Finite Group Databasebeta

← #14927241

Subgroups — #14927241

Order 2816.

1986 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076966C212yesmaximal, complemented
2#13076926C211yesmaximal, characteristic, complemented
3#13074427C214yesmaximal
4#13074285C214yesmaximal, complemented
5#13074280C214yesmaximal, complemented
6#13072331C212yesmaximal, complemented
7#13072325C212yesmaximal, complemented
8#13072310C212yesmaximal, complemented
9#13072305C212yesmaximal, complemented
10#13071347C214yesmaximal, complemented
11#13070998C212yesmaximal
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×#66945C2212yes—
20C2×#66945C2212yes—
21C2×#66941C2212yescomplemented
22C2×#66931C2214yes—
23C2×#66923C2211yescharacteristic, complemented
24C11×#389C2212yescomplemented
25C11×#387C2214yescomplemented
26C11×#385C2214yes—
27C11×#382C2211yescharacteristic, complemented
28C11×#380C2212yes—
29#10622825C2212yes—
30#10622823C2214yes—
31C2×C11⋊#95C2212yes—
32#10622607C2214yes—
33#10622607C2214yes—
34#10622605C2214yes—
35#10622605C2214yes—
36#10622600C2212yes—
37#10622600C2212yes—
38#10622598C2212yescomplemented
39#10622591C2214yescomplemented
40#10622589C2212yescomplemented
41#10622587C2214yescomplemented
42#10622586C2214yescomplemented
43#10622586C2212yescomplemented
44#10622585C2214yescomplemented
45#10622568C2214yes—
46#10622555C2214yes—
47C22⋊C4×Dic11C2214yes—
48C4×(C2×D11)⋊C4C2212yes—
49C4×(C2×D11)⋊C4C2212yes—
50C4×(C2×D11)⋊C4C2212yes—
51C4×(C2×D11)⋊C4C2212yes—
52#10622549C2211yescharacteristic, complemented
53#10622546C2214yescomplemented
54#10622541C2212yescomplemented
55#10622289C2214yes—
56#10622289C2214yes—
57#10622286C2214yes—
58#10622286C2214yes—
59#10622279C2214yes—
60#10622277C2214yes—
61#10622266C2214yescomplemented
62#10622265C2214yescomplemented
63#10622265C2214yescomplemented
64#10622260C2214yescomplemented
65#10622259C2214yescomplemented
66#10622259C2214yescomplemented
67C24×D11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2312yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2312yes—
72C22×C4×D11—42no—
73C22×C4×D11—42no—
74C22×C4×D11Q818yescomplemented
75C22×C4×D11C2312yes—
76C22×C4×D11C2312yes—
77C22×Dic22C2314yes—
78C11×#125—42no—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C4⋊C4C2314yes—
83C2×C11×C22⋊C4C2314yes—
84C2×C42×C11—42no—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2312yes—
88C2×C22⋊Dic11C2314yes—
89C2×(C2×D11)⋊C4—28no—
90C2×(C2×D11)⋊C4C2312yes—
91C2×(C2×D11)⋊C4C2312yes—
92C2×(C2×D11)⋊C4C2312yes—
93C2×(C2×D11)⋊C4C2312yes—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2314yes—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×C4⋊Dic11C2312yes—
99C2×C4⋊Dic11C2314yes—
100C2×C4⋊Dic11C2312yes—
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×Dic11C2314yes—
111C2×C4×Dic11C2311yescharacteristic
112C2×C4×Dic11C2314yes—
113#66945—44no—
114#66945—44no—
115#66941—44no—
116#66931—216no—
117#66923—42no—
118C11×#95C2314yes—
119C11×#95C2314yes—
120C11×#95C2314yes—
121C11⋊#95C2314yes—
122C11⋊#95C2312yes—
123C11⋊#95C2314yes—
124C11⋊#95C2314yes—
125C11⋊#95C2314yes—
126C11⋊#95C2312yes—
127C11⋊#95C2312yes—
128C11⋊#95C2314yes—
129C11⋊#95C2312yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132#35033—111nomaximal, Sylow
133C24×C11C2411yescharacteristic
134C23×D11—24no—
135C23×D11—41no—
136C23×D11—41no—
137C23×D11—42no—
138C23×D11C2×Q814yes—
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—42no—
153C22×Dic11—41no—
154C22×Dic11—41no—
155C22×Dic11—42no—
156C22×Dic11C2×Q814yes—
157C22×Dic11#4118yes—
158C22×Dic11C2414yes—
159C22×Dic11C2414yes—
160C22×Dic11C2412yes—
161C22×Dic11C2412yes—
162C22×Dic11C2412yes—
163C2×C4×D11—24no—
164C2×C4×D11—24no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—416no—
168C2×C4×D11C2×Q818yes—
169C2×C4×D11C2×Q818yes—
170C2×Dic22—28no—
171C2×Dic22—44no—
172C2×Dic22—44no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—44no—
176C11×C4⋊C4—44no—
177C11×C22⋊C4—28no—
178C42×C11—22no—
179C42×C11—22no—
180C42×C11—42no—
181C22⋊Dic11—28no—
182(C2×D11)⋊C4—24no—
183(C2×D11)⋊C4—24no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—24no—
186(C2×D11)⋊C4—44no—
187(C2×D11)⋊C4—44no—
188(C2×D11)⋊C4—44no—
189(C2×D11)⋊C4—44no—
190C4⋊Dic11—28no—
191C4⋊Dic11—24no—
192C4⋊Dic11—24no—
193Dic11⋊C4—28no—
194Dic11⋊C4—28no—
195Dic11⋊C4—44no—
196Dic11⋊C4—44no—
197Dic11⋊C4—44no—
198Dic11⋊C4—44no—
199C4×Dic11—24no—
200C4×Dic11—44no—
201C4×Dic11—44no—
202C4×Dic11—41no—
203C4×Dic11—41no—
204#2857—112no—
205#2851—111no—
206#2851D1111yescharacteristic, complemented
207#2626—114no—
208#2608—114no—
209#2607—114no—
210#2441—112no—
211#2441—112no—
212#2439—112no—
213#2439—112no—
214#2329—114no—
215#2280—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—28no—
224C22×D11—22no—
225C22×D11—22no—
226C22×D11—22no—
227C22×D11—22no—
228C22×D11—22no—
229C22×D11—22no—
230C22×D11—44no—
231C22×D11—44no—
232C22×D11—48no—
233C22×D11—48no—
234C22×D11C22×Q814yes—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—28no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
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—22no—
260C2×Dic11—22no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—44no—
268C2×Dic11—48no—
269C2×Dic11C22×Q814yes—
270C2×Dic11C2×#4114yes—
271C2×Dic11C2×#4114yes—
272C4×D11—216no—
273C4×D11—48no—
274Dic22—88no—
275C24×C4—111no—
276C2×C4⋊Q8—112no—
277C2×#125—111no—
278C2×#125C2×D1111yescharacteristic, complemented
279C2×C22⋊Q8—114no—
280C2×#117—112no—
281C2×#117—112no—
282C22×C22⋊C4—112no—
283C22×C42—111no—
284C22×C42C2×D1111yescharacteristic
285#399—114no—
286#399—114no—
287#396—114no—
288#396—114no—
289#396—114no—
290#396—114no—
291#393—114no—
292#393—114no—
293#391—114no—
294#391—114no—
295#391—114no—
296#389—114no—
297#389—114no—
298#389—112no—
299#389—112no—
300#389—112no—
301#389—114no—
302#389C2×D1112yescomplemented
303#387—114no—
304#387—114no—
305#387—114no—
306#387—114no—
307#387—114no—
308#387C2×D1114yescomplemented
309#385—114no—
310#385C2×D1114yes—
311#384—112no—
312#382—111no—
313#382C2×D1111yescharacteristic, complemented
314#381—114no—
315#380—112no—
316#380—112no—
317#380—112no—
318#380—114no—
319#380C2×D1112yes—
320#379—114no—
321C4×C22⋊C4—114no—
322C4×C22⋊C4—112no—
323C4×C22⋊C4—112no—
324C4×C22⋊C4—112no—
325C4×C22⋊C4—112no—
326C4×C22⋊C4—114no—
327C2×#95—112no—
328C22×C11—22no—
329C22×C11—22no—
330C22×C11—24no—
331C22×C11—24no—
332C22×C11#53314yes—
333C22×C11C23×Q811yescharacteristic
334C22×C11C22×#4112yes—
335C22×C11C2×H(5,𝔽2)11yescharacteristic
336C22×C11C2×H(5,𝔽2)11yescharacteristic
337C22×C11#58512yes—
338C2×D11—24no—
339C2×D11—24no—
340C2×D11—24no—
341C2×D11—416no—
342C2×D11—42no—
343C2×D11—42no—
344C2×D11—42no—
345C2×D11—42no—
346C4×C11—22no—
347C4×C11—44no—
348C4×C11—44no—
349C4×C11—42no—
350C4×C11—42no—
351C4×C11#54314yes—
352Dic11—24no—
353Dic11—24no—
354Dic11—24no—
355Dic11—44no—
356Dic11—44no—
357C25—111no—
358C22×Q8—114no—
359C23×C4—112no—
360C23×C4—111no—
361C23×C4—112no—
362C23×C4—118no—
363C23×C4—112no—
364C23×C4—442no—
365C23×C4—442no—
366C23×C4C22×D1111yescharacteristic
367C23×C4C22×D1112yes—
368C4⋊Q8—444no—
369#125—42no—
370#125—442no—
371C22⋊Q8—2216no—
372#117—444no—
373#117—444no—
374C2×C4⋊C4—112no—
375C2×C4⋊C4—112no—
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⋊C4C22×D1112yes—
384C2×C4⋊C4C22×D1112yes—
385C2×C4⋊C4C22×D1114yes—
386C2×C4⋊C4C22×D1114yes—
387C2×C22⋊C4—114no—
388C2×C22⋊C4—112no—
389C2×C22⋊C4—112no—
390C2×C22⋊C4—112no—
391C2×C22⋊C4—112no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—114no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—114no—
396C2×C22⋊C4—228no—
397C2×C22⋊C4C22×D1114yes—
398C2×C42—42no—
399C2×C42—112no—
400C2×C42—114no—
401C2×C42—114no—
402C2×C42—111no—
403C2×C42—111no—
404C2×C42—442no—
405C2×C42C22×D1111yescharacteristic
406C2×C42C22×D1111yescharacteristic
407C2×C42C22×D1112yes—
408#95—112no—
409#95—112no—
410#95—112no—
411#95—112no—
412#95—114no—
413#95—114no—
414#95—114no—
415#95—114no—
416#95—114no—
417#95—114no—
418#95—114no—
419#95C22×D1114yes—
420#95C22×D1114yes—
421#95C22×D1114yes—
422C2×C11—24no—
423C2×C11C2×#53311yescharacteristic
424C2×C11C2×#54311yescharacteristic
425C2×C11#345811yescharacteristic
426C2×C11#350512yes—
427C2×C11#350612yes—
428D11—44no—
429C24—112no—
430C24—114no—
431C24—224no—
432C24—441no—
433C24—441no—
434C24—442no—
435C24C23×D1111yescharacteristic
436C2×Q8—228no—
437C2×Q8—444no—
438C2×Q8—444no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—112no—
445C22×C4—112no—
446C22×C4—112no—
447C22×C4—114no—
448C22×C4—118no—
449C22×C4—118no—
450C22×C4—118no—
451C22×C4—114no—
452C22×C4—114no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—4416no—
456C22×C4—442no—
457C22×C4—442no—
458C22×C4—442no—
459C22×C4—441no—
460C22×C4—441no—
461C22×C4—442no—
462C22×C4Q8×D1114yes—
463C22×C4C23×D1112yes—
464C22×C4C23×D1112yes—
465C22×C4C23×D1114yes—
466C22×C4C23×D1114yes—
467C22×C4C23×D1111yescharacteristic
468C22×C4C23×D1111yescharacteristic
469C4⋊C4—24no—
470C4⋊C4—24no—
471C4⋊C4—44no—
472C4⋊C4—44no—
473C4⋊C4—228no—
474C4⋊C4—228no—
475C4⋊C4—228no—
476C4⋊C4—224no—
477C4⋊C4—224no—
478C4⋊C4—444no—
479C4⋊C4—444no—
480C4⋊C4—444no—
481C4⋊C4—444no—
482C22⋊C4—28no—
483C22⋊C4—224no—
484C22⋊C4—224no—
485C22⋊C4—224no—
486C22⋊C4—224no—
487C22⋊C4—228no—
488C22⋊C4—444no—
489C22⋊C4—444no—
490C22⋊C4—444no—
491C22⋊C4—444no—
492C42—22no—
493C42—22no—
494C42—42no—
495C42—224no—
496C42—441no—
497C42—441no—
498C42—444no—
499C42—444no—
500C11#3503311yescharacteristic, complemented, Sylow
501C23—21no—
502C23—21no—
503C23—22no—
504C23—114no—
505C23—222no—
506C23—222no—
507C23—222no—
508C23—222no—
509C23—222no—
510C23—222no—
511C23—228no—
512C23—444no—
513C23—444no—
514C23—448no—
515C23—448no—
516C23C2×Q8×D1112yes—
517C23#41×D1114yes—
518C23C24×D1111yescharacteristic
519Q8—888no—
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—24no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—48no—
536C2×C4—114no—
537C2×C4—114no—
538C2×C4—114no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—2216no—
546C2×C4—224no—
547C2×C4—224no—
548C2×C4—224no—
549C2×C4—224no—
550C2×C4—224no—
551C2×C4—224no—
552C2×C4—448no—
553C2×C4—444no—
554C2×C4—448no—
555C2×C4#6703712yes—
556C2×C4C2×Q8×D1112yes—
557C2×C4C2×Q8×D1112yes—
558C2×C4#6704212yes—
559C22—24no—
560C22—24no—
561C22—22no—
562C22—22no—
563C22—224no—
564C22—224no—
565C22—224no—
566C22—4416no—
567C22—442no—
568C22—442no—
569C22—442no—
570C22—442no—
571C22#1062321914yes—
572C22C2×#6703711yescharacteristic
573C22C22×Q8×D1111yescharacteristic
574C22C2×#41×D1112yes—
575C22C2×#6704211yescharacteristic
576C22#1062345312yes—
577C4—22no—
578C4—44no—
579C4—42no—
580C4—42no—
581C4—44no—
582C4—224no—
583C4—224no—
584C4—224no—
585C4—444no—
586C4—444no—
587C4#1062316514yes—
588C2—24no—
589C2—444no—
590C2C2×#1062321911yescharacteristic
591C2C2×#1062316511yescharacteristic
592C2#1308201911yescharacteristic
593C2#1308245112yes—
594C2#1308245912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2851C2
prime radicalC24×D11C23
hypercenter#2851D11
hypocenterC11#35033
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2851

Complements

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

NH ≅ G/Ntype
1. #13076966C2semidirect
2. #13076926C2semidirect
4. #13074285C2semidirect
5. #13074280C2semidirect
6. #13072331C2semidirect
7. #13072325C2semidirect
8. #13072310C2semidirect
9. #13072305C2semidirect
10. #13071347C2semidirect
13. C11×#2851C2semidirect
15. C2×C11×#125C22semidirect
21. C2×#66941C22semidirect
23. C2×#66923C22semidirect
24. C11×#389C22semidirect
25. C11×#387C22semidirect
27. C11×#382C22semidirect
38. #10622598C22semidirect
39. #10622591C22semidirect
40. #10622589C22semidirect
41. #10622587C22semidirect
42. #10622586C22semidirect
43. #10622586C22semidirect
44. #10622585C22semidirect
52. #10622549C22semidirect
53. #10622546C22semidirect
54. #10622541C22semidirect
61. #10622266C22semidirect
62. #10622265C22semidirect
63. #10622265C22semidirect
64. #10622260C22semidirect
65. #10622259C22semidirect
66. #10622259C22semidirect
74. C22×C4×D11Q8semidirect
206. #2851D11semidirect
278. C2×#125C2×D11semidirect
302. #389C2×D11semidirect
308. #387C2×D11semidirect
313. #382C2×D11semidirect
500. C11#35033semidirect

Maximal subgroups

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

subgroupindex
#130769662
#130769262
#130744272
#130742852
#130742802
#130723312
#130723252
#130723102
#130723052
#130713472
#130709982
C2×C4×(C2×D11)⋊C42
C11×#28512
#3503311