Finite Group Databasebeta

← #14729903

Subgroups — #14729903

Order 2816.

1028 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079009C211yesmaximal, characteristic, complemented
2#13078431C211yesmaximal, characteristic, complemented
3#13078103C211yesmaximal, characteristic, complemented
4#13067830C212yesmaximal, complemented
5#13067823C212yesmaximal, complemented
6#13067802C212yesmaximal, complemented
7#13067795C212yesmaximal, complemented
8#13067351C211yesmaximal, characteristic, complemented
9#13067055C211yesmaximal, characteristic, complemented
10#13067055C211yesmaximal, characteristic, complemented
11C11×#3481C211yesmaximal, characteristic
12C11×#559C2211yescharacteristic
13C11×#554C2211yescharacteristic
14C11×#554C2211yescharacteristic
15C11×#553—21no—
16C11×#553—21no—
17C11×#551—22no—
18C11×#546—21no—
19C11×#546—21no—
20D42×C11C2211yescharacteristic
21C11×#532C2211yescharacteristic
22C11×#529—21no—
23C11×#529—21no—
24C11×#525—22no—
25C4×C11×#41C2211yescharacteristic
26C4×C11×#41C2211yescharacteristic
27C2×C4×D4×C11—21no—
28C2×C4×D4×C11—21no—
29C2×#67004—21no—
30C2×#66922C2211yescharacteristic, complemented
31#10622845—21no—
32#10622845—22no—
33#10622694C2212yescomplemented
34#10622683C2212yes—
35#10622668—22no—
36#10622644—21no—
37#10622644C2212yescomplemented
38#10622634—21no—
39#10622633C2212yescomplemented
40#10622632—21no—
41#10622632C2212yes—
42#10622621—21no—
43#10622620C2212yes—
44#10622617—21no—
45#10622608—21no—
46#10622537C2211yescharacteristic, complemented
47#10622537C2211yescharacteristic, complemented
48C4×#4318C2211yescharacteristic, complemented
49#10622184C2212yescomplemented
50#10622182C2212yes—
51Q8⋊(C11⋊C8)C2212yescomplemented
52Q8⋊(C11⋊C8)C2212yescomplemented
53D4⋊(C11⋊C8)C2212yes—
54D4⋊(C11⋊C8)C2212yes—
55C2×C11×#41D411yescharacteristic
56C2×C11×#41D411yescharacteristic
57C2×C11×#41D412yes—
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C23×C4×C11—22no—
61C22×Dic22—21no—
62C11×C4⋊Q8C2311yescharacteristic
63C11×#127C2311yescharacteristic
64C11×#126—22no—
65C11×#126—22no—
66C11×#125—21no—
67C11×#125—21no—
68C11×#124—21no—
69C11×#124—21no—
70C11×#124D412yes—
71C11×#123—22no—
72C11×#123—22no—
73C11×#123—22no—
74C11×#123—22no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×#121—22no—
80C11×#121—22no—
81C11×#121—21no—
82C11×#121—21no—
83C11×#121—21no—
84C11×#121—21no—
85C11×#120—22no—
86C11×#120—22no—
87C4×Q8×C11D411yescharacteristic
88C4×Q8×C11D411yescharacteristic
89C4×Q8×C11C2311yescharacteristic
90C4×Q8×C11C2311yescharacteristic
91C4×D4×C11—22no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11—21no—
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C4×D4×C11—21no—
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C4×D4×C11D411yescharacteristic
106C4×D4×C11D411yescharacteristic
107C4×D4×C11C2311yescharacteristic
108C4×D4×C11C2311yescharacteristic
109C11×#117—22no—
110C11×#117—21no—
111C11×#117—21no—
112C11×#117D411yescharacteristic
113C11×#117D411yescharacteristic
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4—21no—
116C2×C11×C22⋊C4—22no—
117C2×C11×C22⋊C4—22no—
118C2×C42×C11—21no—
119C2×C42×C11—21no—
120C2×C42×C11C2311yescharacteristic
121#67004—44no—
122C2×#4326—22no—
123C2×#4324—22no—
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11—21no—
126C2×#4318—21no—
127C2×#4318—21no—
128C2×#4318—21no—
129#66922—21no—
130#66922—21no—
131#66922—21no—
132#66922C2312yes—
133#66899—22no—
134#66899—24no—
135#66896—22no—
136#66896—24no—
137#66874—22no—
138#66874—22no—
139#66872—22no—
140#66871—22no—
141C4⋊(C11⋊C8)—21no—
142C4⋊(C11⋊C8)—21no—
143C4⋊(C11⋊C8)C2312yes—
144C4⋊(C11⋊C8)C2312yes—
145#66867—21no—
146C4×C11⋊C8C2312yes—
147#18532—111nomaximal, Sylow
148C24×C11—22no—
149C11×#41—22no—
150C11×#41—22no—
151C11×#41—41no—
152C11×#41—41no—
153C11×#41—44no—
154C2×Q8×C11C2×D411yescharacteristic
155C2×Q8×C11C2×D411yescharacteristic
156C2×Q8×C11C2×D412yes—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—22no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—42no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—42no—
168C2×D4×C11C2×D411yescharacteristic
169C2×D4×C11C2×D411yescharacteristic
170C2×D4×C11C2×D412yes—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—22no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—84no—
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×Dic11—41no—
186C2×Dic22—22no—
187C2×Dic22—42no—
188C2×Dic22—42no—
189C2×Dic22—41no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4C2×D411yescharacteristic
201C11×C4⋊C4C2×D411yescharacteristic
202C11×C4⋊C4C2×D411yescharacteristic
203C11×C4⋊C4C2×D411yescharacteristic
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—21no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—21no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—22no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—21no—
217C11×C22⋊C4—21no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—21no—
224C42×C11C2×D411yescharacteristic
225C42×C11C2×D411yescharacteristic
226C42×C11C2×D411yescharacteristic
227C42×C11C2411yescharacteristic
228#4326—44no—
229#4324—44no—
230C4⋊Dic11—22no—
231C4⋊Dic11—22no—
232C4⋊Dic11—41no—
233C4⋊Dic11—41no—
234#4318—42no—
235#4318—42no—
236#4318—42no—
237C2×C11⋊C8—22no—
238C2×C11⋊C8—22no—
239C2×C11⋊C8—22no—
240#3481D1111yescharacteristic
241#3141—111no—
242#3079—111no—
243#3039—111no—
244#1644—112no—
245#1643—112no—
246#1640—112no—
247#1639—112no—
248#1560—111no—
249#1489—111no—
250#1489—111no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—22no—
254C23×C11—44no—
255C23×C11—44no—
256C23×C11—82no—
257C23×C11#12011yescharacteristic
258Q8×C11—21no—
259Q8×C11—21no—
260Q8×C11—21no—
261Q8×C11—21no—
262Q8×C11—42no—
263D4×C11—21no—
264D4×C11—21no—
265D4×C11—42no—
266D4×C11—42no—
267D4×C11—42no—
268D4×C11—44no—
269D4×C11—44no—
270D4×C11—41no—
271D4×C11—41no—
272D4×C11—41no—
273D4×C11—41no—
274D4×C11—82no—
275D4×C11AGL(1,ℤ/8)12yes—
276D4×C11#13712yescomplemented
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—22no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—22no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11—44no—
298C2×C4×C11—82no—
299C2×C4×C11—82no—
300C2×C4×C11—82no—
301C2×C4×C11#12011yescharacteristic
302C2×C4×C11#12011yescharacteristic
303C2×C4×C11#12011yescharacteristic
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×Dic11—42no—
308C2×Dic11—82no—
309Dic22—42no—
310Dic22—42no—
311Dic22—82no—
312C11⋊C8—42no—
313C11⋊C8—42no—
314C11⋊C8—42no—
315C2×#137—221no—
316#559C2×D1111yescharacteristic
317#554C2×D1111yescharacteristic
318#554C2×D1111yescharacteristic
319#553—21no—
320#553—21no—
321#551—22no—
322#546—21no—
323#546—21no—
324D42C2×D1111yescharacteristic
325#532C2×D1111yescharacteristic
326C2×C4⋊Q8—111no—
327#529—21no—
328#529—21no—
329#525—22no—
330C4×#41C2×D1111yescharacteristic
331C4×#41C2×D1111yescharacteristic
332C2×C4×D4—21no—
333C2×C4×D4—21no—
334#489—222no—
335#487—112no—
336#486—112no—
337#477—221no—
338#476—221no—
339#475—112no—
340#474—112no—
341#462—112no—
342#462—221no—
343#461—112no—
344#461—221no—
345#428—221no—
346#423—111no—
347#423—111no—
348#419—221no—
349#417—221no—
350#417—222no—
351C4×M16—111no—
352#333—112no—
353#331—112no—
354Q8⋊C8—112no—
355Q8⋊C8—112no—
356D4⋊C8—112no—
357D4⋊C8—112no—
358C22×C11—21no—
359C22×C11—22no—
360C22×C11—21no—
361C22×C11—22no—
362C22×C11—21no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—42no—
368C22×C11—42no—
369C22×C11—42no—
370C22×C11—88no—
371C22×C11C2×#12011yescharacteristic
372C4×C11—21no—
373C4×C11—21no—
374C4×C11—21no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11—41no—
380C4×C11—41no—
381C4×C11—42no—
382C4×C11#45512yes—
383C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
384C4×C11C2×#13711yescharacteristic
385C4×C11#57511yescharacteristic
386C4×C11#57511yescharacteristic
387Dic11—82no—
388C2×#41C22⋊D1111yescharacteristic
389C2×#41C22⋊D1111yescharacteristic
390C2×#41C22⋊D1112yes—
391C22×Q8—221no—
392C22×D4—21no—
393C22×D4—21no—
394C23×C4—22no—
395#137—444no—
396C2×Q16—222no—
397C2×SD16—222no—
398C2×M16—221no—
399C2×M16—221no—
400C2×M16—221no—
401C4⋊Q8—112no—
402C4⋊Q8—221no—
403C4⋊Q8—221no—
404C4⋊Q8—221no—
405C4⋊Q8C22×D1111yescharacteristic
406#127C22×D1111yescharacteristic
407#126—22no—
408#126—22no—
409#125—21no—
410#125—21no—
411#124—21no—
412#124—21no—
413#124C22⋊D1112yes—
414#123—22no—
415#123—22no—
416#123—22no—
417#123—22no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422#121—22no—
423#121—22no—
424#121—21no—
425#121—21no—
426#121—21no—
427#121—21no—
428#120—22no—
429#120—22no—
430C4×Q8C22⋊D1111yescharacteristic
431C4×Q8C22⋊D1111yescharacteristic
432C4×Q8C22×D1111yescharacteristic
433C4×Q8C22×D1111yescharacteristic
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4—21no—
445C4×D4—21no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4C22⋊D1111yescharacteristic
449C4×D4C22⋊D1111yescharacteristic
450C4×D4C22×D1111yescharacteristic
451C4×D4C22×D1111yescharacteristic
452#117—22no—
453#117—21no—
454#117—21no—
455#117C22⋊D1111yescharacteristic
456#117C22⋊D1111yescharacteristic
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—221no—
460C2×C4⋊C4—221no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42C22×D1111yescharacteristic
466#107—222no—
467#106—222no—
468C4⋊C8—112no—
469C4⋊C8—112no—
470C4⋊C8—221no—
471C4⋊C8—221no—
472#103—222no—
473#103—224no—
474#103—222no—
475#103—222no—
476#102—222no—
477#102—224no—
478#97—221no—
479C4×C8—112no—
480C2×C11—41no—
481C2×C11—42no—
482C2×C11—42no—
483C2×C11—82no—
484C2×C11#300611yescharacteristic
485C2×C11#300711yescharacteristic
486C2×C11C2×#45511yescharacteristic
487C24—22no—
488#41—22no—
489#41—22no—
490#41—41no—
491#41—41no—
492#41—44no—
493C2×Q8—222no—
494C2×Q8—442no—
495C2×Q8—442no—
496C2×Q8—441no—
497C2×Q8C2×C22⋊D1111yescharacteristic
498C2×Q8C2×C22⋊D1111yescharacteristic
499C2×Q8C2×C22⋊D1112yes—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—22no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4C2×C22⋊D1111yescharacteristic
512C2×D4C2×C22⋊D1111yescharacteristic
513C2×D4C2×C22⋊D1112yes—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—84no—
525C22×C4—441no—
526C22×C4C2×C22⋊D1111yescharacteristic
527C22×C4C2×C22⋊D1111yescharacteristic
528C22×C4C2×C22⋊D1111yescharacteristic
529Q16—444no—
530SD16—444no—
531M16—442no—
532M16—442no—
533M16—442no—
534C2×C8—222no—
535C2×C8—222no—
536C2×C8—222no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—222no—
548C4⋊C4—222no—
549C4⋊C4—441no—
550C4⋊C4—441no—
551C4⋊C4C2×C22⋊D1111yescharacteristic
552C4⋊C4C2×C22⋊D1111yescharacteristic
553C4⋊C4C2×C22⋊D1111yescharacteristic
554C4⋊C4C2×C22⋊D1111yescharacteristic
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—21no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42C2×C22⋊D1111yescharacteristic
576C42C2×C22⋊D1111yescharacteristic
577C42C2×C22⋊D1111yescharacteristic
578C42C23×D1111yescharacteristic
579C11#1853211yescharacteristic, complemented, Sylow
580C23—21no—
581C23—21no—
582C23—22no—
583C23—44no—
584C23—44no—
585C23—82no—
586C23#6700611yescharacteristic
587Q8—21no—
588Q8—21no—
589Q8—21no—
590Q8—21no—
591Q8—42no—
592Q8—442no—
593Q8—442no—
594Q8—882no—
595D4—21no—
596D4—21no—
597D4—42no—
598D4—42no—
599D4—42no—
600D4—44no—
601D4—44no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—41no—
606D4—82no—
607D4#6700212yes—
608D4#6700412yescomplemented
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—44no—
630C2×C4—82no—
631C2×C4—82no—
632C2×C4—82no—
633C2×C4—442no—
634C2×C4—882no—
635C2×C4#6700611yescharacteristic
636C2×C4#6700611yescharacteristic
637C2×C4#6700611yescharacteristic
638C2×C4C22×C22⋊D1111yescharacteristic
639C2×C4C22×C22⋊D1111yescharacteristic
640C2×C4C22×C22⋊D1111yescharacteristic
641C8—442no—
642C8—442no—
643C8—442no—
644C22—21no—
645C22—22no—
646C22—21no—
647C22—22no—
648C22—21no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—88no—
657C22C2×#6700611yescharacteristic
658C4—21no—
659C4—21no—
660C4—21no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—42no—
668C4—882no—
669C4#1062285512yes—
670C4C2×#6700211yescharacteristic
671C4#1062335311yescharacteristic
672C4#1062335311yescharacteristic
673C4C2×#6700411yescharacteristic
674C2—41no—
675C2—42no—
676C2—42no—
677C2—82no—
678C2#1307786811yescharacteristic
679C2#1307787611yescharacteristic
680C2C2×#1062285511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3481C2
socleC22×C11C2×#120
hypercenter#3481D11
hypocenterC11#18532
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3481

Complements

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

NH ≅ G/Ntype
1. #13079009C2semidirect
2. #13078431C2semidirect
3. #13078103C2semidirect
4. #13067830C2semidirect
5. #13067823C2semidirect
6. #13067802C2semidirect
7. #13067795C2semidirect
8. #13067351C2semidirect
9. #13067055C2semidirect
10. #13067055C2semidirect
30. C2×#66922C22semidirect
33. #10622694C22semidirect
37. #10622644C22semidirect
39. #10622633C22semidirect
46. #10622537C22semidirect
47. #10622537C22semidirect
48. C4×#4318C22semidirect
49. #10622184C22semidirect
51. Q8⋊(C11⋊C8)C22semidirect
52. Q8⋊(C11⋊C8)C22semidirect
276. D4×C11#137semidirect
579. C11#18532semidirect
608. D4#67004semidirect

Maximal subgroups

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

subgroupindex
#130790092
#130784312
#130781032
#130678302
#130678232
#130678022
#130677952
#130673512
#130670552
C11×#34812
#1853211