Finite Group Databasebeta

← #14730243

Subgroups — #14730243

Order 2816.

1082 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079631C211yesmaximal, characteristic, complemented
2#13079069C211yesmaximal, characteristic, complemented
3C2×#10622640C211yesmaximal, characteristic, complemented
4#13067694C212yesmaximal, complemented
5#13067688C212yesmaximal, complemented
6#13067681C212yesmaximal, complemented
7#13067675C212yesmaximal, complemented
8#13067311C211yesmaximal, characteristic, complemented
9#13067063C211yesmaximal, characteristic, complemented
10#13067029C211yesmaximal, characteristic, complemented
11C11×#3522C211yesmaximal, characteristic, complemented
12C11×#559—21no—
13C11×#559C2211yescharacteristic, complemented
14Q82×C11C2211yescharacteristic, complemented
15C11×#554—21no—
16C11×#554C2211yescharacteristic, complemented
17C11×#550C2211yescharacteristic, complemented
18C11×#548—21no—
19C11×#547—22no—
20C11×#547—21no—
21C11×#542—22no—
22C11×#542—21no—
23C11×#532—21no—
24C11×#532C2211yescharacteristic
25C11×#529—21no—
26C11×#529C2211yescharacteristic
27C11×#520—21no—
28C2×C4×Q8×C11C2211yescharacteristic
29C2×#67002—22no—
30C22×#4325—21no—
31C2×#66927C2211yescharacteristic
32#10622698C2212yes—
33#10622686C2212yes—
34#10622680—21no—
35#10622671—22no—
36#10622671—21no—
37#10622659—21no—
38#10622649—21no—
39#10622640—21no—
40#10622640—21no—
41#10622640C2212yes—
42#10622640C2212yes—
43#10622640C2212yes—
44#10622628C2212yes—
45C2×#66873—21no—
46#10622539C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C4×#4318C2211yescharacteristic
49#10622184C2212yescomplemented
50#10622182C2212yescomplemented
51Q8⋊(C11⋊C8)C2212yescomplemented
52Q8⋊(C11⋊C8)C2212yescomplemented
53Q8⋊(C11⋊C8)C2212yescomplemented
54D4⋊(C11⋊C8)C2212yescomplemented
55C2×C11×#41—22no—
56C2×C11×#41—21no—
57C2×C11×#41D412yes—
58C22×Q8×C11D411yescharacteristic
59C22×D44—21no—
60C22×D44—21no—
61C22×D44—21no—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8C2311yescharacteristic
66C11×#127—21no—
67C11×#127C2311yescharacteristic
68C11×#126—22no—
69C11×#126—21no—
70C11×#125—21no—
71C11×#125D411yescharacteristic
72C11×#124—22no—
73C11×#124—22no—
74C11×#124—21no—
75C11×#124—21no—
76C11×#124D411yescharacteristic
77C11×#124D412yes—
78C11×#123—22no—
79C11×#123—22no—
80C11×#123—22no—
81C11×#123—22no—
82C11×#123—21no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8D411yescharacteristic
89C11×#121—22no—
90C11×#121—22no—
91C11×#121—21no—
92C11×#121—21no—
93C11×#121—21no—
94C11×#121D411yescharacteristic
95C4×Q8×C11—21no—
96C4×Q8×C11—21no—
97C4×Q8×C11—21no—
98C4×Q8×C11—21no—
99C4×Q8×C11D411yescharacteristic
100C4×Q8×C11D411yescharacteristic
101C4×Q8×C11C2311yescharacteristic
102C4×Q8×C11C2311yescharacteristic
103C4×Q8×C11C2311yescharacteristic
104C4×D4×C11—22no—
105C4×D4×C11—22no—
106C4×D4×C11—22no—
107C4×D4×C11—21no—
108C4×D4×C11—21no—
109C4×D4×C11—21no—
110C4×D4×C11—21no—
111C4×D4×C11—21no—
112C4×D4×C11—21no—
113C4×D4×C11—21no—
114C4×D4×C11C2311yescharacteristic
115C11×#117—22no—
116C11×#117—21no—
117C2×C11×C4⋊C4—22no—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4D411yescharacteristic
121C2×C42×C11—21no—
122C2×C42×C11C2311yescharacteristic
123#67002—48no—
124C2×#4325—22no—
125C2×#4325—22no—
126C2×#4325—24no—
127C2×#4325—22no—
128C2×#4325—44no—
129C2×#4323—24no—
130C2×#4323—22no—
131C2×#4318—21no—
132C22×C11⋊C8—21no—
133#66927—21no—
134#66927—21no—
135#66927—21no—
136#66927C2312yes—
137C22⋊(C11⋊C8)—21no—
138#66873—22no—
139#66873—22no—
140#66873—22no—
141#66873—22no—
142C4⋊(C11⋊C8)—21no—
143C4⋊(C11⋊C8)C2312yes—
144C4⋊(C11⋊C8)C2312yes—
145#66867—21no—
146#66867—21no—
147C4×C11⋊C8C2312yes—
148#18564—111nomaximal, Sylow
149C23×D11—41no—
150C11×#41—44no—
151C11×#41—42no—
152C11×#41—42no—
153C11×#41—84no—
154C2×Q8×C11—22no—
155C2×Q8×C11—21no—
156C2×Q8×C11—22no—
157C2×Q8×C11—41no—
158C2×Q8×C11C2×D411yescharacteristic
159C2×Q8×C11C2×D411yescharacteristic
160C2×Q8×C11C2×D411yescharacteristic
161C2×Q8×C11C2×D412yes—
162C2×D4×C11—22no—
163C2×D4×C11—22no—
164C2×D4×C11—21no—
165C2×D4×C11—22no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11C2×D411yescharacteristic
169C2×D4×C11C2×D412yes—
170C22×C4×C11—22no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—21no—
176C22×C4×C11—22no—
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—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4C2×D411yescharacteristic
206C11×C4⋊C4C2×D411yescharacteristic
207C11×C4⋊C4C2×D411yescharacteristic
208C11×C4⋊C4C2×D411yescharacteristic
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—22no—
219C11×C22⋊C4—21no—
220C11×C22⋊C4—21no—
221C42×C11—22no—
222C42×C11—21no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11C2×D411yescharacteristic
228C42×C11C2×D411yescharacteristic
229C42×C11C2×D411yescharacteristic
230C42×C11C2411yescharacteristic
231#4325—44no—
232#4325—48no—
233#4325—44no—
234#4325—82no—
235#4323—48no—
236#4323—82no—
237#4318—24no—
238C2×C11⋊C8—22no—
239C2×C11⋊C8—22no—
240C2×C11⋊C8—22no—
241C2×C11⋊C8—42no—
242#3522D1111yescharacteristic, complemented
243#3217—111no—
244#3151—111no—
245C2×#460—111no—
246#1623—112no—
247#1622—112no—
248#1621—112no—
249#1620—112no—
250#1551—111no—
251#1491—111no—
252#1483—111no—
253C23×C11—21no—
254C23×C11—22no—
255C23×C11#12011yescharacteristic
256C22×D11—42no—
257C22×D11—82no—
258C22×D11—82no—
259C22×D11—82no—
260Q8×C11—21no—
261Q8×C11—21no—
262Q8×C11—21no—
263Q8×C11—22no—
264Q8×C11—42no—
265Q8×C11—42no—
266Q8×C11—82no—
267Q8×C11AGL(1,ℤ/8)12yescomplemented
268D4×C11—22no—
269D4×C11—42no—
270D4×C11—44no—
271D4×C11—44no—
272D4×C11—42no—
273D4×C11—41no—
274D4×C11—41no—
275D4×C11—42no—
276D4×C11—82no—
277C2×C4×C11—21no—
278C2×C4×C11—22no—
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—22no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—42no—
290C2×C4×C11—44no—
291C2×C4×C11—42no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—82no—
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—24no—
312C11⋊C8—42no—
313C11⋊C8—42no—
314C2×AGL(1,ℤ/8)—222no—
315C22×SD16—221no—
316#559—21no—
317#559C2×D1111yescharacteristic, complemented
318Q82C2×D1111yescharacteristic, complemented
319#554—21no—
320#554C2×D1111yescharacteristic, complemented
321#550C2×D1111yescharacteristic, complemented
322#548—21no—
323#547—22no—
324#547—21no—
325#542—22no—
326#542—21no—
327#532—21no—
328#532C2×D1111yescharacteristic
329C2×#127—111no—
330#529—21no—
331#529C2×D1111yescharacteristic
332#520—21no—
333C2×C4×Q8C2×D1111yescharacteristic
334#496—222no—
335#496—221no—
336#493—112no—
337#492—112no—
338#490—221no—
339#460—112no—
340#460—112no—
341#460—112no—
342#460—221no—
343#460—221no—
344#459—112no—
345#450—221no—
346#447—221no—
347#432—111no—
348C2×C4⋊C8—111no—
349C2×#102—221no—
350C4×M16—111no—
351#333—112no—
352#331—112no—
353Q8⋊C8—112no—
354Q8⋊C8—112no—
355Q8⋊C8—112no—
356D4⋊C8—112no—
357C22×C11—21no—
358C22×C11—21no—
359C22×C11—42no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—41no—
365C22×C11#45312yes—
366C22×C11C2×#12011yescharacteristic
367C2×D11—82no—
368C2×D11—82no—
369C2×D11—82no—
370C2×D11—164no—
371C4×C11—21no—
372C4×C11—22no—
373C4×C11—21no—
374C4×C11—21no—
375C4×C11—21no—
376C4×C11—41no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11—41no—
380C4×C11—41no—
381C4×C11—42no—
382C4×C11—41no—
383C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
384C4×C11#57511yescharacteristic
385C4×C11#57712yes—
386C2×#41—22no—
387C2×#41—21no—
388C2×#41C22⋊D1112yes—
389C22×Q8C22⋊D1111yescharacteristic
390C22×D4—221no—
391C22×D4—221no—
392C22×D4—221no—
393AGL(1,ℤ/8)—448no—
394C2×SD16—222no—
395C2×SD16—222no—
396C2×SD16—224no—
397C2×SD16—222no—
398C2×SD16—444no—
399C2×D8—224no—
400C2×D8—222no—
401C2×M16—221no—
402C22×C8—221no—
403C4⋊Q8—22no—
404C4⋊Q8—21no—
405C4⋊Q8—21no—
406C4⋊Q8C22×D1111yescharacteristic
407#127—21no—
408#127—112no—
409#127—221no—
410#127—221no—
411#127—221no—
412#127C22×D1111yescharacteristic
413#126—22no—
414#126—21no—
415#125—21no—
416#125C22⋊D1111yescharacteristic
417#124—22no—
418#124—22no—
419#124—21no—
420#124—21no—
421#124C22⋊D1111yescharacteristic
422#124C22⋊D1112yes—
423#123—22no—
424#123—22no—
425#123—22no—
426#123—22no—
427#123—21no—
428C22⋊Q8—22no—
429C22⋊Q8—22no—
430C22⋊Q8—22no—
431C22⋊Q8—22no—
432C22⋊Q8—21no—
433C22⋊Q8C22⋊D1111yescharacteristic
434#121—22no—
435#121—22no—
436#121—21no—
437#121—21no—
438#121—21no—
439#121C22⋊D1111yescharacteristic
440C4×Q8—21no—
441C4×Q8—21no—
442C4×Q8—21no—
443C4×Q8—21no—
444C4×Q8C22⋊D1111yescharacteristic
445C4×Q8C22⋊D1111yescharacteristic
446C4×Q8C22×D1111yescharacteristic
447C4×Q8C22×D1111yescharacteristic
448C4×Q8C22×D1111yescharacteristic
449C4×D4—22no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4—21no—
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—21no—
456C4×D4—21no—
457C4×D4—21no—
458C4×D4—21no—
459C4×D4C22×D1111yescharacteristic
460#117—22no—
461#117—21no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4C22⋊D1111yescharacteristic
466C2×C42—21no—
467C2×C42C22×D1111yescharacteristic
468C4⋊C8—112no—
469C4⋊C8—112no—
470C4⋊C8—221no—
471#102—222no—
472#102—222no—
473#102—222no—
474#102—222no—
475C22⋊C8—221no—
476#97—221no—
477#97—221no—
478C4×C8—112no—
479C2×C11—22no—
480C2×C11—81no—
481C2×C11—82no—
482C2×C11#300611yescharacteristic
483C2×C11#301011yescharacteristic
484C2×C11C2×#45311yescharacteristic
485D11—162no—
486C24—441no—
487#41—44no—
488#41—42no—
489#41—42no—
490#41—84no—
491C2×Q8—22no—
492C2×Q8—21no—
493C2×Q8—22no—
494C2×Q8—41no—
495C2×Q8C2×C22⋊D1111yescharacteristic
496C2×Q8C2×C22⋊D1111yescharacteristic
497C2×Q8C2×C22⋊D1111yescharacteristic
498C2×Q8C2×C22⋊D1112yes—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—21no—
502C2×D4—22no—
503C2×D4—21no—
504C2×D4—21no—
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⋊D1112yes—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4C2×C22⋊D1111yescharacteristic
525C22×C4C2×C22⋊D1111yescharacteristic
526C22×C4C2×C22⋊D1111yescharacteristic
527SD16—448no—
528SD16—444no—
529SD16—444no—
530SD16—882no—
531D8—448no—
532D8—882no—
533M16—224no—
534C2×C8—222no—
535C2×C8—222no—
536C2×C8—222no—
537C2×C8—442no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
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
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—21no—
563C22⋊C4—22no—
564C22⋊C4—21no—
565C22⋊C4—21no—
566C22⋊C4—22no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C42—22no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42C2×C22⋊D1111yescharacteristic
576C42C2×C22⋊D1111yescharacteristic
577C42C2×C22⋊D1111yescharacteristic
578C42C23×D1111yescharacteristic
579C11#1856411yescharacteristic, complemented, Sylow
580C23—21no—
581C23—22no—
582C23—442no—
583C23—882no—
584C23—882no—
585C23—882no—
586C23#6700611yescharacteristic
587Q8—21no—
588Q8—21no—
589Q8—21no—
590Q8—22no—
591Q8—42no—
592Q8—42no—
593Q8—82no—
594Q8#6700212yescomplemented
595D4—22no—
596D4—42no—
597D4—44no—
598D4—44no—
599D4—42no—
600D4—41no—
601D4—41no—
602D4—42no—
603D4—82no—
604D4—444no—
605D4—442no—
606D4—442no—
607D4—442no—
608D4—442no—
609D4—882no—
610D4—882no—
611D4—882no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—42no—
625C2×C4—44no—
626C2×C4—42no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—82no—
630C2×C4—82no—
631C2×C4—82no—
632C2×C4#6700611yescharacteristic
633C2×C4#6700611yescharacteristic
634C2×C4#6700611yescharacteristic
635C2×C4C22×C22⋊D1111yescharacteristic
636C2×C4C22×C22⋊D1111yescharacteristic
637C2×C4C22×C22⋊D1111yescharacteristic
638C8—224no—
639C8—442no—
640C8—442no—
641C22—21no—
642C22—21no—
643C22—42no—
644C22—41no—
645C22—41no—
646C22—42no—
647C22—42no—
648C22—41no—
649C22—882no—
650C22—882no—
651C22—882no—
652C22—1764no—
653C22#1062285412yes—
654C22C2×#6700611yescharacteristic
655C4—21no—
656C4—22no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—42no—
666C4—41no—
667C4C2×#6700211yescharacteristic
668C4#1062335311yescharacteristic
669C4#1062336812yes—
670C2—22no—
671C2—81no—
672C2—82no—
673C2—1762no—
674C2#1307786811yescharacteristic
675C2#1307790211yescharacteristic
676C2C2×#1062285411yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3522C2
socleC22×C11C2×#120
hypercenter#3522D11
hypocenterC11#18564
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3522

Complements

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

NH ≅ G/Ntype
1. #13079631C2semidirect
2. #13079069C2semidirect
3. C2×#10622640C2semidirect
4. #13067694C2semidirect
5. #13067688C2semidirect
6. #13067681C2semidirect
7. #13067675C2semidirect
8. #13067311C2semidirect
9. #13067063C2semidirect
10. #13067029C2semidirect
11. C11×#3522C2semidirect
13. C11×#559C22semidirect
14. Q82×C11C22semidirect
16. C11×#554C22semidirect
17. C11×#550C22semidirect
49. #10622184C22semidirect
50. #10622182C22semidirect
51. Q8⋊(C11⋊C8)C22semidirect
52. Q8⋊(C11⋊C8)C22semidirect
53. Q8⋊(C11⋊C8)C22semidirect
54. D4⋊(C11⋊C8)C22semidirect
242. #3522D11semidirect
267. Q8×C11AGL(1,ℤ/8)semidirect
317. #559C2×D11semidirect
318. Q82C2×D11semidirect
320. #554C2×D11semidirect
321. #550C2×D11semidirect
579. C11#18564semidirect
594. Q8#67002semidirect

Maximal subgroups

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

subgroupindex
#130796312
#130790692
C2×#106226402
#130676942
#130676882
#130676812
#130676752
#130673112
#130670632
#130670292
C11×#35222
#1856411