Finite Group Databasebeta

← #14960701

Subgroups — #14960701

Order 2816.

4170 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66990C211yesmaximal, characteristic, complemented
2#13076892C212yesmaximal, complemented
3#13075175C214yesmaximal, complemented
4#13074950C214yesmaximal, complemented
5#13074944C218yesmaximal, complemented
6#13074391C212yesmaximal, complemented
7#13072002C214yesmaximal, complemented
8#13071943C212yesmaximal, complemented
9#13071926C212yesmaximal, complemented
10#13071198C211yesmaximal, characteristic, complemented
11C2×C11×#534C211yesmaximal, characteristic, complemented
12C25×D11C2211yescharacteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic, complemented
15C23×C22⋊D11C2212yes—
16C11×#534—28no—
17C2×C11×#123C2212yescomplemented
18C2×C11×#123C2212yescomplemented
19C2×C11×#121C2214yescomplemented
20C2×C11×#120C2212yes—
21C2×C11×#120C2212yescomplemented
22C22×C11×C22⋊C4C2211yescharacteristic, complemented
23C2×#67006C2214yescomplemented
24C22×C22⋊Dic11C2211yescharacteristic, complemented
25C2×#66990—28no—
26C2×#66990C2214yes—
27C2×#66990C2214yes—
28C2×#66990C2214yescomplemented
29C2×#66990C2218yescomplemented
30C2×#66982C2214yescomplemented
31C22×(C2×D11)⋊C4C2212yescomplemented
32C2×#66979C2212yescomplemented
33#10622860C2212yescomplemented
34#10622860C2212yescomplemented
35#10622836C2218yescomplemented
36#10622835C2218yescomplemented
37#10622834C2214yescomplemented
38#10622834C2214yescomplemented
39#10622833C2214yescomplemented
40#10622826C2214yescomplemented
41#10622826C2214yescomplemented
42#10622607C2218yescomplemented
43#10622603C2218yescomplemented
44#10622574C2218yescomplemented
45#10622572C2218yescomplemented
46#10622570C2218yescomplemented
47#10622568C2218yescomplemented
48#10622568C2214yescomplemented
49#10622565C2218yescomplemented
50#10622559C2214yescomplemented
51C25×C11C2311yescharacteristic
52C25×C11C2311yescharacteristic
53C25×C11C2311yescharacteristic, complemented
54C24×D11—24no—
55C24×D11—48no—
56C24×D11—44no—
57C24×D11C2312yes—
58C24×D11C2314yes—
59C22×D4×C11—24no—
60C22×D4×C11—44no—
61C22×D4×C11—44no—
62C22×D4×C11D418yescomplemented
63C22×D4×C11C2312yes—
64C22×D4×C11C2314yes—
65C22×D4×C11C2312yes—
66C22×D4×C11C2312yes—
67C22×D4×C11C2312yescomplemented
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2312yescomplemented
70C23×C4×C11C2311yescharacteristic, complemented
71C22×C22⋊D11—28no—
72C22×C22⋊D11—48no—
73C22×C22⋊D11C2314yes—
74C22×C22⋊D11C2314yes—
75C22×C22⋊D11C2318yes—
76C23×Dic11C2312yes—
77C11×#123—28no—
78C11×#123—28no—
79C11×#121—216no—
80C11×#120—28no—
81C11×#120—28no—
82C2×C11×C4⋊C4C2314yescomplemented
83C2×C11×C22⋊C4—24no—
84C2×C11×C22⋊C4C2312yes—
85C2×C11×C22⋊C4C2314yes—
86C2×C11×C22⋊C4C2314yescomplemented
87C2×C11×C22⋊C4C2312yescomplemented
88#67006—48no—
89C2×C22⋊Dic11—24no—
90C2×C22⋊Dic11C2314yes—
91C2×C22⋊Dic11C2314yes—
92C2×C22⋊Dic11C2318yes—
93C2×C22⋊Dic11C2314yescomplemented
94C2×C22⋊Dic11C2318yescomplemented
95C2×C22⋊Dic11C2314yescomplemented
96#66990—216no—
97#66990—216no—
98#66990—416no—
99#66990—48no—
100#66982—48no—
101C2×(C2×D11)⋊C4—28no—
102C2×(C2×D11)⋊C4C2318yes—
103C2×(C2×D11)⋊C4C2318yes—
104C2×(C2×D11)⋊C4C2318yes—
105C2×(C2×D11)⋊C4C2318yes—
106#66979—44no—
107C2×C4⋊Dic11C2314yescomplemented
108C2×Dic11⋊C4C2318yescomplemented
109C2×C4×Dic11C2314yescomplemented
110C11⋊#95C2318yescomplemented
111C11⋊#95C2318yescomplemented
112#36714—111nomaximal, Sylow
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—22no—
116C24×C11—44no—
117C24×C11—44no—
118C24×C11—42no—
119C24×C11—44no—
120C24×C11C2×D414yes—
121C24×C11C2×D414yes—
122C24×C11C2412yes—
123C24×C11C2412yes—
124C24×C11C2411yescharacteristic
125C24×C11C2411yescharacteristic
126C24×C11C2411yescharacteristic
127C23×D11—24no—
128C23×D11—28no—
129C23×D11—28no—
130C23×D11—28no—
131C23×D11—216no—
132C23×D11—44no—
133C23×D11—44no—
134C23×D11—44no—
135C23×D11—48no—
136C23×D11—432no—
137C23×D11—416no—
138C23×D11—464no—
139C23×D11C2414yes—
140C2×D4×C11—24no—
141C2×D4×C11—24no—
142C2×D4×C11—28no—
143C2×D4×C11—28no—
144C2×D4×C11—416no—
145C2×D4×C11—42no—
146C2×D4×C11—42no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11—44no—
150C2×D4×C11—48no—
151C2×D4×C11—416no—
152C2×D4×C11C2×D418yes—
153C2×D4×C11C2×D418yes—
154C22×C4×C11—24no—
155C22×C4×C11—22no—
156C22×C4×C11—24no—
157C22×C4×C11—42no—
158C22×C4×C11—44no—
159C22×C4×C11C2×D414yes—
160C22×C4×C11C2412yes—
161C22×C4×C11C2414yes—
162C22×C4×C11C2412yes—
163C2×C22⋊D11—28no—
164C2×C22⋊D11—28no—
165C2×C22⋊D11—28no—
166C2×C22⋊D11—28no—
167C2×C22⋊D11—216no—
168C2×C22⋊D11—44no—
169C2×C22⋊D11—44no—
170C2×C22⋊D11—48no—
171C2×C22⋊D11—48no—
172C2×C22⋊D11—432no—
173C22×Dic11—24no—
174C22×Dic11—44no—
175C22×Dic11C2414yes—
176C22×Dic11C2418yes—
177C11×C4⋊C4—28no—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—28no—
181C11×C22⋊C4—28no—
182C22⋊Dic11—28no—
183C22⋊Dic11—28no—
184C22⋊Dic11—44no—
185C22⋊Dic11—48no—
186C22⋊Dic11—44no—
187C22⋊Dic11—48no—
188(C2×D11)⋊C4—216no—
189(C2×D11)⋊C4—216no—
190(C2×D11)⋊C4—48no—
191(C2×D11)⋊C4—48no—
192C4⋊Dic11—44no—
193Dic11⋊C4—48no—
194C4×Dic11—44no—
195C2×#534D1111yescharacteristic, complemented
196C22×#120—111no—
197#2846—112no—
198#2697—114no—
199#2679—114no—
200#2678—118no—
201#2622—112no—
202#2411—114no—
203#2405—112no—
204#2403—112no—
205#2309—111no—
206C23×C11—24no—
207C23×C11—28no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—28no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—28no—
216C23×C11—22no—
217C23×C11—28no—
218C23×C11—24no—
219C23×C11—48no—
220C23×C11—48no—
221C23×C11—416no—
222C23×C11—44no—
223C23×C11—88no—
224C23×C11—84no—
225C23×C11—88no—
226C23×C11C22×D414yes—
227C23×C11C22×D412yes—
228C23×C11C22×D412yes—
229C23×C11C22×D412yes—
230C23×C11H(5,𝔽2)14yes—
231C23×C11C2511yescharacteristic
232C22×D11—216no—
233C22×D11—24no—
234C22×D11—28no—
235C22×D11—28no—
236C22×D11—24no—
237C22×D11—416no—
238C22×D11—432no—
239C22×D11—432no—
240C22×D11—432no—
241C22×D11—48no—
242C22×D11—416no—
243C22×D11—4128no—
244C22×D11—416no—
245C22×D11—48no—
246C22×D11H(5,𝔽2)18yes—
247D4×C11—48no—
248D4×C11—48no—
249D4×C11—48no—
250D4×C11—48no—
251D4×C11—88no—
252C2×C4×C11—28no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—22no—
257C2×C4×C11—28no—
258C2×C4×C11—24no—
259C2×C4×C11—44no—
260C2×C4×C11—84no—
261C2×C4×C11C22×D414yes—
262C22⋊D11—416no—
263C22⋊D11—416no—
264C22⋊D11—816no—
265C2×Dic11—24no—
266C2×Dic11—28no—
267C2×Dic11—24no—
268C2×Dic11—28no—
269C2×Dic11—28no—
270C2×Dic11—24no—
271C2×Dic11—48no—
272C26—111no—
273C23×D4—112no—
274C23×D4C2×D1111yescharacteristic
275C23×D4C2×D1111yescharacteristic, complemented
276#534—28no—
277C2×#123—114no—
278C2×#123C2×D1112yescomplemented
279C2×#123C2×D1112yescomplemented
280C2×#121C2×D1114yescomplemented
281C2×#120—114no—
282C2×#120—114no—
283C2×#120—114no—
284C2×#120—114no—
285C2×#120—118no—
286C2×#120—228no—
287C2×#120C2×D1112yes—
288C2×#120C2×D1112yescomplemented
289C2×#117—112no—
290C22×C22⋊C4—111no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4C2×D1111yescharacteristic, complemented
293#397—118no—
294#396—118no—
295#394—118no—
296#394—118no—
297#394—118no—
298#392—118no—
299#390—114no—
300#390—114no—
301#390—118no—
302#388—118no—
303#386—114no—
304#386—114no—
305#386—114no—
306#385—114no—
307#379—112no—
308#379—112no—
309#379—114no—
310#379—118no—
311C22×C11—24no—
312C22×C11—28no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—24no—
316C22×C11—24no—
317C22×C11—28no—
318C22×C11—24no—
319C22×C11—416no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11—42no—
325C22×C11—44no—
326C22×C11—48no—
327C22×C11—88no—
328C22×C11—88no—
329C22×C11#53414yes—
330C22×C11C23×D411yescharacteristic
331C22×C11C2×H(5,𝔽2)12yes—
332C22×C11C2×H(5,𝔽2)14yes—
333C2×D11—28no—
334C2×D11—216no—
335C2×D11—432no—
336C2×D11—464no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—48no—
340C4×C11—24no—
341C4×C11—42no—
342C4×C11—44no—
343Dic11—44no—
344Dic11—48no—
345C25—112no—
346C25—114no—
347C25—224no—
348C25—444no—
349C25—448no—
350C25C22×D1111yescharacteristic
351C25C22×D1111yescharacteristic
352C25C22×D1111yescharacteristic, complemented
353C22×D4—24no—
354C22×D4—44no—
355C22×D4—44no—
356C22×D4—114no—
357C22×D4—114no—
358C22×D4—118no—
359C22×D4—228no—
360C22×D4—448no—
361C22×D4C22⋊D1118yescomplemented
362C22×D4C22×D1112yes—
363C22×D4C22×D1114yes—
364C22×D4C22×D1112yes—
365C22×D4C22×D1112yes—
366C22×D4C22×D1112yescomplemented
367C23×C4—112no—
368C23×C4C22×D1111yescharacteristic
369C23×C4C22×D1112yescomplemented
370C23×C4C22×D1111yescharacteristic, complemented
371#123—28no—
372#123—28no—
373#123—448no—
374#121—216no—
375#120—28no—
376#120—28no—
377#120—2216no—
378#120—2216no—
379#120—448no—
380#120—4416no—
381#120—448no—
382#117—444no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—118no—
385C2×C4⋊C4C22×D1114yescomplemented
386C2×C22⋊C4—24no—
387C2×C22⋊C4—114no—
388C2×C22⋊C4—114no—
389C2×C22⋊C4—118no—
390C2×C22⋊C4—118no—
391C2×C22⋊C4—118no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—118no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—224no—
398C2×C22⋊C4—228no—
399C2×C22⋊C4C22×D1112yes—
400C2×C22⋊C4C22×D1114yes—
401C2×C22⋊C4C22×D1112yescomplemented
402C2×C22⋊C4C22×D1114yescomplemented
403C2×C42—114no—
404#95—118no—
405#95—118no—
406C2×C11—24no—
407C2×C11—44no—
408C2×C11—42no—
409C2×C11—42no—
410C2×C11—82no—
411C2×C11C2×#53411yescharacteristic
412C2×C11#348412yes—
413C2×C11#353214yes—
414D11—48no—
415C24—24no—
416C24—24no—
417C24—22no—
418C24—44no—
419C24—42no—
420C24—44no—
421C24—44no—
422C24—114no—
423C24—228no—
424C24—2216no—
425C24—224no—
426C24—228no—
427C24—228no—
428C24—444no—
429C24—444no—
430C24—444no—
431C24—448no—
432C24—4416no—
433C24—4432no—
434C24—4464no—
435C24C2×C22⋊D1114yes—
436C24C2×C22⋊D1114yes—
437C24C23×D1112yes—
438C24C23×D1112yes—
439C24C23×D1111yescharacteristic
440C24C23×D1111yescharacteristic
441C24C23×D1111yescharacteristic
442C2×D4—28no—
443C2×D4—24no—
444C2×D4—24no—
445C2×D4—28no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—44no—
451C2×D4—416no—
452C2×D4—48no—
453C2×D4—416no—
454C2×D4—228no—
455C2×D4—228no—
456C2×D4—228no—
457C2×D4—228no—
458C2×D4—2216no—
459C2×D4—444no—
460C2×D4—444no—
461C2×D4—448no—
462C2×D4—448no—
463C2×D4—4432no—
464C2×D4C2×C22⋊D1118yes—
465C2×D4C2×C22⋊D1118yes—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—42no—
470C22×C4—44no—
471C22×C4—114no—
472C22×C4—118no—
473C22×C4—224no—
474C22×C4—444no—
475C22×C4C2×C22⋊D1114yes—
476C22×C4C23×D1112yes—
477C22×C4C23×D1114yes—
478C22×C4C23×D1112yes—
479C4⋊C4—28no—
480C4⋊C4—444no—
481C4⋊C4—448no—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C22⋊C4—28no—
485C22⋊C4—28no—
486C22⋊C4—2216no—
487C22⋊C4—228no—
488C22⋊C4—228no—
489C22⋊C4—2216no—
490C22⋊C4—448no—
491C22⋊C4—448no—
492C22⋊C4—448no—
493C22⋊C4—444no—
494C22⋊C4—448no—
495C22⋊C4—444no—
496C42—444no—
497C11#3671411yescharacteristic, complemented, Sylow
498C23—24no—
499C23—28no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—24no—
505C23—28no—
506C23—24no—
507C23—28no—
508C23—24no—
509C23—28no—
510C23—22no—
511C23—48no—
512C23—48no—
513C23—416no—
514C23—44no—
515C23—88no—
516C23—84no—
517C23—88no—
518C23—118no—
519C23—2216no—
520C23—228no—
521C23—228no—
522C23—224no—
523C23—224no—
524C23—4432no—
525C23—4432no—
526C23—448no—
527C23—4416no—
528C23—4416no—
529C23—4432no—
530C23—44128no—
531C23—4416no—
532C23—448no—
533C23#6703714yes—
534C23C22×C22⋊D1114yes—
535C23C22×C22⋊D1112yes—
536C23C22×C22⋊D1112yes—
537C23C22×C22⋊D1112yes—
538C23C24×D1111yescharacteristic
539D4—48no—
540D4—48no—
541D4—48no—
542D4—48no—
543D4—88no—
544D4—4416no—
545D4—4416no—
546D4—8816no—
547C2×C4—28no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—28no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—44no—
555C2×C4—84no—
556C2×C4—228no—
557C2×C4—228no—
558C2×C4—228no—
559C2×C4—224no—
560C2×C4—224no—
561C2×C4—224no—
562C2×C4—448no—
563C2×C4C22×C22⋊D1114yes—
564C22—24no—
565C22—28no—
566C22—22no—
567C22—22no—
568C22—24no—
569C22—24no—
570C22—28no—
571C22—24no—
572C22—416no—
573C22—44no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—42no—
578C22—44no—
579C22—48no—
580C22—88no—
581C22—88no—
582C22—228no—
583C22—2216no—
584C22—4432no—
585C22—4464no—
586C22—444no—
587C22—444no—
588C22—448no—
589C22#1062333514yes—
590C22C2×#6703712yes—
591C22D11×H(5,𝔽2)14yes—
592C22C23×C22⋊D1111yescharacteristic
593C4—24no—
594C4—42no—
595C4—44no—
596C4—444no—
597C4—448no—
598C2—24no—
599C2—44no—
600C2—42no—
601C2—42no—
602C2—82no—
603C2—448no—
604C2C2×#1062333511yescharacteristic
605C2#1308224712yes—
606C2#1308276814yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#534C2
hypercenterC2×#534D11
hypocenterC11#36714
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. C22×#66990C2semidirect
2. #13076892C2semidirect
3. #13075175C2semidirect
4. #13074950C2semidirect
5. #13074944C2semidirect
6. #13074391C2semidirect
7. #13072002C2semidirect
8. #13071943C2semidirect
9. #13071926C2semidirect
10. #13071198C2semidirect
11. C2×C11×#534C2semidirect
12. C25×D11C22semidirect
14. C23×D4×C11C22semidirect
17. C2×C11×#123C22semidirect
18. C2×C11×#123C22semidirect
19. C2×C11×#121C22semidirect
21. C2×C11×#120C22semidirect
22. C22×C11×C22⋊C4C22semidirect
23. C2×#67006C22semidirect
24. C22×C22⋊Dic11C22semidirect
28. C2×#66990C22semidirect
29. C2×#66990C22semidirect
30. C2×#66982C22semidirect
31. C22×(C2×D11)⋊C4C22semidirect
32. C2×#66979C22semidirect
33. #10622860C22semidirect
34. #10622860C22semidirect
35. #10622836C22semidirect
36. #10622835C22semidirect
37. #10622834C22semidirect
38. #10622834C22semidirect
39. #10622833C22semidirect
40. #10622826C22semidirect
41. #10622826C22semidirect
42. #10622607C22semidirect
43. #10622603C22semidirect
44. #10622574C22semidirect
45. #10622572C22semidirect
46. #10622570C22semidirect
47. #10622568C22semidirect
48. #10622568C22semidirect
49. #10622565C22semidirect
50. #10622559C22semidirect
53. C25×C11C23semidirect
62. C22×D4×C11D4semidirect
67. C22×D4×C11C23semidirect
69. C23×C4×C11C23semidirect
70. C23×C4×C11C23semidirect
82. C2×C11×C4⋊C4C23semidirect
86. C2×C11×C22⋊C4C23semidirect
87. C2×C11×C22⋊C4C23semidirect
93. C2×C22⋊Dic11C23semidirect
94. C2×C22⋊Dic11C23semidirect
95. C2×C22⋊Dic11C23semidirect
107. C2×C4⋊Dic11C23semidirect
108. C2×Dic11⋊C4C23semidirect
109. C2×C4×Dic11C23semidirect
110. C11⋊#95C23semidirect
111. C11⋊#95C23semidirect
195. C2×#534D11semidirect
275. C23×D4C2×D11semidirect
278. C2×#123C2×D11semidirect
279. C2×#123C2×D11semidirect
280. C2×#121C2×D11semidirect
288. C2×#120C2×D11semidirect
292. C22×C22⋊C4C2×D11semidirect
352. C25C22×D11semidirect
361. C22×D4C22⋊D11semidirect
366. C22×D4C22×D11semidirect
369. C23×C4C22×D11semidirect
370. C23×C4C22×D11semidirect
385. C2×C4⋊C4C22×D11semidirect
401. C2×C22⋊C4C22×D11semidirect
402. C2×C22⋊C4C22×D11semidirect
497. C11#36714semidirect

Maximal subgroups

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

subgroupindex
C22×#669902
#130768922
#130751752
#130749502
#130749442
#130743912
#130720022
#130719432
#130719262
#130711982
C2×C11×#5342
#3671411