Finite Group Databasebeta

← #14760625

Subgroups — #14760625

Order 2816.

938 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078224C211yesmaximal, characteristic
2C2×#10622758C211yesmaximal, characteristic, complemented
3#13077321C211yesmaximal, characteristic, complemented
4#13077317C211yesmaximal, characteristic, complemented
5C2×C4×#4313C211yesmaximal, characteristic, complemented
6#13069501C211yesmaximal, characteristic, complemented
7#13069363C211yesmaximal, characteristic, complemented
8#13069329C211yesmaximal, characteristic, complemented
9#13069325C211yesmaximal, characteristic, complemented
10#13069058C211yesmaximal, characteristic, complemented
11#13069056C211yesmaximal, characteristic, complemented
12#13068657C211yesmaximal, characteristic, complemented
13#13068501C211yesmaximal, characteristic, complemented
14#13068453C211yesmaximal, characteristic, complemented
15C11×#1764C211yesmaximal, characteristic, complemented
16C2×C11×#131C2211yescharacteristic
17#10623359C2211yescharacteristic
18C2×#67003C2211yescharacteristic
19C2×#66954C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C22×#4313C2211yescharacteristic
22#10623055C2211yescharacteristic
23C2×C42×D11C2211yescharacteristic
24C2×C11×#104C2211yescharacteristic
25C11×#416C2211yescharacteristic
26C11×#405C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C2×#66901C2211yescharacteristic
29#10622847C2211yescharacteristic
30#10622758—24no—
31C2×#66889C2211yescharacteristic
32#10622742C2211yescharacteristic
33#10622741—22no—
34#10622739C2211yescharacteristic
35#10622739C2211yescharacteristic
36C2×#66886C2211yescharacteristic
37C2×#66886C2211yescharacteristic
38#10622732C2211yescharacteristic
39#10622726C2211yescharacteristic
40#10622724—22no—
41#10622714C2211yescharacteristic
42C2×#66879C2211yescharacteristic
43C2×#66879C2211yescharacteristic
44#10622612C2211yescharacteristic
45#10622611C2211yescharacteristic
46C2×#66869C2211yescharacteristic
47C2×C4×C11⋊C8C2211yescharacteristic
48#10622429C412yescomplemented
49#10622425C412yescomplemented
50#10622395C412yescomplemented
51#10622393C412yescomplemented
52#10622319—22no—
53#10622301—22no—
54C4×#4313—24no—
55C11×#341C2211yescharacteristic
56C11×#339C2211yescharacteristic
57#10622193C2211yescharacteristic
58#10622190C2211yescharacteristic
59#10622170C2211yescharacteristic
60#10622161C2211yescharacteristic
61C2×C11×#41C2311yescharacteristic
62C2×#4339C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11C2311yescharacteristic
65C11×#131—22no—
66C11×#131—22no—
67C2×C11×M16—21no—
68C2×C11×M16C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C22×C8×C11—21no—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#117C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75#67003—22no—
76#67003—22no—
77#66999C2×C412yes—
78C2×#4326C2×C411yescharacteristic, complemented
79C2×#4325C2×C411yescharacteristic, complemented
80#66991C2×C412yes—
81#66990—21no—
82#66988—21no—
83C2×#4324C2×C411yescharacteristic, complemented
84C2×#4323C2×C411yescharacteristic, complemented
85C4×C22⋊D11—22no—
86#66979C2311yescharacteristic
87C2×C4×Dic11—21no—
88C2×C4×Dic11C2311yescharacteristic
89C2×#4318C2311yescharacteristic
90C2×#4318C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93#66954—22no—
94#66954—22no—
95C2×#4313—22no—
96C2×#4313—22no—
97C2×#4313—22no—
98C2×#4313—22no—
99C2×#4313—21no—
100C2×#4313C2×C412yes—
101C2×#4313C2×C412yes—
102C2×#4313D412yes—
103C2×#4313D412yes—
104C2×C8×D11—21no—
105#66950C2×C412yes—
106#66948C2×C412yes—
107#66939—21no—
108#66935—21no—
109C4×D44—22no—
110C42×D11—22no—
111C42×D11—22no—
112C11×#104—22no—
113C11×#103C2×C412yescomplemented
114C11×#102C2×C412yescomplemented
115C11×#97—21no—
116C4×C8×C11—22no—
117C4×C8×C11—21no—
118#66901—22no—
119C22⋊(C11⋊C8)—22no—
120#66889—22no—
121#66886—22no—
122#66886—22no—
123#66885C2×C412yescomplemented
124(C2×D11)⋊C8—22no—
125(C2×D11)⋊C8—22no—
126(C2×D11)⋊C8—22no—
127#66880C2×C412yescomplemented
128#66879—21no—
129#66879—22no—
130#66879D414yescomplemented
131Dic11⋊C8—22no—
132C8×Dic11—21no—
133#66872C2×C412yescomplemented
134#66871C2×C412yescomplemented
135#66869—22no—
136C4⋊(C11⋊C8)—22no—
137C4×C11⋊C8—22no—
138#21551—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—24no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—44no—
167C2×C4×D11C22×C412yes—
168C2×C4×D11C2×D412yes—
169C2×Dic22C22×C411yescharacteristic
170C11×M16—21no—
171C11×M16—21no—
172C11×M16—21no—
173C11×M16—21no—
174C11×M16—42no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—42no—
180C2×C8×C11C22×C412yes—
181C2×C8×C11C2×D411yescharacteristic
182C2×C8×C11C2×D411yescharacteristic
183C2×C8×C11C2×D412yes—
184C2×C8×C11#4112yes—
185C11×C4⋊C4C22×C412yes—
186C11×C22⋊C4—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11#4112yes—
190C22⋊Dic11—22no—
191C22⋊Dic11—21no—
192#4326—22no—
193#4325—22no—
194#4324—22no—
195#4323—22no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—22no—
199C4⋊Dic11—22no—
200C4⋊Dic11C22×C412yes—
201Dic11⋊C4—22no—
202C4×Dic11—24no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11C2×D412yes—
206#4318—21no—
207#4318—21no—
208#4318—21no—
209#4318—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8C22×C411yescharacteristic
215C2×C11⋊C8C22×C411yescharacteristic
216C2×C11⋊C8C2×D412yes—
217C2×C11⋊C8C2×D412yes—
218C2×C11⋊C8#4112yes—
219#4313—24no—
220#4313—24no—
221#4313—24no—
222#4313—24no—
223#4313—42no—
224C8×D11—42no—
225#3054—111no—
226C2×#444—111no—
227#2930—111no—
228#2930—111no—
229C2×C4×M16—111no—
230#1974—111no—
231#1945—111no—
232#1938—111no—
233#1938—111no—
234#1896—111no—
235#1896—111no—
236#1811—111no—
237#1773—111no—
238#1764—111no—
239#1764D1111yescharacteristic, complemented
240C23×C11—21no—
241C23×C11C2×#4111yescharacteristic
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—42no—
246C22×D11C4×D412yes—
247Q8×C11—21no—
248Q8×C11—21no—
249D4×C11—21no—
250D4×C11—21no—
251D4×C11—41no—
252D4×C11—41no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11C23×C411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C22⋊D11—41no—
266C22⋊D11—41no—
267C22⋊D11—82no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—22no—
271C2×Dic11—21no—
272C2×Dic11—22no—
273C2×Dic11—42no—
274C2×Dic11C4×D412yes—
275D44—21no—
276D44—21no—
277D44—82no—
278C4×D11—22no—
279C4×D11—22no—
280C4×D11—22no—
281C4×D11—22no—
282C4×D11—48no—
283C4×D11—41no—
284C4×D11—41no—
285Dic22—21no—
286Dic22—21no—
287C8×C11—22no—
288C8×C11—41no—
289C8×C11—41no—
290C8×C11#12112yes—
291C8×C11#12112yes—
292C11⋊C8—22no—
293C11⋊C8—41no—
294C11⋊C8—41no—
295C11⋊C8C4×D412yes—
296C11⋊C8C4×D412yes—
297C2×#135—111no—
298C2×#131—111no—
299C2×#131C2×D1111yescharacteristic
300C22×M16—111no—
301C22×M16—111no—
302#525—111no—
303#525—111no—
304C22×C42—111no—
305#470—112no—
306#469—112no—
307#468—112no—
308#468—112no—
309#444—224no—
310#436—222no—
311#436—222no—
312#435—222no—
313#435—222no—
314C2×#108—111no—
315C2×#108—111no—
316#427—111no—
317#424—111no—
318#424—111no—
319C2×#104—111no—
320C2×#104—111no—
321C2×#104—111no—
322C2×#104C2×D1111yescharacteristic
323#416—111no—
324#416C2×D1111yescharacteristic
325#408—111no—
326#408—111no—
327#407—111no—
328#407—111no—
329#405—111no—
330#405C2×D1111yescharacteristic
331C4×M16—224no—
332C2×#97—111no—
333C2×#97—111no—
334C2×C4×C8—111no—
335C2×C4×C8C2×D1111yescharacteristic
336#341—111no—
337#341C2×D1111yescharacteristic
338#339—111no—
339#339—111no—
340#339—111no—
341#339C2×D1111yescharacteristic
342C22×C11—22no—
343C22×C11—42no—
344C22×C11—41no—
345C22×C11C2×C4×D411yescharacteristic
346C22×C11#52511yescharacteristic
347C22×C11#52911yescharacteristic
348C2×D11—22no—
349C2×D11—22no—
350C2×D11—22no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—41no—
355C4×C11—24no—
356C4×C11—42no—
357C4×C11—41no—
358C4×C11C2×C4×D411yescharacteristic
359C4×C11C4×#4111yescharacteristic
360C4×C11C2×#12111yescharacteristic
361C4×C11#53211yescharacteristic
362Dic11—22no—
363Dic11—42no—
364Dic11—42no—
365Dic11—41no—
366C2×#41—111no—
367C2×#41C22×D1111yescharacteristic
368C23×C4—111no—
369C23×C4—221no—
370#135—222no—
371#135—222no—
372C2×Q16—111no—
373C2×SD16—111no—
374C2×SD16—111no—
375C2×D8—111no—
376#131—22no—
377#131—22no—
378#131—222no—
379#131—222no—
380C2×M16—21no—
381C2×M16—112no—
382C2×M16—112no—
383C2×M16—112no—
384C2×M16—112no—
385C2×M16—111no—
386C2×M16—111no—
387C2×M16—222no—
388C2×M16—222no—
389C2×M16—222no—
390C2×M16—222no—
391C2×M16—221no—
392C2×M16C22×D1111yescharacteristic
393C2×M16C22×D1111yescharacteristic
394C22×C8—21no—
395C22×C8—111no—
396C22×C8—111no—
397C22×C8—221no—
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400#123—221no—
401#123—221no—
402C22⋊Q8—112no—
403C22⋊Q8—112no—
404#121—112no—
405#121—112no—
406#120—221no—
407#120—221no—
408C4×D4—222no—
409C4×D4—222no—
410#117—111no—
411#117C22×D1111yescharacteristic
412C2×C42—111no—
413C2×C42—222no—
414C2×C42—221no—
415C2×C42—222no—
416C2×C42C22×D1111yescharacteristic
417#108—222no—
418#108—222no—
419#107—112no—
420#106—112no—
421C4⋊C8—222no—
422C4⋊C8—222no—
423#104—22no—
424#104—222no—
425#104—222no—
426#104—222no—
427#103—112no—
428#103C4×D1112yescomplemented
429#102—112no—
430#102C4×D1112yescomplemented
431C22⋊C8—222no—
432C22⋊C8—222no—
433C22⋊C8—222no—
434C22⋊C8—222no—
435#97—21no—
436#97—114no—
437#97—222no—
438#97—221no—
439C4×C8—22no—
440C4×C8—21no—
441C4×C8—222no—
442C4×C8—221no—
443C2×C11—21no—
444C2×C11—21no—
445C2×C11—81no—
446C2×C11C4×#12111yescharacteristic
447C2×C11#295612yes—
448D11—42no—
449D11—81no—
450C24—111no—
451#41—21no—
452#41—21no—
453#41—21no—
454#41—21no—
455#41—221no—
456#41—221no—
457#41—221no—
458#41—221no—
459C2×Q8—111no—
460C2×Q8C2×C4×D1111yescharacteristic
461C2×D4—21no—
462C2×D4—111no—
463C2×D4—222no—
464C2×D4—221no—
465C2×D4—222no—
466C2×D4C2×C4×D1111yescharacteristic
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—111no—
470C22×C4—112no—
471C22×C4—112no—
472C22×C4—224no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—444no—
480C22×C4C23×D1111yescharacteristic
481Q16—222no—
482SD16—222no—
483SD16—222no—
484D8—222no—
485M16—21no—
486M16—21no—
487M16—21no—
488M16—21no—
489M16—42no—
490M16—224no—
491M16—224no—
492M16—224no—
493M16—224no—
494M16—221no—
495M16—221no—
496M16—221no—
497M16—221no—
498M16—442no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—42no—
504C2×C8—111no—
505C2×C8—111no—
506C2×C8—112no—
507C2×C8—112no—
508C2×C8—112no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—442no—
514C2×C8C2×C4×D1112yes—
515C2×C8#433912yes—
516C2×C8D4×D1112yes—
517C2×C8D4×D1111yescharacteristic
518C2×C8D4×D1111yescharacteristic
519C4⋊C4—112no—
520C4⋊C4—222no—
521C4⋊C4—222no—
522C4⋊C4C2×C4×D1112yes—
523C22⋊C4—21no—
524C22⋊C4—222no—
525C22⋊C4—222no—
526C22⋊C4—222no—
527C22⋊C4—222no—
528C22⋊C4—221no—
529C42—21no—
530C42—21no—
531C42—112no—
532C42—224no—
533C42—221no—
534C42—221no—
535C42#433912yes—
536C11#2155111yescharacteristic, complemented, Sylow
537C23—21no—
538C23—112no—
539C23—221no—
540C23—221no—
541C23—221no—
542C23—442no—
543C23#41×D1111yescharacteristic
544Q8—21no—
545Q8—21no—
546Q8—221no—
547Q8—221no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—221no—
553D4—221no—
554D4—441no—
555D4—441no—
556D4—882no—
557D4—882no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—112no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—221no—
573C2×C4—222no—
574C2×C4—448no—
575C2×C4—442no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4C22×C4×D1111yescharacteristic
579C2×C4C2×#433911yescharacteristic
580C2×C4C2×#433911yescharacteristic
581C2×C4C2×D4×D1111yescharacteristic
582C2×C4C2×D4×D1111yescharacteristic
583C2×C4#41×D1111yescharacteristic
584C8—22no—
585C8—41no—
586C8—41no—
587C8—112no—
588C8—112no—
589C8—222no—
590C8—441no—
591C8—441no—
592C8#6693712yes—
593C8#6693712yes—
594C22—22no—
595C22—42no—
596C22—41no—
597C22—222no—
598C22—222no—
599C22—222no—
600C22—442no—
601C22—442no—
602C22—442no—
603C22—441no—
604C22#1062305911yescharacteristic
605C22C4×D4×D1111yescharacteristic
606C22#1062307811yescharacteristic
607C4—24no—
608C4—42no—
609C4—41no—
610C4—222no—
611C4—442no—
612C4—442no—
613C4—441no—
614C4C4×#433911yescharacteristic
615C4C2×#6693711yescharacteristic
616C4C4×D4×D1111yescharacteristic
617C4#1062307911yescharacteristic
618C2—21no—
619C2—21no—
620C2—81no—
621C2—442no—
622C2—881no—
623C2C4×#6693711yescharacteristic
624C2#1307752112yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1764C2
socleC22×C11C2×C4×D4
prime radical#13078224C2
cosocleC22×C4×C11C24
hypercenter#1764D11
hypocenterC11#21551
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1764

Complements

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

NH ≅ G/Ntype
2. C2×#10622758C2semidirect
3. #13077321C2semidirect
4. #13077317C2semidirect
5. C2×C4×#4313C2semidirect
6. #13069501C2semidirect
7. #13069363C2semidirect
8. #13069329C2semidirect
9. #13069325C2semidirect
10. #13069058C2semidirect
11. #13069056C2semidirect
12. #13068657C2semidirect
13. #13068501C2semidirect
14. #13068453C2semidirect
15. C11×#1764C2semidirect
48. #10622429C4semidirect
49. #10622425C4semidirect
50. #10622395C4semidirect
51. #10622393C4semidirect
78. C2×#4326C2×C4semidirect
79. C2×#4325C2×C4semidirect
83. C2×#4324C2×C4semidirect
84. C2×#4323C2×C4semidirect
113. C11×#103C2×C4semidirect
114. C11×#102C2×C4semidirect
123. #66885C2×C4semidirect
127. #66880C2×C4semidirect
130. #66879D4semidirect
133. #66872C2×C4semidirect
134. #66871C2×C4semidirect
239. #1764D11semidirect
428. #103C4×D11semidirect
430. #102C4×D11semidirect
536. C11#21551semidirect

Maximal subgroups

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

subgroupindex
#130782242
C2×#106227582
#130773212
#130773172
C2×C4×#43132
#130695012
#130693632
#130693292
#130693252
#130690582
#130690562
#130686572
#130685012
#130684532
C11×#17642
#2155111