Finite Group Databasebeta

← #14960925

Subgroups — #14960925

Order 2816.

2214 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076895C212yesmaximal, complemented
2#13075830C214yesmaximal, complemented
3#13075730C214yesmaximal, complemented
4#13075266C214yesmaximal, complemented
5#13074854C214yesmaximal, complemented
6#13074586C211yesmaximal, characteristic, complemented
7#13072347C214yesmaximal, complemented
8#13072158C214yesmaximal, complemented
9#13071321C212yesmaximal, complemented
10C2×#10622280C211yesmaximal, characteristic, complemented
11C11×#2656C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C2×C11×#121C2212yes—
14C2×C11×#121C2214yes—
15C2×#66992C2214yes—
16C2×#66991C2212yes—
17C2×#66991C2212yes—
18C2×#66990C2214yes—
19C2×#66988C2214yescomplemented
20C2×D4×Dic11C2214yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×Dic11⋊C4C2212yes—
23C11×#399C2214yescomplemented
24C11×#392C2214yescomplemented
25C2×C11×#95C2211yescharacteristic
26#10622836C2214yes—
27#10622835C2214yescomplemented
28#10622833C2214yes—
29#10622833C2214yes—
30#10622833C2214yescomplemented
31#10622825C2212yes—
32#10622823C2214yes—
33C2×C11⋊#95C2211yescharacteristic
34#10622607C2214yes—
35#10622603C2214yes—
36#10622600C2212yes—
37#10622600C2212yes—
38#10622596C2214yescomplemented
39#10622594C2214yescomplemented
40#10622591C2214yescomplemented
41#10622574C2214yes—
42#10622572C2214yes—
43#10622571C2214yes—
44#10622570C2214yes—
45#10622569C2214yes—
46#10622569C2214yes—
47#10622565C2214yescomplemented
48#10622564C2214yescomplemented
49#10622563C2214yescomplemented
50#10622562C2214yescomplemented
51#10622559C2214yescomplemented
52#10622557C2214yescomplemented
53#10622280C2214yes—
54#10622280C2214yes—
55#10622273C2214yescomplemented
56#10622270C2214yescomplemented
57C24×D11C2311yescharacteristic
58C22×D4×C11C2314yes—
59C22×D4×C11C2312yes—
60C22×D4×C11C2314yes—
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11C2314yes—
64C22×C22⋊D11C2314yes—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2312yes—
67C23×Dic11C2314yes—
68C22×C4×D11—24no—
69C22×C4×D11—44no—
70C22×C4×D11C2312yes—
71C22×C4×D11C2312yes—
72C11×#121—28no—
73C11×#121—48no—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C22⋊C4C2314yes—
77C2×C11×C22⋊C4C2314yes—
78C2×C11×C22⋊C4C2314yes—
79C2×C22⋊Dic11C2314yes—
80C2×C22⋊Dic11C2314yes—
81C2×C22⋊Dic11C2314yes—
82C2×C22⋊Dic11C2314yes—
83C2×C22⋊Dic11C2314yes—
84C2×C22⋊Dic11C2314yes—
85#66992—48no—
86#66991—44no—
87#66991—44no—
88#66990—48no—
89#66988—48no—
90D4×Dic11—48no—
91C2×(C2×D11)⋊C4—44no—
92C2×(C2×D11)⋊C4C2314yes—
93C2×(C2×D11)⋊C4C2314yes—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2314yes—
96C2×C4⋊Dic11C2312yes—
97C2×C4⋊Dic11C2312yes—
98C2×C4⋊Dic11C2314yes—
99C2×Dic11⋊C4—44no—
100C2×Dic11⋊C4C2314yes—
101C2×Dic11⋊C4C2314yes—
102C2×Dic11⋊C4C2314yes—
103C2×Dic11⋊C4C2314yes—
104C2×C4×Dic11C2314yes—
105C11×#95C2314yes—
106C11⋊#95C2314yes—
107C11⋊#95C2314yes—
108C11⋊#95C2314yes—
109C11⋊#95C2314yes—
110C11⋊#95C2314yes—
111C11⋊#95C2314yes—
112C11⋊#95C2314yes—
113C11⋊#95C2314yes—
114#36727—111nomaximal, Sylow
115C24×C11C2414yes—
116C24×C11C2411yescharacteristic
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—24no—
121C23×D11—42no—
122C23×D11C2411yescharacteristic
123C23×D11C2411yescharacteristic
124C2×D4×C11—28no—
125C2×D4×C11—28no—
126C2×D4×C11—28no—
127C2×D4×C11—24no—
128C2×D4×C11—44no—
129C2×D4×C11—42no—
130C2×D4×C11—42no—
131C2×D4×C11—44no—
132C2×D4×C11—44no—
133C22×C4×C11—24no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11#4114yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2412yes—
141C2×C22⋊D11—28no—
142C2×C22⋊D11—28no—
143C2×C22⋊D11—44no—
144C2×C22⋊D11—44no—
145C2×C22⋊D11—44no—
146C2×C22⋊D11—44no—
147C22×Dic11—24no—
148C22×Dic11—22no—
149C22×Dic11—24no—
150C22×Dic11—42no—
151C22×Dic11—42no—
152C22×Dic11—44no—
153C22×Dic11—44no—
154C22×Dic11—44no—
155C22×Dic11C2414yes—
156C22×Dic11C2414yes—
157C22×Dic11C2414yes—
158C22×Dic11C2412yes—
159C2×C4×D11—24no—
160C2×C4×D11—24no—
161C2×C4×D11—24no—
162C2×C4×D11—24no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—416no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—44no—
168C11×C22⋊C4—28no—
169C11×C22⋊C4—44no—
170C11×C22⋊C4—44no—
171C22⋊Dic11—28no—
172C22⋊Dic11—28no—
173C22⋊Dic11—28no—
174C22⋊Dic11—44no—
175C22⋊Dic11—44no—
176C22⋊Dic11—44no—
177(C2×D11)⋊C4—28no—
178(C2×D11)⋊C4—44no—
179(C2×D11)⋊C4—44no—
180(C2×D11)⋊C4—44no—
181C4⋊Dic11—44no—
182C4⋊Dic11—42no—
183C4⋊Dic11—42no—
184Dic11⋊C4—28no—
185Dic11⋊C4—44no—
186Dic11⋊C4—44no—
187Dic11⋊C4—44no—
188C4×Dic11—44no—
189#2847—112no—
190#2748—114no—
191#2741—114no—
192#2703—114no—
193#2671—114no—
194#2656D1111yescharacteristic, complemented
195#2646—111no—
196#2443—114no—
197#2424—114no—
198#2325—112no—
199C2×#380—111no—
200C23×C11—22no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11C2×#4112yes—
211C23×C11H(5,𝔽2)14yes—
212C23×C11C2511yescharacteristic
213C22×D11—28no—
214C22×D11—21no—
215C22×D11—21no—
216C22×D11—21no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—21no—
222C22×D11—48no—
223C22×D11—48no—
224C22×D11—44no—
225C22×D11—44no—
226C22×D11H(5,𝔽2)12yes—
227C22×D112−1+412yes—
228D4×C11—416no—
229D4×C11—84no—
230D4×C11—88no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—44no—
240C2×C4×C11—84no—
241C2×C4×C11C2×#4114yes—
242C22⋊D11—88no—
243C22⋊D11—88no—
244C2×Dic11—28no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—84no—
257C2×Dic11—88no—
258C2×Dic11H(5,𝔽2)14yes—
259C4×D11—48no—
260C4×D11—48no—
261C24×C4—111no—
262C2×#123—114no—
263C2×#121—112no—
264C2×#121—112no—
265C2×#121—114no—
266C2×#121C2×D1112yes—
267C2×#121C2×D1114yes—
268C2×#120—114no—
269C2×C4×D4—114no—
270C22×C4⋊C4—112no—
271C22×C22⋊C4—112no—
272#400—114no—
273#399—114no—
274#399C2×D1114yescomplemented
275#398—114no—
276#398—114no—
277#397—114no—
278#396—114no—
279#394—114no—
280#394—114no—
281#394—114no—
282#392—114no—
283#392C2×D1114yescomplemented
284#390—114no—
285#388—114no—
286#388—114no—
287#388—114no—
288#387—114no—
289#387—114no—
290#386—114no—
291#386—114no—
292#386—114no—
293#386—114no—
294#386—114no—
295#386—114no—
296#385—114no—
297#385—114no—
298#385—114no—
299#380—112no—
300#380—112no—
301#380—112no—
302#380—114no—
303#380—114no—
304C2×#95—111no—
305C2×#95C2×D1111yescharacteristic
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—24no—
309C22×C11—24no—
310C22×C11—44no—
311C22×C11—44no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11#54014yes—
318C22×C11C22×#4111yescharacteristic
319C22×C11C2×H(5,𝔽2)12yes—
320C22×C11C2×H(5,𝔽2)12yes—
321C22×C11C2×H(5,𝔽2)11yescharacteristic
322C22×C11C2×2−1+411yescharacteristic
323C2×D11—22no—
324C2×D11—22no—
325C2×D11—24no—
326C2×D11—24no—
327C2×D11—416no—
328C2×D11—41no—
329C2×D11—41no—
330C2×D11—41no—
331C2×D11—41no—
332C2×D11—42no—
333C2×D11—42no—
334C4×C11—24no—
335C4×C11—44no—
336C4×C11—44no—
337Dic11—24no—
338Dic11—44no—
339Dic11—44no—
340Dic11—44no—
341C25—111no—
342C22×D4—114no—
343C22×D4—114no—
344C22×D4C22×D1114yes—
345C22×D4C22×D1112yes—
346C22×D4C22×D1114yes—
347C23×C4—111no—
348C23×C4—112no—
349C23×C4—114no—
350C23×C4—112no—
351C23×C4—112no—
352C23×C4—224no—
353C23×C4—444no—
354C23×C4C22×D1112yes—
355C23×C4C22×D1111yescharacteristic
356#123—448no—
357#121—28no—
358#121—48no—
359#121—444no—
360#121—444no—
361#121—448no—
362#120—448no—
363C4×D4—448no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—114no—
370C2×C4⋊C4—114no—
371C2×C4⋊C4—444no—
372C2×C4⋊C4C22×D1112yes—
373C2×C4⋊C4C22×D1114yes—
374C2×C22⋊C4—114no—
375C2×C22⋊C4—114no—
376C2×C22⋊C4—114no—
377C2×C22⋊C4—114no—
378C2×C22⋊C4—114no—
379C2×C22⋊C4—114no—
380C2×C22⋊C4—114no—
381C2×C22⋊C4—114no—
382C2×C22⋊C4—114no—
383C2×C22⋊C4—114no—
384C2×C22⋊C4—444no—
385C2×C22⋊C4C22×D1114yes—
386C2×C22⋊C4C22×D1114yes—
387C2×C22⋊C4C22×D1114yes—
388C2×C42—114no—
389#95—114no—
390#95—114no—
391#95—114no—
392#95—114no—
393#95—114no—
394#95—114no—
395#95—114no—
396#95—114no—
397#95C22×D1114yes—
398C2×C11—24no—
399C2×C11—84no—
400C2×C11C2×#54011yescharacteristic
401C2×C11#349011yescharacteristic
402C2×C11#349211yescharacteristic
403C2×C11#353612yes—
404C2×C11#353712yes—
405D11—42no—
406D11—42no—
407C24—111no—
408C24—111no—
409C24—222no—
410C24—222no—
411C24—222no—
412C24—224no—
413C24—442no—
414C24C23×D1114yes—
415C24C23×D1111yescharacteristic
416C2×D4—28no—
417C2×D4—28no—
418C2×D4—28no—
419C2×D4—24no—
420C2×D4—44no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—228no—
426C2×D4—228no—
427C2×D4—444no—
428C2×D4—444no—
429C2×D4—444no—
430C2×D4—444no—
431C22×C4—24no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—112no—
436C22×C4—114no—
437C22×C4—114no—
438C22×C4—114no—
439C22×C4—224no—
440C22×C4—224no—
441C22×C4—224no—
442C22×C4—222no—
443C22×C4—224no—
444C22×C4—224no—
445C22×C4—224no—
446C22×C4—442no—
447C22×C4—442no—
448C22×C4—4416no—
449C22×C4—442no—
450C22×C4—442no—
451C22×C4—444no—
452C22×C4—444no—
453C22×C4—444no—
454C22×C4#434114yes—
455C22×C4C23×D1114yes—
456C22×C4C23×D1114yes—
457C22×C4C23×D1112yes—
458C4⋊C4—24no—
459C4⋊C4—44no—
460C4⋊C4—228no—
461C4⋊C4—444no—
462C4⋊C4—444no—
463C4⋊C4—444no—
464C4⋊C4—442no—
465C4⋊C4—442no—
466C4⋊C4—444no—
467C22⋊C4—28no—
468C22⋊C4—44no—
469C22⋊C4—44no—
470C22⋊C4—228no—
471C22⋊C4—228no—
472C22⋊C4—228no—
473C22⋊C4—228no—
474C22⋊C4—444no—
475C22⋊C4—444no—
476C22⋊C4—444no—
477C22⋊C4—444no—
478C22⋊C4—444no—
479C22⋊C4—444no—
480C42—444no—
481C11#3672711yescharacteristic, complemented, Sylow
482C23—22no—
483C23—21no—
484C23—21no—
485C23—24no—
486C23—24no—
487C23—24no—
488C23—24no—
489C23—24no—
490C23—24no—
491C23—24no—
492C23—112no—
493C23—112no—
494C23—228no—
495C23—221no—
496C23—221no—
497C23—222no—
498C23—222no—
499C23—221no—
500C23—222no—
501C23—222no—
502C23—221no—
503C23—448no—
504C23—448no—
505C23—444no—
506C23—444no—
507C23C2×#434112yes—
508C23#6703714yes—
509C23C24×D1111yescharacteristic
510D4—416no—
511D4—84no—
512D4—88no—
513D4—888no—
514D4—888no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—44no—
524C2×C4—84no—
525C2×C4—114no—
526C2×C4—228no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—448no—
539C2×C4—448no—
540C2×C4—884no—
541C2×C4—888no—
542C2×C4C2×#434114yes—
543C22—22no—
544C22—24no—
545C22—22no—
546C22—24no—
547C22—44no—
548C22—44no—
549C22—44no—
550C22—44no—
551C22—44no—
552C22—44no—
553C22—44no—
554C22—224no—
555C22—222no—
556C22—222no—
557C22—224no—
558C22—4416no—
559C22—441no—
560C22—441no—
561C22—441no—
562C22—441no—
563C22—442no—
564C22—442no—
565C22#1062325014yes—
566C22C22×#434111yescharacteristic
567C22C2×#6703712yes—
568C22D11×H(5,𝔽2)12yes—
569C22D11×H(5,𝔽2)11yescharacteristic
570C22D11×2−1+411yescharacteristic
571C4—24no—
572C4—44no—
573C4—44no—
574C4—224no—
575C4—444no—
576C4—444no—
577C4—444no—
578C2—24no—
579C2—84no—
580C2—442no—
581C2—442no—
582C2C2×#1062325011yescharacteristic
583C2#1308230411yescharacteristic
584C2#1308232311yescharacteristic
585C2#1308283312yes—
586C2#1308285312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2656C2
hypercenter#2656D11
hypocenterC11#36727
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2656

Complements

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

NH ≅ G/Ntype
1. #13076895C2semidirect
2. #13075830C2semidirect
3. #13075730C2semidirect
4. #13075266C2semidirect
5. #13074854C2semidirect
6. #13074586C2semidirect
7. #13072347C2semidirect
8. #13072158C2semidirect
9. #13071321C2semidirect
10. C2×#10622280C2semidirect
11. C11×#2656C2semidirect
19. C2×#66988C22semidirect
23. C11×#399C22semidirect
24. C11×#392C22semidirect
27. #10622835C22semidirect
30. #10622833C22semidirect
38. #10622596C22semidirect
39. #10622594C22semidirect
40. #10622591C22semidirect
47. #10622565C22semidirect
48. #10622564C22semidirect
49. #10622563C22semidirect
50. #10622562C22semidirect
51. #10622559C22semidirect
52. #10622557C22semidirect
55. #10622273C22semidirect
56. #10622270C22semidirect
194. #2656D11semidirect
274. #399C2×D11semidirect
283. #392C2×D11semidirect
481. C11#36727semidirect

Maximal subgroups

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

subgroupindex
#130768952
#130758302
#130757302
#130752662
#130748542
#130745862
#130723472
#130721582
#130713212
C2×#106222802
C11×#26562
#3672711