Finite Group Databasebeta

← #14743255

Subgroups — #14743255

Order 2816.

704 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#13081535C211yesmaximal, characteristic, complemented
2#13081258C211yesmaximal, characteristic, complemented
3D4×#4324C211yesmaximal, characteristic
4#13068235C211yesmaximal, characteristic, complemented
5#13068085C211yesmaximal, characteristic, complemented
6#13068041C211yesmaximal, characteristic, complemented
7#13068005C211yesmaximal, characteristic, complemented
8#13067962C211yesmaximal, characteristic, complemented
9#13067879C211yesmaximal, characteristic, complemented
10#13067877C211yesmaximal, characteristic, complemented
11#13067795C211yesmaximal, characteristic
12#13067711C211yesmaximal, 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
19C22×#4324—21no—
20#10623101C2211yescharacteristic, complemented
21D4×Dic22C2211yescharacteristic
22C11×#492C2211yescharacteristic
23C11×#465—21no—
24C11×#461C2211yescharacteristic
25C11×#460C2211yescharacteristic
26C11×#450—21no—
27C11×#448—21no—
28C4×C11×SD16C2211yescharacteristic
29C8×D4×C11C2211yescharacteristic
30#10622831—21no—
31#10622777—21no—
32#10622707—21no—
33#10622707C2211yescharacteristic, complemented
34#10622706—21no—
35#10622706C2211yescharacteristic, complemented
36#10622692C2211yescharacteristic, complemented
37#10622689C2211yescharacteristic
38#10622688C2211yescharacteristic
39#10622683C2211yescharacteristic
40#10622654—21no—
41#10622653—21no—
42Q8×C11⋊C8C2211yescharacteristic, complemented
43#10622633C2211yescharacteristic, complemented
44#10622632—21no—
45#10622632C2211yescharacteristic
46#10622632C2211yescharacteristic
47C4×#4324—21no—
48C4×#4324C2211yescharacteristic
49D4×C11⋊C8C2211yescharacteristic
50#10622620C2211yescharacteristic
51#10622469—21no—
52#10622407—21no—
53#10622379—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#10622124C2211yescharacteristic, complemented
62#10622124C2211yescharacteristic, complemented
63#10622122C2211yescharacteristic, complemented
64#10622118C2211yescharacteristic, complemented
65#10622096C2211yescharacteristic, complemented
66#10622093C2211yescharacteristic, complemented
67C22×Q8×C11—21no—
68C22×D4×C11—21no—
69C22×D4×C11—21no—
70C22×Dic22—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—21no—
75C2×C11×SD16—44no—
76C2×C11×SD16D411yescharacteristic
77C22×C8×C11—21no—
78C11×C4⋊Q8—21no—
79C11×C4⋊Q8C2311yescharacteristic
80C11×#127C2311yescharacteristic
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—41no—
83C11×#121—21no—
84C11×#121—21no—
85C11×#120—41no—
86C4×Q8×C11C2311yescharacteristic
87C4×D4×C11—21no—
88C4×D4×C11C2311yescharacteristic
89C4×D4×C11C2311yescharacteristic
90Q8×Dic11—21no—
91D4×Dic11—21no—
92C2×#4324—21no—
93C2×#4324—21no—
94C2×#4324—21no—
95C2×#4324—21no—
96C2×#4324—21no—
97C2×#4324—44no—
98C2×#4324D411yescharacteristic
99#66977—21no—
100C22×C11⋊C8—21no—
101#66943—21no—
102#66943—41no—
103#66941—21no—
104#66931—41no—
105#66922—21no—
106#66922C2311yescharacteristic
107#66922C2311yescharacteristic
108C4×Dic22—21no—
109C4×Dic22C2311yescharacteristic
110C11×#106D411yescharacteristic
111C11×C4⋊C8C2311yescharacteristic
112C11×#103—21no—
113C11×#103D411yescharacteristic
114C11×#102—21no—
115C11×#102D411yescharacteristic
116C11×C22⋊C8—21no—
117C4×C8×C11C2311yescharacteristic
118#66899—21no—
119#66896—21no—
120#66896—21no—
121#66896—41no—
122#66896D411yescharacteristic
123C22⋊(C11⋊C8)—21no—
124#66882—21no—
125#66882—21no—
126#66879—21no—
127Dic11⋊C8—21no—
128#66874—21no—
129#66874—21no—
130#66874—21no—
131#66874—21no—
132#66874—21no—
133#66874D411yescharacteristic
134#66872—21no—
135#66872—21no—
136#66872—41no—
137#66872D411yescharacteristic
138#66871—21no—
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4×C11⋊C8—21no—
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#19764—111nomaximal, Sylow
147C24×C11—41no—
148C2×Q8×C11—21no—
149C2×Q8×C11—41no—
150C2×Q8×C11—42no—
151C2×Q8×C11—81no—
152C2×Q8×C11C2×D411yescharacteristic
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—41no—
157C2×D4×C11—41no—
158C2×D4×C11—42no—
159C2×D4×C11—42no—
160C2×D4×C11—81no—
161C2×D4×C11—81no—
162C2×D4×C11C2×D411yescharacteristic
163C2×D4×C11C2×D411yescharacteristic
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—41no—
167C22×Dic11—41no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—41no—
171C2×Dic22—42no—
172C2×Dic22—81no—
173C2×Dic22C2×D411yescharacteristic
174C11×SD16—42no—
175C11×SD16—42no—
176C11×SD16—42no—
177C11×SD16—81no—
178C11×SD16SD1614yescomplemented
179C2×C8×C11—21no—
180C2×C8×C11—42no—
181C2×C8×C11C2×D411yescharacteristic
182C2×C8×C11C2×D411yescharacteristic
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—41no—
187C11×C4⋊C4C2×D411yescharacteristic
188C11×C4⋊C4C2×D411yescharacteristic
189C11×C4⋊C4C2×D411yescharacteristic
190C11×C22⋊C4—21no—
191C11×C22⋊C4—21no—
192C11×C22⋊C4—41no—
193C11×C22⋊C4—41no—
194C42×C11—21no—
195C42×C11C2411yescharacteristic
196C22⋊Dic11—41no—
197#4324—22no—
198#4324—42no—
199#4324—42no—
200#4324—42no—
201#4324—42no—
202#4324—81no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—41no—
208C4⋊Dic11—41no—
209C4⋊Dic11C2×D411yescharacteristic
210Dic11⋊C4—21no—
211Dic11⋊C4—41no—
212Dic11⋊C4—41no—
213C4×Dic11—21no—
214C4×Dic11—41no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—42no—
220C2×C11⋊C8C2×D411yescharacteristic
221C2×C11⋊C8C2×D411yescharacteristic
222#3386—111no—
223#3359—111no—
224D4×SD16—111no—
225D4×SD16D1111yescharacteristic
226#1714—111no—
227#1686—111no—
228#1679—111no—
229#1673—111no—
230#1666—111no—
231#1651—111no—
232#1651—111no—
233#1639—111no—
234#1626—111no—
235#1582—111no—
236SD16⋊C8—111no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—41no—
240C23×C11—82no—
241C23×C11—82no—
242C23×C11—161no—
243Q8×C11—21no—
244Q8×C11—41no—
245Q8×C11—41no—
246Q8×C11—82no—
247Q8×C11C2×SD1612yescomplemented
248D4×C11—21no—
249D4×C11—21no—
250D4×C11—41no—
251D4×C11—41no—
252D4×C11—41no—
253D4×C11—41no—
254D4×C11—81no—
255D4×C11—82no—
256D4×C11—82no—
257D4×C11C2×SD1612yes—
258D4×C11AGL(1,ℤ/8)12yes—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—82no—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—82no—
277Dic22—21no—
278Dic22—21no—
279Dic22—41no—
280Dic22—41no—
281Dic22—41no—
282Dic22—41no—
283Dic22—82no—
284C8×C11—21no—
285C8×C11—41no—
286C8×C11C2×SD1612yescomplemented
287C11⋊C8—21no—
288C11⋊C8—21no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293C22×SD16—21no—
294C22×SD16—221no—
295#557—111no—
296D4×Q8—111no—
297D4×Q8C2×D1111yescharacteristic
298D42C2×D1111yescharacteristic
299#501—221no—
300#500—111no—
301#498—111no—
302#492—111no—
303#492C2×D1111yescharacteristic
304#487—111no—
305#487—221no—
306#486—111no—
307#478—221no—
308#477—221no—
309#475—111no—
310#475—111no—
311#475—221no—
312#474—111no—
313#465—21no—
314#465—221no—
315#461—111no—
316#461—111no—
317#461—221no—
318#461C2×D1111yescharacteristic
319#460—111no—
320#460C2×D1111yescharacteristic
321#450—21no—
322#450—221no—
323#448—21no—
324#448—221no—
325#446—111no—
326C8×Q8—111no—
327#440—221no—
328C4×SD16—111no—
329C4×SD16—221no—
330C4×SD16C2×D1111yescharacteristic
331C8×D4—111no—
332C8×D4C2×D1111yescharacteristic
333#335—111no—
334#334—111no—
335#332—111no—
336#332—111no—
337#332—111no—
338#331—111no—
339Q8⋊C8—111no—
340Q8⋊C8—111no—
341D4⋊C8—111no—
342D4⋊C8—111no—
343#322—111no—
344C22×C11—22no—
345C22×C11—22no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11—164no—
354C22×C11D4211yescharacteristic
355C4×C11—22no—
356C4×C11—21no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—81no—
361C4×C11C22×SD1611yescharacteristic
362C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
363C4×C11#57711yescharacteristic
364C4×C11#57711yescharacteristic
365Dic11—41no—
366Dic11—41no—
367Dic11—81no—
368Dic11—81no—
369C22×Q8—21no—
370C22×Q8—221no—
371C22×D4—21no—
372C22×D4—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—44no—
378C2×SD16—111no—
379C2×SD16—221no—
380C2×SD16—221no—
381C2×SD16—221no—
382C2×SD16—221no—
383C2×SD16—221no—
384C2×SD16—444no—
385C2×SD16C22⋊D1111yescharacteristic
386C22×C8—21no—
387C22×C8—221no—
388C4⋊Q8—21no—
389C4⋊Q8—111no—
390C4⋊Q8—111no—
391C4⋊Q8—221no—
392C4⋊Q8—221no—
393C4⋊Q8C22×D1111yescharacteristic
394#127C22×D1111yescharacteristic
395#125—221no—
396#125—441no—
397C22⋊Q8—21no—
398C22⋊Q8—41no—
399C22⋊Q8—221no—
400C22⋊Q8—441no—
401#121—21no—
402#121—21no—
403#120—41no—
404C4×Q8—111no—
405C4×Q8—221no—
406C4×Q8—221no—
407C4×Q8C22×D1111yescharacteristic
408C4×D4—21no—
409C4×D4—221no—
410C4×D4C22×D1111yescharacteristic
411C4×D4C22×D1111yescharacteristic
412#107—221no—
413#107—221no—
414#107—221no—
415#106—111no—
416#106—221no—
417#106—221no—
418#106—441no—
419#106C22⋊D1111yescharacteristic
420C4⋊C8—111no—
421C4⋊C8—111no—
422C4⋊C8—111no—
423C4⋊C8—221no—
424C4⋊C8—221no—
425C4⋊C8C22×D1111yescharacteristic
426#103—21no—
427#103—111no—
428#103—221no—
429#103—221no—
430#103—221no—
431#103—221no—
432#103—221no—
433#103—221no—
434#103C22⋊D1111yescharacteristic
435#102—21no—
436#102—111no—
437#102—221no—
438#102—221no—
439#102—441no—
440#102C22⋊D1111yescharacteristic
441C22⋊C8—21no—
442C22⋊C8—221no—
443#97—221no—
444C4×C8—111no—
445C4×C8—111no—
446C4×C8—221no—
447C4×C8C22×D1111yescharacteristic
448C2×C11—42no—
449C2×C11—42no—
450C2×C11—161no—
451C2×C11#326511yescharacteristic
452C2×C11D4×SD1611yescharacteristic
453C2×C11#328911yescharacteristic
454C24—41no—
455C2×Q8—21no—
456C2×Q8—41no—
457C2×Q8—42no—
458C2×Q8—81no—
459C2×Q8—111no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—441no—
463C2×Q8—442no—
464C2×Q8—881no—
465C2×Q8C2×C22⋊D1111yescharacteristic
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—81no—
474C2×D4—81no—
475C2×D4D4×D1111yescharacteristic
476C2×D4C2×C22⋊D1111yescharacteristic
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—441no—
481SD16—42no—
482SD16—42no—
483SD16—42no—
484SD16—81no—
485SD16—222no—
486SD16—442no—
487SD16—442no—
488SD16—442no—
489SD16—442no—
490SD16—881no—
491SD16#432414yescomplemented
492C2×C8—21no—
493C2×C8—42no—
494C2×C8—111no—
495C2×C8—111no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—442no—
501C2×C8C2×C22⋊D1111yescharacteristic
502C2×C8C2×C22⋊D1111yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—41no—
507C4⋊C4—111no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—441no—
514C4⋊C4—441no—
515C4⋊C4—441no—
516C4⋊C4—441no—
517C4⋊C4D4×D1111yescharacteristic
518C4⋊C4C2×C22⋊D1111yescharacteristic
519C4⋊C4C2×C22⋊D1111yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—441no—
525C42—21no—
526C42—221no—
527C42—441no—
528C42C23×D1111yescharacteristic
529C11#1976411yescharacteristic, complemented, Sylow
530C23—21no—
531C23—21no—
532C23—41no—
533C23—82no—
534C23—82no—
535C23—161no—
536Q8—21no—
537Q8—41no—
538Q8—41no—
539Q8—82no—
540Q8—221no—
541Q8—221no—
542Q8—441no—
543Q8—441no—
544Q8—441no—
545Q8—441no—
546Q8—882no—
547Q8C2×#432412yescomplemented
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—81no—
555D4—82no—
556D4—82no—
557D4#6696712yes—
558D4C2×#432412yes—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—82no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—882no—
574C2×C4C2×D4×D1111yescharacteristic
575C2×C4#6703711yescharacteristic
576C2×C4C22×C22⋊D1111yescharacteristic
577C8—21no—
578C8—41no—
579C8—221no—
580C8—221no—
581C8—441no—
582C8—441no—
583C8—441no—
584C8—441no—
585C8C2×#432412yescomplemented
586C22—22no—
587C22—22no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—164no—
596C22D4×C22⋊D1111yescharacteristic
597C4—21no—
598C4—22no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—81no—
603C4—441no—
604C4—441no—
605C4—881no—
606C4—881no—
607C4C2×#6696711yescharacteristic
608C4#1062329311yescharacteristic
609C4C22×#432411yescharacteristic
610C4#1062336711yescharacteristic
611C2—42no—
612C2—42no—
613C2—161no—
614C2#1308011111yescharacteristic
615C2D4×#432411yescharacteristic
616C2#1308038911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingD4×C11×SD16C2
socleC22×C11D42
prime radicalD42×C11C22
hypercenterD4×SD16D11
hypocenterC11#19764
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. #13081535C2semidirect
2. #13081258C2semidirect
4. #13068235C2semidirect
5. #13068085C2semidirect
6. #13068041C2semidirect
7. #13068005C2semidirect
8. #13067962C2semidirect
9. #13067879C2semidirect
10. #13067877C2semidirect
12. #13067711C2semidirect
13. #13067452C2semidirect
14. SD16⋊(C11⋊C8)C2semidirect
20. #10623101C22semidirect
33. #10622707C22semidirect
35. #10622706C22semidirect
36. #10622692C22semidirect
42. Q8×C11⋊C8C22semidirect
43. #10622633C22semidirect
54. #10622295C22semidirect
55. #10622292C22semidirect
56. #10622185C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
61. #10622124C22semidirect
62. #10622124C22semidirect
63. #10622122C22semidirect
64. #10622118C22semidirect
65. #10622096C22semidirect
66. #10622093C22semidirect
178. C11×SD16SD16semidirect
247. Q8×C11C2×SD16semidirect
286. C8×C11C2×SD16semidirect
491. SD16#4324semidirect
529. C11#19764semidirect
547. Q8C2×#4324semidirect
585. C8C2×#4324semidirect

Maximal subgroups

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

subgroupindex
#130815352
#130812582
D4×#43242
#130682352
#130680852
#130680412
#130680052
#130679622
#130678792
#130678772
#130677952
#130677112
#130674522
SD16⋊(C11⋊C8)2
D4×C11×SD162
#1976411