Finite Group Databasebeta

← #14916556

Subgroups — #14916556

Order 2816.

2458 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623055C211yesmaximal, characteristic
2#13071756C214yesmaximal, complemented
3#13071746C214yesmaximal, complemented
4#13071567C212yesmaximal, complemented
5#13071563C212yesmaximal, complemented
6#13071548C212yesmaximal, complemented
7#13071542C212yesmaximal, complemented
8#13071380C214yesmaximal, complemented
9#13071368C214yesmaximal, complemented
10#13071225C211yesmaximal, characteristic, complemented
11#13071205C212yesmaximal, complemented
12#13070998C212yesmaximal, complemented
13C11×#2314C211yesmaximal, characteristic, complemented
14C22×#4339C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17#10623055C4116yescomplemented
18C2×#66950C2212yes—
19C2×#66948C2212yes—
20C2×#66945C2212yes—
21C2×#66945C2212yes—
22C2×#66945C2212yescomplemented
23C2×C4⋊C4×D11C2212yescomplemented
24C2×#66939C2212yes—
25C2×#66935C2212yes—
26C2×C4×D44C2212yes—
27C2×C4×D44C2212yes—
28C11×#388C2214yes—
29C11×#387C2214yescomplemented
30C11×#384C2211yescharacteristic, complemented
31C11×#382C2211yescharacteristic, complemented
32C11×#380C2212yes—
33C4×C11×C4⋊C4C2212yescomplemented
34#10622825C2212yes—
35#10622603C2214yes—
36#10622603C2214yescomplemented
37#10622601C2214yes—
38#10622600C2212yes—
39#10622600C2212yes—
40#10622600C2212yescomplemented
41#10622600C2212yescomplemented
42#10622594C2214yescomplemented
43C4⋊C4×Dic11C2214yescomplemented
44#10622570C2214yes—
45#10622569C2214yes—
46#10622568C2214yes—
47#10622564C2214yes—
48C22⋊C4×Dic11C2214yes—
49#10622553C2214yes—
50#10622552C2214yes—
51C4×(C2×D11)⋊C4C2214yescomplemented
52#10622549C2211yescharacteristic, complemented
53#10622548C2211yescharacteristic, complemented
54C4×C4⋊Dic11C2214yescomplemented
55C4×C4⋊Dic11C2212yescomplemented
56#10622283C2214yes—
57#10622283C2214yescomplemented
58#10622282C2214yes—
59#10622279C2214yes—
60#10622279C2214yescomplemented
61#10622278C2214yes—
62#10622278C2214yes—
63#10622278C2214yescomplemented
64#10622277C2214yes—
65#10622267C2214yescomplemented
66#10622266C2214yescomplemented
67#10622259C2214yescomplemented
68C24×D11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×C22⋊D11C2312yes—
71C23×Dic11C2311yescharacteristic
72C2×#4339—42no—
73C2×#4339—42no—
74C2×#4339C2×C418yes—
75C22×D44C2312yes—
76C22×D44C2312yes—
77C22×D44C2311yescharacteristic
78C22×C4×D11—42no—
79C22×C4×D11—42no—
80C22×C4×D11C2×C418yescomplemented
81C22×C4×D11C2312yes—
82C22×C4×D11C2312yes—
83C22×C4×D11C2314yes—
84C22×C4×D11C2312yes—
85C22×Dic22C2311yescharacteristic
86C11×#117C2×C418yescomplemented
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2314yes—
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C22⋊C4C2314yes—
92C2×C11×C22⋊C4C2312yes—
93C2×C42×C11C2314yes—
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2314yes—
102C2×(C2×D11)⋊C4C2314yes—
103C2×(C2×D11)⋊C4C2314yes—
104C2×(C2×D11)⋊C4C2312yes—
105C2×(C2×D11)⋊C4C2312yes—
106C2×(C2×D11)⋊C4C2312yes—
107C2×(C2×D11)⋊C4C2312yes—
108C2×C4⋊Dic11C2312yes—
109C2×C4⋊Dic11C2312yes—
110C2×C4⋊Dic11C2314yes—
111C2×C4⋊Dic11C2312yes—
112C2×C4⋊Dic11C2312yes—
113C2×Dic11⋊C4C2314yes—
114C2×C4×Dic11C2314yes—
115C2×C4×Dic11C2314yes—
116C2×C4×Dic11C2314yes—
117C2×C4×Dic11C2314yes—
118#66950C2×C4116yescomplemented
119#66948C2×C4116yes—
120#66945—44no—
121#66945—44no—
122#66945—44no—
123C4⋊C4×D11—44no—
124#66939C2×C4116yescomplemented
125#66935C2×C4116yescomplemented
126C4×D44C2×C4116yescomplemented
127C4×D44C2×C4116yescomplemented
128C11×#95C2314yes—
129C11×#95C2314yes—
130C11×#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138#34361—111nomaximal, Sylow
139C24×C11C2411yescharacteristic
140C23×D11—41no—
141C23×D11—41no—
142C23×D11—42no—
143C23×D11—42no—
144C23×D11C22×C414yes—
145C23×D11C2412yes—
146C23×D11C2412yes—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11C22×C414yes—
150C22×C4×C11C2414yes—
151C22×C4×C11C2414yes—
152C22×C4×C11C2411yescharacteristic
153C22×C4×C11C2412yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—42no—
157C2×C22⋊D11—42no—
158C2×C22⋊D11C22×C418yes—
159C22×Dic11—41no—
160C22×Dic11—41no—
161C22×Dic11C22×C414yes—
162C22×Dic11C2414yes—
163C22×Dic11C2414yes—
164C22×Dic11C2412yes—
165C22×Dic11C2412yes—
166#4339—416no—
167C2×D44—42no—
168C2×D44—42no—
169C2×D44—42no—
170C2×D44—42no—
171C2×D44—41no—
172C2×D44—41no—
173C2×D44C22×C418yes—
174C2×D44C22×C418yes—
175C2×D44C22×C414yes—
176C2×C4×D11—24no—
177C2×C4×D11—24no—
178C2×C4×D11—24no—
179C2×C4×D11—24no—
180C2×C4×D11—42no—
181C2×C4×D11—42no—
182C2×C4×D11—44no—
183C2×C4×D11—44no—
184C2×C4×D11—44no—
185C2×C4×D11—416no—
186C2×C4×D11C22×C418yes—
187C2×C4×D11C22×C418yes—
188C2×C4×D11C22×C418yes—
189C2×Dic22—41no—
190C2×Dic22—41no—
191C2×Dic22C22×C414yes—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—24no—
194C11×C4⋊C4—44no—
195C11×C4⋊C4C22×C418yes—
196C11×C22⋊C4—44no—
197C11×C22⋊C4C22×C418yes—
198C42×C11—44no—
199C42×C11C22×C414yes—
200C42×C11C22×C414yes—
201C22⋊Dic11—44no—
202(C2×D11)⋊C4—44no—
203(C2×D11)⋊C4—44no—
204(C2×D11)⋊C4—44no—
205(C2×D11)⋊C4—44no—
206(C2×D11)⋊C4—44no—
207(C2×D11)⋊C4—44no—
208(C2×D11)⋊C4—44no—
209(C2×D11)⋊C4C22×C418yes—
210(C2×D11)⋊C4C22×C418yes—
211(C2×D11)⋊C4C22×C418yes—
212(C2×D11)⋊C4C22×C418yes—
213C4⋊Dic11—24no—
214C4⋊Dic11—24no—
215C4⋊Dic11—44no—
216C4⋊Dic11C22×C418yes—
217C4⋊Dic11C22×C418yes—
218Dic11⋊C4—44no—
219C4×Dic11—44no—
220C4×Dic11—44no—
221C4×Dic11—44no—
222C4×Dic11—44no—
223C2×#525—111no—
224#2375—114no—
225#2374—114no—
226#2354—112no—
227#2354—112no—
228#2352—112no—
229#2352—112no—
230#2333—114no—
231#2332—114no—
232#2314—111no—
233#2314D1111yescharacteristic, complemented
234#2311—112no—
235#2280—112no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11C23×C412yes—
241C23×C11C2511yescharacteristic
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—22no—
251C22×D11—22no—
252C22×D11—22no—
253C22×D11—22no—
254C22×D11—44no—
255C22×D11—48no—
256C22×D11—44no—
257C22×D11—44no—
258C22×D11—48no—
259C22×D11C23×C414yes—
260C22×D11C23×C414yes—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—28no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—24no—
272C2×C4×C11—24no—
273C2×C4×C11—24no—
274C2×C4×C11C23×C414yes—
275C2×C4×C11C23×C414yes—
276C2×C4×C11C23×C412yes—
277C2×C4×C11C23×C412yes—
278C2×C4×C11H(5,𝔽2)12yes—
279C2×C4×C11H(5,𝔽2)12yes—
280C22⋊D11—48no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—24no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—24no—
290C2×Dic11—24no—
291C2×Dic11—44no—
292C2×Dic11C23×C414yes—
293C2×Dic11C23×C414yes—
294D44—48no—
295D44—48no—
296D44—44no—
297C4×D11—216no—
298C4×D11—216no—
299C4×D11—48no—
300C4×D11—88no—
301Dic22—44no—
302C22×#41—111no—
303C24×C4—111no—
304#525—1116no—
305C2×#123—112no—
306C2×C22⋊Q8—112no—
307C2×#121—112no—
308C2×#120—112no—
309C2×C4×D4—112no—
310C2×C4×D4—112no—
311C2×#117—112no—
312C2×#117—112no—
313C2×#117—112no—
314C2×#117C2×D1111yescharacteristic
315C22×C4⋊C4—112no—
316#391—114no—
317#390—114no—
318#390—114no—
319#390—114no—
320#388—114no—
321#388—114no—
322#388—114no—
323#388—114no—
324#388—114no—
325#388—114no—
326#388—114no—
327#388C2×D1114yes—
328#387—114no—
329#387—114no—
330#387—114no—
331#387C2×D1114yescomplemented
332#386—114no—
333#386—114no—
334#386—114no—
335#386—114no—
336#384—111no—
337#384C2×D1111yescharacteristic, complemented
338#382—111no—
339#382C2×D1111yescharacteristic, complemented
340#381—114no—
341#380—112no—
342#380—112no—
343#380—112no—
344#380—112no—
345#380—112no—
346#380C2×D1112yes—
347#379—114no—
348C4×C4⋊C4—114no—
349C4×C4⋊C4—112no—
350C4×C4⋊C4—114no—
351C4×C4⋊C4C2×D1112yescomplemented
352C4×C22⋊C4—114no—
353C4×C22⋊C4—114no—
354C4×C22⋊C4—114no—
355C4×C22⋊C4—114no—
356C22×C11—22no—
357C22×C11—24no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—42no—
361C22×C11C24×C411yescharacteristic
362C22×C11C2×H(5,𝔽2)11yescharacteristic
363C22×C11C2×H(5,𝔽2)11yescharacteristic
364C22×C11#58512yes—
365C22×C11#58512yes—
366C2×D11—24no—
367C2×D11—24no—
368C2×D11—24no—
369C2×D11—24no—
370C2×D11—24no—
371C2×D11—24no—
372C2×D11—416no—
373C2×D11—42no—
374C2×D11—42no—
375C2×D11—42no—
376C2×D11—42no—
377C2×D11—42no—
378C2×D11—42no—
379C2×D11—42no—
380C2×D11—42no—
381C4×C11—22no—
382C4×C11—24no—
383C4×C11—24no—
384C4×C11—44no—
385C4×C11—44no—
386C4×C11#51814yes—
387Dic11—24no—
388Dic11—24no—
389Dic11—44no—
390Dic11—44no—
391C25—111no—
392C2×#41—118no—
393C2×#41—442no—
394C2×#41—442no—
395C22×Q8—111no—
396C22×D4—112no—
397C22×D4—112no—
398C22×D4—112no—
399C22×D4—111no—
400C23×C4—111no—
401C23×C4—112no—
402C23×C4—112no—
403C23×C4—118no—
404C23×C4—112no—
405C23×C4—114no—
406C23×C4—442no—
407C23×C4—442no—
408C23×C4C22×D1111yescharacteristic
409#123—1116no—
410C22⋊Q8—1116no—
411#121—1116no—
412#120—1116no—
413C4×D4—1116no—
414C4×D4—1116no—
415#117—444no—
416#117—444no—
417#117—444no—
418#117C4×D1118yescomplemented
419C2×C4⋊C4—112no—
420C2×C4⋊C4—112no—
421C2×C4⋊C4—112no—
422C2×C4⋊C4—112no—
423C2×C4⋊C4—114no—
424C2×C4⋊C4—114no—
425C2×C4⋊C4—444no—
426C2×C4⋊C4C22×D1112yes—
427C2×C4⋊C4C22×D1112yes—
428C2×C4⋊C4C22×D1114yes—
429C2×C4⋊C4C22×D1112yes—
430C2×C22⋊C4—112no—
431C2×C22⋊C4—112no—
432C2×C22⋊C4—112no—
433C2×C22⋊C4—112no—
434C2×C22⋊C4—114no—
435C2×C22⋊C4—114no—
436C2×C22⋊C4—114no—
437C2×C22⋊C4—114no—
438C2×C22⋊C4—114no—
439C2×C22⋊C4—114no—
440C2×C22⋊C4—114no—
441C2×C22⋊C4—114no—
442C2×C22⋊C4C22×D1114yes—
443C2×C22⋊C4C22×D1112yes—
444C2×C42—114no—
445C2×C42—114no—
446C2×C42—114no—
447C2×C42—114no—
448C2×C42C22×D1114yes—
449C2×C42C22×D1111yescharacteristic
450C2×C42C22×D1111yescharacteristic
451#95—114no—
452#95—114no—
453#95—114no—
454#95—114no—
455#95—114no—
456#95—114no—
457#95—114no—
458#95C22×D1114yes—
459#95C22×D1114yes—
460#95C22×D1114yes—
461C2×C11—42no—
462C2×C11C2×#51811yescharacteristic
463C2×C11#342812yes—
464C2×C11#353911yescharacteristic
465C2×C11#353911yescharacteristic
466C2×C11#354012yes—
467D11—44no—
468D11—44no—
469C24—112no—
470C24—112no—
471C24—114no—
472C24—441no—
473C24—441no—
474C24—442no—
475C24—442no—
476C24C23×D1111yescharacteristic
477#41—4416no—
478C2×Q8—114no—
479C2×Q8—441no—
480C2×Q8—441no—
481C2×D4—118no—
482C2×D4—118no—
483C2×D4—118no—
484C2×D4—114no—
485C2×D4—441no—
486C2×D4—441no—
487C2×D4—442no—
488C2×D4—442no—
489C2×D4—442no—
490C2×D4—442no—
491C2×D4—442no—
492C2×D4—442no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—112no—
496C22×C4—112no—
497C22×C4—114no—
498C22×C4—118no—
499C22×C4—118no—
500C22×C4—118no—
501C22×C4—114no—
502C22×C4—114no—
503C22×C4—224no—
504C22×C4—224no—
505C22×C4—224no—
506C22×C4—224no—
507C22×C4—4416no—
508C22×C4—442no—
509C22×C4—442no—
510C22×C4—444no—
511C22×C4—444no—
512C22×C4—444no—
513C22×C4—441no—
514C22×C4—441no—
515C22×C4C2×C4×D1114yes—
516C22×C4C23×D1114yes—
517C22×C4C23×D1114yes—
518C22×C4C23×D1111yescharacteristic
519C22×C4C23×D1112yes—
520C22×C4C23×D1112yes—
521C22×C4C23×D1111yescharacteristic
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—44no—
525C4⋊C4—118no—
526C4⋊C4—118no—
527C4⋊C4—224no—
528C4⋊C4—224no—
529C4⋊C4—444no—
530C4⋊C4—444no—
531C4⋊C4C2×C4×D1118yes—
532C22⋊C4—44no—
533C22⋊C4—118no—
534C22⋊C4—118no—
535C22⋊C4—118no—
536C22⋊C4—118no—
537C22⋊C4—444no—
538C22⋊C4—444no—
539C22⋊C4—444no—
540C22⋊C4—444no—
541C22⋊C4—444no—
542C22⋊C4—444no—
543C22⋊C4—444no—
544C22⋊C4—444no—
545C22⋊C4C2×C4×D1118yes—
546C42—44no—
547C42—444no—
548C42—444no—
549C42—444no—
550C42—444no—
551C42C2×C4×D1114yes—
552C42C2×C4×D1114yes—
553C11#3436111yescharacteristic, complemented, Sylow
554C23—21no—
555C23—21no—
556C23—22no—
557C23—22no—
558C23—114no—
559C23—114no—
560C23—222no—
561C23—222no—
562C23—222no—
563C23—222no—
564C23—222no—
565C23—222no—
566C23—222no—
567C23—222no—
568C23—222no—
569C23—222no—
570C23—222no—
571C23—222no—
572C23—444no—
573C23—448no—
574C23—448no—
575C23—444no—
576C23—444no—
577C23C22×C4×D1112yes—
578C23C24×D1111yescharacteristic
579Q8—444no—
580D4—444no—
581D4—448no—
582D4—448no—
583D4—448no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—28no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—114no—
598C2×C4—114no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—2216no—
604C2×C4—2216no—
605C2×C4—224no—
606C2×C4—224no—
607C2×C4—224no—
608C2×C4—224no—
609C2×C4—224no—
610C2×C4—224no—
611C2×C4—448no—
612C2×C4—444no—
613C2×C4—888no—
614C2×C4C22×C4×D1114yes—
615C2×C4C22×C4×D1114yes—
616C2×C4C22×C4×D1112yes—
617C2×C4C22×C4×D1112yes—
618C2×C4#6704212yes—
619C2×C4#6704212yes—
620C22—22no—
621C22—24no—
622C22—42no—
623C22—41no—
624C22—41no—
625C22—224no—
626C22—224no—
627C22—224no—
628C22—224no—
629C22—224no—
630C22—224no—
631C22—4416no—
632C22—442no—
633C22—442no—
634C22—442no—
635C22—442no—
636C22—442no—
637C22—442no—
638C22—442no—
639C22—442no—
640C22C23×C4×D1111yescharacteristic
641C22C2×#6704211yescharacteristic
642C22C2×#6704211yescharacteristic
643C22#1062345512yes—
644C22#1062345712yes—
645C4—22no—
646C4—24no—
647C4—24no—
648C4—44no—
649C4—44no—
650C4—224no—
651C4—224no—
652C4—444no—
653C4—444no—
654C4#1062305214yes—
655C2—42no—
656C2—444no—
657C2—444no—
658C2C2×#1062305211yescharacteristic
659C2#1308181612yes—
660C2#1308287511yescharacteristic
661C2#1308287811yescharacteristic
662C2#1308288812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2314C2
socle, cosocleC23×C11C25
prime radicalC2×#10623055C2
hypercenter#2314D11
hypocenterC11#34361
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. #13071756C2semidirect
3. #13071746C2semidirect
4. #13071567C2semidirect
5. #13071563C2semidirect
6. #13071548C2semidirect
7. #13071542C2semidirect
8. #13071380C2semidirect
9. #13071368C2semidirect
10. #13071225C2semidirect
11. #13071205C2semidirect
12. #13070998C2semidirect
13. C11×#2314C2semidirect
17. #10623055C4semidirect
22. C2×#66945C22semidirect
23. C2×C4⋊C4×D11C22semidirect
29. C11×#387C22semidirect
30. C11×#384C22semidirect
31. C11×#382C22semidirect
33. C4×C11×C4⋊C4C22semidirect
36. #10622603C22semidirect
40. #10622600C22semidirect
41. #10622600C22semidirect
42. #10622594C22semidirect
43. C4⋊C4×Dic11C22semidirect
51. C4×(C2×D11)⋊C4C22semidirect
52. #10622549C22semidirect
53. #10622548C22semidirect
54. C4×C4⋊Dic11C22semidirect
55. C4×C4⋊Dic11C22semidirect
57. #10622283C22semidirect
60. #10622279C22semidirect
63. #10622278C22semidirect
65. #10622267C22semidirect
66. #10622266C22semidirect
67. #10622259C22semidirect
80. C22×C4×D11C2×C4semidirect
86. C11×#117C2×C4semidirect
118. #66950C2×C4semidirect
124. #66939C2×C4semidirect
125. #66935C2×C4semidirect
126. C4×D44C2×C4semidirect
127. C4×D44C2×C4semidirect
233. #2314D11semidirect
331. #387C2×D11semidirect
337. #384C2×D11semidirect
339. #382C2×D11semidirect
351. C4×C4⋊C4C2×D11semidirect
418. #117C4×D11semidirect
553. C11#34361semidirect

Maximal subgroups

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

subgroupindex
C2×#106230552
#130717562
#130717462
#130715672
#130715632
#130715482
#130715422
#130713802
#130713682
#130712252
#130712052
#130709982
C11×#23142
#3436111