Finite Group Databasebeta

← #14927226

Subgroups — #14927226

Order 2816.

2778 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
1C2×#10623137C212yesmaximal, complemented
2#13076968C211yesmaximal, characteristic, complemented
3#13076915C212yesmaximal, complemented
4#13074352C214yesmaximal, complemented
5#13074225C218yesmaximal, complemented
6#13073080C212yesmaximal, complemented
7#13073066C212yesmaximal, complemented
8#13072246C212yesmaximal, complemented
9#13072232C212yesmaximal, complemented
10#13071321C214yesmaximal, complemented
11C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
12C11×#2856C211yesmaximal, characteristic, complemented
13C22×#4341C2212yes—
14C23×C4×D11C2211yescharacteristic
15C2×C11×#127C2211yescharacteristic, complemented
16C2×C11×#121C2212yes—
17C2×C11×#121C2214yes—
18C22×C42×C11C2211yescharacteristic
19C2×#66991C2212yes—
20C2×#66990C2214yes—
21C2×#66989C2212yescomplemented
22C2×D4×Dic11C2214yes—
23C22×(C2×D11)⋊C4C2212yes—
24C2×#66977C2212yes—
25C22×C4×Dic11C2211yescharacteristic
26#10623137—216no—
27C2×#66950C2212yes—
28C2×#66945C2212yes—
29C2×#66936C2214yes—
30C2×(C22⋊D11)⋊C4C2214yes—
31C2×#66922C2211yescharacteristic, complemented
32C11×#390C2214yescomplemented
33C11×#390C2212yescomplemented
34C11×#384C2211yescharacteristic, complemented
35#10622836C2218yes—
36#10622834C2212yescomplemented
37#10622833C2218yes—
38#10622833C2218yescomplemented
39#10622825C2214yes—
40C2×C11⋊#95C2212yes—
41#10622606C2218yes—
42#10622594C2218yescomplemented
43#10622590C2212yescomplemented
44#10622587C2212yescomplemented
45#10622574C2218yes—
46#10622574C2218yes—
47#10622564C2218yescomplemented
48#10622563C2218yescomplemented
49#10622558C2218yescomplemented
50C4×(C2×D11)⋊C4C2214yes—
51C4×(C2×D11)⋊C4C2212yes—
52C4×(C2×D11)⋊C4C2212yes—
53#10622548C2211yescharacteristic, complemented
54#10622542C2212yescomplemented
55#10622541C2214yescomplemented
56C24×D11C2311yescharacteristic
57C22×D4×C11C2314yes—
58C22×D4×C11C2312yes—
59C22×D4×C11C2314yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2312yes—
62C22×C22⋊D11C2314yes—
63C22×C22⋊D11C2314yes—
64C23×Dic11C2314yes—
65C23×Dic11C2312yes—
66C23×Dic11C2311yescharacteristic
67C2×#4341—28no—
68C2×#4341—44no—
69C2×#4341—44no—
70C22×C4×D11—42no—
71C22×C4×D11—42no—
72C22×C4×D11D418yescomplemented
73C22×C4×D11C2312yes—
74C22×C4×D11C2312yes—
75C22×Dic22C2312yes—
76C11×#127—42no—
77C11×#121—28no—
78C11×#121—216no—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C22⋊C4C2314yes—
82C2×C11×C22⋊C4C2318yes—
83C2×C42×C11—42no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2312yes—
87C2×C22⋊Dic11C2314yes—
88C2×C22⋊Dic11C2314yes—
89C2×C22⋊Dic11C2318yes—
90C2×C22⋊Dic11C2318yes—
91#66991—28no—
92#66990—216no—
93#66989—44no—
94D4×Dic11—216no—
95C2×(C2×D11)⋊C4—28no—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×C4⋊Dic11C2314yes—
101C2×C4⋊Dic11C2312yes—
102C2×C4⋊Dic11C2314yes—
103C2×C4⋊Dic11C2314yes—
104#66977—28no—
105C2×Dic11⋊C4C2314yes—
106C2×C4×Dic11—42no—
107C2×C4×Dic11C2314yes—
108C2×C4×Dic11C2312yes—
109C2×C4×Dic11C2312yes—
110#66950—28no—
111#66945—28no—
112#66936—216no—
113(C22⋊D11)⋊C4—216no—
114#66922—42no—
115C11⋊#95C2318yes—
116C11⋊#95C2314yes—
117C11⋊#95C2314yes—
118C11⋊#95C2318yes—
119C11⋊#95C2318yes—
120#35032—111nomaximal, Sylow
121C24×C11C2414yes—
122C24×C11C2411yescharacteristic
123C23×D11—24no—
124C23×D11—41no—
125C23×D11—41no—
126C23×D11—42no—
127C23×D11C2×D414yes—
128C23×D11C2412yes—
129C2×D4×C11—28no—
130C2×D4×C11—216no—
131C2×D4×C11—24no—
132C2×D4×C11—28no—
133C2×D4×C11—24no—
134C2×D4×C11—24no—
135C2×D4×C11—44no—
136C2×D4×C11—44no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11C2×D414yes—
142C22×C4×C11#4118yescomplemented
143C22×C4×C11C2414yes—
144C22×C4×C11C2411yescharacteristic
145C22×C4×C11C2412yes—
146C22×C4×C11C2412yes—
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—28no—
149C2×C22⋊D11—28no—
150C2×C22⋊D11—44no—
151C2×C22⋊D11—44no—
152C2×C22⋊D11—48no—
153C22×Dic11—28no—
154C22×Dic11—24no—
155C22×Dic11—42no—
156C22×Dic11—41no—
157C22×Dic11—41no—
158C22×Dic11—44no—
159C22×Dic11—44no—
160C22×Dic11—42no—
161C22×Dic11C2×D414yes—
162C22×Dic11C2414yes—
163C22×Dic11C2414yes—
164C22×Dic11C2414yes—
165C22×Dic11C2412yes—
166#4341—432no—
167C2×C4×D11—24no—
168C2×C4×D11—24no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11—416no—
172C2×C4×D11C2×D418yes—
173C2×C4×D11C2×D418yes—
174C2×Dic22—24no—
175C2×Dic22—24no—
176C2×Dic22—24no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—28no—
179C11×C22⋊C4—28no—
180C11×C22⋊C4—216no—
181C42×C11—22no—
182C42×C11—22no—
183C42×C11—42no—
184C22⋊Dic11—28no—
185C22⋊Dic11—28no—
186C22⋊Dic11—48no—
187C22⋊Dic11—48no—
188(C2×D11)⋊C4—28no—
189(C2×D11)⋊C4—28no—
190(C2×D11)⋊C4—28no—
191(C2×D11)⋊C4—28no—
192C4⋊Dic11—28no—
193C4⋊Dic11—24no—
194C4⋊Dic11—44no—
195C4⋊Dic11—44no—
196Dic11⋊C4—28no—
197C4×Dic11—28no—
198C4×Dic11—24no—
199C4×Dic11—42no—
200C2×#525—112no—
201#2857—111no—
202#2856D1111yescharacteristic, complemented
203#2850—112no—
204#2617—114no—
205#2602—118no—
206#2500—112no—
207#2499—112no—
208#2432—112no—
209#2431—112no—
210#2325—114no—
211C2×C4×C22⋊C4—111no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—22no—
215C23×C11—24no—
216C23×C11—28no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—28no—
220C23×C11C22×D412yes—
221C23×C11C2×#4114yes—
222C23×C11C2511yescharacteristic
223C22×D11—28no—
224C22×D11—24no—
225C22×D11—22no—
226C22×D11—22no—
227C22×D11—24no—
228C22×D11—44no—
229C22×D11—44no—
230C22×D11—48no—
231C22×D11—48no—
232C22×D11C22×D414yes—
233D4×C11—416no—
234D4×C11—48no—
235D4×C11—88no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—28no—
243C2×C4×C11—24no—
244C2×C4×C11—28no—
245C2×C4×C11—48no—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D412yes—
248C2×C4×C11C2×#4114yes—
249C2×C4×C11C2×#4114yes—
250C2×C4×C11H(5,𝔽2)12yes—
251C2×C4×C11H(5,𝔽2)12yes—
252C22⋊D11—416no—
253C22⋊D11—416no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—28no—
263C2×Dic11—24no—
264C2×Dic11—44no—
265C2×Dic11—416no—
266C2×Dic11—48no—
267C2×Dic11C22×D414yes—
268C4×D11—216no—
269C4×D11—48no—
270Dic22—48no—
271C22×#41—112no—
272C24×C4—111no—
273C2×C4⋊Q8—111no—
274C2×#127C2×D1111yescharacteristic, complemented
275C2×#124—112no—
276#525—2216no—
277C2×#123—114no—
278C2×C22⋊Q8—112no—
279C2×C22⋊Q8—112no—
280C2×#121—112no—
281C2×#121C2×D1114yes—
282C2×#121C2×D1112yes—
283C2×#120—114no—
284C2×C4×D4—114no—
285C2×C4×D4—114no—
286C2×#117—112no—
287C22×C22⋊C4—112no—
288C22×C42—111no—
289C22×C42C2×D1111yescharacteristic
290#397—118no—
291#394—118no—
292#394—118no—
293#392—118no—
294#391—112no—
295#391—112no—
296#390—112no—
297#390C2×D1114yescomplemented
298#390C2×D1112yescomplemented
299#389—114no—
300#388—118no—
301#388—118no—
302#387—118no—
303#386—118no—
304#386—118no—
305#385—118no—
306#384—111no—
307#384C2×D1111yescharacteristic, complemented
308#382—112no—
309#380—114no—
310C4×C22⋊C4—114no—
311C4×C22⋊C4—112no—
312C4×C22⋊C4—112no—
313C2×#95—112no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—24no—
317C22×C11—24no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—48no—
322C22×C11—48no—
323C22×C11#53214yes—
324C22×C11C23×D411yescharacteristic
325C22×C11C22×#4112yes—
326C22×C11C2×H(5,𝔽2)11yescharacteristic
327C22×C11C2×H(5,𝔽2)11yescharacteristic
328C22×C11#58512yes—
329C2×D11—24no—
330C2×D11—24no—
331C2×D11—24no—
332C2×D11—416no—
333C2×D11—44no—
334C2×D11—44no—
335C4×C11—22no—
336C4×C11—24no—
337C4×C11—24no—
338C4×C11—44no—
339C4×C11#53414yes—
340Dic11—24no—
341Dic11—44no—
342Dic11—44no—
343Dic11—44no—
344C25—111no—
345C2×#41—228no—
346C2×#41—444no—
347C2×#41—444no—
348C22×Q8—112no—
349C22×D4—114no—
350C22×D4—114no—
351C22×D4C22×D1114yes—
352C22×D4C22×D1112yes—
353C22×D4C22×D1114yes—
354C23×C4—111no—
355C23×C4—112no—
356C23×C4—118no—
357C23×C4—112no—
358C23×C4—112no—
359C23×C4—114no—
360C23×C4—442no—
361C23×C4—442no—
362C23×C4C22×D1111yescharacteristic
363C23×C4C22×D1112yes—
364C4⋊Q8—442no—
365#127—42no—
366#124—444no—
367#123—2216no—
368C22⋊Q8—228no—
369C22⋊Q8—228no—
370#121—28no—
371#121—216no—
372#121—228no—
373#120—2216no—
374C4×D4—2216no—
375C4×D4—2216no—
376#117—228no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—114no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—114no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4C22×D1112yes—
383C2×C4⋊C4C22×D1114yes—
384C2×C22⋊C4—114no—
385C2×C22⋊C4—114no—
386C2×C22⋊C4—114no—
387C2×C22⋊C4—114no—
388C2×C22⋊C4—114no—
389C2×C22⋊C4—114no—
390C2×C22⋊C4—118no—
391C2×C22⋊C4—118no—
392C2×C22⋊C4—228no—
393C2×C22⋊C4C22×D1114yes—
394C2×C22⋊C4C22×D1118yes—
395C2×C42—42no—
396C2×C42—114no—
397C2×C42—112no—
398C2×C42—112no—
399C2×C42—442no—
400C2×C42C22×D1111yescharacteristic
401C2×C42C22×D1111yescharacteristic
402C2×C42C22×D1112yes—
403#95—114no—
404#95—114no—
405#95—118no—
406#95—118no—
407#95—118no—
408C2×C11—24no—
409C2×C11—84no—
410C2×C11C2×#53211yescharacteristic
411C2×C11C2×#53411yescharacteristic
412C2×C11#344911yescharacteristic
413C2×C11#350512yes—
414C2×C11#350612yes—
415D11—44no—
416C24—112no—
417C24—114no—
418C24—224no—
419C24—441no—
420C24—441no—
421C24—442no—
422C24C23×D1114yes—
423C24C23×D1111yescharacteristic
424#41—4432no—
425C2×Q8—224no—
426C2×Q8—224no—
427C2×Q8—224no—
428C2×D4—28no—
429C2×D4—216no—
430C2×D4—24no—
431C2×D4—28no—
432C2×D4—24no—
433C2×D4—24no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—228no—
437C2×D4—228no—
438C2×D4—444no—
439C2×D4—444no—
440C2×D4—448no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—112no—
446C22×C4—114no—
447C22×C4—118no—
448C22×C4—118no—
449C22×C4—114no—
450C22×C4—114no—
451C22×C4—114no—
452C22×C4—228no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—224no—
456C22×C4—4416no—
457C22×C4—442no—
458C22×C4—442no—
459C22×C4—442no—
460C22×C4—441no—
461C22×C4—441no—
462C22×C4—444no—
463C22×C4—444no—
464C22×C4—442no—
465C22×C4D4×D1114yes—
466C22×C4#434118yescomplemented
467C22×C4C23×D1114yes—
468C22×C4C23×D1111yescharacteristic
469C22×C4C23×D1112yes—
470C22×C4C23×D1112yes—
471C22×C4C23×D1111yescharacteristic
472C4⋊C4—24no—
473C4⋊C4—28no—
474C4⋊C4—228no—
475C4⋊C4—224no—
476C4⋊C4—228no—
477C4⋊C4—444no—
478C4⋊C4—444no—
479C22⋊C4—28no—
480C22⋊C4—216no—
481C22⋊C4—228no—
482C22⋊C4—228no—
483C22⋊C4—228no—
484C22⋊C4—228no—
485C22⋊C4—228no—
486C22⋊C4—228no—
487C22⋊C4—448no—
488C22⋊C4—448no—
489C42—22no—
490C42—22no—
491C42—42no—
492C42—228no—
493C42—224no—
494C42—442no—
495C11#3503211yescharacteristic, complemented, Sylow
496C23—21no—
497C23—21no—
498C23—22no—
499C23—24no—
500C23—28no—
501C23—24no—
502C23—24no—
503C23—28no—
504C23—114no—
505C23—228no—
506C23—224no—
507C23—222no—
508C23—222no—
509C23—224no—
510C23—444no—
511C23—444no—
512C23—448no—
513C23—448no—
514C23C2×D4×D1112yes—
515C23C2×#434114yes—
516C23C24×D1111yescharacteristic
517Q8—448no—
518D4—416no—
519D4—48no—
520D4—88no—
521D4—4416no—
522D4—4416no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—28no—
530C2×C4—24no—
531C2×C4—28no—
532C2×C4—48no—
533C2×C4—114no—
534C2×C4—222no—
535C2×C4—222no—
536C2×C4—2216no—
537C2×C4—224no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—224no—
543C2×C4—224no—
544C2×C4—228no—
545C2×C4—448no—
546C2×C4—444no—
547C2×C4—4416no—
548C2×C4—448no—
549C2×C4C2×D4×D1112yes—
550C2×C4C2×D4×D1112yes—
551C2×C4C2×#434114yes—
552C2×C4C2×#434114yes—
553C2×C4#6703712yes—
554C2×C4#6704212yes—
555C22—22no—
556C22—24no—
557C22—22no—
558C22—24no—
559C22—44no—
560C22—44no—
561C22—48no—
562C22—44no—
563C22—48no—
564C22—224no—
565C22—224no—
566C22—224no—
567C22—4416no—
568C22—444no—
569C22—444no—
570C22#1062324714yes—
571C22C22×D4×D1111yescharacteristic
572C22C22×#434112yes—
573C22C2×#6703711yescharacteristic
574C22C2×#6704211yescharacteristic
575C22#1062345312yes—
576C4—22no—
577C4—24no—
578C4—24no—
579C4—44no—
580C4—224no—
581C4—444no—
582C4—444no—
583C4—444no—
584C4#1062313614yes—
585C2—24no—
586C2—84no—
587C2—444no—
588C2C2×#1062324711yescharacteristic
589C2C2×#1062313611yescharacteristic
590C2#1308194311yescharacteristic
591C2#1308245012yes—
592C2#1308246512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2856C2
hypercenter#2856D11
hypocenterC11#35032
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2856

Complements

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

NH ≅ G/Ntype
1. C2×#10623137C2semidirect
2. #13076968C2semidirect
3. #13076915C2semidirect
4. #13074352C2semidirect
5. #13074225C2semidirect
6. #13073080C2semidirect
7. #13073066C2semidirect
8. #13072246C2semidirect
9. #13072232C2semidirect
10. #13071321C2semidirect
11. C2×C4×(C2×D11)⋊C4C2semidirect
12. C11×#2856C2semidirect
15. C2×C11×#127C22semidirect
21. C2×#66989C22semidirect
31. C2×#66922C22semidirect
32. C11×#390C22semidirect
33. C11×#390C22semidirect
34. C11×#384C22semidirect
36. #10622834C22semidirect
38. #10622833C22semidirect
42. #10622594C22semidirect
43. #10622590C22semidirect
44. #10622587C22semidirect
47. #10622564C22semidirect
48. #10622563C22semidirect
49. #10622558C22semidirect
53. #10622548C22semidirect
54. #10622542C22semidirect
55. #10622541C22semidirect
72. C22×C4×D11D4semidirect
142. C22×C4×C11#41semidirect
202. #2856D11semidirect
274. C2×#127C2×D11semidirect
297. #390C2×D11semidirect
298. #390C2×D11semidirect
307. #384C2×D11semidirect
466. C22×C4#4341semidirect
495. C11#35032semidirect

Maximal subgroups

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

subgroupindex
C2×#106231372
#130769682
#130769152
#130743522
#130742252
#130730802
#130730662
#130722462
#130722322
#130713212
C2×C4×(C2×D11)⋊C42
C11×#28562
#3503211