Finite Group Databasebeta

← D11×#2210 #14908005

Subgroups — D11×#2210 #14908005

Order 2816.

786 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×SD32C211yesmaximal, characteristic, complemented
2C2×D11×D16C211yesmaximal, characteristic
3D11×#495C211yesmaximal, characteristic, complemented
4C4×D8×D11C211yesmaximal, characteristic, complemented
5#13070674C211yesmaximal, characteristic, complemented
6#13070673C211yesmaximal, characteristic, complemented
7#13070672C211yesmaximal, characteristic, complemented
8#13070671C211yesmaximal, characteristic, complemented
9#13070670C211yesmaximal, characteristic, complemented
10#13070669C211yesmaximal, characteristic, complemented
11#13070668C211yesmaximal, characteristic, complemented
12D11×C4⋊C16C211yesmaximal, characteristic, complemented
13D11×#358C211yesmaximal, characteristic, complemented
14D11×#357C211yesmaximal, characteristic, complemented
15C11×#2210C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C2×SD16×D11—21no—
18C2×D8×D11C2211yescharacteristic
19C2×D8×D11C2211yescharacteristic
20D11×#124—21no—
21C4×D4×D11—21no—
22C2×C11×SD32C2211yescharacteristic, complemented
23C2×C11×D16C2211yescharacteristic
24C11×#495C2211yescharacteristic, complemented
25C4×C11×D8C2211yescharacteristic, complemented
26#10622804C2211yescharacteristic, complemented
27C2×#66892C2211yescharacteristic, complemented
28#10622781—21no—
29#10622768C2211yescharacteristic, complemented
30D8×Dic11C2211yescharacteristic, complemented
31C2×#66891C2211yescharacteristic, complemented
32C2×#66890C2211yescharacteristic
33C2×#66890C2211yescharacteristic
34#10622672—21no—
35C4×#4323—21no—
36D11×SD32—24no—
37D11×D16—24no—
38C2×#66864C2211yescharacteristic, complemented
39C2×D176C2211yescharacteristic
40C2×C16×D11C2211yescharacteristic
41C2×C16×D11C2211yescharacteristic
42D11×#107C2211yescharacteristic
43#10622485C2211yescharacteristic, complemented
44D11×#102—21no—
45#10622369—21no—
46#10622309C2211yescharacteristic, complemented
47C4×D88C2211yescharacteristic, complemented
48C4×C8×D11C2211yescharacteristic
49C11×C4⋊C16C2211yescharacteristic, complemented
50C11×#358C2211yescharacteristic, complemented
51C11×#357C2211yescharacteristic, complemented
52#10622202C2211yescharacteristic, complemented
53#10622200C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic, complemented
55#10622141C2211yescharacteristic, complemented
56Dic11⋊C16C2211yescharacteristic, complemented
57Dic11⋊C16C2211yescharacteristic, complemented
58#10622130C2211yescharacteristic, complemented
59#10622129C2211yescharacteristic, complemented
60C4⋊(C11⋊C16)C2211yescharacteristic, complemented
61C2×Q8×D11—21no—
62C2×D4×D11—21no—
63C2×D4×D11—21no—
64C22×C4×D11—41no—
65C2×C11×Q16C2311yescharacteristic
66C2×C11×SD16—21no—
67C2×C11×D8C2311yescharacteristic
68C2×C11×D8C2311yescharacteristic
69C11×#124—21no—
70C4×D4×C11—21no—
71#67000—21no—
72C2×#4326—21no—
73C2×#4325—21no—
74#66989—21no—
75D4×Dic11—21no—
76C2×#4324—21no—
77C2×#4323—21no—
78C2×#4323—21no—
79C4×C22⋊D11—41no—
80Q16×D11—22no—
81Q16×D11—22no—
82SD16×D11—44no—
83D8×D11—22no—
84D8×D11—22no—
85D8×D11—22no—
86D8×D11D414yes—
87C2×Dic44C2311yescharacteristic
88C2×D88C2311yescharacteristic
89C2×D88C2311yescharacteristic
90C2×#4314—21no—
91C2×C8×D11D411yescharacteristic
92C2×C8×D11C2311yescharacteristic
93#66946—21no—
94C4⋊C4×D11—21no—
95#66938—41no—
96#66938—41no—
97(C22⋊D11)⋊C4—41no—
98C22⋊C4×D11—41no—
99C22⋊C4×D11—41no—
100C22⋊C4×D11—41no—
101#66928—21no—
102C4×D44—21no—
103C42×D11D411yescharacteristic
104C11×SD32—22no—
105C11×D16—22no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#102—21no—
110C4×C8×C11C2311yescharacteristic
111#66896—21no—
112#66892—22no—
113#66891—22no—
114#66890—22no—
115#66890—22no—
116#66885—21no—
117#66882C2311yescharacteristic
118C8×Dic11D411yescharacteristic
119C8×Dic11C2311yescharacteristic
120C2×C11⋊C16C2311yescharacteristic
121C2×C11⋊C16C2311yescharacteristic
122#66873—21no—
123#66871—21no—
124C4×C11⋊C8D411yescharacteristic
125#66864—22no—
126D176—22no—
127C16×D11—22no—
128C16×D11—22no—
129C2×#2210—111nomaximal, Sylow
130C23×D11—41no—
131C23×D11—41no—
132C2×Q8×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C22×C4×C11—41no—
136C2×C22⋊D11—41no—
137C2×C22⋊D11—41no—
138C22×Dic11—41no—
139Q8×D11—42no—
140Q8×D11—42no—
141D4×D11—24no—
142D4×D11—42no—
143D4×D11—42no—
144D4×D11—42no—
145C2×D44—21no—
146C2×D44—21no—
147C2×C4×D11—41no—
148C2×C4×D11—41no—
149C2×C4×D11—41no—
150C2×C4×D11—41no—
151C2×C4×D11—84no—
152C2×C4×D11D811yescharacteristic
153C2×C4×D11D811yescharacteristic
154C2×C4×D11C2×D411yescharacteristic
155C2×Dic22—21no—
156C2×Dic22—41no—
157C11×Q16—21no—
158C11×Q16—21no—
159C11×SD16—42no—
160C11×D8—21no—
161C11×D8—21no—
162C11×D8—21no—
163C11×D8C2×D412yes—
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2411yescharacteristic
166C11×C4⋊C4—21no—
167C11×C22⋊C4—41no—
168C11×C22⋊C4—41no—
169C11×C22⋊C4—41no—
170C42×C11C2×D411yescharacteristic
171C22⋊Dic11—41no—
172C22⋊Dic11—41no—
173C22⋊Dic11—41no—
174#4326—42no—
175#4325—42no—
176#4324—42no—
177#4323—24no—
178#4323—42no—
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—
185C4⋊Dic11—21no—
186Dic11⋊C4—41no—
187C4×Dic11D811yescharacteristic
188C4×Dic11D811yescharacteristic
189C4×Dic11C2×D411yescharacteristic
190C2×C11⋊C8C2×D411yescharacteristic
191C2×C11⋊C8C2×D411yescharacteristic
192Dic44—21no—
193Dic44—21no—
194D88—21no—
195D88—21no—
196D88—21no—
197D88C2×D412yes—
198#4314—42no—
199C8×D11—22no—
200C8×D11C2×D412yes—
201C8×D11#4112yes—
202C11×C16—21no—
203C11×C16—21no—
204C11⋊C16—21no—
205C11⋊C16—21no—
206C22×SD32—111no—
207C22×D16—111no—
208C2×#495—111no—
209C2×C4×D8—111no—
210#2210—111no—
211#2210—111no—
212#2210—111no—
213#2210—111no—
214#2210—111no—
215#2210—111no—
216#2210—111no—
217#2210D1111yescharacteristic, direct product factor
218C2×C4⋊C16—111no—
219C2×#358—111no—
220C2×#357—111no—
221C23×C11—41no—
222C23×C11—41no—
223C22×D11—41no—
224C22×D11—44no—
225C22×D11—41no—
226C22×D11—82no—
227C22×D11—82no—
228C22×D11—82no—
229C22×D11—82no—
230C22×D11—82no—
231C22×D11C2×D811yescharacteristic
232Q8×C11—41no—
233Q8×C11—41no—
234D4×C11—22no—
235D4×C11—41no—
236D4×C11—41no—
237D4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—82no—
241C2×C4×C11C2×D811yescharacteristic
242C2×C4×C11C2×D811yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C22⋊D11—44no—
245C22⋊D11—82no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—82no—
249C2×Dic11C2×D811yescharacteristic
250C2×Dic11C2×D811yescharacteristic
251C2×Dic11C2×D811yescharacteristic
252D44—22no—
253D44—41no—
254D44—41no—
255D44—41no—
256C4×D11—22no—
257C4×D11—22no—
258C4×D11—82no—
259C4×D11—82no—
260C4×D11—82no—
261C4×D11—82no—
262C4×D11#12112yes—
263C4×D11AGL(1,ℤ/8)12yes—
264Dic22—41no—
265Dic22—41no—
266Dic22—82no—
267C8×C11—21no—
268C8×C11C22×D411yescharacteristic
269C8×C11C2×#4111yescharacteristic
270C11⋊C8—21no—
271C11⋊C8#12112yes—
272C22×Q16—111no—
273C22×SD16—221no—
274C22×D8—111no—
275C22×D8—111no—
276C2×#124—221no—
277C2×C4×D4—221no—
278C2×SD32—111no—
279C2×SD32—111no—
280C2×SD32—111no—
281C2×SD32—224no—
282C2×SD32C2×D1111yescharacteristic, complemented
283C2×D16—111no—
284C2×D16—111no—
285C2×D16—111no—
286C2×D16—224no—
287C2×D16C2×D1111yescharacteristic
288C22×C16—111no—
289C22×C16—111no—
290#495—111no—
291#495—111no—
292#495—111no—
293#495—221no—
294#495—221no—
295#495C2×D1111yescharacteristic, complemented
296C4×D8—111no—
297C4×D8—111no—
298C4×D8—111no—
299C4×D8—221no—
300C4×D8—221no—
301C4×D8C2×D1111yescharacteristic, complemented
302C2×#107—111no—
303C2×#102—221no—
304C2×C4×C8—111no—
305C4⋊C16—111no—
306C4⋊C16—111no—
307C4⋊C16—111no—
308C4⋊C16C2×D1111yescharacteristic, complemented
309#358—111no—
310#358—111no—
311#358—111no—
312#358C2×D1111yescharacteristic, complemented
313#357—111no—
314#357—111no—
315#357—111no—
316#357C2×D1111yescharacteristic, complemented
317C22×C11—42no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11C22×D811yescharacteristic
324C2×D11—42no—
325C2×D11—81no—
326C2×D11—81no—
327C2×D11—88no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—81no—
331C2×D11—164no—
332C2×D11#45912yes—
333C2×D11#50812yes—
334C2×D11#50912yes—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11C2×#12111yescharacteristic
340C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
341Dic11—21no—
342Dic11—21no—
343Dic11—81no—
344Dic11—81no—
345Dic11#45912yes—
346C22×Q8—221no—
347C22×D4—221no—
348C22×D4—221no—
349C23×C4—441no—
350C2×Q16—111no—
351C2×Q16—222no—
352C2×Q16—222no—
353C2×Q16—221no—
354C2×Q16C22×D1111yescharacteristic
355C2×SD16—21no—
356C2×SD16—221no—
357C2×SD16—221no—
358C2×SD16—221no—
359C2×SD16—444no—
360C2×D8—114no—
361C2×D8—111no—
362C2×D8—111no—
363C2×D8—222no—
364C2×D8—222no—
365C2×D8—222no—
366C2×D8—221no—
367C2×D8—221no—
368C2×D8C22×D1111yescharacteristic
369C2×D8C22×D1111yescharacteristic
370C22×C8—111no—
371C22×C8—111no—
372#124—21no—
373#124—221no—
374#124—221no—
375#124—221no—
376#124—441no—
377#124—441no—
378C4×D4—21no—
379C4×D4—221no—
380C4×D4—221no—
381C4×D4—221no—
382C4×D4—441no—
383C4×D4—441no—
384C2×C4⋊C4—221no—
385C2×C22⋊C4—441no—
386C2×C22⋊C4—441no—
387C2×C22⋊C4—441no—
388C2×C42—111no—
389SD32—22no—
390SD32—222no—
391SD32—222no—
392SD32—222no—
393D16—22no—
394D16—222no—
395D16—222no—
396D16—222no—
397C2×C16—111no—
398C2×C16—111no—
399C2×C16—222no—
400C2×C16—222no—
401C2×C16C22×D1111yescharacteristic
402C2×C16C22×D1111yescharacteristic
403#107—111no—
404#107—221no—
405#107C22×D1111yescharacteristic
406#102—21no—
407#102—221no—
408#102—221no—
409#102—221no—
410C4×C8—111no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8C22×D1111yescharacteristic
414C2×C11—82no—
415C2×C11—161no—
416C2×C11C2×#45911yescharacteristic
417C2×C11C2×#50811yescharacteristic
418C2×C11C2×#50911yescharacteristic
419D11—82no—
420D11—161no—
421D11#221014yesdirect product factor
422C24—441no—
423C24—441no—
424C2×Q8—21no—
425C2×Q8—221no—
426C2×Q8—441no—
427C2×Q8—442no—
428C2×Q8—442no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—224no—
432C2×D4—221no—
433C2×D4—221no—
434C2×D4—442no—
435C2×D4—442no—
436C2×D4—442no—
437C2×D4—441no—
438C2×D4—441no—
439C22×C4—41no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—441no—
444C22×C4—441no—
445C22×C4—441no—
446C22×C4—441no—
447C22×C4—441no—
448C22×C4—884no—
449Q16—21no—
450Q16—21no—
451Q16—221no—
452Q16—221no—
453Q16—442no—
454SD16—42no—
455SD16—442no—
456SD16—442no—
457SD16—442no—
458D8—21no—
459D8—21no—
460D8—21no—
461D8—112no—
462D8—224no—
463D8—221no—
464D8—221no—
465D8—221no—
466D8—442no—
467D8D4×D1112yes—
468C2×C8—111no—
469C2×C8—112no—
470C2×C8—112no—
471C2×C8—111no—
472C2×C8—222no—
473C2×C8D4×D1111yescharacteristic
474C2×C8C23×D1111yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—221no—
477C4⋊C4—441no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—441no—
482C22⋊C4—441no—
483C22⋊C4—441no—
484C22⋊C4—441no—
485C22⋊C4—441no—
486C22⋊C4—441no—
487C22⋊C4—441no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C42—111no—
491C42—111no—
492C42—111no—
493C42D4×D1111yescharacteristic
494C16—21no—
495C16—21no—
496C16—221no—
497C16—221no—
498C11C2×#221011yescharacteristic, complemented, Sylow
499C23—41no—
500C23—41no—
501C23—111no—
502C23—444no—
503C23—441no—
504C23—441no—
505C23—882no—
506C23—882no—
507C23—882no—
508C23—882no—
509C23—882no—
510Q8—41no—
511Q8—41no—
512Q8—441no—
513Q8—441no—
514Q8—882no—
515D4—22no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—222no—
520D4—444no—
521D4—441no—
522D4—441no—
523D4—441no—
524D4—882no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—111no—
529C2×C4—112no—
530C2×C4—112no—
531C2×C4—111no—
532C2×C4—111no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—882no—
538C2×C4—882no—
539C2×C4—882no—
540C2×C4—882no—
541C2×C4—882no—
542C2×C4D8×D1111yescharacteristic
543C2×C4D8×D1111yescharacteristic
544C2×C4C2×D4×D1111yescharacteristic
545C8—21no—
546C8—112no—
547C8—221no—
548C8C2×D4×D1111yescharacteristic
549C8#41×D1111yescharacteristic
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—112no—
557C22—112no—
558C22—112no—
559C22—442no—
560C22—888no—
561C22—881no—
562C22—881no—
563C22—881no—
564C22—881no—
565C22—881no—
566C22—1764no—
567C22C2×D8×D1111yescharacteristic
568C4—21no—
569C4—21no—
570C4—81no—
571C4—81no—
572C4—112no—
573C4—221no—
574C4—221no—
575C4—881no—
576C4—881no—
577C4D11×#12111yescharacteristic
578C4D11×AGL(1,ℤ/8)11yescharacteristic
579C2—82no—
580C2—114no—
581C2—161no—
582C2—882no—
583C2—1761no—
584C2D11×#45911yescharacteristic
585C2D11×#50811yescharacteristic
586C2D11×#50911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2210C2
socleC22×C11C22×D8
prime radicalC2×D11×D16C2
hypercenter#2210D11
hypocenterC11C2×#2210
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2210

Complements

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

NH ≅ G/Ntype
1. C2×D11×SD32C2semidirect
3. D11×#495C2semidirect
4. C4×D8×D11C2semidirect
5. #13070674C2semidirect
6. #13070673C2semidirect
7. #13070672C2semidirect
8. #13070671C2semidirect
9. #13070670C2semidirect
10. #13070669C2semidirect
11. #13070668C2semidirect
12. D11×C4⋊C16C2semidirect
13. D11×#358C2semidirect
14. D11×#357C2semidirect
15. C11×#2210C2semidirect
22. C2×C11×SD32C22semidirect
24. C11×#495C22semidirect
25. C4×C11×D8C22semidirect
26. #10622804C22semidirect
27. C2×#66892C22semidirect
29. #10622768C22semidirect
30. D8×Dic11C22semidirect
31. C2×#66891C22semidirect
38. C2×#66864C22semidirect
43. #10622485C22semidirect
46. #10622309C22semidirect
47. C4×D88C22semidirect
49. C11×C4⋊C16C22semidirect
50. C11×#358C22semidirect
51. C11×#357C22semidirect
52. #10622202C22semidirect
53. #10622200C22semidirect
54. #10622147C22semidirect
55. #10622141C22semidirect
56. Dic11⋊C16C22semidirect
57. Dic11⋊C16C22semidirect
58. #10622130C22semidirect
59. #10622129C22semidirect
60. C4⋊(C11⋊C16)C22semidirect
217. #2210D11direct (N × H)
282. C2×SD32C2×D11semidirect
295. #495C2×D11semidirect
301. C4×D8C2×D11semidirect
308. C4⋊C16C2×D11semidirect
312. #358C2×D11semidirect
316. #357C2×D11semidirect
421. D11#2210direct (N × H)
498. C11C2×#2210semidirect

Maximal subgroups

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

subgroupindex
C2×D11×SD322
C2×D11×D162
D11×#4952
C4×D8×D112
#130706742
#130706732
#130706722
#130706712
#130706702
#130706692
#130706682
D11×C4⋊C162
D11×#3582
D11×#3572
C11×#22102
C2×#221011