Finite Group Databasebeta

← #14730397

Subgroups — #14730397

Order 2816.

1028 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079631C211yesmaximal, characteristic, complemented
2#13078992C211yesmaximal, characteristic, complemented
3C2×#10622628C211yesmaximal, characteristic, complemented
4#13067726C212yesmaximal, complemented
5#13067719C212yesmaximal, complemented
6#13067705C212yesmaximal, complemented
7#13067705C212yesmaximal, complemented
8#13067316C211yesmaximal, characteristic, complemented
9#13067059C211yesmaximal, characteristic, complemented
10#13067029C211yesmaximal, characteristic, complemented
11C11×#3520C211yesmaximal, characteristic, complemented
12C11×#556C2211yescharacteristic, complemented
13C11×#554—21no—
14C11×#552—21no—
15C11×#551—22no—
16D4×Q8×C11C2211yescharacteristic, complemented
17C11×#548—21no—
18C11×#547C2211yescharacteristic, complemented
19C11×#547C2211yescharacteristic, complemented
20C11×#546—21no—
21C11×#542—21no—
22C11×#539—22no—
23C11×#533C2211yescharacteristic
24C11×#529C2211yescharacteristic
25C11×#525—21no—
26C2×C11×C22⋊Q8—21no—
27C11×#520—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C22×#4323—21no—
30C2×#66927C2211yescharacteristic
31#10622701C2212yescomplemented
32#10622701C2212yescomplemented
33#10622680—21no—
34#10622680—22no—
35#10622671—21no—
36#10622659—21no—
37#10622649—21no—
38#10622640C2212yescomplemented
39#10622628—21no—
40#10622628—21no—
41#10622628C2212yes—
42#10622628C2212yes—
43#10622628C2212yescomplemented
44#10622614—22no—
45C2×#66873—21no—
46#10622539C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C4×#4318C2211yescharacteristic
49#10622185C2212yescomplemented
50#10622185C2212yescomplemented
51Q8⋊(C11⋊C8)C2212yescomplemented
52D4⋊(C11⋊C8)C2212yescomplemented
53D4⋊(C11⋊C8)C2212yescomplemented
54D4⋊(C11⋊C8)C2212yescomplemented
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C22×Q8×C11—21no—
58C22×D4×C11D411yescharacteristic
59C23×C4×C11—21no—
60C22×D44—21no—
61C22×D44—21no—
62C22×D44—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8C2311yescharacteristic
65C11×C4⋊Q8C2311yescharacteristic
66C11×#126—22no—
67C11×#126—22no—
68C11×#126—21no—
69C11×#125—22no—
70C11×#125D411yescharacteristic
71C11×#125D412yes—
72C11×#124—22no—
73C11×#124—21no—
74C11×#124D411yescharacteristic
75C11×#123—22no—
76C11×#123—22no—
77C11×#123—21no—
78C11×#123—22no—
79C11×#123—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—21no—
86C11×C22⋊Q8—21no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—21no—
90C11×C22⋊Q8D411yescharacteristic
91C11×#121—22no—
92C11×#121—21no—
93C11×#121—21no—
94C11×#121D411yescharacteristic
95C11×#120—22no—
96C4×Q8×C11—21no—
97C4×Q8×C11—21no—
98C4×Q8×C11—21no—
99C4×Q8×C11C2311yescharacteristic
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C4×D4×C11—22no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C4×D4×C11—21no—
106C4×D4×C11—21no—
107C4×D4×C11D411yescharacteristic
108C4×D4×C11D411yescharacteristic
109C4×D4×C11C2311yescharacteristic
110C4×D4×C11C2311yescharacteristic
111C4×D4×C11C2311yescharacteristic
112C11×#117—22no—
113C11×#117—21no—
114C11×#117—21no—
115C11×#117D412yes—
116C2×C11×C4⋊C4—22no—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4D411yescharacteristic
120C2×C11×C22⋊C4—22no—
121C2×C11×C22⋊C4—21no—
122C2×C42×C11C2311yescharacteristic
123C2×#4325—22no—
124C2×#4323—22no—
125C2×#4323—22no—
126C2×#4323—22no—
127C2×#4323—44no—
128C2×#4318—21no—
129C22×C11⋊C8—21no—
130#66927—21no—
131#66927—21no—
132#66927—21no—
133#66927C2312yes—
134C22⋊(C11⋊C8)—21no—
135#66873—22no—
136#66873—22no—
137#66873—24no—
138#66873—24no—
139#66873—22no—
140#66873—22no—
141C4⋊(C11⋊C8)—21no—
142C4⋊(C11⋊C8)C2312yes—
143C4⋊(C11⋊C8)C2312yes—
144#66867—21no—
145#66867—21no—
146C4×C11⋊C8C2312yes—
147#18578—111nomaximal, Sylow
148C24×C11—21no—
149C23×D11—41no—
150C11×#41—42no—
151C11×#41—42no—
152C11×#41—82no—
153C2×Q8×C11—22no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—82no—
157C2×Q8×C11C2×D411yescharacteristic
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—21no—
161C2×D4×C11—22no—
162C2×D4×C11—21no—
163C2×D4×C11—41no—
164C2×D4×C11C2×D411yescharacteristic
165C2×D4×C11C2×D411yescharacteristic
166C2×D4×C11C2×D411yescharacteristic
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—82no—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C2×D44—22no—
181C2×D44—22no—
182C2×D44—22no—
183C2×D44—42no—
184C2×D44—44no—
185C2×D44—42no—
186C2×D44—41no—
187C2×D44—41no—
188C2×D44—41no—
189C2×D44—82no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4C2×D411yescharacteristic
204C11×C4⋊C4C2×D411yescharacteristic
205C11×C4⋊C4C2×D411yescharacteristic
206C11×C4⋊C4C2×D411yescharacteristic
207C11×C4⋊C4C2×D412yes—
208C11×C4⋊C4C2×D412yes—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—21no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—21no—
219C11×C22⋊C4—21no—
220C11×C22⋊C4—21no—
221C11×C22⋊C4—21no—
222C11×C22⋊C4—21no—
223C11×C22⋊C4—21no—
224C42×C11—22no—
225C42×C11—22no—
226C42×C11—21no—
227C42×C11C2×D411yescharacteristic
228C42×C11C2×D411yescharacteristic
229C42×C11C2×D411yescharacteristic
230C42×C11C2411yescharacteristic
231#4325—82no—
232#4323—44no—
233#4323—44no—
234#4323—82no—
235#4318—42no—
236C2×C11⋊C8—22no—
237C2×C11⋊C8—22no—
238C2×C11⋊C8—22no—
239C2×C11⋊C8—42no—
240#3520D1111yescharacteristic, complemented
241#3217—111no—
242#3138—111no—
243C2×#459—111no—
244#1628—112no—
245#1627—112no—
246#1625—112no—
247#1625—112no—
248#1552—111no—
249#1490—111no—
250#1483—111no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—42no—
255C23×C11—42no—
256C23×C11—81no—
257C23×C11#12011yescharacteristic
258C22×D11—42no—
259C22×D11—82no—
260C22×D11—82no—
261C22×D11—82no—
262Q8×C11—22no—
263Q8×C11—41no—
264Q8×C11—41no—
265Q8×C11—42no—
266Q8×C11—82no—
267D4×C11—21no—
268D4×C11—21no—
269D4×C11—21no—
270D4×C11—22no—
271D4×C11—42no—
272D4×C11—44no—
273D4×C11—42no—
274D4×C11—82no—
275D4×C11AGL(1,ℤ/8)12yes—
276C2×C4×C11—22no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—22no—
280C2×C4×C11—21no—
281C2×C4×C11—22no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—44no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11—81no—
293C2×C4×C11—81no—
294C2×C4×C11—81no—
295C2×C4×C11—82no—
296C2×C4×C11—82no—
297C2×C4×C11#12011yescharacteristic
298C2×C4×C11#12011yescharacteristic
299C2×C4×C11#12011yescharacteristic
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C22×D411yescharacteristic
302C2×C4×C11C22×D411yescharacteristic
303D44—44no—
304D44—42no—
305D44—42no—
306D44—42no—
307D44—42no—
308D44—82no—
309D44—82no—
310D44—82no—
311C11⋊C8—42no—
312C11⋊C8—42no—
313C11⋊C8—42no—
314C22×D8—221no—
315#556C2×D1111yescharacteristic, complemented
316#554—21no—
317#552—21no—
318#551—22no—
319D4×Q8C2×D1111yescharacteristic, complemented
320#548—21no—
321#547C2×D1111yescharacteristic, complemented
322#547C2×D1111yescharacteristic, complemented
323#546—21no—
324#542—21no—
325#539—22no—
326#533C2×D1111yescharacteristic
327C2×#127—111no—
328#529C2×D1111yescharacteristic
329#525—21no—
330C2×C22⋊Q8—21no—
331#520—21no—
332C2×C4×D4C2×D1111yescharacteristic
333#496—221no—
334#490—222no—
335#490—221no—
336#486—112no—
337#486—112no—
338#460—112no—
339#459—112no—
340#459—112no—
341#459—112no—
342#459—221no—
343#459—221no—
344#450—221no—
345#447—221no—
346#432—111no—
347C2×C4⋊C8—111no—
348#418—222no—
349C2×#102—221no—
350C4×M16—111no—
351#332—112no—
352#332—112no—
353Q8⋊C8—112no—
354D4⋊C8—112no—
355D4⋊C8—112no—
356D4⋊C8—112no—
357C22×C11—21no—
358C22×C11—21no—
359C22×C11—22no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—84no—
369C22×C11#45412yes—
370C22×C11C2×#12011yescharacteristic
371C2×D11—82no—
372C2×D11—82no—
373C2×D11—82no—
374C2×D11—164no—
375C4×C11—21no—
376C4×C11—21no—
377C4×C11—21no—
378C4×C11—21no—
379C4×C11—41no—
380C4×C11—42no—
381C4×C11—41no—
382C4×C11—41no—
383C4×C11—42no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
387C4×C11#57511yescharacteristic
388C4×C11#57612yes—
389C2×#41—21no—
390C2×#41—21no—
391C22×Q8—21no—
392C22×D4—221no—
393C22×D4—221no—
394C22×D4—221no—
395C22×D4C22⋊D1111yescharacteristic
396C23×C4—21no—
397C2×SD16—222no—
398C2×D8—222no—
399C2×D8—222no—
400C2×D8—222no—
401C2×D8—444no—
402C2×M16—221no—
403C22×C8—221no—
404C4⋊Q8—21no—
405C4⋊Q8C22×D1111yescharacteristic
406C4⋊Q8C22×D1111yescharacteristic
407#127—112no—
408#127—221no—
409#127—221no—
410#127—221no—
411#126—22no—
412#126—22no—
413#126—21no—
414#125—22no—
415#125C22⋊D1111yescharacteristic
416#125C22⋊D1112yes—
417#124—22no—
418#124—21no—
419#124C22⋊D1111yescharacteristic
420#123—22no—
421#123—22no—
422#123—21no—
423#123—22no—
424#123—22no—
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428C22⋊Q8—21no—
429C22⋊Q8—21no—
430C22⋊Q8—21no—
431C22⋊Q8—21no—
432C22⋊Q8—21no—
433C22⋊Q8—22no—
434C22⋊Q8—21no—
435C22⋊Q8C22⋊D1111yescharacteristic
436#121—22no—
437#121—21no—
438#121—21no—
439#121C22⋊D1111yescharacteristic
440#120—22no—
441C4×Q8—21no—
442C4×Q8—21no—
443C4×Q8—21no—
444C4×Q8C22×D1111yescharacteristic
445C4×D4—22no—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4—21no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4C22⋊D1111yescharacteristic
453C4×D4C22⋊D1111yescharacteristic
454C4×D4C22×D1111yescharacteristic
455C4×D4C22×D1111yescharacteristic
456C4×D4C22×D1111yescharacteristic
457#117—22no—
458#117—21no—
459#117—21no—
460#117C22⋊D1112yes—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4C22⋊D1111yescharacteristic
465C2×C22⋊C4—22no—
466C2×C22⋊C4—21no—
467C2×C42C22×D1111yescharacteristic
468C4⋊C8—112no—
469C4⋊C8—112no—
470C4⋊C8—221no—
471#102—222no—
472#102—222no—
473#102—224no—
474#102—224no—
475#102—222no—
476#102—222no—
477C22⋊C8—221no—
478#97—221no—
479#97—221no—
480C4×C8—112no—
481C2×C11—22no—
482C2×C11—42no—
483C2×C11—81no—
484C2×C11—81no—
485C2×C11#300611yescharacteristic
486C2×C11#300811yescharacteristic
487C2×C11C2×#45411yescharacteristic
488D11—162no—
489C24—21no—
490C24—441no—
491#41—42no—
492#41—42no—
493#41—82no—
494C2×Q8—22no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—82no—
498C2×Q8C2×C22⋊D1111yescharacteristic
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—21no—
502C2×D4—22no—
503C2×D4—21no—
504C2×D4—41no—
505C2×D4—222no—
506C2×D4—222no—
507C2×D4—222no—
508C2×D4—442no—
509C2×D4—444no—
510C2×D4—442no—
511C2×D4—441no—
512C2×D4—441no—
513C2×D4—441no—
514C2×D4—882no—
515C2×D4C2×C22⋊D1111yescharacteristic
516C2×D4C2×C22⋊D1111yescharacteristic
517C2×D4C2×C22⋊D1111yescharacteristic
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—82no—
528C22×C4C2×C22⋊D1111yescharacteristic
529C22×C4C2×C22⋊D1111yescharacteristic
530C22×C4C2×C22⋊D1111yescharacteristic
531SD16—882no—
532D8—444no—
533D8—444no—
534D8—882no—
535M16—442no—
536C2×C8—222no—
537C2×C8—222no—
538C2×C8—222no—
539C2×C8—442no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—21no—
545C4⋊C4—22no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—22no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4C2×C22⋊D1111yescharacteristic
554C4⋊C4C2×C22⋊D1111yescharacteristic
555C4⋊C4C2×C22⋊D1111yescharacteristic
556C4⋊C4C2×C22⋊D1111yescharacteristic
557C4⋊C4C2×C22⋊D1112yes—
558C4⋊C4C2×C22⋊D1112yes—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—21no—
565C22⋊C4—22no—
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—21no—
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C42—22no—
575C42—22no—
576C42—21no—
577C42C2×C22⋊D1111yescharacteristic
578C42C2×C22⋊D1111yescharacteristic
579C42C2×C22⋊D1111yescharacteristic
580C42C23×D1111yescharacteristic
581C11#1857811yescharacteristic, complemented, Sylow
582C23—21no—
583C23—21no—
584C23—21no—
585C23—42no—
586C23—42no—
587C23—81no—
588C23—442no—
589C23—882no—
590C23—882no—
591C23—882no—
592C23#6700611yescharacteristic
593Q8—22no—
594Q8—41no—
595Q8—41no—
596Q8—42no—
597Q8—82no—
598D4—21no—
599D4—21no—
600D4—21no—
601D4—22no—
602D4—42no—
603D4—44no—
604D4—42no—
605D4—82no—
606D4—444no—
607D4—442no—
608D4—442no—
609D4—442no—
610D4—442no—
611D4—882no—
612D4—882no—
613D4—882no—
614D4#6700212yes—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—44no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—81no—
632C2×C4—81no—
633C2×C4—81no—
634C2×C4—82no—
635C2×C4—82no—
636C2×C4#6700611yescharacteristic
637C2×C4#6700611yescharacteristic
638C2×C4#6700611yescharacteristic
639C2×C4C22×C22⋊D1111yescharacteristic
640C2×C4C22×C22⋊D1111yescharacteristic
641C2×C4C22×C22⋊D1111yescharacteristic
642C8—442no—
643C8—442no—
644C8—442no—
645C22—21no—
646C22—21no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—84no—
657C22—882no—
658C22—882no—
659C22—882no—
660C22—1764no—
661C22#1062285812yes—
662C22C2×#6700611yescharacteristic
663C4—21no—
664C4—21no—
665C4—21no—
666C4—21no—
667C4—41no—
668C4—42no—
669C4—41no—
670C4—41no—
671C4—42no—
672C4—41no—
673C4—41no—
674C4C2×#6700211yescharacteristic
675C4#1062335311yescharacteristic
676C4#1062336612yes—
677C2—22no—
678C2—42no—
679C2—81no—
680C2—81no—
681C2—1762no—
682C2#1307786811yescharacteristic
683C2#1307788411yescharacteristic
684C2C2×#1062285811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3520C2
socleC22×C11C2×#120
hypercenter#3520D11
hypocenterC11#18578
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3520

Complements

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

NH ≅ G/Ntype
1. #13079631C2semidirect
2. #13078992C2semidirect
3. C2×#10622628C2semidirect
4. #13067726C2semidirect
5. #13067719C2semidirect
6. #13067705C2semidirect
7. #13067705C2semidirect
8. #13067316C2semidirect
9. #13067059C2semidirect
10. #13067029C2semidirect
11. C11×#3520C2semidirect
12. C11×#556C22semidirect
16. D4×Q8×C11C22semidirect
18. C11×#547C22semidirect
19. C11×#547C22semidirect
31. #10622701C22semidirect
32. #10622701C22semidirect
38. #10622640C22semidirect
43. #10622628C22semidirect
49. #10622185C22semidirect
50. #10622185C22semidirect
51. Q8⋊(C11⋊C8)C22semidirect
52. D4⋊(C11⋊C8)C22semidirect
53. D4⋊(C11⋊C8)C22semidirect
54. D4⋊(C11⋊C8)C22semidirect
240. #3520D11semidirect
315. #556C2×D11semidirect
319. D4×Q8C2×D11semidirect
321. #547C2×D11semidirect
322. #547C2×D11semidirect
581. C11#18578semidirect

Maximal subgroups

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

subgroupindex
#130796312
#130789922
C2×#106226282
#130677262
#130677192
#130677052
#130673162
#130670592
#130670292
C11×#35202
#1857811