Finite Group Databasebeta

← #14926964

Subgroups — #14926964

Order 2816.

2042 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076926C211yesmaximal, characteristic, complemented
2#13076924C212yesmaximal, complemented
3#13074588C214yesmaximal, complemented
4#13073839C214yesmaximal, complemented
5#13073838C214yesmaximal, complemented
6#13072343C212yesmaximal, complemented
7#13072342C212yesmaximal, complemented
8#13072338C212yesmaximal, complemented
9#13072336C212yesmaximal, complemented
10#13071227C214yesmaximal
11D11×#380C212yesmaximal
12C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
13C11×#2851C211yesmaximal, characteristic, complemented
14C23×C4×D11C2211yescharacteristic
15C2×C11×#125C2211yescharacteristic, complemented
16C22×C42×C11C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×C4×Dic11C2211yescharacteristic
19C2×C4⋊C4×D11C2212yes—
20C2×C4⋊C4×D11C2212yes—
21C2×#66943C2212yescomplemented
22C2×C22⋊C4×D11C2214yes—
23C2×#66923C2211yescharacteristic, complemented
24C11×#389C2212yescomplemented
25C11×#387C2214yescomplemented
26C11×#385C2214yes—
27C11×#382C2211yescharacteristic, complemented
28C11×#380C2212yes—
29#10622825C2212yes—
30#10622823C2214yes—
31C2×C11⋊#95C2212yes—
32#10622602C2214yes—
33#10622602C2214yes—
34#10622600C2214yes—
35#10622600C2214yes—
36#10622600C2212yes—
37#10622600C2212yes—
38#10622598C2212yescomplemented
39#10622597C2214yescomplemented
40#10622596C2214yescomplemented
41#10622595C2214yescomplemented
42#10622593C2214yescomplemented
43#10622590C2212yescomplemented
44#10622586C2212yescomplemented
45#10622563C2214yes—
46#10622559C2214yes—
47#10622555C2214yes—
48C4×(C2×D11)⋊C4C2212yes—
49C4×(C2×D11)⋊C4C2212yes—
50C4×(C2×D11)⋊C4C2212yes—
51C4×(C2×D11)⋊C4C2212yes—
52#10622549C2211yescharacteristic, complemented
53#10622546C2214yescomplemented
54#10622541C2212yescomplemented
55#10622281C2214yes—
56#10622281C2214yes—
57#10622280C2214yes—
58#10622280C2214yes—
59#10622280C2214yes—
60D11×#95C2214yes—
61#10622272C2214yescomplemented
62#10622271C2214yescomplemented
63#10622271C2214yescomplemented
64#10622270C2214yescomplemented
65#10622268C2214yescomplemented
66#10622267C2214yescomplemented
67C24×D11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2312yes—
70C23×Dic11C2312yes—
71C23×Dic11C2311yescharacteristic
72C22×C4×D11—42no—
73C22×C4×D11—42no—
74C22×C4×D11Q818yes—
75C22×C4×D11C2312yes—
76C22×C4×D11C2314yes—
77C22×C4×D11C2314yes—
78C22×C4×D11C2312yes—
79C11×#125—42no—
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2314yes—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C22⋊C4C2314yes—
85C2×C42×C11—42no—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2312yes—
89C2×C22⋊Dic11C2314yes—
90C2×(C2×D11)⋊C4—28no—
91C2×(C2×D11)⋊C4C2314yes—
92C2×(C2×D11)⋊C4C2314yes—
93C2×(C2×D11)⋊C4C2312yes—
94C2×(C2×D11)⋊C4C2312yes—
95C2×(C2×D11)⋊C4C2312yes—
96C2×(C2×D11)⋊C4C2312yes—
97C2×C4⋊Dic11C2312yes—
98C2×C4⋊Dic11C2312yes—
99C2×C4⋊Dic11C2314yes—
100C2×C4⋊Dic11C2314yes—
101C2×Dic11⋊C4C2314yes—
102C2×Dic11⋊C4C2314yes—
103C2×Dic11⋊C4C2314yes—
104C2×Dic11⋊C4C2314yes—
105C2×Dic11⋊C4C2314yes—
106C2×Dic11⋊C4C2314yes—
107C2×C4×Dic11—42no—
108C2×C4×Dic11C2312yes—
109C2×C4×Dic11C2311yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C4⋊C4×D11—44no—
112C4⋊C4×D11—44no—
113#66943—44no—
114C22⋊C4×D11—216no—
115#66923—42no—
116C11×#95C2314yes—
117C11×#95C2314yes—
118C11×#95C2314yes—
119C11⋊#95C2314yes—
120C11⋊#95C2314yes—
121C11⋊#95C2314yes—
122C11⋊#95C2314yes—
123C11⋊#95C2314yes—
124C11⋊#95C2312yes—
125C11⋊#95C2314yes—
126C11⋊#95C2312yes—
127C11⋊#95C2312yes—
128C11⋊#95C2314yes—
129C11⋊#95C2312yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132#35020—111nomaximal, Sylow
133C24×C11C2411yescharacteristic
134C23×D11—41no—
135C23×D11—41no—
136C23×D11—42no—
137C23×D11C2×Q814yes—
138C23×D11#4118yes—
139C23×D11C2412yes—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11C2×Q814yes—
146C22×C4×C11C2412yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2414yes—
150C22×C4×C11C2411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—24no—
153C22×Dic11—42no—
154C22×Dic11—41no—
155C22×Dic11—41no—
156C22×Dic11—42no—
157C22×Dic11C2×Q814yes—
158C22×Dic11C2412yes—
159C22×Dic11C2412yes—
160C22×Dic11C2414yes—
161C22×Dic11C2414yes—
162C22×Dic11C2412yes—
163C2×C4×D11—28no—
164C2×C4×D11—28no—
165C2×C4×D11—24no—
166C2×C4×D11—24no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—44no—
170C2×C4×D11—44no—
171C2×C4×D11—44no—
172C2×C4×D11—44no—
173C2×C4×D11—416no—
174C2×C4×D11C2×Q818yes—
175C2×C4×D11C2×Q818yes—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—44no—
179C11×C4⋊C4—44no—
180C11×C22⋊C4—28no—
181C42×C11—22no—
182C42×C11—22no—
183C42×C11—42no—
184C22⋊Dic11—28no—
185(C2×D11)⋊C4—28no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4—24no—
188(C2×D11)⋊C4—24no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—24no—
191C4⋊Dic11—24no—
192C4⋊Dic11—24no—
193C4⋊Dic11—44no—
194C4⋊Dic11—44no—
195Dic11⋊C4—44no—
196Dic11⋊C4—44no—
197Dic11⋊C4—44no—
198Dic11⋊C4—44no—
199Dic11⋊C4—44no—
200Dic11⋊C4—44no—
201C4×Dic11—24no—
202C4×Dic11—41no—
203C4×Dic11—41no—
204#2851—111no—
205#2851—112no—
206#2851D1111yescharacteristic, complemented
207#2646—114no—
208#2569—114no—
209#2569—114no—
210#2442—112no—
211#2442—112no—
212#2442—112no—
213#2442—112no—
214#2315—114no—
215C2×#380—112no—
216C2×C4×C22⋊C4—111no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—22no—
220C23×C11C22×Q812yes—
221C23×C11C2×#4114yes—
222C23×C11C2511yescharacteristic
223C22×D11—22no—
224C22×D11—22no—
225C22×D11—22no—
226C22×D11—22no—
227C22×D11—44no—
228C22×D11—44no—
229C22×D11—48no—
230C22×D11—48no—
231C22×D11#125116yescomplemented
232C22×D11C22×Q814yes—
233C22×D11C2×#4114yes—
234C22×D11C2×#4114yes—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—28no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—48no—
251C2×C4×C11C22×Q812yes—
252C2×C4×C11C22×Q812yes—
253C2×C4×C11H(5,𝔽2)12yes—
254C2×C4×C11H(5,𝔽2)12yes—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—22no—
267C2×Dic11—24no—
268C2×Dic11—22no—
269C2×Dic11—44no—
270C2×Dic11—48no—
271C2×Dic11C22×Q814yes—
272C4×D11—216no—
273C4×D11—48no—
274C4×D11—88no—
275C4×D11—88no—
276C24×C4—111no—
277C2×#125—112no—
278C2×#125—111no—
279C2×#125C2×D1111yescharacteristic, complemented
280C22×C4⋊C4—112no—
281C22×C4⋊C4—112no—
282C22×C22⋊C4—112no—
283C22×C22⋊C4—114no—
284C22×C42—111no—
285C22×C42C2×D1111yescharacteristic
286#400—114no—
287#400—114no—
288#400—114no—
289#400—114no—
290#398—114no—
291#398—114no—
292#398—114no—
293#398—114no—
294#389—112no—
295#389—112no—
296#389—112no—
297#389C2×D1112yescomplemented
298#387—114no—
299#387—114no—
300#387—114no—
301#387C2×D1114yescomplemented
302#385—114no—
303#385—114no—
304#385—114no—
305#385—114no—
306#385—114no—
307#385—114no—
308#385—114no—
309#385C2×D1114yes—
310#382—112no—
311#382—111no—
312#382C2×D1111yescharacteristic, complemented
313#380—112no—
314#380—114no—
315#380—114no—
316#380—112no—
317#380—112no—
318#380—114no—
319#380—114no—
320#380—114no—
321#380—114no—
322#380C2×D1112yes—
323C4×C22⋊C4—112no—
324C4×C22⋊C4—112no—
325C4×C22⋊C4—112no—
326C4×C22⋊C4—112no—
327C2×#95—112no—
328C2×#95—114no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—24no—
332C22×C11—24no—
333C22×C11C2×#12514yes—
334C22×C11C23×Q811yescharacteristic
335C22×C11C22×#4112yes—
336C22×C11C2×H(5,𝔽2)11yescharacteristic
337C22×C11C2×H(5,𝔽2)11yescharacteristic
338C22×C11#58512yes—
339C2×D11—24no—
340C2×D11—24no—
341C2×D11—24no—
342C2×D11—24no—
343C2×D11—24no—
344C2×D11—24no—
345C2×D11—416no—
346C2×D11C2×#12518yes—
347C4×C11—22no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11—44no—
351C4×C11—44no—
352C4×C11#54314yes—
353Dic11—24no—
354Dic11—44no—
355Dic11—44no—
356Dic11—42no—
357Dic11—42no—
358C25—111no—
359C23×C4—111no—
360C23×C4—112no—
361C23×C4—118no—
362C23×C4—112no—
363C23×C4—112no—
364C23×C4—114no—
365C23×C4—114no—
366C23×C4—442no—
367C23×C4—442no—
368C23×C4C22×D1111yescharacteristic
369C23×C4C22×D1112yes—
370#125—42no—
371#125—442no—
372#125—444no—
373C2×C4⋊C4—112no—
374C2×C4⋊C4—112no—
375C2×C4⋊C4—114no—
376C2×C4⋊C4—114no—
377C2×C4⋊C4—114no—
378C2×C4⋊C4—114no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—114no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4—114no—
383C2×C4⋊C4—444no—
384C2×C4⋊C4—444no—
385C2×C4⋊C4C22×D1112yes—
386C2×C4⋊C4C22×D1112yes—
387C2×C4⋊C4C22×D1114yes—
388C2×C4⋊C4C22×D1114yes—
389C2×C22⋊C4—114no—
390C2×C22⋊C4—112no—
391C2×C22⋊C4—112no—
392C2×C22⋊C4—112no—
393C2×C22⋊C4—112no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—114no—
396C2×C22⋊C4—2216no—
397C2×C22⋊C4—228no—
398C2×C22⋊C4C22×D1114yes—
399C2×C42—42no—
400C2×C42—112no—
401C2×C42—111no—
402C2×C42—111no—
403C2×C42—442no—
404C2×C42C22×D1111yescharacteristic
405C2×C42C22×D1111yescharacteristic
406C2×C42C22×D1112yes—
407#95—112no—
408#95—112no—
409#95—112no—
410#95—112no—
411#95—114no—
412#95—114no—
413#95—114no—
414#95—114no—
415#95—114no—
416#95—114no—
417#95—114no—
418#95—114no—
419#95—114no—
420#95C22×D1114yes—
421#95C22×D1114yes—
422#95C22×D1114yes—
423C2×C11—24no—
424C2×C11C22×#12511yescharacteristic
425C2×C11C2×#54311yescharacteristic
426C2×C11#345811yescharacteristic
427C2×C11#350512yes—
428C2×C11#350512yes—
429D11—28no—
430C24—112no—
431C24—114no—
432C24—118no—
433C24—441no—
434C24—441no—
435C24—442no—
436C24C23×D1111yescharacteristic
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—112no—
443C22×C4—114no—
444C22×C4—118no—
445C22×C4—118no—
446C22×C4—112no—
447C22×C4—112no—
448C22×C4—114no—
449C22×C4—114no—
450C22×C4—228no—
451C22×C4—228no—
452C22×C4—224no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—4416no—
456C22×C4—442no—
457C22×C4—442no—
458C22×C4—444no—
459C22×C4—444no—
460C22×C4—444no—
461C22×C4—444no—
462C22×C4—442no—
463C22×C4—441no—
464C22×C4—441no—
465C22×C4—442no—
466C22×C4Q8×D1114yes—
467C22×C4C23×D1112yes—
468C22×C4C23×D1112yes—
469C22×C4C23×D1114yes—
470C22×C4C23×D1114yes—
471C22×C4C23×D1111yescharacteristic
472C22×C4C23×D1111yescharacteristic
473C4⋊C4—24no—
474C4⋊C4—24no—
475C4⋊C4—44no—
476C4⋊C4—44no—
477C4⋊C4—224no—
478C4⋊C4—224no—
479C4⋊C4—444no—
480C4⋊C4—444no—
481C4⋊C4—444no—
482C4⋊C4—444no—
483C4⋊C4—444no—
484C4⋊C4—444no—
485C4⋊C4—444no—
486C4⋊C4—444no—
487C22⋊C4—28no—
488C22⋊C4—228no—
489C22⋊C4—228no—
490C22⋊C4—224no—
491C22⋊C4—224no—
492C22⋊C4—224no—
493C22⋊C4—224no—
494C22⋊C4—228no—
495C42—22no—
496C42—22no—
497C42—42no—
498C42—224no—
499C42—441no—
500C42—441no—
501C11#3502011yescharacteristic, complemented, Sylow
502C23—21no—
503C23—21no—
504C23—22no—
505C23—114no—
506C23—114no—
507C23—114no—
508C23—1116no—
509C23—222no—
510C23—222no—
511C23—222no—
512C23—222no—
513C23—444no—
514C23—448no—
515C23—448no—
516C23—444no—
517C23C2×Q8×D1112yes—
518C23#41×D1114yes—
519C23C24×D1111yescharacteristic
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—28no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—48no—
536C2×C4—114no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—2216no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—224no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—224no—
548C2×C4—224no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—224no—
552C2×C4—448no—
553C2×C4—444no—
554C2×C4—448no—
555C2×C4—888no—
556C2×C4—888no—
557C2×C4#6703712yes—
558C2×C4C2×Q8×D1112yes—
559C2×C4C2×Q8×D1112yes—
560C2×C4#6704212yes—
561C22—24no—
562C22—24no—
563C22—22no—
564C22—22no—
565C22—118no—
566C22—224no—
567C22—224no—
568C22—224no—
569C22—224no—
570C22—224no—
571C22—224no—
572C22—4416no—
573C22D11×#12514yes—
574C22C2×#6703711yescharacteristic
575C22C22×Q8×D1111yescharacteristic
576C22C2×#41×D1112yes—
577C22C2×#6704211yescharacteristic
578C22#1062345312yes—
579C4—22no—
580C4—42no—
581C4—42no—
582C4—44no—
583C4—44no—
584C4—224no—
585C4—444no—
586C4—442no—
587C4—442no—
588C4—444no—
589C4#1062316514yes—
590C2—24no—
591C2—228no—
592C2C2×D11×#12511yescharacteristic
593C2C2×#1062316511yescharacteristic
594C2#1308201911yescharacteristic
595C2#1308244412yes—
596C2#1308245112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2851C2
prime radicalC24×D11C23
hypercenter#2851D11
hypocenterC11#35020
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2851

Complements

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

NH ≅ G/Ntype
1. #13076926C2semidirect
2. #13076924C2semidirect
3. #13074588C2semidirect
4. #13073839C2semidirect
5. #13073838C2semidirect
6. #13072343C2semidirect
7. #13072342C2semidirect
8. #13072338C2semidirect
9. #13072336C2semidirect
13. C11×#2851C2semidirect
15. C2×C11×#125C22semidirect
21. C2×#66943C22semidirect
23. C2×#66923C22semidirect
24. C11×#389C22semidirect
25. C11×#387C22semidirect
27. C11×#382C22semidirect
38. #10622598C22semidirect
39. #10622597C22semidirect
40. #10622596C22semidirect
41. #10622595C22semidirect
42. #10622593C22semidirect
43. #10622590C22semidirect
44. #10622586C22semidirect
52. #10622549C22semidirect
53. #10622546C22semidirect
54. #10622541C22semidirect
61. #10622272C22semidirect
62. #10622271C22semidirect
63. #10622271C22semidirect
64. #10622270C22semidirect
65. #10622268C22semidirect
66. #10622267C22semidirect
206. #2851D11semidirect
231. C22×D11#125semidirect
279. C2×#125C2×D11semidirect
297. #389C2×D11semidirect
301. #387C2×D11semidirect
312. #382C2×D11semidirect
501. C11#35020semidirect

Maximal subgroups

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

subgroupindex
#130769262
#130769242
#130745882
#130738392
#130738382
#130723432
#130723422
#130723382
#130723362
#130712272
D11×#3802
C2×C4×(C2×D11)⋊C42
C11×#28512
#3502011