Finite Group Databasebeta

← #14916477

Subgroups — #14916477

Order 2816.

2664 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623214C211yesmaximal, characteristic
2#13071789C214yesmaximal, complemented
3#13071788C212yesmaximal, complemented
4#13071787C212yesmaximal, complemented
5#13071756C214yesmaximal, complemented
6#13071754C212yesmaximal, complemented
7#124×Dic11C211yesmaximal, characteristic, complemented
8#13071159C212yesmaximal, complemented
9#13071157C214yesmaximal, complemented
10#13071155C212yesmaximal, complemented
11#13071121C212yesmaximal, complemented
12#13071117C214yesmaximal, complemented
13C11×#2379C211yesmaximal, characteristic, complemented
14C23×C4×D11C2212yescomplemented
15C2×C11×#124C2211yescharacteristic
16C2×#67000C2212yes—
17C2×Q8×Dic11C2211yescharacteristic, complemented
18C2×#66990C2212yes—
19C2×D4×Dic11C2211yescharacteristic
20#10623214C4116yescomplemented
21C2×#66946C2212yes—
22C2×#66946C2212yes—
23C2×#66940C2212yescomplemented
24C2×#66938C2214yes—
25C2×#66935C2214yes—
26C2×(C22⋊D11)⋊C4C2214yes—
27C2×#66928C2212yes—
28C11×#391C2212yescomplemented
29C11×#388C2214yescomplemented
30C11×#386C2212yes—
31C11×#385C2214yescomplemented
32C11×#382C2212yescomplemented
33#10622843C2211yescharacteristic, complemented
34#10622834C2211yescharacteristic
35#10622826C2214yes—
36#10622823C2212yescomplemented
37#10622603C2214yescomplemented
38#10622602C2214yescomplemented
39#10622602C2214yescomplemented
40#10622601C2212yes—
41#10622590C2212yescomplemented
42#10622587C2212yescomplemented
43#10622570C2214yes—
44#10622569C2214yes—
45#10622568C2214yescomplemented
46#10622568C2212yescomplemented
47#10622564C2214yescomplemented
48#10622558C2214yescomplemented
49C22⋊C4×Dic11C2214yescomplemented
50C22⋊C4×Dic11C2212yescomplemented
51#10622553C2214yescomplemented
52#10622552C2212yes—
53#10622549C2211yescharacteristic, complemented
54C42×Dic11C2211yescharacteristic, complemented
55C42×Dic11C2212yescomplemented
56#10622283C2214yescomplemented
57#10622283C2214yescomplemented
58#10622282C2214yescomplemented
59#10622282C2214yescomplemented
60#10622281C2214yescomplemented
61#10622279C2214yescomplemented
62#10622279C2214yescomplemented
63#10622279C2214yescomplemented
64#10622278C2214yes—
65#10622278C2214yes—
66#10622263C2214yescomplemented
67#10622259C2214yescomplemented
68C24×D11C2312yes—
69C22×Q8×C11C2311yescharacteristic
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11C2312yes—
72C22×C22⋊D11C2314yes—
73C23×Dic11C2312yes—
74C22×D44C2312yes—
75C22×D44C2312yes—
76C22×C4×D11—48no—
77C22×C4×D11—44no—
78C22×C4×D11C2314yes—
79C22×C4×D11C2314yes—
80C22×Dic22C2312yes—
81C11×#124C2×C418yescomplemented
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C22⋊C4C2314yes—
86C2×C11×C22⋊C4C2312yes—
87C2×C11×C22⋊C4C2314yes—
88C2×C42×C11C2312yes—
89C2×C42×C11C2311yescharacteristic
90C2×C22⋊Dic11C2314yes—
91C2×C22⋊Dic11C2312yes—
92C2×C22⋊Dic11C2312yes—
93#67000C2×C4116yescomplemented
94Q8×Dic11—42no—
95#66990C2×C4116yescomplemented
96D4×Dic11—42no—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2314yes—
102C2×(C2×D11)⋊C4C2314yes—
103C2×(C2×D11)⋊C4C2314yes—
104C2×(C2×D11)⋊C4C2314yes—
105C2×(C2×D11)⋊C4C2314yes—
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2312yes—
109C2×Dic11⋊C4C2314yes—
110C2×Dic11⋊C4C2314yes—
111C2×C4×Dic11C2314yes—
112C2×C4×Dic11C2312yes—
113C2×C4×Dic11C2312yes—
114C2×C4×Dic11C2311yescharacteristic
115C2×C4×Dic11C2314yes—
116C2×C4×Dic11C2311yescharacteristic
117C2×C4×Dic11C2312yes—
118C2×C4×Dic11C2312yes—
119#66946—44no—
120#66946—44no—
121#66940—44no—
122#66938C2×C4132yescomplemented
123#66935C2×C4132yescomplemented
124(C22⋊D11)⋊C4—48no—
125#66928C2×C4116yescomplemented
126C11×#95C2314yes—
127C11×#95C2314yes—
128C11×#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C4×H(3,𝔽4)—111nomaximal, Sylow
136C24×C11C2412yes—
137C23×D11—42no—
138C23×D11—44no—
139C23×D11—42no—
140C23×D11—44no—
141C23×D11C22×C418yescomplemented
142C23×D11C2414yes—
143C2×Q8×C11—41no—
144C2×Q8×C11—41no—
145C2×Q8×C11C22×C414yescomplemented
146C2×D4×C11—41no—
147C2×D4×C11—41no—
148C2×D4×C11C22×C414yes—
149C22×C4×C11—44no—
150C22×C4×C11—42no—
151C22×C4×C11C2414yes—
152C22×C4×C11C2414yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—44no—
157C2×C22⋊D11—44no—
158C2×C22⋊D11C22×C4116yes—
159C22×Dic11—28no—
160C22×Dic11—24no—
161C22×Dic11C2412yes—
162C22×Dic11C2412yes—
163C22×Dic11C2412yes—
164C22×Dic11C2411yescharacteristic
165C22×Dic11C2414yes—
166C22×Dic11C2411yescharacteristic
167C2×D44—42no—
168C2×D44—42no—
169C2×D44—42no—
170C2×D44—42no—
171C2×D44C22×C418yes—
172C2×D44C22×C418yes—
173C2×C4×D11—28no—
174C2×C4×D11—28no—
175C2×C4×D11—28no—
176C2×C4×D11—44no—
177C2×C4×D11—44no—
178C2×C4×D11—44no—
179C2×C4×D11—432no—
180C2×Dic22—42no—
181C2×Dic22—42no—
182C2×Dic22C22×C418yescomplemented
183C11×C4⋊C4—42no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4—42no—
186C11×C22⋊C4—44no—
187C11×C22⋊C4—42no—
188C11×C22⋊C4C22×C4116yescomplemented
189C42×C11—42no—
190C42×C11C22×C414yescomplemented
191C22⋊Dic11—42no—
192C22⋊Dic11—44no—
193C22⋊Dic11C22×C418yescomplemented
194(C2×D11)⋊C4—44no—
195(C2×D11)⋊C4—44no—
196(C2×D11)⋊C4—44no—
197(C2×D11)⋊C4—44no—
198(C2×D11)⋊C4—44no—
199(C2×D11)⋊C4—44no—
200(C2×D11)⋊C4C22×C4116yescomplemented
201(C2×D11)⋊C4C22×C4116yescomplemented
202(C2×D11)⋊C4C22×C4116yescomplemented
203C4⋊Dic11—41no—
204C4⋊Dic11—41no—
205C4⋊Dic11—42no—
206Dic11⋊C4—44no—
207Dic11⋊C4—44no—
208C4×Dic11—28no—
209C4×Dic11—24no—
210C4×Dic11—24no—
211C4×Dic11—22no—
212C4×Dic11—42no—
213C4×Dic11—41no—
214C4×Dic11—44no—
215C4×Dic11C22×C418yescomplemented
216C2×H(3,𝔽4)—111no—
217#2379—112no—
218#2379—114no—
219#2379—112no—
220#2379D1111yescharacteristic, complemented
221#2375—114no—
222#2375—112no—
223C4×#124—112no—
224C4×#124—114no—
225C4×#124—112no—
226C4×#124—111no—
227C4×#120—112no—
228C4×#120—114no—
229C23×C11—22no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11—22no—
233C23×C11C23×C414yes—
234C23×C11C2511yescharacteristic
235C22×D11—24no—
236C22×D11—24no—
237C22×D11—24no—
238C22×D11—24no—
239C22×D11—24no—
240C22×D11—24no—
241C22×D11—48no—
242C22×D11—416no—
243C22×D11—48no—
244C22×D11—416no—
245C22×D11—48no—
246C22×D11C23×C418yes—
247Q8×C11—44no—
248D4×C11—44no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—24no—
261C2×C4×C11—48no—
262C2×C4×C11C23×C414yes—
263C2×C4×C11C23×C412yes—
264C2×C4×C11C23×C414yes—
265C22⋊D11—416no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—24no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—48no—
278C2×Dic11C23×C418yes—
279C2×Dic11H(5,𝔽2)14yes—
280C2×Dic11H(5,𝔽2)12yes—
281D44—48no—
282D44—48no—
283C4×D11—416no—
284C4×D11—416no—
285Dic22—48no—
286C24×C4—112no—
287H(3,𝔽4)—1116no—
288C2×#124—112no—
289C2×#124—114no—
290C2×#124—112no—
291C2×#124C2×D1111yescharacteristic
292C2×#120—112no—
293C2×#120—114no—
294C2×C4×Q8—111no—
295C2×C4×Q8—112no—
296C2×C4×D4—111no—
297C2×C4×D4—112no—
298C2×C4×D4—112no—
299C2×C4×D4—114no—
300#391—111no—
301#391—112no—
302#391—114no—
303#391C2×D1112yescomplemented
304#390—111no—
305#390—112no—
306#390—114no—
307#390—112no—
308#388—114no—
309#388—114no—
310#388—114no—
311#388—114no—
312#388—114no—
313#388—114no—
314#388—114no—
315#388—114no—
316#388C2×D1114yescomplemented
317#386—114no—
318#386—114no—
319#386—114no—
320#386—114no—
321#386C2×D1112yes—
322#385—112no—
323#385—114no—
324#385—114no—
325#385—114no—
326#385C2×D1114yescomplemented
327#382—112no—
328#382—111no—
329#382—114no—
330#382C2×D1112yescomplemented
331#379—112no—
332#379—114no—
333C4×C22⋊C4—112no—
334C4×C22⋊C4—114no—
335C4×C22⋊C4—114no—
336C4×C22⋊C4—114no—
337C4×C22⋊C4—114no—
338C43—112no—
339C43—111no—
340C22×C11—24no—
341C22×C11—28no—
342C22×C11—42no—
343C22×C11—44no—
344C22×C11—42no—
345C22×C11C24×C411yescharacteristic
346C22×C11C2×H(5,𝔽2)12yes—
347C22×C11C2×H(5,𝔽2)11yescharacteristic
348C22×C11#58511yescharacteristic
349C22×C11#58512yes—
350C2×D11—28no—
351C2×D11—28no—
352C2×D11—28no—
353C2×D11—432no—
354C2×D11—44no—
355C2×D11—44no—
356C2×D11—44no—
357C2×D11—44no—
358C4×C11—22no—
359C4×C11—24no—
360C4×C11—24no—
361C4×C11—44no—
362C4×C11—44no—
363Dic11—28no—
364Dic11—42no—
365Dic11—42no—
366Dic11—42no—
367Dic11—41no—
368Dic11H(3,𝔽4)14yescomplemented
369C25—112no—
370C22×Q8—112no—
371C22×Q8C22×D1111yescharacteristic
372C22×D4—114no—
373C22×D4—112no—
374C22×D4—112no—
375C22×D4C22×D1111yescharacteristic
376C23×C4—112no—
377C23×C4—114no—
378C23×C4—114no—
379C23×C4—448no—
380C23×C4—444no—
381C23×C4C22×D1112yes—
382#124—1116no—
383#124—1132no—
384#124—1116no—
385#124C4×D1118yescomplemented
386#120—1116no—
387#120—1132no—
388C4×Q8—444no—
389C4×Q8—442no—
390C4×D4—448no—
391C4×D4—444no—
392C4×D4—444no—
393C4×D4—442no—
394C2×C4⋊C4—114no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—114no—
397C2×C4⋊C4—112no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4C22×D1112yes—
400C2×C4⋊C4C22×D1112yes—
401C2×C4⋊C4C22×D1112yes—
402C2×C22⋊C4—112no—
403C2×C22⋊C4—114no—
404C2×C22⋊C4—114no—
405C2×C22⋊C4—114no—
406C2×C22⋊C4—112no—
407C2×C22⋊C4—114no—
408C2×C22⋊C4—114no—
409C2×C22⋊C4—114no—
410C2×C22⋊C4—114no—
411C2×C22⋊C4—114no—
412C2×C22⋊C4—114no—
413C2×C22⋊C4—114no—
414C2×C22⋊C4C22×D1114yes—
415C2×C22⋊C4C22×D1112yes—
416C2×C22⋊C4C22×D1114yes—
417C2×C42—112no—
418C2×C42—114no—
419C2×C42—112no—
420C2×C42—112no—
421C2×C42—111no—
422C2×C42—114no—
423C2×C42—112no—
424C2×C42—111no—
425C2×C42C22×D1112yes—
426C2×C42C22×D1111yescharacteristic
427#95—114no—
428#95—114no—
429#95—114no—
430#95—114no—
431#95—114no—
432#95—114no—
433#95C22×D1114yes—
434#95C22×D1114yes—
435#95C22×D1114yes—
436C2×C11—44no—
437C2×C11C4×H(5,𝔽2)11yescharacteristic
438C2×C11C4×H(5,𝔽2)12yes—
439C2×C11C2×H(3,𝔽4)11yescharacteristic
440C2×C11#352912yes—
441C2×C11#352911yescharacteristic
442D11—48no—
443C24—114no—
444C24—118no—
445C24—444no—
446C24—442no—
447C24—442no—
448C24—444no—
449C24C23×D1112yes—
450C2×Q8—41no—
451C2×Q8—41no—
452C2×Q8—118no—
453C2×Q8—442no—
454C2×Q8—442no—
455C2×Q8C2×C4×D1114yescomplemented
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—1116no—
459C2×D4—118no—
460C2×D4—118no—
461C2×D4—442no—
462C2×D4—442no—
463C2×D4—442no—
464C2×D4—442no—
465C2×D4—444no—
466C2×D4—444no—
467C2×D4C2×C4×D1114yes—
468C22×C4—44no—
469C22×C4—42no—
470C22×C4—111no—
471C22×C4—114no—
472C22×C4—112no—
473C22×C4—112no—
474C22×C4—111no—
475C22×C4—112no—
476C22×C4—228no—
477C22×C4—228no—
478C22×C4—228no—
479C22×C4—228no—
480C22×C4—224no—
481C22×C4—444no—
482C22×C4—444no—
483C22×C4—444no—
484C22×C4—4432no—
485C22×C4C23×D1114yes—
486C22×C4C23×D1114yes—
487C22×C4C23×D1112yes—
488C22×C4C23×D1112yes—
489C22×C4C23×D1111yescharacteristic
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4—444no—
494C4⋊C4—441no—
495C4⋊C4—444no—
496C4⋊C4—442no—
497C4⋊C4—441no—
498C22⋊C4—44no—
499C22⋊C4—42no—
500C22⋊C4—118no—
501C22⋊C4—1116no—
502C22⋊C4—1116no—
503C22⋊C4—1116no—
504C22⋊C4—444no—
505C22⋊C4—444no—
506C22⋊C4—444no—
507C22⋊C4—444no—
508C22⋊C4—444no—
509C22⋊C4—444no—
510C22⋊C4—442no—
511C22⋊C4—444no—
512C22⋊C4C2×C4×D11116yescomplemented
513C42—42no—
514C42—118no—
515C42—224no—
516C42—224no—
517C42—222no—
518C42—228no—
519C42—441no—
520C42—442no—
521C42—444no—
522C42C2×C4×D1114yescomplemented
523C11C4×H(3,𝔽4)11yescharacteristic, complemented, Sylow
524C23—24no—
525C23—22no—
526C23—22no—
527C23—24no—
528C23—118no—
529C23—224no—
530C23—224no—
531C23—224no—
532C23—224no—
533C23—224no—
534C23—224no—
535C23—448no—
536C23—4416no—
537C23—448no—
538C23—4416no—
539C23—448no—
540C23C22×C4×D1114yes—
541C23C24×D1111yescharacteristic
542Q8—44no—
543Q8—448no—
544D4—44no—
545D4—448no—
546D4—448no—
547D4—4416no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—48no—
561C2×C4—114no—
562C2×C4—112no—
563C2×C4—118no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—221no—
569C2×C4—224no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—224no—
575C2×C4—4416no—
576C2×C4—4416no—
577C2×C4—448no—
578C2×C4C22×C4×D1114yes—
579C2×C4C22×C4×D1112yes—
580C2×C4C22×C4×D1114yes—
581C22—24no—
582C22—28no—
583C22—42no—
584C22—44no—
585C22—42no—
586C22—228no—
587C22—228no—
588C22—228no—
589C22—4432no—
590C22—444no—
591C22—444no—
592C22—444no—
593C22—444no—
594C22C23×C4×D1111yescharacteristic
595C22D11×H(5,𝔽2)12yes—
596C22D11×H(5,𝔽2)11yescharacteristic
597C22#1062345511yescharacteristic
598C22#1062345712yes—
599C4—22no—
600C4—24no—
601C4—24no—
602C4—44no—
603C4—44no—
604C4—114no—
605C4—228no—
606C4—442no—
607C4—442no—
608C4—442no—
609C4—441no—
610C2—44no—
611C2—448no—
612C2#1308182011yescharacteristic
613C2#1308182212yes—
614C2D11×H(3,𝔽4)11yescharacteristic
615C2#1308275312yes—
616C2#1308275711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2379C2
socle, cosocleC23×C11C25
prime radicalC2×#10623214C2
hypercenter#2379D11
hypocenterC11C4×H(3,𝔽4)
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2379

Complements

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

NH ≅ G/Ntype
2. #13071789C2semidirect
3. #13071788C2semidirect
4. #13071787C2semidirect
5. #13071756C2semidirect
6. #13071754C2semidirect
7. #124×Dic11C2semidirect
8. #13071159C2semidirect
9. #13071157C2semidirect
10. #13071155C2semidirect
11. #13071121C2semidirect
12. #13071117C2semidirect
13. C11×#2379C2semidirect
14. C23×C4×D11C22semidirect
17. C2×Q8×Dic11C22semidirect
20. #10623214C4semidirect
23. C2×#66940C22semidirect
28. C11×#391C22semidirect
29. C11×#388C22semidirect
31. C11×#385C22semidirect
32. C11×#382C22semidirect
33. #10622843C22semidirect
36. #10622823C22semidirect
37. #10622603C22semidirect
38. #10622602C22semidirect
39. #10622602C22semidirect
41. #10622590C22semidirect
42. #10622587C22semidirect
45. #10622568C22semidirect
46. #10622568C22semidirect
47. #10622564C22semidirect
48. #10622558C22semidirect
49. C22⋊C4×Dic11C22semidirect
50. C22⋊C4×Dic11C22semidirect
51. #10622553C22semidirect
53. #10622549C22semidirect
54. C42×Dic11C22semidirect
55. C42×Dic11C22semidirect
56. #10622283C22semidirect
57. #10622283C22semidirect
58. #10622282C22semidirect
59. #10622282C22semidirect
60. #10622281C22semidirect
61. #10622279C22semidirect
62. #10622279C22semidirect
63. #10622279C22semidirect
66. #10622263C22semidirect
67. #10622259C22semidirect
81. C11×#124C2×C4semidirect
93. #67000C2×C4semidirect
95. #66990C2×C4semidirect
122. #66938C2×C4semidirect
123. #66935C2×C4semidirect
125. #66928C2×C4semidirect
141. C23×D11C22×C4semidirect
145. C2×Q8×C11C22×C4semidirect
182. C2×Dic22C22×C4semidirect
188. C11×C22⋊C4C22×C4semidirect
190. C42×C11C22×C4semidirect
193. C22⋊Dic11C22×C4semidirect
200. (C2×D11)⋊C4C22×C4semidirect
201. (C2×D11)⋊C4C22×C4semidirect
202. (C2×D11)⋊C4C22×C4semidirect
215. C4×Dic11C22×C4semidirect
220. #2379D11semidirect
303. #391C2×D11semidirect
316. #388C2×D11semidirect
326. #385C2×D11semidirect
330. #382C2×D11semidirect
368. Dic11H(3,𝔽4)semidirect
385. #124C4×D11semidirect
455. C2×Q8C2×C4×D11semidirect
512. C22⋊C4C2×C4×D11semidirect
522. C42C2×C4×D11semidirect
523. C11C4×H(3,𝔽4)semidirect

Maximal subgroups

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

subgroupindex
C2×#106232142
#130717892
#130717882
#130717872
#130717562
#130717542
#124×Dic112
#130711592
#130711572
#130711552
#130711212
#130711172
C11×#23792
C4×H(3,𝔽4)11