Finite Group Databasebeta

← #15623435

Subgroups — #15623435

Order 2816.

1890 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623219C211yesmaximal, characteristic
2D11×#533C211yesmaximal, characteristic
3#13079169C211yesmaximal, characteristic, complemented
4#13079168C211yesmaximal, characteristic, complemented
5#13079165C211yesmaximal, characteristic, complemented
6#13079164C214yesmaximal, complemented
7#13079161C214yesmaximal, complemented
8#13079160C214yesmaximal, complemented
9#13079137C214yesmaximal, complemented
10#13079129C214yesmaximal, complemented
11#13077203C214yesmaximal
12C4×M16×D11C211yesmaximal, characteristic
13C11×#3166C211yesmaximal, characteristic, complemented
14C11×#533C2211yescharacteristic
15C2×C11×#125C2211yescharacteristic
16C2×M16×D11C2212yes—
17#10623259C2212yes—
18D11×C4⋊Q8C2212yes—
19#10623219—22no—
20#10623219—22no—
21#10623219C2212yes—
22#10623219C2212yes—
23#10623219C2212yes—
24#10623219C2212yes—
25#10623219C2212yes—
26D11×#125C2212yes—
27D11×C22⋊Q8—22no—
28#10623153—22no—
29#10623109—22no—
30C4×Q8×D11—22no—
31D11×#117C2212yes—
32#10623048C2212yes—
33C2×#66949—22no—
34C2×#66945C2212yes—
35C2×#66941C2212yes—
36C2×#66940—22no—
37C2×C42×D11C2211yescharacteristic
38#10623001C2211yescharacteristic
39C2×#66923C2211yescharacteristic
40C11×#501C2214yescomplemented
41C11×#499C2214yescomplemented
42C11×#428C2214yes—
43C4×C11×M16C2211yescharacteristic
44#10622734C2214yes—
45M16×Dic11C2212yes—
46#10622693C2214yescomplemented
47#10622678C2214yescomplemented
48#10622677C2214yescomplemented
49#10622677C2214yescomplemented
50#10622608C2214yes—
51#10622577C2214yes—
52C4×#4318C2211yescharacteristic
53#10622494C2218yes—
54#10622493C2218yes—
55#10622489C2218yescomplemented
56#10622487C2218yescomplemented
57#10622474C2218yes—
58#10622473C2218yes—
59#10622469C2218yescomplemented
60#10622468C2218yescomplemented
61#10622320C2212yes—
62D11×#97C2212yes—
63#10622315C2214yescomplemented
64C4×#4313C2212yes—
65C4×C8×D11C2212yes—
66#10622296C2214yescomplemented
67C2×Q8×D11—22no—
68C22×C4×D11D412yes—
69C22×C4×D11C2311yescharacteristic
70C22×Dic22—22no—
71C2×C11×M16C2312yes—
72C11×C4⋊Q8C2312yes—
73C11×#125—22no—
74C11×#125C2312yes—
75C11×#125C2312yes—
76C11×#125C2312yes—
77C11×C22⋊Q8—22no—
78C4×Q8×C11—22no—
79C11×#117C2312yes—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4C2312yes—
82C2×C42×C11C2311yescharacteristic
83#66999—22no—
84Q8×Dic11—22no—
85#66997—22no—
86C2×(C2×D11)⋊C4—22no—
87#66979C2312yes—
88C2×C4⋊Dic11C2312yes—
89#66977—22no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—22no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11D412yes—
94C2×C4×Dic11C2311yescharacteristic
95C2×#4318C2312yes—
96M16×D11Q8116yescomplemented
97C2×#4313C2314yes—
98C2×C8×D11C2314yes—
99#66950—22no—
100#66949—24no—
101#66949—24no—
102#66949—24no—
103#66949—24no—
104#66949—24no—
105#66945—22no—
106#66945—22no—
107#66945C2314yes—
108#66945C2314yes—
109#66945C2314yes—
110C4⋊C4×D11—22no—
111C4⋊C4×D11—24no—
112C4⋊C4×D11C2314yes—
113#66943C2314yes—
114#66942—24no—
115#66941—22no—
116#66941—22no—
117#66941—22no—
118#66941C2314yes—
119#66941C2314yes—
120#66941C2314yes—
121#66940—22no—
122#66940—24no—
123#66940—24no—
124#66940—24no—
125#66940—24no—
126#66940—24no—
127C22⋊C4×D11—22no—
128#66931—24no—
129#66930—22no—
130#66925—22no—
131C42×D11—22no—
132C42×D11D412yes—
133C42×D11D412yes—
134C42×D11C2311yescharacteristic
135C42×D11C2311yescharacteristic
136C42×D11C2311yescharacteristic
137C42×D11C2311yescharacteristic
138#66923—22no—
139#66923C2312yes—
140#66923C2312yes—
141#66923C2312yes—
142#66922C2312yes—
143C4×Dic22—22no—
144C4×Dic22—24no—
145C11×#107C2318yes—
146C11×#106C2318yes—
147C11×#97C2312yes—
148C4×C8×C11C2312yes—
149#66882C2318yes—
150#66881C2318yes—
151#66879C2314yes—
152C8×Dic11C2314yes—
153#66872C2318yes—
154#66872C2318yes—
155#66871C2318yes—
156#66871C2318yes—
157#66867C2312yes—
158C4×C11⋊C8C2312yes—
159#60663—111nomaximal, Sylow
160C23×D11C2×D411yescharacteristic
161C2×Q8×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2411yescharacteristic
165C22×Dic11—22no—
166C22×Dic11C2×D412yes—
167C22×Dic11C2×D411yescharacteristic
168Q8×D11—48no—
169C2×C4×D11—24no—
170C2×C4×D11—44no—
171C2×C4×D11C2×D412yes—
172C2×C4×D11C2×D412yes—
173C2×C4×D11C2×D412yes—
174C2×C4×D11C2×D412yes—
175C2×C4×D11C2×D411yescharacteristic
176C2×C4×D11C2×D411yescharacteristic
177C2×C4×D11C2×Q818yes—
178C2×C4×D11C2411yescharacteristic
179C2×C4×D11C2411yescharacteristic
180C2×Dic22—24no—
181C2×Dic22—24no—
182C2×Dic22—24no—
183C2×Dic22—22no—
184C2×Dic22—48no—
185C11×M16C2×Q818yescomplemented
186C2×C8×C11C2414yes—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4C2414yes—
193C11×C4⋊C4C2414yes—
194C11×C22⋊C4—22no—
195C42×C11—22no—
196C42×C11C2×D412yes—
197C42×C11C2411yescharacteristic
198C42×C11C2411yescharacteristic
199C22⋊Dic11—22no—
200(C2×D11)⋊C4—24no—
201(C2×D11)⋊C4—24no—
202(C2×D11)⋊C4—24no—
203C4⋊Dic11—24no—
204C4⋊Dic11—22no—
205C4⋊Dic11—22no—
206C4⋊Dic11C2414yes—
207C4⋊Dic11C2414yes—
208Dic11⋊C4—24no—
209Dic11⋊C4—24no—
210Dic11⋊C4—24no—
211Dic11⋊C4—24no—
212Dic11⋊C4—24no—
213Dic11⋊C4—24no—
214Dic11⋊C4—24no—
215Dic11⋊C4—24no—
216C4×Dic11—24no—
217C4×Dic11—24no—
218C4×Dic11—24no—
219C4×Dic11—22no—
220C4×Dic11C2×D412yes—
221C4×Dic11C2×D412yes—
222C4×Dic11C2×D412yes—
223C4×Dic11C2×D412yes—
224C4×Dic11C2×D412yes—
225C4×Dic11C2411yescharacteristic
226C4×Dic11C2411yescharacteristic
227#4318C2×Q818yescomplemented
228C2×C11⋊C8C2414yes—
229#4313C2×Q8116yescomplemented
230C8×D11C2×Q8116yescomplemented
231C2×#533—111no—
232C2×#533—111no—
233#3166—114no—
234#3166—111no—
235#3166—111no—
236#3166—111no—
237#3166D1111yescharacteristic, complemented
238#3165—114no—
239#3165—114no—
240#3162—114no—
241#3160—114no—
242#2911—114no—
243C2×C4×M16—111no—
244C23×C11C22×D411yescharacteristic
245C22×D11—42no—
246C22×D11C4⋊Q814yes—
247C22×D11C22×D411yescharacteristic
248C22×D11C22×D411yescharacteristic
249Q8×C11—44no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—42no—
253C2×C4×C11—44no—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C22×D412yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×Q814yes—
258C2×C4×C11C2511yescharacteristic
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—44no—
263C2×Dic11C4⋊Q814yes—
264C2×Dic11C22×D412yes—
265C2×Dic11C22×D411yescharacteristic
266C2×Dic11C22×D411yescharacteristic
267C2×Dic11C22×D412yes—
268C4×D11—24no—
269C4×D11—24no—
270C4×D11—42no—
271C4×D11—42no—
272C4×D11—48no—
273C4×D11C4⋊Q814yes—
274C4×D11C4⋊Q814yes—
275C4×D11C22×Q814yes—
276C4×D11C22×Q814yes—
277Dic22—48no—
278Dic22—44no—
279Dic22—48no—
280Dic22—48no—
281C8×C11C22×Q818yes—
282C11⋊C8C22×Q818yes—
283C22×M16—112no—
284#533—112no—
285#533—112no—
286#533—112no—
287#533—112no—
288#533—112no—
289#533—112no—
290#533—112no—
291#533—111no—
292#533—222no—
293#533—222no—
294#533—222no—
295#533—222no—
296#533C2×D1111yescharacteristic
297C2×C4⋊Q8—112no—
298C2×C4⋊Q8—112no—
299C2×#125—112no—
300C2×#125—111no—
301C2×#125C2×D1111yescharacteristic
302C2×C22⋊Q8—222no—
303C2×C22⋊Q8—222no—
304C2×C4×Q8—222no—
305C2×C4×Q8—222no—
306C2×#117—112no—
307C2×#117—112no—
308C22×C42—111no—
309#501—114no—
310#501—114no—
311#501—118no—
312#501—118no—
313#501—114no—
314#501C2×D1114yescomplemented
315#500—118no—
316#499—114no—
317#499—114no—
318#499—114no—
319#499C2×D1114yescomplemented
320#498—118no—
321#428—114no—
322#428—114no—
323#428—114no—
324#428—118no—
325#428—118no—
326#428C2×D1114yes—
327#427—118no—
328#427—118no—
329C4×M16—112no—
330C4×M16—111no—
331C4×M16—112no—
332C4×M16—112no—
333C4×M16C2×D1111yescharacteristic
334C2×#97—112no—
335C2×C4×C8—112no—
336C22×C11—22no—
337C22×C11C2×C4⋊Q812yes—
338C22×C11C23×D411yescharacteristic
339C2×D11—22no—
340C2×D11—22no—
341C2×D11—44no—
342C2×D11C2×C4⋊Q812yes—
343C2×D11C2×C4⋊Q812yes—
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—44no—
347C4×C11—44no—
348C4×C11C2×C4⋊Q812yes—
349C4×C11C23×Q812yes—
350Dic11—22no—
351Dic11—44no—
352Dic11—44no—
353Dic11C2×C4⋊Q812yes—
354Dic11C2×C4⋊Q812yes—
355Dic11#57514yes—
356C22×Q8—222no—
357C22×Q8—222no—
358C23×C4—111no—
359C23×C4—112no—
360C2×M16—112no—
361C2×M16—1116no—
362C2×M16—114no—
363C2×M16C22×D1112yes—
364C22×C8—114no—
365C4⋊Q8—114no—
366C4⋊Q8—114no—
367C4⋊Q8—114no—
368C4⋊Q8—112no—
369C4⋊Q8—222no—
370C4⋊Q8—222no—
371C4⋊Q8—222no—
372C4⋊Q8—222no—
373C4⋊Q8C22×D1112yes—
374#125—22no—
375#125—114no—
376#125—112no—
377#125—112no—
378#125—112no—
379#125—224no—
380#125—222no—
381#125C22×D1112yes—
382#125C22×D1112yes—
383#125C22×D1112yes—
384C22⋊Q8—22no—
385C22⋊Q8—224no—
386C22⋊Q8—224no—
387C22⋊Q8—224no—
388C22⋊Q8—224no—
389C22⋊Q8—224no—
390C22⋊Q8—224no—
391C22⋊Q8—222no—
392C22⋊Q8—222no—
393C22⋊Q8—222no—
394C4×Q8—22no—
395C4×Q8—224no—
396C4×Q8—224no—
397C4×Q8—224no—
398C4×Q8—224no—
399C4×Q8—222no—
400C4×Q8—224no—
401C4×Q8—224no—
402C4×Q8—222no—
403C4×Q8—222no—
404#117—112no—
405#117—114no—
406#117—114no—
407#117—114no—
408#117—222no—
409#117—222no—
410#117—222no—
411#117—222no—
412#117C22×D1112yes—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—112no—
415C2×C4⋊C4—114no—
416C2×C4⋊C4—224no—
417C2×C4⋊C4—222no—
418C2×C4⋊C4—222no—
419C2×C4⋊C4—222no—
420C2×C4⋊C4C22×D1112yes—
421C2×C22⋊C4—222no—
422C2×C22⋊C4—222no—
423C2×C42—112no—
424C2×C42—111no—
425C2×C42—112no—
426C2×C42—112no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—111no—
430C2×C42—111no—
431C2×C42—222no—
432C2×C42—222no—
433C2×C42C22×D1111yescharacteristic
434#107—118no—
435#107—118no—
436#107—118no—
437#107C22×D1118yes—
438#106—118no—
439#106—118no—
440#106—118no—
441#106C22×D1118yes—
442#97—114no—
443#97—112no—
444#97C22×D1112yes—
445C4×C8—114no—
446C4×C8—112no—
447C4×C8C22×D1112yes—
448C2×C11—22no—
449C2×C11C22×C4⋊Q811yescharacteristic
450C2×C11C2×#57512yes—
451D11—22no—
452D11—22no—
453C24—111no—
454C2×Q8—22no—
455C2×Q8—224no—
456C2×Q8—224no—
457C2×Q8—224no—
458C2×Q8—222no—
459C2×Q8—448no—
460C2×Q8—448no—
461C22×C4—22no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—118no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—112no—
469C22×C4—112no—
470C22×C4—112no—
471C22×C4—112no—
472C22×C4—112no—
473C22×C4—224no—
474C22×C4—222no—
475C22×C4—444no—
476C22×C4D4×D1112yes—
477C22×C4C23×D1111yescharacteristic
478M16—118no—
479M16—1116no—
480M16Q8×D1118yescomplemented
481C2×C8—114no—
482C2×C8—1116no—
483C2×C8C23×D1114yes—
484C4⋊C4—24no—
485C4⋊C4—24no—
486C4⋊C4—24no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—114no—
490C4⋊C4—114no—
491C4⋊C4—224no—
492C4⋊C4—224no—
493C4⋊C4—224no—
494C4⋊C4—224no—
495C4⋊C4—224no—
496C4⋊C4—224no—
497C4⋊C4—222no—
498C4⋊C4—224no—
499C4⋊C4—224no—
500C4⋊C4—224no—
501C4⋊C4—222no—
502C4⋊C4C23×D1114yes—
503C4⋊C4C23×D1114yes—
504C22⋊C4—22no—
505C22⋊C4—224no—
506C22⋊C4—224no—
507C22⋊C4—224no—
508C22⋊C4—222no—
509C42—22no—
510C42—112no—
511C42—112no—
512C42—112no—
513C42—112no—
514C42—112no—
515C42—111no—
516C42—111no—
517C42—224no—
518C42—224no—
519C42—224no—
520C42—222no—
521C42D4×D1112yes—
522C42C23×D1111yescharacteristic
523C42C23×D1111yescharacteristic
524C11#6066311yescharacteristic, complemented, Sylow
525C23—111no—
526C23—111no—
527C23—114no—
528C23—442no—
529C23C2×D4×D1111yescharacteristic
530Q8—44no—
531Q8—444no—
532Q8—448no—
533Q8—448no—
534Q8—448no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—42no—
538C2×C4—44no—
539C2×C4—114no—
540C2×C4—111no—
541C2×C4—111no—
542C2×C4—112no—
543C2×C4—114no—
544C2×C4—114no—
545C2×C4—114no—
546C2×C4—114no—
547C2×C4—112no—
548C2×C4—224no—
549C2×C4—224no—
550C2×C4—224no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—448no—
556C2×C4—444no—
557C2×C4C2×D4×D1112yes—
558C2×C4C2×D4×D1112yes—
559C2×C4C2×D4×D1111yescharacteristic
560C2×C4C2×Q8×D1114yes—
561C2×C4C24×D1111yescharacteristic
562C8—118no—
563C8C2×Q8×D1118yes—
564C22—22no—
565C22—112no—
566C22—112no—
567C22—222no—
568C22—222no—
569C22—444no—
570C22D11×C4⋊Q812yes—
571C22C22×D4×D1111yescharacteristic
572C4—22no—
573C4—22no—
574C4—44no—
575C4—44no—
576C4—112no—
577C4—112no—
578C4—114no—
579C4—222no—
580C4—444no—
581C4—444no—
582C4D11×C4⋊Q812yes—
583C4C22×Q8×D1112yes—
584C2—22no—
585C2—222no—
586C2—222no—
587C2C2×D11×C4⋊Q811yescharacteristic
588C2D11×#57512yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3166C2
socleC22×C11C23×D4
prime radicalC23×D11C2×D4
hypercenter#3166D11
hypocenterC11#60663
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3166

Complements

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

NH ≅ G/Ntype
3. #13079169C2semidirect
4. #13079168C2semidirect
5. #13079165C2semidirect
6. #13079164C2semidirect
7. #13079161C2semidirect
8. #13079160C2semidirect
9. #13079137C2semidirect
10. #13079129C2semidirect
13. C11×#3166C2semidirect
40. C11×#501C22semidirect
41. C11×#499C22semidirect
46. #10622693C22semidirect
47. #10622678C22semidirect
48. #10622677C22semidirect
49. #10622677C22semidirect
55. #10622489C22semidirect
56. #10622487C22semidirect
59. #10622469C22semidirect
60. #10622468C22semidirect
63. #10622315C22semidirect
66. #10622296C22semidirect
96. M16×D11Q8semidirect
185. C11×M16C2×Q8semidirect
227. #4318C2×Q8semidirect
229. #4313C2×Q8semidirect
230. C8×D11C2×Q8semidirect
237. #3166D11semidirect
314. #501C2×D11semidirect
319. #499C2×D11semidirect
480. M16Q8×D11semidirect
524. C11#60663semidirect

Maximal subgroups

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

subgroupindex
C2×#106232192
D11×#5332
#130791692
#130791682
#130791652
#130791642
#130791612
#130791602
#130791372
#130791292
#130772032
C4×M16×D112
C11×#31662
#6066311