Finite Group Databasebeta

← #14926645

Subgroups — #14926645

Order 2816.

4298 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623136C214yesmaximal, complemented
2C2×D11×#121C212yesmaximal, complemented
3#13076959C214yesmaximal, complemented
4#13074720C212yesmaximal, complemented
5#13074718C211yesmaximal, characteristic, complemented
6#13073543C214yesmaximal, complemented
7#13073541C214yesmaximal, complemented
8#13073082C214yesmaximal, complemented
9#13072248C214yesmaximal, complemented
10C2×#10622279C211yesmaximal, characteristic, complemented
11C11×#2656C211yesmaximal, characteristic, complemented
12C22×D4×D11C2214yes—
13C22×D4×D11C2212yescomplemented
14C23×C4×D11C2211yescharacteristic
15C2×C11×#121C2212yescomplemented
16C2×C11×#121C2214yescomplemented
17C2×#66993C2214yescomplemented
18C2×#66992C2218yescomplemented
19C2×#66992C2214yescomplemented
20C2×#66991C2212yes—
21C2×#66990C2218yescomplemented
22C2×#66983C2212yescomplemented
23C2×#66983C2214yescomplemented
24C22×(C2×D11)⋊C4C2212yes—
25C22×C4×Dic11C2212yescomplemented
26#10623136—232no—
27D11×#121—216no—
28C2×#66948C2212yes—
29C2×#66947C2218yescomplemented
30C2×C4⋊C4×D11C2212yescomplemented
31C2×#66937C2214yes—
32C2×#66936C2218yescomplemented
33C2×#66935C2218yescomplemented
34C2×C22⋊C4×D11C2214yescomplemented
35C11×#399C2214yescomplemented
36C11×#392C2214yescomplemented
37C2×C11×#95C2211yescharacteristic, complemented
38#10622836C2214yescomplemented
39#10622834C2214yescomplemented
40C2×C11⋊#95C2211yescharacteristic, complemented
41#10622605C2214yescomplemented
42#10622601C2214yescomplemented
43#10622589C2214yescomplemented
44#10622573C2214yescomplemented
45#10622570C2218yescomplemented
46#10622570C2218yescomplemented
47#10622562C2214yescomplemented
48#10622290C2214yescomplemented
49#10622284C2214yescomplemented
50#10622279C2214yescomplemented
51#10622279C2214yescomplemented
52C24×D11C2314yes—
53C24×D11C2311yescharacteristic
54C22×D4×C11C2314yes—
55C22×D4×C11C2314yes—
56C22×D4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2312yes—
59C22×C22⋊D11C2314yes—
60C22×C22⋊D11C2314yes—
61C22×C22⋊D11C2314yes—
62C22×C22⋊D11C2318yes—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2312yes—
65C2×D4×D11—216no—
66C2×D4×D11—232no—
67C2×D4×D11—28no—
68C2×D4×D11—48no—
69C22×D44C2314yes—
70C22×D44C2314yes—
71C22×D44C2312yes—
72C22×C4×D11—44no—
73C22×C4×D11D418yescomplemented
74C22×C4×D11C2314yes—
75C22×C4×D11C2312yes—
76C22×C4×D11C2312yes—
77C11×#121—28no—
78C11×#121—216no—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C22⋊C4C2314yes—
82C2×C11×C22⋊C4C2318yes—
83C2×C22⋊Dic11C2314yes—
84C2×C22⋊Dic11C2318yes—
85#66993—48no—
86#66992—216no—
87#66992—232no—
88#66991—28no—
89#66990—232no—
90#66983—28no—
91#66983—216no—
92C2×(C2×D11)⋊C4D4116yescomplemented
93C2×(C2×D11)⋊C4C2314yes—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C2318yes—
98C2×C4⋊Dic11C2314yes—
99C2×C4⋊Dic11C2312yes—
100C2×Dic11⋊C4C2318yes—
101C2×Dic11⋊C4C2314yes—
102C2×C4×Dic11—44no—
103C2×C4×Dic11C2314yes—
104C2×C4×Dic11C2314yes—
105#66948—28no—
106#66947—232no—
107C4⋊C4×D11—28no—
108#66937—216no—
109#66936—232no—
110#66935—232no—
111C22⋊C4×D11—216no—
112C11×#95C2314yes—
113C11⋊#95C2314yes—
114#35001—111nomaximal, Sylow
115C24×C11C2414yes—
116C24×C11C2411yescharacteristic
117C23×D11—28no—
118C23×D11—216no—
119C23×D11—42no—
120C23×D11—41no—
121C23×D11—41no—
122C23×D11—48no—
123C23×D11—44no—
124C23×D11—44no—
125C23×D11C2×D418yes—
126C23×D11C2×D414yes—
127C23×D11C2414yes—
128C23×D11C2412yes—
129C2×D4×C11—28no—
130C2×D4×C11—216no—
131C2×D4×C11—24no—
132C2×D4×C11—28no—
133C2×D4×C11—44no—
134C2×D4×C11—44no—
135C2×D4×C11—44no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11C2×D414yes—
140C22×C4×C11C2×D418yescomplemented
141C22×C4×C11C2414yes—
142C22×C4×C11C2412yes—
143C22×C4×C11C2414yes—
144C2×C22⋊D11—28no—
145C2×C22⋊D11—216no—
146C2×C22⋊D11—216no—
147C2×C22⋊D11—28no—
148C2×C22⋊D11—216no—
149C2×C22⋊D11—216no—
150C2×C22⋊D11—28no—
151C2×C22⋊D11—48no—
152C2×C22⋊D11—48no—
153C22×Dic11—24no—
154C22×Dic11—42no—
155C22×Dic11—42no—
156C22×Dic11C2×D414yes—
157C22×Dic11C2×D418yescomplemented
158C22×Dic11C2414yes—
159C22×Dic11C2414yes—
160C22×Dic11C2411yescharacteristic
161C22×Dic11C2411yescharacteristic
162D4×D11—432no—
163D4×D11—464no—
164C2×D44—216no—
165C2×D44—28no—
166C2×D44—24no—
167C2×D44—28no—
168C2×D44—44no—
169C2×D44—44no—
170C2×D44—44no—
171C2×C4×D11—28no—
172C2×C4×D11—28no—
173C2×C4×D11—216no—
174C2×C4×D11—44no—
175C2×C4×D11—416no—
176C2×C4×D11C2×D418yes—
177C2×C4×D11C2×D418yes—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—28no—
180C11×C22⋊C4—28no—
181C11×C22⋊C4—216no—
182C22⋊Dic11—28no—
183C22⋊Dic11—216no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4—216no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4—216no—
188(C2×D11)⋊C4C2×D4132yescomplemented
189C4⋊Dic11—28no—
190C4⋊Dic11—24no—
191Dic11⋊C4—216no—
192Dic11⋊C4—28no—
193C4×Dic11—28no—
194C4×Dic11—44no—
195C2×#534—114no—
196C22×#121—112no—
197#2856—114no—
198#2656—111no—
199#2656—112no—
200#2656D1111yescharacteristic, complemented
201#2539—114no—
202#2539—114no—
203#2501—114no—
204#2433—114no—
205C2×C4×C22⋊C4—111no—
206C23×C11—22no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—24no—
210C23×C11—28no—
211C23×C11—28no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11C22×D412yes—
215C23×C11C22×D414yes—
216C23×C11C2511yescharacteristic
217C22×D11—24no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—24no—
221C22×D11—28no—
222C22×D11—28no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—44no—
226C22×D11—44no—
227C22×D11—48no—
228C22×D11—48no—
229C22×D11—416no—
230C22×D11—416no—
231C22×D11—416no—
232C22×D11—816no—
233C22×D11—816no—
234C22×D11#127116yescomplemented
235C22×D11C22×D418yes—
236C22×D11C22×D414yes—
237D4×C11—48no—
238D4×C11—416no—
239D4×C11—88no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—28no—
245C2×C4×C11—44no—
246C2×C4×C11—48no—
247C2×C4×C11C22×D418yes—
248C2×C4×C11C22×D414yes—
249C22⋊D11—416no—
250C22⋊D11—416no—
251C22⋊D11—416no—
252C22⋊D11—816no—
253C2×Dic11—24no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—28no—
257C2×Dic11—24no—
258C2×Dic11—28no—
259C2×Dic11—48no—
260C2×Dic11C22×D418yes—
261C2×Dic11C22×D412yes—
262C2×Dic11C22×D412yes—
263C2×Dic11H(5,𝔽2)14yes—
264D44—48no—
265D44—416no—
266D44—88no—
267C4×D11—216no—
268C4×D11—48no—
269C4×D11—416no—
270C23×D4—114no—
271C23×D4—112no—
272C24×C4—111no—
273#534—2232no—
274C2×#127—114no—
275C2×#123—118no—
276C2×#123—118no—
277C2×#121—114no—
278C2×#121—118no—
279C2×#121—112no—
280C2×#121—114no—
281C2×#121—112no—
282C2×#121—112no—
283C2×#121—114no—
284C2×#121—2216no—
285C2×#121C2×D1114yescomplemented
286C2×#121C2×D1112yescomplemented
287C2×#120—118no—
288C2×#120—118no—
289C22×C4⋊C4—112no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4—114no—
292C22×C42—112no—
293#399—114no—
294#399—114no—
295#399—114no—
296#399C2×D1114yescomplemented
297#392—114no—
298#392—114no—
299#392—114no—
300#392C2×D1114yescomplemented
301#390—114no—
302#390—114no—
303#390—118no—
304#390—118no—
305#384—114no—
306C4×C22⋊C4—114no—
307C4×C22⋊C4—114no—
308C2×#95—111no—
309C2×#95C2×D1111yescharacteristic, complemented
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—24no—
313C22×C11—24no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—48no—
318C22×C11—48no—
319C22×C11C2×#12714yes—
320C22×C11C23×D411yescharacteristic
321C22×C11C23×D412yes—
322C22×C11C2×H(5,𝔽2)12yes—
323C22×C11#58511yescharacteristic
324C22×C11#58511yescharacteristic
325C2×D11—24no—
326C2×D11—24no—
327C2×D11—28no—
328C2×D11—28no—
329C2×D11—416no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—48no—
334C2×D11—48no—
335C2×D11—832no—
336C2×D11C2×#12718yes—
337C4×C11—24no—
338C4×C11—28no—
339C4×C11—44no—
340Dic11—22no—
341Dic11—28no—
342Dic11—44no—
343Dic11#53414yescomplemented
344C25—111no—
345C25—114no—
346C22×D4—114no—
347C22×D4—114no—
348C22×D4—114no—
349C22×D4—118no—
350C22×D4—114no—
351C22×D4—114no—
352C22×D4—112no—
353C22×D4—228no—
354C22×D4—2216no—
355C22×D4—2232no—
356C22×D4—448no—
357C22×D4C22×D1114yes—
358C22×D4C22×D1114yes—
359C22×D4C22×D1112yes—
360C23×C4—111no—
361C23×C4—112no—
362C23×C4—112no—
363C23×C4—118no—
364C23×C4—112no—
365C23×C4—114no—
366C23×C4—444no—
367C23×C4C22×D1111yescharacteristic
368C23×C4C22×D1112yes—
369#127—448no—
370#123—2232no—
371#123—2232no—
372#121—28no—
373#121—216no—
374#121—2216no—
375#121—228no—
376#121—228no—
377#121—2216no—
378#121—2232no—
379#121—228no—
380#121—2216no—
381#120—2232no—
382#120—2232no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—112no—
385C2×C4⋊C4—118no—
386C2×C4⋊C4—114no—
387C2×C4⋊C4—228no—
388C2×C4⋊C4C22×D1112yes—
389C2×C4⋊C4C22×D1114yes—
390C2×C22⋊C4—1116no—
391C2×C22⋊C4—118no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—118no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—114no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—2216no—
399C2×C22⋊C4C22×D1114yes—
400C2×C22⋊C4C22×D1118yes—
401C2×C42—114no—
402C2×C42—114no—
403C2×C42—444no—
404#95—114no—
405#95C22×D1114yes—
406C2×C11—24no—
407C2×C11—84no—
408C2×C11C22×#12711yescharacteristic
409C2×C11C2×#53411yescharacteristic
410C2×C11#344911yescharacteristic
411C2×C11#349612yes—
412C2×C11#349612yes—
413D11—28no—
414D11—84no—
415C24—112no—
416C24—118no—
417C24—114no—
418C24—114no—
419C24—228no—
420C24—2216no—
421C24—442no—
422C24—441no—
423C24—441no—
424C24—448no—
425C24—444no—
426C24—444no—
427C24C23×D1114yes—
428C24C23×D1111yescharacteristic
429C2×D4—28no—
430C2×D4—216no—
431C2×D4—24no—
432C2×D4—28no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—2216no—
437C2×D4—228no—
438C2×D4—228no—
439C2×D4—2216no—
440C2×D4—2216no—
441C2×D4—2216no—
442C2×D4—228no—
443C2×D4—228no—
444C2×D4—2216no—
445C2×D4—224no—
446C2×D4—228no—
447C2×D4—444no—
448C2×D4—444no—
449C2×D4—444no—
450C2×D4—4432no—
451C2×D4—448no—
452C2×D4—448no—
453C2×D4—4464no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—111no—
458C22×C4—114no—
459C22×C4—114no—
460C22×C4—111no—
461C22×C4—118no—
462C22×C4—118no—
463C22×C4—118no—
464C22×C4—114no—
465C22×C4—228no—
466C22×C4—228no—
467C22×C4—2216no—
468C22×C4—224no—
469C22×C4—444no—
470C22×C4—4416no—
471C22×C4—442no—
472C22×C4—442no—
473C22×C4D4×D1114yes—
474C22×C4D4×D1118yescomplemented
475C22×C4C23×D1114yes—
476C22×C4C23×D1112yes—
477C22×C4C23×D1114yes—
478C4⋊C4—24no—
479C4⋊C4—28no—
480C4⋊C4—228no—
481C4⋊C4—2216no—
482C4⋊C4—224no—
483C4⋊C4—228no—
484C22⋊C4—28no—
485C22⋊C4—216no—
486C22⋊C4—1132no—
487C22⋊C4—228no—
488C22⋊C4—2216no—
489C22⋊C4—228no—
490C22⋊C4—2216no—
491C22⋊C4—228no—
492C22⋊C4—2216no—
493C42—228no—
494C42—444no—
495C11#3500111yescharacteristic, complemented, Sylow
496C23—22no—
497C23—21no—
498C23—21no—
499C23—28no—
500C23—24no—
501C23—28no—
502C23—24no—
503C23—24no—
504C23—118no—
505C23—114no—
506C23—1116no—
507C23—224no—
508C23—222no—
509C23—222no—
510C23—228no—
511C23—224no—
512C23—228no—
513C23—224no—
514C23—224no—
515C23—444no—
516C23—448no—
517C23—448no—
518C23—444no—
519C23—4416no—
520C23—4416no—
521C23—4416no—
522C23—8816no—
523C23—8816no—
524C23C2×D4×D1112yes—
525C23C2×D4×D1114yes—
526C23C24×D1111yescharacteristic
527D4—48no—
528D4—416no—
529D4—88no—
530D4—448no—
531D4—4416no—
532D4—4416no—
533D4—4416no—
534D4—4416no—
535D4—888no—
536D4—8816no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—28no—
541C2×C4—24no—
542C2×C4—44no—
543C2×C4—48no—
544C2×C4—112no—
545C2×C4—114no—
546C2×C4—118no—
547C2×C4—112no—
548C2×C4—2216no—
549C2×C4—228no—
550C2×C4—224no—
551C2×C4—222no—
552C2×C4—224no—
553C2×C4—228no—
554C2×C4—224no—
555C2×C4—448no—
556C2×C4—4416no—
557C2×C4—448no—
558C2×C4C2×D4×D1118yes—
559C2×C4C2×D4×D1114yes—
560C22—24no—
561C22—24no—
562C22—22no—
563C22—22no—
564C22—48no—
565C22—48no—
566C22—44no—
567C22—44no—
568C22—44no—
569C22—118no—
570C22—228no—
571C22—228no—
572C22—224no—
573C22—224no—
574C22—4416no—
575C22—448no—
576C22—448no—
577C22—444no—
578C22—444no—
579C22—444no—
580C22—8832no—
581C22D11×#12714yes—
582C22C22×D4×D1112yes—
583C22C22×D4×D1111yescharacteristic
584C22D11×H(5,𝔽2)12yes—
585C22#1062345511yescharacteristic
586C22#1062345711yescharacteristic
587C4—28no—
588C4—24no—
589C4—44no—
590C4—114no—
591C4—228no—
592C4—222no—
593C4—444no—
594C2—24no—
595C2—84no—
596C2—228no—
597C2—884no—
598C2C2×D11×#12711yescharacteristic
599C2D11×#53411yescharacteristic
600C2#1308194411yescharacteristic
601C2#1308237712yes—
602C2#1308237912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2656C2
hypercenter#2656D11
hypocenterC11#35001
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2656

Complements

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

NH ≅ G/Ntype
1. C2×#10623136C2semidirect
2. C2×D11×#121C2semidirect
3. #13076959C2semidirect
4. #13074720C2semidirect
5. #13074718C2semidirect
6. #13073543C2semidirect
7. #13073541C2semidirect
8. #13073082C2semidirect
9. #13072248C2semidirect
10. C2×#10622279C2semidirect
11. C11×#2656C2semidirect
13. C22×D4×D11C22semidirect
15. C2×C11×#121C22semidirect
16. C2×C11×#121C22semidirect
17. C2×#66993C22semidirect
18. C2×#66992C22semidirect
19. C2×#66992C22semidirect
21. C2×#66990C22semidirect
22. C2×#66983C22semidirect
23. C2×#66983C22semidirect
25. C22×C4×Dic11C22semidirect
29. C2×#66947C22semidirect
30. C2×C4⋊C4×D11C22semidirect
32. C2×#66936C22semidirect
33. C2×#66935C22semidirect
34. C2×C22⋊C4×D11C22semidirect
35. C11×#399C22semidirect
36. C11×#392C22semidirect
37. C2×C11×#95C22semidirect
38. #10622836C22semidirect
39. #10622834C22semidirect
40. C2×C11⋊#95C22semidirect
41. #10622605C22semidirect
42. #10622601C22semidirect
43. #10622589C22semidirect
44. #10622573C22semidirect
45. #10622570C22semidirect
46. #10622570C22semidirect
47. #10622562C22semidirect
48. #10622290C22semidirect
49. #10622284C22semidirect
50. #10622279C22semidirect
51. #10622279C22semidirect
73. C22×C4×D11D4semidirect
92. C2×(C2×D11)⋊C4D4semidirect
140. C22×C4×C11C2×D4semidirect
157. C22×Dic11C2×D4semidirect
188. (C2×D11)⋊C4C2×D4semidirect
200. #2656D11semidirect
234. C22×D11#127semidirect
285. C2×#121C2×D11semidirect
286. C2×#121C2×D11semidirect
296. #399C2×D11semidirect
300. #392C2×D11semidirect
309. C2×#95C2×D11semidirect
343. Dic11#534semidirect
474. C22×C4D4×D11semidirect
495. C11#35001semidirect

Maximal subgroups

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

subgroupindex
C2×#106231362
C2×D11×#1212
#130769592
#130747202
#130747182
#130735432
#130735412
#130730822
#130722482
C2×#106222792
C11×#26562
#3500111