Finite Group Databasebeta

← #14720791

Subgroups — #14720791

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082226C211yesmaximal, characteristic
2#13077745C211yesmaximal, characteristic, complemented
3#13077258C211yesmaximal, characteristic, complemented
4#13067080C212yesmaximal, complemented
5#13067068C211yesmaximal, characteristic, complemented
6#13067055C211yesmaximal, characteristic, complemented
7#13067039C212yesmaximal, complemented
8#13067032C211yesmaximal, characteristic, complemented
9#13067023C212yesmaximal, complemented
10#13067005C212yesmaximal, complemented
11C11×#1476C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13#10623360C412yes—
14#10623116C411yescharacteristic
15#10623111C2212yes—
16#10623110C411yescharacteristic
17#10623096—21no—
18#10623081—21no—
19D4×D44C411yescharacteristic
20#10623078—22no—
21C4×D4×D11C2212yes—
22#10623074C411yescharacteristic
23#10623061C412yes—
24#10623058—22no—
25#10623010—21no—
26#10623008C2211yescharacteristic
27C4×#4339C2211yescharacteristic
28C2×C4×D44—21no—
29C11×#431C2211yescharacteristic, complemented
30C2×C4×C8×C11C2211yescharacteristic, complemented
31#10622723—21no—
32#10622715—21no—
33#10622537C2211yescharacteristic, complemented
34C4×#4318C2211yescharacteristic, complemented
35#10622450C2212yescomplemented
36#10622446C2212yescomplemented
37#10622342—22no—
38#10622303—22no—
39#10622301—21no—
40#10622298C2212yescomplemented
41#10622298C2212yescomplemented
42C8×Dic22—21no—
43C11×Q8⋊C8C2211yescharacteristic, complemented
44C11×Q8⋊C8C2211yescharacteristic, complemented
45C11×D4⋊C8C2211yescharacteristic
46C11×D4⋊C8C2211yescharacteristic
47Q8⋊(C11⋊C8)C2212yescomplemented
48D4⋊(C11⋊C8)C2212yes—
49#10622121C2212yescomplemented
50#10622121C2212yescomplemented
51#10622097C2212yescomplemented
52#10622097C2212yescomplemented
53C2×C11×#41C2×C411yescharacteristic
54C2×D4×D11C2×C412yes—
55C2×#4339—21no—
56C2×#4339D411yescharacteristic
57C22×D44—21no—
58C22×C4×D11—22no—
59C22×C8×C11—21no—
60C4×Q8×C11C2×C411yescharacteristic
61C4×Q8×C11C2311yescharacteristic
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C4×D4×C11C2×C411yescharacteristic
65C4×D4×C11C2311yescharacteristic
66C11×#117—21no—
67C11×#117C2×C411yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70#67000C2×C412yes—
71#66999C2×C412yes—
72#66992—22no—
73#66990—22no—
74D4×Dic11C2×C412yes—
75#66983—21no—
76#66983—21no—
77#66983C2×C412yes—
78#66982—22no—
79C4×C22⋊D11—22no—
80C4×C22⋊D11C2×C412yes—
81C4×C22⋊D11D412yes—
82C2×(C2×D11)⋊C4—22no—
83#66979D411yescharacteristic
84C2×C4⋊Dic11—21no—
85#66977—21no—
86C2×#4318—21no—
87C2×#4318—21no—
88C2×#4313—22no—
89#66951—22no—
90#66949—22no—
91#66948C2×C412yes—
92#66947—22no—
93#66947—22no—
94#66946C2×C412yes—
95C4⋊C4×D11C2×C412yes—
96#66943C2×C412yes—
97#66937—22no—
98#66936—22no—
99#66935—22no—
100(C22⋊D11)⋊C4—22no—
101C22⋊C4×D11—22no—
102#66931—22no—
103#66929—22no—
104#66928—21no—
105#66928—21no—
106#66927C2×C411yescharacteristic
107C4×D44—21no—
108C4×D44—22no—
109C4×D44—21no—
110C4×D44—22no—
111C4×D44—21no—
112C4×D44C2×C411yescharacteristic
113C4×D44D411yescharacteristic
114C4×D44C2312yes—
115#66925—22no—
116#66925D412yes—
117C42×D11C2312yes—
118#66923—21no—
119#66922C2×C411yescharacteristic
120C4×Dic22C2×C411yescharacteristic
121C4×Dic22D411yescharacteristic
122C11×C4⋊C8C2311yescharacteristic
123C11×C4⋊C8C2311yescharacteristic
124C11×C22⋊C8—21no—
125C4×C8×C11—21no—
126C4×C8×C11—21no—
127C4×C8×C11C2311yescharacteristic
128C4×C8×C11C2311yescharacteristic
129(C2×D11)⋊C8—22no—
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8—22no—
132Dic11⋊C8—22no—
133Dic11⋊C8—22no—
134Dic11⋊C8—22no—
135C8×Dic11—22no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2312yes—
138#66867—21no—
139C4×C11⋊C8C2312yes—
140#17522—111nomaximal, Sylow
141C23×D11—22no—
142C11×#41—22no—
143C11×#41—41no—
144C2×Q8×C11C22×C411yescharacteristic
145C2×D4×C11—21no—
146C2×D4×C11C22×C411yescharacteristic
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C2×C22⋊D11—22no—
154C2×C22⋊D11—22no—
155C2×C22⋊D11C22⋊C412yes—
156C22×Dic11—22no—
157D4×D11—24no—
158D4×D11—42no—
159#4339—42no—
160#4339—81no—
161#4339—81no—
162C2×D44—22no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—44no—
166C2×D44C22⋊C411yescharacteristic
167C2×D44C22×C412yes—
168C2×C4×D11—22no—
169C2×C4×D11—22no—
170C2×C4×D11—22no—
171C2×C4×D11—82no—
172C2×C4×D11—82no—
173C2×C4×D11C22×C412yes—
174C2×C4×D11C2×D412yes—
175C2×C4×D11C2×D412yes—
176C2×Dic22—21no—
177C2×Dic22C22⋊C411yescharacteristic
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—42no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4C22×C411yescharacteristic
186C11×C4⋊C4C22×C411yescharacteristic
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11C22×C411yescharacteristic
194C42×C11C2×D411yescharacteristic
195C42×C11C2×D411yescharacteristic
196C42×C11C2411yescharacteristic
197C22⋊Dic11—22no—
198C22⋊Dic11C22⋊C412yes—
199(C2×D11)⋊C4—22no—
200(C2×D11)⋊C4—22no—
201(C2×D11)⋊C4—22no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—22no—
204(C2×D11)⋊C4—22no—
205(C2×D11)⋊C4—22no—
206(C2×D11)⋊C4C22⋊C412yes—
207(C2×D11)⋊C4C22⋊C412yes—
208C4⋊Dic11—22no—
209C4⋊Dic11—21no—
210C4⋊Dic11C22⋊C411yescharacteristic
211C4⋊Dic11C22⋊C411yescharacteristic
212C4⋊Dic11C22×C412yes—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216Dic11⋊C4C22⋊C412yes—
217Dic11⋊C4C22⋊C412yes—
218C4×Dic11C22×C412yes—
219C4×Dic11C2×D412yes—
220C4×Dic11C2×D412yes—
221#4318—42no—
222#4318—81no—
223C2×C11⋊C8—22no—
224C2×C11⋊C8—22no—
225#4313—82no—
226#3481—111no—
227#2991—111no—
228#2922—111no—
229#1495—112no—
230#1492—111no—
231#1489—111no—
232#1486—112no—
233#1484—111no—
234#1482—112no—
235#1478—112no—
236#1476D1111yescharacteristic, complemented
237C23×C11—21no—
238C23×C11C2×C22⋊C411yescharacteristic
239C22×D11—22no—
240C22×D11—44no—
241C22×D11—44no—
242C22×D11—82no—
243C22×D11C2×C22⋊C412yes—
244Q8×C11—21no—
245Q8×C11—21no—
246D4×C11—21no—
247D4×C11—42no—
248D4×C11#13112yes—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—42no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11C2×C22⋊C411yescharacteristic
262C2×C4×C11C2×C22⋊C411yescharacteristic
263C2×C4×C11C2×C22⋊C411yescharacteristic
264C2×C4×C11C23×C411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C22⋊D11—42no—
268C22⋊D11—44no—
269C22⋊D11—82no—
270C2×Dic11—22no—
271C2×Dic11—82no—
272C2×Dic11C2×C22⋊C412yes—
273C2×Dic11C2×C22⋊C412yes—
274C2×Dic11C2×C22⋊C412yes—
275D44—22no—
276D44—22no—
277D44—22no—
278D44—44no—
279D44—42no—
280D44—81no—
281C4×D11—22no—
282C4×D11—22no—
283C4×D11—22no—
284C4×D11—22no—
285C4×D11—42no—
286C4×D11—42no—
287C4×D11—42no—
288C4×D11—82no—
289C4×D11—82no—
290Dic22—22no—
291Dic22—81no—
292C8×C11—41no—
293C8×C11—41no—
294C8×C11—41no—
295C8×C11—41no—
296C11⋊C8—42no—
297C11⋊C8—42no—
298#559—111no—
299#554—111no—
300#554—111no—
301#553—112no—
302#553—221no—
303#551—222no—
304#546—112no—
305#546—221no—
306D42—111no—
307#532—111no—
308#529—112no—
309#529—221no—
310#525—222no—
311C4×#41—111no—
312C4×#41C2×D1111yescharacteristic
313C2×C4×D4—112no—
314C2×C4×D4—221no—
315C8×Q8—221no—
316#436—221no—
317#436—222no—
318#433—222no—
319#431—112no—
320#431—112no—
321#431—112no—
322#431C2×D1111yescharacteristic, complemented
323#424—221no—
324#423—111no—
325#423—112no—
326#408—221no—
327C4×M16—111no—
328C2×C4×C8C2×D1111yescharacteristic, complemented
329Q8⋊C8—112no—
330Q8⋊C8C2×D1111yescharacteristic, complemented
331Q8⋊C8C2×D1111yescharacteristic, complemented
332D4⋊C8—112no—
333D4⋊C8—112no—
334D4⋊C8—112no—
335D4⋊C8—112no—
336D4⋊C8—112no—
337D4⋊C8C2×D1111yescharacteristic
338D4⋊C8C2×D1111yescharacteristic
339C22×C11—21no—
340C22×C11—22no—
341C22×C11—21no—
342C22×C11—21no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11C22×C22⋊C411yescharacteristic
346C2×D11—22no—
347C2×D11—22no—
348C2×D11—22no—
349C2×D11—42no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—88no—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11#42112yes—
360C4×C11C2×#13111yescharacteristic
361C4×C11#56811yescharacteristic
362C4×C11#57611yescharacteristic
363C4×C11#57711yescharacteristic
364Dic11—22no—
365Dic11—22no—
366Dic11—22no—
367Dic11—42no—
368C2×#41—111no—
369C2×#41—221no—
370C2×#41C4×D1111yescharacteristic
371C22×D4—112no—
372C22×D4—221no—
373C23×C4—222no—
374C2×M16—222no—
375C2×M16—221no—
376C2×M16—221no—
377C22×C8—21no—
378C4⋊Q8—111no—
379#127—111no—
380#126—222no—
381#126—222no—
382#125—112no—
383#125—221no—
384#124—112no—
385#124—221no—
386#124—221no—
387#123—222no—
388#123—222no—
389#123—222no—
390#123—222no—
391C22⋊Q8—112no—
392C22⋊Q8—222no—
393C22⋊Q8—222no—
394C22⋊Q8—221no—
395#121—112no—
396#121—112no—
397#121—222no—
398#121—222no—
399#121—221no—
400#121—221no—
401#120—222no—
402#120—222no—
403C4×Q8—111no—
404C4×Q8—111no—
405C4×Q8C4×D1111yescharacteristic
406C4×Q8C22×D1111yescharacteristic
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—112no—
410C4×D4—112no—
411C4×D4—112no—
412C4×D4—112no—
413C4×D4—111no—
414C4×D4—111no—
415C4×D4—112no—
416C4×D4—222no—
417C4×D4—221no—
418C4×D4—222no—
419C4×D4—221no—
420C4×D4—222no—
421C4×D4—222no—
422C4×D4—221no—
423C4×D4C4×D1111yescharacteristic
424C4×D4C22×D1111yescharacteristic
425#117—21no—
426#117—111no—
427#117—112no—
428#117—222no—
429#117C4×D1111yescharacteristic
430C2×C4⋊C4—112no—
431C2×C4⋊C4—221no—
432C2×C22⋊C4—222no—
433C2×C22⋊C4—222no—
434C2×C42—21no—
435C2×C42—112no—
436C2×C42C22×D1111yescharacteristic
437C4⋊C8—112no—
438C4⋊C8—222no—
439C4⋊C8—222no—
440C4⋊C8—222no—
441C4⋊C8—221no—
442C4⋊C8C22×D1111yescharacteristic
443C4⋊C8C22×D1111yescharacteristic
444C22⋊C8—21no—
445C22⋊C8—222no—
446C22⋊C8—222no—
447C22⋊C8—222no—
448#97—221no—
449C4×C8—21no—
450C4×C8—21no—
451C4×C8—112no—
452C4×C8—222no—
453C4×C8C22×D1111yescharacteristic
454C4×C8C22×D1111yescharacteristic
455C2×C11—42no—
456C2×C11—41no—
457C2×C11#288011yescharacteristic
458C2×C11#289711yescharacteristic
459C2×C11C2×#42111yescharacteristic
460D11—42no—
461D11—82no—
462C24—222no—
463#41—22no—
464#41—41no—
465#41—442no—
466#41—881no—
467#41—881no—
468C2×Q8—111no—
469C2×Q8—221no—
470C2×Q8C2×C4×D1111yescharacteristic
471C2×D4—21no—
472C2×D4—112no—
473C2×D4—111no—
474C2×D4—112no—
475C2×D4—222no—
476C2×D4—222no—
477C2×D4—224no—
478C2×D4—222no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—444no—
482C2×D4—442no—
483C2×D4C2×C4×D1111yescharacteristic
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—112no—
488C22×C4—112no—
489C22×C4—112no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—882no—
495C22×C4—882no—
496C22×C4C2×C4×D1111yescharacteristic
497C22×C4D4×D1111yescharacteristic
498C22×C4D4×D1111yescharacteristic
499M16—442no—
500M16—882no—
501M16—881no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—42no—
507C2×C8—222no—
508C2×C8—222no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—111no—
512C4⋊C4—111no—
513C4⋊C4—112no—
514C4⋊C4—112no—
515C4⋊C4—112no—
516C4⋊C4—222no—
517C4⋊C4—222no—
518C4⋊C4—222no—
519C4⋊C4—222no—
520C4⋊C4—221no—
521C4⋊C4C2×C4×D1111yescharacteristic
522C4⋊C4C2×C4×D1111yescharacteristic
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—112no—
527C22⋊C4—112no—
528C22⋊C4—112no—
529C22⋊C4—222no—
530C22⋊C4—222no—
531C22⋊C4—222no—
532C22⋊C4—222no—
533C22⋊C4—222no—
534C22⋊C4—222no—
535C22⋊C4—222no—
536C22⋊C4—222no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—112no—
541C42—112no—
542C42—112no—
543C42C2×C4×D1111yescharacteristic
544C42D4×D1111yescharacteristic
545C42D4×D1111yescharacteristic
546C42C23×D1111yescharacteristic
547C11#1752211yescharacteristic, complemented, Sylow
548C23—21no—
549C23—112no—
550C23—222no—
551C23—444no—
552C23—444no—
553C23—882no—
554C23C22⋊C4×D1111yescharacteristic
555Q8—21no—
556Q8—21no—
557Q8—222no—
558Q8—881no—
559D4—21no—
560D4—42no—
561D4—222no—
562D4—222no—
563D4—222no—
564D4—444no—
565D4—442no—
566D4—444no—
567D4—442no—
568D4—881no—
569D4—882no—
570D4#6695412yes—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—112no—
584C2×C4—112no—
585C2×C4—112no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—882no—
595C2×C4—882no—
596C2×C4—882no—
597C2×C4C22⋊C4×D1111yescharacteristic
598C2×C4C22⋊C4×D1111yescharacteristic
599C2×C4C22⋊C4×D1111yescharacteristic
600C2×C4C22×C4×D1111yescharacteristic
601C2×C4C2×D4×D1111yescharacteristic
602C2×C4C2×D4×D1111yescharacteristic
603C8—41no—
604C8—41no—
605C8—41no—
606C8—41no—
607C8—442no—
608C8—442no—
609C22—21no—
610C22—22no—
611C22—21no—
612C22—21no—
613C22—41no—
614C22—41no—
615C22—222no—
616C22—222no—
617C22—222no—
618C22—442no—
619C22—442no—
620C22—442no—
621C22—888no—
622C22C2×C22⋊C4×D1111yescharacteristic
623C4—21no—
624C4—21no—
625C4—21no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—222no—
630C4—222no—
631C4—222no—
632C4—442no—
633C4#1062243412yes—
634C4C2×#6695411yescharacteristic
635C4#1062327611yescharacteristic
636C4#1062330011yescharacteristic
637C4#1062330111yescharacteristic
638C2—41no—
639C2—42no—
640C2—442no—
641C2—882no—
642C2#1307706211yescharacteristic
643C2#1307713811yescharacteristic
644C2C2×#1062243411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1476C2
socleC22×C11C22×C22⋊C4
prime radical#13082226C2
cosocleC42×C11C24
hypercenter#1476D11
hypocenterC11#17522
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
2. #13077745C2semidirect
3. #13077258C2semidirect
4. #13067080C2semidirect
5. #13067068C2semidirect
6. #13067055C2semidirect
7. #13067039C2semidirect
8. #13067032C2semidirect
9. #13067023C2semidirect
10. #13067005C2semidirect
11. C11×#1476C2semidirect
29. C11×#431C22semidirect
30. C2×C4×C8×C11C22semidirect
33. #10622537C22semidirect
34. C4×#4318C22semidirect
35. #10622450C22semidirect
36. #10622446C22semidirect
40. #10622298C22semidirect
41. #10622298C22semidirect
43. C11×Q8⋊C8C22semidirect
44. C11×Q8⋊C8C22semidirect
47. Q8⋊(C11⋊C8)C22semidirect
49. #10622121C22semidirect
50. #10622121C22semidirect
51. #10622097C22semidirect
52. #10622097C22semidirect
236. #1476D11semidirect
322. #431C2×D11semidirect
328. C2×C4×C8C2×D11semidirect
330. Q8⋊C8C2×D11semidirect
331. Q8⋊C8C2×D11semidirect
547. C11#17522semidirect

Maximal subgroups

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

subgroupindex
#130822262
#130777452
#130772582
#130670802
#130670682
#130670552
#130670392
#130670322
#130670232
#130670052
C11×#14762
#1752211