Finite Group Databasebeta

← #14960693

Subgroups — #14960693

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
2C22×#66990C211yesmaximal, characteristic, complemented
3#13076894C212yesmaximal, complemented
4#13075178C214yesmaximal, complemented
5#13074951C214yesmaximal, complemented
6#13074936C218yesmaximal, complemented
7#13074392C212yesmaximal, complemented
8#13071995C214yesmaximal, complemented
9#13071944C212yesmaximal, complemented
10#13071929C212yesmaximal, complemented
11C11×#2309C211yesmaximal, characteristic, complemented
12C25×D11C2211yescharacteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C23×C22⋊D11C2211yescharacteristic, complemented
16C2×C11×#117C2212yescomplemented
17C2×#67006C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic, complemented
19C22×C22⋊Dic11C2211yescharacteristic, complemented
20#10623335—28no—
21C2×#66992C2214yescomplemented
22C2×#66990—28no—
23C2×#66990C2214yes—
24C2×#66990C2214yescomplemented
25C2×#66990C2212yescomplemented
26C2×#66988C2212yescomplemented
27C2×#66982C2212yescomplemented
28C22×(C2×D11)⋊C4C2212yescomplemented
29C2×#66939C2214yescomplemented
30C2×#66935C2214yes—
31C2×#66935C2218yescomplemented
32C2×#66935C2214yescomplemented
33C11×#390C2214yescomplemented
34C11×#390C2214yescomplemented
35C11×#379C2212yescomplemented
36C11×#379C2212yescomplemented
37#10622607C2218yescomplemented
38#10622604C2218yescomplemented
39#10622574C2218yescomplemented
40#10622574C2218yescomplemented
41#10622573C2218yescomplemented
42#10622571C2214yescomplemented
43#10622571C2214yescomplemented
44#10622571C2214yescomplemented
45#10622568C2214yescomplemented
46#10622568C2218yescomplemented
47#10622566C2218yescomplemented
48#10622563C2214yescomplemented
49#10622553C2218yescomplemented
50#10622552C2218yescomplemented
51C25×C11C2311yescharacteristic
52C25×C11C2311yescharacteristic
53C24×D11—24no—
54C24×D11—48no—
55C24×D11—44no—
56C24×D11C2312yes—
57C24×D11C2314yes—
58C24×D11C2311yescharacteristic, complemented
59C22×D4×C11—44no—
60C22×D4×C11D418yescomplemented
61C22×D4×C11C2312yes—
62C22×D4×C11C2312yes—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—28no—
65C22×C22⋊D11—24no—
66C22×C22⋊D11—48no—
67C22×C22⋊D11—44no—
68C22×C22⋊D11C2312yes—
69C22×C22⋊D11C2314yes—
70C22×C22⋊D11C2314yes—
71C22×C22⋊D11C2314yes—
72C22×C22⋊D11C2312yescomplemented
73C23×Dic11C2312yes—
74C23×Dic11C2312yescomplemented
75C23×Dic11C2311yescharacteristic, complemented
76C22×D44C2318yes—
77C11×#117—44no—
78C2×C11×C4⋊C4C2314yescomplemented
79C2×C11×C22⋊C4C2314yes—
80C2×C11×C22⋊C4C2318yes—
81C2×C11×C22⋊C4C2314yescomplemented
82C2×C11×C22⋊C4C2314yescomplemented
83C2×C42×C11C2314yescomplemented
84#67006—28no—
85C2×C22⋊Dic11—24no—
86C2×C22⋊Dic11—24no—
87C2×C22⋊Dic11C2312yes—
88C2×C22⋊Dic11C2314yes—
89C2×C22⋊Dic11C2314yes—
90C2×C22⋊Dic11C2312yescomplemented
91#66992—216no—
92#66990—216no—
93#66990—216no—
94#66990—28no—
95#66988—28no—
96#66982—28no—
97C2×(C2×D11)⋊C4—28no—
98C2×(C2×D11)⋊C4C2318yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×(C2×D11)⋊C4C2318yes—
102C2×(C2×D11)⋊C4C2314yescomplemented
103C2×(C2×D11)⋊C4C2318yescomplemented
104C2×C4⋊Dic11C2318yescomplemented
105C2×Dic11⋊C4C2314yescomplemented
106#66939—48no—
107#66935—416no—
108#66935—48no—
109#66935—48no—
110C11⋊#95C2318yescomplemented
111C11⋊#95C2318yescomplemented
112#36714—111nomaximal, Sylow
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—44no—
116C24×C11—44no—
117C24×C11C2×D414yes—
118C24×C11C2×D414yes—
119C24×C11C2412yes—
120C24×C11C2411yescharacteristic
121C24×C11C2411yescharacteristic
122C24×C11C2411yescharacteristic
123C23×D11—24no—
124C23×D11—28no—
125C23×D11—28no—
126C23×D11—28no—
127C23×D11—22no—
128C23×D11—216no—
129C23×D11—44no—
130C23×D11—44no—
131C23×D11—44no—
132C23×D11—48no—
133C23×D11—42no—
134C23×D11—44no—
135C23×D11—432no—
136C23×D11—416no—
137C23×D11—464no—
138C23×D11C2412yes—
139C23×D11C2414yes—
140C2×D4×C11—416no—
141C2×D4×C11—42no—
142C2×D4×C11—42no—
143C2×D4×C11—42no—
144C2×D4×C11—42no—
145C2×D4×C11C2×D418yes—
146C2×D4×C11C2×D418yes—
147C22×C4×C11—24no—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2418yes—
150C22×C4×C11C2412yes—
151C2×C22⋊D11—24no—
152C2×C22⋊D11—28no—
153C2×C22⋊D11—28no—
154C2×C22⋊D11—24no—
155C2×C22⋊D11—28no—
156C2×C22⋊D11—28no—
157C2×C22⋊D11—28no—
158C2×C22⋊D11—28no—
159C2×C22⋊D11—44no—
160C2×C22⋊D11—44no—
161C2×C22⋊D11—44no—
162C2×C22⋊D11—48no—
163C2×C22⋊D11—432no—
164C2×C22⋊D11—416no—
165C22×Dic11—24no—
166C22×Dic11—22no—
167C22×Dic11—24no—
168C22×Dic11—44no—
169C22×Dic11—42no—
170C22×Dic11—44no—
171C22×Dic11C2412yes—
172C22×Dic11C2414yes—
173C22×Dic11C2414yes—
174C2×D44—216no—
175C2×D44—48no—
176C2×D44—48no—
177C11×C4⋊C4—44no—
178C11×C22⋊C4—28no—
179C11×C22⋊C4—48no—
180C11×C22⋊C4—44no—
181C11×C22⋊C4—44no—
182C42×C11—44no—
183C22⋊Dic11—24no—
184C22⋊Dic11—24no—
185C22⋊Dic11—28no—
186C22⋊Dic11—28no—
187(C2×D11)⋊C4—216no—
188(C2×D11)⋊C4—216no—
189(C2×D11)⋊C4—28no—
190(C2×D11)⋊C4—48no—
191(C2×D11)⋊C4—48no—
192(C2×D11)⋊C4—48no—
193C4⋊Dic11—48no—
194Dic11⋊C4—28no—
195C2×#534—111no—
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#2309D1111yescharacteristic, complemented
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—48no—
217C23×C11—48no—
218C23×C11—416no—
219C23×C11—88no—
220C23×C11C22×D414yes—
221C23×C11C22×D412yes—
222C23×C11C22×D412yes—
223C23×C11C22×D412yes—
224C23×C11H(5,𝔽2)14yes—
225C23×C11C2511yescharacteristic
226C22×D11—216no—
227C22×D11—24no—
228C22×D11—28no—
229C22×D11—28no—
230C22×D11—24no—
231C22×D11—22no—
232C22×D11—28no—
233C22×D11—24no—
234C22×D11—416no—
235C22×D11—432no—
236C22×D11—432no—
237C22×D11—432no—
238C22×D11—48no—
239C22×D11—416no—
240C22×D11—4128no—
241C22×D11—416no—
242C22×D11—48no—
243C22×D11—44no—
244C22×D11—84no—
245C22×D11—88no—
246C22×D11H(5,𝔽2)18yes—
247D4×C11—48no—
248D4×C11—48no—
249C2×C4×C11—28no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—28no—
253C2×C4×C11—28no—
254C2×C4×C11—28no—
255C2×C4×C11C22×D414yes—
256C22⋊D11—416no—
257C22⋊D11—416no—
258C22⋊D11—48no—
259C22⋊D11—48no—
260C22⋊D11—88no—
261C2×Dic11—22no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—28no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—44no—
269C2×Dic11—48no—
270C2×Dic11—84no—
271D44—816no—
272C26—111no—
273C23×D4—111no—
274C23×D4—112no—
275C23×D4C2×D1111yescharacteristic
276#534—228no—
277C2×#123—112no—
278C2×#123—112no—
279C2×#123—114no—
280C2×#121—114no—
281C2×#120—112no—
282C2×#120—114no—
283C2×#120—114no—
284C2×#120—112no—
285C2×#120—114no—
286C2×#120—118no—
287C2×#120—114no—
288C2×#120—228no—
289C2×#117C2×D1112yescomplemented
290C22×C22⋊C4—111no—
291C22×C22⋊C4—111no—
292C22×C22⋊C4—112no—
293#397—118no—
294#396—118no—
295#394—118no—
296#394—118no—
297#394—118no—
298#392—118no—
299#390—118no—
300#390C2×D1114yescomplemented
301#390C2×D1114yescomplemented
302#388—118no—
303#386—114no—
304#386—114no—
305#386—114no—
306#385—114no—
307#379—114no—
308#379—118no—
309#379C2×D1112yescomplemented
310#379C2×D1112yescomplemented
311C22×C11—24no—
312C22×C11—28no—
313C22×C11—24no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—28no—
317C22×C11—24no—
318C22×C11—24no—
319C22×C11—416no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11—88no—
325C22×C11#53414yes—
326C22×C11C23×D411yescharacteristic
327C22×C11C2×H(5,𝔽2)12yes—
328C22×C11C2×H(5,𝔽2)14yes—
329C2×D11—28no—
330C2×D11—216no—
331C2×D11—432no—
332C2×D11—464no—
333C2×D11—44no—
334C2×D11—44no—
335C2×D11—48no—
336C2×D11—42no—
337C2×D11—44no—
338C2×D11—48no—
339C2×D11—88no—
340C4×C11—24no—
341C4×C11—48no—
342Dic11—42no—
343Dic11—44no—
344Dic11—44no—
345C25—112no—
346C25—114no—
347C25—111no—
348C25—224no—
349C25—444no—
350C25—448no—
351C25C22×D1111yescharacteristic
352C25C22×D1111yescharacteristic
353C22×D4—44no—
354C22×D4—112no—
355C22×D4—114no—
356C22×D4—114no—
357C22×D4—114no—
358C22×D4—112no—
359C22×D4—118no—
360C22×D4—228no—
361C22×D4—224no—
362C22×D4—444no—
363C22×D4—448no—
364C22×D4D4418yescomplemented
365C22×D4C22×D1112yes—
366C22×D4C22×D1112yes—
367C23×C4—112no—
368C23×C4—112no—
369C23×C4—111no—
370C23×C4C22×D1111yescharacteristic
371#123—228no—
372#123—228no—
373#123—448no—
374#121—2216no—
375#120—228no—
376#120—2216no—
377#120—2216no—
378#120—228no—
379#120—448no—
380#120—4416no—
381#120—448no—
382#117—44no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—118no—
385C2×C4⋊C4C22×D1114yescomplemented
386C2×C22⋊C4—114no—
387C2×C22⋊C4—112no—
388C2×C22⋊C4—112no—
389C2×C22⋊C4—114no—
390C2×C22⋊C4—118no—
391C2×C22⋊C4—114no—
392C2×C22⋊C4—118no—
393C2×C22⋊C4—118no—
394C2×C22⋊C4—118no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—224no—
397C2×C22⋊C4—224no—
398C2×C22⋊C4—228no—
399C2×C22⋊C4C22×D1114yes—
400C2×C22⋊C4C22×D1118yes—
401C2×C22⋊C4C22×D1114yescomplemented
402C2×C22⋊C4C22×D1114yescomplemented
403C2×C42C22×D1114yescomplemented
404#95—118no—
405#95—118no—
406C2×C11—24no—
407C2×C11—44no—
408C2×C11—42no—
409C2×C11—42no—
410C2×C11C2×#53411yescharacteristic
411C2×C11#348412yes—
412C2×C11#353214yes—
413D11—48no—
414D11—82no—
415C24—24no—
416C24—24no—
417C24—44no—
418C24—44no—
419C24—114no—
420C24—112no—
421C24—228no—
422C24—2216no—
423C24—224no—
424C24—228no—
425C24—228no—
426C24—222no—
427C24—444no—
428C24—444no—
429C24—444no—
430C24—448no—
431C24—442no—
432C24—444no—
433C24—4416no—
434C24—4432no—
435C24—4464no—
436C24C2×D4414yes—
437C24C2×D4414yes—
438C24C23×D1112yes—
439C24C23×D1111yescharacteristic
440C24C23×D1111yescharacteristic
441C24C23×D1111yescharacteristic
442C2×D4—42no—
443C2×D4—42no—
444C2×D4—42no—
445C2×D4—42no—
446C2×D4—416no—
447C2×D4—2216no—
448C2×D4—228no—
449C2×D4—228no—
450C2×D4—228no—
451C2×D4—228no—
452C2×D4—224no—
453C2×D4—224no—
454C2×D4—228no—
455C2×D4—228no—
456C2×D4—448no—
457C2×D4—448no—
458C2×D4—444no—
459C2×D4—444no—
460C2×D4—444no—
461C2×D4—448no—
462C2×D4—4416no—
463C2×D4—4432no—
464C2×D4C2×D4418yes—
465C2×D4C2×D4418yes—
466C22×C4—24no—
467C22×C4—114no—
468C22×C4—112no—
469C22×C4—114no—
470C22×C4—224no—
471C22×C4—222no—
472C22×C4—224no—
473C22×C4—442no—
474C22×C4—444no—
475C22×C4—444no—
476C22×C4C2×D4414yes—
477C22×C4C23×D1118yes—
478C22×C4C23×D1112yes—
479C4⋊C4—44no—
480C4⋊C4—228no—
481C4⋊C4—448no—
482C22⋊C4—28no—
483C22⋊C4—48no—
484C22⋊C4—44no—
485C22⋊C4—44no—
486C22⋊C4—2216no—
487C22⋊C4—228no—
488C22⋊C4—224no—
489C22⋊C4—224no—
490C22⋊C4—228no—
491C22⋊C4—2216no—
492C22⋊C4—228no—
493C22⋊C4—448no—
494C22⋊C4—448no—
495C22⋊C4—448no—
496C42—44no—
497C11#3671411yescharacteristic, complemented, Sylow
498C23—24no—
499C23—28no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—24no—
505C23—24no—
506C23—28no—
507C23—28no—
508C23—48no—
509C23—48no—
510C23—416no—
511C23—88no—
512C23—118no—
513C23—2216no—
514C23—224no—
515C23—228no—
516C23—228no—
517C23—224no—
518C23—222no—
519C23—224no—
520C23—228no—
521C23—4432no—
522C23—4432no—
523C23—448no—
524C23—4416no—
525C23—444no—
526C23—4416no—
527C23—4432no—
528C23—44128no—
529C23—4416no—
530C23—448no—
531C23—884no—
532C23—888no—
533C23C22×D4414yes—
534C23C22×D4412yes—
535C23C22×D4412yes—
536C23C22×D4412yes—
537C23#6703714yes—
538C23C24×D1111yescharacteristic
539D4—48no—
540D4—48no—
541D4—4416no—
542D4—4416no—
543D4—448no—
544D4—448no—
545D4—8816no—
546D4—888no—
547C2×C4—28no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—28no—
551C2×C4—28no—
552C2×C4—28no—
553C2×C4—224no—
554C2×C4—224no—
555C2×C4—222no—
556C2×C4—224no—
557C2×C4—228no—
558C2×C4—224no—
559C2×C4—224no—
560C2×C4—444no—
561C2×C4—448no—
562C2×C4—884no—
563C2×C4C22×D4414yes—
564C22—24no—
565C22—28no—
566C22—22no—
567C22—22no—
568C22—24no—
569C22—24no—
570C22—24no—
571C22—28no—
572C22—416no—
573C22—44no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—88no—
578C22—228no—
579C22—2216no—
580C22—4432no—
581C22—4464no—
582C22—444no—
583C22—444no—
584C22—448no—
585C22—442no—
586C22—444no—
587C22—448no—
588C22—888no—
589C22#1062302414yes—
590C22C23×D4411yescharacteristic
591C22C2×#6703712yes—
592C22D11×H(5,𝔽2)14yes—
593C4—24no—
594C4—48no—
595C4—442no—
596C4—444no—
597C4—444no—
598C2—24no—
599C2—44no—
600C2—42no—
601C2—42no—
602C2—448no—
603C2—882no—
604C2C2×#1062302411yescharacteristic
605C2#1308225212yes—
606C2#1308277014yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2309C2
hypercenter#2309D11
hypocenterC11#36714
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2309

Complements

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

NH ≅ G/Ntype
1. C2×#10623335C2semidirect
2. C22×#66990C2semidirect
3. #13076894C2semidirect
4. #13075178C2semidirect
5. #13074951C2semidirect
6. #13074936C2semidirect
7. #13074392C2semidirect
8. #13071995C2semidirect
9. #13071944C2semidirect
10. #13071929C2semidirect
11. C11×#2309C2semidirect
12. C25×D11C22semidirect
15. C23×C22⋊D11C22semidirect
16. C2×C11×#117C22semidirect
18. C22×C22⋊Dic11C22semidirect
19. C22×C22⋊Dic11C22semidirect
21. C2×#66992C22semidirect
24. C2×#66990C22semidirect
25. C2×#66990C22semidirect
26. C2×#66988C22semidirect
27. C2×#66982C22semidirect
28. C22×(C2×D11)⋊C4C22semidirect
29. C2×#66939C22semidirect
31. C2×#66935C22semidirect
32. C2×#66935C22semidirect
33. C11×#390C22semidirect
34. C11×#390C22semidirect
35. C11×#379C22semidirect
36. C11×#379C22semidirect
37. #10622607C22semidirect
38. #10622604C22semidirect
39. #10622574C22semidirect
40. #10622574C22semidirect
41. #10622573C22semidirect
42. #10622571C22semidirect
43. #10622571C22semidirect
44. #10622571C22semidirect
45. #10622568C22semidirect
46. #10622568C22semidirect
47. #10622566C22semidirect
48. #10622563C22semidirect
49. #10622553C22semidirect
50. #10622552C22semidirect
58. C24×D11C23semidirect
60. C22×D4×C11D4semidirect
72. C22×C22⋊D11C23semidirect
74. C23×Dic11C23semidirect
75. C23×Dic11C23semidirect
78. C2×C11×C4⋊C4C23semidirect
81. C2×C11×C22⋊C4C23semidirect
82. C2×C11×C22⋊C4C23semidirect
83. C2×C42×C11C23semidirect
90. C2×C22⋊Dic11C23semidirect
102. C2×(C2×D11)⋊C4C23semidirect
103. C2×(C2×D11)⋊C4C23semidirect
104. C2×C4⋊Dic11C23semidirect
105. C2×Dic11⋊C4C23semidirect
110. C11⋊#95C23semidirect
111. C11⋊#95C23semidirect
205. #2309D11semidirect
289. C2×#117C2×D11semidirect
300. #390C2×D11semidirect
301. #390C2×D11semidirect
309. #379C2×D11semidirect
310. #379C2×D11semidirect
364. C22×D4D44semidirect
385. C2×C4⋊C4C22×D11semidirect
401. C2×C22⋊C4C22×D11semidirect
402. C2×C22⋊C4C22×D11semidirect
403. C2×C42C22×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
C22×#669902
#130768942
#130751782
#130749512
#130749362
#130743922
#130719952
#130719442
#130719292
C11×#23092
#3671411