Finite Group Databasebeta

← #14725354

Subgroups — #14725354

Order 2816.

640 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#13077634C211yesmaximal, characteristic
2M16×Dic22C211yesmaximal, characteristic, complemented
3C4×#66962C211yesmaximal, characteristic
4#13067520C211yesmaximal, characteristic, complemented
5#13067508C211yesmaximal, characteristic, complemented
6#13067496C211yesmaximal, characteristic, complemented
7#13067489C211yesmaximal, characteristic, complemented
8#13067468C211yesmaximal, characteristic, complemented
9#13067461C211yesmaximal, characteristic, complemented
10#13067436C211yesmaximal, characteristic, complemented
11C8×Dic44C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067064C211yesmaximal, characteristic, complemented
14#13067056C211yesmaximal, characteristic
15C11×#1455C211yesmaximal, characteristic, complemented
16C2×#66962C411yescharacteristic
17C4×#4339C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C4×C11×M16C2211yescharacteristic
20C4×C11×M16C2211yescharacteristic
21C4×C11×M16C2211yescharacteristic
22#10622746C411yescharacteristic
23#10622741—21no—
24#10622741—21no—
25#10622734C411yescharacteristic
26#10622733C411yescharacteristic
27#10622731—21no—
28M16×Dic11—21no—
29#10622539C2211yescharacteristic
30#10622537C2211yescharacteristic
31#10622329C411yescharacteristic
32#10622329C411yescharacteristic
33#10622323C411yescharacteristic
34#10622323C411yescharacteristic
35#10622320—21no—
36#10622318—21no—
37#10622314—21no—
38#10622314—21no—
39C4×Dic44C2211yescharacteristic
40C4×Dic44C2211yescharacteristic
41C4×#4314C2211yescharacteristic
42C4×#4314C2211yescharacteristic
43#10622301C2211yescharacteristic
44#10622301C2211yescharacteristic
45#10622292C2211yescharacteristic
46#10622292C2211yescharacteristic
47C8×Dic22C2211yescharacteristic
48C8×Dic22C2211yescharacteristic
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#322C2211yescharacteristic
52C11×#322C2211yescharacteristic
53C11×#322C2211yescharacteristic
54C82×C11C2211yescharacteristic
55#10622097C2211yescharacteristic
56#10622097C2211yescharacteristic
57#10622096C2211yescharacteristic
58#10622096C2211yescharacteristic
59#10622095C2211yescharacteristic
60#10622095C2211yescharacteristic
61#10622094C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622094C2211yescharacteristic
65#10622094C2211yescharacteristic
66#10622094C2211yescharacteristic
67C2×#4339C2×C411yescharacteristic
68C22×Dic22C2×C411yescharacteristic
69C2×C11×M16—21no—
70C2×C11×M16C2×C411yescharacteristic
71C2×C11×M16C2×C411yescharacteristic
72C2×C11×M16D411yescharacteristic
73C2×C11×M16D411yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C4×C22⋊D11—21no—
76C4×C22⋊D11—21no—
77#66979C2×C411yescharacteristic
78C2×C4⋊Dic11C2×C411yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×C4×Dic11—21no—
81C2×#4318—21no—
82#66962—24no—
83C2×Dic44C2×C411yescharacteristic
84C2×Dic44C2×C411yescharacteristic
85C2×#4314C2×C411yescharacteristic
86C2×#4314C2×C411yescharacteristic
87C2×#4313—21no—
88C2×#4313—21no—
89C4×D44C2×C411yescharacteristic
90C4×D44C2311yescharacteristic
91#66925—21no—
92C42×D11—21no—
93C4×Dic22—21no—
94C4×Dic22—21no—
95C4×Dic22C2×C411yescharacteristic
96C4×Dic22C2×C411yescharacteristic
97C4×Dic22C2×C411yescharacteristic
98C4×Dic22C2311yescharacteristic
99C4×Dic22C2311yescharacteristic
100C4×Dic22C2311yescharacteristic
101C11×#97—21no—
102C11×#97C2×C411yescharacteristic
103C11×#97C2×C411yescharacteristic
104C11×#97D411yescharacteristic
105C11×#97D411yescharacteristic
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C22⋊(C11⋊C8)—21no—
113#66885C2×C411yescharacteristic
114#66885C2×C411yescharacteristic
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8—21no—
117#66882C2×C411yescharacteristic
118#66882C2×C411yescharacteristic
119#66881C2×C411yescharacteristic
120#66881C2×C411yescharacteristic
121#66880C2×C411yescharacteristic
122#66880C2×C411yescharacteristic
123#66880C2×C411yescharacteristic
124#66880C2×C411yescharacteristic
125#66880C2×C411yescharacteristic
126#66880C2×C411yescharacteristic
127#66879—21no—
128#66879—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134Dic11⋊C8—21no—
135C8×Dic11—21no—
136C8×Dic11—21no—
137C8×Dic11—21no—
138C8×Dic11—21no—
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144#66867—21no—
145#18049—111nomaximal, Sylow
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C2×C22⋊D11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152#4339—22no—
153#4339—41no—
154C2×D44C22×C411yescharacteristic
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×Dic22—22no—
159C2×Dic22—21no—
160C2×Dic22—41no—
161C2×Dic22C22×C411yescharacteristic
162C2×Dic22C22×C411yescharacteristic
163C2×Dic22C22×C411yescharacteristic
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—41no—
167C11×M16—41no—
168C11×M16—42no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C22×C411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C42×C11C22×C411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11#4111yescharacteristic
182C42×C11C2411yescharacteristic
183C22⋊Dic11—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11C22×C411yescharacteristic
188C4⋊Dic11C22×C411yescharacteristic
189C4⋊Dic11C22×C411yescharacteristic
190C4⋊Dic11C22×C411yescharacteristic
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204#4318—42no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209Dic44—22no—
210Dic44M1614yescomplemented
211#4314—22no—
212#4314—22no—
213#4313—42no—
214#4313—42no—
215#2971—111no—
216Q8×M16—111no—
217C4×#137—111no—
218#1592—111no—
219#1590—111no—
220#1588—111no—
221#1587—111no—
222#1584—111no—
223#1583—111no—
224#1579—111no—
225C8×Q16—111no—
226#1569—111no—
227#1491—111no—
228#1489—111no—
229#1455D1111yescharacteristic, complemented
230C23×C11C4×D411yescharacteristic
231C22×D11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—41no—
237C2×C4×C11C4×D411yescharacteristic
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11C4×D411yescharacteristic
240C2×C4×C11C23×C411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C22⋊D11—42no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—42no—
252C2×Dic11—81no—
253D44—21no—
254D44—21no—
255C4×D11—42no—
256C4×D11—41no—
257C4×D11—41no—
258C4×D11—81no—
259Dic22—21no—
260Dic22—21no—
261Dic22—21no—
262Dic22—21no—
263Dic22—42no—
264Dic22C2×M1612yes—
265Dic22C2×M1612yes—
266C8×C11—22no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—41no—
274C8×C11C2×M1612yes—
275C8×C11#13712yescomplemented
276C11⋊C8—41no—
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—221no—
286#446—221no—
287C8×Q8—111no—
288C8×Q8—111no—
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#436—111no—
300#436—111no—
301#436—221no—
302#436—221no—
303#432—111no—
304#432—221no—
305#428—111no—
306#423—111no—
307#423—221no—
308#419—111no—
309#417—111no—
310C4×M16—221no—
311C4×M16—221no—
312C4×M16C2×D1111yescharacteristic
313C4×M16C2×D1111yescharacteristic
314C4×M16C2×D1111yescharacteristic
315#335—111no—
316#335—111no—
317#334—111no—
318#334—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322Q8⋊C8—111no—
323Q8⋊C8—111no—
324Q8⋊C8—111no—
325D4⋊C8—111no—
326D4⋊C8—111no—
327#322C2×D1111yescharacteristic
328#322C2×D1111yescharacteristic
329#322C2×D1111yescharacteristic
330C82C2×D1111yescharacteristic
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11C2×C4×D411yescharacteristic
335C2×D11—41no—
336C2×D11—41no—
337C2×D11—41no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11C22×M1611yescharacteristic
343C4×C11#56811yescharacteristic
344C4×C11C2×#13711yescharacteristic
345C4×C11#57511yescharacteristic
346Dic11—22no—
347Dic11—22no—
348Dic11—41no—
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×SD16—111no—
360C2×M16—21no—
361C2×M16—221no—
362C2×M16—221no—
363C2×M16—221no—
364C2×M16C4×D1111yescharacteristic
365C2×M16C4×D1111yescharacteristic
366C2×M16D4411yescharacteristic
367C2×M16D4411yescharacteristic
368C4×Q8—111no—
369C4×Q8—111no—
370C4×Q8—111no—
371C4×Q8—111no—
372C4×Q8—111no—
373C4×Q8—111no—
374C4×Q8—221no—
375C4×Q8—221no—
376C4×D4—111no—
377C4×D4—111no—
378C4×D4—221no—
379C4×D4—221no—
380#117—111no—
381#117—221no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—221no—
384C2×C42—221no—
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—111no—
394C4⋊C8—111no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8—221no—
399C4⋊C8—221no—
400C4⋊C8—221no—
401C4⋊C8—221no—
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—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—21no—
414#97—221no—
415#97—221no—
416#97—221no—
417#97C4×D1111yescharacteristic
418#97C4×D1111yescharacteristic
419#97D4411yescharacteristic
420#97D4411yescharacteristic
421C4×C8—221no—
422C4×C8—221no—
423C4×C8—221no—
424C4×C8—221no—
425C4×C8C22×D1111yescharacteristic
426C4×C8C22×D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C4×C8C22×D1111yescharacteristic
429C4×C8C22×D1111yescharacteristic
430C4×C8C22×D1111yescharacteristic
431C2×C11—41no—
432C2×C11D4×M1611yescharacteristic
433C2×C11C4×#13711yescharacteristic
434C2×C11#295611yescharacteristic
435D11—81no—
436#41—222no—
437#41—441no—
438C2×Q8—111no—
439C2×Q8—111no—
440C2×Q8—111no—
441C2×Q8—222no—
442C2×Q8—221no—
443C2×Q8—441no—
444C2×D4—111no—
445C2×D4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4C2×C4×D1111yescharacteristic
452C22×C4C2×D4411yescharacteristic
453C22×C4#433911yescharacteristic
454Q16—114no—
455Q16—222no—
456SD16—222no—
457SD16—222no—
458M16—22no—
459M16—22no—
460M16—41no—
461M16—41no—
462M16—42no—
463M16—442no—
464M16—442no—
465M16—442no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8C2×C4×D1111yescharacteristic
473C2×C8C2×C4×D1111yescharacteristic
474C2×C8C2×C4×D1111yescharacteristic
475C2×C8C2×C4×D1111yescharacteristic
476C2×C8C2×D4411yescharacteristic
477C2×C8C2×D4411yescharacteristic
478C2×C8C2×D4411yescharacteristic
479C2×C8C2×D4411yescharacteristic
480C4⋊C4—111no—
481C4⋊C4—111no—
482C4⋊C4—111no—
483C4⋊C4—111no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C22⋊C4—221no—
492C22⋊C4—221no—
493C22⋊C4—221no—
494C42—221no—
495C42—221no—
496C42—221no—
497C42—221no—
498C42—221no—
499C42—221no—
500C42—221no—
501C42C2×C4×D1111yescharacteristic
502C42C2×D4411yescharacteristic
503C42#433911yescharacteristic
504C42C23×D1111yescharacteristic
505C11#1804911yescharacteristic, complemented, Sylow
506C23—221no—
507C23C4×D4411yescharacteristic
508Q8—112no—
509Q8—112no—
510Q8—221no—
511Q8—221no—
512Q8—221no—
513Q8—221no—
514Q8—442no—
515D4—221no—
516D4—221no—
517D4—442no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—881no—
535C2×C4—881no—
536C2×C4C4×D4411yescharacteristic
537C2×C4C4×D4411yescharacteristic
538C2×C4C4×D4411yescharacteristic
539C2×C4C22×C4×D1111yescharacteristic
540C2×C4C22×D4411yescharacteristic
541C2×C4C2×#433911yescharacteristic
542C8—22no—
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—41no—
550C8—441no—
551C8—441no—
552C8—441no—
553C8—441no—
554C8M16×D1112yes—
555C8#6696212yescomplemented
556C22—21no—
557C22—21no—
558C22—21no—
559C22—441no—
560C22—441no—
561C22—441no—
562C22C2×C4×D4411yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—222no—
568C4—222no—
569C4—441no—
570C4—441no—
571C4—441no—
572C4—441no—
573C4—441no—
574C4C2×M16×D1111yescharacteristic
575C4#1062327611yescharacteristic
576C4C2×#6696211yescharacteristic
577C4#1062327911yescharacteristic
578C2—41no—
579C2—881no—
580C2M16×D4411yescharacteristic
581C2C4×#6696211yescharacteristic
582C2#1307752711yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1455C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenter#1455D11
hypocenterC11#18049
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1455

Complements

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

NH ≅ G/Ntype
2. M16×Dic22C2semidirect
4. #13067520C2semidirect
5. #13067508C2semidirect
6. #13067496C2semidirect
7. #13067489C2semidirect
8. #13067468C2semidirect
9. #13067461C2semidirect
10. #13067436C2semidirect
11. C8×Dic44C2semidirect
12. #13067383C2semidirect
13. #13067064C2semidirect
15. C11×#1455C2semidirect
210. Dic44M16semidirect
229. #1455D11semidirect
275. C8×C11#137semidirect
505. C11#18049semidirect
555. C8#66962semidirect

Maximal subgroups

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

subgroupindex
#130776342
M16×Dic222
C4×#669622
#130675202
#130675082
#130674962
#130674892
#130674682
#130674612
#130674362
C8×Dic442
#130673832
#130670642
#130670562
C11×#14552
#1804911