Finite Group Databasebeta

← #14720684

Subgroups — #14720684

Order 2816.

1004 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082180C211yesmaximal, characteristic
2#13077184C211yesmaximal, characteristic, complemented
3#13067082C212yesmaximal, complemented
4#13067072C211yesmaximal, characteristic, complemented
5#13067056C212yesmaximal, complemented
6#13067042C211yesmaximal, characteristic, complemented
7#13067030C212yesmaximal, complemented
8#13067020C211yesmaximal, characteristic, complemented
9#13067004C212yesmaximal, complemented
10C2×#10622097C211yesmaximal, characteristic, complemented
11C11×#2965C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13#10623359—21no—
14C2×#67001—21no—
15#10623115C411yescharacteristic
16#10623112—21no—
17#10623110C411yescharacteristic
18#10623094C411yescharacteristic
19#10623089—21no—
20#10623087—22no—
21#10623082C411yescharacteristic
22#10623081C412yes—
23#10623072C412yes—
24#10623059—22no—
25D11×#117—21no—
26#10623010C2212yes—
27C4×#4339C2212yes—
28C2×C4×D44C2211yescharacteristic
29#10623001C2211yescharacteristic
30C11×#446—21no—
31C11×#436—21no—
32C11×#435—22no—
33C11×#431C2211yescharacteristic
34C11×#431C2212yescomplemented
35C4×C11×M16C2212yescomplemented
36C2×C4×C8×C11C2211yescharacteristic
37#10622612—22no—
38#10622612—21no—
39#10622537C2211yescharacteristic
40#10622537C2212yescomplemented
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2212yescomplemented
43#10622097C2211yescharacteristic
44#10622097C2212yes—
45#10622097C2212yes—
46#10622097C2211yescharacteristic
47#10622097C2211yescharacteristic
48#10622097C2211yescharacteristic
49#10622094C2212yescomplemented
50#10622094C2212yescomplemented
51#10622094C2212yescomplemented
52#10622094C2212yescomplemented
53C2×C11×#41D411yescharacteristic
54C2×#4339C2×C412yes—
55C22×D44C2×C411yescharacteristic
56C22×C4×D11—21no—
57C2×C11×M16—22no—
58C22×C8×C11—21no—
59C4×Q8×C11C2×C411yescharacteristic
60C4×Q8×C11D411yescharacteristic
61C4×D4×C11C2×C412yes—
62C4×D4×C11C2×C411yescharacteristic
63C4×D4×C11D412yes—
64C4×D4×C11D411yescharacteristic
65C11×#117D411yescharacteristic
66C11×#117D412yes—
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2312yes—
69#67001—44no—
70#66999—21no—
71#66999—21no—
72#66991—21no—
73#66991—21no—
74#66990—22no—
75#66988—22no—
76#66983C2×C412yes—
77#66982—22no—
78C4×C22⋊D11—22no—
79C4×C22⋊D11—22no—
80C4×C22⋊D11—22no—
81C2×(C2×D11)⋊C4—21no—
82#66979—21no—
83#66979C2×C412yes—
84C2×C4⋊Dic11C2×C411yescharacteristic
85#66977—21no—
86#66977C2×C412yes—
87#66977C2×C412yes—
88C2×#4318—21no—
89C2×#4318—22no—
90C22×C11⋊C8—21no—
91C22×C11⋊C8—22no—
92#66951—22no—
93#66949—22no—
94#66947—22no—
95#66945—21no—
96#66945—21no—
97C4⋊C4×D11—21no—
98C4⋊C4×D11—21no—
99#66942—22no—
100#66938—22no—
101#66937—22no—
102#66936—22no—
103C22⋊C4×D11—22no—
104#66932—22no—
105#66930—22no—
106#66929—22no—
107#66928C2×C412yes—
108C4×D44—21no—
109C4×D44—21no—
110C4×D44C2×C411yescharacteristic
111C4×D44C2×C411yescharacteristic
112C4×D44C2×C412yes—
113C4×D44C2311yescharacteristic
114C4×D44C2311yescharacteristic
115#66925—22no—
116#66925—22no—
117C42×D11—22no—
118#66923—21no—
119#66923C2×C412yes—
120#66922C2×C411yescharacteristic
121#66922C2×C411yescharacteristic
122C4×Dic22—21no—
123C4×Dic22C2×C412yes—
124C4×Dic22C2312yes—
125C11×C4⋊C8—21no—
126C11×C4⋊C8—22no—
127C11×C22⋊C8—21no—
128C11×C22⋊C8—22no—
129C11×#97—22no—
130C4×C8×C11—21no—
131C4×C8×C11C2311yescharacteristic
132C4×C8×C11C2311yescharacteristic
133C4×C8×C11C2312yes—
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)—22no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)—22no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2312yes—
141#17512—111nomaximal, Sylow
142C23×D11—21no—
143C11×#41—22no—
144C11×#41—22no—
145C2×Q8×C11C22⋊C411yescharacteristic
146C2×D4×C11C22⋊C412yes—
147C2×D4×C11C22⋊C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C22×C412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D411yescharacteristic
154C2×C22⋊D11—22no—
155C2×C22⋊D11—22no—
156C22×Dic11—21no—
157#4339—24no—
158#4339—42no—
159C2×D44—22no—
160C2×D44—21no—
161C2×D44—41no—
162C2×D44C22×C411yescharacteristic
163C2×D44C22×C411yescharacteristic
164C2×C4×D11—22no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—22no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×Dic22—21no—
173C2×Dic22C22×C412yes—
174C11×M16—44no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—22no—
178C2×C8×C11—42no—
179C11×C4⋊C4C22⋊C412yes—
180C11×C4⋊C4C22⋊C411yescharacteristic
181C11×C4⋊C4C22⋊C411yescharacteristic
182C11×C4⋊C4C22⋊C412yes—
183C11×C22⋊C4C22⋊C412yes—
184C11×C22⋊C4C22⋊C412yes—
185C11×C22⋊C4C22⋊C412yes—
186C42×C11C22×C412yes—
187C42×C11C22×C411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D412yes—
190C42×C11C2×D411yescharacteristic
191C42×C11C2×D412yes—
192C42×C11C2411yescharacteristic
193C22⋊Dic11—22no—
194C22⋊Dic11—22no—
195C22⋊Dic11—22no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—22no—
199(C2×D11)⋊C4—21no—
200(C2×D11)⋊C4—21no—
201(C2×D11)⋊C4—22no—
202(C2×D11)⋊C4—21no—
203(C2×D11)⋊C4—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11C22×C411yescharacteristic
209C4⋊Dic11C22×C412yes—
210C4⋊Dic11C22×C411yescharacteristic
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216Dic11⋊C4—22no—
217C4×Dic11—22no—
218C4×Dic11—22no—
219C4×Dic11—22no—
220#4318—44no—
221#4318—42no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—22no—
225C2×C11⋊C8—44no—
226C2×C11⋊C8—42no—
227#3475—111no—
228#2965D1111yescharacteristic, complemented
229#2906—111no—
230#1495—112no—
231#1493—111no—
232#1489—112no—
233#1486—111no—
234#1483—112no—
235#1481—111no—
236#1477—112no—
237C2×D4⋊C8—111no—
238C23×C11C2×C22⋊C412yes—
239C23×C11C2×C22⋊C411yescharacteristic
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—42no—
243C22×D11—42no—
244C22×D11—81no—
245Q8×C11—22no—
246D4×C11—24no—
247D4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—41no—
255C2×C4×C11—42no—
256C2×C4×C11C2×C22⋊C412yes—
257C2×C4×C11C2×C22⋊C412yes—
258C2×C4×C11C2×C22⋊C411yescharacteristic
259C2×C4×C11C2×C22⋊C412yes—
260C2×C4×C11C2×C22⋊C411yescharacteristic
261C2×C4×C11C2×C22⋊C411yescharacteristic
262C2×C4×C11AGL(1,ℤ/8)12yes—
263C2×C4×C11#13712yes—
264C2×C4×C11C23×C411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C22⋊D11—44no—
268C22⋊D11—82no—
269C2×Dic11—21no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—21no—
273C2×Dic11—42no—
274D44—21no—
275D44—21no—
276D44—21no—
277D44—42no—
278D44#13112yescomplemented
279C4×D11—44no—
280C4×D11—41no—
281C4×D11—41no—
282C4×D11—41no—
283C4×D11—41no—
284C4×D11—42no—
285C4×D11—42no—
286C4×D11—82no—
287Dic22—22no—
288Dic22—22no—
289Dic22—81no—
290C8×C11—22no—
291C8×C11—41no—
292C8×C11—42no—
293C11⋊C8—41no—
294C11⋊C8—42no—
295C11⋊C8—41no—
296C2×#131—221no—
297#556—111no—
298#555—111no—
299#554—111no—
300#553—221no—
301#552—112no—
302#552—221no—
303#551—222no—
304#547—111no—
305#546—112no—
306#533—111no—
307#529—112no—
308#529—222no—
309#525—221no—
310C4×#41—112no—
311C4×#41C2×D1111yescharacteristic
312C2×C4×D4—111no—
313C2×#117—221no—
314#446—21no—
315#436—21no—
316#435—22no—
317#431C2×D1111yescharacteristic
318#431C2×D1112yescomplemented
319#424—221no—
320#424—222no—
321#423—111no—
322#423—112no—
323C2×C4⋊C8—111no—
324C2×C4⋊C8—112no—
325C4×M16C2×D1112yescomplemented
326C2×C4×C8C2×D1111yescharacteristic
327Q8⋊C8—112no—
328Q8⋊C8—112no—
329Q8⋊C8—112no—
330Q8⋊C8—112no—
331D4⋊C8—111no—
332D4⋊C8—111no—
333D4⋊C8—111no—
334D4⋊C8—111no—
335D4⋊C8—112no—
336D4⋊C8—112no—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11#41712yes—
343C22×C11C22×C22⋊C411yescharacteristic
344C2×D11—22no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—84no—
351C4×C11—22no—
352C4×C11—21no—
353C4×C11—22no—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—22no—
357C4×C11#41712yes—
358C4×C11C2×#13111yescharacteristic
359C4×C11#56811yescharacteristic
360C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
361C4×C11C2×#13711yescharacteristic
362Dic11—42no—
363Dic11—41no—
364Dic11—41no—
365Dic11—42no—
366C2×#41—112no—
367C2×#41D4411yescharacteristic
368C22×D4—111no—
369C23×C4—221no—
370#131—444no—
371C2×M16—22no—
372C2×M16—222no—
373C2×M16—221no—
374C22×C8—21no—
375C22×C8—222no—
376C22×C8—221no—
377C4⋊Q8—111no—
378C4⋊Q8—111no—
379#126—222no—
380#126—222no—
381#126—222no—
382#125—112no—
383#125—222no—
384#125—221no—
385#124—112no—
386#124—222no—
387#123—222no—
388#123—222no—
389#123—222no—
390#123—222no—
391C22⋊Q8—112no—
392C22⋊Q8—112no—
393C22⋊Q8—221no—
394C22⋊Q8—221no—
395C22⋊Q8—221no—
396C22⋊Q8—222no—
397#121—112no—
398#121—221no—
399#121—221no—
400#121—222no—
401#120—222no—
402C4×Q8—112no—
403C4×Q8—112no—
404C4×Q8—221no—
405C4×Q8C4×D1111yescharacteristic
406C4×Q8C22⋊D1111yescharacteristic
407C4×D4—111no—
408C4×D4—111no—
409C4×D4—112no—
410C4×D4—111no—
411C4×D4—111no—
412C4×D4—222no—
413C4×D4—222no—
414C4×D4—222no—
415C4×D4—221no—
416C4×D4—221no—
417C4×D4C4×D1112yes—
418C4×D4C4×D1111yescharacteristic
419C4×D4C22⋊D1112yes—
420C4×D4C22⋊D1111yescharacteristic
421#117—112no—
422#117—221no—
423#117—221no—
424#117—221no—
425#117—222no—
426#117—222no—
427#117—222no—
428#117D4411yescharacteristic
429#117D4412yes—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—222no—
435C2×C42—222no—
436C2×C42C22×D1111yescharacteristic
437C2×C42C22×D1112yes—
438C4⋊C8—21no—
439C4⋊C8—22no—
440C4⋊C8—111no—
441C4⋊C8—111no—
442C4⋊C8—112no—
443C4⋊C8—222no—
444C4⋊C8—221no—
445C4⋊C8—222no—
446C4⋊C8—221no—
447C22⋊C8—21no—
448C22⋊C8—22no—
449#97—22no—
450C4×C8—21no—
451C4×C8C22×D1111yescharacteristic
452C4×C8C22×D1111yescharacteristic
453C4×C8C22×D1112yes—
454C2×C11—22no—
455C2×C11—42no—
456C2×C11#288011yescharacteristic
457C2×C11C2×#41711yescharacteristic
458C2×C11#290111yescharacteristic
459D11—42no—
460D11—81no—
461C24—221no—
462#41—22no—
463#41—22no—
464#41—224no—
465#41—442no—
466C2×Q8—112no—
467C2×Q8—221no—
468C2×Q8(C2×D11)⋊C411yescharacteristic
469C2×D4—111no—
470C2×D4—111no—
471C2×D4—222no—
472C2×D4—222no—
473C2×D4—222no—
474C2×D4—221no—
475C2×D4—441no—
476C2×D4(C2×D11)⋊C412yes—
477C2×D4(C2×D11)⋊C411yescharacteristic
478C22×C4—221no—
479C22×C4—222no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—222no—
485C22×C4—442no—
486C22×C4—442no—
487C22×C4C2×C4×D1111yescharacteristic
488C22×C4C2×C4×D1112yes—
489C22×C4C2×D4412yes—
490C22×C4C2×D4411yescharacteristic
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C2×C22⋊D1112yes—
493M16—44no—
494M16—444no—
495M16—442no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—22no—
499C2×C8—42no—
500C2×C8—221no—
501C2×C8—222no—
502C2×C8—221no—
503C2×C8—444no—
504C2×C8—442no—
505C4⋊C4—111no—
506C4⋊C4—111no—
507C4⋊C4—112no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4—222no—
514C4⋊C4—222no—
515C4⋊C4—222no—
516C4⋊C4—221no—
517C4⋊C4—222no—
518C4⋊C4(C2×D11)⋊C411yescharacteristic
519C4⋊C4(C2×D11)⋊C411yescharacteristic
520C4⋊C4(C2×D11)⋊C412yes—
521C4⋊C4(C2×D11)⋊C412yes—
522C22⋊C4—222no—
523C22⋊C4—222no—
524C22⋊C4—222no—
525C22⋊C4—222no—
526C22⋊C4—222no—
527C22⋊C4—221no—
528C22⋊C4—221no—
529C22⋊C4—222no—
530C22⋊C4—222no—
531C22⋊C4—221no—
532C22⋊C4—221no—
533C22⋊C4(C2×D11)⋊C412yes—
534C22⋊C4(C2×D11)⋊C412yes—
535C22⋊C4(C2×D11)⋊C412yes—
536C42—222no—
537C42—222no—
538C42—222no—
539C42C2×C4×D1111yescharacteristic
540C42C2×C4×D1112yes—
541C42C2×D4412yes—
542C42C2×D4411yescharacteristic
543C42C2×C22⋊D1111yescharacteristic
544C42C2×C22⋊D1112yes—
545C42C23×D1111yescharacteristic
546C11#1751211yescharacteristic, complemented, Sylow
547C23—221no—
548C23—221no—
549C23—442no—
550C23—442no—
551C23—881no—
552C23C2×(C2×D11)⋊C412yes—
553C23C2×(C2×D11)⋊C411yescharacteristic
554Q8—22no—
555Q8—222no—
556Q8—222no—
557Q8—881no—
558D4—24no—
559D4—22no—
560D4—112no—
561D4—221no—
562D4—221no—
563D4—221no—
564D4—442no—
565D4—444no—
566D4—882no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—221no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—221no—
579C2×C4—444no—
580C2×C4—442no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—882no—
588C2×C4#6696112yes—
589C2×C4#6696212yes—
590C2×C4C2×(C2×D11)⋊C412yes—
591C2×C4C2×(C2×D11)⋊C412yes—
592C2×C4C2×(C2×D11)⋊C411yescharacteristic
593C2×C4C2×(C2×D11)⋊C412yes—
594C2×C4C2×(C2×D11)⋊C411yescharacteristic
595C2×C4C2×(C2×D11)⋊C411yescharacteristic
596C2×C4C22×C4×D1111yescharacteristic
597C2×C4C22×D4411yescharacteristic
598C2×C4C22×C22⋊D1111yescharacteristic
599C8—22no—
600C8—41no—
601C8—42no—
602C8—441no—
603C8—442no—
604C8—441no—
605C22—21no—
606C22—21no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—222no—
611C22—441no—
612C22—441no—
613C22—441no—
614C22—441no—
615C22—441no—
616C22—884no—
617C22#1062274612yes—
618C22C22×(C2×D11)⋊C411yescharacteristic
619C4—22no—
620C4—21no—
621C4—22no—
622C4—21no—
623C4—22no—
624C4—21no—
625C4—442no—
626C4—441no—
627C4—441no—
628C4—442no—
629C4#1062274612yes—
630C4C2×#6696111yescharacteristic
631C4C2×#6696211yescharacteristic
632C4D11×#13111yescharacteristic
633C4#1062328111yescharacteristic
634C2—22no—
635C2—42no—
636C2—442no—
637C2—881no—
638C2#1307706311yescharacteristic
639C2C2×#1062274611yescharacteristic
640C2#1307716411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2965C2
socleC22×C11C22×C22⋊C4
prime radical#13082180C2
cosocleC42×C11C24
hypercenter#2965D11
hypocenterC11#17512
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2965

Complements

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

NH ≅ G/Ntype
2. #13077184C2semidirect
3. #13067082C2semidirect
4. #13067072C2semidirect
5. #13067056C2semidirect
6. #13067042C2semidirect
7. #13067030C2semidirect
8. #13067020C2semidirect
9. #13067004C2semidirect
10. C2×#10622097C2semidirect
11. C11×#2965C2semidirect
34. C11×#431C22semidirect
35. C4×C11×M16C22semidirect
40. #10622537C22semidirect
42. C2×C4⋊(C11⋊C8)C22semidirect
49. #10622094C22semidirect
50. #10622094C22semidirect
51. #10622094C22semidirect
52. #10622094C22semidirect
228. #2965D11semidirect
278. D44#131semidirect
318. #431C2×D11semidirect
325. C4×M16C2×D11semidirect
546. C11#17512semidirect

Maximal subgroups

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

subgroupindex
#130821802
#130771842
#130670822
#130670722
#130670562
#130670422
#130670302
#130670202
#130670042
C2×#106220972
C11×#29652
#1751211