Finite Group Databasebeta

← D11×#2213 #14908149

Subgroups — D11×#2213 #14908149

Order 2816.

790 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#509C212yesmaximal, complemented
2D11×#493C211yesmaximal, characteristic, complemented
3D11×#443C211yesmaximal, characteristic, complemented
4#13070693C211yesmaximal, characteristic, complemented
5#13070692C211yesmaximal, characteristic, complemented
6#13070691C212yesmaximal, complemented
7#13070690C212yesmaximal, complemented
8#13070689C211yesmaximal, characteristic, complemented
9D11×#364C211yesmaximal, characteristic, complemented
10D11×#361C212yesmaximal, complemented
11C11×#2213C211yesmaximal, characteristic, complemented
12D11×#135C2211yescharacteristic
13C2×D8×D11—21no—
14C2×D8×D11C2212yes—
15D11×#131—21no—
16D11×#127—21no—
17C11×#509C2212yescomplemented
18C11×#493C2211yescharacteristic, complemented
19C11×#443C2211yescharacteristic, complemented
20#10622809C2211yescharacteristic, complemented
21#10622806C2212yescomplemented
22#10622764—21no—
23#10622764C2212yescomplemented
24#10622760C2212yescomplemented
25#10622757—21no—
26#10622686—21no—
27#10622527—22no—
28D11×SD32—22no—
29#10622524—22no—
30D11×D16—22no—
31#10622521C2212yescomplemented
32D11×M32C2212yes—
33#10622508C2211yescharacteristic, complemented
34D11×#108C2211yescharacteristic
35#10622437—21no—
36D11×#104—21no—
37#10622313C2211yescharacteristic, complemented
38#10622308C2211yescharacteristic, complemented
39C4×C8×D11C2211yescharacteristic
40C11×#364C2211yescharacteristic, complemented
41C11×#361C2212yescomplemented
42#10622201C2212yescomplemented
43#10622154C2212yescomplemented
44#10622149C2212yescomplemented
45#10622133C2212yescomplemented
46#10622101C2211yescharacteristic, complemented
47#41×D11—21no—
48C2×D4×D11—22no—
49C2×D4×D11—42no—
50C11×#135C2311yescharacteristic
51C2×C11×D8—21no—
52C2×C11×D8C2312yes—
53C11×#131—21no—
54C11×#127—21no—
55#67003—21no—
56#67001—21no—
57#66993—22no—
58#66993—42no—
59C2×#4323—22no—
60C2×#4323—22no—
61#66972D411yescharacteristic, complemented
62Q16×D11D411yescharacteristic, complemented
63#66969—21no—
64SD16×D11—21no—
65#66965D411yescharacteristic, complemented
66D8×D11—22no—
67D8×D11—22no—
68D8×D11—22no—
69D8×D11—22no—
70D8×D11—41no—
71D8×D11—41no—
72D8×D11—41no—
73D8×D11—41no—
74D8×D11D411yescharacteristic, complemented
75#66960—21no—
76#66960—41no—
77M16×D11—21no—
78M16×D11—41no—
79#66957C2311yescharacteristic
80C2×D88—21no—
81C2×D88C2312yes—
82#66954—21no—
83#66954—41no—
84C2×C8×D11—41no—
85C2×C8×D11D411yescharacteristic
86C2×C8×D11C2311yescharacteristic
87#66927—21no—
88C42×D11D411yescharacteristic
89C11×SD32—22no—
90C11×D16—22no—
91C11×M32C2312yes—
92C11×#108C2311yescharacteristic
93C11×#104—21no—
94C4×C8×C11C2311yescharacteristic
95#66901—21no—
96#66892—22no—
97#66891—22no—
98#66890—22no—
99#66890—22no—
100#66889—21no—
101#66886—21no—
102#66883C2311yescharacteristic
103C8×Dic11D411yescharacteristic
104C8×Dic11C2311yescharacteristic
105#66876C2312yes—
106#66869—21no—
107C4×C11⋊C8D411yescharacteristic
108#66864—22no—
109D176—22no—
110#66862—22no—
111C16×D11—22no—
112C2×#2213—111nomaximal, Sylow
113C23×D11—42no—
114C11×#41—21no—
115C2×D4×C11—22no—
116C2×D4×C11—42no—
117C2×C22⋊D11—44no—
118C2×C22⋊D11—42no—
119#4343—21no—
120Q8×D11—21no—
121#4341—21no—
122#4341—41no—
123D4×D11—21no—
124D4×D11—41no—
125D4×D11—42no—
126D4×D11—42no—
127D4×D11—42no—
128D4×D11—42no—
129D4×D11—88no—
130#4339—21no—
131#4339—41no—
132C2×D44—22no—
133C2×D44—42no—
134C2×C4×D11—21no—
135C2×C4×D11—41no—
136C2×C4×D11C2×D411yescharacteristic
137C11×Q16C2×D411yescharacteristic, complemented
138C11×SD16—21no—
139C11×D8—22no—
140C11×D8—22no—
141C11×D8—41no—
142C11×D8—41no—
143C11×D8C2×D411yescharacteristic, complemented
144C11×M16—21no—
145C11×M16—41no—
146C2×C8×C11—41no—
147C2×C8×C11C2×D411yescharacteristic
148C2×C8×C11C2411yescharacteristic
149C42×C11C2×D411yescharacteristic
150#4326—21no—
151#4325—21no—
152#4324—21no—
153#4323—21no—
154#4323—42no—
155#4323—42no—
156#4323—42no—
157#4323—42no—
158C4×Dic11—21no—
159C4×Dic11C2×D411yescharacteristic
160#4318—21no—
161#4318—41no—
162C2×C11⋊C8—41no—
163C2×C11⋊C8C2×D411yescharacteristic
164C2×C11⋊C8C2×D411yescharacteristic
165Dic44C2×D411yescharacteristic, complemented
166D88—22no—
167D88—22no—
168D88—41no—
169D88—41no—
170D88C2×D411yescharacteristic, complemented
171#4314—21no—
172#4313—41no—
173#4313—41no—
174#4313—41no—
175C8×D11—41no—
176C8×D11—41no—
177C8×D11—41no—
178C8×D11D811yescharacteristic
179C8×D11D811yescharacteristic
180C8×D11D811yescharacteristic
181C8×D11D811yescharacteristic
182C8×D11C2×D411yescharacteristic
183C8×D11C2×D411yescharacteristic
184C8×D11#4111yescharacteristic
185C8×D11#4111yescharacteristic
186C11×C16—22no—
187C11⋊C16—22no—
188C2×#509—112no—
189C2×#493—111no—
190C2×#443—111no—
191#2213—112no—
192#2213—111no—
193#2213—111no—
194#2213—111no—
195#2213—112no—
196#2213D1111yescharacteristic, direct product factor
197C2×#364—111no—
198C2×#361—112no—
199C23×C11—42no—
200C22×D11—41no—
201C22×D11—42no—
202C22×D11—88no—
203C22×D11—82no—
204C22×D11—82no—
205C22×D11AGL(1,ℤ/8)11yescharacteristic
206Q8×C11—21no—
207D4×C11—21no—
208D4×C11—41no—
209D4×C11—42no—
210D4×C11—42no—
211D4×C11—84no—
212C2×C4×C11—21no—
213C2×C4×C11—41no—
214C2×C4×C11C22×D411yescharacteristic
215C22⋊D11—41no—
216C22⋊D11—41no—
217C22⋊D11—41no—
218C22⋊D11—88no—
219C22⋊D11—82no—
220C22⋊D11—82no—
221C2×Dic11—21no—
222C2×Dic11—41no—
223C2×Dic11AGL(1,ℤ/8)11yescharacteristic
224D44—21no—
225D44—41no—
226D44—42no—
227D44—42no—
228D44—84no—
229C4×D11—24no—
230C4×D11—41no—
231C4×D11—41no—
232C4×D11—41no—
233C4×D11#12111yescharacteristic
234C4×D11#12111yescharacteristic
235C4×D11C2×D811yescharacteristic
236C4×D11C2×D811yescharacteristic
237Dic22—21no—
238Dic22—41no—
239C8×C11—41no—
240C8×C11C2×D811yescharacteristic
241C8×C11C2×D811yescharacteristic
242C8×C11C22×D411yescharacteristic
243C8×C11C2×#4111yescharacteristic
244C11⋊C8—41no—
245C11⋊C8#12111yescharacteristic
246C11⋊C8#12111yescharacteristic
247C11⋊C8C2×D811yescharacteristic
248C11⋊C8C2×D811yescharacteristic
249C2×#135—111no—
250C22×D8—112no—
251C22×D8—221no—
252C2×#131—221no—
253C2×#127—221no—
254#509—112no—
255#509—112no—
256#509—112no—
257#509—222no—
258#509—222no—
259#509C2×D1112yescomplemented
260C2×SD32—222no—
261C2×D16—222no—
262C2×M32—112no—
263#493—112no—
264#493—111no—
265#493—221no—
266#493—221no—
267#493C2×D1111yescharacteristic, complemented
268#443—111no—
269#443—111no—
270#443—111no—
271#443—221no—
272#443—221no—
273#443C2×D1111yescharacteristic, complemented
274C2×#108—111no—
275C2×#104—221no—
276C2×C4×C8—111no—
277#364—112no—
278#364—111no—
279#364C2×D1111yescharacteristic, complemented
280#361—112no—
281#361—112no—
282#361—112no—
283#361C2×D1112yescomplemented
284C22×C11—41no—
285C22×C11—84no—
286C22×C11—82no—
287C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
288C2×D11—22no—
289C2×D11—41no—
290C2×D11—82no—
291C2×D11—84no—
292C2×D11—82no—
293C2×D11—164no—
294C2×D11—164no—
295C2×D11#45911yescharacteristic
296C2×D11#45911yescharacteristic
297C4×C11—22no—
298C4×C11—41no—
299C4×C11C2×#12111yescharacteristic
300C4×C11C22×D811yescharacteristic
301Dic11—22no—
302Dic11—41no—
303Dic11#45911yescharacteristic
304Dic11#45911yescharacteristic
305C2×#41—221no—
306C22×D4—222no—
307C22×D4—442no—
308#135—111no—
309#135—111no—
310#135—111no—
311#135—221no—
312#135—221no—
313#135C22×D1111yescharacteristic
314C2×Q16—111no—
315C2×SD16—221no—
316C2×D8—21no—
317C2×D8—111no—
318C2×D8—112no—
319C2×D8—222no—
320C2×D8—222no—
321C2×D8—222no—
322C2×D8—222no—
323C2×D8—222no—
324C2×D8—222no—
325C2×D8—221no—
326C2×D8—441no—
327C2×D8—441no—
328C2×D8—441no—
329C2×D8—441no—
330C2×D8C22×D1112yes—
331#131—21no—
332#131—221no—
333#131—221no—
334#131—221no—
335#131—441no—
336#131—441no—
337C2×M16—221no—
338C2×M16—441no—
339C22×C8—111no—
340C22×C8—111no—
341C22×C8—441no—
342#127—21no—
343#127—222no—
344#127—221no—
345#127—442no—
346C2×C42—111no—
347SD32—22no—
348SD32—222no—
349SD32—222no—
350SD32—222no—
351D16—22no—
352D16—222no—
353D16—222no—
354D16—222no—
355M32—112no—
356M32—222no—
357M32C22×D1112yes—
358C2×C16—222no—
359#108—111no—
360#108—221no—
361#108C22×D1111yescharacteristic
362#104—21no—
363#104—221no—
364#104—221no—
365#104—221no—
366C4×C8—111no—
367C4×C8—111no—
368C4×C8—111no—
369C4×C8C22×D1111yescharacteristic
370C2×C11—21no—
371C2×C11—81no—
372C2×C11—162no—
373C2×C11C2×#45911yescharacteristic
374D11—21no—
375D11—81no—
376D11—162no—
377D11#221312yesdirect product factor
378C24—442no—
379#41—21no—
380#41—221no—
381#41—221no—
382#41—221no—
383#41—441no—
384#41—441no—
385C2×Q8—221no—
386C2×D4—22no—
387C2×D4—42no—
388C2×D4—221no—
389C2×D4—222no—
390C2×D4—442no—
391C2×D4—442no—
392C2×D4—442no—
393C2×D4—442no—
394C2×D4—442no—
395C2×D4—442no—
396C2×D4—444no—
397C2×D4—441no—
398C2×D4—888no—
399C22×C4—111no—
400C22×C4—221no—
401C22×C4—441no—
402Q16—111no—
403Q16—221no—
404Q16D4×D1111yescharacteristic, complemented
405SD16—21no—
406SD16—221no—
407SD16—221no—
408SD16—221no—
409D8—22no—
410D8—22no—
411D8—41no—
412D8—41no—
413D8—111no—
414D8—221no—
415D8—222no—
416D8—222no—
417D8—442no—
418D8—442no—
419D8—442no—
420D8—442no—
421D8—441no—
422D8—441no—
423D8D4×D1111yescharacteristic, complemented
424M16—21no—
425M16—41no—
426M16—221no—
427M16—441no—
428M16—441no—
429M16—441no—
430M16—441no—
431C2×C8—41no—
432C2×C8—111no—
433C2×C8—111no—
434C2×C8—111no—
435C2×C8—111no—
436C2×C8—111no—
437C2×C8—111no—
438C2×C8—111no—
439C2×C8—111no—
440C2×C8—111no—
441C2×C8—111no—
442C2×C8—441no—
443C2×C8—441no—
444C2×C8—441no—
445C2×C8—441no—
446C2×C8D4×D1111yescharacteristic
447C2×C8C23×D1111yescharacteristic
448C42—111no—
449C42—221no—
450C42D4×D1111yescharacteristic
451C16—22no—
452C16—222no—
453C11C2×#221311yescharacteristic, complemented, Sylow
454C23—42no—
455C23—111no—
456C23—441no—
457C23—442no—
458C23—882no—
459C23—882no—
460C23—888no—
461Q8—21no—
462Q8—221no—
463Q8—441no—
464D4—21no—
465D4—41no—
466D4—42no—
467D4—42no—
468D4—84no—
469D4—221no—
470D4—441no—
471D4—441no—
472D4—441no—
473D4—441no—
474D4—442no—
475D4—442no—
476D4—884no—
477D4—882no—
478D4—882no—
479D4—888no—
480C2×C4—21no—
481C2×C4—41no—
482C2×C4—111no—
483C2×C4—111no—
484C2×C4—111no—
485C2×C4—111no—
486C2×C4—111no—
487C2×C4—224no—
488C2×C4—221no—
489C2×C4—441no—
490C2×C4—441no—
491C2×C4—441no—
492C2×C4—441no—
493C2×C4C2×D4×D1111yescharacteristic
494C8—41no—
495C8—111no—
496C8—111no—
497C8—111no—
498C8—111no—
499C8—441no—
500C8D8×D1111yescharacteristic
501C8D8×D1111yescharacteristic
502C8C2×D4×D1111yescharacteristic
503C8#41×D1111yescharacteristic
504C22—41no—
505C22—84no—
506C22—82no—
507C22—111no—
508C22—111no—
509C22—222no—
510C22—441no—
511C22—884no—
512C22—882no—
513C22—882no—
514C22—1764no—
515C22—1764no—
516C22D11×AGL(1,ℤ/8)11yescharacteristic
517C4—22no—
518C4—41no—
519C4—111no—
520C4—111no—
521C4—222no—
522C4—441no—
523C4D11×#12111yescharacteristic
524C4C2×D8×D1111yescharacteristic
525C2—21no—
526C2—81no—
527C2—112no—
528C2—162no—
529C2—221no—
530C2—881no—
531C2—1762no—
532C2D11×#45911yescharacteristic
subgroupG/H
centerC2D11×#459
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2213C2
socleC2×C11C2×#459
hypercenter#2213D11
hypocenterC11C2×#2213
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2213

Complements

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

NH ≅ G/Ntype
1. D11×#509C2semidirect
2. D11×#493C2semidirect
3. D11×#443C2semidirect
4. #13070693C2semidirect
5. #13070692C2semidirect
6. #13070691C2semidirect
7. #13070690C2semidirect
8. #13070689C2semidirect
9. D11×#364C2semidirect
10. D11×#361C2semidirect
11. C11×#2213C2semidirect
17. C11×#509C22semidirect
18. C11×#493C22semidirect
19. C11×#443C22semidirect
20. #10622809C22semidirect
21. #10622806C22semidirect
23. #10622764C22semidirect
24. #10622760C22semidirect
31. #10622521C22semidirect
33. #10622508C22semidirect
37. #10622313C22semidirect
38. #10622308C22semidirect
40. C11×#364C22semidirect
41. C11×#361C22semidirect
42. #10622201C22semidirect
43. #10622154C22semidirect
44. #10622149C22semidirect
45. #10622133C22semidirect
46. #10622101C22semidirect
61. #66972D4semidirect
62. Q16×D11D4semidirect
65. #66965D4semidirect
74. D8×D11D4semidirect
137. C11×Q16C2×D4semidirect
143. C11×D8C2×D4semidirect
165. Dic44C2×D4semidirect
170. D88C2×D4semidirect
196. #2213D11direct (N × H)
259. #509C2×D11semidirect
267. #493C2×D11semidirect
273. #443C2×D11semidirect
279. #364C2×D11semidirect
283. #361C2×D11semidirect
377. D11#2213direct (N × H)
404. Q16D4×D11semidirect
423. D8D4×D11semidirect
453. C11C2×#2213semidirect

Maximal subgroups

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

subgroupindex
D11×#5092
D11×#4932
D11×#4432
#130706932
#130706922
#130706912
#130706902
#130706892
D11×#3642
D11×#3612
C11×#22132
C2×#221311