Finite Group Databasebeta

← #14960700

Subgroups — #14960700

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
1C2×#10623335C211yesmaximal, characteristic, complemented
2#13076893C212yesmaximal, complemented
3#13075177C214yesmaximal, complemented
4#13074950C214yesmaximal, complemented
5#13074941C218yesmaximal, complemented
6#13074389C212yesmaximal, complemented
7#13072001C214yesmaximal, complemented
8#13071939C212yesmaximal, complemented
9#13071926C212yesmaximal, complemented
10#13071198C211yesmaximal, characteristic, complemented
11C22×C11×#120C211yesmaximal, characteristic, complemented
12C26×C11C2211yescharacteristic, complemented
13C23×D4×C11C2212yes—
14C23×D4×C11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic, complemented
16C2×C11×#120—28no—
17C2×C11×#120C2214yes—
18C2×C11×#120C2214yescomplemented
19C22×C11×C22⋊C4C2212yescomplemented
20C22×C11×C22⋊C4C2211yescharacteristic, complemented
21C2×#67006C2212yes—
22C2×#67006C2214yes—
23C2×#67006C2218yescomplemented
24C22×C22⋊Dic11C2211yescharacteristic, complemented
25#10623335—28no—
26C2×#66992C2214yescomplemented
27C2×#66990C2212yescomplemented
28C2×#66990C2214yescomplemented
29C2×#66988C2212yescomplemented
30C2×#66988C2214yescomplemented
31C2×#66982C2212yescomplemented
32C2×#66979C2212yescomplemented
33#10622860C2214yescomplemented
34#10622860C2212yescomplemented
35#10622860C2218yescomplemented
36#10622860C2212yescomplemented
37#10622836C2218yescomplemented
38#10622835C2218yescomplemented
39#10622834C2214yescomplemented
40#10622834C2214yescomplemented
41#10622833C2214yescomplemented
42#10622833C2214yescomplemented
43#10622826C2214yescomplemented
44#10622823C2214yescomplemented
45#10622574C2218yescomplemented
46#10622572C2218yescomplemented
47#10622570C2218yescomplemented
48#10622565C2218yescomplemented
49#10622561C2218yescomplemented
50#10622558C2218yescomplemented
51C25×C11—24no—
52C25×C11—48no—
53C25×C11—44no—
54C25×C11C2312yes—
55C25×C11C2314yes—
56C25×C11C2311yescharacteristic
57C25×C11C2311yescharacteristic
58C24×D11C2311yescharacteristic, complemented
59C22×D4×C11—28no—
60C22×D4×C11—44no—
61C22×D4×C11—48no—
62C22×D4×C11D418yescomplemented
63C22×D4×C11C2314yes—
64C22×D4×C11C2314yes—
65C22×D4×C11C2312yes—
66C22×D4×C11C2312yes—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2312yes—
69C22×C22⋊D11—24no—
70C22×C22⋊D11—44no—
71C22×C22⋊D11C2312yes—
72C22×C22⋊D11C2314yes—
73C22×C22⋊D11C2318yes—
74C22×C22⋊D11C2312yescomplemented
75C23×Dic11C2312yescomplemented
76C23×Dic11C2311yescharacteristic, complemented
77C11×#120—216no—
78C11×#120—216no—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—28no—
81C2×C11×C22⋊C4C2318yes—
82C2×C11×C22⋊C4C2314yes—
83#67006—28no—
84#67006—48no—
85#67006—416no—
86C2×C22⋊Dic11—24no—
87C2×C22⋊Dic11C2314yes—
88C2×C22⋊Dic11C2312yes—
89C2×C22⋊Dic11C2318yes—
90C2×C22⋊Dic11C2314yes—
91C2×C22⋊Dic11C2318yes—
92C2×C22⋊Dic11C2318yes—
93C2×C22⋊Dic11C2318yes—
94C2×C22⋊Dic11C2312yescomplemented
95C2×C22⋊Dic11C2314yescomplemented
96C2×C22⋊Dic11C2314yescomplemented
97#66992—216no—
98#66990—28no—
99#66990—48no—
100#66988—28no—
101#66988—48no—
102#66982—28no—
103C2×(C2×D11)⋊C4C2314yescomplemented
104C2×(C2×D11)⋊C4C2318yescomplemented
105#66979—44no—
106C2×C4⋊Dic11C2314yescomplemented
107C2×Dic11⋊C4C2314yescomplemented
108C2×Dic11⋊C4C2318yescomplemented
109C2×C4×Dic11C2314yescomplemented
110C11⋊#95C2318yescomplemented
111C11⋊#95C2318yescomplemented
112#36714—111nomaximal, Sylow
113C24×C11—24no—
114C24×C11—28no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11—28no—
118C24×C11—216no—
119C24×C11—28no—
120C24×C11—44no—
121C24×C11—44no—
122C24×C11—48no—
123C24×C11—44no—
124C24×C11—44no—
125C24×C11—44no—
126C24×C11—432no—
127C24×C11—416no—
128C24×C11—464no—
129C24×C11C2×D414yes—
130C24×C11C2×D414yes—
131C24×C11C2412yes—
132C24×C11C2411yescharacteristic
133C24×C11C2411yescharacteristic
134C24×C11C2414yes—
135C24×C11C2411yescharacteristic
136C23×D11—22no—
137C23×D11—42no—
138C23×D11—44no—
139C23×D11C2412yes—
140C2×D4×C11—28no—
141C2×D4×C11—28no—
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—44no—
151C2×D4×C11—432no—
152C2×D4×C11C2×D418yes—
153C2×D4×C11C2×D418yes—
154C22×C4×C11—24no—
155C22×C4×C11—24no—
156C22×C4×C11—44no—
157C22×C4×C11C2×D414yes—
158C22×C4×C11C2414yes—
159C22×C4×C11C2412yes—
160C2×C22⋊D11—24no—
161C2×C22⋊D11—24no—
162C2×C22⋊D11—28no—
163C2×C22⋊D11—28no—
164C2×C22⋊D11—216no—
165C2×C22⋊D11—44no—
166C2×C22⋊D11—48no—
167C2×C22⋊D11—48no—
168C2×C22⋊D11—48no—
169C2×C22⋊D11—416no—
170C22×Dic11—22no—
171C22×Dic11—24no—
172C22×Dic11—42no—
173C22×Dic11—44no—
174C22×Dic11C2412yes—
175C22×Dic11C2418yes—
176C22×Dic11C2414yes—
177C11×C22⋊C4—28no—
178C11×C22⋊C4—216no—
179C22⋊Dic11—24no—
180C22⋊Dic11—24no—
181C22⋊Dic11—28no—
182C22⋊Dic11—28no—
183C22⋊Dic11—216no—
184C22⋊Dic11—44no—
185C22⋊Dic11—44no—
186C22⋊Dic11—48no—
187C22⋊Dic11—48no—
188C22⋊Dic11—48no—
189(C2×D11)⋊C4—28no—
190(C2×D11)⋊C4—48no—
191C4⋊Dic11—44no—
192Dic11⋊C4—28no—
193Dic11⋊C4—48no—
194C4×Dic11—44no—
195C2×#534—111no—
196C22×#120D1111yescharacteristic, complemented
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—216no—
208C23×C11—28no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—28no—
212C23×C11—28no—
213C23×C11—28no—
214C23×C11—24no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—24no—
220C23×C11—28no—
221C23×C11—48no—
222C23×C11—48no—
223C23×C11—432no—
224C23×C11—432no—
225C23×C11—416no—
226C23×C11—48no—
227C23×C11—416no—
228C23×C11—416no—
229C23×C11—432no—
230C23×C11—4128no—
231C23×C11—416no—
232C23×C11—48no—
233C23×C11—88no—
234C23×C11C22×D414yes—
235C23×C11C22×D412yes—
236C23×C11C22×D412yes—
237C23×C11C22×D412yes—
238C23×C11H(5,𝔽2)18yes—
239C23×C11H(5,𝔽2)14yes—
240C23×C11C2511yescharacteristic
241C22×D11—22no—
242C22×D11—28no—
243C22×D11—24no—
244C22×D11—44no—
245C22×D11—84no—
246C22×D11—88no—
247D4×C11—48no—
248D4×C11—48no—
249D4×C11—416no—
250D4×C11—416no—
251C2×C4×C11—28no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—48no—
258C2×C4×C11C22×D414yes—
259C22⋊D11—48no—
260C22⋊D11—48no—
261C22⋊D11—88no—
262C22⋊D11—816no—
263C2×Dic11—22no—
264C2×Dic11—24no—
265C2×Dic11—28no—
266C2×Dic11—28no—
267C2×Dic11—28no—
268C2×Dic11—28no—
269C2×Dic11—24no—
270C2×Dic11—44no—
271C2×Dic11—84no—
272C26C2×D1111yescharacteristic, complemented
273C23×D4—111no—
274C23×D4C2×D1112yes—
275C23×D4C2×D1111yescharacteristic
276#534—228no—
277C2×#123—112no—
278C2×#123—112no—
279C2×#123—114no—
280C2×#121—114no—
281C2×#120—28no—
282C2×#120—112no—
283C2×#120—112no—
284C2×#120—114no—
285C2×#120—118no—
286C2×#120—114no—
287C2×#120C2×D1114yes—
288C2×#120C2×D1114yescomplemented
289C2×#117—112no—
290C22×C22⋊C4—111no—
291C22×C22⋊C4C2×D1111yescharacteristic, complemented
292C22×C22⋊C4C2×D1112yescomplemented
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—24no—
315C22×C11—22no—
316C22×C11—24no—
317C22×C11—28no—
318C22×C11—24no—
319C22×C11—28no—
320C22×C11—216no—
321C22×C11—432no—
322C22×C11—416no—
323C22×C11—464no—
324C22×C11—44no—
325C22×C11—44no—
326C22×C11—44no—
327C22×C11—44no—
328C22×C11—48no—
329C22×C11—44no—
330C22×C11—44no—
331C22×C11—88no—
332C22×C11#53414yes—
333C22×C11C23×D411yescharacteristic
334C22×C11C2×H(5,𝔽2)12yes—
335C22×C11C2×H(5,𝔽2)14yes—
336C2×D11—42no—
337C2×D11—44no—
338C2×D11—48no—
339C2×D11—88no—
340C4×C11—24no—
341C4×C11—44no—
342Dic11—42no—
343Dic11—44no—
344Dic11—48no—
345C25—24no—
346C25—48no—
347C25—44no—
348C25—111no—
349C25C22×D1112yes—
350C25C22×D1114yes—
351C25C22×D1111yescharacteristic
352C25C22×D1111yescharacteristic
353C22×D4—28no—
354C22×D4—44no—
355C22×D4—48no—
356C22×D4—112no—
357C22×D4—114no—
358C22×D4—118no—
359C22×D4—112no—
360C22×D4—224no—
361C22×D4—444no—
362C22×D4C22⋊D1118yescomplemented
363C22×D4C22×D1114yes—
364C22×D4C22×D1114yes—
365C22×D4C22×D1112yes—
366C22×D4C22×D1112yes—
367C23×C4—112no—
368C23×C4—111no—
369C23×C4C22×D1111yescharacteristic
370C23×C4C22×D1112yes—
371#123—228no—
372#123—228no—
373#123—448no—
374#121—2216no—
375#120—216no—
376#120—216no—
377#120—228no—
378#120—228no—
379#120—448no—
380#120—4416no—
381#120—448no—
382#117—444no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—114no—
385C2×C4⋊C4—118no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—112no—
389C2×C22⋊C4—112no—
390C2×C22⋊C4—114no—
391C2×C22⋊C4—114no—
392C2×C22⋊C4—118no—
393C2×C22⋊C4—114no—
394C2×C22⋊C4—118no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—114no—
398C2×C22⋊C4—114no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4C22×D1118yes—
402C2×C22⋊C4C22×D1114yes—
403C2×C42—114no—
404#95—118no—
405#95—118no—
406C2×C11—24no—
407C2×C11—42no—
408C2×C11—44no—
409C2×C11—48no—
410C2×C11—42no—
411C2×C11C2×#53411yescharacteristic
412C2×C11#348412yes—
413C2×C11#353214yes—
414D11—82no—
415C24—28no—
416C24—24no—
417C24—24no—
418C24—24no—
419C24—216no—
420C24—28no—
421C24—28no—
422C24—44no—
423C24—44no—
424C24—48no—
425C24—44no—
426C24—44no—
427C24—44no—
428C24—432no—
429C24—416no—
430C24—464no—
431C24—112no—
432C24—222no—
433C24—442no—
434C24—444no—
435C24C2×C22⋊D1114yes—
436C24C2×C22⋊D1114yes—
437C24C23×D1114yes—
438C24C23×D1112yes—
439C24C23×D1111yescharacteristic
440C24C23×D1111yescharacteristic
441C24C23×D1111yescharacteristic
442C2×D4—28no—
443C2×D4—28no—
444C2×D4—28no—
445C2×D4—28no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—416no—
453C2×D4—432no—
454C2×D4—228no—
455C2×D4—224no—
456C2×D4—224no—
457C2×D4—2216no—
458C2×D4—228no—
459C2×D4—444no—
460C2×D4—448no—
461C2×D4—448no—
462C2×D4—448no—
463C2×D4—4416no—
464C2×D4C2×C22⋊D1118yes—
465C2×D4C2×C22⋊D1118yes—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—44no—
469C22×C4—112no—
470C22×C4—118no—
471C22×C4—114no—
472C22×C4—222no—
473C22×C4—224no—
474C22×C4—442no—
475C22×C4—444no—
476C22×C4C2×C22⋊D1114yes—
477C22×C4C23×D1114yes—
478C22×C4C23×D1112yes—
479C4⋊C4—228no—
480C4⋊C4—444no—
481C4⋊C4—448no—
482C22⋊C4—28no—
483C22⋊C4—216no—
484C22⋊C4—228no—
485C22⋊C4—2216no—
486C22⋊C4—224no—
487C22⋊C4—224no—
488C22⋊C4—228no—
489C22⋊C4—228no—
490C22⋊C4—448no—
491C22⋊C4—448no—
492C22⋊C4—448no—
493C22⋊C4—448no—
494C22⋊C4—444no—
495C22⋊C4—444no—
496C42—444no—
497C11#3671411yescharacteristic, complemented, Sylow
498C23—24no—
499C23—216no—
500C23—28no—
501C23—24no—
502C23—24no—
503C23—28no—
504C23—28no—
505C23—28no—
506C23—22no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—24no—
511C23—24no—
512C23—28no—
513C23—48no—
514C23—48no—
515C23—432no—
516C23—432no—
517C23—416no—
518C23—48no—
519C23—416no—
520C23—416no—
521C23—432no—
522C23—4128no—
523C23—416no—
524C23—48no—
525C23—88no—
526C23—228no—
527C23—224no—
528C23—222no—
529C23—444no—
530C23—884no—
531C23—888no—
532C23#6703718yes—
533C23#6703714yes—
534C23C22×C22⋊D1114yes—
535C23C22×C22⋊D1112yes—
536C23C22×C22⋊D1112yes—
537C23C22×C22⋊D1112yes—
538C23C24×D1111yescharacteristic
539D4—48no—
540D4—48no—
541D4—416no—
542D4—416no—
543D4—448no—
544D4—448no—
545D4—888no—
546D4—8816no—
547C2×C4—28no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—48no—
554C2×C4—228no—
555C2×C4—228no—
556C2×C4—228no—
557C2×C4—228no—
558C2×C4—224no—
559C2×C4—224no—
560C2×C4—222no—
561C2×C4—444no—
562C2×C4—884no—
563C2×C4C22×C22⋊D1114yes—
564C22—24no—
565C22—28no—
566C22—22no—
567C22—22no—
568C22—24no—
569C22—24no—
570C22—28no—
571C22—24no—
572C22—28no—
573C22—216no—
574C22—432no—
575C22—416no—
576C22—464no—
577C22—44no—
578C22—44no—
579C22—44no—
580C22—48no—
581C22—44no—
582C22—44no—
583C22—44no—
584C22—88no—
585C22—442no—
586C22—444no—
587C22—448no—
588C22—888no—
589C22#1062333514yes—
590C22C2×#6703712yes—
591C22C2×#6703714yes—
592C22C23×C22⋊D1111yescharacteristic
593C4—24no—
594C4—44no—
595C4—442no—
596C4—444no—
597C4—448no—
598C2—24no—
599C2—44no—
600C2—48no—
601C2—42no—
602C2—42no—
603C2—882no—
604C2C2×#1062333511yescharacteristic
605C2#1308225112yes—
606C2#1308277114yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C11×#120C2
hypercenterC22×#120D11
hypocenterC11#36714
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#120

Complements

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

NH ≅ G/Ntype
1. C2×#10623335C2semidirect
2. #13076893C2semidirect
3. #13075177C2semidirect
4. #13074950C2semidirect
5. #13074941C2semidirect
6. #13074389C2semidirect
7. #13072001C2semidirect
8. #13071939C2semidirect
9. #13071926C2semidirect
10. #13071198C2semidirect
11. C22×C11×#120C2semidirect
12. C26×C11C22semidirect
15. C23×C22⋊D11C22semidirect
18. C2×C11×#120C22semidirect
19. C22×C11×C22⋊C4C22semidirect
20. C22×C11×C22⋊C4C22semidirect
23. C2×#67006C22semidirect
24. C22×C22⋊Dic11C22semidirect
26. C2×#66992C22semidirect
27. C2×#66990C22semidirect
28. C2×#66990C22semidirect
29. C2×#66988C22semidirect
30. C2×#66988C22semidirect
31. C2×#66982C22semidirect
32. C2×#66979C22semidirect
33. #10622860C22semidirect
34. #10622860C22semidirect
35. #10622860C22semidirect
36. #10622860C22semidirect
37. #10622836C22semidirect
38. #10622835C22semidirect
39. #10622834C22semidirect
40. #10622834C22semidirect
41. #10622833C22semidirect
42. #10622833C22semidirect
43. #10622826C22semidirect
44. #10622823C22semidirect
45. #10622574C22semidirect
46. #10622572C22semidirect
47. #10622570C22semidirect
48. #10622565C22semidirect
49. #10622561C22semidirect
50. #10622558C22semidirect
58. C24×D11C23semidirect
62. C22×D4×C11D4semidirect
74. C22×C22⋊D11C23semidirect
75. C23×Dic11C23semidirect
76. C23×Dic11C23semidirect
94. C2×C22⋊Dic11C23semidirect
95. C2×C22⋊Dic11C23semidirect
96. C2×C22⋊Dic11C23semidirect
103. C2×(C2×D11)⋊C4C23semidirect
104. C2×(C2×D11)⋊C4C23semidirect
106. C2×C4⋊Dic11C23semidirect
107. C2×Dic11⋊C4C23semidirect
108. C2×Dic11⋊C4C23semidirect
109. C2×C4×Dic11C23semidirect
110. C11⋊#95C23semidirect
111. C11⋊#95C23semidirect
196. C22×#120D11semidirect
272. C26C2×D11semidirect
288. C2×#120C2×D11semidirect
291. C22×C22⋊C4C2×D11semidirect
292. C22×C22⋊C4C2×D11semidirect
362. C22×D4C22⋊D11semidirect
497. C11#36714semidirect

Maximal subgroups

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

subgroupindex
C2×#106233352
#130768932
#130751772
#130749502
#130749412
#130743892
#130720012
#130719392
#130719262
#130711982
C22×C11×#1202
#3671411