Finite Group Databasebeta

← #14769688

Subgroups — #14769688

Order 2816.

1336 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×#10623368C211yesmaximal, characteristic
2#13077475C212yesmaximal, complemented
3#13077075C211yesmaximal, characteristic, complemented
4#13069511C212yesmaximal, complemented
5#13069110C212yesmaximal, complemented
6#13069106C212yesmaximal, complemented
7#13068660C211yesmaximal, characteristic, complemented
8#13068591C211yesmaximal, characteristic, complemented
9#13068584C211yesmaximal, characteristic, complemented
10#13068418C211yesmaximal, characteristic, complemented
11C11×#2884C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2211yescharacteristic
13C2×#67042C2211yescharacteristic
14C11×#519C2212yescomplemented
15#10623368—24no—
16#10623368—24no—
17C2×#67003C412yescomplemented
18C2×#67003C2211yescharacteristic
19C2×#67002C412yescomplemented
20C2×#67002C2211yescharacteristic
21C2×#67001C2211yescharacteristic
22C2×#66995C412yescomplemented
23C2×#66995C2211yescharacteristic
24C22×#4325C412yescomplemented
25C22×#4325C2211yescharacteristic
26#10623052C2212yes—
27C11×#410—24no—
28C11×#410C2211yescharacteristic
29C11×#410C2211yescharacteristic
30C11×#410C2212yescomplemented
31#10622853C2211yescharacteristic
32#10622850C2211yescharacteristic
33#10622849C2212yescomplemented
34#10622838C2212yescomplemented
35#10622639—24no—
36C4×#4325—24no—
37#10622619C2212yes—
38#10622618C2212yes—
39#10622614C2212yes—
40#10622611C2212yescomplemented
41#10622610C2212yescomplemented
42D11×#99—24no—
43#10622171C2212yescomplemented
44#10622169C2212yescomplemented
45C11×2−1+4—24no—
46C11×2−1+4—42no—
47C2×C11×#41—22no—
48C2×C11×#41—21no—
49C2×C11×#41C2×C412yescomplemented
50C2×C11×#41C2311yescharacteristic
51C2×C11×#41C2311yescharacteristic
52C22×Q8×C11—21no—
53C22×Q8×C11C2×C412yescomplemented
54C22×Q8×C11C2311yescharacteristic
55#67042—24no—
56#67042—42no—
57C2×#4343—21no—
58C2×D4×D11—22no—
59C2×D4×D11—21no—
60C2×#4339C2×C412yes—
61C2×#4339C2311yescharacteristic
62C22×D44C2×C412yes—
63C22×D44C2311yescharacteristic
64C4×Q8×C11—24no—
65C4×Q8×C11—42no—
66C11×#117—24no—
67C11×#117C2312yes—
68C11×#117C2312yes—
69#67003—24no—
70#67003—24no—
71#67003—22no—
72#67003—22no—
73#67002—24no—
74#67002—28no—
75#67001—22no—
76#67001—22no—
77C2×#4326C2×C411yescharacteristic, complemented
78C2×#4326C2×C412yescomplemented
79#66995—24no—
80#66995—28no—
81C2×#4325—24no—
82C2×#4325—24no—
83C2×#4325C2×C412yes—
84C2×#4325C2×C412yes—
85C2×#4325C2×C412yes—
86C2×#4325C2×C411yescharacteristic, complemented
87C2×#4325C2×C412yescomplemented
88C2×#4325D414yes—
89C2×#4325D414yes—
90C2×#4324C2×C411yescharacteristic, complemented
91C2×#4323C2×C412yes—
92C2×#4323C2×C411yescharacteristic, complemented
93#66979C2312yes—
94C2×#4318C2×C412yescomplemented
95C2×#4318C2312yes—
96C2×#4318C2311yescharacteristic
97C22×C11⋊C8C2×C412yescomplemented
98C22×C11⋊C8C2311yescharacteristic
99#66946—42no—
100C22⋊C4×D11—24no—
101C4×D44—24no—
102C11×#99—22no—
103C11×#99—24no—
104C11×#99D414yes—
105#66901—42no—
106#66900—21no—
107#66899—24no—
108#66898—22no—
109#66897—21no—
110#66873—24no—
111#66872—22no—
112#66871—22no—
113#66870—24no—
114#66869—42no—
115#66867—22no—
116C4×C11⋊C8—22no—
117#22456—111nomaximal, Sylow
118C23×D11—21no—
119C23×D11—22no—
120C11×#41—22no—
121C11×#41—22no—
122C11×#41—24no—
123C11×#41—22no—
124C11×#41—22no—
125C11×#41—42no—
126C11×#41—48no—
127C11×#41—44no—
128C2×Q8×C11—22no—
129C2×Q8×C11—21no—
130C2×Q8×C11—22no—
131C2×Q8×C11—24no—
132C2×Q8×C11—42no—
133C2×Q8×C11—44no—
134C2×Q8×C11C22×C411yescharacteristic
135C2×Q8×C11C22×C412yes—
136C2×Q8×C11C2×D414yes—
137C2×Q8×C11#4111yescharacteristic
138C2×D4×C11—22no—
139C2×D4×C11—21no—
140C2×D4×C11C22×C411yescharacteristic
141C2×D4×C11C2×D412yes—
142C2×D4×C11#4111yescharacteristic
143C22×C4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C2411yescharacteristic
149C2×C22⋊D11—22no—
150C2×C22⋊D11—21no—
151#4343—44no—
152D4×D11—48no—
153D4×D11—44no—
154#4339—24no—
155#4339—22no—
156#4339—22no—
157#4339—42no—
158C2×D44—24no—
159C2×D44—22no—
160C2×D44—21no—
161C2×D44—22no—
162C2×D44—42no—
163C2×D44C22×C411yescharacteristic
164C2×D44C22×C412yes—
165C2×D44C2×D414yes—
166C2×C4×D11—22no—
167C2×C4×D11—21no—
168C2×C4×D11—44no—
169C2×Dic22C22×C411yescharacteristic
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—44no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4C2×D414yes—
175C42×C11—22no—
176C42×C11—22no—
177C42×C11—44no—
178C22⋊Dic11—22no—
179#4326—22no—
180#4326—24no—
181#4325—24no—
182#4325—21no—
183#4325—21no—
184#4325—24no—
185#4325C22⋊C414yes—
186#4325C22⋊C414yes—
187#4325C22⋊C418yes—
188#4324—21no—
189#4324—21no—
190#4323—24no—
191#4323—22no—
192(C2×D11)⋊C4—44no—
193C4⋊Dic11—22no—
194C4×Dic11—22no—
195#4318—24no—
196#4318—22no—
197#4318—22no—
198#4318—22no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8C22×C412yes—
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C2×D412yes—
206C2×C11⋊C8C2×D412yes—
207C2×#577—111no—
208#2949—112no—
209#2884D1111yescharacteristic, complemented
210#2883—111no—
211#1976—112no—
212#1905—112no—
213#1904—112no—
214#1812—111no—
215#1796—111no—
216#1795—111no—
217#1757—111no—
218C23×C11—21no—
219C23×C11C4×D412yes—
220C23×C11C22×D411yescharacteristic
221C22×D11—22no—
222C22×D11—24no—
223C22×D11—21no—
224C22×D11—44no—
225C22×D11—161no—
226C22×D11—162no—
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—24no—
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11—44no—
233Q8×C11C2×C22⋊C414yes—
234D4×C11—24no—
235D4×C11—21no—
236D4×C11—21no—
237D4×C11—22no—
238D4×C11—44no—
239D4×C11—42no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—24no—
246C2×C4×C11—44no—
247C2×C4×C11—44no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11C4×D412yes—
251C2×C4×C11C23×C411yescharacteristic
252C2×C4×C11C22×D412yes—
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11H(5,𝔽2)12yes—
255C22⋊D11—44no—
256C22⋊D11—42no—
257C2×Dic11—21no—
258C2×Dic11—42no—
259D44—21no—
260D44—22no—
261D44—21no—
262D44—24no—
263D44—44no—
264D44C2×C22⋊C414yes—
265C4×D11—44no—
266C4×D11—42no—
267C4×D11—164no—
268Dic22—21no—
269Dic22—21no—
270C11⋊C8—22no—
271C11⋊C8—42no—
272C11⋊C8C2×C22⋊C411yescharacteristic
273C11⋊C8C2×C22⋊C411yescharacteristic
274C11⋊C8C2×C22⋊C412yes—
275C2×2−1+4C2×D1111yescharacteristic
276C2×H(5,𝔽2)—111no—
277#577—224no—
278#577—224no—
279C2×#137—111no—
280C2×#137—112no—
281C2×AGL(1,ℤ/8)—111no—
282C2×AGL(1,ℤ/8)—112no—
283C2×#135—111no—
284C2×#135—112no—
285C22×SD16—111no—
286C22×SD16—112no—
287C2×#131—111no—
288#519C2×D1112yescomplemented
289#518—112no—
290#440—224no—
291C4×SD16—224no—
292#427—112no—
293#421—112no—
294#421—112no—
295#419—112no—
296#418—112no—
297#413—111no—
298#410—24no—
299#410—111no—
300#410—112no—
301#410C2×D1111yescharacteristic
302#410C2×D1111yescharacteristic
303#410C2×D1112yescomplemented
304C2×#99—224no—
305#405—112no—
306#344—112no—
307H(3,ℤ/4)—112no—
308C22×C11—22no—
309C22×C11—41no—
310C22×C11—42no—
311C22×C11—41no—
312C22×C11—81no—
313C22×C11C2×C4×D411yescharacteristic
314C22×C11D4212yes—
315C2×D11—24no—
316C2×D11—41no—
317C2×D11—82no—
318C2×D11—84no—
319C2×D11—81no—
320C2×D11—164no—
321C4×C11—24no—
322C4×C11—22no—
323C4×C11—44no—
324C4×C11—41no—
325C4×C11—82no—
326C4×C11C22×C22⋊C411yescharacteristic
327C4×C11#51811yescharacteristic
328C4×C11#54612yes—
329Dic11—41no—
330Dic11—82no—
3312−1+4—24no—
3322−1+4—42no—
333H(5,𝔽2)—224no—
334H(5,𝔽2)—442no—
335C2×#41—21no—
336C2×#41—22no—
337C2×#41—112no—
338C2×#41—111no—
339C2×#41—221no—
340C2×#41C4×D1112yescomplemented
341C2×#41C22×D1111yescharacteristic
342C2×#41C22×D1111yescharacteristic
343C22×Q8—21no—
344C22×Q8C4×D1112yescomplemented
345C22×Q8C22×D1111yescharacteristic
346C22×D4—112no—
347C22×D4—111no—
348C22×D4—221no—
349C22×D4—222no—
350#137—228no—
351#137—224no—
352AGL(1,ℤ/8)—228no—
353AGL(1,ℤ/8)—224no—
354#135—222no—
355#135—222no—
356#135—224no—
357#135—224no—
358C2×Q16—111no—
359C2×Q16—112no—
360C2×SD16—112no—
361C2×SD16—112no—
362C2×SD16—114no—
363C2×SD16—114no—
364C2×SD16—111no—
365C2×SD16—112no—
366C2×SD16—112no—
367C2×SD16—111no—
368C2×SD16—224no—
369C2×SD16—224no—
370C2×D8—112no—
371C2×D8—111no—
372#131—222no—
373#131—222no—
374C2×M16—112no—
375C2×M16—111no—
376C2×M16—112no—
377C22×C8—111no—
378C22×C8—112no—
379C4×Q8—24no—
380C4×Q8—42no—
381C4×D4—224no—
382C4×D4—442no—
383#117—24no—
384#117—112no—
385#117C22×D1112yes—
386#117C22×D1112yes—
387C2×C22⋊C4—224no—
388#107—222no—
389#106—222no—
390#104—442no—
391#104—442no—
392#103—224no—
393#102—224no—
394#101—221no—
395#100—221no—
396#99—22no—
397#99—24no—
398#99—222no—
399#99—224no—
400#99C22⋊D1114yes—
401#97—222no—
402C4×C8—222no—
403C2×C11—22no—
404C2×C11—21no—
405C2×C11—42no—
406C2×C11—81no—
407C2×C11D4×C22⋊C411yescharacteristic
408D11—44no—
409D11—81no—
410C24—221no—
411C24—222no—
412#41—22no—
413#41—22no—
414#41—24no—
415#41—22no—
416#41—22no—
417#41—42no—
418#41—48no—
419#41—44no—
420#41—224no—
421#41—222no—
422#41—222no—
423#41—442no—
424#41—444no—
425C2×Q8—22no—
426C2×Q8—21no—
427C2×Q8—22no—
428C2×Q8—24no—
429C2×Q8—42no—
430C2×Q8—44no—
431C2×Q8—111no—
432C2×Q8C2×C4×D1111yescharacteristic
433C2×Q8C2×C4×D1112yes—
434C2×Q8#433911yescharacteristic
435C2×Q8D4×D1114yes—
436C2×D4—22no—
437C2×D4—21no—
438C2×D4—112no—
439C2×D4—111no—
440C2×D4—114no—
441C2×D4—224no—
442C2×D4—222no—
443C2×D4—221no—
444C2×D4—222no—
445C2×D4—221no—
446C2×D4—222no—
447C2×D4—442no—
448C2×D4—444no—
449C2×D4—448no—
450C2×D4C2×C4×D1111yescharacteristic
451C2×D4#433911yescharacteristic
452C2×D4C2×C22⋊D1112yes—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—222no—
458C22×C4—221no—
459C22×C4—444no—
460C22×C4C2×C4×D1112yes—
461C22×C4C23×D1111yescharacteristic
462Q16—222no—
463Q16—224no—
464SD16—114no—
465SD16—114no—
466SD16—118no—
467SD16—221no—
468SD16—221no—
469SD16—221no—
470SD16—221no—
471SD16—224no—
472SD16—224no—
473D8—222no—
474D8—224no—
475M16—224no—
476M16—222no—
477M16—222no—
478M16—222no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—112no—
482C2×C8—112no—
483C2×C8—112no—
484C2×C8—222no—
485C2×C8—222no—
486C2×C8—222no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—44no—
490C4⋊C4—222no—
491C22⋊C4—22no—
492C22⋊C4—222no—
493C22⋊C4—444no—
494C22⋊C4C2×C22⋊D1114yes—
495C42—22no—
496C42—22no—
497C42—44no—
498C42—222no—
499C11#2245611yescharacteristic, complemented, Sylow
500C23—21no—
501C23—222no—
502C23—224no—
503C23—221no—
504C23—444no—
505C23—1761no—
506C23—1762no—
507C23C4×C22⋊D1112yes—
508C23C22×C22⋊D1111yescharacteristic
509Q8—22no—
510Q8—24no—
511Q8—22no—
512Q8—21no—
513Q8—21no—
514Q8—44no—
515Q8—221no—
516Q8—221no—
517Q8C22⋊C4×D1114yes—
518D4—24no—
519D4—21no—
520D4—21no—
521D4—22no—
522D4—44no—
523D4—42no—
524D4—114no—
525D4—221no—
526D4—222no—
527D4—221no—
528D4—224no—
529D4—444no—
530D4—444no—
531D4—442no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—24no—
538C2×C4—44no—
539C2×C4—44no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—221no—
543C2×C4—444no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—1764no—
547C2×C4C4×C22⋊D1112yes—
548C2×C4C22×C4×D1111yescharacteristic
549C2×C4C2×#433911yescharacteristic
550C2×C4C2×D4×D1112yes—
551C2×C4#6703712yes—
552C8—111no—
553C8—111no—
554C8—112no—
555C8—222no—
556C8—442no—
557C22—22no—
558C22—41no—
559C22—42no—
560C22—41no—
561C22—81no—
562C22—224no—
563C22—441no—
564C22—884no—
565C22—882no—
566C22—881no—
567C22—1764no—
568C22C2×C4×C22⋊D1111yescharacteristic
569C22D4×C22⋊D1112yes—
570C4—24no—
571C4—22no—
572C4—44no—
573C4—41no—
574C4—82no—
575C4—441no—
576C4—882no—
577C4C2×C22⋊C4×D1111yescharacteristic
578C4#1062301711yescharacteristic
579C4#1062302112yes—
580C2—22no—
581C2—21no—
582C2—42no—
583C2—81no—
584C2—444no—
585C2—881no—
586C2C22⋊C4×C22⋊D1111yescharacteristic
subgroupG/H
centerC2C22⋊C4×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2884C2
socleC2×C11D4×C22⋊C4
prime radicalC2×#10623368C2
cosocleC22×C4×C11C24
hypercenter#2884D11
hypocenterC11#22456
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2884

Complements

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

NH ≅ G/Ntype
2. #13077475C2semidirect
3. #13077075C2semidirect
4. #13069511C2semidirect
5. #13069110C2semidirect
6. #13069106C2semidirect
7. #13068660C2semidirect
8. #13068591C2semidirect
9. #13068584C2semidirect
10. #13068418C2semidirect
11. C11×#2884C2semidirect
14. C11×#519C22semidirect
17. C2×#67003C4semidirect
19. C2×#67002C4semidirect
22. C2×#66995C4semidirect
24. C22×#4325C4semidirect
30. C11×#410C22semidirect
33. #10622849C22semidirect
34. #10622838C22semidirect
40. #10622611C22semidirect
41. #10622610C22semidirect
43. #10622171C22semidirect
44. #10622169C22semidirect
49. C2×C11×#41C2×C4semidirect
53. C22×Q8×C11C2×C4semidirect
77. C2×#4326C2×C4semidirect
78. C2×#4326C2×C4semidirect
86. C2×#4325C2×C4semidirect
87. C2×#4325C2×C4semidirect
90. C2×#4324C2×C4semidirect
92. C2×#4323C2×C4semidirect
94. C2×#4318C2×C4semidirect
97. C22×C11⋊C8C2×C4semidirect
209. #2884D11semidirect
288. #519C2×D11semidirect
303. #410C2×D11semidirect
340. C2×#41C4×D11semidirect
344. C22×Q8C4×D11semidirect
499. C11#22456semidirect

Maximal subgroups

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

subgroupindex
C2×#106233682
#130774752
#130770752
#130695112
#130691102
#130691062
#130686602
#130685912
#130685842
#130684182
C11×#28842
#2245611