Finite Group Databasebeta

← D11×#2217 #14908199

Subgroups — D11×#2217 #14908199

Order 2816.

754 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×SD32C211yesmaximal, characteristic, complemented
2C22×C16×D11C211yesmaximal, characteristic, complemented
3D11×#467C211yesmaximal, characteristic, complemented
4D11×#466C211yesmaximal, characteristic
5#13070715C211yesmaximal, characteristic, complemented
6#13070714C211yesmaximal, characteristic, complemented
7#13070713C211yesmaximal, characteristic, complemented
8#13070712C211yesmaximal, characteristic, complemented
9#13070711C211yesmaximal, characteristic, complemented
10#13070710C211yesmaximal, characteristic, complemented
11#13070709C211yesmaximal, characteristic, complemented
12D11×#367C211yesmaximal, characteristic, complemented
13D11×#358C211yesmaximal, characteristic, complemented
14D11×#357C211yesmaximal, characteristic, complemented
15C11×#2217C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C2×D8×D11C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19D11×C22⋊Q8—21no—
20D11×#121—21no—
21C2×C11×SD32C2211yescharacteristic, complemented
22C22×C11×C16C2211yescharacteristic, complemented
23C11×#467C2211yescharacteristic, complemented
24C11×#466C2211yescharacteristic
25#10622801C2211yescharacteristic, complemented
26C2×#66892C2211yescharacteristic, complemented
27#10622770C2211yescharacteristic
28C2×#66891C2211yescharacteristic, complemented
29#10622729C2211yescharacteristic, complemented
30#10622728C2211yescharacteristic
31C22×C11⋊C16C2211yescharacteristic, complemented
32#10622664—21no—
33#10622651—21no—
34D11×SD32—24no—
35C2×#66864C2211yescharacteristic, complemented
36C2×C16×D11—24no—
37C2×C16×D11C2211yescharacteristic
38C2×C16×D11C2211yescharacteristic
39C2×C16×D11C2211yescharacteristic, complemented
40C2×C16×D11C2211yescharacteristic, complemented
41#10622500C2211yescharacteristic, complemented
42#10622496C2211yescharacteristic
43D11×#107C2211yescharacteristic
44D11×#107C2211yescharacteristic
45#10622426—21no—
46D11×#103—21no—
47#10622388—21no—
48D11×#102—21no—
49C11×#367C2211yescharacteristic, complemented
50C11×#358C2211yescharacteristic, complemented
51C11×#357C2211yescharacteristic, complemented
52#10622202C2211yescharacteristic, complemented
53#10622200C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic, complemented
55#10622143C2211yescharacteristic, complemented
56#10622141C2211yescharacteristic, complemented
57#10622130C2211yescharacteristic, complemented
58#10622129C2211yescharacteristic, complemented
59#10622128C2211yescharacteristic, complemented
60#10622128C2211yescharacteristic, complemented
61C2×Q8×D11—21no—
62C2×D4×D11—21no—
63C2×D4×D11—41no—
64C22×C4×D11D411yescharacteristic
65C2×C11×Q16C2311yescharacteristic
66C2×C11×D8C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C22⋊Q8—21no—
69C11×#121—21no—
70#66999—21no—
71C2×#4326—21no—
72#66992—41no—
73#66991—21no—
74C2×#4323—21no—
75#66983—21no—
76#66977—21no—
77C22×C11⋊C8D411yescharacteristic
78Q16×D11—22no—
79Q16×D11—22no—
80D8×D11—22no—
81D8×D11—22no—
82C2×Dic44C2311yescharacteristic
83C2×D88C2311yescharacteristic
84C2×C8×D11—22no—
85C2×C8×D11—22no—
86C2×C8×D11D411yescharacteristic
87C2×C8×D11D411yescharacteristic
88C2×C8×D11C2311yescharacteristic
89C2×C8×D11C2311yescharacteristic
90#66950—21no—
91#66949—41no—
92#66948—21no—
93C4⋊C4×D11—21no—
94C4⋊C4×D11—21no—
95C4⋊C4×D11—41no—
96#66937—41no—
97C22⋊C4×D11—41no—
98C22⋊C4×D11—41no—
99#66931—41no—
100C11×SD32—22no—
101C2×C11×C16—22no—
102C2×C11×C16C2311yescharacteristic
103C2×C11×C16C2311yescharacteristic
104C11×#107C2311yescharacteristic
105C11×#107C2311yescharacteristic
106C11×#103—21no—
107C11×#102—21no—
108#66899—21no—
109#66896—21no—
110#66892—22no—
111#66891—22no—
112#66885—21no—
113#66882C2311yescharacteristic
114#66882C2311yescharacteristic
115#66880—21no—
116C2×C11⋊C16—22no—
117C2×C11⋊C16C2311yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119#66874—21no—
120#66873—21no—
121#66871—21no—
122#66871—21no—
123#66864—22no—
124C16×D11—22no—
125C16×D11—22no—
126C16×D11—22no—
127C16×D11D414yescomplemented
128C2×#2217—111nomaximal, Sylow
129C23×D11—41no—
130C23×D11D811yescharacteristic
131C2×Q8×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—41no—
134C22×C4×C11C2×D411yescharacteristic
135C2×C22⋊D11—41no—
136C2×C22⋊D11—41no—
137C2×C22⋊D11—41no—
138C22×Dic11D811yescharacteristic
139Q8×D11—42no—
140Q8×D11—42no—
141D4×D11—42no—
142D4×D11—42no—
143D4×D11—84no—
144C2×D44—21no—
145C2×D44—41no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—41no—
149C2×C4×D11—41no—
150C2×C4×D11—41no—
151C2×C4×D11D811yescharacteristic
152C2×C4×D11D811yescharacteristic
153C2×C4×D11C2×D411yescharacteristic
154C2×C4×D11C2×D411yescharacteristic
155C2×Dic22—21no—
156C2×Dic22—41no—
157C11×Q16—21no—
158C11×Q16—21no—
159C11×D8—21no—
160C11×D8—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11C2×D411yescharacteristic
164C2×C8×C11C2411yescharacteristic
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—41no—
168C11×C22⋊C4—41no—
169C11×C22⋊C4—41no—
170C22⋊Dic11—41no—
171C22⋊Dic11—41no—
172#4326—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—21no—
180C4⋊Dic11—41no—
181Dic11⋊C4—41no—
182Dic11⋊C4—41no—
183Dic11⋊C4—41no—
184Dic11⋊C4—41no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8C2×D411yescharacteristic
187C2×C11⋊C8C2×D411yescharacteristic
188Dic44—21no—
189Dic44—21no—
190D88—21no—
191D88—21no—
192C8×D11—22no—
193C8×D11—21no—
194C8×D11—21no—
195C8×D11—22no—
196C8×D11C2×D412yes—
197C8×D11#4112yes—
198C11×C16—21no—
199C11×C16C2×D412yescomplemented
200C11⋊C16—21no—
201C11⋊C16C2×D412yescomplemented
202C22×SD32—111no—
203C23×C16—111no—
204C2×#467—111no—
205C2×#466—111no—
206#2217—111no—
207#2217—111no—
208#2217—111no—
209#2217—111no—
210#2217—111no—
211#2217—111no—
212#2217—111no—
213#2217D1111yescharacteristic, direct product factor
214C2×#367—111no—
215C2×#358—111no—
216C2×#357—111no—
217C23×C11—41no—
218C23×C11C2×D811yescharacteristic
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—41no—
222C22×D11—82no—
223C22×D11—82no—
224C22×D11—82no—
225C22×D11SD3214yescomplemented
226C22×D11C2×D811yescharacteristic
227C22×D11C2×D811yescharacteristic
228Q8×C11—41no—
229Q8×C11—41no—
230D4×C11—41no—
231D4×C11—41no—
232D4×C11—82no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11C2×D811yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C22⋊D11—82no—
241C22⋊D11—82no—
242C22⋊D11—82no—
243C2×Dic11—22no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11C2×D811yescharacteristic
248C2×Dic11C2×D811yescharacteristic
249D44—41no—
250D44—41no—
251D44—82no—
252C4×D11—22no—
253C4×D11—21no—
254C4×D11—21no—
255C4×D11—22no—
256C4×D11—82no—
257C4×D11—82no—
258C4×D11—82no—
259C4×D11#12112yes—
260C4×D11#13512yes—
261Dic22—41no—
262Dic22—41no—
263Dic22—82no—
264C8×C11—21no—
265C8×C11C22×D411yescharacteristic
266C8×C11C2×#4111yescharacteristic
267C11⋊C8—21no—
268C11⋊C8#12112yes—
269C22×Q16—111no—
270C22×D8—111no—
271C23×C8—111no—
272C2×C22⋊Q8—221no—
273C2×#121—221no—
274C2×SD32—111no—
275C2×SD32—111no—
276C2×SD32—111no—
277C2×SD32—224no—
278C2×SD32C2×D1111yescharacteristic, complemented
279C22×C16—111no—
280C22×C16—111no—
281C22×C16—111no—
282C22×C16—111no—
283C22×C16—111no—
284C22×C16—224no—
285C22×C16C2×D1111yescharacteristic, complemented
286#467—111no—
287#467—111no—
288#467—111no—
289#467—221no—
290#467—221no—
291#467C2×D1111yescharacteristic, complemented
292#466—111no—
293#466—111no—
294#466—111no—
295#466—221no—
296#466—221no—
297#466C2×D1111yescharacteristic
298C2×#107—111no—
299C2×#107—111no—
300C2×#103—221no—
301C2×#102—221no—
302#367—111no—
303#367—111no—
304#367—111no—
305#367C2×D1111yescharacteristic, complemented
306#358—111no—
307#358—111no—
308#358—111no—
309#358C2×D1111yescharacteristic, complemented
310#357—111no—
311#357—111no—
312#357—111no—
313#357C2×D1111yescharacteristic, complemented
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—81no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11C2×SD3212yescomplemented
320C22×C11C22×D811yescharacteristic
321C2×D11—21no—
322C2×D11—21no—
323C2×D11—28no—
324C2×D11—81no—
325C2×D11—81no—
326C2×D11—81no—
327C2×D11—164no—
328C2×D11#46612yes—
329C2×D11C2×SD3212yes—
330C2×D11C2×SD3212yescomplemented
331C2×D11#50812yes—
332C4×C11—21no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11C2×#12111yescharacteristic
337C4×C11C2×#13511yescharacteristic
338Dic11—21no—
339Dic11—81no—
340Dic11—81no—
341Dic11—81no—
342Dic11#46612yes—
343C22×Q8—221no—
344C22×D4—221no—
345C22×D4—441no—
346C23×C4—111no—
347C2×Q16—111no—
348C2×Q16—222no—
349C2×Q16—222no—
350C2×Q16—221no—
351C2×Q16C22×D1111yescharacteristic
352C2×D8—111no—
353C2×D8—222no—
354C2×D8—222no—
355C2×D8—221no—
356C2×D8C22×D1111yescharacteristic
357C22×C8—111no—
358C22×C8—111no—
359C22×C8—111no—
360C22×C8—111no—
361C22×C8—111no—
362C22×C8—222no—
363C22×C8—222no—
364C22×C8C22×D1111yescharacteristic
365C22⋊Q8—21no—
366C22⋊Q8—221no—
367C22⋊Q8—221no—
368C22⋊Q8—221no—
369C22⋊Q8—441no—
370C22⋊Q8—441no—
371#121—21no—
372#121—221no—
373#121—221no—
374#121—221no—
375#121—441no—
376#121—441no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—441no—
380C2×C22⋊C4—441no—
381C2×C22⋊C4—441no—
382SD32—22no—
383SD32—222no—
384SD32—222no—
385SD32—222no—
386C2×C16—22no—
387C2×C16—111no—
388C2×C16—114no—
389C2×C16—111no—
390C2×C16—222no—
391C2×C16—222no—
392C2×C16—222no—
393C2×C16—222no—
394C2×C16C22×D1111yescharacteristic
395C2×C16C22×D1111yescharacteristic
396#107—111no—
397#107—111no—
398#107—221no—
399#107—221no—
400#107C22×D1111yescharacteristic
401#107C22×D1111yescharacteristic
402#103—21no—
403#103—221no—
404#103—221no—
405#103—221no—
406#102—21no—
407#102—221no—
408#102—221no—
409#102—221no—
410C2×C11—22no—
411C2×C11—161no—
412C2×C11C2×#46611yescharacteristic
413C2×C11C22×SD3211yescharacteristic
414C2×C11C2×#50811yescharacteristic
415D11—22no—
416D11—161no—
417D11#221714yesdirect product factor
418C24—111no—
419C24—441no—
420C2×Q8—21no—
421C2×Q8—221no—
422C2×Q8—441no—
423C2×Q8—442no—
424C2×Q8—442no—
425C2×D4—21no—
426C2×D4—41no—
427C2×D4—221no—
428C2×D4—441no—
429C2×D4—442no—
430C2×D4—442no—
431C2×D4—441no—
432C2×D4—441no—
433C2×D4—441no—
434C2×D4—884no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—111no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—441no—
443C22×C4—441no—
444C22×C4—441no—
445C22×C4D4×D1111yescharacteristic
446Q16—21no—
447Q16—21no—
448Q16—221no—
449Q16—221no—
450Q16—442no—
451D8—21no—
452D8—21no—
453D8—221no—
454D8—221no—
455D8—442no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—111no—
459C2×C8—112no—
460C2×C8—112no—
461C2×C8—111no—
462C2×C8—222no—
463C2×C8—222no—
464C2×C8—222no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8D4×D1111yescharacteristic
468C2×C8C23×D1111yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—41no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—441no—
475C4⋊C4—441no—
476C4⋊C4—441no—
477C4⋊C4—441no—
478C4⋊C4—441no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—441no—
482C22⋊C4—441no—
483C22⋊C4—441no—
484C22⋊C4—441no—
485C22⋊C4—441no—
486C22⋊C4—441no—
487C16—21no—
488C16—112no—
489C16—221no—
490C16D4×D1112yescomplemented
491C11C2×#221711yescharacteristic, complemented, Sylow
492C23—41no—
493C23—111no—
494C23—111no—
495C23—114no—
496C23—222no—
497C23—222no—
498C23—441no—
499C23—882no—
500C23—882no—
501C23—882no—
502C23D8×D1111yescharacteristic
503Q8—41no—
504Q8—41no—
505Q8—441no—
506Q8—441no—
507Q8—882no—
508D4—41no—
509D4—41no—
510D4—82no—
511D4—441no—
512D4—441no—
513D4—882no—
514D4—882no—
515D4—882no—
516D4—882no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—111no—
523C2×C4—112no—
524C2×C4—112no—
525C2×C4—111no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—882no—
535C2×C4—882no—
536C2×C4—882no—
537C2×C4D8×D1111yescharacteristic
538C2×C4C2×D4×D1111yescharacteristic
539C8—21no—
540C8—112no—
541C8—221no—
542C8C2×D4×D1111yescharacteristic
543C8#41×D1111yescharacteristic
544C22—21no—
545C22—21no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22—112no—
550C22—112no—
551C22—112no—
552C22—112no—
553C22—228no—
554C22—221no—
555C22—221no—
556C22—881no—
557C22—881no—
558C22—881no—
559C22—1764no—
560C22D11×SD3212yescomplemented
561C22C2×D8×D1111yescharacteristic
562C4—21no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—112no—
567C4—221no—
568C4—881no—
569C4—881no—
570C4—881no—
571C4D11×#12111yescharacteristic
572C4D11×#13511yescharacteristic
573C2—22no—
574C2—114no—
575C2—161no—
576C2—222no—
577C2—1761no—
578C2D11×#46611yescharacteristic
579C2C2×D11×SD3211yescharacteristic
580C2D11×#50811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2217C2
socleC22×C11C22×D8
prime radicalD11×#466C2
hypercenter#2217D11
hypocenterC11C2×#2217
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. C2×D11×SD32C2semidirect
2. C22×C16×D11C2semidirect
3. D11×#467C2semidirect
5. #13070715C2semidirect
6. #13070714C2semidirect
7. #13070713C2semidirect
8. #13070712C2semidirect
9. #13070711C2semidirect
10. #13070710C2semidirect
11. #13070709C2semidirect
12. D11×#367C2semidirect
13. D11×#358C2semidirect
14. D11×#357C2semidirect
15. C11×#2217C2semidirect
21. C2×C11×SD32C22semidirect
22. C22×C11×C16C22semidirect
23. C11×#467C22semidirect
25. #10622801C22semidirect
26. C2×#66892C22semidirect
28. C2×#66891C22semidirect
29. #10622729C22semidirect
31. C22×C11⋊C16C22semidirect
35. C2×#66864C22semidirect
39. C2×C16×D11C22semidirect
40. C2×C16×D11C22semidirect
41. #10622500C22semidirect
49. C11×#367C22semidirect
50. C11×#358C22semidirect
51. C11×#357C22semidirect
52. #10622202C22semidirect
53. #10622200C22semidirect
54. #10622147C22semidirect
55. #10622143C22semidirect
56. #10622141C22semidirect
57. #10622130C22semidirect
58. #10622129C22semidirect
59. #10622128C22semidirect
60. #10622128C22semidirect
127. C16×D11D4semidirect
199. C11×C16C2×D4semidirect
201. C11⋊C16C2×D4semidirect
213. #2217D11direct (N × H)
225. C22×D11SD32semidirect
278. C2×SD32C2×D11semidirect
285. C22×C16C2×D11semidirect
291. #467C2×D11semidirect
305. #367C2×D11semidirect
309. #358C2×D11semidirect
313. #357C2×D11semidirect
319. C22×C11C2×SD32semidirect
330. C2×D11C2×SD32semidirect
417. D11#2217direct (N × H)
490. C16D4×D11semidirect
491. C11C2×#2217semidirect
560. C22D11×SD32semidirect

Maximal subgroups

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

subgroupindex
C2×D11×SD322
C22×C16×D112
D11×#4672
D11×#4662
#130707152
#130707142
#130707132
#130707122
#130707112
#130707102
#130707092
D11×#3672
D11×#3582
D11×#3572
C11×#22172
C2×#221711