Finite Group Databasebeta

← D11×#2211 #14908025

Subgroups — D11×#2211 #14908025

Order 2816.

722 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×Q32C211yesmaximal, characteristic, complemented
2C2×D11×SD32C211yesmaximal, characteristic
3D11×#495C211yesmaximal, characteristic
4C4×Q16×D11C211yesmaximal, characteristic, complemented
5#13070681C211yesmaximal, characteristic, complemented
6#13070680C211yesmaximal, characteristic, complemented
7#13070679C211yesmaximal, characteristic, complemented
8#13070678C211yesmaximal, characteristic, complemented
9#13070677C211yesmaximal, characteristic, complemented
10#13070676C211yesmaximal, characteristic, complemented
11#13070675C211yesmaximal, characteristic, complemented
12D11×C4⋊C16C211yesmaximal, characteristic, complemented
13D11×#358C211yesmaximal, characteristic, complemented
14D11×#357C211yesmaximal, characteristic
15C11×#2211C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C2×Q16×D11C2211yescharacteristic
18C2×SD16×D11—21no—
19C2×D8×D11C2211yescharacteristic
20D11×#124—21no—
21C4×Q8×D11—21no—
22C2×C11×Q32C2211yescharacteristic, complemented
23C2×C11×SD32C2211yescharacteristic
24C11×#495C2211yescharacteristic
25C4×C11×Q16C2211yescharacteristic, complemented
26#10622804C2211yescharacteristic
27Q16×Dic11C2211yescharacteristic, complemented
28C2×#66893C2211yescharacteristic, complemented
29C2×#66893C2211yescharacteristic, complemented
30C2×#66892C2211yescharacteristic
31#10622781—21no—
32#10622768C2211yescharacteristic
33C2×#66891C2211yescharacteristic
34#10622672—21no—
35C4×#4326—21no—
36D11×Q32—24no—
37D11×SD32—24no—
38C2×Dic88C2211yescharacteristic, complemented
39C2×#66864C2211yescharacteristic
40C2×C16×D11C2211yescharacteristic
41C2×C16×D11C2211yescharacteristic
42D11×#107C2211yescharacteristic
43#10622486C2211yescharacteristic, complemented
44D11×#103—21no—
45#10622403—21no—
46C4×Dic44C2211yescharacteristic, complemented
47#10622309C2211yescharacteristic
48C4×C8×D11C2211yescharacteristic
49C11×C4⋊C16C2211yescharacteristic, complemented
50C11×#358C2211yescharacteristic, complemented
51C11×#357C2211yescharacteristic
52#10622202C2211yescharacteristic, complemented
53#10622200C2211yescharacteristic
54#10622147C2211yescharacteristic
55#10622141C2211yescharacteristic, complemented
56Dic11⋊C16C2211yescharacteristic, complemented
57Dic11⋊C16C2211yescharacteristic, complemented
58#10622130C2211yescharacteristic, complemented
59#10622129C2211yescharacteristic
60C4⋊(C11⋊C16)C2211yescharacteristic, complemented
61C2×Q8×D11—21no—
62C2×Q8×D11—21no—
63C2×D4×D11—21no—
64C2×C11×Q16C2311yescharacteristic
65C2×C11×Q16C2311yescharacteristic
66C2×C11×SD16—21no—
67C2×C11×D8C2311yescharacteristic
68C11×#124—21no—
69C4×Q8×C11—21no—
70#67000—21no—
71Q8×Dic11—21no—
72C2×#4326—21no—
73C2×#4326—21no—
74C2×#4325—21no—
75#66989—21no—
76C2×#4324—21no—
77C2×#4323—21no—
78Q16×D11—22no—
79Q16×D11—22no—
80Q16×D11—22no—
81Q16×D11D414yes—
82SD16×D11—44no—
83D8×D11—22no—
84D8×D11—22no—
85C2×Dic44C2311yescharacteristic
86C2×Dic44C2311yescharacteristic
87C2×D88C2311yescharacteristic
88C2×#4314—21no—
89C2×C8×D11D411yescharacteristic
90C2×C8×D11C2311yescharacteristic
91C4⋊C4×D11—21no—
92C4⋊C4×D11—41no—
93#66940—21no—
94#66940—41no—
95#66938—41no—
96#66938—41no—
97C22⋊C4×D11—41no—
98C22⋊C4×D11—41no—
99#66928—21no—
100C42×D11—41no—
101C42×D11D411yescharacteristic
102C4×Dic22—21no—
103C4×Dic22—41no—
104C11×Q32—22no—
105C11×SD32—22no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#103—21no—
110C4×C8×C11C2311yescharacteristic
111#66899—21no—
112#66893—22no—
113#66893—22no—
114#66892—22no—
115#66891—22no—
116#66882C2311yescharacteristic
117#66880—21no—
118C8×Dic11D411yescharacteristic
119C8×Dic11C2311yescharacteristic
120C2×C11⋊C16C2311yescharacteristic
121C2×C11⋊C16C2311yescharacteristic
122#66874—21no—
123#66871—21no—
124C4×C11⋊C8D411yescharacteristic
125Dic88—22no—
126#66864—22no—
127C16×D11—22no—
128C16×D11—22no—
129C2×#2211—111nomaximal, Sylow
130C23×D11—41no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×D4×C11—21no—
134C2×C22⋊D11—41no—
135Q8×D11—24no—
136Q8×D11—42no—
137Q8×D11—42no—
138Q8×D11—42no—
139D4×D11—42no—
140D4×D11—42no—
141C2×D44—21no—
142C2×C4×D11—41no—
143C2×C4×D11—41no—
144C2×C4×D11—41no—
145C2×C4×D11D811yescharacteristic
146C2×C4×D11D811yescharacteristic
147C2×C4×D11C2×D411yescharacteristic
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—41no—
151C2×Dic22—41no—
152C11×Q16—21no—
153C11×Q16—21no—
154C11×Q16—21no—
155C11×Q16C2×D412yes—
156C11×SD16—42no—
157C11×D8—21no—
158C11×D8—21no—
159C2×C8×C11C2×D411yescharacteristic
160C2×C8×C11C2411yescharacteristic
161C11×C4⋊C4—21no—
162C11×C4⋊C4—41no—
163C11×C22⋊C4—41no—
164C11×C22⋊C4—41no—
165C42×C11—41no—
166C42×C11C2×D411yescharacteristic
167C22⋊Dic11—41no—
168C22⋊Dic11—41no—
169#4326—24no—
170#4326—42no—
171#4325—42no—
172#4324—42no—
173#4323—42no—
174(C2×D11)⋊C4—41no—
175(C2×D11)⋊C4—41no—
176(C2×D11)⋊C4—41no—
177(C2×D11)⋊C4—41no—
178C4⋊Dic11—21no—
179C4⋊Dic11—41no—
180Dic11⋊C4—41no—
181Dic11⋊C4—41no—
182Dic11⋊C4—41no—
183C4×Dic11—41no—
184C4×Dic11—41no—
185C4×Dic11—41no—
186C4×Dic11D811yescharacteristic
187C4×Dic11D811yescharacteristic
188C4×Dic11C2×D411yescharacteristic
189C2×C11⋊C8C2×D411yescharacteristic
190C2×C11⋊C8C2×D411yescharacteristic
191Dic44—21no—
192Dic44—21no—
193Dic44—21no—
194Dic44C2×D412yes—
195D88—21no—
196D88—21no—
197#4314—42no—
198C8×D11—22no—
199C8×D11C2×D412yes—
200C8×D11#4112yes—
201C11×C16—21no—
202C11×C16—21no—
203C11⋊C16—21no—
204C11⋊C16—21no—
205C22×Q32—111no—
206C22×SD32—111no—
207C2×#495—111no—
208C2×C4×Q16—111no—
209#2211—111no—
210#2211—111no—
211#2211—111no—
212#2211—111no—
213#2211—111no—
214#2211—111no—
215#2211—111no—
216#2211D1111yescharacteristic, direct product factor
217C2×C4⋊C16—111no—
218C2×#358—111no—
219C2×#357—111no—
220C23×C11—41no—
221C22×D11—41no—
222C22×D11—82no—
223C22×D11—82no—
224C22×D11—82no—
225C22×D11C2×D811yescharacteristic
226Q8×C11—22no—
227Q8×C11—41no—
228Q8×C11—41no—
229Q8×C11—41no—
230D4×C11—41no—
231D4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11C2×D811yescharacteristic
236C2×C4×C11C2×D811yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C22⋊D11—82no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11C2×D811yescharacteristic
243C2×Dic11C2×D811yescharacteristic
244C2×Dic11C2×D811yescharacteristic
245D44—41no—
246D44—41no—
247C4×D11—22no—
248C4×D11—22no—
249C4×D11—44no—
250C4×D11—82no—
251C4×D11—82no—
252C4×D11#12112yes—
253C4×D11AGL(1,ℤ/8)12yes—
254Dic22—22no—
255Dic22—41no—
256Dic22—44no—
257Dic22—41no—
258Dic22—41no—
259Dic22—82no—
260C8×C11—21no—
261C8×C11C22×D411yescharacteristic
262C8×C11C2×#4111yescharacteristic
263C11⋊C8—21no—
264C11⋊C8#12112yes—
265C22×Q16—111no—
266C22×Q16—111no—
267C22×SD16—221no—
268C22×D8—111no—
269C2×#124—221no—
270C2×C4×Q8—221no—
271C2×Q32—111no—
272C2×Q32—111no—
273C2×Q32—111no—
274C2×Q32—224no—
275C2×Q32C2×D1111yescharacteristic, complemented
276C2×SD32—111no—
277C2×SD32—111no—
278C2×SD32—111no—
279C2×SD32—224no—
280C2×SD32C2×D1111yescharacteristic
281C22×C16—111no—
282C22×C16—111no—
283#495—111no—
284#495—111no—
285#495—111no—
286#495—221no—
287#495—221no—
288#495C2×D1111yescharacteristic
289C4×Q16—111no—
290C4×Q16—111no—
291C4×Q16—111no—
292C4×Q16—221no—
293C4×Q16—221no—
294C4×Q16C2×D1111yescharacteristic, complemented
295C2×#107—111no—
296C2×#103—221no—
297C2×C4×C8—111no—
298C4⋊C16—111no—
299C4⋊C16—111no—
300C4⋊C16—111no—
301C4⋊C16C2×D1111yescharacteristic, complemented
302#358—111no—
303#358—111no—
304#358—111no—
305#358C2×D1111yescharacteristic, complemented
306#357—111no—
307#357—111no—
308#357—111no—
309#357C2×D1111yescharacteristic
310C22×C11—81no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11C22×D811yescharacteristic
314C2×D11—81no—
315C2×D11—81no—
316C2×D11—81no—
317C2×D11—164no—
318C2×D11#45912yes—
319C2×D11#50812yes—
320C2×D11#51012yes—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—42no—
324C4×C11—81no—
325C4×C11—81no—
326C4×C11C2×#12111yescharacteristic
327C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
328Dic11—21no—
329Dic11—21no—
330Dic11—42no—
331Dic11—81no—
332Dic11—81no—
333Dic11#45912yes—
334C22×Q8—221no—
335C22×Q8—221no—
336C22×D4—221no—
337C2×Q16—114no—
338C2×Q16—111no—
339C2×Q16—111no—
340C2×Q16—222no—
341C2×Q16—222no—
342C2×Q16—222no—
343C2×Q16—221no—
344C2×Q16—221no—
345C2×Q16C22×D1111yescharacteristic
346C2×Q16C22×D1111yescharacteristic
347C2×SD16—21no—
348C2×SD16—221no—
349C2×SD16—221no—
350C2×SD16—221no—
351C2×SD16—444no—
352C2×D8—111no—
353C2×D8—222no—
354C2×D8—222no—
355C2×D8—221no—
356C2×D8C22×D1111yescharacteristic
357C22×C8—111no—
358C22×C8—111no—
359#124—21no—
360#124—221no—
361#124—221no—
362#124—221no—
363#124—441no—
364#124—441no—
365C4×Q8—21no—
366C4×Q8—221no—
367C4×Q8—221no—
368C4×Q8—221no—
369C4×Q8—441no—
370C4×Q8—441no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—441no—
373C2×C22⋊C4—441no—
374C2×C22⋊C4—441no—
375C2×C42—111no—
376C2×C42—441no—
377Q32—22no—
378Q32—222no—
379Q32—222no—
380Q32—222no—
381SD32—22no—
382SD32—222no—
383SD32—222no—
384SD32—222no—
385C2×C16—111no—
386C2×C16—111no—
387C2×C16—222no—
388C2×C16—222no—
389C2×C16C22×D1111yescharacteristic
390C2×C16C22×D1111yescharacteristic
391#107—111no—
392#107—221no—
393#107C22×D1111yescharacteristic
394#103—21no—
395#103—221no—
396#103—221no—
397#103—221no—
398C4×C8—111no—
399C4×C8—111no—
400C4×C8—111no—
401C4×C8C22×D1111yescharacteristic
402C2×C11—161no—
403C2×C11C2×#45911yescharacteristic
404C2×C11C2×#50811yescharacteristic
405C2×C11C2×#51011yescharacteristic
406D11—161no—
407D11#221114yesdirect product factor
408C24—441no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—224no—
412C2×Q8—221no—
413C2×Q8—221no—
414C2×Q8—441no—
415C2×Q8—441no—
416C2×Q8—442no—
417C2×Q8—442no—
418C2×Q8—442no—
419C2×D4—21no—
420C2×D4—221no—
421C2×D4—442no—
422C2×D4—442no—
423C2×D4—441no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—441no—
428C22×C4—441no—
429C22×C4—441no—
430Q16—21no—
431Q16—21no—
432Q16—21no—
433Q16—112no—
434Q16—224no—
435Q16—221no—
436Q16—221no—
437Q16—221no—
438Q16—442no—
439Q16D4×D1112yes—
440SD16—42no—
441SD16—442no—
442SD16—442no—
443SD16—442no—
444D8—21no—
445D8—21no—
446D8—221no—
447D8—221no—
448D8—442no—
449C2×C8—111no—
450C2×C8—112no—
451C2×C8—112no—
452C2×C8—111no—
453C2×C8—222no—
454C2×C8D4×D1111yescharacteristic
455C2×C8C23×D1111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—41no—
458C4⋊C4—221no—
459C4⋊C4—441no—
460C4⋊C4—441no—
461C4⋊C4—441no—
462C4⋊C4—441no—
463C22⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—441no—
466C22⋊C4—441no—
467C22⋊C4—441no—
468C22⋊C4—441no—
469C22⋊C4—441no—
470C22⋊C4—441no—
471C42—41no—
472C42—111no—
473C42—111no—
474C42—111no—
475C42—441no—
476C42—441no—
477C42—441no—
478C42D4×D1111yescharacteristic
479C16—21no—
480C16—21no—
481C16—221no—
482C16—221no—
483C11C2×#221111yescharacteristic, complemented, Sylow
484C23—41no—
485C23—111no—
486C23—441no—
487C23—882no—
488C23—882no—
489C23—882no—
490Q8—22no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—222no—
495Q8—444no—
496Q8—441no—
497Q8—441no—
498Q8—441no—
499Q8—882no—
500D4—41no—
501D4—41no—
502D4—441no—
503D4—441no—
504D4—882no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—111no—
509C2×C4—112no—
510C2×C4—112no—
511C2×C4—111no—
512C2×C4—111no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—444no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—882no—
520C2×C4—882no—
521C2×C4D8×D1111yescharacteristic
522C2×C4D8×D1111yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C8—21no—
525C8—112no—
526C8—221no—
527C8C2×D4×D1111yescharacteristic
528C8#41×D1111yescharacteristic
529C22—81no—
530C22—81no—
531C22—81no—
532C22—112no—
533C22—112no—
534C22—112no—
535C22—881no—
536C22—881no—
537C22—881no—
538C22—1764no—
539C22C2×D8×D1111yescharacteristic
540C4—21no—
541C4—21no—
542C4—42no—
543C4—81no—
544C4—81no—
545C4—112no—
546C4—221no—
547C4—221no—
548C4—442no—
549C4—881no—
550C4—881no—
551C4D11×#12111yescharacteristic
552C4D11×AGL(1,ℤ/8)11yescharacteristic
553C2—114no—
554C2—161no—
555C2—1761no—
556C2D11×#45911yescharacteristic
557C2D11×#50811yescharacteristic
558C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2211C2
socleC22×C11C22×D8
prime radicalC2×D8×D11C22
hypercenter#2211D11
hypocenterC11C2×#2211
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2211

Complements

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

NH ≅ G/Ntype
1. C2×D11×Q32C2semidirect
4. C4×Q16×D11C2semidirect
5. #13070681C2semidirect
6. #13070680C2semidirect
7. #13070679C2semidirect
8. #13070678C2semidirect
9. #13070677C2semidirect
10. #13070676C2semidirect
11. #13070675C2semidirect
12. D11×C4⋊C16C2semidirect
13. D11×#358C2semidirect
15. C11×#2211C2semidirect
22. C2×C11×Q32C22semidirect
25. C4×C11×Q16C22semidirect
27. Q16×Dic11C22semidirect
28. C2×#66893C22semidirect
29. C2×#66893C22semidirect
38. C2×Dic88C22semidirect
43. #10622486C22semidirect
46. C4×Dic44C22semidirect
49. C11×C4⋊C16C22semidirect
50. C11×#358C22semidirect
52. #10622202C22semidirect
55. #10622141C22semidirect
56. Dic11⋊C16C22semidirect
57. Dic11⋊C16C22semidirect
58. #10622130C22semidirect
60. C4⋊(C11⋊C16)C22semidirect
216. #2211D11direct (N × H)
275. C2×Q32C2×D11semidirect
294. C4×Q16C2×D11semidirect
301. C4⋊C16C2×D11semidirect
305. #358C2×D11semidirect
407. D11#2211direct (N × H)
483. C11C2×#2211semidirect

Maximal subgroups

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

subgroupindex
C2×D11×Q322
C2×D11×SD322
D11×#4952
C4×Q16×D112
#130706812
#130706802
#130706792
#130706782
#130706772
#130706762
#130706752
D11×C4⋊C162
D11×#3582
D11×#3572
C11×#22112
C2×#221111