Finite Group Databasebeta

← #14725313

Subgroups — #14725313

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#13077624C211yesmaximal, characteristic
2Q8×#4313C211yesmaximal, characteristic, complemented
3C4×#66968C211yesmaximal, characteristic
4#13067524C211yesmaximal, characteristic, complemented
5#13067514C211yesmaximal, characteristic, complemented
6#13067484C211yesmaximal, characteristic, complemented
7#13067470C211yesmaximal, characteristic, complemented
8#13067466C211yesmaximal, characteristic, complemented
9#13067452C211yesmaximal, characteristic, complemented
10SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11#13067380C211yesmaximal, characteristic, complemented
12#13067061C211yesmaximal, characteristic, complemented
13#13067052C211yesmaximal, characteristic
14#13066918C211yesmaximal, characteristic, complemented
15C8×C11×SD16C211yesmaximal, characteristic, complemented
16C2×#66968C411yescharacteristic
17C4×Q8×D11C2211yescharacteristic
18C4×#4341C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C4×C11×SD16C2211yescharacteristic
21C8×D4×C11C2211yescharacteristic
22#10622777C411yescharacteristic
23#10622724—21no—
24C2×#66879—21no—
25C4×#4326C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622474C411yescharacteristic
30#10622466C411yescharacteristic
31#10622450—21no—
32#10622450C2211yescharacteristic
33#10622448C2211yescharacteristic
34#10622444—21no—
35#10622444C2211yescharacteristic
36#10622444C2211yescharacteristic
37#10622415C411yescharacteristic
38#10622402C411yescharacteristic
39#10622384C411yescharacteristic
40#10622370C411yescharacteristic
41#10622343—21no—
42#10622332—21no—
43C4×Dic44C2211yescharacteristic
44C4×#4313—21no—
45C4×#4313C2211yescharacteristic
46C4×#4313C2211yescharacteristic
47C4×#4313C2211yescharacteristic
48#10622292—21no—
49#10622292C2211yescharacteristic
50#10622292C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C82×C11C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622096C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622093C2211yescharacteristic
66#10622093C2211yescharacteristic
67C2×Q8×D11C2×C411yescharacteristic
68C2×#4341C2×C411yescharacteristic
69C2×C11×SD16C2×C411yescharacteristic
70C22×C8×C11—21no—
71C4×Q8×C11C2311yescharacteristic
72C4×D4×C11C2311yescharacteristic
73Q8×Dic11C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75D4×Dic11C2×C411yescharacteristic
76C2×#4324C2×C411yescharacteristic
77C4×C22⋊D11—21no—
78C2×C4×Dic11—21no—
79C22×C11⋊C8—21no—
80#66968—24no—
81C2×Dic44C2×C411yescharacteristic
82C2×#4313—21no—
83C2×#4313—21no—
84C2×#4313C2×C411yescharacteristic
85C2×#4313C2×C411yescharacteristic
86C2×#4313D411yescharacteristic
87C2×#4313D411yescharacteristic
88#66945C2×C411yescharacteristic
89C4⋊C4×D11—21no—
90C4⋊C4×D11C2×C411yescharacteristic
91#66940—21no—
92#66940C2×C411yescharacteristic
93#66940C2×C411yescharacteristic
94(C22⋊D11)⋊C4—21no—
95#66930—21no—
96C42×D11—21no—
97C42×D11C2311yescharacteristic
98C4×Dic22—21no—
99C4×Dic22C2311yescharacteristic
100C4×Dic22C2311yescharacteristic
101C11×#106C2×C411yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×#103C2×C411yescharacteristic
106C11×#102C2×C411yescharacteristic
107C11×C22⋊C8—21no—
108C4×C8×C11—21no—
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66899C2×C411yescharacteristic
113#66896C2×C411yescharacteristic
114C22⋊(C11⋊C8)—21no—
115(C2×D11)⋊C8—21no—
116#66882C2×C411yescharacteristic
117#66880C2×C411yescharacteristic
118#66880C2×C411yescharacteristic
119#66879—21no—
120#66879—21no—
121#66879—21no—
122#66879—21no—
123#66879—21no—
124#66879—21no—
125#66879C2×C411yescharacteristic
126#66879C2×C411yescharacteristic
127#66879D411yescharacteristic
128#66879D411yescharacteristic
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134#66874C2×C411yescharacteristic
135#66874C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137#66871C2×C411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18047—111nomaximal, Sylow
146C2×Q8×C11C22×C411yescharacteristic
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152Q8×D11—22no—
153Q8×D11—41no—
154#4341—22no—
155#4341—41no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11C22×C411yescharacteristic
159C2×C4×D11C2×D411yescharacteristic
160C2×C4×D11#4111yescharacteristic
161C2×Dic22—21no—
162C2×Dic22C22×C411yescharacteristic
163C2×Dic22C22×C411yescharacteristic
164C11×SD16M1614yescomplemented
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—42no—
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C11×C4⋊C4—21no—
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C22⋊C4—21no—
177C42×C11—21no—
178C42×C11C2411yescharacteristic
179C22⋊Dic11—21no—
180#4326—22no—
181#4324—22no—
182(C2×D11)⋊C4—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11C22×C411yescharacteristic
185C4⋊Dic11C22×C411yescharacteristic
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11C22×C411yescharacteristic
198C4×Dic11C2×D411yescharacteristic
199C4×Dic11#4111yescharacteristic
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—42no—
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208Dic44—22no—
209#4313—22no—
210#4313—22no—
211#4313—41no—
212#4313—41no—
213#4313—42no—
214#4313—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×SD16D1111yescharacteristic, complemented
226#1569—111no—
227#1491—111no—
228#1489—111no—
229#1455—111no—
230C23×C11—21no—
231C22×D11C4×D411yescharacteristic
232Q8×C11—21no—
233Q8×C11C2×M1612yes—
234D4×C11—21no—
235D4×C11C2×M1612yes—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C22⋊D11—42no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—42no—
250C2×Dic11—81no—
251C2×Dic11C4×D411yescharacteristic
252C2×Dic11C4×D411yescharacteristic
253C2×Dic11C4×D411yescharacteristic
254C4×D11—21no—
255C4×D11—21no—
256C4×D11—21no—
257C4×D11—21no—
258C4×D11—41no—
259C4×D11—42no—
260C4×D11—81no—
261Dic22—21no—
262Dic22—21no—
263Dic22—21no—
264Dic22—21no—
265Dic22—42no—
266C8×C11—22no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—41no—
270C8×C11—41no—
271C8×C11C2×M1612yes—
272C8×C11#13712yescomplemented
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280C2×#137—111no—
281C4×#41—111no—
282C2×C4×Q8—111no—
283#446—111no—
284#446—111no—
285#446—111no—
286#446—111no—
287#446—221no—
288#446—221no—
289C8×Q8—111no—
290C8×Q8C2×D1111yescharacteristic
291#441—111no—
292#441—111no—
293#440—111no—
294#440—111no—
295C4×Q16—111no—
296C4×Q16—111no—
297C4×SD16—111no—
298C4×SD16C2×D1111yescharacteristic
299#435—221no—
300#435—221no—
301C8×D4—111no—
302C8×D4C2×D1111yescharacteristic
303#432—111no—
304#432—221no—
305#428—111no—
306#423—111no—
307#423—221no—
308#419—111no—
309#417—111no—
310C4×M16—111no—
311C4×M16—111no—
312C4×M16—111no—
313C4×M16—221no—
314C2×#97—221no—
315#335—111no—
316#335—111no—
317#334—111no—
318#334C2×D1111yescharacteristic
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322Q8⋊C8—111no—
323Q8⋊C8—111no—
324Q8⋊C8C2×D1111yescharacteristic
325D4⋊C8—111no—
326D4⋊C8C2×D1111yescharacteristic
327#322—111no—
328#322—111no—
329#322—111no—
330C82C2×D1111yescharacteristic
331C22×C11—22no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11C2×C4×D411yescharacteristic
335C2×D11—21no—
336C2×D11—21no—
337C2×D11—21no—
338C4×C11—22no—
339C4×C11—21no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11C22×M1611yescharacteristic
343C4×C11#56811yescharacteristic
344C4×C11C2×#13711yescharacteristic
345C4×C11#57511yescharacteristic
346Dic11—21no—
347Dic11—21no—
348Dic11—21no—
349Dic11—41no—
350Dic11—41no—
351Dic11—41no—
352Dic11—41no—
353C2×#41—111no—
354C22×Q8—111no—
355#137—224no—
356C2×Q16—111no—
357C2×Q16—111no—
358C2×SD16—111no—
359C2×SD16C4×D1111yescharacteristic
360C2×M16—111no—
361C2×M16—111no—
362C2×M16—111no—
363C2×M16—111no—
364C2×M16—221no—
365C2×M16—221no—
366C22×C8—21no—
367C22×C8—221no—
368C4×Q8—111no—
369C4×Q8—111no—
370C4×Q8—111no—
371C4×Q8—111no—
372C4×Q8—111no—
373C4×Q8—221no—
374C4×Q8—221no—
375C4×Q8C22×D1111yescharacteristic
376C4×D4—111no—
377C4×D4—221no—
378C4×D4—221no—
379C4×D4C22×D1111yescharacteristic
380#117—111no—
381#117—221no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—221no—
384C2×C42—111no—
385C2×C42—221no—
386C2×C42—221no—
387#107—111no—
388#107—111no—
389#106—111no—
390#106C4×D1111yescharacteristic
391C4⋊C8—21no—
392C4⋊C8—111no—
393C4⋊C8—111no—
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#103C4×D1111yescharacteristic
408#102—111no—
409#102C4×D1111yescharacteristic
410C22⋊C8—21no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—111no—
414#97—111no—
415#97—111no—
416#97—111no—
417#97—221no—
418#97—221no—
419#97—221no—
420#97—221no—
421#97—221no—
422#97—221no—
423C4×C8—21no—
424C4×C8—111no—
425C4×C8—111no—
426C4×C8—111no—
427C4×C8—221no—
428C4×C8C22×D1111yescharacteristic
429C4×C8C22×D1111yescharacteristic
430C4×C8C22×D1111yescharacteristic
431C2×C11—42no—
432C2×C11D4×M1611yescharacteristic
433C2×C11C4×#13711yescharacteristic
434C2×C11#295611yescharacteristic
435D11—41no—
436#41—222no—
437#41—441no—
438C2×Q8—111no—
439C2×Q8—111no—
440C2×Q8—221no—
441C2×Q8—222no—
442C2×Q8—441no—
443C2×Q8C2×C4×D1111yescharacteristic
444C2×D4—221no—
445C2×D4C2×C4×D1111yescharacteristic
446C22×C4—21no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454Q16—222no—
455Q16—222no—
456SD16—222no—
457SD16#431314yescomplemented
458M16—222no—
459M16—222no—
460M16—441no—
461M16—441no—
462M16—442no—
463M16—442no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—42no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—111no—
471C2×C8—111no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—442no—
476C2×C8C2×C4×D1111yescharacteristic
477C2×C8C2×C4×D1111yescharacteristic
478C2×C8D4×D1111yescharacteristic
479C2×C8D4×D1111yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—111no—
482C4⋊C4—111no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4C2×C4×D1111yescharacteristic
490C4⋊C4C2×C4×D1111yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—221no—
493C22⋊C4—221no—
494C42—21no—
495C42—111no—
496C42—111no—
497C42—111no—
498C42—221no—
499C42—221no—
500C42—221no—
501C42—221no—
502C42—221no—
503C42—221no—
504C42C23×D1111yescharacteristic
505C11#1804711yescharacteristic, complemented, Sylow
506C23—21no—
507C23—111no—
508Q8—21no—
509Q8—221no—
510Q8—221no—
511Q8—221no—
512Q8—221no—
513Q8—442no—
514Q8C2×#431312yes—
515D4—21no—
516D4—442no—
517D4C2×#431312yes—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—111no—
524C2×C4—111no—
525C2×C4—111no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—441no—
535C2×C4—442no—
536C2×C4—442no—
537C2×C4—881no—
538C2×C4—881no—
539C2×C4C22×C4×D1111yescharacteristic
540C2×C4C2×D4×D1111yescharacteristic
541C2×C4#41×D1111yescharacteristic
542C8—22no—
543C8—21no—
544C8—21no—
545C8—41no—
546C8—41no—
547C8—221no—
548C8—221no—
549C8—221no—
550C8—221no—
551C8—441no—
552C8—441no—
553C8—441no—
554C8C2×#431312yes—
555C8#6696812yescomplemented
556C22—22no—
557C22—41no—
558C22—41no—
559C22—221no—
560C22—221no—
561C22—221no—
562C22C4×D4×D1111yescharacteristic
563C4—21no—
564C4—22no—
565C4—41no—
566C4—41no—
567C4—221no—
568C4—221no—
569C4—221no—
570C4—441no—
571C4—441no—
572C4—441no—
573C4—441no—
574C4C22×#431311yescharacteristic
575C4#1062328111yescharacteristic
576C4C2×#6696811yescharacteristic
577C4#1062329911yescharacteristic
578C2—42no—
579C2—441no—
580C2D4×#431311yescharacteristic
581C2C4×#6696811yescharacteristic
582C2#1307752111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC8×C11×SD16C2
socleC22×C11C2×C4×D4
prime radicalC2×#4341C2×C4
cosocleC42×C11C24
hypercenterC8×SD16D11
hypocenterC11#18047
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
2. Q8×#4313C2semidirect
4. #13067524C2semidirect
5. #13067514C2semidirect
6. #13067484C2semidirect
7. #13067470C2semidirect
8. #13067466C2semidirect
9. #13067452C2semidirect
10. SD16⋊(C11⋊C8)C2semidirect
11. #13067380C2semidirect
12. #13067061C2semidirect
14. #13066918C2semidirect
15. C8×C11×SD16C2semidirect
164. C11×SD16M16semidirect
225. C8×SD16D11semidirect
272. C8×C11#137semidirect
457. SD16#4313semidirect
505. C11#18047semidirect
555. C8#66968semidirect

Maximal subgroups

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

subgroupindex
#130776242
Q8×#43132
C4×#669682
#130675242
#130675142
#130674842
#130674702
#130674662
#130674522
SD16⋊(C11⋊C8)2
#130673802
#130670612
#130670522
#130669182
C8×C11×SD162
#1804711