Finite Group Databasebeta

← #14731549

Subgroups — #14731549

Order 2816.

1000 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079923C211yesmaximal, characteristic, complemented
2#13079176C211yesmaximal, characteristic, complemented
3#13078080C211yesmaximal, characteristic, complemented
4#13067900C212yesmaximal, complemented
5#13067844C212yesmaximal, complemented
6#13067705C212yesmaximal, complemented
7#13067699C212yesmaximal, complemented
8#13067306C211yesmaximal, characteristic, complemented
9#13067067C211yesmaximal, characteristic, complemented
10C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11C11×#3506C211yesmaximal, characteristic, complemented
12C11×#559—22no—
13C11×#556—21no—
14C11×#555C2212yes—
15C11×#553—22no—
16C11×#550—21no—
17C11×#547C2212yes—
18C11×#538—22no—
19C11×#535—21no—
20C11×#533C2211yescharacteristic
21C11×#532C2211yescharacteristic
22C11×#525—22no—
23C11×#520—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C2×#66985—21no—
26#10623008C2211yescharacteristic
27#10622701C2211yescharacteristic, complemented
28#10622700—21no—
29#10622698C2211yescharacteristic, complemented
30#10622694C2211yescharacteristic, complemented
31#10622692C2211yescharacteristic, complemented
32#10622685—21no—
33#10622661—22no—
34#10622651—22no—
35C4×#4325—22no—
36#10622632C2212yes—
37#10622629—22no—
38#10622628C2212yes—
39#10622628C2212yescomplemented
40#10622620C2212yescomplemented
41#10622579—21no—
42#10622537C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622185C2212yescomplemented
46#10622184C2212yescomplemented
47D4⋊(C11⋊C8)C2212yes—
48D4⋊(C11⋊C8)C2212yes—
49D4⋊(C11⋊C8)C2212yescomplemented
50D4⋊(C11⋊C8)C2212yescomplemented
51C2×C11×#41—22no—
52C2×C11×#41—21no—
53C22×D4×C11D411yescharacteristic
54C23×C4×C11—21no—
55C2×#4339—21no—
56C11×C4⋊Q8D411yescharacteristic
57C11×C4⋊Q8C2311yescharacteristic
58C11×C4⋊Q8C2311yescharacteristic
59C11×#127—22no—
60C11×#127D411yescharacteristic
61C11×#126—24no—
62C11×#125—21no—
63C11×#124—22no—
64C11×#124—24no—
65C11×#124—21no—
66C11×#123—24no—
67C11×#123—24no—
68C11×C22⋊Q8—21no—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8D412yes—
71C11×#121—24no—
72C11×#121—22no—
73C11×#121—22no—
74C11×#121—22no—
75C11×#121—21no—
76C11×#121D412yes—
77C11×#120—24no—
78C4×Q8×C11—22no—
79C4×Q8×C11—21no—
80C4×Q8×C11D412yes—
81C4×D4×C11—24no—
82C4×D4×C11—22no—
83C4×D4×C11—24no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11D412yes—
88C4×D4×C11C2312yes—
89C4×D4×C11C2312yes—
90C11×#117—21no—
91C11×#117—22no—
92C11×#117—22no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C22⋊C4—21no—
96C2×C42×C11C2311yescharacteristic
97C2×#4325—22no—
98C2×#4324—22no—
99#66985—44no—
100C2×#4323—22no—
101C2×#4323—22no—
102#66983—21no—
103#66983—21no—
104C2×#4318—21no—
105C22×C11⋊C8—21no—
106C22×C11⋊C8—21no—
107#66928—21no—
108#66927C2311yescharacteristic
109C4×D44—21no—
110C4×D44—21no—
111#66922C2311yescharacteristic
112#66899—22no—
113#66896—22no—
114#66874—22no—
115#66873—22no—
116#66873—22no—
117#66873—22no—
118#66872—22no—
119#66871—22no—
120C4⋊(C11⋊C8)—21no—
121C4⋊(C11⋊C8)—21no—
122C4⋊(C11⋊C8)C2312yes—
123C4⋊(C11⋊C8)C2312yes—
124C4×C11⋊C8—21no—
125C4×C11⋊C8C2311yescharacteristic
126C4×C11⋊C8C2311yescharacteristic
127#18680—111nomaximal, Sylow
128C24×C11—21no—
129C11×#41—42no—
130C11×#41—42no—
131C11×#41—82no—
132C11×#41—82no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11C2×D412yes—
136C2×D4×C11—22no—
137C2×D4×C11—24no—
138C2×D4×C11—24no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11C2×D412yes—
145C2×D4×C11C2×D412yes—
146C22×C4×C11—24no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—81no—
152C22×C4×C11—81no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C2×C22⋊D11—41no—
157#4339—42no—
158#4339—42no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×C4×D11—41no—
163C2×Dic22—21no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4C2×D412yes—
173C11×C4⋊C4C2×D412yes—
174C11×C4⋊C4C2×D412yes—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C42×C11—24no—
184C42×C11—22no—
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11C2411yescharacteristic
189#4325—44no—
190#4324—44no—
191#4323—44no—
192#4323—82no—
193(C2×D11)⋊C4—41no—
194(C2×D11)⋊C4—41no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197#4318—42no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—42no—
203C2×C11⋊C8—81no—
204#3506D1111yescharacteristic, complemented
205#3245—111no—
206#3167—111no—
207#3036—111no—
208#1654—112no—
209#1646—112no—
210#1625—112no—
211#1624—112no—
212#1550—111no—
213#1492—111no—
214C2×D4⋊C8—111no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—42no—
218C23×C11—81no—
219C23×C11—81no—
220C23×C11#12011yescharacteristic
221C22×D11—41no—
222Q8×C11—42no—
223Q8×C11—41no—
224Q8×C11—41no—
225Q8×C11—42no—
226D4×C11—22no—
227D4×C11—22no—
228D4×C11—22no—
229D4×C11—22no—
230D4×C11—44no—
231D4×C11—42no—
232D4×C11—42no—
233D4×C11—81no—
234D4×C11—84no—
235D4×C11—84no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—41no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—82no—
248C2×C4×C11—81no—
249C2×C4×C11—84no—
250C2×C4×C11#12011yescharacteristic
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#13512yes—
254C2×C4×C11AGL(1,ℤ/8)12yes—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C22⋊D11—82no—
259C2×Dic11—41no—
260D44—42no—
261D44—41no—
262D44—41no—
263D44—41no—
264D44—41no—
265C4×D11—82no—
266Dic22—41no—
267Dic22—41no—
268C11⋊C8—22no—
269C11⋊C8—41no—
270C11⋊C8—42no—
271C11⋊C8—42no—
272C2×AGL(1,ℤ/8)—221no—
273#559—22no—
274#556—21no—
275#555C2×D1112yes—
276#553—22no—
277#550—21no—
278#547C2×D1112yes—
279#538—22no—
280#535—21no—
281#533C2×D1111yescharacteristic
282#532—111no—
283#532C2×D1111yescharacteristic
284#525—22no—
285#520—21no—
286C2×C4×D4C2×D1111yescharacteristic
287#498—111no—
288#492—111no—
289#487—111no—
290#486—111no—
291#474—112no—
292#474—221no—
293#466—222no—
294#465—222no—
295#463—222no—
296#461—112no—
297#459—112no—
298#459—112no—
299#459—221no—
300C4×SD16—222no—
301#423—111no—
302C2×C4⋊C8—111no—
303#417—221no—
304C2×C4×C8—111no—
305#333—112no—
306#332—112no—
307D4⋊C8—112no—
308D4⋊C8—112no—
309D4⋊C8—112no—
310D4⋊C8—112no—
311C22×C11—21no—
312C22×C11—21no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—84no—
320C22×C11#44912yes—
321C22×C11C2×#12011yescharacteristic
322C2×D11—81no—
323C2×D11—81no—
324C2×D11—81no—
325C4×C11—21no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—42no—
329C4×C11—42no—
330C4×C11—42no—
331C4×C11—42no—
332C4×C11#44912yes—
333C4×C11C2×#13511yescharacteristic
334C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
335C4×C11#57611yescharacteristic
336C4×C11#57711yescharacteristic
337Dic11—81no—
338C2×#41—22no—
339C2×#41—21no—
340C2×#41—221no—
341C22×D4C22⋊D1111yescharacteristic
342C23×C4—21no—
343AGL(1,ℤ/8)—444no—
344C2×SD16—222no—
345C2×SD16—222no—
346C2×D8—222no—
347C2×D8—222no—
348C2×M16—221no—
349C22×C8—221no—
350C22×C8—221no—
351C4⋊Q8—111no—
352C4⋊Q8C22⋊D1111yescharacteristic
353C4⋊Q8C22×D1111yescharacteristic
354C4⋊Q8C22×D1111yescharacteristic
355#127—22no—
356#127—111no—
357#127C22⋊D1111yescharacteristic
358#126—24no—
359#125—21no—
360#124—22no—
361#124—24no—
362#124—21no—
363#124—221no—
364#123—24no—
365#123—24no—
366C22⋊Q8—21no—
367C22⋊Q8—22no—
368C22⋊Q8C22⋊D1112yes—
369#121—24no—
370#121—22no—
371#121—22no—
372#121—22no—
373#121—21no—
374#121—221no—
375#121—221no—
376#121C22⋊D1112yes—
377#120—24no—
378C4×Q8—22no—
379C4×Q8—21no—
380C4×Q8C22⋊D1112yes—
381C4×D4—24no—
382C4×D4—22no—
383C4×D4—24no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—221no—
388C4×D4—221no—
389C4×D4C22⋊D1112yes—
390C4×D4C22×D1112yes—
391C4×D4C22×D1112yes—
392#117—21no—
393#117—22no—
394#117—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4C22⋊D1111yescharacteristic
397C2×C22⋊C4—21no—
398C2×C42C22×D1111yescharacteristic
399#107—222no—
400#106—222no—
401C4⋊C8—112no—
402C4⋊C8—112no—
403C4⋊C8—221no—
404C4⋊C8—221no—
405#103—222no—
406#103—222no—
407#102—222no—
408#102—222no—
409#102—222no—
410#102—222no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—221no—
414C2×C11—22no—
415C2×C11—82no—
416C2×C11—82no—
417C2×C11C2×#44911yescharacteristic
418C2×C11#301211yescharacteristic
419C2×C11#301811yescharacteristic
420D11—161no—
421C24—21no—
422#41—42no—
423#41—42no—
424#41—82no—
425#41—82no—
426#41—442no—
427#41—442no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—221no—
431C2×Q8C2×C22⋊D1112yes—
432C2×D4—22no—
433C2×D4—24no—
434C2×D4—24no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—221no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—441no—
444C2×D4C2×C22⋊D1112yes—
445C2×D4C2×C22⋊D1112yes—
446C22×C4—24no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—81no—
452C22×C4—81no—
453C22×C4—441no—
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457SD16—444no—
458SD16—444no—
459D8—444no—
460D8—882no—
461M16—442no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—222no—
465C2×C8—222no—
466C2×C8—442no—
467C2×C8—881no—
468C4⋊C4—24no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4C2×C22⋊D1112yes—
479C4⋊C4C2×C22⋊D1112yes—
480C4⋊C4C2×C22⋊D1112yes—
481C22⋊C4—24no—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—441no—
490C22⋊C4—441no—
491C42—24no—
492C42—22no—
493C42C2×C22⋊D1111yescharacteristic
494C42C2×C22⋊D1111yescharacteristic
495C42C2×C22⋊D1111yescharacteristic
496C42C23×D1111yescharacteristic
497C11#1868011yescharacteristic, complemented, Sylow
498C23—22no—
499C23—22no—
500C23—42no—
501C23—81no—
502C23—81no—
503C23—441no—
504C23#6700611yescharacteristic
505Q8—42no—
506Q8—42no—
507Q8—41no—
508Q8—41no—
509Q8—441no—
510Q8—441no—
511D4—22no—
512D4—22no—
513D4—22no—
514D4—22no—
515D4—44no—
516D4—42no—
517D4—42no—
518D4—81no—
519D4—84no—
520D4—84no—
521D4—442no—
522D4—441no—
523D4—441no—
524D4—441no—
525D4—441no—
526D4—882no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—82no—
539C2×C4—81no—
540C2×C4—84no—
541C2×C4—441no—
542C2×C4—882no—
543C2×C4#6700212yes—
544C2×C4#6700312yes—
545C2×C4#6700611yescharacteristic
546C2×C4#6700611yescharacteristic
547C2×C4#6700611yescharacteristic
548C2×C4C22×C22⋊D1111yescharacteristic
549C2×C4C22×C22⋊D1111yescharacteristic
550C2×C4C22×C22⋊D1111yescharacteristic
551C8—222no—
552C8—441no—
553C8—442no—
554C8—442no—
555C22—21no—
556C22—21no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—84no—
564C22—881no—
565C22—881no—
566C22—881no—
567C22#1062285112yes—
568C22C2×#6700611yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—42no—
573C4—42no—
574C4—42no—
575C4—42no—
576C4—881no—
577C4#1062285112yes—
578C4C2×#6700211yescharacteristic
579C4C2×#6700311yescharacteristic
580C4#1062336611yescharacteristic
581C4#1062336711yescharacteristic
582C2—22no—
583C2—82no—
584C2—82no—
585C2—1761no—
586C2C2×#1062285111yescharacteristic
587C2#1307792011yescharacteristic
588C2#1307796511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3506C2
socleC22×C11C2×#120
hypercenter#3506D11
hypocenterC11#18680
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. #13079923C2semidirect
2. #13079176C2semidirect
3. #13078080C2semidirect
4. #13067900C2semidirect
5. #13067844C2semidirect
6. #13067705C2semidirect
7. #13067699C2semidirect
8. #13067306C2semidirect
9. #13067067C2semidirect
10. C2×D4⋊(C11⋊C8)C2semidirect
11. C11×#3506C2semidirect
27. #10622701C22semidirect
29. #10622698C22semidirect
30. #10622694C22semidirect
31. #10622692C22semidirect
39. #10622628C22semidirect
40. #10622620C22semidirect
45. #10622185C22semidirect
46. #10622184C22semidirect
49. D4⋊(C11⋊C8)C22semidirect
50. D4⋊(C11⋊C8)C22semidirect
204. #3506D11semidirect
497. C11#18680semidirect

Maximal subgroups

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

subgroupindex
#130799232
#130791762
#130780802
#130679002
#130678442
#130677052
#130676992
#130673062
#130670672
C2×D4⋊(C11⋊C8)2
C11×#35062
#1868011