Finite Group Databasebeta

← #2607×D83 #35575805

Subgroups — #2607×D83 #35575805

Order 21248.

2398 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24913128C211yesmaximal, characteristic, complemented
2#24913127C214yesmaximal, complemented
3#24913126C214yesmaximal, complemented
4#24913125C212yesmaximal, complemented
5#24913124C212yesmaximal, complemented
6#24913123C212yesmaximal, complemented
7#399×D83C212yesmaximal
8#393×D83C212yesmaximal
9#391×D83C214yesmaximal, complemented
10#387×D83C214yesmaximal, complemented
11#381×D83C211yesmaximal, characteristic
12C4×C22⋊C4×D83C212yesmaximal
13C83×#2607C211yesmaximal, characteristic, complemented
14C22×Q8×D83C2212yes—
15C23×C4×D83C2211yescharacteristic
16C2×C4⋊C4×D83C2214yes—
17C2×C4⋊C4×D83C2212yes—
18C2×C22⋊C4×D83C2214yes—
19C2×C22⋊C4×D83C2211yescharacteristic
20C2×C22⋊C4×D83C2211yescharacteristic
21C2×C42×D83C2212yes—
22C2×C42×D83C2212yes—
23#19127638C2212yes—
24#19127637C2214yes—
25#19127637C2212yes—
26#19127636C2214yes—
27#19127636C2212yes—
28#19127614C2214yes—
29#19127614C2212yes—
30#19127613C2212yes—
31#19127613C2214yes—
32#19127612C2212yes—
33#19127608C2214yescomplemented
34#19127607C2214yescomplemented
35#19127606C2214yescomplemented
36#19127605C2214yescomplemented
37#19127605C2214yescomplemented
38#19127605C2214yescomplemented
39#19127605C2214yescomplemented
40#19127588C2214yescomplemented
41#19127587C2214yescomplemented
42#19127586C2214yescomplemented
43#19127585C2214yescomplemented
44#19127584C2214yescomplemented
45#19127583C2214yescomplemented
46#19127582C2214yescomplemented
47#19127564C2211yescharacteristic
48#19127563C2214yes—
49#19127562C2211yescharacteristic
50#19127562C2211yescharacteristic
51C22⋊C4×Dic83C2214yes—
52C4×(C2×D83)⋊C4C2212yes—
53C4×(C2×D83)⋊C4C2212yes—
54C4×C22⋊Dic83C2212yes—
55#19127548C2214yes—
56#95×D83C2214yes—
57#95×D83C2212yes—
58#95×D83C2214yes—
59#95×D83C2214yes—
60#95×D83C2212yes—
61#399×C83C2212yes—
62#393×C83C2212yes—
63#391×C83C2214yescomplemented
64#387×C83C2214yescomplemented
65#381×C83C2211yescharacteristic
66C4×C22⋊C4×C83C2212yes—
67C24×D83C2311yescharacteristic
68C22×Dic166C2312yes—
69C22×Dic166C2314yes—
70C2×Q8×D83—216no—
71C2×Q8×D83—44no—
72C23×Dic83C2311yescharacteristic
73C22×C4×D83—42no—
74C22×C4×D83—42no—
75C22×C4×D83Q818yescomplemented
76C22×C4×D83C2314yes—
77C22×C4×D83C2312yes—
78C22×C4×D83C2312yes—
79C22×C4×D83C2312yes—
80C22×C4×D83C2314yes—
81C22×C4×D83C2312yes—
82C2×C4⋊Dic83C2314yes—
83C2×C4⋊Dic83C2312yes—
84C2×Dic83⋊C4C2314yes—
85C2×Dic83⋊C4C2314yes—
86C2×Dic83⋊C4C2314yes—
87C4⋊C4×D83—216no—
88C4⋊C4×D83—44no—
89C2×C22⋊Dic83C2314yes—
90C2×C22⋊Dic83C2311yescharacteristic
91C2×C22⋊Dic83C2311yescharacteristic
92C2×(C2×D83)⋊C4C2314yes—
93C2×(C2×D83)⋊C4C2314yes—
94C2×(C2×D83)⋊C4C2312yes—
95C2×(C2×D83)⋊C4C2312yes—
96C22⋊C4×D83—216no—
97C22⋊C4×D83—42no—
98C22⋊C4×D83—42no—
99C2×C4×Dic83C2314yes—
100C2×C4×Dic83C2312yes—
101C2×C4×Dic83C2312yes—
102C2×C4×Dic83C2314yes—
103C42×D83—44no—
104C42×D83—44no—
105C83⋊#95C2314yes—
106C83⋊#95C2314yes—
107C83⋊#95C2314yes—
108C83⋊#95C2314yes—
109C83⋊#95C2314yes—
110C83⋊#95C2314yes—
111C83⋊#95C2314yes—
112C83⋊#95C2314yes—
113C83⋊#95C2314yes—
114C83⋊#95C2312yes—
115C83⋊#95C2314yes—
116C83⋊#95C2312yes—
117C83⋊#95C2314yes—
118C22×Q8×C83C2312yes—
119C23×C4×C83C2311yescharacteristic
120C2×C4⋊C4×C83C2314yes—
121C2×C4⋊C4×C83C2312yes—
122C2×C22⋊C4×C83C2314yes—
123C2×C22⋊C4×C83C2311yescharacteristic
124C2×C22⋊C4×C83C2311yescharacteristic
125C2×C42×C83C2312yes—
126C2×C42×C83C2312yes—
127#95×C83C2314yes—
128#95×C83C2312yes—
129#95×C83C2314yes—
130#95×C83C2314yes—
131#95×C83C2312yes—
132C23×D83—28no—
133C23×D83—22no—
134C23×D83—22no—
135C23×D83C2×Q814yes—
136C23×D83C2411yescharacteristic
137C23×D83C2411yescharacteristic
138C2×Dic166—28no—
139C2×Dic166—28no—
140C2×Dic166—28no—
141C2×Dic166—42no—
142C2×Dic166—44no—
143Q8×D83—432no—
144C22×Dic83—41no—
145C22×Dic83—41no—
146C22×Dic83C2×Q814yescomplemented
147C22×Dic83C2412yes—
148C22×Dic83C2414yes—
149C22×Dic83C2412yes—
150C22×Dic83C2412yes—
151C22×Dic83C2414yes—
152C2×C4×D83—28no—
153C2×C4×D83—24no—
154C2×C4×D83—24no—
155C2×C4×D83—28no—
156C2×C4×D83—28no—
157C2×C4×D83—28no—
158C2×C4×D83—28no—
159C2×C4×D83—28no—
160C2×C4×D83—24no—
161C2×C4×D83—28no—
162C2×C4×D83—24no—
163C2×C4×D83—416no—
164C2×C4×D83—42no—
165C2×C4×D83—42no—
166C2×C4×D83C2×Q818yes—
167C2×C4×D83C2×Q818yescomplemented
168C2×C4×D83#41116yes—
169C4⋊Dic83—28no—
170C4⋊Dic83—42no—
171Dic83⋊C4—28no—
172Dic83⋊C4—28no—
173Dic83⋊C4—44no—
174C22⋊Dic83—28no—
175C22⋊Dic83—41no—
176C22⋊Dic83—41no—
177(C2×D83)⋊C4—28no—
178(C2×D83)⋊C4—28no—
179(C2×D83)⋊C4—42no—
180(C2×D83)⋊C4—42no—
181C4×Dic83—44no—
182C4×Dic83—44no—
183C4×Dic83—42no—
184C4×Dic83—42no—
185C24×C83C2411yescharacteristic
186C2×Q8×C83—28no—
187C2×Q8×C83—42no—
188C22×C4×C83—41no—
189C22×C4×C83—41no—
190C22×C4×C83C2×Q814yescomplemented
191C22×C4×C83C2412yes—
192C22×C4×C83C2414yes—
193C22×C4×C83C2412yes—
194C22×C4×C83C2412yes—
195C22×C4×C83C2414yes—
196C4⋊C4×C83—28no—
197C4⋊C4×C83—42no—
198C22⋊C4×C83—28no—
199C22⋊C4×C83—41no—
200C22⋊C4×C83—41no—
201C42×C83—42no—
202C42×C83—42no—
203C23×C83—24no—
204C23×C83—21no—
205C23×C83—21no—
206C23×C83C22×Q812yes—
207C23×C83C2511yescharacteristic
208C22×D83—24no—
209C22×D83—21no—
210C22×D83—21no—
211C22×D83—216no—
212C22×D83—28no—
213C22×D83—48no—
214C22×D83—48no—
215C22×D83C22×Q812yes—
216C22×D83C22×Q812yes—
217C22×D83C2×#4118yes—
218C22×D83H(5,𝔽2)12yes—
219C22×D83H(5,𝔽2)12yes—
220Q8×C83—48no—
221C2×C4×C83—24no—
222C2×C4×C83—22no—
223C2×C4×C83—22no—
224C2×C4×C83—24no—
225C2×C4×C83—24no—
226C2×C4×C83—24no—
227C2×C4×C83—24no—
228C2×C4×C83—24no—
229C2×C4×C83—24no—
230C2×C4×C83—22no—
231C2×C4×C83—22no—
232C2×C4×C83—44no—
233C2×C4×C83C22×Q814yes—
234C2×C4×C83C2×#4118yes—
235C2×Dic83—24no—
236C2×Dic83—22no—
237C2×Dic83—22no—
238C2×Dic83—24no—
239C2×Dic83—24no—
240C2×Dic83—24no—
241C2×Dic83—24no—
242C2×Dic83—24no—
243C2×Dic83—24no—
244C2×Dic83—22no—
245C2×Dic83—22no—
246C2×Dic83—44no—
247C2×Dic83C22×Q814yes—
248C2×Dic83C2×#4118yes—
249C4×D83—216no—
250C4×D83—232no—
251C4×D83—48no—
252C4×D83—48no—
253C4×D83—416no—
254C4×D83—48no—
255Dic166—48no—
256Dic166—416no—
257C22×C83—24no—
258C22×C83—22no—
259C22×C83—42no—
260C22×C83—42no—
261C22×C83C23×Q811yescharacteristic
262C22×C83C22×#4114yes—
263C22×C83C2×H(5,𝔽2)11yescharacteristic
264C22×C83C2×H(5,𝔽2)11yescharacteristic
265C2×D83—24no—
266C2×D83—22no—
267C2×D83—42no—
268C2×D83—42no—
269C2×D83—416no—
270C2×D83#53318yes—
271C2×D83#54314yes—
272C2×D83#55118yes—
273C2×D83#55918yes—
274C4×C83—24no—
275C4×C83—28no—
276C4×C83—42no—
277C4×C83—44no—
278C4×C83—42no—
279Dic83—24no—
280Dic83—28no—
281Dic83—42no—
282Dic83—44no—
283Dic83—42no—
284C2×#2607—831nomaximal, Sylow
285C2×C83—42no—
286C2×C83C2×#53312yes—
287C2×C83C2×#54311yescharacteristic
288C2×C83C2×#55112yes—
289C2×C83C2×#55912yes—
290D83—42no—
291D83#260718yesdirect product factor
292#2607—832no—
293#2607—832no—
294#2607—834no—
295#2607—834no—
296#2607—831no—
297#2607—832no—
298#2607D8311yescharacteristic, direct product factor
299C2×#399—832no—
300C2×#393—832no—
301C2×#391—834no—
302C2×#387—834no—
303C2×#381—831no—
304C2×C4×C22⋊C4—832no—
305C83C2×#260711yescharacteristic, complemented, Sylow
306C23×Q8—832no—
307C24×C4—831no—
308C22×C4⋊C4—832no—
309C22×C4⋊C4—834no—
310C22×C22⋊C4—831no—
311C22×C22⋊C4—831no—
312C22×C22⋊C4—834no—
313C22×C42—832no—
314C22×C42—832no—
315#399—834no—
316#399—832no—
317#399—834no—
318#399—832no—
319#399—832no—
320#399C2×D8312yes—
321#393—832no—
322#393—834no—
323#393—832no—
324#393—834no—
325#393—832no—
326#393C2×D8312yes—
327#391—834no—
328#391—834no—
329#391—834no—
330#391—834no—
331#391—834no—
332#391—834no—
333#391—834no—
334#391C2×D8314yescomplemented
335#387—834no—
336#387—834no—
337#387—834no—
338#387—834no—
339#387—834no—
340#387—834no—
341#387—834no—
342#387C2×D8314yescomplemented
343#381—831no—
344#381—831no—
345#381—831no—
346#381—834no—
347#381C2×D8311yescharacteristic
348C4×C22⋊C4—832no—
349C4×C22⋊C4—834no—
350C4×C22⋊C4—832no—
351C4×C22⋊C4—832no—
352C4×C22⋊C4—834no—
353C4×C22⋊C4C2×D8312yes—
354C2×#95—832no—
355C2×#95—834no—
356C2×#95—832no—
357C2×#95—834no—
358C2×#95—834no—
359C25—831no—
360C22×Q8—3324no—
361C22×Q8—832no—
362C22×Q8—834no—
363C22×Q8—16616no—
364C22×Q8C22×D8312yes—
365C23×C4—3322no—
366C23×C4—3322no—
367C23×C4—831no—
368C23×C4—838no—
369C23×C4—832no—
370C23×C4—834no—
371C23×C4—832no—
372C23×C4—832no—
373C23×C4—834no—
374C23×C4—832no—
375C23×C4C22×D8311yescharacteristic
376C2×C4⋊C4—3324no—
377C2×C4⋊C4—834no—
378C2×C4⋊C4—832no—
379C2×C4⋊C4—834no—
380C2×C4⋊C4—834no—
381C2×C4⋊C4—834no—
382C2×C4⋊C4—16616no—
383C2×C4⋊C4C22×D8314yes—
384C2×C4⋊C4C22×D8312yes—
385C2×C22⋊C4—3322no—
386C2×C22⋊C4—3322no—
387C2×C22⋊C4—831no—
388C2×C22⋊C4—831no—
389C2×C22⋊C4—832no—
390C2×C22⋊C4—832no—
391C2×C22⋊C4—834no—
392C2×C22⋊C4—834no—
393C2×C22⋊C4—834no—
394C2×C22⋊C4—16616no—
395C2×C22⋊C4C22×D8314yes—
396C2×C22⋊C4C22×D8311yescharacteristic
397C2×C22⋊C4C22×D8311yescharacteristic
398C2×C42—3324no—
399C2×C42—3324no—
400C2×C42—834no—
401C2×C42—832no—
402C2×C42—834no—
403C2×C42—832no—
404C2×C42C22×D8312yes—
405C2×C42C22×D8312yes—
406#95—834no—
407#95—834no—
408#95—834no—
409#95—834no—
410#95—834no—
411#95—834no—
412#95—834no—
413#95—832no—
414#95—834no—
415#95—834no—
416#95—834no—
417#95—832no—
418#95—834no—
419#95C22×D8314yes—
420#95C22×D8314yes—
421#95C22×D8312yes—
422#95C22×D8314yes—
423#95C22×D8312yes—
424C24—831no—
425C24—834no—
426C24—831no—
427C24—1662no—
428C24—1662no—
429C24—1668no—
430C24C23×D8311yescharacteristic
431C2×Q8—28no—
432C2×Q8—42no—
433C2×Q8—3324no—
434C2×Q8—3322no—
435C2×Q8—33232no—
436C2×Q8—1668no—
437C2×Q8—1668no—
438C2×Q8—1668no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—3322no—
442C22×C4—3322no—
443C22×C4—33216no—
444C22×C4—3321no—
445C22×C4—3321no—
446C22×C4—834no—
447C22×C4—838no—
448C22×C4—832no—
449C22×C4—834no—
450C22×C4—838no—
451C22×C4—8316no—
452C22×C4—832no—
453C22×C4—834no—
454C22×C4—832no—
455C22×C4—1668no—
456C22×C4—1664no—
457C22×C4—1664no—
458C22×C4—1668no—
459C22×C4—1668no—
460C22×C4—1668no—
461C22×C4—1668no—
462C22×C4—1664no—
463C22×C4—1664no—
464C22×C4—1668no—
465C22×C4—1668no—
466C22×C4Q8×D8314yescomplemented
467C22×C4C23×D8312yes—
468C22×C4C23×D8314yes—
469C22×C4C23×D8312yes—
470C22×C4C23×D8312yes—
471C22×C4C23×D8314yes—
472C4⋊C4—28no—
473C4⋊C4—42no—
474C4⋊C4—3324no—
475C4⋊C4—3322no—
476C4⋊C4—1668no—
477C4⋊C4—1668no—
478C4⋊C4—1668no—
479C22⋊C4—28no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—3322no—
483C22⋊C4—3322no—
484C22⋊C4—3321no—
485C22⋊C4—3321no—
486C22⋊C4—1668no—
487C22⋊C4—1668no—
488C22⋊C4—1668no—
489C42—42no—
490C42—42no—
491C42—3322no—
492C42—3322no—
493C42—3324no—
494C42—3324no—
495C23—24no—
496C23—21no—
497C23—21no—
498C23—3328no—
499C23—3328no—
500C23—832no—
501C23—838no—
502C23—832no—
503C23—832no—
504C23—832no—
505C23—1668no—
506C23—16616no—
507C23—1664no—
508C23—1661no—
509C23—1661no—
510C23C2×Q8×D8312yes—
511C23C24×D8311yescharacteristic
512Q8—48no—
513Q8—33216no—
514Q8—3328no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—44no—
527C2×C4—3328no—
528C2×C4—3328no—
529C2×C4—33216no—
530C2×C4—3328no—
531C2×C4—3324no—
532C2×C4—834no—
533C2×C4—838no—
534C2×C4—16616no—
535C2×C4—16632no—
536C2×C4—1664no—
537C2×C4—1664no—
538C2×C4—1664no—
539C2×C4—1664no—
540C2×C4—1664no—
541C2×C4—1662no—
542C2×C4—1662no—
543C2×C4—1664no—
544C2×C4—1662no—
545C2×C4—1662no—
546C2×C4—1664no—
547C2×C4C2×Q8×D8314yes—
548C2×C4#41×D8318yes—
549C22—22no—
550C22—24no—
551C22—42no—
552C22—42no—
553C22—33216no—
554C22—3322no—
555C22—3322no—
556C22—834no—
557C22—838no—
558C22—838no—
559C22—838no—
560C22—1662no—
561C22—1664no—
562C22C22×Q8×D8311yescharacteristic
563C22C2×#41×D8314yes—
564C22H(5,𝔽2)×D8311yescharacteristic
565C22H(5,𝔽2)×D8311yescharacteristic
566C4—24no—
567C4—28no—
568C4—42no—
569C4—44no—
570C4—42no—
571C4—3322no—
572C4—3324no—
573C4—3322no—
574C4—1664no—
575C4—1668no—
576C2—42no—
577C2—3322no—
578C2—838no—
579C2#533×D8312yes—
580C2#543×D8311yescharacteristic
581C2#551×D8312yes—
582C2#559×D8312yes—
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2607C2
prime radicalC24×D83C23
hypercenter#2607D83
hypocenterC83C2×#2607
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2607

Complements

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

NH ≅ G/Ntype
1. #24913128C2semidirect
2. #24913127C2semidirect
3. #24913126C2semidirect
4. #24913125C2semidirect
5. #24913124C2semidirect
6. #24913123C2semidirect
9. #391×D83C2semidirect
10. #387×D83C2semidirect
13. C83×#2607C2semidirect
33. #19127608C22semidirect
34. #19127607C22semidirect
35. #19127606C22semidirect
36. #19127605C22semidirect
37. #19127605C22semidirect
38. #19127605C22semidirect
39. #19127605C22semidirect
40. #19127588C22semidirect
41. #19127587C22semidirect
42. #19127586C22semidirect
43. #19127585C22semidirect
44. #19127584C22semidirect
45. #19127583C22semidirect
46. #19127582C22semidirect
63. #391×C83C22semidirect
64. #387×C83C22semidirect
75. C22×C4×D83Q8semidirect
146. C22×Dic83C2×Q8semidirect
167. C2×C4×D83C2×Q8semidirect
190. C22×C4×C83C2×Q8semidirect
291. D83#2607direct (N × H)
298. #2607D83direct (N × H)
305. C83C2×#2607semidirect
334. #391C2×D83semidirect
342. #387C2×D83semidirect
466. C22×C4Q8×D83semidirect

Maximal subgroups

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

subgroupindex
#249131282
#249131272
#249131262
#249131252
#249131242
#249131232
#399×D832
#393×D832
#391×D832
#387×D832
#381×D832
C4×C22⋊C4×D832
C83×#26072
C2×#260783