Finite Group Databasebeta

← #14743270

Subgroups — #14743270

Order 2816.

668 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081524C211yesmaximal, characteristic, complemented
2Q8×#4324C211yesmaximal, characteristic, complemented
3#13080440C211yesmaximal, characteristic
4#13068235C211yesmaximal, characteristic, complemented
5#13068085C211yesmaximal, characteristic, complemented
6#13068030C211yesmaximal, characteristic, complemented
7#13068015C211yesmaximal, characteristic, complemented
8#13067989C211yesmaximal, characteristic, complemented
9#13067821C211yesmaximal, characteristic, complemented
10#13067781C211yesmaximal, characteristic, complemented
11#13067732C211yesmaximal, characteristic
12#13067693C211yesmaximal, characteristic, complemented
13#13067452C211yesmaximal, characteristic, complemented
14SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
15D4×C11×SD16C211yesmaximal, characteristic
16C22×C11×SD16—21no—
17D4×Q8×C11C2211yescharacteristic
18D42×C11C2211yescharacteristic
19Q8×Dic22C2211yescharacteristic, complemented
20#10623074C2211yescharacteristic
21C11×#492C2211yescharacteristic
22C11×#465—21no—
23C11×#461C2211yescharacteristic
24C11×#460C2211yescharacteristic
25C11×#450—21no—
26C11×#448—21no—
27C4×C11×SD16C2211yescharacteristic
28C8×D4×C11C2211yescharacteristic
29#10622831—21no—
30C2×#66896—21no—
31#10622777—21no—
32#10622707—21no—
33#10622707C2211yescharacteristic, complemented
34#10622706C2211yescharacteristic, complemented
35#10622692—21no—
36#10622692C2211yescharacteristic, complemented
37#10622689C2211yescharacteristic
38#10622688C2211yescharacteristic
39#10622683C2211yescharacteristic
40#10622654—21no—
41#10622647—21no—
42Q8×C11⋊C8C2211yescharacteristic, complemented
43#10622634C2211yescharacteristic, complemented
44C4×#4324—21no—
45C4×#4324C2211yescharacteristic
46D4×C11⋊C8C2211yescharacteristic
47#10622621—21no—
48#10622621C2211yescharacteristic
49#10622621C2211yescharacteristic
50#10622621C2211yescharacteristic
51#10622469—21no—
52#10622409—21no—
53#10622372—21no—
54#10622295C2211yescharacteristic, complemented
55#10622292C2211yescharacteristic, complemented
56#10622185C2211yescharacteristic, complemented
57#10622182C2211yescharacteristic
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622122C2211yescharacteristic, complemented
62#10622119C2211yescharacteristic, complemented
63#10622119C2211yescharacteristic, complemented
64#10622118C2211yescharacteristic, complemented
65#10622096C2211yescharacteristic, complemented
66#10622093C2211yescharacteristic, complemented
67C22×Q8×C11—21no—
68C22×D4×C11—21no—
69C22×D4×C11—21no—
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—44no—
75C2×C11×SD16D411yescharacteristic
76C22×C8×C11—21no—
77C11×C4⋊Q8—21no—
78C11×C4⋊Q8C2311yescharacteristic
79C11×#127C2311yescharacteristic
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—41no—
82C11×#121—21no—
83C11×#121—21no—
84C11×#120—41no—
85C4×Q8×C11C2311yescharacteristic
86C4×D4×C11—21no—
87C4×D4×C11C2311yescharacteristic
88C4×D4×C11C2311yescharacteristic
89Q8×Dic11—21no—
90D4×Dic11—21no—
91C2×#4324—21no—
92C2×#4324—41no—
93C2×#4324D411yescharacteristic
94C2×C4⋊Dic11—21no—
95#66977—21no—
96C22×C11⋊C8—21no—
97#66943—21no—
98#66941—21no—
99#66941—41no—
100#66931—41no—
101#66922—21no—
102#66922C2311yescharacteristic
103#66922C2311yescharacteristic
104C4×Dic22—21no—
105C4×Dic22C2311yescharacteristic
106C11×#106D411yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×#103—21no—
109C11×#103D411yescharacteristic
110C11×#102—21no—
111C11×#102D411yescharacteristic
112C11×C22⋊C8—21no—
113C4×C8×C11C2311yescharacteristic
114#66899—21no—
115#66896—21no—
116#66896—21no—
117#66896—21no—
118#66896—21no—
119#66896—21no—
120#66896—21no—
121#66896D411yescharacteristic
122C22⋊(C11⋊C8)—21no—
123#66882—21no—
124#66882—21no—
125#66879—21no—
126Dic11⋊C8—21no—
127#66874—21no—
128#66874—41no—
129#66874D411yescharacteristic
130#66872—21no—
131#66872—21no—
132#66872—21no—
133#66872—21no—
134#66872—21no—
135#66872—21no—
136#66872D411yescharacteristic
137#66871—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8—21no—
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19765—111nomaximal, Sylow
146C24×C11—41no—
147C2×Q8×C11—21no—
148C2×Q8×C11—41no—
149C2×Q8×C11—42no—
150C2×Q8×C11—81no—
151C2×Q8×C11C2×D411yescharacteristic
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—41no—
156C2×D4×C11—41no—
157C2×D4×C11—42no—
158C2×D4×C11—42no—
159C2×D4×C11—81no—
160C2×D4×C11—81no—
161C2×D4×C11C2×D411yescharacteristic
162C2×D4×C11C2×D411yescharacteristic
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—41no—
166C22×Dic11—41no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—41no—
170C2×Dic22C2×D411yescharacteristic
171C11×SD16—42no—
172C11×SD16—42no—
173C11×SD16—42no—
174C11×SD16—81no—
175C11×SD16SD1614yescomplemented
176C2×C8×C11—21no—
177C2×C8×C11—42no—
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—41no—
184C11×C4⋊C4C2×D411yescharacteristic
185C11×C4⋊C4C2×D411yescharacteristic
186C11×C4⋊C4C2×D411yescharacteristic
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—41no—
190C11×C22⋊C4—41no—
191C42×C11—21no—
192C42×C11C2411yescharacteristic
193C22⋊Dic11—41no—
194#4324—22no—
195#4324—81no—
196#4324—82no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—41no—
202C4⋊Dic11—41no—
203C4⋊Dic11C2×D411yescharacteristic
204Dic11⋊C4—21no—
205Dic11⋊C4—41no—
206Dic11⋊C4—41no—
207C4×Dic11—21no—
208C4×Dic11—41no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—81no—
214C2×C11⋊C8C2×D411yescharacteristic
215C2×C11⋊C8C2×D411yescharacteristic
216#3385—111no—
217Q8×SD16—111no—
218#3295—111no—
219D4×SD16D1111yescharacteristic
220#1714—111no—
221#1686—111no—
222#1678—111no—
223#1675—111no—
224#1671—111no—
225#1643—111no—
226#1637—111no—
227#1629—111no—
228#1623—111no—
229#1582—111no—
230SD16⋊C8—111no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—41no—
234C23×C11—82no—
235C23×C11—82no—
236C23×C11—161no—
237Q8×C11—21no—
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—82no—
241Q8×C11C2×SD1612yes—
242D4×C11—21no—
243D4×C11—21no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—81no—
249D4×C11—82no—
250D4×C11—82no—
251D4×C11C2×SD1612yes—
252D4×C11#13712yes—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—82no—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—161no—
271Dic22—21no—
272Dic22—21no—
273Dic22—81no—
274Dic22—81no—
275Dic22—161no—
276C8×C11—21no—
277C8×C11—41no—
278C8×C11C2×SD1612yes—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C22×SD16—21no—
286Q82—111no—
287#554—111no—
288D4×Q8C2×D1111yescharacteristic
289D42C2×D1111yescharacteristic
290#501—221no—
291#500—111no—
292#498—111no—
293#498—221no—
294#492—111no—
295#492C2×D1111yescharacteristic
296#487—111no—
297#486—111no—
298#481—221no—
299#479—221no—
300#477—111no—
301#476—111no—
302#476—111no—
303#476—111no—
304#476—221no—
305#475—111no—
306#475—221no—
307#474—221no—
308#465—21no—
309#465—221no—
310#461C2×D1111yescharacteristic
311#460—111no—
312#460C2×D1111yescharacteristic
313#450—21no—
314#450—221no—
315#448—21no—
316#446—111no—
317C8×Q8—111no—
318#440—221no—
319C4×SD16—111no—
320C4×SD16—221no—
321C4×SD16C2×D1111yescharacteristic
322C8×D4—111no—
323C8×D4C2×D1111yescharacteristic
324C2×#102—221no—
325#335—111no—
326#334—111no—
327#333—111no—
328#333—111no—
329#332—111no—
330#331—111no—
331Q8⋊C8—111no—
332Q8⋊C8—111no—
333D4⋊C8—111no—
334D4⋊C8—111no—
335#322—111no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—164no—
346C22×C11D4211yescharacteristic
347C4×C11—22no—
348C4×C11—21no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—81no—
353C4×C11C22×SD1611yescharacteristic
354C4×C11C2×#13711yescharacteristic
355C4×C11#57711yescharacteristic
356C4×C11#57711yescharacteristic
357Dic11—41no—
358Dic11—41no—
359Dic11—81no—
360Dic11—81no—
361C22×Q8—21no—
362C22×D4—21no—
363C22×D4—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—44no—
369C2×SD16—111no—
370C2×SD16—221no—
371C2×SD16—441no—
372C2×SD16C22⋊D1111yescharacteristic
373C22×C8—21no—
374C22×C8—221no—
375C4⋊Q8—21no—
376C4⋊Q8—111no—
377C4⋊Q8—111no—
378C4⋊Q8—221no—
379C4⋊Q8—221no—
380C4⋊Q8—441no—
381C4⋊Q8C22×D1111yescharacteristic
382#127C22×D1111yescharacteristic
383#125—221no—
384C22⋊Q8—21no—
385C22⋊Q8—41no—
386C22⋊Q8—221no—
387C22⋊Q8—441no—
388#121—21no—
389#121—21no—
390#120—41no—
391C4×Q8—111no—
392C4×Q8—221no—
393C4×Q8—221no—
394C4×Q8C22×D1111yescharacteristic
395C4×D4—21no—
396C4×D4—221no—
397C4×D4C22×D1111yescharacteristic
398C4×D4C22×D1111yescharacteristic
399C2×C4⋊C4—221no—
400#107—221no—
401#107—221no—
402#107—221no—
403#106—111no—
404#106—221no—
405#106—221no—
406#106—221no—
407#106—221no—
408#106—221no—
409#106—221no—
410#106C22⋊D1111yescharacteristic
411C4⋊C8—111no—
412C4⋊C8—111no—
413C4⋊C8—111no—
414C4⋊C8—221no—
415C4⋊C8—221no—
416C4⋊C8C22×D1111yescharacteristic
417#103—21no—
418#103—111no—
419#103—221no—
420#103—221no—
421#103—441no—
422#103C22⋊D1111yescharacteristic
423#102—21no—
424#102—111no—
425#102—221no—
426#102—221no—
427#102—221no—
428#102—221no—
429#102—221no—
430#102—221no—
431#102C22⋊D1111yescharacteristic
432C22⋊C8—21no—
433C22⋊C8—221no—
434#97—221no—
435C4×C8—111no—
436C4×C8—111no—
437C4×C8—221no—
438C4×C8C22×D1111yescharacteristic
439C2×C11—42no—
440C2×C11—42no—
441C2×C11—161no—
442C2×C11#326611yescharacteristic
443C2×C11D4×SD1611yescharacteristic
444C2×C11#328811yescharacteristic
445C24—41no—
446C2×Q8—21no—
447C2×Q8—41no—
448C2×Q8—42no—
449C2×Q8—81no—
450C2×Q8—111no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—441no—
454C2×Q8C2×C22⋊D1111yescharacteristic
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—81no—
463C2×D4—81no—
464C2×D4D4×D1111yescharacteristic
465C2×D4C2×C22⋊D1111yescharacteristic
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—441no—
470SD16—42no—
471SD16—42no—
472SD16—42no—
473SD16—81no—
474SD16—222no—
475SD16—881no—
476SD16—882no—
477SD16#432414yescomplemented
478C2×C8—21no—
479C2×C8—42no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—881no—
487C2×C8C2×C22⋊D1111yescharacteristic
488C2×C8C2×C22⋊D1111yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—41no—
493C4⋊C4—111no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—441no—
500C4⋊C4—441no—
501C4⋊C4—441no—
502C4⋊C4—441no—
503C4⋊C4D4×D1111yescharacteristic
504C4⋊C4C2×C22⋊D1111yescharacteristic
505C4⋊C4C2×C22⋊D1111yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—441no—
511C42—21no—
512C42—221no—
513C42—441no—
514C42C23×D1111yescharacteristic
515C11#1976511yescharacteristic, complemented, Sylow
516C23—21no—
517C23—21no—
518C23—41no—
519C23—82no—
520C23—82no—
521C23—161no—
522Q8—21no—
523Q8—41no—
524Q8—41no—
525Q8—82no—
526Q8—221no—
527Q8—221no—
528Q8—881no—
529Q8—881no—
530Q8—1761no—
531Q8C2×#432412yes—
532D4—21no—
533D4—21no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—81no—
539D4—82no—
540D4—82no—
541D4#6696812yes—
542D4C2×#432412yes—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—82no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—1761no—
558C2×C4C2×D4×D1111yescharacteristic
559C2×C4#6703711yescharacteristic
560C2×C4C22×C22⋊D1111yescharacteristic
561C8—21no—
562C8—41no—
563C8—221no—
564C8—221no—
565C8—441no—
566C8—441no—
567C8—441no—
568C8—441no—
569C8C2×#432412yes—
570C22—22no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—164no—
580C22D4×C22⋊D1111yescharacteristic
581C4—21no—
582C4—22no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—81no—
587C4—441no—
588C4—441no—
589C4—881no—
590C4—881no—
591C4C2×#6696811yescharacteristic
592C4#1062329311yescharacteristic
593C4C22×#432411yescharacteristic
594C4#1062336711yescharacteristic
595C2—42no—
596C2—42no—
597C2—161no—
598C2#1308012611yescharacteristic
599C2D4×#432411yescharacteristic
600C2#1308037811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingD4×C11×SD16C2
socleC22×C11D42
prime radicalD42×C11C22
hypercenterD4×SD16D11
hypocenterC11#19765
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ D4×SD16

Complements

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

NH ≅ G/Ntype
1. #13081524C2semidirect
2. Q8×#4324C2semidirect
4. #13068235C2semidirect
5. #13068085C2semidirect
6. #13068030C2semidirect
7. #13068015C2semidirect
8. #13067989C2semidirect
9. #13067821C2semidirect
10. #13067781C2semidirect
12. #13067693C2semidirect
13. #13067452C2semidirect
14. SD16⋊(C11⋊C8)C2semidirect
19. Q8×Dic22C22semidirect
33. #10622707C22semidirect
34. #10622706C22semidirect
36. #10622692C22semidirect
42. Q8×C11⋊C8C22semidirect
43. #10622634C22semidirect
54. #10622295C22semidirect
55. #10622292C22semidirect
56. #10622185C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
61. #10622122C22semidirect
62. #10622119C22semidirect
63. #10622119C22semidirect
64. #10622118C22semidirect
65. #10622096C22semidirect
66. #10622093C22semidirect
175. C11×SD16SD16semidirect
477. SD16#4324semidirect
515. C11#19765semidirect

Maximal subgroups

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

subgroupindex
#130815242
Q8×#43242
#130804402
#130682352
#130680852
#130680302
#130680152
#130679892
#130678212
#130677812
#130677322
#130676932
#130674522
SD16⋊(C11⋊C8)2
D4×C11×SD162
#1976511