Finite Group Databasebeta

← #14907244

Subgroups — #14907244

Order 2816.

668 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#509C211yesmaximal, characteristic
2#13077530C211yesmaximal, characteristic, complemented
3#13077465C211yesmaximal, characteristic, complemented
4#13070517C211yesmaximal, characteristic, complemented
5#13070516C211yesmaximal, characteristic, complemented
6#13070515C211yesmaximal, characteristic, complemented
7#13070514C211yesmaximal, characteristic, complemented
8#13070513C211yesmaximal, characteristic, complemented
9#13070512C211yesmaximal, characteristic, complemented
10#13070511C211yesmaximal, characteristic, complemented
11#13070387C211yesmaximal, characteristic, complemented
12D11×#361C211yesmaximal, characteristic, complemented
13#13070350C211yesmaximal, characteristic, complemented
14#13070219C211yesmaximal, characteristic, complemented
15C11×AGL(1,ℤ/16)C211yesmaximal, characteristic, complemented
16D11×#135C2211yescharacteristic
17C2×D8×D11C2211yescharacteristic
18#10623281—21no—
19#10623076—21no—
20C11×#509C2211yescharacteristic
21C11×#444C2211yescharacteristic, complemented
22C11×#442C2211yescharacteristic, complemented
23#10622810C2211yescharacteristic, complemented
24#10622806C2211yescharacteristic
25#10622765C2211yescharacteristic, complemented
26#10622760C2211yescharacteristic
27#10622757—21no—
28C4×#4323—21no—
29#10622527C412yescomplemented
30D11×SD32C412yescomplemented
31#10622524C412yescomplemented
32D11×D16C412yescomplemented
33#10622521C2211yescharacteristic
34D11×M32C2211yescharacteristic
35D11×M32C2211yescharacteristic
36#10622507C2211yescharacteristic, complemented
37D11×#108C2211yescharacteristic
38#10622482C2211yescharacteristic, complemented
39#10622473C2211yescharacteristic
40#10622437—21no—
41#10622434—21no—
42#10622383—21no—
43#10622369—21no—
44#10622330C2211yescharacteristic, complemented
45#10622324C2211yescharacteristic, complemented
46#10622321C2211yescharacteristic
47C11×#365C2211yescharacteristic, complemented
48C11×#361C2211yescharacteristic, complemented
49C11×#360C2211yescharacteristic, complemented
50C11×#347C2211yescharacteristic, complemented
51#10622204C2211yescharacteristic, complemented
52#10622201C2211yescharacteristic, complemented
53#10622156C2211yescharacteristic, complemented
54#10622154C2211yescharacteristic, complemented
55#10622151C2211yescharacteristic, complemented
56#10622150C2211yescharacteristic, complemented
57#10622150C2211yescharacteristic, complemented
58#10622133C2211yescharacteristic, complemented
59#10622132C2211yescharacteristic, complemented
60#10622126C2211yescharacteristic, complemented
61#10622125C2211yescharacteristic, complemented
62#10622104C2211yescharacteristic, complemented
63#41×D11—21no—
64C2×D4×D11—21no—
65C11×#135C2311yescharacteristic
66C2×C11×D8C2311yescharacteristic
67C11×#131—21no—
68C4×D4×C11—21no—
69#67003—21no—
70#67001—21no—
71D4×Dic11—21no—
72C2×#4323—21no—
73C4×C22⋊D11—41no—
74C2×(C2×D11)⋊C4—41no—
75#66972C2×C411yescharacteristic, complemented
76Q16×D11C2×C411yescharacteristic, complemented
77#66969—21no—
78SD16×D11—21no—
79#66965C2×C411yescharacteristic, complemented
80D8×D11—21no—
81D8×D11—21no—
82D8×D11C2×C412yes—
83D8×D11C2×C412yes—
84D8×D11C2×C411yescharacteristic, complemented
85#66960—21no—
86#66960—41no—
87M16×D11—21no—
88M16×D11—41no—
89#66957C2311yescharacteristic
90C2×D88C2311yescharacteristic
91#66954—21no—
92#66954—41no—
93C2×#4313—41no—
94C2×#4313D411yescharacteristic
95C2×C8×D11C2311yescharacteristic
96#66946—21no—
97#66945—21no—
98(C22⋊D11)⋊C4—41no—
99C22⋊C4×D11—41no—
100C4×D44—21no—
101#66925D411yescharacteristic
102C11×SD32C2×C412yescomplemented
103C11×D16C2×C412yescomplemented
104C11×M32C2311yescharacteristic
105C11×M32C2311yescharacteristic
106C11×#108C2311yescharacteristic
107C11×#106C2311yescharacteristic
108C11×#104—21no—
109C11×#102—21no—
110C11×#97C2311yescharacteristic
111#66901—21no—
112#66896—21no—
113#66892C2×C412yescomplemented
114#66891C2×C412yescomplemented
115#66890C2×C412yescomplemented
116#66890C2×C412yescomplemented
117#66889—21no—
118#66886—21no—
119#66885—21no—
120#66883C2311yescharacteristic
121#66881C2311yescharacteristic
122#66879C2311yescharacteristic
123C8×Dic11D411yescharacteristic
124#66876C2311yescharacteristic
125#66876C2311yescharacteristic
126#66873—21no—
127#66871—21no—
128#66869—21no—
129C4×C11⋊C8D411yescharacteristic
130#66864C2×C412yescomplemented
131D176C2×C412yescomplemented
132#66862—21no—
133#66862C2×C412yescomplemented
134C16×D11—21no—
135C16×D11C2×C412yescomplemented
136#33471—111nomaximal, Sylow
137C23×D11—41no—
138C11×#41—21no—
139C2×D4×C11—21no—
140C22×C4×C11—41no—
141C2×C22⋊D11—41no—
142C22×Dic11—41no—
143#4343—21no—
144Q8×D11—21no—
145#4341—21no—
146#4341—41no—
147D4×D11—22no—
148D4×D11—22no—
149D4×D11—21no—
150D4×D11—41no—
151D4×D11—41no—
152D4×D11—41no—
153#4339—21no—
154#4339—41no—
155C2×D44—21no—
156C2×C4×D11—41no—
157C2×C4×D11—41no—
158C2×C4×D11—41no—
159C2×C4×D11C2×D411yescharacteristic
160C11×Q16C22×C411yescharacteristic
161C11×SD16—21no—
162C11×D8—21no—
163C11×D8C22×C411yescharacteristic
164C11×D8C22×C412yes—
165C11×M16—21no—
166C11×M16—41no—
167C2×C8×C11—41no—
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2411yescharacteristic
170C11×C4⋊C4—21no—
171C11×C22⋊C4—41no—
172C42×C11C2×D411yescharacteristic
173C22⋊Dic11—41no—
174#4326—21no—
175#4325—21no—
176#4324—21no—
177#4323—22no—
178#4323—22no—
179#4323—21no—
180(C2×D11)⋊C4—21no—
181(C2×D11)⋊C4—41no—
182(C2×D11)⋊C4—41no—
183(C2×D11)⋊C4—41no—
184C4⋊Dic11—21no—
185Dic11⋊C4—21no—
186C4×Dic11—41no—
187C4×Dic11C2×D411yescharacteristic
188#4318—21no—
189#4318—41no—
190C2×C11⋊C8—41no—
191C2×C11⋊C8C2×D411yescharacteristic
192C2×C11⋊C8C2×D411yescharacteristic
193Dic44C22×C411yescharacteristic
194D88—21no—
195D88C22×C411yescharacteristic
196D88C22×C412yes—
197#4314—21no—
198#4313—21no—
199#4313—21no—
200#4313—41no—
201#4313—41no—
202#4313—41no—
203C8×D11—41no—
204C8×D11—41no—
205C8×D11—41no—
206C8×D11C22×C411yescharacteristic
207C8×D11C22×C411yescharacteristic
208C8×D11#4111yescharacteristic
209C8×D11#4111yescharacteristic
210C11×C16—21no—
211C11×C16C22×C412yes—
212C11⋊C16—21no—
213C11⋊C16C22×C412yes—
214C2×#509—111no—
215#2957—111no—
216#2948—111no—
217AGL(1,ℤ/16)—111no—
218AGL(1,ℤ/16)—111no—
219AGL(1,ℤ/16)—111no—
220AGL(1,ℤ/16)—111no—
221AGL(1,ℤ/16)—111no—
222AGL(1,ℤ/16)—111no—
223AGL(1,ℤ/16)—111no—
224AGL(1,ℤ/16)D1111yescharacteristic, complemented
225#2155—111no—
226C2×#361—111no—
227#2145—111no—
228#2110—111no—
229C23×C11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11—161no—
235C22×D11—161no—
236C22×D11AGL(1,ℤ/8)11yescharacteristic
237Q8×C11—21no—
238D4×C11—22no—
239D4×C11—21no—
240D4×C11—41no—
241D4×C11—41no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—161no—
246C2×C4×C11C22×D411yescharacteristic
247C22⋊D11—41no—
248C22⋊D11—41no—
249C22⋊D11—41no—
250C22⋊D11—42no—
251C22⋊D11—42no—
252C2×Dic11—21no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—161no—
256C2×Dic11AGL(1,ℤ/8)11yescharacteristic
257D44—21no—
258D44—22no—
259D44—41no—
260D44—41no—
261C4×D11—41no—
262C4×D11—41no—
263C4×D11—41no—
264C4×D11—161no—
265C4×D11—161no—
266C4×D11C4×D411yescharacteristic
267C4×D11C4×D411yescharacteristic
268C4×D11AGL(1,ℤ/8)11yescharacteristic
269C4×D11AGL(1,ℤ/8)11yescharacteristic
270Dic22—21no—
271Dic22—41no—
272C8×C11—21no—
273C8×C11—41no—
274C8×C11C23×C411yescharacteristic
275C8×C11C2×#4111yescharacteristic
276C11⋊C8—21no—
277C11⋊C8—41no—
278C11⋊C8C4×D411yescharacteristic
279C11⋊C8C4×D411yescharacteristic
280C2×#135—111no—
281C22×D8—111no—
282#568—221no—
283#518—221no—
284#509—111no—
285#509—111no—
286#509—112no—
287#509—112no—
288#509—111no—
289#509C2×D1111yescharacteristic
290C2×SD32—112no—
291C2×D16—112no—
292C2×M32—111no—
293C2×M32—111no—
294#444—111no—
295#444—111no—
296#444—111no—
297#444C2×D1111yescharacteristic, complemented
298#443—221no—
299#443—221no—
300#442—111no—
301#442—111no—
302#442—111no—
303#442C2×D1111yescharacteristic, complemented
304C4×D8—221no—
305C4×D8—221no—
306C2×#108—111no—
307#427—111no—
308#421—221no—
309#418—221no—
310#405—111no—
311#365—111no—
312#365—111no—
313#365—111no—
314#365C2×D1111yescharacteristic, complemented
315#361—111no—
316#361—111no—
317#361—111no—
318#361C2×D1111yescharacteristic, complemented
319#360—111no—
320#360—111no—
321#360—111no—
322#360C2×D1111yescharacteristic, complemented
323#347—111no—
324#347—111no—
325#347—111no—
326#347C2×D1111yescharacteristic, complemented
327C22×C11—41no—
328C22×C11—42no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
332C2×D11—41no—
333C2×D11—42no—
334C2×D11—41no—
335C2×D11—81no—
336C2×D11—81no—
337C2×D11—161no—
338C2×D11—162no—
339C2×D11—162no—
340C2×D11#44211yescharacteristic
341C2×D11#44211yescharacteristic
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—81no—
345C4×C11C2×C4×D411yescharacteristic
346C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
347Dic11—41no—
348Dic11—41no—
349Dic11—81no—
350Dic11#44211yescharacteristic
351Dic11#44211yescharacteristic
352C2×#41—221no—
353C22×D4—221no—
354#135—111no—
355#135—111no—
356#135—111no—
357#135—221no—
358#135—221no—
359#135C22×D1111yescharacteristic
360C2×Q16—111no—
361C2×SD16—221no—
362C2×D8—112no—
363C2×D8—112no—
364C2×D8—111no—
365C2×D8—111no—
366C2×D8—221no—
367C2×D8—221no—
368C2×D8—221no—
369C2×D8C22×D1111yescharacteristic
370#131—21no—
371#131—221no—
372#131—221no—
373#131—221no—
374#131—441no—
375#131—441no—
376C2×M16—111no—
377C2×M16—221no—
378C2×M16—441no—
379C2×M16—441no—
380C22×C8—111no—
381C4×D4—21no—
382C4×D4—221no—
383C4×D4—221no—
384C4×D4—221no—
385C4×D4—441no—
386C4×D4—441no—
387#117—111no—
388#117—221no—
389C2×C22⋊C4—441no—
390C2×C22⋊C4—441no—
391SD32—112no—
392SD32—112no—
393SD32—112no—
394SD32C4×D1112yescomplemented
395D16—112no—
396D16—112no—
397D16—112no—
398D16C4×D1112yescomplemented
399M32—111no—
400M32—112no—
401M32—111no—
402M32—221no—
403M32C22×D1111yescharacteristic
404M32C22×D1111yescharacteristic
405C2×C16—112no—
406C2×C16—221no—
407#108—111no—
408#108—221no—
409#108C22×D1111yescharacteristic
410#107—221no—
411#106—111no—
412#106C22×D1111yescharacteristic
413#104—21no—
414#104—221no—
415#104—221no—
416#104—221no—
417#102—21no—
418#102—221no—
419#102—221no—
420#102—221no—
421#97—111no—
422#97C22×D1111yescharacteristic
423C4×C8—111no—
424C4×C8—111no—
425C2×C11—21no—
426C2×C11—82no—
427C2×C11—81no—
428C2×C11C2×#44211yescharacteristic
429D11—21no—
430D11—21no—
431D11—82no—
432D11—81no—
433C24—441no—
434#41—21no—
435#41—221no—
436#41—221no—
437#41—221no—
438#41—441no—
439#41—441no—
440C2×Q8—221no—
441C2×D4—21no—
442C2×D4—222no—
443C2×D4—222no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—441no—
447C2×D4—441no—
448C2×D4—441no—
449C2×D4—441no—
450C22×C4—41no—
451C22×C4—111no—
452C22×C4—441no—
453C22×C4—441no—
454C22×C4—441no—
455C22×C4—441no—
456Q16—111no—
457Q16—221no—
458Q16C2×C4×D1111yescharacteristic
459SD16—21no—
460SD16—221no—
461SD16—221no—
462SD16—221no—
463D8—21no—
464D8—111no—
465D8—112no—
466D8—222no—
467D8—222no—
468D8—221no—
469D8—221no—
470D8C2×C4×D1111yescharacteristic
471D8C2×C4×D1112yes—
472M16—21no—
473M16—41no—
474M16—221no—
475M16—221no—
476M16—221no—
477M16—441no—
478M16—441no—
479M16—441no—
480M16—441no—
481C2×C8—41no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—111no—
485C2×C8—111no—
486C2×C8—111no—
487C2×C8—111no—
488C2×C8—441no—
489C2×C8—441no—
490C2×C8—441no—
491C2×C8—441no—
492C2×C8D4×D1111yescharacteristic
493C2×C8C23×D1111yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C22⋊C4—41no—
498C22⋊C4—221no—
499C22⋊C4—441no—
500C22⋊C4—441no—
501C22⋊C4—441no—
502C22⋊C4—441no—
503C42—111no—
504C42—441no—
505C42D4×D1111yescharacteristic
506C16—21no—
507C16—112no—
508C16—221no—
509C16C2×C4×D1112yes—
510C11#3347111yescharacteristic, complemented, Sylow
511C23—41no—
512C23—111no—
513C23—441no—
514C23—442no—
515C23—442no—
516C23—441no—
517C23—1761no—
518C23—1761no—
519Q8—21no—
520Q8—221no—
521Q8—441no—
522D4—22no—
523D4—21no—
524D4—41no—
525D4—41no—
526D4—222no—
527D4—221no—
528D4—441no—
529D4—442no—
530D4—442no—
531D4—441no—
532D4—441no—
533D4—441no—
534D4—441no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—111no—
539C2×C4—111no—
540C2×C4—111no—
541C2×C4—111no—
542C2×C4—111no—
543C2×C4—161no—
544C2×C4—221no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—1761no—
551C2×C4—1761no—
552C2×C4—1761no—
553C2×C4C2×D4×D1111yescharacteristic
554C8—21no—
555C8—41no—
556C8—111no—
557C8—111no—
558C8—221no—
559C8—441no—
560C8C22×C4×D1111yescharacteristic
561C8#41×D1111yescharacteristic
562C22—41no—
563C22—42no—
564C22—81no—
565C22—81no—
566C22—111no—
567C22—111no—
568C22—441no—
569C22—441no—
570C22—442no—
571C22—881no—
572C22—881no—
573C22—1762no—
574C22—1762no—
575C22—1761no—
576C22D11×AGL(1,ℤ/8)11yescharacteristic
577C4—41no—
578C4—41no—
579C4—81no—
580C4—111no—
581C4—111no—
582C4—441no—
583C4—441no—
584C4—881no—
585C4C4×D4×D1111yescharacteristic
586C4D11×AGL(1,ℤ/8)11yescharacteristic
587C2—21no—
588C2—82no—
589C2—81no—
590C2—221no—
591C2—221no—
592C2—882no—
593C2—881no—
594C2D11×#44211yescharacteristic
subgroupG/H
centerC2D11×#442
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×AGL(1,ℤ/16)C2
socleC2×C11C2×#442
prime radicalD11×#509C2
cosocleC2×C8×C11C24
hypercenterAGL(1,ℤ/16)D11
hypocenterC11#33471
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ AGL(1,ℤ/16)

Complements

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

NH ≅ G/Ntype
2. #13077530C2semidirect
3. #13077465C2semidirect
4. #13070517C2semidirect
5. #13070516C2semidirect
6. #13070515C2semidirect
7. #13070514C2semidirect
8. #13070513C2semidirect
9. #13070512C2semidirect
10. #13070511C2semidirect
11. #13070387C2semidirect
12. D11×#361C2semidirect
13. #13070350C2semidirect
14. #13070219C2semidirect
15. C11×AGL(1,ℤ/16)C2semidirect
21. C11×#444C22semidirect
22. C11×#442C22semidirect
23. #10622810C22semidirect
25. #10622765C22semidirect
29. #10622527C4semidirect
30. D11×SD32C4semidirect
31. #10622524C4semidirect
32. D11×D16C4semidirect
36. #10622507C22semidirect
38. #10622482C22semidirect
44. #10622330C22semidirect
45. #10622324C22semidirect
47. C11×#365C22semidirect
48. C11×#361C22semidirect
49. C11×#360C22semidirect
50. C11×#347C22semidirect
51. #10622204C22semidirect
52. #10622201C22semidirect
53. #10622156C22semidirect
54. #10622154C22semidirect
55. #10622151C22semidirect
56. #10622150C22semidirect
57. #10622150C22semidirect
58. #10622133C22semidirect
59. #10622132C22semidirect
60. #10622126C22semidirect
61. #10622125C22semidirect
62. #10622104C22semidirect
75. #66972C2×C4semidirect
76. Q16×D11C2×C4semidirect
79. #66965C2×C4semidirect
84. D8×D11C2×C4semidirect
102. C11×SD32C2×C4semidirect
103. C11×D16C2×C4semidirect
113. #66892C2×C4semidirect
114. #66891C2×C4semidirect
115. #66890C2×C4semidirect
116. #66890C2×C4semidirect
130. #66864C2×C4semidirect
131. D176C2×C4semidirect
133. #66862C2×C4semidirect
135. C16×D11C2×C4semidirect
224. AGL(1,ℤ/16)D11semidirect
297. #444C2×D11semidirect
303. #442C2×D11semidirect
314. #365C2×D11semidirect
318. #361C2×D11semidirect
322. #360C2×D11semidirect
326. #347C2×D11semidirect
394. SD32C4×D11semidirect
398. D16C4×D11semidirect
510. C11#33471semidirect

Maximal subgroups

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

subgroupindex
D11×#5092
#130775302
#130774652
#130705172
#130705162
#130705152
#130705142
#130705132
#130705122
#130705112
#130703872
D11×#3612
#130703502
#130702192
C11×AGL(1,ℤ/16)2
#3347111