Finite Group Databasebeta

← #15626026

Subgroups — #15626026

Order 2816.

1654 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082006C211yesmaximal, characteristic
2#13079914C214yesmaximal, complemented
3#13079899C214yesmaximal, complemented
4#13079884C214yesmaximal, complemented
5#13079869C214yesmaximal, complemented
6#13079138C211yesmaximal, characteristic, complemented
7#13079126C211yesmaximal, characteristic, complemented
8#13078964C211yesmaximal, characteristic, complemented
9#13078941C211yesmaximal, characteristic, complemented
10#13078529C214yesmaximal, complemented
11#13078398C214yesmaximal, complemented
12C2×#10622613C211yesmaximal, characteristic, complemented
13C11×#3458C211yesmaximal, characteristic, complemented
14C11×#544—22no—
15C11×#544C2214yes—
16C11×#544C2214yes—
17C11×#543—22no—
18C11×#533—24no—
19C11×#533C2211yescharacteristic
20C11×#533C2211yescharacteristic
21C11×#533C2212yes—
22C2×C11×#117C2212yes—
23C2×C11×#117C2211yescharacteristic
24#10623322C2212yes—
25#10623066C2212yes—
26#10623065C2214yes—
27#10623059—24no—
28#10623049C2212yes—
29#10623046—22no—
30#10623025—22no—
31#10623008C2211yescharacteristic
32C4×#4339C2212yes—
33#10623001C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2212yes—
35#10622707C2214yescomplemented
36#10622706C2212yescomplemented
37#10622704C2214yescomplemented
38#10622702C2214yescomplemented
39#10622701C2212yescomplemented
40#10622700C2214yescomplemented
41#10622697C2214yescomplemented
42#10622693C2214yescomplemented
43#10622692C2212yescomplemented
44#10622691C2212yescomplemented
45#10622682C2212yescomplemented
46#10622681C2212yescomplemented
47#10622681C2212yescomplemented
48#10622680C2212yescomplemented
49#10622679C2214yescomplemented
50#10622679C2214yescomplemented
51#10622678C2214yescomplemented
52#10622677C2214yescomplemented
53#10622676C2214yescomplemented
54#10622676C2214yescomplemented
55#10622616C2214yes—
56#10622616C2214yes—
57#10622615C2214yes—
58#10622615C2214yes—
59#10622613C2214yes—
60#10622613C2212yes—
61#10622613C2212yes—
62#10622611C2214yes—
63#10622611C2214yes—
64#10622609C2214yes—
65#10622609C2214yes—
66#10622584C2214yes—
67#10622583C2214yes—
68#10622581C2214yes—
69#10622580C2214yes—
70C2×C4⋊(C11⋊C8)C2212yes—
71C2×#66867C2211yescharacteristic
72C2×C4×C11⋊C8C2211yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C2×#4339C2312yes—
75C11×C4⋊Q8—24no—
76C11×C4⋊Q8—24no—
77C11×C4⋊Q8C2312yes—
78C11×C4⋊Q8C2312yes—
79C11×C4⋊Q8C2314yes—
80C11×#125—24no—
81C11×#125—24no—
82C11×#125C2314yes—
83C11×#125C2312yes—
84C11×#125C2312yes—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—24no—
88C11×C22⋊Q8—24no—
89C11×C22⋊Q8—24no—
90C11×C22⋊Q8—24no—
91C11×C22⋊Q8—24no—
92C4×Q8×C11—22no—
93C4×Q8×C11—22no—
94C4×Q8×C11—24no—
95C11×#117—22no—
96C11×#117—22no—
97C11×#117D414yes—
98C11×#117C2314yes—
99C11×#117C2312yes—
100C11×#117C2312yes—
101C11×#117C2312yes—
102C11×#117C2312yes—
103C2×C11×C4⋊C4D412yes—
104C2×C11×C4⋊C4C2314yes—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4D412yes—
107C2×C42×C11—22no—
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110#67006—22no—
111#66983—22no—
112#66983C2314yes—
113#66982—22no—
114C4×C22⋊D11—24no—
115C4×C22⋊D11—24no—
116#66979C2312yes—
117#66977—22no—
118#66977C2314yes—
119C22×C11⋊C8C2312yes—
120C22×C11⋊C8C2312yes—
121#66951—24no—
122#66949—24no—
123#66947—24no—
124#66942—24no—
125#66938—24no—
126#66937—24no—
127#66936—24no—
128#66932—24no—
129#66928C2312yes—
130#66927C2311yescharacteristic
131C4×D44—22no—
132C4×D44C2314yes—
133#66925—22no—
134C42×D11—22no—
135#66923C2312yes—
136#66922C2311yescharacteristic
137#66922C2312yes—
138C4×Dic22—22no—
139C4×Dic22C2314yes—
140C22⋊(C11⋊C8)C2314yes—
141C22⋊(C11⋊C8)C2314yes—
142#66874C2314yes—
143#66874C2314yes—
144#66874C2314yes—
145#66874C2314yes—
146#66873C2314yes—
147#66873C2314yes—
148#66873C2314yes—
149#66873C2314yes—
150#66872C2314yes—
151#66872C2314yes—
152#66872C2314yes—
153#66872C2314yes—
154#66871C2314yes—
155#66871C2314yes—
156#66871C2314yes—
157#66871C2314yes—
158C4⋊(C11⋊C8)C2314yes—
159C4⋊(C11⋊C8)C2314yes—
160#66867C2312yes—
161#66867C2312yes—
162C4×C11⋊C8C2312yes—
163C4×C11⋊C8C2311yescharacteristic
164C4×C11⋊C8C2311yescharacteristic
165#60859—111nomaximal, Sylow
166C24×C11C2×D411yescharacteristic
167C2×Q8×C11—24no—
168C2×Q8×C11—22no—
169C2×Q8×C11—22no—
170C22×C4×C11—24no—
171C22×C4×C11—24no—
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2411yescharacteristic
178C2×C22⋊D11—22no—
179C2×C22⋊D11—24no—
180#4339—28no—
181C2×D44—22no—
182C2×D44C2412yes—
183C2×C4×D11—22no—
184C2×C4×D11—24no—
185C2×Dic22—22no—
186C2×Dic22C2412yes—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—24no—
194C11×C4⋊C4—24no—
195C11×C4⋊C4C2×D414yes—
196C11×C4⋊C4C2×D414yes—
197C11×C4⋊C4C2414yes—
198C11×C4⋊C4C2414yes—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4C2×D414yes—
203C11×C22⋊C4C2×D414yes—
204C42×C11—22no—
205C42×C11—22no—
206C42×C11—24no—
207C42×C11C2×D412yes—
208C42×C11C2×D412yes—
209C42×C11C2411yescharacteristic
210C42×C11C2411yescharacteristic
211C42×C11C2412yes—
212C22⋊Dic11—24no—
213C22⋊Dic11—22no—
214(C2×D11)⋊C4—24no—
215(C2×D11)⋊C4—24no—
216(C2×D11)⋊C4—24no—
217C4⋊Dic11—22no—
218C4⋊Dic11—22no—
219C4⋊Dic11C2414yes—
220Dic11⋊C4—24no—
221Dic11⋊C4—24no—
222Dic11⋊C4—24no—
223C4×Dic11—22no—
224C4×Dic11—24no—
225C2×C11⋊C8—24no—
226C2×C11⋊C8—24no—
227C2×C11⋊C8C2412yes—
228C2×C11⋊C8C2412yes—
229C2×C11⋊C8C2414yes—
230#3458D1111yescharacteristic, complemented
231#3455—111no—
232#3244—114no—
233#3243—114no—
234#3242—114no—
235#3241—114no—
236#3162—111no—
237#3160—111no—
238#3135—111no—
239#3131—111no—
240#3091—114no—
241#3076—114no—
242C2×#433—111no—
243C23×C11—22no—
244C23×C11—42no—
245C23×C11C22×D412yes—
246C23×C11C22×D411yescharacteristic
247C22×D11—22no—
248Q8×C11—82no—
249Q8×C11—84no—
250Q8×C11—82no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—84no—
259C2×C4×C11C22×D414yes—
260C2×C4×C11C22×D412yes—
261C2×C4×C11C22×D412yes—
262C2×C4×C11C22×D412yes—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C112−1+414yes—
265C2×C4×C11C2511yescharacteristic
266C22⋊D11—44no—
267C22⋊D11—84no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270D44—24no—
271D44—82no—
272C4×D11—44no—
273C4×D11—84no—
274Dic22—24no—
275Dic22—82no—
276C11⋊C8—22no—
277C11⋊C8—22no—
278C11⋊C8—24no—
279#544—22no—
280#544C2×D1114yes—
281#544C2×D1114yes—
282#543—22no—
283#542—114no—
284#541—112no—
285#540—112no—
286#539—222no—
287#538—222no—
288#533—24no—
289#533—111no—
290#533C2×D1112yes—
291#533C2×D1111yescharacteristic
292#533C2×D1111yescharacteristic
293#532—111no—
294#529—224no—
295#525—112no—
296C4×#41—112no—
297C2×#117C2×D1112yes—
298C2×#117C2×D1111yescharacteristic
299#501—114no—
300#501—114no—
301#500—112no—
302#499—114no—
303#498—112no—
304#491—112no—
305#490—112no—
306#489—114no—
307#488—112no—
308#488—112no—
309#487—112no—
310#486—112no—
311#485—114no—
312#485—114no—
313#484—114no—
314#483—114no—
315#482—114no—
316#482—114no—
317#481—114no—
318#480—114no—
319#479—114no—
320#479—114no—
321#478—114no—
322#478—114no—
323#477—114no—
324#476—114no—
325#475—114no—
326#474—114no—
327#433—114no—
328#433—112no—
329#433—112no—
330#427—114no—
331#427—114no—
332C2×C4⋊C8—112no—
333#416—114no—
334#416—114no—
335C2×C22⋊C8—112no—
336C2×#97—111no—
337C2×C4×C8—111no—
338C22×C11—22no—
339C22×C11—24no—
340C22×C11—22no—
341C22×C11—82no—
342C22×C11#53612yes—
343C22×C11C23×D411yescharacteristic
344C2×D11—44no—
345C2×D11—42no—
346C4×C11—22no—
347C4×C11—24no—
348C4×C11—22no—
349C4×C11—22no—
350C4×C11—44no—
351C4×C11—44no—
352C4×C11#53612yes—
353C4×C11C2×2−1+412yes—
354Dic11—44no—
355Dic11—42no—
356C2×#41—112no—
357C23×C4C22×D1111yescharacteristic
358C22×C8—112no—
359C22×C8—112no—
360C4⋊Q8—24no—
361C4⋊Q8—24no—
362C4⋊Q8—112no—
363C4⋊Q8—111no—
364C4⋊Q8C22×D1114yes—
365C4⋊Q8C22×D1112yes—
366C4⋊Q8C22×D1112yes—
367#127—111no—
368#126—224no—
369#126—224no—
370#125—24no—
371#125—24no—
372#125—112no—
373#125—224no—
374#125C22×D1114yes—
375#125C22×D1112yes—
376#125C22×D1112yes—
377#124—112no—
378#124—224no—
379#123—222no—
380#123—224no—
381#123—224no—
382C22⋊Q8—24no—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385C22⋊Q8—24no—
386C22⋊Q8—24no—
387C22⋊Q8—24no—
388C22⋊Q8—24no—
389C22⋊Q8—114no—
390C22⋊Q8—222no—
391C22⋊Q8—224no—
392#121—114no—
393#121—222no—
394#121—224no—
395#120—222no—
396C4×Q8—24no—
397C4×Q8—22no—
398C4×Q8—22no—
399C4×Q8—114no—
400C4×Q8—222no—
401C4×D4—114no—
402C4×D4—224no—
403C4×D4—224no—
404C4×D4—222no—
405#117—22no—
406#117—22no—
407#117—112no—
408#117—222no—
409#117C22⋊D1114yes—
410#117C22×D1112yes—
411#117C22×D1112yes—
412#117C22×D1114yes—
413#117C22×D1112yes—
414#117C22×D1112yes—
415C2×C4⋊C4C22⋊D1112yes—
416C2×C4⋊C4C22×D1114yes—
417C2×C22⋊C4—22no—
418C2×C22⋊C4C22⋊D1112yes—
419C2×C42—22no—
420C2×C42—222no—
421C2×C42C22×D1111yescharacteristic
422C2×C42C22×D1111yescharacteristic
423#107—114no—
424#107—114no—
425#107—114no—
426#107—114no—
427#106—114no—
428#106—114no—
429#106—114no—
430#106—114no—
431C4⋊C8—114no—
432C4⋊C8—114no—
433#103—114no—
434#103—114no—
435#103—114no—
436#103—114no—
437#102—114no—
438#102—114no—
439#102—114no—
440#102—114no—
441C22⋊C8—114no—
442C22⋊C8—114no—
443#97—112no—
444#97—112no—
445C4×C8—112no—
446C4×C8—111no—
447C4×C8—111no—
448C2×C11—22no—
449C2×C11—42no—
450C2×C11C2×#53611yescharacteristic
451C2×C11#358412yes—
452D11—82no—
453C24C2×C22⋊D1111yescharacteristic
454#41—228no—
455C2×Q8—24no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—112no—
459C2×Q8—222no—
460C2×D4—112no—
461C2×D4—222no—
462C2×D4—224no—
463C2×D4—222no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—222no—
467C22×C4—224no—
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1112yes—
470C22×C4C2×C22⋊D1112yes—
471C22×C4C2×C22⋊D1112yes—
472C22×C4C23×D1112yes—
473C22×C4C23×D1111yescharacteristic
474C2×C8—112no—
475C2×C8—112no—
476C2×C8—114no—
477C2×C8—224no—
478C2×C8—224no—
479C4⋊C4—24no—
480C4⋊C4—24no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—24no—
484C4⋊C4—24no—
485C4⋊C4—24no—
486C4⋊C4—24no—
487C4⋊C4—114no—
488C4⋊C4—224no—
489C4⋊C4—222no—
490C4⋊C4—224no—
491C4⋊C4—224no—
492C4⋊C4—222no—
493C4⋊C4C2×C22⋊D1114yes—
494C4⋊C4C2×C22⋊D1114yes—
495C4⋊C4C23×D1114yes—
496C4⋊C4C23×D1114yes—
497C22⋊C4—24no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—222no—
501C22⋊C4—224no—
502C22⋊C4—224no—
503C22⋊C4—224no—
504C22⋊C4—224no—
505C22⋊C4C2×C22⋊D1114yes—
506C22⋊C4C2×C22⋊D1114yes—
507C42—24no—
508C42—22no—
509C42—22no—
510C42—224no—
511C42—222no—
512C42C2×C22⋊D1112yes—
513C42C2×C22⋊D1112yes—
514C42C23×D1111yescharacteristic
515C42C23×D1111yescharacteristic
516C42C23×D1112yes—
517C11#6085911yescharacteristic, complemented, Sylow
518C23—22no—
519C23—42no—
520C23—222no—
521C23C22×C22⋊D1112yes—
522C23C22×C22⋊D1111yescharacteristic
523Q8—84no—
524Q8—82no—
525Q8—82no—
526Q8—224no—
527Q8—882no—
528D4—224no—
529D4—444no—
530D4—882no—
531D4—884no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—84no—
540C2×C4—224no—
541C2×C4—222no—
542C2×C4—444no—
543C2×C4—884no—
544C2×C4#6704014yes—
545C2×C4C22×C22⋊D1112yes—
546C2×C4C22×C22⋊D1114yes—
547C2×C4C22×C22⋊D1112yes—
548C2×C4C22×C22⋊D1112yes—
549C2×C4C22×C22⋊D1111yescharacteristic
550C2×C4C24×D1111yescharacteristic
551C8—222no—
552C8—222no—
553C8—224no—
554C22—22no—
555C22—22no—
556C22—24no—
557C22—82no—
558C22—442no—
559C22—444no—
560C22#1062334712yes—
561C22C23×C22⋊D1111yescharacteristic
562C4—22no—
563C4—24no—
564C4—22no—
565C4—22no—
566C4—44no—
567C4—44no—
568C4—442no—
569C4—444no—
570C4#1062334712yes—
571C4C2×#6704012yes—
572C2—22no—
573C2—42no—
574C2—882no—
575C2C2×#1062334711yescharacteristic
576C2#1308338712yes—
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3458C2
socleC22×C11C23×D4
prime radical#13082006C2
hypercenter#3458D11
hypocenterC11#60859
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#117 ◁ #3458

Complements

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

NH ≅ G/Ntype
2. #13079914C2semidirect
3. #13079899C2semidirect
4. #13079884C2semidirect
5. #13079869C2semidirect
6. #13079138C2semidirect
7. #13079126C2semidirect
8. #13078964C2semidirect
9. #13078941C2semidirect
10. #13078529C2semidirect
11. #13078398C2semidirect
12. C2×#10622613C2semidirect
13. C11×#3458C2semidirect
35. #10622707C22semidirect
36. #10622706C22semidirect
37. #10622704C22semidirect
38. #10622702C22semidirect
39. #10622701C22semidirect
40. #10622700C22semidirect
41. #10622697C22semidirect
42. #10622693C22semidirect
43. #10622692C22semidirect
44. #10622691C22semidirect
45. #10622682C22semidirect
46. #10622681C22semidirect
47. #10622681C22semidirect
48. #10622680C22semidirect
49. #10622679C22semidirect
50. #10622679C22semidirect
51. #10622678C22semidirect
52. #10622677C22semidirect
53. #10622676C22semidirect
54. #10622676C22semidirect
230. #3458D11semidirect
517. C11#60859semidirect

Maximal subgroups

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

subgroupindex
#130820062
#130799142
#130798992
#130798842
#130798692
#130791382
#130791262
#130789642
#130789412
#130785292
#130783982
C2×#106226132
C11×#34582
#6085911