Finite Group Databasebeta

← #14760615

Subgroups — #14760615

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#13078224C211yesmaximal, characteristic
2C2×#10622436C211yesmaximal, characteristic, complemented
3#13077313C211yesmaximal, characteristic, complemented
4#13077309C211yesmaximal, characteristic, complemented
5C2×#10622302C211yesmaximal, characteristic, complemented
6#13069503C211yesmaximal, characteristic, complemented
7#13069361C211yesmaximal, characteristic, complemented
8#13069320C211yesmaximal, characteristic, complemented
9#13069063C211yesmaximal, characteristic, complemented
10#13069061C211yesmaximal, characteristic, complemented
11#13068657C211yesmaximal, characteristic, complemented
12#13068499C211yesmaximal, characteristic, complemented
13#13068463C211yesmaximal, characteristic, complemented
14#13068459C211yesmaximal, characteristic, complemented
15C11×#1937C211yesmaximal, characteristic, complemented
16#10623359C2211yescharacteristic
17C2×#67003C2211yescharacteristic
18C2×#67001C2211yescharacteristic
19C2×#66960C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22#10623055C2211yescharacteristic
23C2×#66925C2211yescharacteristic
24C11×#424C2211yescharacteristic
25C2×C11×#104C2211yescharacteristic
26C11×#416C2211yescharacteristic
27C11×#408C2211yescharacteristic
28C2×C4×C8×C11C2211yescharacteristic
29C2×#66901C2211yescharacteristic
30C2×#66889C2211yescharacteristic
31#10622739C2211yescharacteristic
32#10622739C2211yescharacteristic
33C2×#66886C2211yescharacteristic
34C2×#66886C2211yescharacteristic
35#10622735C2211yescharacteristic
36#10622726C2211yescharacteristic
37#10622723C2211yescharacteristic
38#10622715C2211yescharacteristic
39C2×#66879C2211yescharacteristic
40C2×C8×Dic11C2211yescharacteristic
41#10622611C2211yescharacteristic
42#10622610C2211yescharacteristic
43C2×#66869C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45#10622449—22no—
46#10622447—22no—
47#10622436—24no—
48#10622429C412yescomplemented
49#10622425C412yescomplemented
50#10622395C412yescomplemented
51#10622393C412yescomplemented
52#10622341—22no—
53(C22⋊D11)⋊C8—22no—
54#10622302—24no—
55C11×#341C2211yescharacteristic
56C11×#339C2211yescharacteristic
57#10622193C2211yescharacteristic
58#10622190C2211yescharacteristic
59#10622170C2211yescharacteristic
60#10622161C2211yescharacteristic
61C2×C11×#41C2311yescharacteristic
62C2×#4339C2311yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C2×C11×M16C2311yescharacteristic
65C2×C11×M16C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×#117C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70#67003—22no—
71#67003—22no—
72#67001—22no—
73#67001—22no—
74#66999C2×C412yes—
75C2×#4326C2×C411yescharacteristic
76C2×#4325C2×C411yescharacteristic
77#66991C2×C412yes—
78#66990—21no—
79#66988—21no—
80C2×#4324C2×C411yescharacteristic
81C2×#4323C2×C411yescharacteristic
82C4×C22⋊D11—22no—
83C2×(C2×D11)⋊C4—21no—
84#66979C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11C2311yescharacteristic
87C2×#4318—21no—
88C2×#4318C2311yescharacteristic
89C2×#4318C2311yescharacteristic
90C22×C11⋊C8—21no—
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93#66960—22no—
94#66960—22no—
95C2×#4313—22no—
96C2×#4313—22no—
97C2×#4313—21no—
98C2×#4313C2×C412yes—
99C2×#4313C2×C412yes—
100C2×C8×D11—22no—
101C2×C8×D11—22no—
102C2×C8×D11—21no—
103C2×C8×D11D412yes—
104C2×C8×D11D412yes—
105#66950C2×C412yes—
106#66948C2×C412yes—
107#66939—21no—
108#66935—21no—
109C4×D44—22no—
110#66925—22no—
111#66925—22no—
112C11×C4⋊C8—22no—
113C11×#104—22no—
114C11×#103C2×C412yes—
115C11×#102C2×C412yes—
116C11×C22⋊C8—22no—
117C4×C8×C11—22no—
118#66901—22no—
119#66889—22no—
120#66886—22no—
121#66886—22no—
122#66885C2×C412yes—
123(C2×D11)⋊C8—22no—
124(C2×D11)⋊C8—22no—
125(C2×D11)⋊C8—22no—
126#66880C2×C412yes—
127#66879—21no—
128#66879—22no—
129Dic11⋊C8—22no—
130C8×Dic11—21no—
131C8×Dic11—22no—
132#66872C2×C412yes—
133#66871C2×C412yes—
134#66869—22no—
135#66867—21no—
136#66867D414yescomplemented
137C4×C11⋊C8—21no—
138#21550—111nomaximal, Sylow
139C23×D11#4111yescharacteristic
140C11×#41—21no—
141C11×#41—21no—
142C11×#41—21no—
143C11×#41—21no—
144C2×Q8×C11C22×C411yescharacteristic
145C2×D4×C11—21no—
146C2×D4×C11C22×C411yescharacteristic
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11—21no—
151C2×C22⋊D11—22no—
152C22×Dic11—21no—
153C22×Dic11#4111yescharacteristic
154#4339—21no—
155#4339—21no—
156#4339—21no—
157#4339—21no—
158C2×D44—22no—
159C2×D44C22×C411yescharacteristic
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11C22×C412yes—
166C2×C4×D11C2×D412yes—
167C2×Dic22C22×C411yescharacteristic
168C11×M16—21no—
169C11×M16—21no—
170C11×M16—21no—
171C11×M16—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11C22×C412yes—
179C2×C8×C11C2×D412yes—
180C11×C4⋊C4C22×C412yes—
181C11×C22⋊C4—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11C2×D412yes—
185C22⋊Dic11—22no—
186C22⋊Dic11—21no—
187#4326—22no—
188#4325—22no—
189#4324—22no—
190#4323—22no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—22no—
193(C2×D11)⋊C4—22no—
194(C2×D11)⋊C4—22no—
195C4⋊Dic11—22no—
196C4⋊Dic11C22×C412yes—
197Dic11⋊C4—24no—
198Dic11⋊C4—22no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11#4112yes—
202#4318—21no—
203#4318—21no—
204#4318—21no—
205#4318—21no—
206#4318—42no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—42no—
210C2×C11⋊C8C22×C411yescharacteristic
211C2×C11⋊C8C22×C411yescharacteristic
212C2×C11⋊C8C2×D412yes—
213C2×C11⋊C8C2×D411yescharacteristic
214C2×C11⋊C8C2×D411yescharacteristic
215C2×C11⋊C8C2×D412yes—
216C2×C11⋊C8#4112yes—
217C2×C11⋊C8#4112yes—
218#4313—24no—
219#4313—24no—
220#4313—42no—
221C8×D11—24no—
222C8×D11—24no—
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#1937D1111yescharacteristic, complemented
233#1897—111no—
234#1897—111no—
235#1811—111no—
236#1773—111no—
237#1765—111no—
238#1765—111no—
239C23×C11—21no—
240C23×C11C2×#4111yescharacteristic
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—42no—
245C22×D11C4×D412yes—
246Q8×C11—21no—
247Q8×C11—21no—
248D4×C11—21no—
249D4×C11—21no—
250D4×C11—41no—
251D4×C11—41no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—42no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11C23×C411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C22⋊D11—44no—
265C22⋊D11—41no—
266C22⋊D11—41no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—22no—
272C2×Dic11—42no—
273C2×Dic11C4×D412yes—
274D44—21no—
275D44—21no—
276D44—44no—
277C4×D11—22no—
278C4×D11—22no—
279C4×D11—22no—
280C4×D11—22no—
281C4×D11—41no—
282C4×D11—41no—
283Dic22—21no—
284Dic22—21no—
285C8×C11—22no—
286C8×C11—22no—
287C8×C11—41no—
288C8×C11—41no—
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#525—111no—
302C2×#117—111no—
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#424C2×D1111yescharacteristic
317C2×#104—111no—
318C2×#104—111no—
319C2×#104—111no—
320C2×#104C2×D1111yescharacteristic
321#416—111no—
322#416C2×D1111yescharacteristic
323#408—111no—
324#408C2×D1111yescharacteristic
325#407—111no—
326#407—111no—
327#405—111no—
328#405—111no—
329#405—224no—
330C2×#97—111no—
331C2×#97—111no—
332C2×C4×C8—111no—
333C2×C4×C8C2×D1111yescharacteristic
334#341—111no—
335#341C2×D1111yescharacteristic
336#339—111no—
337#339—111no—
338#339—111no—
339#339C2×D1111yescharacteristic
340C22×C11—22no—
341C22×C11—42no—
342C22×C11—41no—
343C22×C11C2×C4×D411yescharacteristic
344C22×C11#52511yescharacteristic
345C22×C11#52911yescharacteristic
346C2×D11—22no—
347C2×D11—22no—
348C2×D11—22no—
349C2×D11—42no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—41no—
353C4×C11—42no—
354C4×C11—42no—
355C4×C11—41no—
356C4×C11C2×C4×D411yescharacteristic
357C4×C11C4×#4111yescharacteristic
358C4×C11C2×#12111yescharacteristic
359C4×C11#53211yescharacteristic
360Dic11—22no—
361Dic11—42no—
362Dic11—42no—
363Dic11—41no—
364C2×#41—111no—
365C2×#41C22×D1111yescharacteristic
366C23×C4—111no—
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—222no—
382C2×M16—222no—
383C2×M16—221no—
384C2×M16—221no—
385C2×M16C22×D1111yescharacteristic
386C2×M16C22×D1111yescharacteristic
387C22×C8—111no—
388C22×C8—111no—
389C22×C8—112no—
390C22×C8—112no—
391C22×C8—222no—
392C22×C8—222no—
393C22×C8—221no—
394C22×C8—221no—
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397#123—221no—
398#123—221no—
399C22⋊Q8—112no—
400C22⋊Q8—112no—
401#121—112no—
402#121—112no—
403#120—221no—
404#120—221no—
405C4×D4—222no—
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×C42C22×D1111yescharacteristic
415#108—222no—
416#108—222no—
417#107—112no—
418#106—112no—
419C4⋊C8—22no—
420C4⋊C8—222no—
421#104—22no—
422#104—222no—
423#104—222no—
424#104—222no—
425#103—112no—
426#103C4×D1112yes—
427#102—112no—
428#102C4×D1112yes—
429C22⋊C8—22no—
430C22⋊C8—222no—
431C22⋊C8—222no—
432C22⋊C8—222no—
433#97—114no—
434#97—221no—
435#97—222no—
436#97—221no—
437C4×C8—22no—
438C4×C8—221no—
439C4×C8—222no—
440C4×C8—221no—
441C2×C11—21no—
442C2×C11—21no—
443C2×C11—81no—
444C2×C11C4×#12111yescharacteristic
445C2×C11#295512yes—
446D11—42no—
447D11—81no—
448C24—111no—
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—21no—
460C2×D4—111no—
461C2×D4—222no—
462C2×D4—222no—
463C2×D4—221no—
464C2×D4C2×C4×D1111yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—111no—
468C22×C4—112no—
469C22×C4—112no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
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—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—111no—
500C2×C8—111no—
501C2×C8—112no—
502C2×C8—112no—
503C2×C8—111no—
504C2×C8—111no—
505C2×C8—112no—
506C2×C8—112no—
507C2×C8—224no—
508C2×C8—224no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—442no—
512C2×C8—442no—
513C2×C8C2×C4×D1112yes—
514C2×C8D4×D1112yes—
515C4⋊C4—112no—
516C4⋊C4—222no—
517C4⋊C4—222no—
518C4⋊C4—224no—
519C4⋊C4C2×C4×D1112yes—
520C22⋊C4—21no—
521C22⋊C4—222no—
522C22⋊C4—222no—
523C22⋊C4—222no—
524C22⋊C4—224no—
525C22⋊C4—222no—
526C22⋊C4—221no—
527C42—21no—
528C42—21no—
529C42—112no—
530C42—221no—
531C42—221no—
532C42D4×D1112yes—
533C11#2155011yescharacteristic, complemented, Sylow
534C23—21no—
535C23—112no—
536C23—221no—
537C23—221no—
538C23—221no—
539C23—442no—
540C23#41×D1111yescharacteristic
541Q8—21no—
542Q8—21no—
543Q8—221no—
544Q8—221no—
545D4—21no—
546D4—21no—
547D4—41no—
548D4—41no—
549D4—221no—
550D4—221no—
551D4—444no—
552D4—444no—
553D4—441no—
554D4—441no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—112no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—221no—
570C2×C4—222no—
571C2×C4—442no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4C22×C4×D1111yescharacteristic
575C2×C4C2×D4×D1111yescharacteristic
576C2×C4C2×D4×D1111yescharacteristic
577C2×C4#41×D1111yescharacteristic
578C2×C4#41×D1111yescharacteristic
579C2×C4#41×D1111yescharacteristic
580C8—22no—
581C8—22no—
582C8—41no—
583C8—41no—
584C8—112no—
585C8—112no—
586C8—112no—
587C8—112no—
588C8—441no—
589C8—441no—
590C22—22no—
591C22—42no—
592C22—41no—
593C22—222no—
594C22—222no—
595C22—222no—
596C22—442no—
597C22—442no—
598C22—442no—
599C22—441no—
600C22C4×D4×D1111yescharacteristic
601C22#1062318711yescharacteristic
602C22#1062323711yescharacteristic
603C4—42no—
604C4—42no—
605C4—41no—
606C4—222no—
607C4—442no—
608C4—442no—
609C4—441no—
610C4#1062305311yescharacteristic
611C4C4×D4×D1111yescharacteristic
612C4D11×#12111yescharacteristic
613C4#1062319911yescharacteristic
614C2—21no—
615C2—21no—
616C2—81no—
617C2—442no—
618C2—881no—
619C2#1307112811yescharacteristic
620C2#1307751412yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1937C2
socleC22×C11C2×C4×D4
prime radical#13078224C2
cosocleC22×C4×C11C24
hypercenter#1937D11
hypocenterC11#21550
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1937

Complements

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

NH ≅ G/Ntype
2. C2×#10622436C2semidirect
3. #13077313C2semidirect
4. #13077309C2semidirect
5. C2×#10622302C2semidirect
6. #13069503C2semidirect
7. #13069361C2semidirect
8. #13069320C2semidirect
9. #13069063C2semidirect
10. #13069061C2semidirect
11. #13068657C2semidirect
12. #13068499C2semidirect
13. #13068463C2semidirect
14. #13068459C2semidirect
15. C11×#1937C2semidirect
48. #10622429C4semidirect
49. #10622425C4semidirect
50. #10622395C4semidirect
51. #10622393C4semidirect
136. #66867D4semidirect
232. #1937D11semidirect
533. C11#21550semidirect

Maximal subgroups

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

subgroupindex
#130782242
C2×#106224362
#130773132
#130773092
C2×#106223022
#130695032
#130693612
#130693202
#130690632
#130690612
#130686572
#130684992
#130684632
#130684592
C11×#19372
#2155011