Finite Group Databasebeta

← #14960790

Subgroups — #14960790

Order 2816.

2970 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66936C211yesmaximal, characteristic, complemented
2#13076895C212yesmaximal, complemented
3#13075298C218yesmaximal, complemented
4#13074937C218yesmaximal, complemented
5#13074360C212yesmaximal, complemented
6#13073548C212yesmaximal, complemented
7#13073109C212yesmaximal, complemented
8#13071939C212yesmaximal, complemented
9#13071926C212yesmaximal, complemented
10#13071214C211yesmaximal, characteristic, complemented
11C2×C11×#534C211yesmaximal, characteristic, complemented
12C23×D4×C11C2212yes—
13C23×C22⋊D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic, complemented
15C11×#534—28no—
16C2×C11×#123C2214yescomplemented
17C2×C11×#121C2212yes—
18C2×C11×#121C2212yes—
19C2×C11×#120C2214yescomplemented
20C22×C11×C22⋊C4C2211yescharacteristic
21C2×#67006C2214yescomplemented
22C22×C22⋊Dic11C2211yescharacteristic
23C2×#66991C2214yescomplemented
24C2×#66990C2214yescomplemented
25C2×#66988C2214yescomplemented
26C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
27C22×C4⋊Dic11C2211yescharacteristic, complemented
28C22×Dic11⋊C4C2211yescharacteristic, complemented
29C2×#66936—28no—
30C2×#66936C2218yescomplemented
31#10622860C2212yes—
32#10622860C2214yescomplemented
33#10622836C2218yes—
34#10622836C2214yescomplemented
35#10622835C2218yescomplemented
36#10622835C2214yescomplemented
37#10622834C2214yescomplemented
38#10622833C2214yescomplemented
39#10622833C2214yescomplemented
40#10622826C2214yescomplemented
41#10622825C2212yescomplemented
42#10622823C2214yescomplemented
43C4×C22⋊Dic11C2212yescomplemented
44#10622605C2214yescomplemented
45#10622600C2214yescomplemented
46#10622593C2214yescomplemented
47#10622590C2214yescomplemented
48#10622570C2218yescomplemented
49#10622569C2218yescomplemented
50#10622566C2218yescomplemented
51#10622564C2218yescomplemented
52#10622561C2218yescomplemented
53C25×C11C2311yescharacteristic
54C25×C11C2312yes—
55C24×D11C2311yescharacteristic
56C22×D4×C11—28no—
57C22×D4×C11—48no—
58C22×D4×C11C2314yes—
59C22×D4×C11C2312yes—
60C22×D4×C11C2312yes—
61C22×D4×C11C2314yes—
62C23×C4×C11C2312yes—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11—24no—
66C22×C22⋊D11—44no—
67C22×C22⋊D11C2314yes—
68C22×C22⋊D11C2318yes—
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C22×C4×D11—24no—
73C22×C4×D11—44no—
74C22×C4×D11C2314yes—
75C11×#123—216no—
76C11×#121—28no—
77C11×#121—28no—
78C11×#120—216no—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C22⋊C4D418yescomplemented
82C2×C11×C22⋊C4C2314yes—
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2314yes—
85#67006—48no—
86C2×C22⋊Dic11—24no—
87C2×C22⋊Dic11C2314yes—
88C2×C22⋊Dic11C2314yes—
89C2×C22⋊Dic11C2318yes—
90C2×C22⋊Dic11C2318yes—
91C2×C22⋊Dic11C2318yes—
92C2×C22⋊Dic11C2314yes—
93C2×C22⋊Dic11C2314yes—
94#66991—48no—
95#66990—48no—
96#66988—48no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×C4⋊Dic11—24no—
101C2×C4⋊Dic11C2314yes—
102C2×C4⋊Dic11C2314yes—
103C2×Dic11⋊C4—24no—
104C2×Dic11⋊C4C2314yes—
105C2×Dic11⋊C4C2318yes—
106C2×C4×Dic11C2314yes—
107#66936—232no—
108C11⋊#95C2318yes—
109C11⋊#95C2314yes—
110C11⋊#95C2314yes—
111C11⋊#95C2318yes—
112#36721—111nomaximal, Sylow
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—42no—
116C24×C11—44no—
117C24×C11—42no—
118C24×C11—44no—
119C24×C11—44no—
120C24×C11C2×D414yes—
121C24×C11C2414yes—
122C24×C11C2412yes—
123C24×C11C2411yescharacteristic
124C23×D11—22no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—42no—
128C23×D11C2412yes—
129C2×D4×C11—28no—
130C2×D4×C11—28no—
131C2×D4×C11—28no—
132C2×D4×C11—28no—
133C2×D4×C11—24no—
134C2×D4×C11—24no—
135C2×D4×C11—44no—
136C2×D4×C11—44no—
137C2×D4×C11—44no—
138C2×D4×C11—44no—
139C2×D4×C11—432no—
140C22×C4×C11—24no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11—44no—
144C22×C4×C11C2×D414yes—
145C22×C4×C11C2×D414yes—
146C22×C4×C11C2414yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2412yes—
149C2×C22⋊D11—28no—
150C2×C22⋊D11—28no—
151C2×C22⋊D11—216no—
152C2×C22⋊D11—44no—
153C2×C22⋊D11—48no—
154C2×C22⋊D11—48no—
155C2×C22⋊D11—416no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—24no—
160C22×Dic11—42no—
161C22×Dic11—42no—
162C22×Dic11C2418yes—
163C22×Dic11C2412yes—
164C22×Dic11C2412yes—
165C22×Dic11C2412yes—
166C2×C4×D11—28no—
167C2×C4×D11—28no—
168C2×C4×D11—44no—
169C2×C4×D11—416no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—24no—
172C11×C22⋊C4—28no—
173C11×C22⋊C4—28no—
174C11×C22⋊C4C2×D4116yes—
175C22⋊Dic11—28no—
176C22⋊Dic11—28no—
177C22⋊Dic11—48no—
178C22⋊Dic11—48no—
179C22⋊Dic11—44no—
180C22⋊Dic11—44no—
181C22⋊Dic11—48no—
182(C2×D11)⋊C4—28no—
183(C2×D11)⋊C4—48no—
184C4⋊Dic11—28no—
185C4⋊Dic11—44no—
186Dic11⋊C4—28no—
187Dic11⋊C4—48no—
188C4×Dic11—44no—
189C2×#534D1111yescharacteristic, complemented
190C22×#123—111no—
191#2847—112no—
192#2706—118no—
193#2678—118no—
194#2618—112no—
195#2539—112no—
196#2504—112no—
197#2405—112no—
198#2403—112no—
199#2312—111no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—28no—
206C23×C11—24no—
207C23×C11—28no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—28no—
211C23×C11—44no—
212C23×C11—44no—
213C23×C11—48no—
214C23×C11—88no—
215C23×C11—84no—
216C23×C11—84no—
217C23×C11—816no—
218C23×C11C22×D414yes—
219C23×C11C22×D412yes—
220C23×C11H(5,𝔽2)14yes—
221C23×C11C2511yescharacteristic
222C22×D11—28no—
223C22×D11—22no—
224C22×D11—24no—
225C22×D11—22no—
226C22×D11—24no—
227C22×D11—416no—
228C22×D11—44no—
229C22×D11—44no—
230C22×D11H(5,𝔽2)14yes—
231D4×C11—416no—
232D4×C11—416no—
233D4×C11—84no—
234D4×C11—84no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—44no—
241C2×C4×C11—44no—
242C2×C4×C11—48no—
243C2×C4×C11C22×D414yes—
244C2×C4×C11C22×D414yes—
245C22⋊D11—416no—
246C22⋊D11—816no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—28no—
252C2×Dic11—28no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—28no—
256C2×Dic11—44no—
257C2×Dic11—44no—
258C2×Dic11—44no—
259C4×D11—416no—
260C23×D4—111no—
261C23×D4C2×D1112yes—
262C24×C4—111no—
263#534—28no—
264C2×#123—114no—
265C2×#123—118no—
266C2×#123—228no—
267C2×#123C2×D1114yescomplemented
268C2×#121—114no—
269C2×#121C2×D1112yes—
270C2×#121C2×D1112yes—
271C2×#120—114no—
272C2×#120—114no—
273C2×#120C2×D1114yescomplemented
274C22×C4⋊C4—111no—
275C22×C4⋊C4—111no—
276C22×C22⋊C4—111no—
277C22×C22⋊C4—111no—
278C22×C22⋊C4C2×D1111yescharacteristic
279#399—114no—
280#398—114no—
281#397—118no—
282#396—118no—
283#394—114no—
284#394—118no—
285#392—118no—
286#392—114no—
287#390—114no—
288#390—118no—
289#388—118no—
290#386—114no—
291#386—114no—
292#386—114no—
293#386—118no—
294#385—114no—
295#382—114no—
296#380—112no—
297#380—114no—
298#379—112no—
299#379—114no—
300C4×C22⋊C4—112no—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—28no—
304C22×C11—24no—
305C22×C11—24no—
306C22×C11—24no—
307C22×C11—48no—
308C22×C11—44no—
309C22×C11—44no—
310C22×C11—44no—
311C22×C11—48no—
312C22×C11—48no—
313C22×C11—88no—
314C22×C11—816no—
315C22×C11#53514yes—
316C22×C11C23×D411yescharacteristic
317C22×C11C2×H(5,𝔽2)12yes—
318C22×C11C2×H(5,𝔽2)12yes—
319C22×C11#58512yes—
320C2×D11—24no—
321C2×D11—28no—
322C2×D11—416no—
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—44no—
326C4×C11—24no—
327C4×C11—24no—
328C4×C11—44no—
329Dic11—42no—
330Dic11—42no—
331Dic11—42no—
332Dic11—48no—
333C25—111no—
334C25C22×D1111yescharacteristic
335C25C22×D1112yes—
336C22×D4—28no—
337C22×D4—48no—
338C22×D4—114no—
339C22×D4—118no—
340C22×D4—224no—
341C22×D4—444no—
342C22×D4C22×D1114yes—
343C22×D4C22×D1112yes—
344C22×D4C22×D1112yes—
345C22×D4C22×D1114yes—
346C23×C4—111no—
347C23×C4—111no—
348C23×C4—111no—
349C23×C4—114no—
350C23×C4—224no—
351C23×C4—444no—
352C23×C4C22×D1112yes—
353C23×C4C22×D1111yescharacteristic
354C23×C4C22×D1111yescharacteristic
355#123—216no—
356#123—2232no—
357#123—448no—
358#121—28no—
359#121—28no—
360#121—448no—
361#120—216no—
362#120—448no—
363#120—448no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4—118no—
368C2×C4⋊C4—224no—
369C2×C4⋊C4—224no—
370C2×C4⋊C4C22×D1112yes—
371C2×C4⋊C4C22×D1112yes—
372C2×C22⋊C4—114no—
373C2×C22⋊C4—114no—
374C2×C22⋊C4—114no—
375C2×C22⋊C4—114no—
376C2×C22⋊C4—118no—
377C2×C22⋊C4—118no—
378C2×C22⋊C4—118no—
379C2×C22⋊C4—114no—
380C2×C22⋊C4—118no—
381C2×C22⋊C4—224no—
382C2×C22⋊C4—224no—
383C2×C22⋊C4C22⋊D1118yescomplemented
384C2×C22⋊C4C22×D1114yes—
385C2×C22⋊C4C22×D1114yes—
386C2×C22⋊C4C22×D1114yes—
387C2×C42—114no—
388#95—114no—
389#95—118no—
390#95—114no—
391#95—118no—
392C2×C11—24no—
393C2×C11—44no—
394C2×C11—84no—
395C2×C11C2×#53511yescharacteristic
396C2×C11#348411yescharacteristic
397C2×C11#348511yescharacteristic
398C2×C11#353414yes—
399D11—44no—
400C24—24no—
401C24—24no—
402C24—44no—
403C24—42no—
404C24—42no—
405C24—44no—
406C24—44no—
407C24—112no—
408C24—224no—
409C24—222no—
410C24—224no—
411C24—442no—
412C24C2×C22⋊D1114yes—
413C24C23×D1114yes—
414C24C23×D1112yes—
415C24C23×D1111yescharacteristic
416C2×D4—28no—
417C2×D4—28no—
418C2×D4—28no—
419C2×D4—28no—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—432no—
427C2×D4—228no—
428C2×D4—228no—
429C2×D4—2216no—
430C2×D4—444no—
431C2×D4—448no—
432C2×D4—448no—
433C2×D4—4416no—
434C22×C4—24no—
435C22×C4—42no—
436C22×C4—44no—
437C22×C4—42no—
438C22×C4—118no—
439C22×C4—112no—
440C22×C4—112no—
441C22×C4—112no—
442C22×C4—228no—
443C22×C4—224no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—228no—
448C22×C4—444no—
449C22×C4—4416no—
450C22×C4—442no—
451C22×C4—442no—
452C22×C4C2×C22⋊D1114yes—
453C22×C4C2×C22⋊D1114yes—
454C22×C4C23×D1114yes—
455C22×C4C23×D1112yes—
456C22×C4C23×D1112yes—
457C4⋊C4—24no—
458C4⋊C4—24no—
459C4⋊C4—228no—
460C4⋊C4—228no—
461C4⋊C4—444no—
462C4⋊C4—448no—
463C22⋊C4—28no—
464C22⋊C4—28no—
465C22⋊C4—228no—
466C22⋊C4—228no—
467C22⋊C4—228no—
468C22⋊C4—448no—
469C22⋊C4—444no—
470C22⋊C4—448no—
471C22⋊C4—448no—
472C22⋊C4—448no—
473C22⋊C4—444no—
474C22⋊C4C2×C22⋊D11116yes—
475C42—444no—
476C11#3672111yescharacteristic, complemented, Sylow
477C23—22no—
478C23—22no—
479C23—24no—
480C23—24no—
481C23—24no—
482C23—28no—
483C23—24no—
484C23—24no—
485C23—28no—
486C23—28no—
487C23—24no—
488C23—44no—
489C23—44no—
490C23—48no—
491C23—88no—
492C23—84no—
493C23—84no—
494C23—816no—
495C23—114no—
496C23—228no—
497C23—224no—
498C23—222no—
499C23—224no—
500C23—222no—
501C23—4416no—
502C23—444no—
503C23—444no—
504C23#6703714yes—
505C23C22×C22⋊D1114yes—
506C23C22×C22⋊D1112yes—
507C23C24×D1111yescharacteristic
508D4—416no—
509D4—416no—
510D4—84no—
511D4—84no—
512D4—4416no—
513D4—8816no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—44no—
520C2×C4—44no—
521C2×C4—48no—
522C2×C4—228no—
523C2×C4—224no—
524C2×C4—228no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—228no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—4416no—
532C2×C4—444no—
533C2×C4—444no—
534C2×C4—444no—
535C2×C4C22×C22⋊D1114yes—
536C2×C4C22×C22⋊D1114yes—
537C22—22no—
538C22—22no—
539C22—28no—
540C22—24no—
541C22—24no—
542C22—24no—
543C22—48no—
544C22—44no—
545C22—44no—
546C22—44no—
547C22—48no—
548C22—48no—
549C22—88no—
550C22—816no—
551C22—224no—
552C22—228no—
553C22—4416no—
554C22—442no—
555C22—442no—
556C22—444no—
557C22#1062333614yes—
558C22C2×#6703712yes—
559C22D11×H(5,𝔽2)12yes—
560C22#1062345512yes—
561C22C23×C22⋊D1111yescharacteristic
562C4—24no—
563C4—24no—
564C4—44no—
565C4—442no—
566C4—442no—
567C4—442no—
568C4—448no—
569C2—24no—
570C2—44no—
571C2—84no—
572C2—444no—
573C2C2×#1062333611yescharacteristic
574C2#1308224711yescharacteristic
575C2#1308225611yescharacteristic
576C2#1308280314yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#534C2
hypercenterC2×#534D11
hypocenterC11#36721
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. C22×#66936C2semidirect
2. #13076895C2semidirect
3. #13075298C2semidirect
4. #13074937C2semidirect
5. #13074360C2semidirect
6. #13073548C2semidirect
7. #13073109C2semidirect
8. #13071939C2semidirect
9. #13071926C2semidirect
10. #13071214C2semidirect
11. C2×C11×#534C2semidirect
14. C23×C4×D11C22semidirect
16. C2×C11×#123C22semidirect
19. C2×C11×#120C22semidirect
21. C2×#67006C22semidirect
23. C2×#66991C22semidirect
24. C2×#66990C22semidirect
25. C2×#66988C22semidirect
26. C22×(C2×D11)⋊C4C22semidirect
27. C22×C4⋊Dic11C22semidirect
28. C22×Dic11⋊C4C22semidirect
30. C2×#66936C22semidirect
32. #10622860C22semidirect
34. #10622836C22semidirect
35. #10622835C22semidirect
36. #10622835C22semidirect
37. #10622834C22semidirect
38. #10622833C22semidirect
39. #10622833C22semidirect
40. #10622826C22semidirect
41. #10622825C22semidirect
42. #10622823C22semidirect
43. C4×C22⋊Dic11C22semidirect
44. #10622605C22semidirect
45. #10622600C22semidirect
46. #10622593C22semidirect
47. #10622590C22semidirect
48. #10622570C22semidirect
49. #10622569C22semidirect
50. #10622566C22semidirect
51. #10622564C22semidirect
52. #10622561C22semidirect
81. C2×C11×C22⋊C4D4semidirect
189. C2×#534D11semidirect
267. C2×#123C2×D11semidirect
273. C2×#120C2×D11semidirect
383. C2×C22⋊C4C22⋊D11semidirect
476. C11#36721semidirect

Maximal subgroups

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

subgroupindex
C22×#669362
#130768952
#130752982
#130749372
#130743602
#130735482
#130731092
#130719392
#130719262
#130712142
C2×C11×#5342
#3672111