×C11⋊C8C22×C412yes—
213C2×C11⋊C8C22×C411yescharacteristic
214C2×C11⋊C8C22×C411yescharacteristic
215C2×C11⋊C8C2×D412yes—
216C2×C11⋊C8C2×D412yes—
217C2×C11⋊C8C2×D411yescharacteristic
218C2×C11⋊C8C2×D412yes—
219C2×C11⋊C8C2×D411yescharacteristic
220C2×C11⋊C8#4112yes—
221C2×C11⋊C8#4112yes—
222#4313—42no—
223C8×D11—42no—
224#3054—111no—
225C2×#444—111no—
226#2929—111no—
227#2929—111no—
228C2×#405—111no—
229#1974—111no—
230#1945—111no—
231#1937—111no—
232#1937—111no—
233#1897—111no—
234#1897D1111yescharacteristic, complemented
235#1811—111no—
236#1773—111no—
237#1765—111no—
238#1765—111no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—42no—
243C23×C11C4×D412yes—
244C23×C11C2×#4111yescharacteristic
245C22×D11—21no—
246Q8×C11—21no—
247Q8×C11—21no—
248D4×C11—21no—
249D4×C11—21no—
250D4×C11—44no—
251D4×C11—41no—
252D4×C11—41no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11C4×D412yes—
268C2×C4×C11C23×C411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C22⋊D11—44no—
275C22⋊D11—41no—
276C22⋊D11—41no—
277C2×Dic11—22no—
278C2×Dic11—21no—
279D44—21no—
280D44—21no—
281C4×D11—41no—
282C4×D11—41no—
283Dic22—21no—
284Dic22—21no—
285C8×C11—41no—
286C8×C11—41no—
287C11⋊C8—22no—
288C11⋊C8—22no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C11⋊C8C4×D412yes—
292C11⋊C8C4×D412yes—
293C11⋊C8#12112yes—
294C11⋊C8#12112yes—
295C2×#135—111no—
296C2×#131—111no—
297C2×#131—111no—
298C22×M16—111no—
299C23×C8—111no—
300#525—111no—
301#525C2×D1111yescharacteristic
302C2×#117C2×D1111yescharacteristic
303#470—112no—
304#469—112no—
305#468—112no—
306#468—112no—
307#444—224no—
308#435—222no—
309#435—222no—
310C8×D4—222no—
311C8×D4—222no—
312C2×#108—111no—
313C2×#108—111no—
314#427—111no—
315#424—111no—
316#424—111no—
317C2×#104—111no—
318C2×#104—111no—
319C2×#104C2×D1111yescharacteristic
320C2×#104C2×D1111yescharacteristic
321#416—111no—
322#416—111no—
323#408—111no—
324#408—111no—
325#407—111no—
326#407C2×D1111yescharacteristic
327#405—111no—
328#405—111no—
329#405—224no—
330C2×#97—111no—
331C2×#97—111no—
332C2×C4×C8—111no—
333C2×C4×C8—111no—
334#341—111no—
335#341—111no—
336#339—111no—
337#339—111no—
338#339C2×D1111yescharacteristic
339#339C2×D1111yescharacteristic
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—41no—
348C22×C11C2×C4×D411yescharacteristic
349C22×C11#52511yescharacteristic
350C22×C11#52911yescharacteristic
351C2×D11—42no—
352C2×D11—41no—
353C4×C11—22no—
354C4×C11—42no—
355C4×C11—42no—
356C4×C11—42no—
357C4×C11—41no—
358C4×C11C2×C4×D411yescharacteristic
359C4×C11C4×#4111yescharacteristic
360C4×C11C2×#12111yescharacteristic
361C4×C11#53211yescharacteristic
362Dic11—42no—
363Dic11—41no—
364C2×#41—111no—
365C2×#41C22×D1111yescharacteristic
366C23×C4C22×D1111yescharacteristic
367#135—222no—
368#135—222no—
369C2×Q16—111no—
370C2×SD16—111no—
371C2×SD16—111no—
372C2×D8—111no—
373#131—222no—
374#131—222no—
375#131—222no—
376#131—222no—
377C2×M16—112no—
378C2×M16—112no—
379C2×M16—111no—
380C2×M16—111no—
381C2×M16—221no—
382C2×M16—222no—
383C2×M16—222no—
384C2×M16—221no—
385C2×M16C22×D1111yescharacteristic
386C2×M16C22×D1111yescharacteristic
387C22×C8—111no—
388C22×C8—111no—
389C22×C8—112no—
390C22×C8—112no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8—221no—
394C22×C8—222no—
395C22×C8—222no—
396C22×C8—221no—
397#123—21no—
398#123—221no—
399C22⋊Q8—112no—
400C22⋊Q8C4×D1112yes—
401#121—112no—
402#121C4×D1112yes—
403#120—21no—
404#120—221no—
405C4×D4—22no—
406C4×D4—222no—
407#117—22no—
408#117—22no—
409#117—111no—
410#117C22×D1111yescharacteristic
411C2×C4⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C42C22×D1111yescharacteristic
414C2×C42C22×D1111yescharacteristic
415#108—222no—
416#108—222no—
417#107—112no—
418#106—112no—
419C4⋊C8—222no—
420C4⋊C8—222no—
421#104—22no—
422#104—22no—
423#104—222no—
424#104—222no—
425#103—112no—
426#103—112no—
427#102—112no—
428#102—112no—
429C22⋊C8—22no—
430C22⋊C8—222no—
431C22⋊C8—222no—
432C22⋊C8—222no—
433#97—114no—
434#97—222no—
435#97—221no—
436#97—221no—
437C4×C8—222no—
438C4×C8—221no—
439C4×C8—221no—
440C4×C8—222no—
441C2×C11—21no—
442C2×C11—21no—
443C2×C11—42no—
444C2×C11—81no—
445C2×C11C4×#12111yescharacteristic
446C2×C11#295512yes—
447D11—81no—
448C24#434111yescharacteristic
449#41—21no—
450#41—21no—
451#41—21no—
452#41—21no—
453#41—221no—
454#41—221no—
455#41—221no—
456#41—221no—
457C2×Q8—111no—
458C2×Q8C2×C4×D1111yescharacteristic
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—111no—
462C2×D4—222no—
463C2×D4—221no—
464C2×D4C2×C4×D1111yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—221no—
473C22×C4C2×C4×D1112yes—
474C22×C4D4×D1112yes—
475C22×C4#434111yescharacteristic
476C22×C4C23×D1111yescharacteristic
477Q16—222no—
478SD16—222no—
479SD16—222no—
480D8—222no—
481M16—21no—
482M16—21no—
483M16—21no—
484M16—21no—
485M16—224no—
486M16—224no—
487M16—221no—
488M16—221no—
489M16—221no—
490M16—221no—
491M16—442no—
492M16—442no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—111no—
496C2×C8—111no—
497C2×C8—112no—
498C2×C8—112no—
499C2×C8—111no—
500C2×C8—111no—
501C2×C8—112no—
502C2×C8—112no—
503C2×C8—112no—
504C2×C8—112no—
505C2×C8—224no—
506C2×C8—224no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—442no—
514C2×C8—442no—
515C4⋊C4—24no—
516C4⋊C4—22no—
517C4⋊C4—112no—
518C4⋊C4—222no—
519C4⋊C4C2×C4×D1112yes—
520C22⋊C4—24no—
521C22⋊C4—22no—
522C22⋊C4—21no—
523C22⋊C4—22no—
524C22⋊C4—222no—
525C22⋊C4—221no—
526C22⋊C4—222no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—221no—
531C42D4×D1112yes—
532C42#434112yes—
533C11#2155011yescharacteristic, complemented, Sylow
534C23—21no—
535C23—21no—
536C23—21no—
537C23—42no—
538C23—221no—
539C23(C22⋊D11)⋊C412yes—
540C23C2×#434111yescharacteristic
541Q8—21no—
542Q8—21no—
543Q8—221no—
544Q8—221no—
545D4—21no—
546D4—21no—
547D4—44no—
548D4—41no—
549D4—41no—
550D4—221no—
551D4—221no—
552D4—444no—
553D4—441no—
554D4—441no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—222no—
570C2×C4—221no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4(C22⋊D11)⋊C412yes—
574C2×C4C22×C4×D1111yescharacteristic
575C2×C4C2×D4×D1111yescharacteristic
576C2×C4C2×D4×D1111yescharacteristic
577C2×C4C2×#434111yescharacteristic
578C2×C4#41×D1111yescharacteristic
579C2×C4#41×D1111yescharacteristic
580C8—41no—
581C8—41no—
582C8—112no—
583C8—112no—
584C8—112no—
585C8—112no—
586C8—222no—
587C8—222no—
588C8—441no—
589C8—441no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—22no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22—41no—
598C22—442no—
599C22—441no—
600C22C2×(C22⋊D11)⋊C411yescharacteristic
601C22#1062311711yescharacteristic
602C22#1062318011yescharacteristic
603C4—22no—
604C4—42no—
605C4—42no—
606C4—42no—
607C4—41no—
608C4—442no—
609C4—441no—
610C4C4×#434111yescharacteristic
611C4C4×D4×D1111yescharacteristic
612C4#1062312711yescharacteristic
613C4D11×#12111yescharacteristic
614C2—21no—
615C2—21no—
616C2—42no—
617C2—81no—
618C2—881no—
619C2#1307112611yescharacteristic
620C2#1307751512yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1897C2
socleC22×C11C2×C4×D4
prime radical#13078222C2
cosocleC22×C4×C11C24
hypercenter#1897D11
hypocenterC11#21550
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1897

Complements

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

NH ≅ G/Ntype
2. C2×#10622436C2semidirect
3. #13077311C2semidirect
4. #13077306C2semidirect
5. C2×#10622610C2semidirect
6. #13069501C2semidirect
7. #13069363C2semidirect
8. #13069321C2semidirect
9. #13069317C2semidirect
10. #13069064C2semidirect
11. #13068656C2semidirect
12. #13068499C2semidirect
13. #13068461C2semidirect
14. #13068457C2semidirect
15. C11×#1897C2semidirect
35. #10622665C4semidirect
36. #10622662C4semidirect
37. #10622655C4semidirect
38. #10622652C4semidirect
134. #66867D4semidirect
234. #1897D11semidirect
533. C11#21550semidirect

Maximal subgroups

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

subgroupindex
#130782222
C2×#106224362
#130773112
#130773062
C2×#106226102
#130695012
#130693632
#130693212
#130693172
#130690642
#130686562
#130684992
#130684612
#130684572
C11×#18972
#2155011