Finite Group Databasebeta

← #14760612

Subgroups — #14760612

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×#10622758C211yesmaximal, characteristic, complemented
3#13077310C211yesmaximal, characteristic, complemented
4C2×#10622714C211yesmaximal, characteristic, complemented
5#13069503C211yesmaximal, characteristic, complemented
6#13069361C211yesmaximal, characteristic, complemented
7#13069323C211yesmaximal, characteristic, complemented
8#13069319C211yesmaximal, characteristic, complemented
9#13069065C211yesmaximal, characteristic, complemented
10#13069062C211yesmaximal, characteristic, complemented
11#13068656C211yesmaximal, characteristic, complemented
12#13068501C211yesmaximal, characteristic, complemented
13#13068462C211yesmaximal, characteristic, complemented
14#13068458C211yesmaximal, characteristic, complemented
15C11×#2929C211yesmaximal, characteristic, complemented
16C2×C11×#131C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C11×#525C2211yescharacteristic
19C2×#67003C2211yescharacteristic
20#10623322C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C2×#66954C2211yescharacteristic
24C11×#435—22no—
25C8×D4×C11—22no—
26C11×#424C2211yescharacteristic
27C11×#408C2211yescharacteristic
28C11×#407C2211yescharacteristic
29C11×#405C2211yescharacteristic
30C2×#66901C2211yescharacteristic
31C2×#66901C2211yescharacteristic
32#10622846C2211yescharacteristic
33#10622820C2211yescharacteristic
34#10622758—24no—
35C2×#66889C2211yescharacteristic
36C2×#66889C2211yescharacteristic
37C2×#66886C2211yescharacteristic
38C2×#66886C2211yescharacteristic
39#10622724—22no—
40#10622723C2211yescharacteristic
41C8×C22⋊D11—22no—
42#10622715C2211yescharacteristic
43#10622714—24no—
44#10622714C2211yescharacteristic
45C2×#66879C2211yescharacteristic
46C2×#66879C2211yescharacteristic
47C2×C8×Dic11C2211yescharacteristic
48C2×C8×Dic11C2211yescharacteristic
49#10622665C412yescomplemented
50#10622662C412yescomplemented
51#10622655C412yescomplemented
52#10622652C412yescomplemented
53#10622615C2211yescharacteristic
54#10622611C2211yescharacteristic
55#10622196C2211yescharacteristic
56#10622196C2211yescharacteristic
57#10622193C2211yescharacteristic
58#10622193C2211yescharacteristic
59#10622170C2211yescharacteristic
60#10622170C2211yescharacteristic
61C2×C11×#41C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C2×#4339C2311yescharacteristic
64C11×#131—22no—
65C11×#131—22no—
66C2×C11×M16—21no—
67C2×C11×M16C2311yescharacteristic
68C2×C11×M16C2311yescharacteristic
69C22×C8×C11—22no—
70C22×C8×C11—22no—
71C22×C8×C11—21no—
72C22×C8×C11D412yes—
73C22×C8×C11D412yes—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×#123—21no—
77C11×C22⋊Q8C2×C412yes—
78C11×#121C2×C412yes—
79C11×#120—21no—
80C4×D4×C11—22no—
81C11×#117C2311yescharacteristic
82#67006—21no—
83C2×C22⋊Dic11—21no—
84#67003—22no—
85#67003—22no—
86C2×#4326C2×C411yescharacteristic
87C2×#4325C2×C411yescharacteristic
88C2×#4324C2×C411yescharacteristic
89C2×#4323C2×C411yescharacteristic
90#66983C2×C412yes—
91#66982—21no—
92C4×C22⋊D11—22no—
93#66979—22no—
94#66979—22no—
95#66979C2311yescharacteristic
96C2×C4⋊Dic11—21no—
97#66977C2×C412yes—
98C2×C4×Dic11C2311yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C2×#4318—22no—
101C2×#4318—22no—
102C2×#4318C2×C412yes—
103C2×#4318C2×C412yes—
104C2×#4318C2311yescharacteristic
105C2×#4318C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108#66954—22no—
109#66954—22no—
110C2×#4313—21no—
111C2×C8×D11—21no—
112C11×C4⋊C8—22no—
113C11×C22⋊C8—22no—
114C11×C22⋊C8—22no—
115C11×#97—21no—
116C4×C8×C11—21no—
117#66901—22no—
118#66901—22no—
119#66899C2×C412yes—
120#66896C2×C412yes—
121C22⋊(C11⋊C8)—22no—
122#66889—22no—
123#66889—22no—
124#66886—22no—
125#66886—22no—
126(C2×D11)⋊C8—22no—
127#66879—21no—
128#66879—22no—
129#66879D414yescomplemented
130Dic11⋊C8—22no—
131C8×Dic11—21no—
132C8×Dic11—22no—
133C8×Dic11—22no—
134#66874C2×C412yes—
135#66873C2×C412yes—
136#66872C2×C412yes—
137#66871C2×C412yes—
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×C11C22×C412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11#4111yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—22no—
158C2×C22⋊D11—21no—
159C22×Dic11—21no—
160C22×Dic11—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—
172C11×M16—42no—
173C2×C8×C11—24no—
174C2×C8×C11—24no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—42no—
180C2×C8×C11C2×D412yes—
181C2×C8×C11C2×D412yes—
182C2×C8×C11C2×D411yescharacteristic
183C2×C8×C11C2×D411yescharacteristic
184C2×C8×C11#4112yes—
185C11×C4⋊C4—22no—
186C11×C4⋊C4C22×C412yes—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—22no—
190C42×C11—21no—
191C22⋊Dic11—24no—
192C22⋊Dic11—22no—
193C22⋊Dic11—21no—
194#4326—22no—
195#4325—22no—
196#4324—22no—
197#4323—22no—
198(C2×D11)⋊C4—22no—
199C4⋊Dic11—24no—
200C4⋊Dic11C22×C412yes—
201Dic11⋊C4—22no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11C2×D412yes—
206C4×Dic11#4112yes—
207#4318—24no—
208#4318—24no—
209#4318—21no—
210#4318—21no—
211#4318—21no—
212#4318—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8C22×C412yes—
218C2×C11⋊C8C22×C411yescharacteristic
219C2×C11⋊C8C22×C411yescharacteristic
220C2×C11⋊C8C2×D412yes—
221C2×C11⋊C8#4112yes—
222#4313—42no—
223C8×D11—42no—
224#3054—111no—
225C2×#444—111no—
226#2929—111no—
227#2929D1111yescharacteristic, complemented
228C2×#405—111no—
229#1974—111no—
230#1945—111no—
231#1937—111no—
232#1937—111no—
233#1897—111no—
234#1897—111no—
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—41no—
262C2×C4×C11—41no—
263C2×C4×C11C4×D412yes—
264C2×C4×C11C23×C411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C22⋊D11—44no—
271C22⋊D11—41no—
272C22⋊D11—41no—
273C2×Dic11—22no—
274C2×Dic11—21no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279D44—21no—
280D44—21no—
281C4×D11—41no—
282C4×D11—41no—
283Dic22—21no—
284Dic22—21no—
285C8×C11—22no—
286C8×C11—41no—
287C8×C11—41no—
288C8×C11#12112yes—
289C8×C11#12112yes—
290C11⋊C8—22no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293C11⋊C8C4×D412yes—
294C11⋊C8C4×D412yes—
295C2×#135—111no—
296C2×#131—111no—
297C2×#131C2×D1111yescharacteristic
298C22×M16—111no—
299C23×C8C2×D1111yescharacteristic
300#525—111no—
301#525C2×D1111yescharacteristic
302C2×#117—111no—
303#470—112no—
304#469—112no—
305#468—112no—
306#468—112no—
307#444—224no—
308#435—22no—
309#435—222no—
310C8×D4—22no—
311C8×D4—222no—
312C2×#108—111no—
313C2×#108—111no—
314#427—111no—
315#424—111no—
316#424C2×D1111yescharacteristic
317C2×#104—111no—
318C2×#104—111no—
319C2×#104—111no—
320C2×#104—111no—
321#416—111no—
322#416—111no—
323#408—111no—
324#408C2×D1111yescharacteristic
325#407—111no—
326#407C2×D1111yescharacteristic
327#405—111no—
328#405—224no—
329#405C2×D1111yescharacteristic
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#339—111no—
339#339—111no—
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—41no—
356C4×C11C2×C4×D411yescharacteristic
357C4×C11C4×#4111yescharacteristic
358C4×C11C2×#12111yescharacteristic
359C4×C11#53211yescharacteristic
360Dic11—42no—
361Dic11—42no—
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—22no—
374#131—22no—
375#131—222no—
376#131—222no—
377C2×M16—21no—
378C2×M16—112no—
379C2×M16—112no—
380C2×M16—111no—
381C2×M16—111no—
382C2×M16—222no—
383C2×M16—222no—
384C2×M16—221no—
385C2×M16C22×D1111yescharacteristic
386C2×M16C22×D1111yescharacteristic
387C22×C8—22no—
388C22×C8—22no—
389C22×C8—21no—
390C22×C8—111no—
391C22×C8—111no—
392C22×C8—221no—
393C22×C8C22⋊D1112yes—
394C22×C8C22⋊D1112yes—
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
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—111no—
408#117—222no—
409#117—222no—
410#117C22×D1111yescharacteristic
411C2×C4⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C42—111no—
414C2×C42—111no—
415#108—222no—
416#108—222no—
417#107—112no—
418#106—112no—
419C4⋊C8—22no—
420C4⋊C8—222no—
421#104—222no—
422#104—222no—
423#104—222no—
424#104—222no—
425#103—112no—
426#103—112no—
427#102—112no—
428#102—112no—
429C22⋊C8—22no—
430C22⋊C8—22no—
431C22⋊C8—222no—
432C22⋊C8—222no—
433#97—21no—
434#97—114no—
435#97—222no—
436#97—221no—
437C4×C8—21no—
438C4×C8—222no—
439C4×C8—222no—
440C4×C8—221no—
441C2×C11—21no—
442C2×C11—21no—
443C2×C11—42no—
444C2×C11—81no—
445C2×C11C4×#12111yescharacteristic
446C2×C11#295512yes—
447D11—81no—
448C24#433911yescharacteristic
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—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4C2×C4×D1112yes—
474C22×C4#433911yescharacteristic
475C22×C4C2×C22⋊D1112yes—
476C22×C4C23×D1111yescharacteristic
477Q16—222no—
478SD16—222no—
479SD16—222no—
480D8—222no—
481M16—21no—
482M16—21no—
483M16—21no—
484M16—21no—
485M16—42no—
486M16—224no—
487M16—224no—
488M16—221no—
489M16—221no—
490M16—221no—
491M16—221no—
492M16—442no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—24no—
496C2×C8—24no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—42no—
500C2×C8—111no—
501C2×C8—111no—
502C2×C8—112no—
503C2×C8—112no—
504C2×C8—112no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—442no—
510C2×C8D4×D1112yes—
511C2×C8#434112yes—
512C2×C8C2×C22⋊D1112yes—
513C2×C8C2×C22⋊D1111yescharacteristic
514C2×C8C2×C22⋊D1111yescharacteristic
515C4⋊C4—22no—
516C4⋊C4—112no—
517C4⋊C4—224no—
518C4⋊C4—222no—
519C4⋊C4C2×C4×D1112yes—
520C22⋊C4—22no—
521C22⋊C4—21no—
522C22⋊C4—22no—
523C22⋊C4—224no—
524C22⋊C4—222no—
525C22⋊C4—221no—
526C22⋊C4—222no—
527C42—21no—
528C42—112no—
529C42—112no—
530C42—221no—
531C42—221no—
532C42—221no—
533C11#2155011yescharacteristic, complemented, Sylow
534C23—21no—
535C23—21no—
536C23—21no—
537C23—42no—
538C23—221no—
539C23C4×C22⋊D1112yes—
540C23C2×#433911yescharacteristic
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—41no—
564C2×C4—41no—
565C2×C4—222no—
566C2×C4—221no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—442no—
570C2×C4—442no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4C4×C22⋊D1112yes—
574C2×C4C22×C4×D1111yescharacteristic
575C2×C4C2×D4×D1111yescharacteristic
576C2×C4C2×#434111yescharacteristic
577C2×C4#41×D1111yescharacteristic
578C2×C4#41×D1111yescharacteristic
579C2×C4C22×C22⋊D1111yescharacteristic
580C8—22no—
581C8—41no—
582C8—41no—
583C8—112no—
584C8—112no—
585C8—222no—
586C8—441no—
587C8—441no—
588C8#6699212yes—
589C8#6699212yes—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—22no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22—41no—
598C22—442no—
599C22—441no—
600C22#1062306911yescharacteristic
601C22#1062307811yescharacteristic
602C22C2×C4×C22⋊D1111yescharacteristic
603C4—22no—
604C4—42no—
605C4—41no—
606C4—442no—
607C4—442no—
608C4—442no—
609C4—441no—
610C4C4×#434111yescharacteristic
611C4C4×D4×D1111yescharacteristic
612C4C2×#6699211yescharacteristic
613C4#1062336311yescharacteristic
614C2—21no—
615C2—21no—
616C2—42no—
617C2—81no—
618C2—881no—
619C2C4×#6699211yescharacteristic
620C2#1307751712yes—
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2929C2
socleC22×C11C2×C4×D4
prime radical#13078222C2
cosocleC22×C4×C11C24
hypercenter#2929D11
hypocenterC11#21550
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ #2929

Complements

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

NH ≅ G/Ntype
2. C2×#10622758C2semidirect
3. #13077310C2semidirect
4. C2×#10622714C2semidirect
5. #13069503C2semidirect
6. #13069361C2semidirect
7. #13069323C2semidirect
8. #13069319C2semidirect
9. #13069065C2semidirect
10. #13069062C2semidirect
11. #13068656C2semidirect
12. #13068501C2semidirect
13. #13068462C2semidirect
14. #13068458C2semidirect
15. C11×#2929C2semidirect
49. #10622665C4semidirect
50. #10622662C4semidirect
51. #10622655C4semidirect
52. #10622652C4semidirect
129. #66879D4semidirect
227. #2929D11semidirect
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×#106227582
#130773102
C2×#106227142
#130695032
#130693612
#130693232
#130693192
#130690652
#130690622
#130686562
#130685012
#130684622
#130684582
C11×#29292
#2155011