Finite Group Databasebeta

← #15617109

Subgroups — #15617109

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#13076562C211yesmaximal, characteristic, complemented
2#13076560C212yesmaximal, complemented
3#13074951C211yesmaximal, characteristic, complemented
4#13074182C212yesmaximal, complemented
5#13074178C214yesmaximal, complemented
6#13073865C212yesmaximal, complemented
7#13073860C214yesmaximal, complemented
8#13071933C214yesmaximal, complemented
9#13071931C212yesmaximal, complemented
10#13071598C214yesmaximal, complemented
11#13071597C212yesmaximal, complemented
12#13071106C212yesmaximal, complemented
13C11×#2297C211yesmaximal, characteristic, complemented
14C22×C11×#41C2211yescharacteristic
15C22×#4339C2212yes—
16C2×C11×#117C2211yescharacteristic, complemented
17C22×C42×C11C2211yescharacteristic, complemented
18C2×#66990C2212yes—
19C2×#66990C2212yescomplemented
20C22×(C2×D11)⋊C4C2212yescomplemented
21C2×#66979C2212yescomplemented
22C2×#66935C2214yes—
23C2×(C22⋊D11)⋊C4C2214yes—
24C2×C22⋊C4×D11C2214yescomplemented
25C2×C4×D44C2212yes—
26C11×#391C2211yescharacteristic, complemented
27C11×#391C2211yescharacteristic, complemented
28C11×#390C2211yescharacteristic
29C11×#390C2211yescharacteristic
30C11×#386C2214yescomplemented
31C4×C11×C22⋊C4C2214yescomplemented
32#10622844C2214yescomplemented
33#10622836C2214yes—
34#10622833C2212yes—
35#10622833C2212yescomplemented
36#10622826C2214yes—
37#10622826C2214yescomplemented
38#10622826C2214yescomplemented
39#10622824C2212yescomplemented
40#10622604C2212yes—
41#10622602C2214yescomplemented
42#10622599C2212yescomplemented
43#10622574C2214yes—
44#10622573C2212yes—
45#10622569C2214yes—
46#10622569C2214yescomplemented
47#10622563C2214yescomplemented
48#10622562C2212yescomplemented
49#10622560C2214yescomplemented
50#10622557C2214yescomplemented
51#10622553C2214yescomplemented
52#10622552C2212yes—
53#10622552C2212yes—
54C4×(C2×D11)⋊C4C2214yescomplemented
55C4×(C2×D11)⋊C4C2214yescomplemented
56#10622550C2212yescomplemented
57#10622542C2212yescomplemented
58#10622542C2212yescomplemented
59#10622286C2214yescomplemented
60#10622283C2214yescomplemented
61#10622281C2214yescomplemented
62#10622278C2214yes—
63#10622278C2214yes—
64#10622277C2214yescomplemented
65#10622273C2214yescomplemented
66#10622264C2214yescomplemented
67C24×D11C2312yes—
68C2×C11×#41—24no—
69C2×C11×#41—42no—
70C2×C11×#41—42no—
71C22×Q8×C11C2311yescharacteristic
72C22×D4×C11C2312yes—
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11C2312yes—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2312yes—
77C22×C22⋊D11C2314yes—
78C22×C22⋊D11C2314yes—
79C23×Dic11C2312yes—
80C2×#4339—28no—
81C2×#4339—44no—
82C2×#4339—44no—
83C22×D44C2312yes—
84C22×D44C2312yes—
85C22×C4×D11C2314yes—
86C22×C4×D11C2314yes—
87C22×Dic22C2312yes—
88C11×#117—42no—
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4C2314yes—
92C2×C11×C22⋊C4C2314yes—
93C2×C11×C22⋊C4C2312yes—
94C2×C42×C11—42no—
95C2×C42×C11C2312yes—
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2312yes—
98C2×C42×C11C2311yescharacteristic
99C2×C22⋊Dic11C2312yes—
100C2×C22⋊Dic11C2314yes—
101C2×C22⋊Dic11C2314yes—
102C2×C22⋊Dic11C2312yes—
103#66990—28no—
104#66990—44no—
105C2×(C2×D11)⋊C4—44no—
106C2×(C2×D11)⋊C4C2314yes—
107C2×(C2×D11)⋊C4C2314yes—
108C2×(C2×D11)⋊C4C2314yes—
109C2×(C2×D11)⋊C4C2314yes—
110C2×(C2×D11)⋊C4C2314yes—
111C2×(C2×D11)⋊C4C2314yes—
112C2×(C2×D11)⋊C4C2314yes—
113C2×(C2×D11)⋊C4C2314yes—
114#66979—44no—
115C2×C4⋊Dic11C2312yes—
116C2×C4⋊Dic11C2312yes—
117C2×C4⋊Dic11C2312yes—
118C2×Dic11⋊C4C2314yes—
119C2×C4×Dic11C2314yes—
120#66935—216no—
121(C22⋊D11)⋊C4—48no—
122C22⋊C4×D11—48no—
123C4×D44—44no—
124C11×#95C2314yes—
125C11×#95C2314yes—
126C11⋊#95C2312yes—
127C11⋊#95C2314yes—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2312yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136#60045—111nomaximal, Sylow
137C24×C11C2412yes—
138C24×C11C2411yescharacteristic
139C23×D11—24no—
140C23×D11—28no—
141C23×D11—44no—
142C23×D11—42no—
143C23×D11—42no—
144C23×D11C2414yes—
145C11×#41—416no—
146C2×Q8×C11—22no—
147C2×Q8×C11—41no—
148C2×Q8×C11—41no—
149C2×D4×C11—24no—
150C2×D4×C11—24no—
151C2×D4×C11—41no—
152C2×D4×C11—41no—
153C2×D4×C11—42no—
154C2×D4×C11#4114yescomplemented
155C22×C4×C11—24no—
156C22×C4×C11—22no—
157C22×C4×C11—24no—
158C22×C4×C11—22no—
159C22×C4×C11—24no—
160C22×C4×C11—22no—
161C22×C4×C11—24no—
162C22×C4×C11—24no—
163C22×C4×C11—42no—
164C22×C4×C11C2412yes—
165C22×C4×C11C2412yes—
166C22×C4×C11C2412yes—
167C22×C4×C11C2411yescharacteristic
168C22×C4×C11C2412yes—
169C22×C4×C11C2411yescharacteristic
170C22×C4×C11C2412yes—
171C2×C22⋊D11—28no—
172C2×C22⋊D11—28no—
173C2×C22⋊D11—28no—
174C2×C22⋊D11—28no—
175C2×C22⋊D11—44no—
176C2×C22⋊D11—44no—
177C22×Dic11—44no—
178C22×Dic11—42no—
179C22×Dic11C2414yes—
180C22×Dic11C2414yes—
181C22×Dic11C2414yes—
182#4339—432no—
183C2×D44—28no—
184C2×D44—42no—
185C2×D44—42no—
186C2×D44—42no—
187C2×D44#4118yescomplemented
188C2×C4×D11—28no—
189C2×C4×D11—28no—
190C2×C4×D11—44no—
191C2×C4×D11—44no—
192C2×C4×D11—44no—
193C2×C4×D11—44no—
194C2×Dic22—24no—
195C2×Dic22—42no—
196C2×Dic22—42no—
197C11×C4⋊C4—41no—
198C11×C4⋊C4—41no—
199C11×C22⋊C4—28no—
200C11×C22⋊C4—28no—
201C11×C22⋊C4—42no—
202C42×C11—24no—
203C42×C11—41no—
204C42×C11—42no—
205C42×C11—41no—
206C22⋊Dic11—24no—
207C22⋊Dic11—44no—
208C22⋊Dic11—44no—
209C22⋊Dic11—42no—
210(C2×D11)⋊C4—28no—
211(C2×D11)⋊C4—28no—
212(C2×D11)⋊C4—28no—
213(C2×D11)⋊C4—28no—
214(C2×D11)⋊C4—28no—
215(C2×D11)⋊C4—44no—
216(C2×D11)⋊C4—44no—
217(C2×D11)⋊C4—44no—
218C4⋊Dic11—42no—
219C4⋊Dic11—42no—
220C4⋊Dic11—42no—
221Dic11⋊C4—44no—
222C4×Dic11—28no—
223#2804—112no—
224#2804—111no—
225#2679—111no—
226#2598—114no—
227#2598—112no—
228#2572—112no—
229#2572—114no—
230#2404—114no—
231#2404—112no—
232#2358—112no—
233#2358—114no—
234#2297—112no—
235#2297D1111yescharacteristic, complemented
236C23×C11—24no—
237C23×C11—22no—
238C23×C11—21no—
239C23×C11—22no—
240C23×C11—24no—
241C23×C11—22no—
242C23×C11—21no—
243C23×C11—22no—
244C23×C11C2×#4114yes—
245C23×C11H(5,𝔽2)12yes—
246C23×C11C2511yescharacteristic
247C22×D11—24no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—24no—
251C22×D11—24no—
252C22×D11—24no—
253C22×D11—48no—
254C22×D11—416no—
255C22×D11—88no—
256C22×D11—84no—
257C22×D11—84no—
258C22×D11C2×#4118yes—
259Q8×C11—44no—
260D4×C11—44no—
261D4×C11—48no—
262C2×C4×C11—216no—
263C2×C4×C11—28no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—24no—
273C2×C4×C11—22no—
274C2×C4×C11—24no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—48no—
280C2×C4×C11C2×#4112yes—
281C2×C4×C11C2×#4114yes—
282C2×C4×C11H(5,𝔽2)12yes—
283C2×C4×C11H(5,𝔽2)14yes—
284C22⋊D11—416no—
285C22⋊D11—416no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—24no—
290C2×Dic11—24no—
291C2×Dic11—24no—
292C2×Dic11—24no—
293C2×Dic11—24no—
294C2×Dic11—24no—
295C2×Dic11—84no—
296D44—48no—
297D44—48no—
298C4×D11—416no—
299C4×D11—88no—
300Dic22—48no—
301C22×#41—112no—
302C22×#41C2×D1111yescharacteristic
303C2×#120—112no—
304C2×#120—112no—
305C2×#120—114no—
306C2×C4×D4—114no—
307C2×C4×D4—112no—
308C2×#117—112no—
309C2×#117C2×D1111yescharacteristic, complemented
310C22×C22⋊C4—112no—
311C22×C22⋊C4—114no—
312C22×C42C2×D1111yescharacteristic, complemented
313#400—112no—
314#400—114no—
315#399—112no—
316#394—112no—
317#394—114no—
318#393—114no—
319#393—114no—
320#393—114no—
321#392—114no—
322#392—112no—
323#391—112no—
324#391—112no—
325#391C2×D1111yescharacteristic, complemented
326#391C2×D1111yescharacteristic, complemented
327#390—112no—
328#390—112no—
329#390C2×D1111yescharacteristic
330#390C2×D1111yescharacteristic
331#388—114no—
332#388—114no—
333#388—114no—
334#386—112no—
335#386—112no—
336#386—114no—
337#386—114no—
338#386—114no—
339#386—114no—
340#386—114no—
341#386—114no—
342#386—114no—
343#386C2×D1114yescomplemented
344#385—114no—
345#385—114no—
346#385—114no—
347#383—112no—
348#383—114no—
349#381—112no—
350#381—114no—
351C4×C22⋊C4—114no—
352C4×C22⋊C4—114no—
353C4×C22⋊C4C2×D1114yescomplemented
354C22×C11—28no—
355C22×C11—22no—
356C22×C11—24no—
357C22×C11—24no—
358C22×C11—42no—
359C22×C11—41no—
360C22×C11—42no—
361C22×C11—44no—
362C22×C11—42no—
363C22×C11—41no—
364C22×C11C22×#4111yescharacteristic
365C22×C11C22×#4112yes—
366C22×C11C2×H(5,𝔽2)11yescharacteristic
367C22×C11C2×H(5,𝔽2)11yescharacteristic
368C22×C11C2×H(5,𝔽2)12yes—
369C2×D11—28no—
370C2×D11—28no—
371C2×D11—28no—
372C2×D11—44no—
373C2×D11—44no—
374C2×D11—44no—
375C2×D11—44no—
376C2×D11—816no—
377C4×C11—22no—
378C4×C11—22no—
379C4×C11—24no—
380C4×C11—24no—
381C4×C11—42no—
382C4×C11—42no—
383C4×C11—42no—
384Dic11—44no—
385Dic11—44no—
386Dic11—44no—
387C25—112no—
388C2×#41—24no—
389C2×#41—42no—
390C2×#41—42no—
391C2×#41—228no—
392C2×#41—444no—
393C2×#41—444no—
394C22×Q8—112no—
395C22×Q8C22×D1111yescharacteristic
396C22×D4—114no—
397C22×D4—114no—
398C22×D4—112no—
399C22×D4—112no—
400C22×D4C22×D1112yes—
401C22×D4C22×D1111yescharacteristic
402C23×C4—112no—
403C23×C4—114no—
404C23×C4—114no—
405C23×C4C22×D1112yes—
406C23×C4C22×D1111yescharacteristic
407C23×C4C22×D1112yes—
408#120—2216no—
409#120—228no—
410#120—444no—
411C4×D4—444no—
412C4×D4—448no—
413#117—42no—
414#117—444no—
415C2×C4⋊C4—112no—
416C2×C4⋊C4—112no—
417C2×C4⋊C4—114no—
418C2×C4⋊C4—112no—
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C22⋊C4—112no—
422C2×C22⋊C4—114no—
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—112no—
430C2×C22⋊C4—114no—
431C2×C22⋊C4—114no—
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—42no—
439C2×C42—114no—
440C2×C42C22×D1112yes—
441C2×C42C22×D1111yescharacteristic
442C2×C42C22×D1112yes—
443C2×C42C22×D1111yescharacteristic
444#95—114no—
445#95—114no—
446#95—114no—
447#95—114no—
448#95—112no—
449#95—114no—
450#95—112no—
451#95—114no—
452#95—114no—
453#95—114no—
454#95C22×D1114yes—
455#95C22×D1114yes—
456C2×C11—44no—
457C2×C11—42no—
458C2×C11#348111yescharacteristic
459C2×C11#348112yes—
460C2×C11#349012yes—
461C2×C11#349011yescharacteristic
462C2×C11#354911yescharacteristic
463D11—48no—
464C24—114no—
465C24—228no—
466C24—224no—
467C24—442no—
468C24—444no—
469C24—442no—
470C24C23×D1112yes—
471C24C23×D1111yescharacteristic
472#41—416no—
473#41—4432no—
474C2×Q8—22no—
475C2×Q8—41no—
476C2×Q8—41no—
477C2×Q8—224no—
478C2×Q8—442no—
479C2×Q8—442no—
480C2×D4—24no—
481C2×D4—24no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—42no—
485C2×D4—118no—
486C2×D4—228no—
487C2×D4—228no—
488C2×D4—228no—
489C2×D4—228no—
490C2×D4—228no—
491C2×D4—442no—
492C2×D4—442no—
493C2×D4—442no—
494C2×D4—444no—
495C2×D4—444no—
496C2×D4#433914yescomplemented
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—42no—
506C22×C4—114no—
507C22×C4—114no—
508C22×C4—114no—
509C22×C4—228no—
510C22×C4—228no—
511C22×C4—444no—
512C22×C4—444no—
513C22×C4—444no—
514C22×C4—444no—
515C22×C4—442no—
516C22×C4—444no—
517C22×C4C23×D1112yes—
518C22×C4C23×D1112yes—
519C22×C4C23×D1112yes—
520C22×C4C23×D1111yescharacteristic
521C22×C4C23×D1111yescharacteristic
522C22×C4C23×D1112yes—
523C22×C4C23×D1112yes—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—442no—
527C4⋊C4—442no—
528C4⋊C4—444no—
529C4⋊C4—442no—
530C22⋊C4—28no—
531C22⋊C4—28no—
532C22⋊C4—42no—
533C22⋊C4—228no—
534C22⋊C4—224no—
535C22⋊C4—228no—
536C22⋊C4—228no—
537C22⋊C4—228no—
538C22⋊C4—228no—
539C22⋊C4—444no—
540C22⋊C4—444no—
541C22⋊C4—444no—
542C22⋊C4—444no—
543C22⋊C4—444no—
544C22⋊C4—442no—
545C42—24no—
546C42—42no—
547C42—41no—
548C42—41no—
549C42—228no—
550C11#6004511yescharacteristic, complemented, Sylow
551C23—21no—
552C23—21no—
553C23—22no—
554C23—22no—
555C23—24no—
556C23—22no—
557C23—24no—
558C23—22no—
559C23—118no—
560C23—224no—
561C23—224no—
562C23—224no—
563C23—224no—
564C23—224no—
565C23—224no—
566C23—4416no—
567C23—448no—
568C23—884no—
569C23—888no—
570C23—884no—
571C23C2×#433914yes—
572C23#6703712yes—
573C23C24×D1111yescharacteristic
574Q8—44no—
575Q8—448no—
576D4—44no—
577D4—48no—
578D4—448no—
579D4—448no—
580D4—4416no—
581D4—4416no—
582C2×C4—28no—
583C2×C4—216no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—48no—
600C2×C4—224no—
601C2×C4—224no—
602C2×C4—224no—
603C2×C4—224no—
604C2×C4—224no—
605C2×C4—224no—
606C2×C4—224no—
607C2×C4—224no—
608C2×C4—224no—
609C2×C4—4416no—
610C2×C4—888no—
611C2×C4—884no—
612C2×C4C2×#433912yes—
613C2×C4#6703712yes—
614C2×C4#41×D1114yes—
615C2×C4#6704214yes—
616C22—28no—
617C22—24no—
618C22—22no—
619C22—24no—
620C22—42no—
621C22—41no—
622C22—42no—
623C22—42no—
624C22—41no—
625C22—44no—
626C22—228no—
627C22—228no—
628C22—228no—
629C22—444no—
630C22—444no—
631C22—444no—
632C22—444no—
633C22—8816no—
634C22C22×#433911yescharacteristic
635C22C2×#6703711yescharacteristic
636C22C2×#6703711yescharacteristic
637C22C2×#41×D1112yes—
638C22C2×#6704212yes—
639C4—24no—
640C4—24no—
641C4—22no—
642C4—22no—
643C4—42no—
644C4—42no—
645C4—42no—
646C4—444no—
647C4—444no—
648C4—444no—
649C2—44no—
650C2—42no—
651C2—448no—
652C2#1308222411yescharacteristic
653C2#1308222612yes—
654C2#1308229912yes—
655C2#1308230511yescharacteristic
656C2#1308302111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2297C2
hypercenter#2297D11
hypocenterC11#60045
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2297

Complements

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

NH ≅ G/Ntype
1. #13076562C2semidirect
2. #13076560C2semidirect
3. #13074951C2semidirect
4. #13074182C2semidirect
5. #13074178C2semidirect
6. #13073865C2semidirect
7. #13073860C2semidirect
8. #13071933C2semidirect
9. #13071931C2semidirect
10. #13071598C2semidirect
11. #13071597C2semidirect
12. #13071106C2semidirect
13. C11×#2297C2semidirect
16. C2×C11×#117C22semidirect
17. C22×C42×C11C22semidirect
19. C2×#66990C22semidirect
20. C22×(C2×D11)⋊C4C22semidirect
21. C2×#66979C22semidirect
24. C2×C22⋊C4×D11C22semidirect
26. C11×#391C22semidirect
27. C11×#391C22semidirect
30. C11×#386C22semidirect
31. C4×C11×C22⋊C4C22semidirect
32. #10622844C22semidirect
35. #10622833C22semidirect
37. #10622826C22semidirect
38. #10622826C22semidirect
39. #10622824C22semidirect
41. #10622602C22semidirect
42. #10622599C22semidirect
46. #10622569C22semidirect
47. #10622563C22semidirect
48. #10622562C22semidirect
49. #10622560C22semidirect
50. #10622557C22semidirect
51. #10622553C22semidirect
54. C4×(C2×D11)⋊C4C22semidirect
55. C4×(C2×D11)⋊C4C22semidirect
56. #10622550C22semidirect
57. #10622542C22semidirect
58. #10622542C22semidirect
59. #10622286C22semidirect
60. #10622283C22semidirect
61. #10622281C22semidirect
64. #10622277C22semidirect
65. #10622273C22semidirect
66. #10622264C22semidirect
154. C2×D4×C11#41semidirect
187. C2×D44#41semidirect
235. #2297D11semidirect
309. C2×#117C2×D11semidirect
312. C22×C42C2×D11semidirect
325. #391C2×D11semidirect
326. #391C2×D11semidirect
343. #386C2×D11semidirect
353. C4×C22⋊C4C2×D11semidirect
496. C2×D4#4339semidirect
550. C11#60045semidirect

Maximal subgroups

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

subgroupindex
#130765622
#130765602
#130749512
#130741822
#130741782
#130738652
#130738602
#130719332
#130719312
#130715982
#130715972
#130711062
C11×#22972
#6004511