Finite Group Databasebeta

← #15617110

Subgroups — #15617110

Order 2816.

2490 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076560C212yesmaximal, complemented
2#13074951C211yesmaximal, characteristic, complemented
3#13074185C212yesmaximal, complemented
4#13074181C214yesmaximal, complemented
5#13073866C212yesmaximal, complemented
6#13073861C214yesmaximal, complemented
7#13071936C214yesmaximal, complemented
8#13071934C212yesmaximal, complemented
9#13071599C212yesmaximal, complemented
10#13071592C214yesmaximal, complemented
11#13071105C212yesmaximal, complemented
12#13071103C211yesmaximal, characteristic, complemented
13C11×#2804C211yesmaximal, characteristic, complemented
14C22×#4343C2212yes—
15C22×#4341C2211yescharacteristic
16C2×#66990C2212yes—
17C2×C4×C22⋊D11C2214yes—
18C22×(C2×D11)⋊C4C2212yescomplemented
19C2×#66946C2212yes—
20C2×#66945C2212yescomplemented
21C2×#66945C2211yescharacteristic, complemented
22C2×#66935C2214yes—
23C2×#66935C2212yescomplemented
24C2×C22⋊C4×D11C2214yescomplemented
25C2×C42×D11C2211yescharacteristic, complemented
26C11×#400C2212yescomplemented
27C11×#393C2214yescomplemented
28C11×#391C2212yescomplemented
29C11×#390C2211yescharacteristic
30C11×#386C2212yes—
31C11×#385C2214yescomplemented
32#10622844C2214yescomplemented
33#10622843C2212yescomplemented
34#10622834C2211yescharacteristic
35#10622826C2212yescomplemented
36#10622605C2212yescomplemented
37#10622604C2212yes—
38#10622603C2214yescomplemented
39#10622602C2214yescomplemented
40#10622601C2212yes—
41#10622587C2211yescharacteristic, complemented
42#10622574C2214yes—
43#10622573C2214yes—
44#10622571C2214yes—
45#10622569C2214yes—
46#10622569C2214yescomplemented
47#10622558C2214yescomplemented
48#10622556C2212yescomplemented
49C22⋊C4×Dic11C2214yescomplemented
50#10622552C2212yes—
51#10622542C2211yescharacteristic, complemented
52#10622286C2214yescomplemented
53#10622284C2212yes—
54#10622282C2214yescomplemented
55#10622281C2214yescomplemented
56#10622279C2214yescomplemented
57#10622279C2214yescomplemented
58#10622278C2214yes—
59#10622278C2214yes—
60#10622278C2214yescomplemented
61#10622278C2214yescomplemented
62#10622278C2214yescomplemented
63#10622277C2214yescomplemented
64#10622273C2214yescomplemented
65#10622264C2214yescomplemented
66#10622264C2212yescomplemented
67C24×D11C2312yes—
68C22×Q8×C11C2312yes—
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11C2312yes—
71C22×C22⋊D11C2314yes—
72C22×C22⋊D11C2312yes—
73C23×Dic11C2312yes—
74C2×#4343—28no—
75C2×#4343—44no—
76C2×#4343—44no—
77C2×#4341—24no—
78C2×#4341—42no—
79C2×#4341—42no—
80C22×D44C2312yes—
81C22×D44C2314yes—
82C22×D44C2312yes—
83C22×C4×D11C2311yescharacteristic
84C22×C4×D11C2312yes—
85C22×C4×D11C2314yes—
86C22×C4×D11C2314yes—
87C22×Dic22C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C22⋊C4C2314yes—
92C2×C11×C22⋊C4C2314yes—
93C2×C11×C22⋊C4C2312yes—
94C2×C42×C11C2311yescharacteristic
95C2×C22⋊Dic11C2314yes—
96C2×C22⋊Dic11C2312yes—
97#66990—28no—
98C4×C22⋊D11—48no—
99C2×(C2×D11)⋊C4—44no—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2314yes—
102C2×(C2×D11)⋊C4C2314yes—
103C2×(C2×D11)⋊C4C2314yes—
104C2×(C2×D11)⋊C4C2314yes—
105C2×(C2×D11)⋊C4C2314yes—
106C2×(C2×D11)⋊C4C2314yes—
107C2×(C2×D11)⋊C4C2314yes—
108C2×(C2×D11)⋊C4C2312yes—
109C2×(C2×D11)⋊C4C2314yes—
110C2×C4⋊Dic11C2312yes—
111C2×C4⋊Dic11C2311yescharacteristic
112C2×Dic11⋊C4C2314yes—
113C2×C4×Dic11C2312yes—
114C2×C4×Dic11C2314yes—
115C2×C4×Dic11C2311yescharacteristic
116C2×C4×Dic11C2312yes—
117#66946—44no—
118#66945—42no—
119#66945—44no—
120#66935—216no—
121#66935—44no—
122C22⋊C4×D11—48no—
123C42×D11—42no—
124C11×#95C2312yes—
125C11×#95C2314yes—
126C11×#95C2314yes—
127C11×#95C2314yes—
128C11⋊#95C2312yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136#60045—111nomaximal, Sylow
137C24×C11C2412yes—
138C23×D11—24no—
139C23×D11—28no—
140C23×D11—44no—
141C23×D11—42no—
142C23×D11—42no—
143C23×D11C2414yes—
144C23×D11C2411yescharacteristic
145C2×Q8×C11—24no—
146C2×Q8×C11—42no—
147C2×Q8×C11—42no—
148C2×D4×C11—41no—
149C2×D4×C11—41no—
150C2×D4×C11#4114yescomplemented
151C22×C4×C11—42no—
152C22×C4×C11—44no—
153C22×C4×C11C2414yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2414yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2411yescharacteristic
158C2×C22⋊D11—28no—
159C2×C22⋊D11—24no—
160C2×C22⋊D11—28no—
161C2×C22⋊D11—24no—
162C2×C22⋊D11—44no—
163C2×C22⋊D11—42no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—42no—
167C22×Dic11C2412yes—
168C22×Dic11C2414yes—
169C22×Dic11C2412yes—
170C22×Dic11C2411yescharacteristic
171C22×Dic11C2412yes—
172#4343—432no—
173#4341—416no—
174C2×D44—28no—
175C2×D44—28no—
176C2×D44—28no—
177C2×D44—42no—
178C2×D44—42no—
179C2×D44—42no—
180C2×D44—44no—
181C2×D44#4118yescomplemented
182C2×C4×D11—22no—
183C2×C4×D11—24no—
184C2×C4×D11—28no—
185C2×C4×D11—28no—
186C2×C4×D11—22no—
187C2×C4×D11—24no—
188C2×C4×D11—22no—
189C2×C4×D11—24no—
190C2×C4×D11—44no—
191C2×C4×D11—44no—
192C2×C4×D11—44no—
193C2×C4×D11—44no—
194C2×Dic22—22no—
195C2×Dic22—41no—
196C2×Dic22—41no—
197C11×C4⋊C4—41no—
198C11×C4⋊C4—42no—
199C11×C4⋊C4—42no—
200C11×C22⋊C4—28no—
201C11×C22⋊C4—44no—
202C11×C22⋊C4—42no—
203C42×C11—41no—
204C22⋊Dic11—28no—
205C22⋊Dic11—24no—
206(C2×D11)⋊C4—28no—
207(C2×D11)⋊C4—28no—
208(C2×D11)⋊C4—28no—
209(C2×D11)⋊C4—28no—
210(C2×D11)⋊C4—28no—
211(C2×D11)⋊C4—44no—
212(C2×D11)⋊C4—44no—
213(C2×D11)⋊C4—42no—
214(C2×D11)⋊C4—44no—
215(C2×D11)⋊C4—44no—
216C4⋊Dic11—41no—
217C4⋊Dic11—42no—
218Dic11⋊C4—44no—
219C4×Dic11—24no—
220C4×Dic11—28no—
221C4×Dic11—41no—
222C4×Dic11—42no—
223#2804—112no—
224#2804D1111yescharacteristic, complemented
225#2679—111no—
226#2598—112no—
227#2598—114no—
228#2572—112no—
229#2572—114no—
230#2404—114no—
231#2404—112no—
232#2358—112no—
233#2358—114no—
234#2297—112no—
235#2297—111no—
236C23×C11—24no—
237C23×C11—24no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11C2×#4114yes—
241C23×C11C2511yescharacteristic
242C22×D11—24no—
243C22×D11—24no—
244C22×D11—22no—
245C22×D11—21no—
246C22×D11—24no—
247C22×D11—24no—
248C22×D11—22no—
249C22×D11—21no—
250C22×D11—24no—
251C22×D11—24no—
252C22×D11—48no—
253C22×D11—416no—
254C22×D11—88no—
255C22×D11—84no—
256C22×D11—84no—
257C22×D11C2×#4118yes—
258C22×D11H(5,𝔽2)12yes—
259Q8×C11—48no—
260D4×C11—44no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—24no—
266C2×C4×C11—24no—
267C2×C4×C11—22no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—24no—
272C2×C4×C11—24no—
273C2×C4×C11—84no—
274C2×C4×C11C2×#4112yes—
275C2×C4×C11C2×#4114yes—
276C22⋊D11—48no—
277C22⋊D11—416no—
278C2×Dic11—22no—
279C2×Dic11—21no—
280C2×Dic11—22no—
281C2×Dic11—21no—
282C2×Dic11—24no—
283C2×Dic11—24no—
284C2×Dic11—22no—
285C2×Dic11—24no—
286C2×Dic11—22no—
287C2×Dic11—24no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—48no—
291C2×Dic11H(5,𝔽2)12yes—
292C2×Dic11H(5,𝔽2)14yes—
293D44—48no—
294D44—48no—
295D44—416no—
296C4×D11—28no—
297C4×D11—216no—
298C4×D11—416no—
299C4×D11—88no—
300Dic22—44no—
301C22×#41—112no—
302C22×#41—111no—
303C2×#120—112no—
304C2×#120—114no—
305C2×#120—112no—
306C2×C4×D4—114no—
307C2×C4×D4—112no—
308C2×#117—111no—
309C2×#117—112no—
310C22×C22⋊C4—112no—
311C22×C22⋊C4—114no—
312C22×C42—111no—
313#400—114no—
314#400C2×D1112yescomplemented
315#399—112no—
316#394—112no—
317#394—114no—
318#393—114no—
319#393—114no—
320#393C2×D1114yescomplemented
321#392—114no—
322#392—112no—
323#391—112no—
324#391—111no—
325#391—111no—
326#391C2×D1112yescomplemented
327#390—111no—
328#390—112no—
329#390—112no—
330#390C2×D1111yescharacteristic
331#388—114no—
332#388—114no—
333#388—114no—
334#386—112no—
335#386—114no—
336#386—114no—
337#386—114no—
338#386—114no—
339#386—114no—
340#386—114no—
341#386—114no—
342#386—114no—
343#386C2×D1112yes—
344#385—114no—
345#385—114no—
346#385C2×D1114yescomplemented
347#383—114no—
348#383—112no—
349#381—112no—
350#381—114no—
351C4×C22⋊C4—114no—
352C4×C22⋊C4—114no—
353C4×C22⋊C4—114no—
354C22×C11—28no—
355C22×C11—24no—
356C22×C11—42no—
357C22×C11—44no—
358C22×C11—42no—
359C22×C11C22×#4111yescharacteristic
360C22×C11C22×#4112yes—
361C22×C11C2×H(5,𝔽2)11yescharacteristic
362C22×C11C2×H(5,𝔽2)12yes—
363C22×C11C2×H(5,𝔽2)11yescharacteristic
364C2×D11—28no—
365C2×D11—28no—
366C2×D11—28no—
367C2×D11—24no—
368C2×D11—22no—
369C2×D11—41no—
370C2×D11—42no—
371C2×D11—44no—
372C2×D11—44no—
373C2×D11—44no—
374C2×D11—41no—
375C2×D11—44no—
376C2×D11—816no—
377C4×C11—22no—
378C4×C11—24no—
379C4×C11—42no—
380C4×C11—44no—
381C4×C11—44no—
382Dic11—24no—
383Dic11—22no—
384Dic11—44no—
385Dic11—42no—
386Dic11—42no—
387C25—112no—
388C2×#41—228no—
389C2×#41—224no—
390C2×#41—442no—
391C2×#41—444no—
392C2×#41—442no—
393C2×#41—444no—
394C22×Q8—111no—
395C22×Q8C22×D1112yes—
396C22×D4—114no—
397C22×D4—112no—
398C22×D4—112no—
399C22×D4—112no—
400C22×D4—114no—
401C22×D4C22×D1111yescharacteristic
402C23×C4—112no—
403C23×C4—111no—
404C23×C4—112no—
405C23×C4—114no—
406C23×C4—114no—
407C23×C4C22×D1112yes—
408#120—2216no—
409#120—228no—
410#120—444no—
411C4×D4—444no—
412C4×D4—448no—
413#117—442no—
414#117—444no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—112no—
417C2×C4⋊C4—114no—
418C2×C4⋊C4C22×D1112yes—
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1112yes—
421C2×C22⋊C4—114no—
422C2×C22⋊C4—112no—
423C2×C22⋊C4—114no—
424C2×C22⋊C4—114no—
425C2×C22⋊C4—114no—
426C2×C22⋊C4—114no—
427C2×C22⋊C4—114no—
428C2×C22⋊C4—114no—
429C2×C22⋊C4—114no—
430C2×C22⋊C4—114no—
431C2×C22⋊C4—112no—
432C2×C22⋊C4—114no—
433C2×C22⋊C4—448no—
434C2×C22⋊C4—444no—
435C2×C22⋊C4C22×D1114yes—
436C2×C22⋊C4C22×D1114yes—
437C2×C22⋊C4C22×D1112yes—
438C2×C42—114no—
439C2×C42—112no—
440C2×C42—111no—
441C2×C42—112no—
442C2×C42—442no—
443C2×C42C22×D1111yescharacteristic
444#95—114no—
445#95—114no—
446#95—114no—
447#95—114no—
448#95—114no—
449#95—112no—
450#95—114no—
451#95—114no—
452#95C22×D1114yes—
453#95C22×D1114yes—
454#95C22×D1112yes—
455#95C22×D1114yes—
456C2×C11—44no—
457C2×C11#348111yescharacteristic
458C2×C11#348112yes—
459C2×C11#349012yes—
460C2×C11#349011yescharacteristic
461C2×C11#354911yescharacteristic
462D11—42no—
463D11—48no—
464C24—114no—
465C24—111no—
466C24—228no—
467C24—224no—
468C24—444no—
469C24—442no—
470C24—442no—
471C24C23×D1112yes—
472#41—4416no—
473#41—4432no—
474C2×Q8—24no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—222no—
478C2×Q8—441no—
479C2×Q8—441no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—118no—
483C2×D4—228no—
484C2×D4—228no—
485C2×D4—228no—
486C2×D4—228no—
487C2×D4—224no—
488C2×D4—228no—
489C2×D4—224no—
490C2×D4—442no—
491C2×D4—442no—
492C2×D4—442no—
493C2×D4—444no—
494C2×D4—444no—
495C2×D4—442no—
496C2×D4#434314yescomplemented
497C22×C4—42no—
498C22×C4—44no—
499C22×C4—111no—
500C22×C4—112no—
501C22×C4—112no—
502C22×C4—114no—
503C22×C4—112no—
504C22×C4—222no—
505C22×C4—224no—
506C22×C4—228no—
507C22×C4—222no—
508C22×C4—224no—
509C22×C4—228no—
510C22×C4—224no—
511C22×C4—222no—
512C22×C4—224no—
513C22×C4—224no—
514C22×C4—444no—
515C22×C4—444no—
516C22×C4—444no—
517C22×C4—444no—
518C22×C4—442no—
519C22×C4C23×D1114yes—
520C22×C4C23×D1112yes—
521C22×C4C23×D1114yes—
522C22×C4C23×D1111yescharacteristic
523C22×C4C23×D1112yes—
524C4⋊C4—41no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4—441no—
528C4⋊C4—442no—
529C4⋊C4—444no—
530C22⋊C4—28no—
531C22⋊C4—44no—
532C22⋊C4—42no—
533C22⋊C4—228no—
534C22⋊C4—228no—
535C22⋊C4—228no—
536C22⋊C4—228no—
537C22⋊C4—224no—
538C22⋊C4—228no—
539C22⋊C4—228no—
540C22⋊C4—444no—
541C22⋊C4—444no—
542C22⋊C4—442no—
543C22⋊C4—444no—
544C22⋊C4—444no—
545C42—41no—
546C42—224no—
547C42—228no—
548C42—441no—
549C42—442no—
550C11#6004511yescharacteristic, complemented, Sylow
551C23—24no—
552C23—24no—
553C23—22no—
554C23—22no—
555C23—118no—
556C23—112no—
557C23—224no—
558C23—221no—
559C23—224no—
560C23—222no—
561C23—224no—
562C23—224no—
563C23—222no—
564C23—221no—
565C23—224no—
566C23—224no—
567C23—4416no—
568C23—448no—
569C23—884no—
570C23—888no—
571C23—884no—
572C23C2×#434314yes—
573C23C24×D1111yescharacteristic
574Q8—48no—
575Q8—444no—
576D4—44no—
577D4—448no—
578D4—4416no—
579D4—448no—
580D4—448no—
581D4—4416no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—84no—
595C2×C4—114no—
596C2×C4—112no—
597C2×C4—2216no—
598C2×C4—228no—
599C2×C4—221no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—221no—
603C2×C4—224no—
604C2×C4—222no—
605C2×C4—224no—
606C2×C4—224no—
607C2×C4—222no—
608C2×C4—224no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—4416no—
612C2×C4—448no—
613C2×C4—888no—
614C2×C4C2×#434312yes—
615C2×C4#41×D1114yes—
616C22—28no—
617C22—24no—
618C22—42no—
619C22—42no—
620C22—44no—
621C22—228no—
622C22—228no—
623C22—224no—
624C22—228no—
625C22—222no—
626C22—441no—
627C22—444no—
628C22—442no—
629C22—444no—
630C22—441no—
631C22—444no—
632C22—444no—
633C22—8816no—
634C22C22×#434311yescharacteristic
635C22C2×#41×D1112yes—
636C22D11×H(5,𝔽2)11yescharacteristic
637C22D11×H(5,𝔽2)12yes—
638C22D11×H(5,𝔽2)11yescharacteristic
639C4—24no—
640C4—22no—
641C4—42no—
642C4—44no—
643C4—44no—
644C4—224no—
645C4—222no—
646C4—444no—
647C4—442no—
648C4—442no—
649C2—44no—
650C2—448no—
651C2—442no—
652C2#1308222511yescharacteristic
653C2#1308222712yes—
654C2#1308230212yes—
655C2#1308230611yescharacteristic
656C2#1308302011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2804C2
hypercenter#2804D11
hypocenterC11#60045
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2804

Complements

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

NH ≅ G/Ntype
1. #13076560C2semidirect
2. #13074951C2semidirect
3. #13074185C2semidirect
4. #13074181C2semidirect
5. #13073866C2semidirect
6. #13073861C2semidirect
7. #13071936C2semidirect
8. #13071934C2semidirect
9. #13071599C2semidirect
10. #13071592C2semidirect
11. #13071105C2semidirect
12. #13071103C2semidirect
13. C11×#2804C2semidirect
18. C22×(C2×D11)⋊C4C22semidirect
20. C2×#66945C22semidirect
21. C2×#66945C22semidirect
23. C2×#66935C22semidirect
24. C2×C22⋊C4×D11C22semidirect
25. C2×C42×D11C22semidirect
26. C11×#400C22semidirect
27. C11×#393C22semidirect
28. C11×#391C22semidirect
31. C11×#385C22semidirect
32. #10622844C22semidirect
33. #10622843C22semidirect
35. #10622826C22semidirect
36. #10622605C22semidirect
38. #10622603C22semidirect
39. #10622602C22semidirect
41. #10622587C22semidirect
46. #10622569C22semidirect
47. #10622558C22semidirect
48. #10622556C22semidirect
49. C22⋊C4×Dic11C22semidirect
51. #10622542C22semidirect
52. #10622286C22semidirect
54. #10622282C22semidirect
55. #10622281C22semidirect
56. #10622279C22semidirect
57. #10622279C22semidirect
60. #10622278C22semidirect
61. #10622278C22semidirect
62. #10622278C22semidirect
63. #10622277C22semidirect
64. #10622273C22semidirect
65. #10622264C22semidirect
66. #10622264C22semidirect
150. C2×D4×C11#41semidirect
181. C2×D44#41semidirect
224. #2804D11semidirect
314. #400C2×D11semidirect
320. #393C2×D11semidirect
326. #391C2×D11semidirect
346. #385C2×D11semidirect
496. C2×D4#4343semidirect
550. C11#60045semidirect

Maximal subgroups

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

subgroupindex
#130765602
#130749512
#130741852
#130741812
#130738662
#130738612
#130719362
#130719342
#130715992
#130715922
#130711052
#130711032
C11×#28042
#6004511