Finite Group Databasebeta

← #14720840

Subgroups — #14720840

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082242C211yesmaximal, characteristic
2#13077260C211yesmaximal, characteristic, complemented
3#13067084C212yesmaximal, complemented
4#13067066C211yesmaximal, characteristic, complemented
5#13067053C211yesmaximal, characteristic, complemented
6#13067048C212yesmaximal, complemented
7#13067032C211yesmaximal, characteristic, complemented
8#13067014C212yesmaximal, complemented
9#13067001C212yesmaximal, complemented
10#13066996C211yesmaximal, characteristic, complemented
11C11×#2990C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13#10623365—21no—
14#10623108C411yescharacteristic
15C4×#4343—21no—
16Q8×Dic22C411yescharacteristic
17#10623094C412yes—
18#10623094C411yescharacteristic
19#10623084C412yes—
20#10623084C411yescharacteristic
21#10623079—21no—
22#10623079—22no—
23#10623063—21no—
24#10623063—22no—
25#10623008C2212yes—
26#10623008C2211yescharacteristic
27C4×#4339C2212yes—
28C4×#4339C2211yescharacteristic
29C11×#446—21no—
30C11×#435—22no—
31C8×D4×C11—21no—
32C11×#432C2212yes—
33C11×#431C2211yescharacteristic
34C11×#423C2211yescharacteristic
35C2×C11×C4⋊C8C2212yes—
36#10622847—21no—
37#10622613—22no—
38#10622612—21no—
39#10622538C2212yes—
40#10622538C2212yes—
41C4×#4318C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622122C2211yescharacteristic
44#10622122C2212yes—
45#10622122C2211yescharacteristic
46#10622121C2211yescharacteristic
47#10622121C2212yes—
48#10622121C2212yes—
49#10622121C2212yes—
50#10622121C2212yes—
51#10622121C2212yes—
52#10622121C2211yescharacteristic
53C2×C11×#41D411yescharacteristic
54C2×#4343—21no—
55C2×#4339—22no—
56C2×#4339—21no—
57C2×#4339C2×C412yes—
58C2×#4339C2×C411yescharacteristic
59C2×C11×M16—21no—
60C22×C8×C11—22no—
61C4×Q8×C11C2×C411yescharacteristic
62C4×Q8×C11D411yescharacteristic
63C4×D4×C11C2×C411yescharacteristic
64C4×D4×C11C2×C412yes—
65C4×D4×C11D411yescharacteristic
66C4×D4×C11D412yes—
67C11×#117D411yescharacteristic
68C11×#117D412yes—
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2312yes—
71Q8×Dic11—21no—
72#66993—21no—
73#66993—22no—
74#66991—21no—
75#66991—22no—
76#66983—21no—
77#66983—22no—
78#66983C2×C412yes—
79#66983C2×C412yes—
80#66983C2×C412yes—
81C4×C22⋊D11—21no—
82C4×C22⋊D11—22no—
83C4×C22⋊D11—22no—
84C4×C22⋊D11—21no—
85#66979C2×C412yes—
86#66979C2×C411yescharacteristic
87C2×#4318—21no—
88C22×C11⋊C8—21no—
89#66948—22no—
90#66948—21no—
91#66946—22no—
92#66946—21no—
93#66945—22no—
94#66945—21no—
95#66941—22no—
96#66941—21no—
97#66938—22no—
98#66938—22no—
99#66938—22no—
100#66937—22no—
101#66937—22no—
102#66937—22no—
103#66928—21no—
104#66928—22no—
105#66927C2×C412yes—
106#66927C2×C411yescharacteristic
107C4×D44—21no—
108C4×D44—22no—
109C4×D44C2×C412yes—
110C4×D44C2×C411yescharacteristic
111C4×D44C2312yes—
112C4×D44C2311yescharacteristic
113#66925—21no—
114#66925—22no—
115C42×D11—21no—
116C42×D11—22no—
117#66922C2×C412yes—
118#66922C2×C411yescharacteristic
119C4×Dic22C2×C412yes—
120C4×Dic22C2×C411yescharacteristic
121C4×Dic22C2311yescharacteristic
122C11×C4⋊C8—22no—
123C11×C4⋊C8—21no—
124C11×C4⋊C8C2311yescharacteristic
125C11×C4⋊C8C2312yes—
126C11×C4⋊C8C2311yescharacteristic
127C11×C22⋊C8—21no—
128C11×C22⋊C8—22no—
129C11×#97—22no—
130C4×C8×C11—21no—
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#17526—111nomaximal, Sylow
141C11×#41—42no—
142C2×Q8×C11C22⋊C411yescharacteristic
143C2×D4×C11C22⋊C411yescharacteristic
144C2×D4×C11C22⋊C412yes—
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C2×C22⋊D11—21no—
152C2×C22⋊D11—22no—
153C2×C22⋊D11—22no—
154C2×C22⋊D11—22no—
155C2×C22⋊D11—22no—
156#4343—44no—
157#4339—24no—
158#4339—22no—
159#4339—42no—
160#4339—41no—
161#4339—82no—
162#4339—81no—
163#4339—82no—
164#4339—81no—
165C2×D44—22no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—22no—
169C2×D44C22×C412yes—
170C2×D44C22×C411yescharacteristic
171C2×C4×D11—21no—
172C2×C4×D11—22no—
173C2×C4×D11—22no—
174C2×C4×D11—21no—
175C2×C4×D11—21no—
176C2×C4×D11—22no—
177C2×Dic22—21no—
178C2×Dic22—22no—
179C2×Dic22C22×C411yescharacteristic
180C11×M16—81no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—22no—
184C2×C8×C11—82no—
185C11×C4⋊C4C22⋊C412yes—
186C11×C4⋊C4C22⋊C411yescharacteristic
187C11×C4⋊C4C22⋊C412yes—
188C11×C4⋊C4C22⋊C411yescharacteristic
189C11×C22⋊C4C22⋊C412yes—
190C11×C22⋊C4C22⋊C412yes—
191C11×C22⋊C4C22⋊C412yes—
192C42×C11C22×C412yes—
193C42×C11C22×C411yescharacteristic
194C42×C11C2×D411yescharacteristic
195C42×C11C2×D412yes—
196C42×C11C2×D411yescharacteristic
197C42×C11C2×D412yes—
198C42×C11C2411yescharacteristic
199C22⋊Dic11—21no—
200C22⋊Dic11—22no—
201(C2×D11)⋊C4—21no—
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—22no—
209C4⋊Dic11—21no—
210C4⋊Dic11C22×C412yes—
211C4⋊Dic11C22×C411yescharacteristic
212C4⋊Dic11C22×C411yescharacteristic
213Dic11⋊C4—21no—
214Dic11⋊C4—22no—
215Dic11⋊C4—21no—
216C4×Dic11—22no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C4×Dic11—22no—
220C4×Dic11—21no—
221#4318—42no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—22no—
225C2×C11⋊C8—42no—
226#3483—111no—
227#2990D1111yescharacteristic, complemented
228#2922—111no—
229#1496—112no—
230#1492—111no—
231#1489—111no—
232#1488—112no—
233#1484—111no—
234#1480—112no—
235#1477—112no—
236#1476—111no—
237C23×C11C2×C22⋊C411yescharacteristic
238C23×C11C2×C22⋊C412yes—
239C22×D11—22no—
240C22×D11—21no—
241Q8×C11—22no—
242D4×C11—22no—
243D4×C11—42no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—42no—
254C2×C4×C11C2×C22⋊C412yes—
255C2×C4×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C2×C22⋊C412yes—
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11C2×C22⋊C412yes—
259C2×C4×C11C2×C22⋊C411yescharacteristic
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C22⋊D11—42no—
264C22⋊D11—44no—
265C22⋊D11—82no—
266C22⋊D11—82no—
267C22⋊D11—82no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—22no—
271C2×Dic11—21no—
272D44—22no—
273D44—21no—
274D44—22no—
275D44—21no—
276D44—44no—
277D44—42no—
278D44—82no—
279D44—81no—
280C4×D11—42no—
281C4×D11—44no—
282C4×D11—44no—
283C4×D11—41no—
284C4×D11—42no—
285C4×D11—41no—
286C4×D11—42no—
287C4×D11—42no—
288Dic22—21no—
289Dic22—82no—
290Dic22—81no—
291Dic22#13112yes—
292C8×C11—41no—
293C8×C11—42no—
294C8×C11—41no—
295C11⋊C8—41no—
296C11⋊C8—41no—
297C11⋊C8—42no—
298Q82—111no—
299#555—112no—
300#555—111no—
301#555—221no—
302#555—222no—
303#550—111no—
304#550—111no—
305#550—112no—
306#550—221no—
307#532—112no—
308#532—111no—
309#532—221no—
310#532—222no—
311C4×#41—111no—
312C4×#41—112no—
313C4×#41—221no—
314C4×#41C2×D1111yescharacteristic
315#446—21no—
316#435—22no—
317C8×D4—21no—
318#433—222no—
319#432C2×D1112yes—
320#431—112no—
321#431—112no—
322#431C2×D1111yescharacteristic
323#424—221no—
324#423C2×D1111yescharacteristic
325C2×C4⋊C8C2×D1112yes—
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—21no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—21no—
343C22×C11—21no—
344C22×C11—22no—
345C22×C11C22×C22⋊C411yescharacteristic
346C2×D11—42no—
347C2×D11—41no—
348C2×D11—42no—
349C2×D11—41no—
350C2×D11—42no—
351C2×D11—41no—
352C4×C11—21no—
353C4×C11—22no—
354C4×C11—22no—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—22no—
358C4×C11#42112yes—
359C4×C11C2×#13111yescharacteristic
360C4×C11#56811yescharacteristic
361C4×C11#57611yescharacteristic
362C4×C11#57711yescharacteristic
363Dic11—22no—
364Dic11—41no—
365Dic11—42no—
366Dic11—41no—
367C2×#41—111no—
368C2×#41—112no—
369C2×#41—221no—
370C2×#41—222no—
371C2×#41—221no—
372C2×#41D4411yescharacteristic
373C2×M16—21no—
374C2×M16—221no—
375C22×C8—22no—
376C22×C8—221no—
377C4⋊Q8—112no—
378C4⋊Q8—111no—
379C4⋊Q8—222no—
380C4⋊Q8—221no—
381#127—112no—
382#127—111no—
383#127—221no—
384#127—222no—
385#124—222no—
386#124—222no—
387#124—222no—
388#124—221no—
389#124—222no—
390#121—112no—
391#121—112no—
392#121—112no—
393#121—221no—
394#121—222no—
395#121—221no—
396#121—222no—
397#121—222no—
398#121—221no—
399#121—222no—
400#121—222no—
401#121—222no—
402C4×Q8—111no—
403C4×Q8—112no—
404C4×Q8—111no—
405C4×Q8—221no—
406C4×Q8C4×D1111yescharacteristic
407C4×Q8C22⋊D1111yescharacteristic
408C4×D4—111no—
409C4×D4—112no—
410C4×D4—111no—
411C4×D4—112no—
412C4×D4—221no—
413C4×D4—222no—
414C4×D4—222no—
415C4×D4—221no—
416C4×D4—222no—
417C4×D4—221no—
418C4×D4—221no—
419C4×D4—222no—
420C4×D4C4×D1111yescharacteristic
421C4×D4C4×D1112yes—
422C4×D4C22⋊D1111yescharacteristic
423C4×D4C22⋊D1112yes—
424#117—111no—
425#117—112no—
426#117—222no—
427#117—221no—
428#117—221no—
429#117—222no—
430#117D4411yescharacteristic
431#117D4412yes—
432C2×C42—221no—
433C2×C42—222no—
434C2×C42C22×D1111yescharacteristic
435C2×C42C22×D1112yes—
436C4⋊C8—22no—
437C4⋊C8—21no—
438C4⋊C8—222no—
439C4⋊C8—222no—
440C4⋊C8C22×D1111yescharacteristic
441C4⋊C8C22×D1112yes—
442C4⋊C8C22×D1111yescharacteristic
443C22⋊C8—21no—
444C22⋊C8—22no—
445C22⋊C8—222no—
446C22⋊C8—222no—
447#97—22no—
448#97—221no—
449C4×C8—21no—
450C4×C8—111no—
451C4×C8—111no—
452C4×C8—112no—
453C4×C8—221no—
454C2×C11—41no—
455C2×C11—42no—
456C2×C11#288011yescharacteristic
457C2×C11#289711yescharacteristic
458C2×C11C2×#42111yescharacteristic
459D11—82no—
460D11—81no—
461#41—42no—
462#41—222no—
463#41—224no—
464#41—441no—
465#41—442no—
466#41—444no—
467#41—882no—
468#41—881no—
469#41—882no—
470#41—881no—
471C2×Q8—111no—
472C2×Q8—221no—
473C2×Q8—222no—
474C2×Q8(C2×D11)⋊C411yescharacteristic
475C2×D4—111no—
476C2×D4—112no—
477C2×D4—221no—
478C2×D4—222no—
479C2×D4—222no—
480C2×D4—222no—
481C2×D4—222no—
482C2×D4—222no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—222no—
486C2×D4(C2×D11)⋊C411yescharacteristic
487C2×D4(C2×D11)⋊C412yes—
488C22×C4—222no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—222no—
492C22×C4—221no—
493C22×C4—222no—
494C22×C4C2×C4×D1111yescharacteristic
495C22×C4C2×C4×D1112yes—
496C22×C4C2×D4411yescharacteristic
497C22×C4C2×D4412yes—
498C22×C4C2×C22⋊D1112yes—
499C22×C4C2×C22⋊D1111yescharacteristic
500M16—81no—
501M16—442no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—22no—
505C2×C8—82no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—222no—
509C2×C8—442no—
510C4⋊C4—111no—
511C4⋊C4—111no—
512C4⋊C4—112no—
513C4⋊C4—221no—
514C4⋊C4—222no—
515C4⋊C4—222no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4(C2×D11)⋊C412yes—
519C4⋊C4(C2×D11)⋊C411yescharacteristic
520C4⋊C4(C2×D11)⋊C412yes—
521C4⋊C4(C2×D11)⋊C411yescharacteristic
522C22⋊C4—221no—
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(C2×D11)⋊C412yes—
532C22⋊C4(C2×D11)⋊C412yes—
533C22⋊C4(C2×D11)⋊C412yes—
534C42—221no—
535C42—222no—
536C42—222no—
537C42—221no—
538C42—221no—
539C42C2×C4×D1112yes—
540C42C2×C4×D1111yescharacteristic
541C42C2×D4411yescharacteristic
542C42C2×D4412yes—
543C42C2×C22⋊D1111yescharacteristic
544C42C2×C22⋊D1112yes—
545C42C23×D1111yescharacteristic
546C11#1752611yescharacteristic, complemented, Sylow
547C23—222no—
548C23—221no—
549C23C2×(C2×D11)⋊C411yescharacteristic
550C23C2×(C2×D11)⋊C412yes—
551Q8—22no—
552Q8—112no—
553Q8—221no—
554Q8—882no—
555Q8—881no—
556D4—22no—
557D4—42no—
558D4—221no—
559D4—222no—
560D4—221no—
561D4—222no—
562D4—444no—
563D4—442no—
564D4—444no—
565D4—442no—
566D4—882no—
567D4—881no—
568D4—882no—
569D4—882no—
570D4—882no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—42no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—222no—
584C2×C4—221no—
585C2×C4—442no—
586C2×C4—444no—
587C2×C4—444no—
588C2×C4—442no—
589C2×C4—441no—
590C2×C4—442no—
591C2×C4—441no—
592C2×C4—442no—
593C2×C4C2×(C2×D11)⋊C412yes—
594C2×C4C2×(C2×D11)⋊C411yescharacteristic
595C2×C4C2×(C2×D11)⋊C412yes—
596C2×C4C2×(C2×D11)⋊C411yescharacteristic
597C2×C4C2×(C2×D11)⋊C412yes—
598C2×C4C2×(C2×D11)⋊C411yescharacteristic
599C2×C4C22×C4×D1111yescharacteristic
600C2×C4C22×D4411yescharacteristic
601C2×C4C22×C22⋊D1111yescharacteristic
602C8—41no—
603C8—42no—
604C8—41no—
605C8—441no—
606C8—441no—
607C8—442no—
608C22—21no—
609C22—22no—
610C22—22no—
611C22—21no—
612C22—21no—
613C22—22no—
614C22—442no—
615C22—441no—
616C22—442no—
617C22—441no—
618C22—442no—
619C22—441no—
620C22C22×(C2×D11)⋊C411yescharacteristic
621C4—21no—
622C4—22no—
623C4—22no—
624C4—21no—
625C4—21no—
626C4—22no—
627C4—222no—
628C4—442no—
629C4—441no—
630C4—441no—
631C4#1062275212yes—
632C4D11×#13111yescharacteristic
633C4#1062328111yescharacteristic
634C4#1062336611yescharacteristic
635C4#1062336811yescharacteristic
636C2—41no—
637C2—42no—
638C2—882no—
639C2—881no—
640C2#1307706311yescharacteristic
641C2#1307713911yescharacteristic
642C2C2×#1062275211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2990C2
socleC22×C11C22×C22⋊C4
prime radical#13082242C2
cosocleC42×C11C24
hypercenter#2990D11
hypocenterC11#17526
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
2. #13077260C2semidirect
3. #13067084C2semidirect
4. #13067066C2semidirect
5. #13067053C2semidirect
6. #13067048C2semidirect
7. #13067032C2semidirect
8. #13067014C2semidirect
9. #13067001C2semidirect
10. #13066996C2semidirect
11. C11×#2990C2semidirect
227. #2990D11semidirect
546. C11#17526semidirect

Maximal subgroups

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

subgroupindex
#130822422
#130772602
#130670842
#130670662
#130670532
#130670482
#130670322
#130670142
#130670012
#130669962
C11×#29902
#1752611