Finite Group Databasebeta

← #14914307

Subgroups — #14914307

Order 2816.

2138 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2#13071720C214yesmaximal, complemented
3#13071698C214yesmaximal
4#13071578C214yesmaximal, complemented
5#13071471C214yesmaximal
6#13071364C211yesmaximal, characteristic, complemented
7#13071362C211yesmaximal, characteristic, complemented
8#13071336C211yesmaximal, characteristic, complemented
9#13071261C212yesmaximal, complemented
10#13071154C212yesmaximal
11C4×#66999C212yesmaximal
12#13071009C211yesmaximal, characteristic
13#13070981C212yesmaximal, complemented
14D11×#376C211yesmaximal, characteristic
15C11×#2327C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2212yes—
18C2×#66999C2212yes—
19C2×Q8×Dic11C2212yes—
20C2×Q8×Dic11C2212yes—
21#10623259C4116yescomplemented
22C2×#66950C2212yes—
23C2×#66945C2212yes—
24C2×#66943C2212yes—
25C2×#66940C2212yes—
26C2×C42×D11C2211yescharacteristic
27C2×C42×D11C2211yescharacteristic
28C2×C42×D11C2211yescharacteristic
29C2×#66922C2211yescharacteristic
30C11×#391C2212yes—
31C11×#387C2214yes—
32C11×#387C2214yes—
33C11×#382C2211yescharacteristic
34C11×#376C2211yescharacteristic
35#10622843C2212yes—
36#10622602C2214yes—
37#10622600C2212yes—
38#10622594C2214yes—
39#10622594C2214yes—
40#10622591C2214yes—
41C4⋊C4×Dic11C2212yes—
42C4⋊C4×Dic11C2214yes—
43C4⋊C4×Dic11C2214yes—
44C4⋊C4×Dic11C2212yes—
45#10622586C2212yes—
46C4×(C2×D11)⋊C4C2214yes—
47#10622549C2211yescharacteristic
48C4×C4⋊Dic11C2212yes—
49C4×C4⋊Dic11C2214yes—
50#10622545C2211yescharacteristic
51#10622545C2211yescharacteristic
52#10622545C2211yescharacteristic
53#10622545C2214yes—
54C4×Dic11⋊C4C2214yes—
55#10622541C2212yes—
56#10622281C2214yes—
57#10622279C2214yes—
58#10622279C2212yes—
59#10622277C2212yes—
60D11×#95C2212yes—
61D11×#95C2212yes—
62#10622268C2214yes—
63#10622267C2214yes—
64#10622267C2214yes—
65#10622266C2214yes—
66#10622266C2214yes—
67#10622264C2214yes—
68#10622264C2212yes—
69#10622263C2214yes—
70#10622262C2214yes—
71#10622261C2212yes—
72#10622261C2212yes—
73#10622261C2212yes—
74#10622259C2214yes—
75#10622259C2214yes—
76C22×Q8×C11C2312yes—
77C22×C4×D11C2312yes—
78C22×C4×D11C2312yes—
79C22×C4×D11C2311yescharacteristic
80C22×C4×D11C2311yescharacteristic
81C22×C4×D11C2311yescharacteristic
82C22×Dic22C2312yes—
83C11×C4⋊Q8C2×C418yescomplemented
84C4×Q8×C11—28no—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2314yes—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2314yes—
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2311yescharacteristic
93#66999C2×C4116yes—
94Q8×Dic11—28no—
95Q8×Dic11C2×C4116yescomplemented
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×C4⋊Dic11C2314yes—
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2312yes—
101C2×C4⋊Dic11C2312yes—
102C2×C4⋊Dic11C2314yes—
103C2×Dic11⋊C4C2314yes—
104C2×Dic11⋊C4C2314yes—
105C2×Dic11⋊C4C2314yes—
106C2×C4×Dic11C2312yes—
107C2×C4×Dic11C2312yes—
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2314yes—
110C2×C4×Dic11C2314yes—
111C2×C4×Dic11C2314yes—
112C2×C4×Dic11C2314yes—
113C2×C4×Dic11C2311yescharacteristic
114C2×C4×Dic11C2311yescharacteristic
115C2×C4×Dic11C2311yescharacteristic
116C2×C4×Dic11C2314yes—
117C2×C4×Dic11C2311yescharacteristic
118#66950C2×C4116yes—
119#66945C2×C4116yes—
120#66943C2×C4116yescomplemented
121#66940C2×C4116yescomplemented
122C42×D11—24no—
123C42×D11—24no—
124C42×D11C2×C418yes—
125#66922C2×C418yescomplemented
126C11×#95C2312yes—
127C11×#95C2312yes—
128C11×#95C2312yes—
129C11×#95C2312yes—
130C11×#95C2314yes—
131C11×#95C2314yes—
132C11⋊#95C2312yes—
133C11⋊#95C2312yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2312yes—
140C11⋊#95C2312yes—
141C11⋊#95C2312yes—
142C11⋊#95C2312yes—
143C11⋊#95C2312yes—
144C11⋊#95C2312yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148#34221—111nomaximal, Sylow
149C23×D11C2411yescharacteristic
150C2×Q8×C11—24no—
151C2×Q8×C11—24no—
152C2×Q8×C11C22×C418yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2414yes—
155C22×C4×C11C2411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×C4×C11C2414yes—
158C22×C4×C11C2412yes—
159C22×C4×C11C2411yescharacteristic
160C22×Dic11C2412yes—
161C22×Dic11C2414yes—
162C22×Dic11C2411yescharacteristic
163C22×Dic11C2411yescharacteristic
164C22×Dic11C2411yescharacteristic
165C22×Dic11C2414yes—
166C22×Dic11C2412yes—
167C2×C4×D11—24no—
168C2×C4×D11—24no—
169C2×C4×D11—24no—
170C2×C4×D11—24no—
171C2×C4×D11—22no—
172C2×C4×D11—22no—
173C2×C4×D11—24no—
174C2×C4×D11—42no—
175C2×C4×D11—42no—
176C2×C4×D11—42no—
177C2×C4×D11C22×C414yes—
178C2×C4×D11C22×C414yes—
179C2×C4×D11C22×C414yes—
180C2×Dic22—44no—
181C2×Dic22C22×C418yes—
182C11×C4⋊C4—28no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4C22×C418yes—
185C11×C4⋊C4C22×C418yes—
186C42×C11—22no—
187C42×C11—28no—
188C42×C11C22×C414yes—
189C42×C11#4114yes—
190(C2×D11)⋊C4—28no—
191(C2×D11)⋊C4C22×C4116yes—
192C4⋊Dic11—28no—
193C4⋊Dic11—24no—
194C4⋊Dic11C22×C418yes—
195C4⋊Dic11C22×C418yes—
196C4⋊Dic11C22×C4116yes—
197Dic11⋊C4—44no—
198Dic11⋊C4—44no—
199Dic11⋊C4C22×C4116yes—
200C4×Dic11—24no—
201C4×Dic11—28no—
202C4×Dic11—24no—
203C4×Dic11—22no—
204C4×Dic11—44no—
205C4×Dic11—44no—
206C4×Dic11—44no—
207C4×Dic11C22×C414yes—
208C4×Dic11C22×C414yes—
209C4×Dic11C22×C414yes—
210C4×Dic11C22×C4116yes—
211C4×Dic11#4114yes—
212C2×#533—111no—
213#2371—114no—
214#2368—114no—
215#2356—114no—
216#2343—114no—
217#2331—111no—
218#2331—111no—
219#2327—111no—
220#2327D1111yescharacteristic, complemented
221#2320—112no—
222C4×C22⋊Q8—112no—
223C4×C22⋊Q8—112no—
224#2283—111no—
225#2276—112no—
226C2×#376—111no—
227C23×C11C2511yescharacteristic
228C22×D11—21no—
229C22×D11—21no—
230C22×D11—22no—
231C22×D11C23×C412yes—
232C22×D112−1+414yes—
233Q8×C11—216no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11C23×C418yes—
247C2×C4×C11C23×C412yes—
248C2×C4×C11C23×C412yes—
249C2×C4×C11C23×C412yes—
250C2×C4×C11C2×#4114yes—
251C2×C4×C11C2×#4112yes—
252C2×C4×C11C2×#4112yes—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—24no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—24no—
261C2×Dic11—22no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—22no—
265C2×Dic11—24no—
266C2×Dic11—22no—
267C2×Dic11C23×C412yes—
268C2×Dic11C23×C412yes—
269C2×Dic11C23×C412yes—
270C2×Dic11C23×C418yes—
271C2×Dic11C2×#4114yes—
272C4×D11—28no—
273C4×D11—28no—
274C4×D11—44no—
275C4×D11—48no—
276C4×D11—48no—
277Dic22—48no—
278#533—1116no—
279C2×C4⋊Q8—111no—
280C2×C4⋊Q8C2×D1111yescharacteristic
281C2×#125—112no—
282C2×C22⋊Q8—112no—
283C2×C22⋊Q8—112no—
284C2×C4×Q8—112no—
285C2×C4×Q8—112no—
286C2×C4×Q8—112no—
287C2×C4×Q8C2×D1112yes—
288C2×#117—112no—
289C22×C42—111no—
290C22×C42—111no—
291C22×C42—111no—
292#391—112no—
293#391—114no—
294#391—114no—
295#391C2×D1112yes—
296#389—112no—
297#389—112no—
298#387—114no—
299#387—114no—
300#387—114no—
301#387—114no—
302#387—114no—
303#387—114no—
304#387—114no—
305#387—114no—
306#387C2×D1114yes—
307#387C2×D1114yes—
308#385—114no—
309#385—114no—
310#383—114no—
311#383—112no—
312#382—111no—
313#382—114no—
314#382C2×D1111yescharacteristic
315#381—112no—
316#380—112no—
317C4×C4⋊C4—112no—
318C4×C4⋊C4—112no—
319C4×C4⋊C4—114no—
320C4×C4⋊C4—114no—
321C4×C4⋊C4—112no—
322C4×C4⋊C4—114no—
323C4×C4⋊C4—114no—
324C4×C4⋊C4—114no—
325C4×C22⋊C4—114no—
326C4×C22⋊C4—114no—
327C4×C22⋊C4—112no—
328#376—111no—
329#376—111no—
330#376—114no—
331#376—111no—
332#376—112no—
333#376—112no—
334#376—112no—
335#376C2×D1111yescharacteristic
336C2×#95—112no—
337C2×#95—112no—
338C22×C11C24×C411yescharacteristic
339C22×C11C22×#4111yescharacteristic
340C22×C11C22×#4111yescharacteristic
341C22×C11C2×2−1+412yes—
342C22×C11#58512yes—
343C2×D11—22no—
344C2×D11—22no—
345C2×D11—24no—
346C2×D11—24no—
347C2×D11#51914yes—
348C4×C11—28no—
349C4×C11—22no—
350C4×C11—22no—
351C4×C11—24no—
352C4×C11—44no—
353C4×C11—42no—
354C4×C11C4×#4114yes—
355Dic11—22no—
356Dic11—22no—
357Dic11—28no—
358Dic11—22no—
359Dic11—24no—
360Dic11—42no—
361Dic11—44no—
362C22×Q8—112no—
363C22×Q8C22×D1112yes—
364C23×C4—111no—
365C23×C4—111no—
366C23×C4—111no—
367C23×C4—112no—
368C23×C4—112no—
369C4⋊Q8—118no—
370C4⋊Q8C4×D1118yescomplemented
371#125—1116no—
372C22⋊Q8—1116no—
373C22⋊Q8—1116no—
374C4×Q8—28no—
375C4×Q8—1116no—
376C4×Q8—1116no—
377C4×Q8—228no—
378#117—1116no—
379C2×C4⋊C4—112no—
380C2×C4⋊C4—114no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4—112no—
383C2×C4⋊C4—112no—
384C2×C4⋊C4—114no—
385C2×C4⋊C4—114no—
386C2×C4⋊C4—114no—
387C2×C4⋊C4C22×D1112yes—
388C2×C4⋊C4C22×D1114yes—
389C2×C4⋊C4C22×D1112yes—
390C2×C4⋊C4C22×D1112yes—
391C2×C22⋊C4—114no—
392C2×C22⋊C4—114no—
393C2×C42—114no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—118no—
399C2×C42—114no—
400C2×C42—112no—
401C2×C42—112no—
402C2×C42—111no—
403C2×C42—114no—
404C2×C42—114no—
405C2×C42—114no—
406C2×C42—224no—
407C2×C42—224no—
408C2×C42C22×D1114yes—
409C2×C42C22×D1111yescharacteristic
410C2×C42C22×D1111yescharacteristic
411C2×C42C22×D1111yescharacteristic
412#95—112no—
413#95—112no—
414#95—112no—
415#95—112no—
416#95—112no—
417#95—112no—
418#95—114no—
419#95—114no—
420#95—114no—
421#95—114no—
422#95—112no—
423#95—112no—
424#95—114no—
425#95—114no—
426#95—114no—
427#95—114no—
428#95C22×D1112yes—
429#95C22×D1112yes—
430#95C22×D1112yes—
431#95C22×D1114yes—
432#95C22×D1112yes—
433#95C22×D1114yes—
434C2×C11C2×C4×#4111yescharacteristic
435C2×C11C2×#51911yescharacteristic
436C2×C11#342811yescharacteristic
437C2×C11#349512yes—
438C2×C11#349512yes—
439D11—24no—
440C24—111no—
441C2×Q8—24no—
442C2×Q8—24no—
443C2×Q8—118no—
444C2×Q8—444no—
445C2×Q8C2×C4×D1118yes—
446C22×C4—111no—
447C22×C4—112no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—114no—
451C22×C4—114no—
452C22×C4—114no—
453C22×C4—114no—
454C22×C4—112no—
455C22×C4—114no—
456C22×C4—224no—
457C22×C4—224no—
458C22×C4—224no—
459C22×C4—224no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—224no—
463C22×C4—442no—
464C22×C4—442no—
465C22×C4—442no—
466C22×C4C23×D1112yes—
467C22×C4C23×D1114yes—
468C22×C4C23×D1111yescharacteristic
469C22×C4C23×D1111yescharacteristic
470C22×C4C23×D1114yes—
471C22×C4C23×D1112yes—
472C22×C4C23×D1111yescharacteristic
473C4⋊C4—28no—
474C4⋊C4—24no—
475C4⋊C4—118no—
476C4⋊C4—1116no—
477C4⋊C4—1116no—
478C4⋊C4—118no—
479C4⋊C4—228no—
480C4⋊C4—224no—
481C4⋊C4—444no—
482C4⋊C4—444no—
483C4⋊C4C2×C4×D1118yes—
484C4⋊C4C2×C4×D1118yes—
485C22⋊C4—1116no—
486C22⋊C4—228no—
487C42—28no—
488C42—22no—
489C42—114no—
490C42—114no—
491C42—114no—
492C42—1116no—
493C42—114no—
494C42—224no—
495C42—228no—
496C42—224no—
497C42—222no—
498C42—444no—
499C42—444no—
500C42—444no—
501C42C2×C4×D1114yes—
502C42#434114yes—
503C11#3422111yescharacteristic, complemented, Sylow
504C23—112no—
505C23—114no—
506C23—221no—
507C23—221no—
508C23—222no—
509C23C24×D1111yescharacteristic
510Q8—216no—
511Q8—448no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—112no—
525C2×C4—112no—
526C2×C4—112no—
527C2×C4—118no—
528C2×C4—114no—
529C2×C4—228no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—222no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—228no—
539C2×C4—222no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—222no—
543C2×C4—224no—
544C2×C4—222no—
545C2×C4—444no—
546C2×C4—448no—
547C2×C4—448no—
548C2×C4C22×C4×D1112yes—
549C2×C4C22×C4×D1112yes—
550C2×C4C22×C4×D1118yes—
551C2×C4C22×C4×D1112yes—
552C2×C4C2×#434114yes—
553C2×C4C2×#434112yes—
554C2×C4#41×D1112yes—
555C22—114no—
556C22—222no—
557C22—222no—
558C22—224no—
559C22—224no—
560C22C23×C4×D1111yescharacteristic
561C22C22×#434111yescharacteristic
562C22C2×#41×D1111yescharacteristic
563C22D11×2−1+412yes—
564C22#1062345712yes—
565C4—28no—
566C4—22no—
567C4—22no—
568C4—24no—
569C4—42no—
570C4—44no—
571C4—222no—
572C4—222no—
573C4—222no—
574C4—228no—
575C4—224no—
576C4—444no—
577C4—442no—
578C4C4×#434114yes—
579C2—224no—
580C2C2×C4×#434111yescharacteristic
581C2D11×#51911yescharacteristic
582C2#1308181811yescharacteristic
583C2#1308236012yes—
584C2#1308236512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2327C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2327D11
hypocenterC11#34221
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2327

Complements

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

NH ≅ G/Ntype
2. #13071720C2semidirect
4. #13071578C2semidirect
6. #13071364C2semidirect
7. #13071362C2semidirect
8. #13071336C2semidirect
9. #13071261C2semidirect
13. #13070981C2semidirect
15. C11×#2327C2semidirect
21. #10623259C4semidirect
83. C11×C4⋊Q8C2×C4semidirect
95. Q8×Dic11C2×C4semidirect
120. #66943C2×C4semidirect
121. #66940C2×C4semidirect
125. #66922C2×C4semidirect
220. #2327D11semidirect
370. C4⋊Q8C4×D11semidirect
503. C11#34221semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
#130717202
#130716982
#130715782
#130714712
#130713642
#130713622
#130713362
#130712612
#130711542
C4×#669992
#130710092
#130709812
D11×#3762
C11×#23272
#3422111