Finite Group Databasebeta

← #14720644

Subgroups — #14720644

Order 2816.

980 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082180C211yesmaximal, characteristic
2#13077282C211yesmaximal, characteristic, complemented
3#13067077C212yesmaximal, complemented
4#13067072C211yesmaximal, characteristic, complemented
5#13067051C212yesmaximal, complemented
6#13067042C211yesmaximal, characteristic, complemented
7#13067025C212yesmaximal, complemented
8#13067020C211yesmaximal, characteristic, complemented
9#13066999C212yesmaximal, complemented
10C2×#10622097C211yesmaximal, characteristic, complemented
11C8×C11×#41C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13#10623359—21no—
14#10623115C411yescharacteristic
15#10623112—21no—
16#10623110C411yescharacteristic
17#10623094C411yescharacteristic
18#10623089—21no—
19#10623087—22no—
20#10623082C411yescharacteristic
21#10623081C412yes—
22#10623072C412yes—
23#10623059—22no—
24D11×#117—21no—
25#10623010C2212yes—
26C4×#4339C2212yes—
27C2×C4×D44C2211yescharacteristic
28#10623001C2211yescharacteristic
29C8×Q8×C11—21no—
30C8×D4×C11—21no—
31C8×D4×C11—22no—
32C11×#431C2211yescharacteristic
33C11×#431C2212yescomplemented
34C2×C4×C8×C11C2211yescharacteristic
35C2×C4×C8×C11C2212yescomplemented
36#10622847—21no—
37#10622613—22no—
38#10622610—21no—
39#10622539C2212yescomplemented
40#10622538C2212yescomplemented
41#10622537C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
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—
57C22×C8×C11—21no—
58C22×C8×C11—22no—
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#66999—21no—
70#66999—21no—
71#66991—21no—
72#66991—21no—
73#66990—22no—
74#66988—22no—
75#66983C2×C412yes—
76#66982—22no—
77C4×C22⋊D11—22no—
78C4×C22⋊D11—22no—
79C4×C22⋊D11—22no—
80C2×(C2×D11)⋊C4—21no—
81#66979—21no—
82#66979C2×C412yes—
83C2×C4⋊Dic11C2×C411yescharacteristic
84#66977—21no—
85#66977C2×C412yes—
86#66977C2×C412yes—
87C2×#4318—21no—
88C22×C11⋊C8—21no—
89#66951—22no—
90#66949—22no—
91#66947—22no—
92#66945—21no—
93#66945—21no—
94C4⋊C4×D11—21no—
95C4⋊C4×D11—21no—
96#66942—22no—
97#66938—22no—
98#66937—22no—
99#66936—22no—
100C22⋊C4×D11—22no—
101#66932—22no—
102#66930—22no—
103#66929—22no—
104#66928C2×C412yes—
105C4×D44—21no—
106C4×D44—21no—
107C4×D44C2×C411yescharacteristic
108C4×D44C2×C411yescharacteristic
109C4×D44C2×C412yes—
110C4×D44C2311yescharacteristic
111C4×D44C2311yescharacteristic
112#66925—22no—
113#66925—22no—
114C42×D11—22no—
115#66923—21no—
116#66923C2×C412yes—
117#66922C2×C411yescharacteristic
118#66922C2×C411yescharacteristic
119C4×Dic22—21no—
120C4×Dic22C2×C412yes—
121C4×Dic22C2312yes—
122C11×C4⋊C8—21no—
123C11×C4⋊C8—22no—
124C11×C22⋊C8—21no—
125C11×C22⋊C8—22no—
126C4×C8×C11—21no—
127C4×C8×C11—22no—
128C4×C8×C11C2311yescharacteristic
129C4×C8×C11C2311yescharacteristic
130C4×C8×C11C2312yes—
131C22⋊(C11⋊C8)—22no—
132C22⋊(C11⋊C8)—22no—
133C4⋊(C11⋊C8)—21no—
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2312yes—
138#66867—22no—
139C4×C11⋊C8—22no—
140#17508—111nomaximal, Sylow
141C23×D11—21no—
142C11×#41—22no—
143C11×#41—22no—
144C2×Q8×C11C22⋊C411yescharacteristic
145C2×D4×C11C22⋊C412yes—
146C2×D4×C11C22⋊C411yescharacteristic
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C22×C412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D411yescharacteristic
153C2×C22⋊D11—22no—
154C2×C22⋊D11—22no—
155C22×Dic11—21no—
156#4339—24no—
157#4339—42no—
158C2×D44—22no—
159C2×D44—21no—
160C2×D44—41no—
161C2×D44C22×C411yescharacteristic
162C2×D44C22×C411yescharacteristic
163C2×C4×D11—22no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—22no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×Dic22—21no—
172C2×Dic22C22×C412yes—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—22no—
176C2×C8×C11—42no—
177C2×C8×C11—44no—
178C11×C4⋊C4C22⋊C412yes—
179C11×C4⋊C4C22⋊C411yescharacteristic
180C11×C4⋊C4C22⋊C411yescharacteristic
181C11×C4⋊C4C22⋊C412yes—
182C11×C22⋊C4C22⋊C412yes—
183C11×C22⋊C4C22⋊C412yes—
184C11×C22⋊C4C22⋊C412yes—
185C42×C11C22×C412yes—
186C42×C11C22×C411yescharacteristic
187C42×C11C2×D412yes—
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11C2×D412yes—
191C42×C11C2411yescharacteristic
192C22⋊Dic11—22no—
193C22⋊Dic11—22no—
194C22⋊Dic11—22no—
195(C2×D11)⋊C4—22no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—21no—
199(C2×D11)⋊C4—21no—
200(C2×D11)⋊C4—22no—
201(C2×D11)⋊C4—21no—
202(C2×D11)⋊C4—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11C22×C411yescharacteristic
208C4⋊Dic11C22×C412yes—
209C4⋊Dic11C22×C411yescharacteristic
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216C4×Dic11—22no—
217C4×Dic11—22no—
218C4×Dic11—22no—
219#4318—42no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—22no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—42no—
224#3475—111no—
225C8×#41D1111yescharacteristic, complemented
226#2925—111no—
227#1494—112no—
228#1493—111no—
229#1488—112no—
230#1486—111no—
231#1482—112no—
232#1481—111no—
233#1476—112no—
234C2×D4⋊C8—111no—
235C23×C11C2×C22⋊C412yes—
236C23×C11C2×C22⋊C411yescharacteristic
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—42no—
240C22×D11—42no—
241C22×D11—81no—
242Q8×C11—22no—
243D4×C11—24no—
244D4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—41no—
252C2×C4×C11—42no—
253C2×C4×C11C2×C22⋊C412yes—
254C2×C4×C11C2×C22⋊C412yes—
255C2×C4×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C2×C22⋊C412yes—
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11C2×C22⋊C411yescharacteristic
259C2×C4×C11#13512yes—
260C2×C4×C11#13512yes—
261C2×C4×C11C23×C411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C22⋊D11—44no—
265C22⋊D11—82no—
266C2×Dic11—21no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—21no—
270C2×Dic11—42no—
271D44—21no—
272D44—21no—
273D44—21no—
274D44—42no—
275D44#13112yes—
276C4×D11—44no—
277C4×D11—41no—
278C4×D11—41no—
279C4×D11—41no—
280C4×D11—41no—
281C4×D11—42no—
282C4×D11—42no—
283C4×D11—82no—
284Dic22—22no—
285Dic22—22no—
286Dic22—81no—
287C8×C11—22no—
288C8×C11—41no—
289C8×C11—42no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C11⋊C8—42no—
293#556—111no—
294#555—111no—
295#554—111no—
296#553—221no—
297#552—112no—
298#552—221no—
299#551—222no—
300#547—111no—
301#546—112no—
302#533—111no—
303#529—112no—
304#529—222no—
305#525—221no—
306C4×#41—112no—
307C4×#41C2×D1111yescharacteristic
308C2×C4×D4—111no—
309C2×#117—221no—
310C8×Q8—21no—
311C8×D4—21no—
312C8×D4—22no—
313#433—222no—
314#432—112no—
315#431—112no—
316#431C2×D1111yescharacteristic
317#431C2×D1112yescomplemented
318#423—111no—
319C2×C4⋊C8—111no—
320#408—221no—
321#405—221no—
322C2×C4×C8C2×D1111yescharacteristic
323C2×C4×C8C2×D1112yescomplemented
324Q8⋊C8—112no—
325Q8⋊C8—112no—
326Q8⋊C8—112no—
327Q8⋊C8—112no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8—111no—
332D4⋊C8—112no—
333D4⋊C8—112no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—22no—
339C22×C11#41612yes—
340C22×C11C22×C22⋊C411yescharacteristic
341C2×D11—22no—
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—84no—
348C4×C11—22no—
349C4×C11—21no—
350C4×C11—22no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—22no—
354C4×C11#41612yes—
355C4×C11C2×#13111yescharacteristic
356C4×C11#56811yescharacteristic
357C4×C11C2×#13511yescharacteristic
358C4×C11C2×#13511yescharacteristic
359Dic11—42no—
360Dic11—41no—
361Dic11—41no—
362Dic11—42no—
363C2×#41—112no—
364C2×#41D4411yescharacteristic
365C22×D4—111no—
366C23×C4—221no—
367C2×M16—221no—
368C22×C8—21no—
369C22×C8—22no—
370C22×C8—221no—
371C4⋊Q8—111no—
372C4⋊Q8—111no—
373#126—222no—
374#126—222no—
375#126—222no—
376#125—112no—
377#125—222no—
378#125—221no—
379#124—112no—
380#124—222no—
381#123—222no—
382#123—222no—
383#123—222no—
384#123—222no—
385C22⋊Q8—112no—
386C22⋊Q8—112no—
387C22⋊Q8—221no—
388C22⋊Q8—221no—
389C22⋊Q8—221no—
390C22⋊Q8—222no—
391#121—112no—
392#121—221no—
393#121—221no—
394#121—222no—
395#120—222no—
396C4×Q8—112no—
397C4×Q8—112no—
398C4×Q8—221no—
399C4×Q8C4×D1111yescharacteristic
400C4×Q8C22⋊D1111yescharacteristic
401C4×D4—111no—
402C4×D4—111no—
403C4×D4—112no—
404C4×D4—111no—
405C4×D4—111no—
406C4×D4—222no—
407C4×D4—222no—
408C4×D4—222no—
409C4×D4—221no—
410C4×D4—221no—
411C4×D4C4×D1112yes—
412C4×D4C4×D1111yescharacteristic
413C4×D4C22⋊D1112yes—
414C4×D4C22⋊D1111yescharacteristic
415#117—112no—
416#117—221no—
417#117—221no—
418#117—221no—
419#117—222no—
420#117—222no—
421#117—222no—
422#117D4411yescharacteristic
423#117D4412yes—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—222no—
429C2×C42—222no—
430C2×C42C22×D1111yescharacteristic
431C2×C42C22×D1112yes—
432C4⋊C8—21no—
433C4⋊C8—22no—
434C4⋊C8—111no—
435C4⋊C8—111no—
436C4⋊C8—112no—
437C4⋊C8—221no—
438C4⋊C8—221no—
439C22⋊C8—21no—
440C22⋊C8—22no—
441C22⋊C8—222no—
442C22⋊C8—222no—
443#97—222no—
444C4×C8—21no—
445C4×C8—22no—
446C4×C8—222no—
447C4×C8C22×D1111yescharacteristic
448C4×C8C22×D1111yescharacteristic
449C4×C8C22×D1112yes—
450C2×C11—22no—
451C2×C11—42no—
452C2×C11#288011yescharacteristic
453C2×C11C2×#41611yescharacteristic
454C2×C11#290111yescharacteristic
455D11—42no—
456D11—81no—
457C24—221no—
458#41—22no—
459#41—22no—
460#41—224no—
461#41—442no—
462C2×Q8—112no—
463C2×Q8—221no—
464C2×Q8(C2×D11)⋊C411yescharacteristic
465C2×D4—111no—
466C2×D4—111no—
467C2×D4—222no—
468C2×D4—222no—
469C2×D4—222no—
470C2×D4—221no—
471C2×D4—441no—
472C2×D4(C2×D11)⋊C412yes—
473C2×D4(C2×D11)⋊C411yescharacteristic
474C22×C4—221no—
475C22×C4—222no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—222no—
481C22×C4—442no—
482C22×C4—442no—
483C22×C4C2×C4×D1111yescharacteristic
484C22×C4C2×C4×D1112yes—
485C22×C4C2×D4412yes—
486C22×C4C2×D4411yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C22×C4C2×C22⋊D1112yes—
489M16—442no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—22no—
493C2×C8—42no—
494C2×C8—44no—
495C2×C8—221no—
496C2×C8—222no—
497C2×C8—221no—
498C2×C8—442no—
499C4⋊C4—111no—
500C4⋊C4—111no—
501C4⋊C4—112no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—222no—
506C4⋊C4—222no—
507C4⋊C4—222no—
508C4⋊C4—222no—
509C4⋊C4—222no—
510C4⋊C4—221no—
511C4⋊C4—222no—
512C4⋊C4(C2×D11)⋊C411yescharacteristic
513C4⋊C4(C2×D11)⋊C411yescharacteristic
514C4⋊C4(C2×D11)⋊C412yes—
515C4⋊C4(C2×D11)⋊C412yes—
516C22⋊C4—222no—
517C22⋊C4—222no—
518C22⋊C4—222no—
519C22⋊C4—222no—
520C22⋊C4—222no—
521C22⋊C4—221no—
522C22⋊C4—221no—
523C22⋊C4—222no—
524C22⋊C4—222no—
525C22⋊C4—221no—
526C22⋊C4—221no—
527C22⋊C4(C2×D11)⋊C412yes—
528C22⋊C4(C2×D11)⋊C412yes—
529C22⋊C4(C2×D11)⋊C412yes—
530C42—222no—
531C42—222no—
532C42—222no—
533C42C2×C4×D1111yescharacteristic
534C42C2×C4×D1112yes—
535C42C2×D4412yes—
536C42C2×D4411yescharacteristic
537C42C2×C22⋊D1112yes—
538C42C2×C22⋊D1111yescharacteristic
539C42C23×D1111yescharacteristic
540C11#1750811yescharacteristic, complemented, Sylow
541C23—221no—
542C23—221no—
543C23—442no—
544C23—442no—
545C23—881no—
546C23C2×(C2×D11)⋊C412yes—
547C23C2×(C2×D11)⋊C411yescharacteristic
548Q8—22no—
549Q8—222no—
550Q8—222no—
551Q8—881no—
552D4—24no—
553D4—22no—
554D4—112no—
555D4—221no—
556D4—221no—
557D4—221no—
558D4—442no—
559D4—444no—
560D4—882no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—221no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—221no—
573C2×C4—444no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—882no—
582C2×C4#6695712yes—
583C2×C4#6695712yes—
584C2×C4C2×(C2×D11)⋊C412yes—
585C2×C4C2×(C2×D11)⋊C412yes—
586C2×C4C2×(C2×D11)⋊C411yescharacteristic
587C2×C4C2×(C2×D11)⋊C412yes—
588C2×C4C2×(C2×D11)⋊C411yescharacteristic
589C2×C4C2×(C2×D11)⋊C411yescharacteristic
590C2×C4C22×C4×D1111yescharacteristic
591C2×C4C22×D4411yescharacteristic
592C2×C4C22×C22⋊D1111yescharacteristic
593C8—22no—
594C8—41no—
595C8—42no—
596C8—441no—
597C8—441no—
598C8—442no—
599C22—21no—
600C22—21no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—222no—
605C22—441no—
606C22—441no—
607C22—441no—
608C22—441no—
609C22—441no—
610C22—884no—
611C22#1062272612yes—
612C22C22×(C2×D11)⋊C411yescharacteristic
613C4—22no—
614C4—21no—
615C4—22no—
616C4—21no—
617C4—22no—
618C4—21no—
619C4—442no—
620C4—441no—
621C4—441no—
622C4—442no—
623C4#1062272612yes—
624C4C2×#6695711yescharacteristic
625C4C2×#6695711yescharacteristic
626C4D11×#13111yescharacteristic
627C4#1062328111yescharacteristic
628C2—22no—
629C2—42no—
630C2—442no—
631C2—881no—
632C2#1307706311yescharacteristic
633C2C2×#1062272611yescharacteristic
634C2#1307716411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC8×C11×#41C2
socleC22×C11C22×C22⋊C4
prime radical#13082180C2
cosocleC42×C11C24
hypercenterC8×#41D11
hypocenterC11#17508
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
2. #13077282C2semidirect
3. #13067077C2semidirect
4. #13067072C2semidirect
5. #13067051C2semidirect
6. #13067042C2semidirect
7. #13067025C2semidirect
8. #13067020C2semidirect
9. #13066999C2semidirect
10. C2×#10622097C2semidirect
11. C8×C11×#41C2semidirect
33. C11×#431C22semidirect
35. C2×C4×C8×C11C22semidirect
39. #10622539C22semidirect
40. #10622538C22semidirect
49. #10622094C22semidirect
50. #10622094C22semidirect
51. #10622094C22semidirect
52. #10622094C22semidirect
225. C8×#41D11semidirect
317. #431C2×D11semidirect
323. C2×C4×C8C2×D11semidirect
540. C11#17508semidirect

Maximal subgroups

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

subgroupindex
#130821802
#130772822
#130670772
#130670722
#130670512
#130670422
#130670252
#130670202
#130669992
C2×#106220972
C8×C11×#412
#1750811