Finite Group Databasebeta

← #15624181

Subgroups — #15624181

Order 2816.

1846 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082514C211yesmaximal, characteristic
2#13082503C211yesmaximal, characteristic, complemented
3#13079327C214yesmaximal, complemented
4#13079289C218yesmaximal, complemented
5#13079224C214yesmaximal, complemented
6C2×#10622328C211yesmaximal, characteristic, complemented
7#13079005C211yesmaximal, characteristic, complemented
8#13078998C211yesmaximal, characteristic, complemented
9#13078272C212yesmaximal, complemented
10#13078256C212yesmaximal
11#13077483C212yesmaximal, complemented
12#13077474C212yesmaximal, complemented
13#13077041C211yesmaximal, characteristic, complemented
14C11×#3162C211yesmaximal, characteristic, complemented
15C11×#533C2211yescharacteristic
16C11×#533C2211yescharacteristic
17C22×Dic44C2212yes—
18C22×#4314C2212yes—
19C2×#66954C2212yes—
20#10623264C2214yes—
21#10623259C2214yescomplemented
22#10623228C2214yescomplemented
23#10623222C2214yes—
24#10623173—24no—
25#10623168—24no—
26#10623116—22no—
27#10623115—22no—
28#10623115—22no—
29#10623101—22no—
30#10623057C2211yescharacteristic
31#10623057C2212yes—
32#10623056C2211yescharacteristic
33#10623052C2211yescharacteristic
34#10623047C2212yes—
35#10623047C2211yescharacteristic
36C2×#66928C2211yescharacteristic
37C4×#4339C2211yescharacteristic
38C2×#66922C2211yescharacteristic
39C11×#501C2212yescomplemented
40C11×#501C2212yescomplemented
41C11×#501C2214yescomplemented
42C11×#427C2212yes—
43C11×#427C2212yes—
44C2×C11×#97C2211yescharacteristic
45#10622714C2212yes—
46#10622706C2214yescomplemented
47#10622702C2214yes—
48#10622682C2214yescomplemented
49#10622681C2214yes—
50#10622617C2212yes—
51#10622617C2212yes—
52#10622617C2212yes—
53#10622614C2212yes—
54C4×#4318C2211yescharacteristic
55#10622502C2218yes—
56#10622500C2218yescomplemented
57#10622499C2218yes—
58#10622486C2218yescomplemented
59#10622481C2218yescomplemented
60#10622477C2218yes—
61#10622466C2218yescomplemented
62#10622465C2218yes—
63#10622328C2212yes—
64#10622328C2212yes—
65#10622328C2214yes—
66#10622321C2214yescomplemented
67#10622320C2212yescomplemented
68D11×#97C2212yescomplemented
69C2×#4339C2311yescharacteristic
70C22×D44C2311yescharacteristic
71C22×Dic22C2312yes—
72C22×Dic22C2311yescharacteristic
73C22×C8×C11C2312yes—
74C11×C4⋊Q8C2312yes—
75C11×C4⋊Q8C2312yes—
76C11×#125C2312yes—
77C11×#125C2312yes—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C11×#117C2311yescharacteristic
83C11×#117C2312yes—
84C11×#117C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86#67000—24no—
87#66999—24no—
88#66999—24no—
89Q8×Dic11—24no—
90C4×C22⋊D11D414yes—
91C2×(C2×D11)⋊C4—22no—
92#66979C2311yescharacteristic
93C2×C4⋊Dic11—22no—
94C2×#4318C2312yes—
95C2×Dic44—28no—
96C2×Dic44C2314yes—
97C2×Dic44C2314yes—
98C2×#4314—28no—
99C2×#4314C2314yes—
100C2×#4314C2314yes—
101#66954—28no—
102C2×#4313C2314yes—
103C2×C8×D11C2314yes—
104#66951—28no—
105#66951—24no—
106#66951—24no—
107#66950C2318yes—
108#66950C2314yes—
109#66948C2314yes—
110#66947—24no—
111#66947—24no—
112#66946—24no—
113#66946C2314yes—
114#66945—24no—
115#66945—24no—
116#66943—28no—
117#66943—24no—
118#66940C2318yes—
119#66940C2314yes—
120#66939—22no—
121#66939—24no—
122#66935—22no—
123C22⋊C4×D11—22no—
124#66930—22no—
125#66930—24no—
126#66928—22no—
127#66928—21no—
128#66928—21no—
129#66928—22no—
130#66928C2312yes—
131#66928C2312yes—
132#66927—21no—
133C4×D44—22no—
134C4×D44D412yes—
135#66925C2312yes—
136C42×D11C2312yes—
137#66922—22no—
138#66922—21no—
139#66922—22no—
140#66922C2312yes—
141#66922C2312yes—
142C4×Dic22—24no—
143C4×Dic22—22no—
144C4×Dic22D412yes—
145C11×#107C2314yes—
146C11×#107C2314yes—
147C11×#106C2314yes—
148C11×#106C2314yes—
149C11×#97C2311yescharacteristic
150C11×#97C2311yescharacteristic
151C11×#97C2312yes—
152#66879C2314yes—
153C8×Dic11C2314yes—
154#66874C2318yes—
155#66874C2318yes—
156#66874C2318yes—
157#66873C2318yes—
158#66867C2312yes—
159C4×C11⋊C8C2312yes—
160#60720—111nomaximal, Sylow
161C23×D11—21no—
162C2×Q8×C11—22no—
163C2×Q8×C11—22no—
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2411yescharacteristic
166C2×C22⋊D11C2×D412yes—
167C22×Dic11—22no—
168C22×Dic11—21no—
169#4339—24no—
170C2×D44—24no—
171C2×D44—21no—
172C2×D44—24no—
173C2×D44C2×D411yescharacteristic
174C2×D44C2412yes—
175C2×C4×D11—24no—
176C2×C4×D11C2×D414yes—
177C2×C4×D11C2412yes—
178C2×Dic22—22no—
179C2×Dic22—21no—
180C2×Dic22—24no—
181C2×Dic22—24no—
182C2×Dic22—24no—
183C2×Dic22C2×D411yescharacteristic
184C2×Dic22C2414yes—
185C2×Dic22C2412yes—
186C2×C8×C11#4118yes—
187C2×C8×C11C2412yes—
188C2×C8×C11C2412yes—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4C2414yes—
195C11×C4⋊C4C2412yes—
196C11×C4⋊C4C2412yes—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—21no—
200C42×C11—22no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11C2×D412yes—
204C42×C11C2411yescharacteristic
205C42×C11C2411yescharacteristic
206C22⋊Dic11C2×D412yes—
207(C2×D11)⋊C4—24no—
208(C2×D11)⋊C4—24no—
209(C2×D11)⋊C4—28no—
210(C2×D11)⋊C4—24no—
211(C2×D11)⋊C4—24no—
212(C2×D11)⋊C4—24no—
213(C2×D11)⋊C4C2×D414yes—
214C4⋊Dic11—28no—
215C4⋊Dic11—24no—
216C4⋊Dic11—24no—
217C4⋊Dic11—24no—
218C4⋊Dic11C2×D412yes—
219Dic11⋊C4—28no—
220Dic11⋊C4—24no—
221Dic11⋊C4C2×D414yes—
222C4×Dic11—28no—
223C4×Dic11—24no—
224C4×Dic11C2×D414yes—
225C4×Dic11C2412yes—
226#4318—24no—
227C2×C11⋊C8C2414yes—
228Dic44—28no—
229Dic44—28no—
230#4314—28no—
231#4314—28no—
232#4313—28no—
233C8×D11—28no—
234#3510—111no—
235#3509—111no—
236#3181—114no—
237#3178—118no—
238#3172—114no—
239#3162D1111yescharacteristic, complemented
240C2×#497—111no—
241#3140—111no—
242#3139—111no—
243#3059—112no—
244#3057—112no—
245#2950—112no—
246#2949—112no—
247#2875—111no—
248C23×C11C22×D411yescharacteristic
249C22×D11—22no—
250C22×D11—42no—
251C22×D11—82no—
252C22×D11C22×D412yes—
253Q8×C11—44no—
254Q8×C11—82no—
255C2×C4×C11—24no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—42no—
259C2×C4×C11C22×D412yes—
260C2×C4×C11C22×D412yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4114yes—
263C2×C4×C11C2511yescharacteristic
264C22⋊D11—24no—
265C2×Dic11—24no—
266C2×Dic11—22no—
267C2×Dic11—44no—
268C2×Dic11—42no—
269C2×Dic11C22×D414yes—
270C2×Dic11C22×D412yes—
271D44—22no—
272D44—24no—
273D44—42no—
274D44—84no—
275C4×D11—24no—
276C4×D11—44no—
277C4×D11—84no—
278Dic22—22no—
279Dic22—24no—
280Dic22—24no—
281Dic22—24no—
282Dic22—44no—
283Dic22—42no—
284C8×C11C2×#4114yes—
285C8×C11C2×#4114yes—
286C11⋊C8—24no—
287C22×Q16—112no—
288C22×SD16—112no—
289C2×#131—112no—
290#559—222no—
291#557—222no—
292#556—222no—
293#556—222no—
294#552—224no—
295#551—224no—
296#542—114no—
297#541—114no—
298#536—112no—
299#536—111no—
300#535—111no—
301#533—114no—
302#533C2×D1111yescharacteristic
303#533C2×D1111yescharacteristic
304C2×C4⋊Q8—111no—
305#529—114no—
306C2×#124—111no—
307#519—112no—
308#519—111no—
309#518—111no—
310C4×#41—111no—
311#501C2×D1112yescomplemented
312#501C2×D1114yescomplemented
313#501C2×D1112yescomplemented
314#497—112no—
315#497—114no—
316#497—112no—
317#491—114no—
318#489—114no—
319#488—114no—
320#487—114no—
321#470—118no—
322#468—118no—
323#467—118no—
324#465—118no—
325#441—118no—
326#440—118no—
327C4×Q16—118no—
328C4×SD16—118no—
329#427C2×D1112yes—
330#427C2×D1112yes—
331#419—112no—
332#419—112no—
333#419—112no—
334#418—112no—
335#405—112no—
336#405—114no—
337C4×M16—111no—
338C4×M16—112no—
339C2×#97—112no—
340C2×#97C2×D1111yescharacteristic
341C22×C11—22no—
342C22×C11#53212yes—
343C22×C11C23×D411yescharacteristic
344C2×D11—24no—
345C2×D11—22no—
346C2×D11—44no—
347C2×D11—42no—
348C2×D11—162no—
349C4×C11—22no—
350C4×C11—22no—
351C4×C11—44no—
352C4×C11—42no—
353C4×C11—42no—
354C4×C11#53212yes—
355C4×C11C22×#4112yes—
356Dic11—24no—
357Dic11—22no—
358Dic11—44no—
359Dic11—42no—
360C2×#41—111no—
361C22×Q8—111no—
362C22×Q8—112no—
363C22×D4—111no—
364C2×Q16—114no—
365C2×Q16—114no—
366C2×Q16—228no—
367C2×SD16—114no—
368C2×SD16—114no—
369C2×SD16—228no—
370#131—228no—
371C2×M16—112no—
372C2×M16—114no—
373C22×C8—114no—
374C22×C8C22×D1112yes—
375C4⋊Q8—112no—
376C4⋊Q8—112no—
377C4⋊Q8—221no—
378C4⋊Q8—222no—
379C4⋊Q8—222no—
380C4⋊Q8C22×D1112yes—
381C4⋊Q8C22×D1112yes—
382#127—221no—
383#126—224no—
384#126—228no—
385#126—224no—
386#125—224no—
387#125—228no—
388#125C22×D1112yes—
389#125C22×D1112yes—
390#124—112no—
391#124—112no—
392#124—222no—
393#124—221no—
394#124—221no—
395#124—224no—
396#124—222no—
397#123—222no—
398#123—224no—
399#123—224no—
400#123—224no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C22⋊Q8—114no—
404C22⋊Q8—118no—
405C22⋊Q8—224no—
406C22⋊Q8—224no—
407#121—114no—
408#120—222no—
409C4×Q8—22no—
410C4×Q8—22no—
411C4×Q8—112no—
412C4×Q8—114no—
413C4×Q8—118no—
414C4×Q8—224no—
415C4×Q8—222no—
416C4×Q8—224no—
417C4×D4—114no—
418C4×D4—114no—
419C4×D4—112no—
420C4×D4—222no—
421C4×D4—224no—
422#117—111no—
423#117—112no—
424#117—224no—
425#117—222no—
426#117—224no—
427#117—224no—
428#117C22×D1111yescharacteristic
429#117C22×D1111yescharacteristic
430#117C22×D1112yes—
431C2×C4⋊C4—222no—
432C2×C22⋊C4—222no—
433C2×C22⋊C4—222no—
434C2×C42—112no—
435C2×C42C22×D1111yescharacteristic
436#107C22×D1114yes—
437#107C22×D1114yes—
438#106C22×D1114yes—
439#106C22×D1114yes—
440#103—118no—
441#103—118no—
442#103—118no—
443#102—118no—
444#97—114no—
445#97—112no—
446#97C22×D1111yescharacteristic
447#97C22×D1111yescharacteristic
448#97C22×D1112yes—
449C4×C8—114no—
450C4×C8—112no—
451C2×C11—22no—
452C2×C11C2×#53211yescharacteristic
453C2×C11#358612yes—
454D11—42no—
455D11—82no—
456C24—221no—
457#41—224no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—111no—
461C2×Q8—112no—
462C2×Q8—114no—
463C2×Q8—221no—
464C2×Q8—222no—
465C2×Q8—224no—
466C2×Q8—224no—
467C2×Q8—224no—
468C2×D4—112no—
469C2×D4—111no—
470C2×D4—112no—
471C2×D4—224no—
472C2×D4—221no—
473C2×D4—224no—
474C22×C4—112no—
475C22×C4—114no—
476C22×C4—224no—
477C22×C4—221no—
478C22×C4—222no—
479C22×C4D4×D1112yes—
480C22×C4C23×D1111yescharacteristic
481Q16—228no—
482Q16—228no—
483SD16—228no—
484SD16—228no—
485M16—224no—
486M16—228no—
487C2×C8—114no—
488C2×C8—228no—
489C2×C8#434318yes—
490C2×C8C23×D1112yes—
491C2×C8C23×D1112yes—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—24no—
497C4⋊C4—112no—
498C4⋊C4—114no—
499C4⋊C4—224no—
500C4⋊C4—228no—
501C4⋊C4—224no—
502C4⋊C4—228no—
503C4⋊C4—224no—
504C4⋊C4—224no—
505C4⋊C4C23×D1114yes—
506C4⋊C4C23×D1112yes—
507C4⋊C4C23×D1112yes—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—22no—
511C22⋊C4—112no—
512C22⋊C4—114no—
513C22⋊C4—224no—
514C22⋊C4—224no—
515C22⋊C4—228no—
516C22⋊C4—224no—
517C22⋊C4—224no—
518C22⋊C4—224no—
519C42—21no—
520C42—21no—
521C42—22no—
522C42—114no—
523C42—112no—
524C42—224no—
525C42—228no—
526C42D4×D1112yes—
527C42C23×D1111yescharacteristic
528C42C23×D1111yescharacteristic
529C11#6072011yescharacteristic, complemented, Sylow
530C23—112no—
531C23—222no—
532C23—442no—
533C23—882no—
534C23C2×D4×D1111yescharacteristic
535Q8—44no—
536Q8—82no—
537Q8—222no—
538Q8—224no—
539Q8—224no—
540Q8—224no—
541Q8—442no—
542Q8—444no—
543D4—224no—
544D4—222no—
545D4—224no—
546D4—442no—
547D4—884no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—42no—
552C2×C4—114no—
553C2×C4—112no—
554C2×C4—224no—
555C2×C4—222no—
556C2×C4—224no—
557C2×C4—444no—
558C2×C4—442no—
559C2×C4—444no—
560C2×C4—884no—
561C2×C4C2×D4×D1112yes—
562C2×C4C2×D4×D1112yes—
563C2×C4C2×D4×D1111yescharacteristic
564C2×C4C2×#434314yes—
565C2×C4C24×D1111yescharacteristic
566C8—224no—
567C8C2×#434314yes—
568C8C2×#434314yes—
569C22—22no—
570C22—224no—
571C22—222no—
572C22—444no—
573C22—442no—
574C22—1762no—
575C22#1062325612yes—
576C22C22×D4×D1111yescharacteristic
577C4—22no—
578C4—22no—
579C4—42no—
580C4—42no—
581C4—44no—
582C4—224no—
583C4—222no—
584C4—442no—
585C4—444no—
586C4#1062325612yes—
587C4C22×#434312yes—
588C2—22no—
589C2—442no—
590C2—882no—
591C2C2×#1062325611yescharacteristic
592C2#1308340012yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3162C2
socleC22×C11C23×D4
prime radical#10623056C22
hypercenter#3162D11
hypocenterC11#60720
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3162

Complements

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

NH ≅ G/Ntype
2. #13082503C2semidirect
3. #13079327C2semidirect
4. #13079289C2semidirect
5. #13079224C2semidirect
6. C2×#10622328C2semidirect
7. #13079005C2semidirect
8. #13078998C2semidirect
9. #13078272C2semidirect
11. #13077483C2semidirect
12. #13077474C2semidirect
13. #13077041C2semidirect
14. C11×#3162C2semidirect
21. #10623259C22semidirect
22. #10623228C22semidirect
39. C11×#501C22semidirect
40. C11×#501C22semidirect
41. C11×#501C22semidirect
46. #10622706C22semidirect
48. #10622682C22semidirect
56. #10622500C22semidirect
58. #10622486C22semidirect
59. #10622481C22semidirect
61. #10622466C22semidirect
66. #10622321C22semidirect
67. #10622320C22semidirect
68. D11×#97C22semidirect
239. #3162D11semidirect
311. #501C2×D11semidirect
312. #501C2×D11semidirect
313. #501C2×D11semidirect
529. C11#60720semidirect

Maximal subgroups

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

subgroupindex
#130825142
#130825032
#130793272
#130792892
#130792242
C2×#106223282
#130790052
#130789982
#130782722
#130782562
#130774832
#130774742
#130770412
C11×#31622
#6072011