Finite Group Databasebeta

← #14720792

Subgroups — #14720792

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#13077260C211yesmaximal, characteristic, complemented
3#13067079C212yesmaximal, complemented
4#13067066C211yesmaximal, characteristic, complemented
5#13067053C211yesmaximal, characteristic, complemented
6#13067040C212yesmaximal, complemented
7#13067032C211yesmaximal, characteristic, complemented
8#13067022C212yesmaximal, complemented
9#13067006C212yesmaximal, complemented
10#13066996C211yesmaximal, characteristic, complemented
11C11×#2991C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13#10623360—21no—
14#10623116C411yescharacteristic
15#10623111—21no—
16#10623110C411yescharacteristic
17#10623096C412yes—
18#10623081C412yes—
19D4×D44C411yescharacteristic
20#10623078—22no—
21C4×D4×D11—21no—
22#10623074C411yescharacteristic
23#10623061—21no—
24#10623058—22no—
25#10623010C2212yes—
26#10623008C2211yescharacteristic
27C4×#4339C2211yescharacteristic
28C2×C4×D44C2212yes—
29C8×Q8×C11—21no—
30C11×#436—21no—
31C11×#436—22no—
32C11×#431C2212yescomplemented
33C11×#431C2211yescharacteristic, complemented
34C11×#423C2212yescomplemented
35C11×#423C2211yescharacteristic, complemented
36#10622847—21no—
37#10622613—22no—
38#10622612—21no—
39#10622538C2212yescomplemented
40#10622538C2212yescomplemented
41C4×#4318C2211yescharacteristic, complemented
42C2×C4×C11⋊C8C2211yescharacteristic, complemented
43#10622122C2211yescharacteristic, complemented
44#10622122C2212yescomplemented
45#10622122C2211yescharacteristic, complemented
46#10622121C2211yescharacteristic
47#10622121C2212yes—
48#10622121C2211yescharacteristic
49#10622121C2212yescomplemented
50#10622121C2212yescomplemented
51#10622121C2212yescomplemented
52#10622121C2212yescomplemented
53C2×C11×#41D411yescharacteristic
54C2×D4×D11—21no—
55C2×#4339—21no—
56C2×#4339C2×C411yescharacteristic
57C22×D44C2×C412yes—
58C22×C4×D11—22no—
59C2×C11×M16—22no—
60C2×C11×M16—21no—
61C4×Q8×C11C2×C411yescharacteristic
62C4×Q8×C11D411yescharacteristic
63C4×D4×C11C2×C411yescharacteristic
64C4×D4×C11C2×C412yes—
65C4×D4×C11D411yescharacteristic
66C4×D4×C11D412yes—
67C11×#117D412yes—
68C11×#117D411yescharacteristic
69C2×C42×C11C2312yes—
70C2×C42×C11C2311yescharacteristic
71#67000—21no—
72#66999—21no—
73#66992—22no—
74#66990—22no—
75D4×Dic11—21no—
76#66983—21no—
77#66983C2×C412yes—
78#66983C2×C412yes—
79#66982—22no—
80C4×C22⋊D11—21no—
81C4×C22⋊D11—21no—
82C4×C22⋊D11—22no—
83C2×(C2×D11)⋊C4—22no—
84#66979C2×C411yescharacteristic
85C2×C4⋊Dic11C2×C412yes—
86#66977C2×C412yes—
87C2×#4318—21no—
88C22×C11⋊C8—21no—
89#66951—22no—
90#66949—22no—
91#66948—21no—
92#66947—22no—
93#66947—22no—
94#66946—21no—
95C4⋊C4×D11—21no—
96#66943—21no—
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#66928C2×C412yes—
106#66927C2×C411yescharacteristic
107C4×D44—22no—
108C4×D44—22no—
109C4×D44—21no—
110C4×D44C2×C412yes—
111C4×D44C2×C412yes—
112C4×D44C2×C411yescharacteristic
113C4×D44C2311yescharacteristic
114C4×D44C2312yes—
115#66925—21no—
116#66925—22no—
117C42×D11—21no—
118#66923C2×C412yes—
119#66922C2×C411yescharacteristic
120C4×Dic22C2×C411yescharacteristic
121C4×Dic22C2311yescharacteristic
122C11×C4⋊C8—21no—
123C11×C4⋊C8—22no—
124C11×C4⋊C8C2311yescharacteristic
125C11×C4⋊C8C2312yes—
126C11×C4⋊C8C2311yescharacteristic
127C11×C22⋊C8—22no—
128C11×C22⋊C8—21no—
129C4×C8×C11—21no—
130C4×C8×C11—22no—
131C22⋊(C11⋊C8)—22no—
132C22⋊(C11⋊C8)—22no—
133C4⋊(C11⋊C8)—22no—
134C4⋊(C11⋊C8)—22no—
135#66867—21no—
136C4×C11⋊C8—21no—
137C4×C11⋊C8C2311yescharacteristic
138C4×C11⋊C8C2311yescharacteristic
139C4×C11⋊C8C2312yes—
140#17522—111nomaximal, Sylow
141C23×D11—22no—
142C11×#41—42no—
143C2×Q8×C11C22⋊C411yescharacteristic
144C2×D4×C11C22⋊C411yescharacteristic
145C2×D4×C11C22⋊C412yes—
146C22×C4×C11C22×C412yes—
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C2×C22⋊D11—22no—
153C2×C22⋊D11—21no—
154C2×C22⋊D11—22no—
155C22×Dic11—22no—
156D4×D11—44no—
157#4339—22no—
158#4339—41no—
159#4339—81no—
160#4339—81no—
161C2×D44—24no—
162C2×D44—22no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—42no—
166C2×D44C22×C412yes—
167C2×D44C22×C411yescharacteristic
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—22no—
171C2×C4×D11—22no—
172C2×C4×D11—21no—
173C2×C4×D11—22no—
174C2×C4×D11—82no—
175C2×C4×D11—82no—
176C2×Dic22—21no—
177C2×Dic22C22×C411yescharacteristic
178C11×M16—82no—
179C11×M16—81no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—22no—
183C11×C4⋊C4C22⋊C411yescharacteristic
184C11×C4⋊C4C22⋊C411yescharacteristic
185C11×C4⋊C4C22⋊C412yes—
186C11×C4⋊C4C22⋊C412yes—
187C11×C22⋊C4C22⋊C412yes—
188C11×C22⋊C4C22⋊C412yes—
189C11×C22⋊C4C22⋊C412yes—
190C42×C11C22×C411yescharacteristic
191C42×C11C22×C412yes—
192C42×C11C2×D411yescharacteristic
193C42×C11C2×D412yes—
194C42×C11C2×D411yescharacteristic
195C42×C11C2×D412yes—
196C42×C11C2411yescharacteristic
197C22⋊Dic11—22no—
198C22⋊Dic11—21no—
199(C2×D11)⋊C4—21no—
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)⋊C4—21no—
207(C2×D11)⋊C4—22no—
208C4⋊Dic11—21no—
209C4⋊Dic11—22no—
210C4⋊Dic11C22×C411yescharacteristic
211C4⋊Dic11C22×C411yescharacteristic
212C4⋊Dic11C22×C412yes—
213Dic11⋊C4—21no—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216Dic11⋊C4—22no—
217Dic11⋊C4—21no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11—21no—
221#4318—42no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—22no—
225C2×C11⋊C8—42no—
226#3481—111no—
227#2991D1111yescharacteristic, complemented
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#1476—111no—
237C23×C11C2×C22⋊C412yes—
238C23×C11C2×C22⋊C411yescharacteristic
239C22×D11—21no—
240C22×D11—22no—
241C22×D11—44no—
242C22×D11—44no—
243C22×D11—82no—
244Q8×C11—22no—
245D4×C11—22no—
246D4×C11—42no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—42no—
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11C2×C22⋊C412yes—
259C2×C4×C11C2×C22⋊C412yes—
260C2×C4×C11C2×C22⋊C411yescharacteristic
261C2×C4×C11C2×C22⋊C412yes—
262C2×C4×C11C2×C22⋊C411yescharacteristic
263C2×C4×C11C23×C411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C22⋊D11—42no—
267C22⋊D11—44no—
268C22⋊D11—82no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—22no—
273C2×Dic11—82no—
274D44—22no—
275D44—21no—
276D44—22no—
277D44—44no—
278D44—42no—
279D44—81no—
280D44#13112yes—
281C4×D11—42no—
282C4×D11—41no—
283C4×D11—42no—
284C4×D11—41no—
285C4×D11—42no—
286C4×D11—42no—
287C4×D11—82no—
288C4×D11—82no—
289Dic22—21no—
290Dic22—21no—
291Dic22—81no—
292C8×C11—41no—
293C8×C11—42no—
294C8×C11—41no—
295C11⋊C8—41no—
296C11⋊C8—41no—
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—21no—
316#436—21no—
317#436—22no—
318#433—222no—
319#431—112no—
320#431—112no—
321#431C2×D1111yescharacteristic, complemented
322#431C2×D1112yescomplemented
323#424—221no—
324#423C2×D1112yescomplemented
325#423C2×D1111yescharacteristic, complemented
326#408—221no—
327C4×M16—111no—
328C2×C4×C8—111no—
329Q8⋊C8—111no—
330Q8⋊C8—111no—
331Q8⋊C8—112no—
332D4⋊C8—111no—
333D4⋊C8—111no—
334D4⋊C8—112no—
335D4⋊C8—112no—
336D4⋊C8—112no—
337D4⋊C8—112no—
338D4⋊C8—112no—
339C22×C11—22no—
340C22×C11—21no—
341C22×C11—22no—
342C22×C11—21no—
343C22×C11—21no—
344C22×C11—22no—
345C22×C11C22×C22⋊C411yescharacteristic
346C2×D11—22no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—42no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—88no—
353C4×C11—21no—
354C4×C11—22no—
355C4×C11—21no—
356C4×C11—22no—
357C4×C11—21no—
358C4×C11—22no—
359C4×C11#42112yes—
360C4×C11C2×#13111yescharacteristic
361C4×C11#56811yescharacteristic
362C4×C11#57611yescharacteristic
363C4×C11#57711yescharacteristic
364Dic11—41no—
365Dic11—42no—
366Dic11—41no—
367Dic11—41no—
368C2×#41—111no—
369C2×#41—221no—
370C2×#41D4411yescharacteristic
371C22×D4—112no—
372C22×D4—221no—
373C23×C4—222no—
374C2×M16—22no—
375C2×M16—21no—
376C2×M16—221no—
377C22×C8—221no—
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—221no—
393C22⋊Q8—222no—
394C22⋊Q8—222no—
395#121—112no—
396#121—112no—
397#121—222no—
398#121—221no—
399#121—221no—
400#121—222no—
401#120—222no—
402#120—222no—
403C4×Q8—111no—
404C4×Q8—111no—
405C4×Q8C4×D1111yescharacteristic
406C4×Q8C22⋊D1111yescharacteristic
407C4×D4—112no—
408C4×D4—112no—
409C4×D4—111no—
410C4×D4—111no—
411C4×D4—112no—
412C4×D4—221no—
413C4×D4—221no—
414C4×D4—222no—
415C4×D4—221no—
416C4×D4—221no—
417C4×D4—222no—
418C4×D4—222no—
419C4×D4—222no—
420C4×D4—221no—
421C4×D4C4×D1111yescharacteristic
422C4×D4C4×D1112yes—
423C4×D4C22⋊D1111yescharacteristic
424C4×D4C22⋊D1112yes—
425#117—111no—
426#117—221no—
427#117—222no—
428#117D4412yes—
429#117D4411yescharacteristic
430C2×C4⋊C4—112no—
431C2×C4⋊C4—221no—
432C2×C22⋊C4—222no—
433C2×C22⋊C4—222no—
434C2×C42—221no—
435C2×C42C22×D1112yes—
436C2×C42C22×D1111yescharacteristic
437C4⋊C8—21no—
438C4⋊C8—22no—
439C4⋊C8—222no—
440C4⋊C8—222no—
441C4⋊C8C22×D1111yescharacteristic
442C4⋊C8C22×D1112yes—
443C4⋊C8C22×D1111yescharacteristic
444C22⋊C8—22no—
445C22⋊C8—21no—
446C22⋊C8—222no—
447C22⋊C8—222no—
448#97—221no—
449C4×C8—21no—
450C4×C8—22no—
451C4×C8—111no—
452C4×C8—111no—
453C4×C8—112no—
454C4×C8—221no—
455C2×C11—42no—
456C2×C11—41no—
457C2×C11#288011yescharacteristic
458C2×C11#289711yescharacteristic
459C2×C11C2×#42111yescharacteristic
460D11—42no—
461D11—82no—
462C24—222no—
463#41—42no—
464#41—222no—
465#41—441no—
466#41—881no—
467#41—881no—
468C2×Q8—111no—
469C2×Q8—221no—
470C2×Q8(C2×D11)⋊C411yescharacteristic
471C2×D4—111no—
472C2×D4—112no—
473C2×D4—224no—
474C2×D4—221no—
475C2×D4—222no—
476C2×D4—222no—
477C2×D4—222no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—442no—
481C2×D4—444no—
482C2×D4(C2×D11)⋊C411yescharacteristic
483C2×D4(C2×D11)⋊C412yes—
484C22×C4—222no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—882no—
492C22×C4—882no—
493C22×C4C2×C4×D1112yes—
494C22×C4C2×C4×D1111yescharacteristic
495C22×C4C2×D4411yescharacteristic
496C22×C4C2×D4412yes—
497C22×C4C2×C22⋊D1112yes—
498C22×C4C2×C22⋊D1111yescharacteristic
499M16—82no—
500M16—81no—
501M16—442no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—22no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—222no—
508C2×C8—442no—
509C4⋊C4—111no—
510C4⋊C4—112no—
511C4⋊C4—111no—
512C4⋊C4—222no—
513C4⋊C4—221no—
514C4⋊C4—222no—
515C4⋊C4—221no—
516C4⋊C4—222no—
517C4⋊C4—222no—
518C4⋊C4—221no—
519C4⋊C4(C2×D11)⋊C411yescharacteristic
520C4⋊C4(C2×D11)⋊C411yescharacteristic
521C4⋊C4(C2×D11)⋊C412yes—
522C4⋊C4(C2×D11)⋊C412yes—
523C22⋊C4—222no—
524C22⋊C4—221no—
525C22⋊C4—222no—
526C22⋊C4—222no—
527C22⋊C4—222no—
528C22⋊C4—222no—
529C22⋊C4—221no—
530C22⋊C4—222no—
531C22⋊C4—222no—
532C22⋊C4—221no—
533C22⋊C4—222no—
534C22⋊C4(C2×D11)⋊C412yes—
535C22⋊C4(C2×D11)⋊C412yes—
536C22⋊C4(C2×D11)⋊C412yes—
537C42—221no—
538C42—221no—
539C42—221no—
540C42C2×C4×D1112yes—
541C42C2×C4×D1111yescharacteristic
542C42C2×D4411yescharacteristic
543C42C2×D4412yes—
544C42C2×C22⋊D1111yescharacteristic
545C42C2×C22⋊D1112yes—
546C42C23×D1111yescharacteristic
547C11#1752211yescharacteristic, complemented, Sylow
548C23—221no—
549C23—222no—
550C23—444no—
551C23—444no—
552C23—882no—
553C23C2×(C2×D11)⋊C412yes—
554C23C2×(C2×D11)⋊C411yescharacteristic
555Q8—22no—
556Q8—221no—
557Q8—221no—
558Q8—881no—
559D4—22no—
560D4—42no—
561D4—112no—
562D4—222no—
563D4—221no—
564D4—222no—
565D4—444no—
566D4—442no—
567D4—444no—
568D4—442no—
569D4—881no—
570D4—882no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—42no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—222no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4—441no—
588C2×C4—442no—
589C2×C4—441no—
590C2×C4—442no—
591C2×C4—882no—
592C2×C4—882no—
593C2×C4—882no—
594C2×C4C2×(C2×D11)⋊C411yescharacteristic
595C2×C4C2×(C2×D11)⋊C412yes—
596C2×C4C2×(C2×D11)⋊C411yescharacteristic
597C2×C4C2×(C2×D11)⋊C412yes—
598C2×C4C2×(C2×D11)⋊C412yes—
599C2×C4C2×(C2×D11)⋊C411yescharacteristic
600C2×C4C22×C4×D1111yescharacteristic
601C2×C4C22×D4411yescharacteristic
602C2×C4C22×C22⋊D1111yescharacteristic
603C8—41no—
604C8—42no—
605C8—41no—
606C8—441no—
607C8—441no—
608C8—442no—
609C22—21no—
610C22—22no—
611C22—22no—
612C22—21no—
613C22—21no—
614C22—22no—
615C22—222no—
616C22—441no—
617C22—441no—
618C22—442no—
619C22—442no—
620C22—442no—
621C22—888no—
622C22C22×(C2×D11)⋊C411yescharacteristic
623C4—21no—
624C4—22no—
625C4—22no—
626C4—21no—
627C4—21no—
628C4—22no—
629C4—441no—
630C4—441no—
631C4—442no—
632C4—441no—
633C4#1062275212yes—
634C4D11×#13111yescharacteristic
635C4#1062328111yescharacteristic
636C4#1062336611yescharacteristic
637C4#1062336811yescharacteristic
638C2—42no—
639C2—41no—
640C2—442no—
641C2—882no—
642C2#1307706311yescharacteristic
643C2#1307713911yescharacteristic
644C2C2×#1062275211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2991C2
socleC22×C11C22×C22⋊C4
prime radical#13082226C2
cosocleC42×C11C24
hypercenter#2991D11
hypocenterC11#17522
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2991

Complements

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

NH ≅ G/Ntype
2. #13077260C2semidirect
3. #13067079C2semidirect
4. #13067066C2semidirect
5. #13067053C2semidirect
6. #13067040C2semidirect
7. #13067032C2semidirect
8. #13067022C2semidirect
9. #13067006C2semidirect
10. #13066996C2semidirect
11. C11×#2991C2semidirect
32. C11×#431C22semidirect
33. C11×#431C22semidirect
34. C11×#423C22semidirect
35. C11×#423C22semidirect
39. #10622538C22semidirect
40. #10622538C22semidirect
41. C4×#4318C22semidirect
42. C2×C4×C11⋊C8C22semidirect
43. #10622122C22semidirect
44. #10622122C22semidirect
45. #10622122C22semidirect
49. #10622121C22semidirect
50. #10622121C22semidirect
51. #10622121C22semidirect
52. #10622121C22semidirect
227. #2991D11semidirect
321. #431C2×D11semidirect
322. #431C2×D11semidirect
324. #423C2×D11semidirect
325. #423C2×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
#130772602
#130670792
#130670662
#130670532
#130670402
#130670322
#130670222
#130670062
#130669962
C11×#29912
#1752211