Finite Group Databasebeta

← #14730897

Subgroups — #14730897

Order 2816.

1410 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079531C211yesmaximal, characteristic, complemented
2C2×#10622686C211yesmaximal, characteristic, complemented
3#13078096C211yesmaximal, characteristic, complemented
4#13067681C214yesmaximal, complemented
5#13067670C214yesmaximal, complemented
6#13067284C211yesmaximal, characteristic, complemented
7#13067067C211yesmaximal, characteristic, complemented
8#13066998C211yesmaximal, characteristic, complemented
9C11×#3498C211yesmaximal, characteristic, complemented
10C2×C11×H(5,𝔽2)—21no—
11C11×#550—21no—
12C11×#550C2212yescomplemented
13D42×C11—22no—
14D42×C11—22no—
15D42×C11—21no—
16D42×C11C2212yescomplemented
17C11×#535—22no—
18C11×#535—21no—
19C11×#532—21no—
20C11×#532C2211yescharacteristic
21C2×C11×#127—21no—
22C2×C11×#127C2211yescharacteristic
23C4×C11×#41C2211yescharacteristic
24C2×#67002—21no—
25C22×#4323—22no—
26C2×#66927C2211yescharacteristic, complemented
27#10622701—21no—
28#10622686—21no—
29#10622686—22no—
30#10622686C2214yescomplemented
31#10622649—22no—
32#10622640—21no—
33#10622640C2212yescomplemented
34#10622628—21no—
35#10622628C2212yescomplemented
36#10622628C2214yescomplemented
37#10622614—21no—
38#10622538C2211yescharacteristic, complemented
39#10622537C2211yescharacteristic, complemented
40C2×C4×C11⋊C8C2211yescharacteristic, complemented
41#10622182C2214yescomplemented
42Q8⋊(C11⋊C8)C2212yescomplemented
43D4⋊(C11⋊C8)C2214yescomplemented
44D4⋊(C11⋊C8)C2212yescomplemented
45C11×H(5,𝔽2)—44no—
46C11×H(5,𝔽2)—44no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—21no—
50C2×C11×#41D411yescharacteristic
51C22×D4×C11—22no—
52C22×D4×C11—24no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11—22no—
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11D412yes—
59C22×D44—21no—
60C22×D44—21no—
61C22×D44—21no—
62C11×C4⋊Q8D411yescharacteristic
63C11×#127—22no—
64C11×#127—22no—
65C11×#127—22no—
66C11×#127—21no—
67C11×#127—21no—
68C11×#127D411yescharacteristic
69C11×#127D412yes—
70C11×#127C2312yes—
71C11×#124—22no—
72C11×#124—21no—
73C11×#121—22no—
74C11×#121—24no—
75C11×#121—24no—
76C11×#121—21no—
77C11×#121—22no—
78C11×#121—22no—
79C11×#121—22no—
80C11×#121D412yes—
81C11×#120—24no—
82C11×#120—24no—
83C11×#120—24no—
84C4×Q8×C11D411yescharacteristic
85C4×Q8×C11C2311yescharacteristic
86C4×D4×C11—22no—
87C4×D4×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11—22no—
90C4×D4×C11—21no—
91C4×D4×C11D411yescharacteristic
92C4×D4×C11C2311yescharacteristic
93C4×D4×C11C2312yes—
94C11×#117—21no—
95C11×#117D411yescharacteristic
96C2×C42×C11—21no—
97C2×C42×C11C2311yescharacteristic
98#67002—44no—
99C2×#4325—22no—
100C2×#4323—28no—
101C2×#4323—22no—
102C2×#4323—24no—
103C2×#4323—48no—
104C2×#4318—21no—
105C22×C11⋊C8—21no—
106#66927—21no—
107#66927—21no—
108#66927—21no—
109#66927C2312yes—
110C22⋊(C11⋊C8)—21no—
111#66873—22no—
112#66873—22no—
113#66873—24no—
114C4⋊(C11⋊C8)—21no—
115C4⋊(C11⋊C8)C2312yes—
116C4⋊(C11⋊C8)C2312yes—
117C4×C11⋊C8—21no—
118C4×C11⋊C8—21no—
119C4×C11⋊C8C2312yes—
120#18620—111nomaximal, Sylow
121C24×C11—24no—
122C24×C11—22no—
123C23×D11—41no—
124C11×#41—22no—
125C11×#41—48no—
126C11×#41—44no—
127C11×#41—44no—
128C11×#41—42no—
129C11×#41—42no—
130C11×#41D814yescomplemented
131C2×Q8×C11—21no—
132C2×Q8×C11C2×D411yescharacteristic
133C2×D4×C11—21no—
134C2×D4×C11—24no—
135C2×D4×C11—24no—
136C2×D4×C11—22no—
137C2×D4×C11—24no—
138C2×D4×C11—24no—
139C2×D4×C11—22no—
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—21no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—48no—
147C2×D4×C11—44no—
148C2×D4×C11—416no—
149C2×D4×C11—44no—
150C2×D4×C11—44no—
151C2×D4×C11—42no—
152C2×D4×C11—42no—
153C2×D4×C11—82no—
154C2×D4×C11—84no—
155C2×D4×C11—84no—
156C2×D4×C11C2×D412yes—
157C2×D4×C11C2×D411yescharacteristic
158C2×D4×C11C2×D414yes—
159C22×C4×C11—21no—
160C22×C4×C11—24no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—22no—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C2×D44—22no—
168C2×D44—22no—
169C2×D44—22no—
170C2×D44—44no—
171C2×D44—41no—
172C2×D44—41no—
173C2×D44—41no—
174C2×D44—42no—
175C2×D44—42no—
176C2×D44—82no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4C2×D411yescharacteristic
181C11×C4⋊C4C2×D411yescharacteristic
182C11×C4⋊C4C2×D412yes—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—22no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11C2×D411yescharacteristic
194C42×C11C2×D411yescharacteristic
195C42×C11C2×D411yescharacteristic
196C42×C11C2411yescharacteristic
197#4325—44no—
198#4323—416no—
199#4323—44no—
200#4323—84no—
201#4318—42no—
202C2×C11⋊C8—24no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—22no—
206#3498D1111yescharacteristic, complemented
207#3205—111no—
208C2×#493—111no—
209#3038—111no—
210#1621—114no—
211#1619—114no—
212#1545—111no—
213#1492—111no—
214#1476—111no—
215C23×C11—21no—
216C23×C11—22no—
217C23×C11—24no—
218C23×C11—48no—
219C23×C11—44no—
220C23×C11—82no—
221C23×C11—82no—
222C23×C11—84no—
223C23×C11—84no—
224C23×C11#12011yescharacteristic
225C22×D11—42no—
226C22×D11—82no—
227C22×D11—82no—
228C22×D11—82no—
229Q8×C11—21no—
230Q8×C11—42no—
231Q8×C11C2×D812yescomplemented
232D4×C11—24no—
233D4×C11—21no—
234D4×C11—24no—
235D4×C11—44no—
236D4×C11—48no—
237D4×C11—48no—
238D4×C11—44no—
239D4×C11—42no—
240D4×C11—42no—
241D4×C11—44no—
242D4×C11—42no—
243D4×C11—44no—
244D4×C11—44no—
245D4×C11—42no—
246D4×C11—82no—
247D4×C11—84no—
248D4×C11—84no—
249D4×C11C2×D812yescomplemented
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—48no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11#12011yescharacteristic
263C2×C4×C11#12011yescharacteristic
264C2×C4×C11#12011yescharacteristic
265C2×C4×C11C2×D812yes—
266C2×C4×C11AGL(1,ℤ/8)12yes—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270D44—44no—
271D44—42no—
272D44—42no—
273D44—44no—
274D44—82no—
275D44—82no—
276D44—82no—
277C11⋊C8—24no—
278C11⋊C8—42no—
279C11⋊C8—42no—
280C2×H(5,𝔽2)—21no—
281C2×AGL(1,ℤ/8)—221no—
282C22×D8—222no—
283#550—21no—
284#550C2×D1112yescomplemented
285D42—22no—
286D42—22no—
287D42—21no—
288D42C2×D1112yescomplemented
289#535—22no—
290#535—21no—
291#532—21no—
292#532C2×D1111yescharacteristic
293C2×#127—21no—
294C2×#127—111no—
295C2×#127C2×D1111yescharacteristic
296C4×#41C2×D1111yescharacteristic
297#493—114no—
298#493—222no—
299#493—221no—
300#486—221no—
301#460—112no—
302#460—221no—
303#459—112no—
304#459—114no—
305#459—221no—
306#447—222no—
307#431—111no—
308#423—111no—
309#418—221no—
310C2×C4×C8—111no—
311#331—114no—
312Q8⋊C8—112no—
313D4⋊C8—112no—
314D4⋊C8—114no—
315C22×C11—21no—
316C22×C11—21no—
317C22×C11—22no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—44no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—44no—
324C22×C11—44no—
325C22×C11—42no—
326C22×C11—164no—
327C22×C11—168no—
328C22×C11#44712yes—
329C22×C11C2×#12011yescharacteristic
330C2×D11—82no—
331C2×D11—82no—
332C2×D11—82no—
333C2×D11—164no—
334C4×C11—22no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—42no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11#44712yes—
341C4×C11#45312yes—
342C4×C11C22×D811yescharacteristic
343C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
344C4×C11#57612yes—
345H(5,𝔽2)—44no—
346H(5,𝔽2)—44no—
347C2×#41—22no—
348C2×#41—22no—
349C2×#41—21no—
350C2×#41C22⋊D1111yescharacteristic
351C22×D4—22no—
352C22×D4—24no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—21no—
357C22×D4—21no—
358C22×D4—221no—
359C22×D4—221no—
360C22×D4—221no—
361C22×D4C22⋊D1112yes—
362AGL(1,ℤ/8)—444no—
363C2×SD16—222no—
364C2×D8—228no—
365C2×D8—222no—
366C2×D8—224no—
367C2×D8—448no—
368C2×M16—221no—
369C22×C8—221no—
370C4⋊Q8C22⋊D1111yescharacteristic
371#127—22no—
372#127—22no—
373#127—22no—
374#127—21no—
375#127—21no—
376#127—112no—
377#127—221no—
378#127—221no—
379#127—221no—
380#127C22⋊D1111yescharacteristic
381#127C22⋊D1112yes—
382#127C22×D1112yes—
383#124—22no—
384#124—21no—
385#121—22no—
386#121—24no—
387#121—24no—
388#121—21no—
389#121—22no—
390#121—22no—
391#121—22no—
392#121C22⋊D1112yes—
393#120—24no—
394#120—24no—
395#120—24no—
396C4×Q8C22⋊D1111yescharacteristic
397C4×Q8C22×D1111yescharacteristic
398C4×D4—22no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—22no—
402C4×D4—21no—
403C4×D4C22⋊D1111yescharacteristic
404C4×D4C22×D1111yescharacteristic
405C4×D4C22×D1112yes—
406#117—21no—
407#117C22⋊D1111yescharacteristic
408C2×C42—21no—
409C2×C42C22×D1111yescharacteristic
410C4⋊C8—112no—
411C4⋊C8—112no—
412C4⋊C8—221no—
413#102—222no—
414#102—222no—
415#102—224no—
416C22⋊C8—221no—
417C4×C8—112no—
418C4×C8—221no—
419C4×C8—221no—
420C2×C11—22no—
421C2×C11—42no—
422C2×C11—82no—
423C2×C11—84no—
424C2×C11C2×#44711yescharacteristic
425C2×C11#300811yescharacteristic
426C2×C11C2×#45311yescharacteristic
427D11—162no—
428C24—24no—
429C24—22no—
430C24—441no—
431#41—22no—
432#41—48no—
433#41—44no—
434#41—44no—
435#41—42no—
436#41—42no—
437#41#432314yescomplemented
438C2×Q8—21no—
439C2×Q8C2×C22⋊D1111yescharacteristic
440C2×D4—21no—
441C2×D4—24no—
442C2×D4—24no—
443C2×D4—22no—
444C2×D4—24no—
445C2×D4—24no—
446C2×D4—22no—
447C2×D4—21no—
448C2×D4—22no—
449C2×D4—21no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—48no—
454C2×D4—44no—
455C2×D4—416no—
456C2×D4—44no—
457C2×D4—44no—
458C2×D4—42no—
459C2×D4—42no—
460C2×D4—82no—
461C2×D4—84no—
462C2×D4—84no—
463C2×D4—222no—
464C2×D4—222no—
465C2×D4—222no—
466C2×D4—444no—
467C2×D4—442no—
468C2×D4—442no—
469C2×D4—441no—
470C2×D4—441no—
471C2×D4—441no—
472C2×D4—882no—
473C2×D4C2×C22⋊D1112yes—
474C2×D4C2×C22⋊D1111yescharacteristic
475C2×D4C2×C22⋊D1114yes—
476C22×C4—21no—
477C22×C4—24no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484SD16—444no—
485D8—4416no—
486D8—444no—
487D8—884no—
488M16—442no—
489C2×C8—224no—
490C2×C8—222no—
491C2×C8—222no—
492C2×C8—222no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4C2×C22⋊D1111yescharacteristic
497C4⋊C4C2×C22⋊D1111yescharacteristic
498C4⋊C4C2×C22⋊D1112yes—
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—22no—
504C22⋊C4—21no—
505C22⋊C4—22no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42C2×C22⋊D1111yescharacteristic
510C42C2×C22⋊D1111yescharacteristic
511C42C2×C22⋊D1111yescharacteristic
512C42C23×D1111yescharacteristic
513C11#1862011yescharacteristic, complemented, Sylow
514C23—21no—
515C23—22no—
516C23—24no—
517C23—48no—
518C23—44no—
519C23—82no—
520C23—82no—
521C23—84no—
522C23—84no—
523C23—442no—
524C23—882no—
525C23—882no—
526C23—882no—
527C23#6700611yescharacteristic
528Q8—21no—
529Q8—42no—
530Q8C2×#432312yescomplemented
531D4—24no—
532D4—21no—
533D4—24no—
534D4—44no—
535D4—48no—
536D4—48no—
537D4—44no—
538D4—42no—
539D4—42no—
540D4—42no—
541D4—44no—
542D4—44no—
543D4—42no—
544D4—44no—
545D4—82no—
546D4—84no—
547D4—84no—
548D4—444no—
549D4—442no—
550D4—442no—
551D4—444no—
552D4—882no—
553D4—882no—
554D4—882no—
555D4C2×#432312yescomplemented
556C2×C4—21no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—48no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4C2×#432312yes—
569C2×C4#6698512yes—
570C2×C4#6700611yescharacteristic
571C2×C4#6700611yescharacteristic
572C2×C4#6700611yescharacteristic
573C2×C4C22×C22⋊D1111yescharacteristic
574C2×C4C22×C22⋊D1111yescharacteristic
575C2×C4C22×C22⋊D1111yescharacteristic
576C8—224no—
577C8—442no—
578C8—442no—
579C22—21no—
580C22—21no—
581C22—22no—
582C22—41no—
583C22—41no—
584C22—44no—
585C22—42no—
586C22—42no—
587C22—44no—
588C22—44no—
589C22—42no—
590C22—164no—
591C22—168no—
592C22—882no—
593C22—882no—
594C22—882no—
595C22—1764no—
596C22#1062283012yes—
597C22C2×#6700611yescharacteristic
598C4—22no—
599C4—21no—
600C4—21no—
601C4—42no—
602C4—41no—
603C4—41no—
604C4#1062283012yes—
605C4#1062285412yes—
606C4C22×#432311yescharacteristic
607C4C2×#6698511yescharacteristic
608C4#1062336612yes—
609C2—22no—
610C2—42no—
611C2—82no—
612C2—84no—
613C2—1762no—
614C2C2×#1062283011yescharacteristic
615C2#1307788411yescharacteristic
616C2C2×#1062285411yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3498C2
socleC22×C11C2×#120
hypercenter#3498D11
hypocenterC11#18620
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3498

Complements

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

NH ≅ G/Ntype
1. #13079531C2semidirect
2. C2×#10622686C2semidirect
3. #13078096C2semidirect
4. #13067681C2semidirect
5. #13067670C2semidirect
6. #13067284C2semidirect
7. #13067067C2semidirect
8. #13066998C2semidirect
9. C11×#3498C2semidirect
12. C11×#550C22semidirect
16. D42×C11C22semidirect
26. C2×#66927C22semidirect
30. #10622686C22semidirect
33. #10622640C22semidirect
35. #10622628C22semidirect
36. #10622628C22semidirect
38. #10622538C22semidirect
39. #10622537C22semidirect
40. C2×C4×C11⋊C8C22semidirect
41. #10622182C22semidirect
42. Q8⋊(C11⋊C8)C22semidirect
43. D4⋊(C11⋊C8)C22semidirect
44. D4⋊(C11⋊C8)C22semidirect
130. C11×#41D8semidirect
206. #3498D11semidirect
231. Q8×C11C2×D8semidirect
249. D4×C11C2×D8semidirect
284. #550C2×D11semidirect
288. D42C2×D11semidirect
437. #41#4323semidirect
513. C11#18620semidirect
530. Q8C2×#4323semidirect
555. D4C2×#4323semidirect

Maximal subgroups

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

subgroupindex
#130795312
C2×#106226862
#130780962
#130676812
#130676702
#130672842
#130670672
#130669982
C11×#34982
#1862011