Finite Group Databasebeta

← #14909003

Subgroups — #14909003

Order 2816.

564 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079351C211yesmaximal, characteristic, complemented
2#13077524C211yesmaximal, characteristic, complemented
3#13070832C211yesmaximal, characteristic, complemented
4#13070829C211yesmaximal, characteristic, complemented
5#13070786C211yesmaximal, characteristic, complemented
6#13070785C211yesmaximal, characteristic, complemented
7#13070691C211yesmaximal, characteristic, complemented
8#13070690C211yesmaximal, characteristic, complemented
9#13070563C211yesmaximal, characteristic, complemented
10#13070560C211yesmaximal, characteristic, complemented
11#13070516C211yesmaximal, characteristic, complemented
12#13070514C211yesmaximal, characteristic, complemented
13#13070512C211yesmaximal, characteristic, complemented
14#13070426C211yesmaximal, characteristic, complemented
15C11×AGL(1,ℤ/16)C211yesmaximal, characteristic, complemented
16#10623299C2211yescharacteristic
17#10623281—21no—
18#10623079—21no—
19C11×#509C2211yescharacteristic
20C11×#444C2211yescharacteristic
21C11×#442C2211yescharacteristic, complemented
22#10622809C2211yescharacteristic
23#10622806C2211yescharacteristic
24#10622772C2211yescharacteristic
25#10622764C2211yescharacteristic, complemented
26#10622760C2211yescharacteristic
27#10622757—21no—
28#10622627—21no—
29#10622521C2211yescharacteristic
30#10622508C2211yescharacteristic
31#10622506C2211yescharacteristic
32#10622478C2211yescharacteristic
33#10622468C2211yescharacteristic, complemented
34#10622436—21no—
35D11×#104—21no—
36#10622395—21no—
37#10622373—21no—
38#10622330C2211yescharacteristic
39#10622324C2211yescharacteristic, complemented
40#10622320C2211yescharacteristic
41C11×#365C2211yescharacteristic, complemented
42C11×#361C2211yescharacteristic, complemented
43C11×#360C2211yescharacteristic
44C11×#347C2211yescharacteristic, complemented
45#10622204C2211yescharacteristic
46#10622201C2211yescharacteristic, complemented
47#10622156C2211yescharacteristic
48#10622154C2211yescharacteristic, complemented
49#10622152C2211yescharacteristic
50#10622152C2211yescharacteristic
51#10622151C2211yescharacteristic, complemented
52#10622149C2211yescharacteristic, complemented
53#10622149C2211yescharacteristic, complemented
54#10622133C2211yescharacteristic, complemented
55#10622132C2211yescharacteristic, complemented
56#10622126C2211yescharacteristic
57#10622125C2211yescharacteristic, complemented
58#10622104C2211yescharacteristic, complemented
59#41×D11—21no—
60C2×#4339—41no—
61C11×#135C2311yescharacteristic
62C2×C11×D8C2311yescharacteristic
63C11×#131—21no—
64C4×D4×C11—21no—
65#67003—21no—
66#67001—21no—
67#66993—21no—
68#66991—21no—
69C2×#4323—21no—
70C4×C22⋊D11—41no—
71#66971—21no—
72#66968—21no—
73#66967—21no—
74#66964—21no—
75#66960—21no—
76#66960—41no—
77M16×D11—21no—
78M16×D11—41no—
79#66957C2311yescharacteristic
80C2×D88C2311yescharacteristic
81#66954—21no—
82#66954—41no—
83C2×#4313—41no—
84C2×#4313D411yescharacteristic
85C2×#4313C2311yescharacteristic
86#66948—21no—
87#66941—21no—
88#66938—41no—
89#66937—41no—
90C4×D44—21no—
91C42×D11D411yescharacteristic
92C11×SD32—21no—
93C11×D16—21no—
94C11×M32C2311yescharacteristic
95C11×M32C2311yescharacteristic
96C11×#108C2311yescharacteristic
97C11×#106C2311yescharacteristic
98C11×#104—21no—
99C11×#102—21no—
100C11×#97C2311yescharacteristic
101#66901—21no—
102#66896—21no—
103#66892—21no—
104#66891—21no—
105#66890—21no—
106#66890—21no—
107#66889—21no—
108#66886—21no—
109#66885—21no—
110#66883C2311yescharacteristic
111#66881C2311yescharacteristic
112C8×Dic11D411yescharacteristic
113C8×Dic11C2311yescharacteristic
114#66876C2311yescharacteristic
115#66876C2311yescharacteristic
116#66873—21no—
117#66872—21no—
118#66869—21no—
119#66867D411yescharacteristic
120#66864—21no—
121D176—21no—
122#33688—111nomaximal, Sylow
123C11×#41—21no—
124C2×D4×C11—21no—
125C22×C4×C11—41no—
126C2×C22⋊D11—41no—
127C2×C22⋊D11—41no—
128C2×C22⋊D11—41no—
129#4343—21no—
130Q8×D11—21no—
131#4341—21no—
132#4341—41no—
133D4×D11—21no—
134D4×D11—41no—
135#4339—21no—
136#4339—41no—
137#4339—84no—
138C2×D44—21no—
139C2×D44—41no—
140C2×C4×D11—21no—
141C2×C4×D11—41no—
142C2×C4×D11—41no—
143C2×C4×D11C2×D411yescharacteristic
144C2×Dic22—41no—
145C11×Q16#4111yescharacteristic, complemented
146C11×SD16—21no—
147C11×D8—21no—
148C11×D8—21no—
149C11×D8#4111yescharacteristic, complemented
150C11×M16—21no—
151C11×M16—41no—
152C2×C8×C11—41no—
153C2×C8×C11C2×D411yescharacteristic
154C2×C8×C11C2411yescharacteristic
155C11×C4⋊C4—21no—
156C11×C22⋊C4—41no—
157C42×C11C2×D411yescharacteristic
158C22⋊Dic11—41no—
159#4326—21no—
160#4325—21no—
161#4324—21no—
162#4323—21no—
163#4323—41no—
164#4323—41no—
165(C2×D11)⋊C4—41no—
166(C2×D11)⋊C4—41no—
167C4⋊Dic11—21no—
168Dic11⋊C4—41no—
169C4×Dic11—21no—
170C4×Dic11C2×D411yescharacteristic
171#4318—21no—
172#4318—41no—
173C2×C11⋊C8—41no—
174C2×C11⋊C8C2×D411yescharacteristic
175C2×C11⋊C8C2×D411yescharacteristic
176Dic44#4111yescharacteristic, complemented
177D88—21no—
178D88—21no—
179D88#4111yescharacteristic, complemented
180#4314—21no—
181#4313—21no—
182#4313—21no—
183#4313—21no—
184#4313—21no—
185#4313—41no—
186#4313—41no—
187#4313—41no—
188C8×D11—41no—
189C8×D11—41no—
190C8×D11—41no—
191C11×C16—21no—
192C11×C16—21no—
193C11⋊C16—21no—
194C11⋊C16—21no—
195#3184—111no—
196#2956—111no—
197#2238—111no—
198#2238—111no—
199#2230—111no—
200#2230—111no—
201#2213—111no—
202#2213—111no—
203#2190—111no—
204#2190—111no—
205AGL(1,ℤ/16)—111no—
206AGL(1,ℤ/16)—111no—
207AGL(1,ℤ/16)—111no—
208AGL(1,ℤ/16)D1111yescharacteristic, complemented
209#2165—111no—
210C23×C11—41no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11AGL(1,ℤ/8)11yescharacteristic
214Q8×C11—21no—
215D4×C11—21no—
216D4×C11—41no—
217D4×C11—41no—
218D4×C11—41no—
219C2×C4×C11—21no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—82no—
223C2×C4×C11C22×D411yescharacteristic
224C22⋊D11—41no—
225C22⋊D11—41no—
226C22⋊D11—41no—
227C22⋊D11—82no—
228C22⋊D11—82no—
229C22⋊D11—82no—
230C2×Dic11—21no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11AGL(1,ℤ/8)11yescharacteristic
234D44—21no—
235D44—41no—
236D44—41no—
237D44—41no—
238D44—82no—
239C4×D11—21no—
240C4×D11—21no—
241C4×D11—42no—
242C4×D11—41no—
243C4×D11—41no—
244C4×D11—41no—
245C4×D11—82no—
246Dic22—21no—
247Dic22—41no—
248Dic22—82no—
249C8×C11—21no—
250C8×C11—41no—
251C8×C11C2×#4111yescharacteristic
252C8×C11C2×#4111yescharacteristic
253C11⋊C8—21no—
254C11⋊C8—41no—
255C11⋊C8AGL(1,ℤ/8)11yescharacteristic
256C11⋊C8AGL(1,ℤ/8)11yescharacteristic
257#575—111no—
258#568—221no—
259#532—221no—
260#509—111no—
261#509—111no—
262#509—111no—
263#509C2×D1111yescharacteristic
264#498—111no—
265#493—111no—
266#486—221no—
267#469—111no—
268#469—111no—
269#469—221no—
270#444—111no—
271#444—221no—
272#444C2×D1111yescharacteristic
273#443—111no—
274#443—111no—
275#443—221no—
276#442—111no—
277#442—221no—
278#442C2×D1111yescharacteristic, complemented
279#430—111no—
280C2×#104—221no—
281C4×M16—111no—
282#365—111no—
283#365—111no—
284#365—111no—
285#365C2×D1111yescharacteristic, complemented
286#364—111no—
287#364—111no—
288#361—111no—
289#361—111no—
290#361—111no—
291#361C2×D1111yescharacteristic, complemented
292#360—111no—
293#360—111no—
294#360—111no—
295#360C2×D1111yescharacteristic
296#349—111no—
297#349—111no—
298#347—111no—
299#347C2×D1111yescharacteristic, complemented
300C22×C11—41no—
301C22×C11—81no—
302C22×C11—81no—
303C22×C11—81no—
304C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
305C2×D11—21no—
306C2×D11—41no—
307C2×D11—41no—
308C2×D11—81no—
309C2×D11—81no—
310C2×D11—81no—
311C2×D11—161no—
312C4×C11—41no—
313C4×C11—41no—
314C4×C11—81no—
315C4×C11#52511yescharacteristic
316C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
317Dic11—22no—
318Dic11—21no—
319Dic11—41no—
320Dic11—81no—
321C2×#41—221no—
322C2×#41—441no—
323#137—221no—
324#137—221no—
325AGL(1,ℤ/8)—221no—
326AGL(1,ℤ/8)—221no—
327#135—111no—
328#135—221no—
329#135C22×D1111yescharacteristic
330C2×D8—111no—
331C2×D8—221no—
332C2×D8C22×D1111yescharacteristic
333#131—21no—
334#131—221no—
335#131—221no—
336#131—221no—
337#131—441no—
338#131—441no—
339C2×M16—111no—
340C2×M16—111no—
341C2×M16—221no—
342C2×M16—441no—
343C2×M16—441no—
344C4⋊Q8—221no—
345#127—221no—
346#124—441no—
347#121—221no—
348#121—221no—
349#121—441no—
350C4×D4—21no—
351C4×D4—221no—
352C4×D4—441no—
353C2×C42—111no—
354SD32—21no—
355SD32—221no—
356SD32—221no—
357SD32—221no—
358D16—21no—
359D16—221no—
360D16—221no—
361D16—221no—
362M32—111no—
363M32—111no—
364M32C22×D1111yescharacteristic
365M32C22×D1111yescharacteristic
366#108—111no—
367#108—221no—
368#108C22×D1111yescharacteristic
369#106—111no—
370#106—221no—
371#106C22×D1111yescharacteristic
372#104—21no—
373#104—221no—
374#104—221no—
375#104—221no—
376#102—21no—
377#102—221no—
378#102—221no—
379#102—221no—
380#97—111no—
381#97C22×D1111yescharacteristic
382C4×C8—111no—
383C4×C8—111no—
384C2×C11—21no—
385C2×C11—81no—
386C2×C11—161no—
387C2×C11#310911yescharacteristic
388D11—41no—
389D11—81no—
390D11—161no—
391#41—21no—
392#41—221no—
393#41—221no—
394#41—221no—
395#41—441no—
396#41—441no—
397#41—884no—
398C2×Q8—221no—
399C2×Q8—441no—
400C2×D4—21no—
401C2×D4—221no—
402C2×D4—221no—
403C2×D4—441no—
404C2×D4—441no—
405C2×D4—441no—
406C2×D4—441no—
407C2×D4—441no—
408C22×C4—41no—
409C22×C4—111no—
410C22×C4—221no—
411C22×C4—441no—
412C22×C4—441no—
413Q16—111no—
414Q16—221no—
415Q16#433911yescharacteristic, complemented
416SD16—21no—
417SD16—221no—
418SD16—221no—
419SD16—221no—
420D8—21no—
421D8—21no—
422D8—111no—
423D8—221no—
424D8—221no—
425D8—221no—
426D8—441no—
427D8—441no—
428D8#433911yescharacteristic, complemented
429M16—21no—
430M16—41no—
431M16—221no—
432M16—221no—
433M16—221no—
434M16—221no—
435M16—221no—
436M16—441no—
437M16—441no—
438M16—441no—
439M16—441no—
440C2×C8—41no—
441C2×C8—111no—
442C2×C8—111no—
443C2×C8—441no—
444C2×C8—441no—
445C2×C8—441no—
446C2×C8—441no—
447C2×C8D4×D1111yescharacteristic
448C2×C8C23×D1111yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—221no—
451C4⋊C4—441no—
452C22⋊C4—41no—
453C22⋊C4—441no—
454C22⋊C4—441no—
455C22⋊C4—441no—
456C42—111no—
457C42—221no—
458C42D4×D1111yescharacteristic
459C16—21no—
460C16—21no—
461C16—221no—
462C16—221no—
463C11#3368811yescharacteristic, complemented, Sylow
464C23—41no—
465C23—111no—
466C23—441no—
467C23—441no—
468Q8—21no—
469Q8—221no—
470Q8—441no—
471Q8—882no—
472D4—21no—
473D4—41no—
474D4—41no—
475D4—41no—
476D4—221no—
477D4—441no—
478D4—441no—
479D4—441no—
480D4—441no—
481D4—441no—
482D4—441no—
483D4—882no—
484D4—882no—
485D4—882no—
486D4—882no—
487C2×C4—21no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—82no—
491C2×C4—111no—
492C2×C4—221no—
493C2×C4—221no—
494C2×C4—221no—
495C2×C4—442no—
496C2×C4—441no—
497C2×C4—441no—
498C2×C4—441no—
499C2×C4—441no—
500C2×C4—441no—
501C2×C4—882no—
502C2×C4C2×D4×D1111yescharacteristic
503C8—21no—
504C8—41no—
505C8—111no—
506C8—111no—
507C8—221no—
508C8—441no—
509C8C2×#433911yescharacteristic
510C8#41×D1111yescharacteristic
511C22—41no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22—221no—
516C22—441no—
517C22—441no—
518C22—881no—
519C22—881no—
520C22—881no—
521C22—1761no—
522C22D11×AGL(1,ℤ/8)11yescharacteristic
523C4—41no—
524C4—41no—
525C4—81no—
526C4—222no—
527C4—221no—
528C4—441no—
529C4—881no—
530C4#1062307811yescharacteristic
531C4D11×AGL(1,ℤ/8)11yescharacteristic
532C2—21no—
533C2—81no—
534C2—161no—
535C2—441no—
536C2—881no—
537C2—1761no—
538C2#1307870511yescharacteristic
subgroupG/H
centerC2#13078705
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×AGL(1,ℤ/16)C2
socleC2×C11#3109
hypercenterAGL(1,ℤ/16)D11
hypocenterC11#33688
LCSG ▷ C2×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
1. #13079351C2semidirect
2. #13077524C2semidirect
3. #13070832C2semidirect
4. #13070829C2semidirect
5. #13070786C2semidirect
6. #13070785C2semidirect
7. #13070691C2semidirect
8. #13070690C2semidirect
9. #13070563C2semidirect
10. #13070560C2semidirect
11. #13070516C2semidirect
12. #13070514C2semidirect
13. #13070512C2semidirect
14. #13070426C2semidirect
15. C11×AGL(1,ℤ/16)C2semidirect
21. C11×#442C22semidirect
25. #10622764C22semidirect
33. #10622468C22semidirect
39. #10622324C22semidirect
41. C11×#365C22semidirect
42. C11×#361C22semidirect
44. C11×#347C22semidirect
46. #10622201C22semidirect
48. #10622154C22semidirect
51. #10622151C22semidirect
52. #10622149C22semidirect
53. #10622149C22semidirect
54. #10622133C22semidirect
55. #10622132C22semidirect
57. #10622125C22semidirect
58. #10622104C22semidirect
145. C11×Q16#41semidirect
149. C11×D8#41semidirect
176. Dic44#41semidirect
179. D88#41semidirect
208. AGL(1,ℤ/16)D11semidirect
278. #442C2×D11semidirect
285. #365C2×D11semidirect
291. #361C2×D11semidirect
299. #347C2×D11semidirect
415. Q16#4339semidirect
428. D8#4339semidirect
463. C11#33688semidirect

Maximal subgroups

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

subgroupindex
#130793512
#130775242
#130708322
#130708292
#130707862
#130707852
#130706912
#130706902
#130705632
#130705602
#130705162
#130705142
#130705122
#130704262
C11×AGL(1,ℤ/16)2
#3368811