Finite Group Databasebeta

← #14725314

Subgroups — #14725314

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077628C211yesmaximal, characteristic
2Q8×#4318C211yesmaximal, characteristic, complemented
3C4×#66995C211yesmaximal, characteristic
4#13067522C211yesmaximal, characteristic, complemented
5#13067510C211yesmaximal, characteristic, complemented
6#13067484C211yesmaximal, characteristic, complemented
7#13067476C211yesmaximal, characteristic, complemented
8#13067463C211yesmaximal, characteristic, complemented
9#13067455C211yesmaximal, characteristic, complemented
10#13067431C211yesmaximal, characteristic, complemented
11#13067413C211yesmaximal, characteristic, complemented
12#13067384C211yesmaximal, characteristic, complemented
13#13067056C211yesmaximal, characteristic
14#13066919C211yesmaximal, characteristic, complemented
15C11×#1491C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66995C411yescharacteristic
18C4×#4339C2211yescharacteristic
19C11×#432C2211yescharacteristic
20C4×C11×M16C2211yescharacteristic
21#10622838C411yescharacteristic
22#10622643C411yescharacteristic
23#10622643C411yescharacteristic
24C4×#4326C2211yescharacteristic
25C4×#4326C2211yescharacteristic
26#10622639C411yescharacteristic
27#10622639C411yescharacteristic
28C4×#4325C2211yescharacteristic
29C4×#4325C2211yescharacteristic
30#10622637—21no—
31#10622637—21no—
32#10622637C2211yescharacteristic
33#10622637C2211yescharacteristic
34Q8×C11⋊C8C2211yescharacteristic
35Q8×C11⋊C8C2211yescharacteristic
36#10622579C411yescharacteristic
37#10622577C411yescharacteristic
38#10622537—21no—
39#10622537C2211yescharacteristic
40C4×#4318—21no—
41C4×#4318C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622447C2211yescharacteristic
44#10622447C2211yescharacteristic
45#10622444C2211yescharacteristic
46#10622444C2211yescharacteristic
47#10622341—21no—
48#10622341—21no—
49#10622318—21no—
50D11×#97—21no—
51C11×Q8⋊C8C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×Q8⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic
56#10622118C2211yescharacteristic
57#10622117C2211yescharacteristic
58#10622117C2211yescharacteristic
59#10622097C2211yescharacteristic
60#10622097C2211yescharacteristic
61#10622094C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C22×Q8×C11C2×C411yescharacteristic
68C2×#4339C2×C411yescharacteristic
69C2×C11×M16—21no—
70C4×Q8×C11—21no—
71C4×Q8×C11—21no—
72C4×Q8×C11C2×C411yescharacteristic
73C4×Q8×C11C2×C411yescharacteristic
74C4×Q8×C11C2311yescharacteristic
75C4×Q8×C11C2311yescharacteristic
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2×C411yescharacteristic
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×#4326C2×C411yescharacteristic
81C2×#4326C2×C411yescharacteristic
82#66995—24no—
83C2×#4325C2×C411yescharacteristic
84C2×#4325C2×C411yescharacteristic
85C4×C22⋊D11—21no—
86C4×C22⋊D11—21no—
87#66979C2×C411yescharacteristic
88C2×#4318—21no—
89C2×#4318C2×C411yescharacteristic
90C2×#4318C2×C411yescharacteristic
91C2×#4318D411yescharacteristic
92C2×#4318D411yescharacteristic
93C2×C8×D11—21no—
94C2×C8×D11—21no—
95C4×D44C2×C411yescharacteristic
96C4×D44C2311yescharacteristic
97#66925—21no—
98C42×D11—21no—
99C4×Dic22C2×C411yescharacteristic
100C4×Dic22C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×C22⋊C8—21no—
104C11×#97—21no—
105C11×#97—21no—
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108#66899C2×C411yescharacteristic
109#66899C2×C411yescharacteristic
110#66899C2×C411yescharacteristic
111#66899C2×C411yescharacteristic
112(C2×D11)⋊C8—21no—
113(C2×D11)⋊C8—21no—
114#66879—21no—
115#66879—21no—
116Dic11⋊C8—21no—
117Dic11⋊C8—21no—
118#66874C2×C411yescharacteristic
119#66874C2×C411yescharacteristic
120#66873C2×C411yescharacteristic
121#66873C2×C411yescharacteristic
122#66872C2×C411yescharacteristic
123#66872C2×C411yescharacteristic
124#66871C2×C411yescharacteristic
125#66871C2×C411yescharacteristic
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)C2311yescharacteristic
132C4⋊(C11⋊C8)C2311yescharacteristic
133#66867—21no—
134#66867—21no—
135#66867C2×C411yescharacteristic
136#66867C2×C411yescharacteristic
137#66867D411yescharacteristic
138#66867D411yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18047—111nomaximal, Sylow
146C2×Q8×C11—21no—
147C2×Q8×C11—22no—
148C2×Q8×C11—41no—
149C2×Q8×C11C22×C411yescharacteristic
150C2×Q8×C11C22×C411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C2×C22⋊D11—21no—
157#4339—22no—
158#4339—41no—
159C2×D44C22×C411yescharacteristic
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×Dic22C22×C411yescharacteristic
164C11×M16—42no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C4⋊C4C22×C411yescharacteristic
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11C22×C411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11#4111yescharacteristic
183C42×C11C2411yescharacteristic
184C22⋊Dic11—21no—
185#4326—22no—
186#4326—22no—
187#4325—22no—
188#4325M1614yescomplemented
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191C4⋊Dic11C22×C411yescharacteristic
192C4⋊Dic11C22×C411yescharacteristic
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198#4318—22no—
199#4318—22no—
200#4318—41no—
201#4318—41no—
202#4318—42no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213C8×D11—42no—
214C8×D11—42no—
215#2970—111no—
216Q8×M16—111no—
217C4×#137—111no—
218#1593—111no—
219#1591—111no—
220#1587—111no—
221#1585—111no—
222#1584—111no—
223#1582—111no—
224SD16⋊C8—111no—
225C8×SD16—111no—
226#1569—111no—
227#1491D1111yescharacteristic, complemented
228#1489—111no—
229#1455—111no—
230C23×C11C4×D411yescharacteristic
231C22×D11—21no—
232Q8×C11—21no—
233Q8×C11—21no—
234Q8×C11—21no—
235Q8×C11—42no—
236Q8×C11C2×M1612yes—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—81no—
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C23×C411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C22⋊D11—42no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258D44—21no—
259D44C2×M1612yes—
260C4×D11—42no—
261C4×D11—41no—
262C4×D11—41no—
263C4×D11—81no—
264Dic22—21no—
265Dic22—21no—
266C8×C11—22no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11—41no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8C2×M1612yes—
279C11⋊C8#13712yescomplemented
280C2×#137—111no—
281C4×#41—111no—
282C2×C4×Q8C2×D1111yescharacteristic
283#446—111no—
284#446—111no—
285#446—111no—
286#446—111no—
287#446—221no—
288#446—221no—
289C8×Q8—111no—
290C8×Q8—111no—
291#441—111no—
292#441—111no—
293#440—111no—
294#440—111no—
295C4×Q16—111no—
296C4×Q16—111no—
297C4×SD16—111no—
298C4×SD16—111no—
299#435—221no—
300#435—221no—
301C8×D4—111no—
302C8×D4—111no—
303#432—221no—
304#432C2×D1111yescharacteristic
305#428—111no—
306#423—111no—
307#423—221no—
308#419—111no—
309#417—111no—
310C4×M16—111no—
311C4×M16—111no—
312C4×M16—221no—
313C4×M16C2×D1111yescharacteristic
314C2×#97—221no—
315#335—111no—
316#335—111no—
317#334—111no—
318#334—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8C2×D1111yescharacteristic
322Q8⋊C8C2×D1111yescharacteristic
323Q8⋊C8C2×D1111yescharacteristic
324Q8⋊C8C2×D1111yescharacteristic
325D4⋊C8—111no—
326D4⋊C8—111no—
327#322—111no—
328#322—111no—
329#322—111no—
330C82—111no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11C2×C4×D411yescharacteristic
335C2×D11—22no—
336C2×D11—41no—
337C2×D11—41no—
338C4×C11—21no—
339C4×C11—22no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11C22×M1611yescharacteristic
347C4×C11#56811yescharacteristic
348C4×C11C2×#13711yescharacteristic
349C4×C11#57511yescharacteristic
350Dic11—41no—
351Dic11—41no—
352Dic11—41no—
353C2×#41—111no—
354C22×Q8C4×D1111yescharacteristic
355#137—224no—
356C2×Q16—111no—
357C2×Q16—111no—
358C2×SD16—111no—
359C2×SD16—111no—
360C2×M16—21no—
361C2×M16—111no—
362C2×M16—111no—
363C2×M16—111no—
364C2×M16—111no—
365C2×M16—221no—
366C22×C8—221no—
367C22×C8—221no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—111no—
371C4×Q8—111no—
372C4×Q8C4×D1111yescharacteristic
373C4×Q8C4×D1111yescharacteristic
374C4×Q8C22×D1111yescharacteristic
375C4×Q8C22×D1111yescharacteristic
376C4×D4—111no—
377C4×D4—111no—
378C4×D4—221no—
379C4×D4—221no—
380#117—111no—
381#117—221no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4C4×D1111yescharacteristic
384C2×C42—21no—
385C2×C42—221no—
386C2×C42C22×D1111yescharacteristic
387#107—111no—
388#107—111no—
389#106—111no—
390#106—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8—221no—
399C4⋊C8—221no—
400C4⋊C8C22×D1111yescharacteristic
401C4⋊C8C22×D1111yescharacteristic
402#103—111no—
403#103—111no—
404#103—111no—
405#103—111no—
406#103—111no—
407#103—111no—
408#102—111no—
409#102—111no—
410C22⋊C8—21no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—21no—
414#97—21no—
415#97—111no—
416#97—111no—
417#97—111no—
418#97—111no—
419#97—221no—
420#97—221no—
421#97—221no—
422#97—221no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—111no—
426C4×C8—111no—
427C4×C8—221no—
428C4×C8—221no—
429C4×C8C22×D1111yescharacteristic
430C4×C8C22×D1111yescharacteristic
431C2×C11—41no—
432C2×C11D4×M1611yescharacteristic
433C2×C11C4×#13711yescharacteristic
434C2×C11#295611yescharacteristic
435D11—42no—
436#41—222no—
437#41—441no—
438C2×Q8—21no—
439C2×Q8—22no—
440C2×Q8—41no—
441C2×Q8—111no—
442C2×Q8C2×C4×D1111yescharacteristic
443C2×Q8C2×C4×D1111yescharacteristic
444C2×D4—111no—
445C2×D4—221no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4C2×C4×D1111yescharacteristic
452C22×C4D4×D1111yescharacteristic
453C22×C4#434111yescharacteristic
454Q16—222no—
455Q16—222no—
456SD16—114no—
457SD16—222no—
458M16—42no—
459M16—222no—
460M16—222no—
461M16—441no—
462M16—441no—
463M16—442no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—111no—
471C2×C8—111no—
472C2×C8—111no—
473C2×C8—111no—
474C2×C8—111no—
475C2×C8—111no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—442no—
479C2×C8—442no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—111no—
486C4⋊C4—111no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4C2×C4×D1111yescharacteristic
490C4⋊C4C2×C4×D1111yescharacteristic
491C22⋊C4—221no—
492C22⋊C4—221no—
493C22⋊C4—221no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—221no—
499C42—221no—
500C42—221no—
501C42C2×C4×D1111yescharacteristic
502C42D4×D1111yescharacteristic
503C42#434111yescharacteristic
504C42C23×D1111yescharacteristic
505C11#1804711yescharacteristic, complemented, Sylow
506C23—221no—
507C23(C22⋊D11)⋊C411yescharacteristic
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—42no—
512Q8—221no—
513Q8—221no—
514Q8M16×D1112yes—
515D4—112no—
516D4—221no—
517D4—442no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—81no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—442no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—881no—
536C2×C4(C22⋊D11)⋊C411yescharacteristic
537C2×C4(C22⋊D11)⋊C411yescharacteristic
538C2×C4(C22⋊D11)⋊C411yescharacteristic
539C2×C4C22×C4×D1111yescharacteristic
540C2×C4C2×D4×D1111yescharacteristic
541C2×C4C2×#434111yescharacteristic
542C8—22no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—112no—
547C8—112no—
548C8—221no—
549C8—221no—
550C8—221no—
551C8—221no—
552C8—221no—
553C8—221no—
554C8—441no—
555C8—441no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—222no—
560C22—441no—
561C22—441no—
562C22C2×(C22⋊D11)⋊C411yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—22no—
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—441no—
572C4—441no—
573C4—441no—
574C4C2×M16×D1111yescharacteristic
575C4#1062327611yescharacteristic
576C4D11×#13711yescharacteristic
577C4#1062330811yescharacteristic
578C2—41no—
579C2—442no—
580C2#1307734811yescharacteristic
581C2#1307743111yescharacteristic
582C2#1307752211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1491C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenter#1491D11
hypocenterC11#18047
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
2. Q8×#4318C2semidirect
4. #13067522C2semidirect
5. #13067510C2semidirect
6. #13067484C2semidirect
7. #13067476C2semidirect
8. #13067463C2semidirect
9. #13067455C2semidirect
10. #13067431C2semidirect
11. #13067413C2semidirect
12. #13067384C2semidirect
14. #13066919C2semidirect
15. C11×#1491C2semidirect
188. #4325M16semidirect
227. #1491D11semidirect
279. C11⋊C8#137semidirect
505. C11#18047semidirect

Maximal subgroups

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

subgroupindex
#130776282
Q8×#43182
C4×#669952
#130675222
#130675102
#130674842
#130674762
#130674632
#130674552
#130674312
#130674132
#130673842
#130670562
#130669192
C11×#14912
#1804711