Finite Group Databasebeta

← #14910451

Subgroups — #14910451

Order 2816.

696 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622532C211yesmaximal, characteristic, complemented
2C22×#66892C211yesmaximal, characteristic, complemented
3#13080357C211yesmaximal, characteristic, complemented
4#13080298C211yesmaximal, characteristic, complemented
5#13070878C211yesmaximal, characteristic, complemented
6#13070715C211yesmaximal, characteristic, complemented
7#13070714C211yesmaximal, characteristic, complemented
8#13070680C211yesmaximal, characteristic, complemented
9#13070674C211yesmaximal, characteristic, complemented
10#13070555C211yesmaximal, characteristic, complemented
11#13070542C211yesmaximal, characteristic, complemented
12#13070530C211yesmaximal, characteristic, complemented
13#13070465C211yesmaximal, characteristic, complemented
14(C22⋊D11)⋊C16C211yesmaximal, characteristic, complemented
15C11×#2188C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17#10623348—21no—
18C2×#66972C2211yescharacteristic
19C2×#66972C2211yescharacteristic, complemented
20C22×D88C2211yescharacteristic
21#10623161—21no—
22C2×C11×Q32C2211yescharacteristic, complemented
23C2×C11×Q32C2211yescharacteristic, complemented
24C11×#467C2211yescharacteristic
25#10622840—21no—
26#10622804C2211yescharacteristic
27#10622804C2211yescharacteristic, complemented
28#10622801C2211yescharacteristic, complemented
29#10622800—21no—
30#10622798—21no—
31Q16×Dic11C2211yescharacteristic, complemented
32C2×#66892—24no—
33C2×#66892C2211yescharacteristic
34C2×#66892C2211yescharacteristic
35C2×#66892C2211yescharacteristic
36C2×#66892C2211yescharacteristic
37C2×#66892C2211yescharacteristic, complemented
38#10622728C2211yescharacteristic
39C8×C22⋊D11C2211yescharacteristic
40C22×C11⋊C16C2211yescharacteristic
41#10622659—21no—
42#10622532—24no—
43C2×D176C2211yescharacteristic
44C2×D176C2211yescharacteristic
45C2×C16×D11C2211yescharacteristic, complemented
46#10622496C2211yescharacteristic
47#10622485C2211yescharacteristic
48#10622432—21no—
49#10622424—21no—
50C11×#358C2211yescharacteristic, complemented
51C11×#358C2211yescharacteristic, complemented
52C11×C22⋊C16C2211yescharacteristic
53#10622202C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic
55#10622147C2211yescharacteristic
56(C2×D11)⋊C16C2211yescharacteristic, complemented
57Dic11⋊C16C2211yescharacteristic, complemented
58C16×Dic11C2211yescharacteristic, complemented
59#10622129C2211yescharacteristic, complemented
60#10622128C2211yescharacteristic, complemented
61C22×Q8×C11—21no—
62C2×#4343—21no—
63C2×#4343—21no—
64C22×D44—21no—
65C2×C11×Q16—22no—
66C2×C11×Q16—21no—
67C2×C11×Q16—41no—
68C2×C11×Q16C2311yescharacteristic
69C2×C11×Q16C2311yescharacteristic
70C2×C11×Q16C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×C22⋊Q8—21no—
73#67000—21no—
74#67000—21no—
75#67000—41no—
76#66999—21no—
77#66999—41no—
78Q8×Dic11—21no—
79C2×#4325—21no—
80C2×#4325—21no—
81C2×#4325—21no—
82C2×#4325—21no—
83#66983—21no—
84#66983—41no—
85C4×C22⋊D11—41no—
86C4×C22⋊D11D411yescharacteristic
87#66972—22no—
88#66972—22no—
89#66972—41no—
90#66972—41no—
91C2×D88—22no—
92C2×D88—21no—
93C2×D88—41no—
94C2×D88C2311yescharacteristic
95C2×D88C2311yescharacteristic
96C2×D88C2311yescharacteristic
97C2×C8×D11C2311yescharacteristic
98#66948—21no—
99#66948—41no—
100#66947—41no—
101#66946—21no—
102#66935—41no—
103C22⋊C4×D11—41no—
104C11×Q32—22no—
105C11×Q32—41no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#103—21no—
110#66899—21no—
111#66899—21no—
112C22⋊(C11⋊C8)D411yescharacteristic
113#66892—22no—
114#66892—22no—
115#66892—22no—
116#66892—22no—
117#66892D414yescomplemented
118#66885—21no—
119(C2×D11)⋊C8D411yescharacteristic
120#66882C2311yescharacteristic
121Dic11⋊C8D411yescharacteristic
122C8×Dic11C2311yescharacteristic
123C2×C11⋊C16—22no—
124C2×C11⋊C16C2311yescharacteristic
125C2×C11⋊C16C2311yescharacteristic
126#66873—21no—
127#66873—21no—
128D176—22no—
129D176—41no—
130C16×D11—22no—
131#33848—111nomaximal, Sylow
132C23×D11—41no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—42no—
137C2×Q8×C11—41no—
138C2×Q8×C11—81no—
139C22×C4×C11—41no—
140C22×C4×C11C2×D411yescharacteristic
141C2×C22⋊D11—41no—
142C2×C22⋊D11D811yescharacteristic
143#4343—42no—
144#4343—42no—
145#4343—81no—
146#4343—81no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—42no—
151C2×D44—41no—
152C2×D44—41no—
153C2×D44—41no—
154C2×D44—41no—
155C2×D44—81no—
156C2×C4×D11—41no—
157C2×C4×D11—41no—
158C2×C4×D11—41no—
159C2×C4×D11C2×D411yescharacteristic
160C11×Q16—21no—
161C11×Q16—21no—
162C11×Q16—21no—
163C11×Q16—21no—
164C11×Q16—21no—
165C11×Q16—42no—
166C11×Q16C2×D412yes—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2411yescharacteristic
171C11×C4⋊C4—21no—
172C11×C4⋊C4—41no—
173C11×C22⋊C4—41no—
174C22⋊Dic11D811yescharacteristic
175#4325—42no—
176#4325—42no—
177#4325—81no—
178#4325—81no—
179(C2×D11)⋊C4—41no—
180(C2×D11)⋊C4—41no—
181(C2×D11)⋊C4—41no—
182(C2×D11)⋊C4—41no—
183(C2×D11)⋊C4—41no—
184(C2×D11)⋊C4—41no—
185(C2×D11)⋊C4—41no—
186(C2×D11)⋊C4—41no—
187(C2×D11)⋊C4D811yescharacteristic
188C4⋊Dic11—21no—
189C4⋊Dic11—41no—
190Dic11⋊C4—41no—
191Dic11⋊C4D811yescharacteristic
192C4×Dic11—41no—
193C4×Dic11C2×D411yescharacteristic
194C2×C11⋊C8C2×D411yescharacteristic
195C2×C11⋊C8C2×D411yescharacteristic
196D88—21no—
197D88—21no—
198D88—21no—
199D88—21no—
200D88—21no—
201D88—42no—
202D88C2×D412yes—
203C8×D11—21no—
204C8×D11—21no—
205C11×C16—21no—
206C11×C16—21no—
207C11⋊C16—21no—
208C11⋊C16C2×D412yes—
209C2×#508—111no—
210C22×SD32—111no—
211#3285—111no—
212#3280—111no—
213#2249—111no—
214#2217—111no—
215#2217—111no—
216#2211—111no—
217#2210—111no—
218#2189—111no—
219#2188D1111yescharacteristic, complemented
220#2186—111no—
221#2184—111no—
222C4×SD32—111no—
223D4×C16—111no—
224C23×C11C2×D811yescharacteristic
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—82no—
229C22×D11—82no—
230C22×D11—161no—
231C22×D11C2×D811yescharacteristic
232Q8×C11—22no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11—82no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—82no—
246C2×C4×C11C2×D811yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C22⋊D11—22no—
249C22⋊D11—82no—
250C2×Dic11—41no—
251C2×Dic11C2×D811yescharacteristic
252C2×Dic11C2×D811yescharacteristic
253C2×Dic11C2×D811yescharacteristic
254D44—22no—
255D44—41no—
256D44—41no—
257D44—41no—
258D44—41no—
259D44—41no—
260D44—82no—
261D44—82no—
262D44—82no—
263D44—161no—
264C4×D11—21no—
265C4×D11—21no—
266C4×D11—82no—
267C4×D11—82no—
268C4×D11—161no—
269C8×C11—21no—
270C8×C11C22×D411yescharacteristic
271C8×C11H(5,𝔽2)11yescharacteristic
272C11⋊C8—21no—
273C11⋊C8—21no—
274C2×#135—111no—
275C2×#135—111no—
276C22×Q16C2×D1111yescharacteristic
277C22×D8—111no—
278#548—221no—
279#546—221no—
280#508—224no—
281C2×Q32C2×D1111yescharacteristic, complemented
282C2×Q32C2×D1111yescharacteristic, complemented
283C2×SD32—111no—
284C2×SD32—111no—
285C2×SD32—111no—
286C2×SD32—111no—
287C2×SD32—111no—
288C2×SD32—224no—
289C2×D16—111no—
290C2×D16—111no—
291C22×C16—111no—
292C22×C16—111no—
293#495—111no—
294#495—111no—
295#467—111no—
296#467C2×D1111yescharacteristic
297#466—111no—
298#466—111no—
299#464—221no—
300#463—221no—
301#452—221no—
302#450—221no—
303#449—221no—
304#448—221no—
305C4×Q16—111no—
306C4×D8—111no—
307C8×D4—111no—
308#367—111no—
309C4⋊C16—111no—
310#358—111no—
311#358C2×D1111yescharacteristic, complemented
312#358C2×D1111yescharacteristic, complemented
313#357—111no—
314#357—111no—
315#357—111no—
316C22⋊C16—111no—
317C22⋊C16C2×D1111yescharacteristic
318C4×C16—111no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11#50812yescomplemented
322C22×C11C22×D811yescharacteristic
323C2×D11—21no—
324C2×D11—21no—
325C2×D11—21no—
326C2×D11—42no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—81no—
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C2×D11—81no—
335C2×D11—164no—
336C4×C11—21no—
337C4×C11—42no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11D4211yescharacteristic
342C4×C11#57611yescharacteristic
343Dic11—21no—
344Dic11—21no—
345Dic11—21no—
346Dic11—81no—
347C2×#41—221no—
348C2×#41—221no—
349C22×Q8—21no—
350C22×D4—221no—
351#135—222no—
352#135—222no—
353#135—441no—
354#135—441no—
355C2×Q16—22no—
356C2×Q16—21no—
357C2×Q16—41no—
358C2×Q16C22×D1111yescharacteristic
359C2×Q16C22×D1111yescharacteristic
360C2×Q16C22×D1111yescharacteristic
361C2×SD16—221no—
362C2×SD16—221no—
363C2×SD16—221no—
364C2×SD16—221no—
365C2×D8—111no—
366C2×D8—111no—
367C2×D8—111no—
368C2×D8—222no—
369C2×D8—221no—
370C2×D8—441no—
371C22×C8—111no—
372C22×C8C22×D1111yescharacteristic
373#124—221no—
374#124—221no—
375#124—441no—
376#123—441no—
377C22⋊Q8—21no—
378C22⋊Q8—221no—
379C22⋊Q8—441no—
380#121—221no—
381#121—221no—
382#121—441no—
383#121—441no—
384#120—441no—
385C4×Q8—221no—
386C4×D4—111no—
387C4×D4—221no—
388C4×D4—441no—
389C2×C22⋊C4—441no—
390Q32—22no—
391Q32—41no—
392SD32—114no—
393SD32—222no—
394SD32—222no—
395SD32—222no—
396SD32—222no—
397D16—222no—
398D16—441no—
399C2×C16—111no—
400C2×C16—111no—
401C2×C16—222no—
402C2×C16—222no—
403C2×C16C22×D1111yescharacteristic
404C2×C16C22×D1111yescharacteristic
405#107—111no—
406#107C22×D1111yescharacteristic
407C4⋊C8—111no—
408#103—21no—
409#103—221no—
410#103—221no—
411#102—221no—
412#102—221no—
413#102—221no—
414C22⋊C8—111no—
415C22⋊C8—111no—
416C4×C8—111no—
417C2×C11—22no—
418C2×C11D4×D811yescharacteristic
419C2×C11C2×#50811yescharacteristic
420C2×C11#341611yescharacteristic
421D11—41no—
422D11—82no—
423D11—161no—
424D11—161no—
425C24—441no—
426#41—442no—
427#41—442no—
428#41—881no—
429#41—881no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—42no—
434C2×Q8—41no—
435C2×Q8—81no—
436C2×D4—111no—
437C2×D4—221no—
438C2×D4—221no—
439C2×D4—221no—
440C2×D4—442no—
441C2×D4—441no—
442C2×D4—441no—
443C2×D4—441no—
444C2×D4—441no—
445C2×D4—441no—
446C2×D4—881no—
447C22×C4—41no—
448C22×C4—111no—
449C22×C4—441no—
450C22×C4—441no—
451C22×C4—441no—
452C22×C4D4×D1111yescharacteristic
453Q16—21no—
454Q16—21no—
455Q16—21no—
456Q16—21no—
457Q16—21no—
458Q16—42no—
459Q16D4×D1112yes—
460SD16—442no—
461SD16—442no—
462SD16—881no—
463SD16—881no—
464D8—112no—
465D8—221no—
466D8—221no—
467D8—221no—
468D8—221no—
469D8—221no—
470D8—442no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—111no—
474C2×C8—111no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8D4×D1111yescharacteristic
478C2×C8C23×D1111yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—111no—
482C4⋊C4—221no—
483C4⋊C4—441no—
484C4⋊C4—441no—
485C22⋊C4—41no—
486C22⋊C4—111no—
487C22⋊C4—111no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C22⋊C4—441no—
491C22⋊C4—441no—
492C22⋊C4—441no—
493C22⋊C4—441no—
494C22⋊C4—441no—
495C22⋊C4—441no—
496C42—111no—
497C42—441no—
498C16—21no—
499C16—21no—
500C16—112no—
501C16—221no—
502C11#3384811yescharacteristic, complemented, Sylow
503C23—111no—
504C23—441no—
505C23—441no—
506C23—441no—
507C23—882no—
508C23—882no—
509C23—1761no—
510C23D8×D1111yescharacteristic
511Q8—22no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—82no—
518D4—222no—
519D4—222no—
520D4—441no—
521D4—441no—
522D4—441no—
523D4—441no—
524D4—441no—
525D4—882no—
526D4—882no—
527D4—882no—
528D4—882no—
529D4—1761no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4—111no—
538C2×C4—111no—
539C2×C4—111no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—441no—
543C2×C4—882no—
544C2×C4—882no—
545C2×C4—1761no—
546C2×C4D8×D1111yescharacteristic
547C2×C4C2×D4×D1111yescharacteristic
548C8—21no—
549C8—221no—
550C8—221no—
551C8C2×D4×D1111yescharacteristic
552C8#6703711yescharacteristic
553C22—21no—
554C22—21no—
555C22—221no—
556C22—221no—
557C22—221no—
558C22—442no—
559C22—881no—
560C22—881no—
561C22—881no—
562C22—881no—
563C22—881no—
564C22—881no—
565C22—881no—
566C22—881no—
567C22—1764no—
568C22#1062253212yescomplemented
569C22C2×D8×D1111yescharacteristic
570C4—21no—
571C4—42no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—221no—
576C4—221no—
577C4—221no—
578C4—881no—
579C4#1062312111yescharacteristic
580C4#1062330511yescharacteristic
581C2—22no—
582C2—441no—
583C2—882no—
584C2—1761no—
585C2—1761no—
586C2#1308028611yescharacteristic
587C2C2×#1062253211yescharacteristic
588C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2188C2
socleC22×C11C22×D8
hypercenter#2188D11
hypocenterC11#33848
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2188

Complements

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

NH ≅ G/Ntype
1. C2×#10622532C2semidirect
2. C22×#66892C2semidirect
3. #13080357C2semidirect
4. #13080298C2semidirect
5. #13070878C2semidirect
6. #13070715C2semidirect
7. #13070714C2semidirect
8. #13070680C2semidirect
9. #13070674C2semidirect
10. #13070555C2semidirect
11. #13070542C2semidirect
12. #13070530C2semidirect
13. #13070465C2semidirect
14. (C22⋊D11)⋊C16C2semidirect
15. C11×#2188C2semidirect
19. C2×#66972C22semidirect
22. C2×C11×Q32C22semidirect
23. C2×C11×Q32C22semidirect
27. #10622804C22semidirect
28. #10622801C22semidirect
31. Q16×Dic11C22semidirect
37. C2×#66892C22semidirect
45. C2×C16×D11C22semidirect
50. C11×#358C22semidirect
51. C11×#358C22semidirect
53. #10622202C22semidirect
56. (C2×D11)⋊C16C22semidirect
57. Dic11⋊C16C22semidirect
58. C16×Dic11C22semidirect
59. #10622129C22semidirect
60. #10622128C22semidirect
117. #66892D4semidirect
219. #2188D11semidirect
281. C2×Q32C2×D11semidirect
282. C2×Q32C2×D11semidirect
311. #358C2×D11semidirect
312. #358C2×D11semidirect
321. C22×C11#508semidirect
502. C11#33848semidirect
568. C22#10622532semidirect

Maximal subgroups

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

subgroupindex
C2×#106225322
C22×#668922
#130803572
#130802982
#130708782
#130707152
#130707142
#130706802
#130706742
#130705552
#130705422
#130705302
#130704652
(C22⋊D11)⋊C162
C11×#21882
#3384811