Finite Group Databasebeta

← #14731527

Subgroups — #14731527

Order 2816.

1000 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C211yesmaximal, characteristic, complemented
2#13079191C211yesmaximal, characteristic, complemented
3#13078080C211yesmaximal, characteristic, complemented
4#13067872C212yesmaximal, complemented
5#13067816C212yesmaximal, complemented
6#13067726C212yesmaximal, complemented
7#13067681C212yesmaximal, complemented
8#13067293C211yesmaximal, characteristic, complemented
9#13067071C211yesmaximal, characteristic, complemented
10C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11C11×#3506C211yesmaximal, characteristic, complemented
12C11×#559—22no—
13C11×#556C2212yes—
14C11×#555—21no—
15C11×#553—22no—
16C11×#550C2212yes—
17C11×#547—21no—
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#10622697—21no—
29#10622696—21no—
30#10622691C2211yescharacteristic, complemented
31#10622686C2211yescharacteristic, complemented
32#10622683C2211yescharacteristic, complemented
33#10622661—22no—
34#10622651—22no—
35#10622640C2212yescomplemented
36#10622633C2212yescomplemented
37#10622632C2212yes—
38#10622629—22no—
39#10622628C2212yes—
40C4×#4323—22no—
41#10622579—21no—
42#10622537C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622185C2212yescomplemented
46#10622182C2212yescomplemented
47Q8⋊(C11⋊C8)C2212yescomplemented
48Q8⋊(C11⋊C8)C2212yescomplemented
49D4⋊(C11⋊C8)C2212yes—
50D4⋊(C11⋊C8)C2212yes—
51C2×C11×#41—22no—
52C2×C11×#41—21no—
53C22×D4×C11D411yescharacteristic
54C23×C4×C11—21no—
55C2×#4339—21no—
56C11×C4⋊Q8D411yescharacteristic
57C11×C4⋊Q8D411yescharacteristic
58C11×C4⋊Q8C2311yescharacteristic
59C11×#127—22no—
60C11×#127C2311yescharacteristic
61C11×#126—24no—
62C11×#125—21no—
63C11×#124—24no—
64C11×#124—22no—
65C11×#124—21no—
66C11×#123—24no—
67C11×#123—24no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8D412yes—
71C11×#121—22no—
72C11×#121—22no—
73C11×#121—24no—
74C11×#121—21no—
75C11×#121—22no—
76C11×#121D412yes—
77C11×#120—24no—
78C4×Q8×C11—22no—
79C4×Q8×C11—21no—
80C4×Q8×C11C2312yes—
81C4×D4×C11—24no—
82C4×D4×C11—24no—
83C4×D4×C11—22no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11D412yes—
88C4×D4×C11D412yes—
89C4×D4×C11C2312yes—
90C11×#117—22no—
91C11×#117—21no—
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#18678—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—22no—
141C2×D4×C11—22no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
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—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
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—82no—
190#4324—44no—
191#4323—44no—
192#4323—44no—
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#3246—111no—
206#3169—111no—
207#3036—111no—
208#1650—112no—
209#1642—112no—
210#1628—112no—
211#1621—112no—
212#1547—111no—
213#1493—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—22no—
223Q8×C11—22no—
224Q8×C11—41no—
225Q8×C11—41no—
226Q8×C11—81no—
227D4×C11—22no—
228D4×C11—22no—
229D4×C11—42no—
230D4×C11—44no—
231D4×C11—41no—
232D4×C11—41no—
233D4×C11—41no—
234D4×C11—41no—
235D4×C11—42no—
236D4×C11—84no—
237D4×C11—84no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—44no—
248C2×C4×C11—82no—
249C2×C4×C11—81no—
250C2×C4×C11—84no—
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11#13512yes—
255C2×C4×C11AGL(1,ℤ/8)12yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C22⋊D11—82no—
260C2×Dic11—41no—
261D44—42no—
262D44—41no—
263D44—41no—
264D44—41no—
265D44—41no—
266C4×D11—82no—
267Dic22—41no—
268Dic22—41no—
269C11⋊C8—22no—
270C11⋊C8—41no—
271C11⋊C8—42no—
272C11⋊C8—42no—
273C2×AGL(1,ℤ/8)—221no—
274#559—22no—
275#556C2×D1112yes—
276#555—21no—
277#553—22no—
278#550C2×D1112yes—
279#547—21no—
280#538—22no—
281#535—21no—
282#533C2×D1111yescharacteristic
283#532—111no—
284#532C2×D1111yescharacteristic
285#525—22no—
286#520—21no—
287C2×C4×D4C2×D1111yescharacteristic
288#500—111no—
289#493—111no—
290#486—111no—
291#486—111no—
292#476—221no—
293#475—112no—
294#466—222no—
295#465—222no—
296#463—222no—
297#461—112no—
298#461—221no—
299#460—112no—
300#459—112no—
301C4×D8—222no—
302#423—111no—
303C2×C4⋊C8—111no—
304#417—221no—
305C2×C4×C8—111no—
306#332—112no—
307#331—112no—
308Q8⋊C8—112no—
309Q8⋊C8—112no—
310D4⋊C8—112no—
311D4⋊C8—112no—
312C22×C11—21no—
313C22×C11—21no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—84no—
321C22×C11#44912yes—
322C22×C11C2×#12011yescharacteristic
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—81no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—42no—
330C4×C11—42no—
331C4×C11—42no—
332C4×C11—42no—
333C4×C11#44912yes—
334C4×C11C2×#13511yescharacteristic
335C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
336C4×C11#57611yescharacteristic
337C4×C11#57711yescharacteristic
338Dic11—81no—
339C2×#41—22no—
340C2×#41—21no—
341C2×#41—221no—
342C22×D4C22⋊D1111yescharacteristic
343C23×C4—21no—
344AGL(1,ℤ/8)—444no—
345C2×SD16—222no—
346C2×SD16—222no—
347C2×D8—222no—
348C2×D8—222no—
349C2×M16—221no—
350C22×C8—221no—
351C22×C8—221no—
352C4⋊Q8—111no—
353C4⋊Q8C22⋊D1111yescharacteristic
354C4⋊Q8C22⋊D1111yescharacteristic
355C4⋊Q8C22×D1111yescharacteristic
356#127—22no—
357#127—111no—
358#127C22×D1111yescharacteristic
359#126—24no—
360#125—21no—
361#124—24no—
362#124—22no—
363#124—21no—
364#124—221no—
365#123—24no—
366#123—24no—
367C22⋊Q8—22no—
368C22⋊Q8—21no—
369C22⋊Q8C22⋊D1112yes—
370#121—22no—
371#121—22no—
372#121—24no—
373#121—21no—
374#121—22no—
375#121—221no—
376#121—221no—
377#121C22⋊D1112yes—
378#120—24no—
379C4×Q8—22no—
380C4×Q8—21no—
381C4×Q8C22×D1112yes—
382C4×D4—24no—
383C4×D4—24no—
384C4×D4—22no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—221no—
389C4×D4—221no—
390C4×D4C22⋊D1112yes—
391C4×D4C22⋊D1112yes—
392C4×D4C22×D1112yes—
393#117—22no—
394#117—21no—
395#117—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4C22⋊D1111yescharacteristic
398C2×C22⋊C4—21no—
399C2×C42C22×D1111yescharacteristic
400#107—222no—
401#106—222no—
402C4⋊C8—112no—
403C4⋊C8—112no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406#103—222no—
407#103—222no—
408#102—222no—
409#102—222no—
410#102—222no—
411#102—222no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—221no—
415C2×C11—22no—
416C2×C11—82no—
417C2×C11—82no—
418C2×C11C2×#44911yescharacteristic
419C2×C11#301211yescharacteristic
420C2×C11#301811yescharacteristic
421D11—161no—
422C24—21no—
423#41—42no—
424#41—42no—
425#41—82no—
426#41—82no—
427#41—442no—
428#41—442no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—221no—
432C2×Q8C2×C22⋊D1112yes—
433C2×D4—22no—
434C2×D4—24no—
435C2×D4—24no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—441no—
445C2×D4C2×C22⋊D1112yes—
446C2×D4C2×C22⋊D1112yes—
447C22×C4—24no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—81no—
453C22×C4—81no—
454C22×C4—441no—
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C2×C22⋊D1111yescharacteristic
458SD16—444no—
459SD16—882no—
460D8—444no—
461D8—444no—
462M16—442no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—222no—
466C2×C8—222no—
467C2×C8—442no—
468C2×C8—881no—
469C4⋊C4—24no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—22no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—22no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4C2×C22⋊D1112yes—
480C4⋊C4C2×C22⋊D1112yes—
481C4⋊C4C2×C22⋊D1112yes—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—441no—
491C22⋊C4—441no—
492C42—24no—
493C42—22no—
494C42C2×C22⋊D1111yescharacteristic
495C42C2×C22⋊D1111yescharacteristic
496C42C2×C22⋊D1111yescharacteristic
497C42C23×D1111yescharacteristic
498C11#1867811yescharacteristic, complemented, Sylow
499C23—22no—
500C23—22no—
501C23—42no—
502C23—81no—
503C23—81no—
504C23—441no—
505C23#6700611yescharacteristic
506Q8—22no—
507Q8—22no—
508Q8—41no—
509Q8—41no—
510Q8—81no—
511Q8—441no—
512Q8—441no—
513D4—22no—
514D4—22no—
515D4—42no—
516D4—44no—
517D4—41no—
518D4—41no—
519D4—42no—
520D4—41no—
521D4—41no—
522D4—84no—
523D4—84no—
524D4—442no—
525D4—441no—
526D4—441no—
527D4—441no—
528D4—441no—
529D4—882no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—41no—
537C2×C4—44no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—82no—
541C2×C4—81no—
542C2×C4—84no—
543C2×C4—441no—
544C2×C4—882no—
545C2×C4#6700212yes—
546C2×C4#6700312yes—
547C2×C4#6700611yescharacteristic
548C2×C4#6700611yescharacteristic
549C2×C4#6700611yescharacteristic
550C2×C4C22×C22⋊D1111yescharacteristic
551C2×C4C22×C22⋊D1111yescharacteristic
552C2×C4C22×C22⋊D1111yescharacteristic
553C8—222no—
554C8—441no—
555C8—442no—
556C8—442no—
557C22—21no—
558C22—21no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—84no—
566C22—881no—
567C22—881no—
568C22—881no—
569C22#1062285112yes—
570C22C2×#6700611yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—42no—
575C4—42no—
576C4—42no—
577C4—42no—
578C4—881no—
579C4#1062285112yes—
580C4C2×#6700211yescharacteristic
581C4C2×#6700311yescharacteristic
582C4#1062336611yescharacteristic
583C4#1062336711yescharacteristic
584C2—22no—
585C2—82no—
586C2—82no—
587C2—1761no—
588C2C2×#1062285111yescharacteristic
589C2#1307792011yescharacteristic
590C2#1307796511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3506C2
socleC22×C11C2×#120
hypercenter#3506D11
hypocenterC11#18678
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. #13079928C2semidirect
2. #13079191C2semidirect
3. #13078080C2semidirect
4. #13067872C2semidirect
5. #13067816C2semidirect
6. #13067726C2semidirect
7. #13067681C2semidirect
8. #13067293C2semidirect
9. #13067071C2semidirect
10. C2×D4⋊(C11⋊C8)C2semidirect
11. C11×#3506C2semidirect
27. #10622701C22semidirect
30. #10622691C22semidirect
31. #10622686C22semidirect
32. #10622683C22semidirect
35. #10622640C22semidirect
36. #10622633C22semidirect
45. #10622185C22semidirect
46. #10622182C22semidirect
47. Q8⋊(C11⋊C8)C22semidirect
48. Q8⋊(C11⋊C8)C22semidirect
204. #3506D11semidirect
498. C11#18678semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130791912
#130780802
#130678722
#130678162
#130677262
#130676812
#130672932
#130670712
C2×D4⋊(C11⋊C8)2
C11×#35062
#1867811