Finite Group Databasebeta

← #14760623

Subgroups — #14760623

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#13078222C211yesmaximal, characteristic
2C2×#10622758C211yesmaximal, characteristic, complemented
3#13077319C211yesmaximal, characteristic, complemented
4C2×M16×Dic11C211yesmaximal, characteristic, complemented
5#13069503C211yesmaximal, characteristic, complemented
6#13069361C211yesmaximal, characteristic, complemented
7#13069330C211yesmaximal, characteristic, complemented
8#13069326C211yesmaximal, characteristic, complemented
9#13069060C211yesmaximal, characteristic, complemented
10#13069057C211yesmaximal, characteristic, complemented
11#13068656C211yesmaximal, characteristic, complemented
12#13068501C211yesmaximal, characteristic, complemented
13#13068455C211yesmaximal, characteristic, complemented
14#13068451C211yesmaximal, characteristic, complemented
15C11×#2930C211yesmaximal, characteristic, complemented
16C2×C11×#131C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C11×#525C2211yescharacteristic
19C2×#67003C2211yescharacteristic
20#10623322C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C2×#66954C2211yescharacteristic
24C11×#436—22no—
25C11×#435—22no—
26C11×#424C2211yescharacteristic
27C11×#408C2211yescharacteristic
28C11×#407C2211yescharacteristic
29C11×#405C2211yescharacteristic
30C2×#66901C2211yescharacteristic
31C2×#66901C2211yescharacteristic
32#10622846C2211yescharacteristic
33#10622820C2211yescharacteristic
34#10622758—24no—
35C2×#66889C2211yescharacteristic
36C2×#66889C2211yescharacteristic
37#10622741—22no—
38#10622740—22no—
39C2×#66886C2211yescharacteristic
40C2×#66886C2211yescharacteristic
41M16×Dic11—24no—
42#10622723C2211yescharacteristic
43#10622715C2211yescharacteristic
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
63C23×Dic11—21no—
64C2×#4339C2311yescharacteristic
65C11×#131—22no—
66C11×#131—22no—
67C2×C11×M16—22no—
68C2×C11×M16—21no—
69C2×C11×M16—22no—
70C2×C11×M16D412yes—
71C2×C11×M16D412yes—
72C2×C11×M16C2311yescharacteristic
73C2×C11×M16C2311yescharacteristic
74C22×C8×C11—21no—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×#123—21no—
78C11×C22⋊Q8C2×C412yes—
79C11×#121C2×C412yes—
80C11×#120—21no—
81C4×D4×C11—22no—
82C11×#117C2311yescharacteristic
83#67006—21no—
84#67003—22no—
85#67003—22no—
86C2×#4326C2×C411yescharacteristic, complemented
87C2×#4325C2×C411yescharacteristic, complemented
88C2×#4324C2×C411yescharacteristic, complemented
89C2×#4323C2×C411yescharacteristic, complemented
90#66983C2×C412yes—
91#66982—21no—
92C4×C22⋊D11—22no—
93#66979C2311yescharacteristic
94#66977C2×C412yes—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—22no—
97C2×C4×Dic11—22no—
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×C412yescomplemented
120#66896C2×C412yescomplemented
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—22no—
132C8×Dic11—21no—
133C8×Dic11—22no—
134#66874C2×C412yescomplemented
135#66873C2×C412yescomplemented
136#66872C2×C412yescomplemented
137#66871C2×C412yescomplemented
138#21551—111nomaximal, Sylow
139C24×C11#4111yescharacteristic
140C11×#41—21no—
141C11×#41—21no—
142C11×#41—21no—
143C11×#41—21no—
144C2×Q8×C11C22×C411yescharacteristic
145C2×D4×C11—21no—
146C2×D4×C11—22no—
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—24no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—44no—
163#4339—21no—
164#4339—21no—
165#4339—21no—
166#4339—21no—
167C2×D44C22×C411yescharacteristic
168C2×C4×D11—21no—
169C2×Dic22C22×C411yescharacteristic
170C11×M16—24no—
171C11×M16—24no—
172C11×M16—21no—
173C11×M16—21no—
174C11×M16—21no—
175C11×M16—21no—
176C11×M16—42no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—42no—
182C2×C8×C11C2×D412yes—
183C2×C8×C11C2×D412yes—
184C2×C8×C11C2×D411yescharacteristic
185C2×C8×C11C2×D411yescharacteristic
186C2×C8×C11#4112yes—
187C11×C4⋊C4—22no—
188C11×C4⋊C4C22×C412yes—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—21no—
191C11×C22⋊C4—22no—
192C42×C11—21no—
193C22⋊Dic11—22no—
194C22⋊Dic11—21no—
195#4326—22no—
196#4325—22no—
197#4324—22no—
198#4323—22no—
199(C2×D11)⋊C4—22no—
200C4⋊Dic11C22×C412yes—
201Dic11⋊C4—22no—
202C4×Dic11—24no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11C2×D412yes—
207C4×Dic11#4112yes—
208#4318—24no—
209#4318—24no—
210#4318—21no—
211#4318—21no—
212#4318—21no—
213#4318—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8C22×C412yes—
219C2×C11⋊C8C22×C411yescharacteristic
220C2×C11⋊C8C22×C411yescharacteristic
221C2×C11⋊C8C2×D412yes—
222C2×C11⋊C8#4112yes—
223#4313—42no—
224C8×D11—42no—
225#3054—111no—
226C2×#444—111no—
227#2930—111no—
228#2930D1111yescharacteristic, complemented
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#1764—111no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—42no—
244C23×C11C4×D412yes—
245C23×C11C2×#4111yescharacteristic
246C22×D11—21no—
247Q8×C11—21no—
248Q8×C11—21no—
249D4×C11—21no—
250D4×C11—21no—
251D4×C11—41no—
252D4×C11—41no—
253D4×C11—82no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11C4×D412yes—
265C2×C4×C11C23×C411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C22⋊D11—41no—
272C22⋊D11—41no—
273C22⋊D11—82no—
274C2×Dic11—24no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—21no—
278C2×Dic11—22no—
279C2×Dic11—48no—
280C2×Dic11—42no—
281D44—21no—
282D44—21no—
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×M16C2×D1111yescharacteristic
302#525—111no—
303#525C2×D1111yescharacteristic
304C22×C42—111no—
305#470—112no—
306#469—112no—
307#468—112no—
308#468—112no—
309#444—224no—
310#436—22no—
311#436—222no—
312#435—22no—
313#435—222no—
314C2×#108—111no—
315C2×#108—111no—
316#427—111no—
317#424—111no—
318#424C2×D1111yescharacteristic
319C2×#104—111no—
320C2×#104—111no—
321C2×#104—111no—
322C2×#104—111no—
323#416—111no—
324#416—111no—
325#408—111no—
326#408C2×D1111yescharacteristic
327#407—111no—
328#407C2×D1111yescharacteristic
329#405—111no—
330#405C2×D1111yescharacteristic
331C4×M16—224no—
332C2×#97—111no—
333C2×#97—111no—
334C2×C4×C8—111no—
335C2×C4×C8—111no—
336#341—111no—
337#341—111no—
338#339—111no—
339#339—111no—
340#339—111no—
341#339—111no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—22no—
345C22×C11—22no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—41no—
350C22×C11C2×C4×D411yescharacteristic
351C22×C11#52511yescharacteristic
352C22×C11#52911yescharacteristic
353C2×D11—42no—
354C2×D11—41no—
355C4×C11—22no—
356C4×C11—42no—
357C4×C11—41no—
358C4×C11C2×C4×D411yescharacteristic
359C4×C11C4×#4111yescharacteristic
360C4×C11C2×#12111yescharacteristic
361C4×C11#53211yescharacteristic
362Dic11—24no—
363Dic11—42no—
364Dic11—42no—
365Dic11—41no—
366C2×#41—111no—
367C2×#41C22×D1111yescharacteristic
368C23×C4—221no—
369C23×C4C22×D1111yescharacteristic
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—22no—
381C2×M16—22no—
382C2×M16—21no—
383C2×M16—112no—
384C2×M16—112no—
385C2×M16—111no—
386C2×M16—111no—
387C2×M16—222no—
388C2×M16—222no—
389C2×M16—221no—
390C2×M16C22⋊D1112yes—
391C2×M16C22⋊D1112yes—
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—21no—
401#123—221no—
402C22⋊Q8—112no—
403C22⋊Q8C4×D1112yes—
404#121—112no—
405#121C4×D1112yes—
406#120—21no—
407#120—221no—
408C4×D4—22no—
409C4×D4—222no—
410#117—111no—
411#117C22×D1111yescharacteristic
412C2×C42—111no—
413C2×C42—111no—
414C2×C42—222no—
415C2×C42—222no—
416C2×C42—221no—
417#108—222no—
418#108—222no—
419#107—112no—
420#106—112no—
421C4⋊C8—22no—
422C4⋊C8—222no—
423#104—222no—
424#104—222no—
425#104—222no—
426#104—222no—
427#103—112no—
428#103—112no—
429#102—112no—
430#102—112no—
431C22⋊C8—22no—
432C22⋊C8—22no—
433C22⋊C8—222no—
434C22⋊C8—222no—
435#97—21no—
436#97—114no—
437#97—222no—
438#97—221no—
439C4×C8—21no—
440C4×C8—222no—
441C4×C8—222no—
442C4×C8—221no—
443C2×C11—21no—
444C2×C11—21no—
445C2×C11—42no—
446C2×C11—81no—
447C2×C11C4×#12111yescharacteristic
448C2×C11#295612yes—
449D11—81no—
450C24#433911yescharacteristic
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—22no—
463C2×D4—111no—
464C2×D4—221no—
465C2×D4—222no—
466C2×D4C2×C4×D1111yescharacteristic
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—221no—
473C22×C4—224no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—444no—
477C22×C4C2×C4×D1112yes—
478C22×C4#433911yescharacteristic
479C22×C4C2×C22⋊D1112yes—
480C22×C4C23×D1111yescharacteristic
481Q16—222no—
482SD16—222no—
483SD16—222no—
484D8—222no—
485M16—24no—
486M16—24no—
487M16—21no—
488M16—21no—
489M16—21no—
490M16—21no—
491M16—42no—
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×C8D4×D1112yes—
515C2×C8#434112yes—
516C2×C8C2×C22⋊D1112yes—
517C2×C8C2×C22⋊D1111yescharacteristic
518C2×C8C2×C22⋊D1111yescharacteristic
519C4⋊C4—22no—
520C4⋊C4—112no—
521C4⋊C4—222no—
522C4⋊C4C2×C4×D1112yes—
523C22⋊C4—22no—
524C22⋊C4—21no—
525C22⋊C4—22no—
526C22⋊C4—222no—
527C22⋊C4—221no—
528C22⋊C4—222no—
529C42—21no—
530C42—112no—
531C42—112no—
532C42—224no—
533C42—221no—
534C42—221no—
535C42—221no—
536C11#2155111yescharacteristic, complemented, Sylow
537C23—21no—
538C23—21no—
539C23—21no—
540C23—42no—
541C23—221no—
542C23C4×C22⋊D1112yes—
543C23C2×#433911yescharacteristic
544Q8—21no—
545Q8—21no—
546Q8—221no—
547Q8—221no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—82no—
553D4—221no—
554D4—221no—
555D4—441no—
556D4—441no—
557D4—882no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—224no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—221no—
572C2×C4—222no—
573C2×C4—448no—
574C2×C4—442no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4C4×C22⋊D1112yes—
578C2×C4C22×C4×D1111yescharacteristic
579C2×C4C2×D4×D1111yescharacteristic
580C2×C4C2×#434111yescharacteristic
581C2×C4#41×D1111yescharacteristic
582C2×C4#41×D1111yescharacteristic
583C2×C4C22×C22⋊D1111yescharacteristic
584C8—22no—
585C8—41no—
586C8—41no—
587C8—112no—
588C8—112no—
589C8—222no—
590C8—441no—
591C8—441no—
592C8#6699212yes—
593C8#6699212yes—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—41no—
602C22—442no—
603C22—441no—
604C22#1062306911yescharacteristic
605C22#1062307811yescharacteristic
606C22C2×C4×C22⋊D1111yescharacteristic
607C4—22no—
608C4—42no—
609C4—41no—
610C4—224no—
611C4—442no—
612C4—442no—
613C4—441no—
614C4C4×#434111yescharacteristic
615C4C4×D4×D1111yescharacteristic
616C4C2×#6699211yescharacteristic
617C4#1062336311yescharacteristic
618C2—21no—
619C2—21no—
620C2—42no—
621C2—81no—
622C2—881no—
623C2C4×#6699211yescharacteristic
624C2#1307752312yes—
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2930C2
socleC22×C11C2×C4×D4
prime radical#13078222C2
cosocleC22×C4×C11C24
hypercenter#2930D11
hypocenterC11#21551
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ #2930

Complements

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

NH ≅ G/Ntype
2. C2×#10622758C2semidirect
3. #13077319C2semidirect
4. C2×M16×Dic11C2semidirect
5. #13069503C2semidirect
6. #13069361C2semidirect
7. #13069330C2semidirect
8. #13069326C2semidirect
9. #13069060C2semidirect
10. #13069057C2semidirect
11. #13068656C2semidirect
12. #13068501C2semidirect
13. #13068455C2semidirect
14. #13068451C2semidirect
15. C11×#2930C2semidirect
49. #10622665C4semidirect
50. #10622662C4semidirect
51. #10622655C4semidirect
52. #10622652C4semidirect
86. C2×#4326C2×C4semidirect
87. C2×#4325C2×C4semidirect
88. C2×#4324C2×C4semidirect
89. C2×#4323C2×C4semidirect
119. #66899C2×C4semidirect
120. #66896C2×C4semidirect
129. #66879D4semidirect
134. #66874C2×C4semidirect
135. #66873C2×C4semidirect
136. #66872C2×C4semidirect
137. #66871C2×C4semidirect
228. #2930D11semidirect
536. C11#21551semidirect

Maximal subgroups

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

subgroupindex
#130782222
C2×#106227582
#130773192
C2×M16×Dic112
#130695032
#130693612
#130693302
#130693262
#130690602
#130690572
#130686562
#130685012
#130684552
#130684512
C11×#29302
#2155111