Finite Group Databasebeta

← #2483×D83 #35573324

Subgroups — #2483×D83 #35573324

Order 21248.

4382 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D83C212yesmaximal
2#24911744C211yesmaximal, characteristic, complemented
3#24911743C214yesmaximal, complemented
4#24911742C214yesmaximal, complemented
5#24911741C212yesmaximal, complemented
6#24911740C214yesmaximal, complemented
7#397×D83C214yesmaximal, complemented
8#385×D83C214yesmaximal, complemented
9#381×D83C214yesmaximal, complemented
10#379×D83C211yesmaximal, characteristic
11C83×#2483C211yesmaximal, characteristic, complemented
12C25×D83C2211yescharacteristic
13C23×C4×D83C2212yes—
14C23×C4×D83C2212yes—
15C2×C4⋊C4×D83C2214yescomplemented
16C22×C22⋊Dic83C2212yes—
17C22×(C2×D83)⋊C4C2212yes—
18C22×(C2×D83)⋊C4C2212yes—
19C2×C22⋊C4×D83—216no—
20C2×C22⋊C4×D83C2214yes—
21C2×C22⋊C4×D83C2214yes—
22C2×C22⋊C4×D83C2214yes—
23C2×C22⋊C4×D83C2214yes—
24C2×C22⋊C4×D83C2214yes—
25C2×C22⋊C4×D83C2212yes—
26#19127630C2218yescomplemented
27#19127629C2218yescomplemented
28#19127628C2214yescomplemented
29#19127627C2214yescomplemented
30#19127626C2214yescomplemented
31#19127576C2214yescomplemented
32#19127575C2218yescomplemented
33#19127574C2214yescomplemented
34#19127573C2214yescomplemented
35#19127572C2218yescomplemented
36#19127564C2214yescomplemented
37#19127563C2218yescomplemented
38#19127563C2218yescomplemented
39#19127562C2214yescomplemented
40#19127562C2214yescomplemented
41#19127557C2211yescharacteristic
42#19127556C2212yes—
43#19127556C2214yes—
44#95×D83C2214yescomplemented
45#95×D83C2218yescomplemented
46C22×C22⋊C4×C83C2212yes—
47#397×C83C2214yescomplemented
48#385×C83C2214yescomplemented
49#381×C83C2214yescomplemented
50#379×C83C2211yescharacteristic
51C24×D83—216no—
52C24×D83—44no—
53C24×D83D418yes—
54C24×D83C2311yescharacteristic
55C24×D83C2311yescharacteristic
56C24×D83C2312yes—
57C24×D83C2312yes—
58C23×Dic83C2312yes—
59C23×Dic83C2312yes—
60C22×C4×D83—28no—
61C22×C4×D83—28no—
62C22×C4×D83—216no—
63C22×C4×D83—48no—
64C22×C4×D83C2314yes—
65C22×C4×D83C2314yes—
66C22×C4×D83C2314yes—
67C22×C4×D83C2314yes—
68C22×C4×D83C2314yes—
69C2×C4⋊Dic83C2314yescomplemented
70C2×Dic83⋊C4C2318yescomplemented
71C4⋊C4×D83—48no—
72C2×C22⋊Dic83—28no—
73C2×C22⋊Dic83C2314yes—
74C2×C22⋊Dic83C2314yes—
75C2×C22⋊Dic83C2314yes—
76C2×C22⋊Dic83C2312yes—
77C2×(C2×D83)⋊C4—28no—
78C2×(C2×D83)⋊C4—28no—
79C2×(C2×D83)⋊C4C2318yes—
80C2×(C2×D83)⋊C4C2314yes—
81C2×(C2×D83)⋊C4C2314yes—
82C2×(C2×D83)⋊C4C2314yes—
83C2×(C2×D83)⋊C4C2314yes—
84C2×(C2×D83)⋊C4C2314yes—
85C22⋊C4×D83—216no—
86C22⋊C4×D83—216no—
87C22⋊C4×D83—216no—
88C22⋊C4×D83—216no—
89C22⋊C4×D83—216no—
90C22⋊C4×D83—44no—
91C83⋊#95C2314yescomplemented
92C83⋊#95C2318yescomplemented
93C83⋊#95C2318yescomplemented
94C83⋊#95C2318yescomplemented
95C83⋊#95C2318yescomplemented
96C25×C83C2311yescharacteristic
97C23×C4×C83C2312yes—
98C23×C4×C83C2312yes—
99C2×C4⋊C4×C83C2314yescomplemented
100C2×C22⋊C4×C83—28no—
101C2×C22⋊C4×C83C2314yes—
102C2×C22⋊C4×C83C2314yes—
103C2×C22⋊C4×C83C2314yes—
104C2×C22⋊C4×C83C2312yes—
105#95×C83C2314yescomplemented
106#95×C83C2318yescomplemented
107C23×D83—28no—
108C23×D83—28no—
109C23×D83—28no—
110C23×D83—264no—
111C23×D83—28no—
112C23×D83—28no—
113C23×D83—28no—
114C23×D83—24no—
115C23×D83—416no—
116C23×D83—42no—
117C23×D83—44no—
118C23×D83—464no—
119C23×D83C2×D414yes—
120C23×D83C2×D414yes—
121C23×D83C2×D418yes—
122C23×D83C2×D418yes—
123C23×D83#41116yes—
124C23×D83C2411yescharacteristic
125C23×D83C2412yes—
126C23×D83C2411yescharacteristic
127C22×Dic83—24no—
128C22×Dic83—24no—
129C22×Dic83—28no—
130C22×Dic83—44no—
131C22×Dic83C2414yes—
132C22×Dic83C2414yes—
133C22×Dic83C2414yes—
134C2×C4×D83—28no—
135C2×C4×D83—28no—
136C2×C4×D83—28no—
137C2×C4×D83—28no—
138C2×C4×D83—216no—
139C2×C4×D83—216no—
140C2×C4×D83—216no—
141C2×C4×D83—216no—
142C2×C4×D83—28no—
143C2×C4×D83—48no—
144C2×C4×D83—432no—
145C2×C4×D83—432no—
146C4⋊Dic83—44no—
147Dic83⋊C4—48no—
148C22⋊Dic83—28no—
149C22⋊Dic83—28no—
150C22⋊Dic83—28no—
151C22⋊Dic83—42no—
152(C2×D83)⋊C4—28no—
153(C2×D83)⋊C4—28no—
154(C2×D83)⋊C4—28no—
155(C2×D83)⋊C4—28no—
156(C2×D83)⋊C4—216no—
157(C2×D83)⋊C4—44no—
158C24×C83—28no—
159C24×C83—42no—
160C24×C83C2×D414yes—
161C24×C83C2411yescharacteristic
162C24×C83C2412yes—
163C22×C4×C83—24no—
164C22×C4×C83—24no—
165C22×C4×C83—28no—
166C22×C4×C83—44no—
167C22×C4×C83C2414yes—
168C22×C4×C83C2414yes—
169C22×C4×C83C2414yes—
170C4⋊C4×C83—44no—
171C22⋊C4×C83—28no—
172C22⋊C4×C83—28no—
173C22⋊C4×C83—28no—
174C22⋊C4×C83—42no—
175C23×C83—24no—
176C23×C83—24no—
177C23×C83—216no—
178C23×C83—24no—
179C23×C83—22no—
180C23×C83—44no—
181C23×C83—416no—
182C23×C83C22×D412yes—
183C23×C83C22×D414yes—
184C23×C83C2×#4118yes—
185C23×C83C2511yescharacteristic
186C22×D83—24no—
187C22×D83—24no—
188C22×D83—216no—
189C22×D83—216no—
190C22×D83—264no—
191C22×D83—216no—
192C22×D83—24no—
193C22×D83—22no—
194C22×D83—216no—
195C22×D83—216no—
196C22×D83—216no—
197C22×D83—28no—
198C22×D83—44no—
199C22×D83—48no—
200C22×D83—416no—
201C22×D83—4128no—
202C22×D83—432no—
203C22×D83—416no—
204C22×D83#123132yes—
205C22×D83C22×D412yes—
206C22×D83C22×D414yes—
207C22×D83C22×D412yes—
208C22×D83C2×#4118yes—
209C22×D83C2×#4118yes—
210C22×D83H(5,𝔽2)14yes—
211C2×C4×C83—24no—
212C2×C4×C83—24no—
213C2×C4×C83—28no—
214C2×C4×C83—28no—
215C2×C4×C83—24no—
216C2×C4×C83—28no—
217C2×C4×C83—48no—
218C2×C4×C83—48no—
219C2×Dic83—24no—
220C2×Dic83—24no—
221C2×Dic83—28no—
222C2×Dic83—28no—
223C2×Dic83—24no—
224C2×Dic83—28no—
225C2×Dic83—48no—
226C2×Dic83—48no—
227C4×D83—416no—
228C4×D83—416no—
229C4×D83—416no—
230C4×D83—416no—
231C4×D83—416no—
232C22×C83—24no—
233C22×C83—24no—
234C22×C83—216no—
235C22×C83—24no—
236C22×C83—22no—
237C22×C83—416no—
238C22×C83—44no—
239C22×C83C2×#12318yes—
240C22×C83C23×D411yescharacteristic
241C22×C83C22×#4114yes—
242C22×C83C2×H(5,𝔽2)12yes—
243C2×D83—24no—
244C2×D83—24no—
245C2×D83—216no—
246C2×D83—264no—
247C2×D83—24no—
248C2×D83—22no—
249C2×D83—416no—
250C2×D83—432no—
251C2×D83—44no—
252C2×D83—416no—
253C2×D83C2×#12318yes—
254C2×D83C2×#12318yes—
255C2×D83#53414yes—
256C2×D83#551116yes—
257C4×C83—44no—
258C4×C83—44no—
259C4×C83—44no—
260Dic83—44no—
261Dic83—44no—
262Dic83—44no—
263C2×#2483—831nomaximal, Sylow
264C2×C83—28no—
265C2×C83—42no—
266C2×C83C22×#12312yes—
267C2×C83C2×#53411yescharacteristic
268C2×C83C2×#55114yes—
269D83—28no—
270D83—42no—
271D83#248318yesdirect product factor
272C23×C22⋊C4—832no—
273#2483—834no—
274#2483—834no—
275#2483—834no—
276#2483—831no—
277#2483—832no—
278#2483D8311yescharacteristic, direct product factor
279C2×#397—834no—
280C2×#385—834no—
281C2×#381—834no—
282C2×#379—831no—
283C83C2×#248311yescharacteristic, complemented, Sylow
284C26—831no—
285C24×C4—832no—
286C24×C4—832no—
287C22×C4⋊C4—834no—
288C22×C22⋊C4—832no—
289C22×C22⋊C4—832no—
290C22×C22⋊C4—832no—
291C22×C22⋊C4—832no—
292C22×C22⋊C4—834no—
293C22×C22⋊C4—834no—
294C22×C22⋊C4—834no—
295C22×C22⋊C4—834no—
296C22×C22⋊C4—834no—
297C22×C22⋊C4—16616no—
298C22×C22⋊C4C2×D8312yes—
299#397—834no—
300#397—834no—
301#397—838no—
302#397—834no—
303#397—838no—
304#397C2×D8314yescomplemented
305#385—834no—
306#385—838no—
307#385—834no—
308#385—834no—
309#385—838no—
310#385C2×D8314yescomplemented
311#381—834no—
312#381—834no—
313#381—834no—
314#381—838no—
315#381—838no—
316#381C2×D8314yescomplemented
317#379—831no—
318#379—832no—
319#379—834no—
320#379C2×D8311yescharacteristic
321C2×#95—834no—
322C2×#95—838no—
323C25—3324no—
324C25—838no—
325C25—831no—
326C25—832no—
327C25—832no—
328C25—831no—
329C25—16616no—
330C25C22×D8311yescharacteristic
331C23×C4—3328no—
332C23×C4—832no—
333C23×C4—834no—
334C23×C4—832no—
335C23×C4—834no—
336C23×C4—834no—
337C23×C4—834no—
338C23×C4—834no—
339C23×C4—1668no—
340C23×C4—1668no—
341C23×C4—16616no—
342C23×C4C22×D8312yes—
343C23×C4C22×D8312yes—
344C2×C4⋊C4—3328no—
345C2×C4⋊C4—838no—
346C2×C4⋊C4—834no—
347C2×C4⋊C4C22×D8314yescomplemented
348C2×C22⋊C4—28no—
349C2×C22⋊C4—3324no—
350C2×C22⋊C4—832no—
351C2×C22⋊C4—834no—
352C2×C22⋊C4—834no—
353C2×C22⋊C4—834no—
354C2×C22⋊C4—834no—
355C2×C22⋊C4—834no—
356C2×C22⋊C4—834no—
357C2×C22⋊C4—834no—
358C2×C22⋊C4—834no—
359C2×C22⋊C4—838no—
360C2×C22⋊C4—16616no—
361C2×C22⋊C4—16616no—
362C2×C22⋊C4—16616no—
363C2×C22⋊C4—16616no—
364C2×C22⋊C4—16616no—
365C2×C22⋊C4—1668no—
366C2×C22⋊C4—1668no—
367C2×C22⋊C4—1668no—
368C2×C22⋊C4C22×D8314yes—
369C2×C22⋊C4C22×D8314yes—
370C2×C22⋊C4C22×D8314yes—
371C2×C22⋊C4C22×D8312yes—
372#95—834no—
373#95—838no—
374#95—838no—
375#95—838no—
376#95—838no—
377#95C22×D8314yescomplemented
378#95C22×D8318yescomplemented
379C24—28no—
380C24—42no—
381C24—3324no—
382C24—3322no—
383C24—33264no—
384C24—33216no—
385C24—834no—
386C24—838no—
387C24—831no—
388C24—838no—
389C24—8316no—
390C24—832no—
391C24—834no—
392C24—831no—
393C24—1664no—
394C24—1668no—
395C24—16664no—
396C24—1668no—
397C24—1668no—
398C24—1668no—
399C24—1668no—
400C24—1668no—
401C24D4×D8314yes—
402C24C23×D8311yescharacteristic
403C24C23×D8312yes—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—28no—
407C22×C4—44no—
408C22×C4—3328no—
409C22×C4—33232no—
410C22×C4—33232no—
411C22×C4—3324no—
412C22×C4—834no—
413C22×C4—834no—
414C22×C4—834no—
415C22×C4—1668no—
416C22×C4—1668no—
417C22×C4—1668no—
418C22×C4—1668no—
419C22×C4—1668no—
420C22×C4—16616no—
421C22×C4—16616no—
422C22×C4—16616no—
423C22×C4—16616no—
424C22×C4—1664no—
425C22×C4—1664no—
426C22×C4—1668no—
427C22×C4C23×D8314yes—
428C22×C4C23×D8314yes—
429C22×C4C23×D8314yes—
430C4⋊C4—44no—
431C4⋊C4—3328no—
432C4⋊C4—3324no—
433C22⋊C4—28no—
434C22⋊C4—28no—
435C22⋊C4—28no—
436C22⋊C4—42no—
437C22⋊C4—3324no—
438C22⋊C4—3322no—
439C22⋊C4—1668no—
440C22⋊C4—1668no—
441C22⋊C4—1668no—
442C22⋊C4—1668no—
443C22⋊C4—16616no—
444C22⋊C4—1668no—
445C22⋊C4—1668no—
446C22⋊C4—1668no—
447C23—24no—
448C23—24no—
449C23—216no—
450C23—24no—
451C23—22no—
452C23—44no—
453C23—416no—
454C23—33232no—
455C23—3328no—
456C23—3324no—
457C23—33216no—
458C23—332128no—
459C23—33216no—
460C23—832no—
461C23—838no—
462C23—834no—
463C23—8332no—
464C23—834no—
465C23—838no—
466C23—832no—
467C23—1668no—
468C23—16616no—
469C23—16616no—
470C23—16616no—
471C23—16616no—
472C23—16664no—
473C23—16616no—
474C23—16616no—
475C23—1664no—
476C23—1662no—
477C23—1664no—
478C23—1664no—
479C23C2×D4×D8312yes—
480C23C2×D4×D8314yes—
481C23#41×D8318yes—
482C23C24×D8311yescharacteristic
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—28no—
486C2×C4—28no—
487C2×C4—24no—
488C2×C4—28no—
489C2×C4—48no—
490C2×C4—48no—
491C2×C4—33216no—
492C2×C4—33216no—
493C2×C4—33216no—
494C2×C4—33216no—
495C2×C4—33216no—
496C2×C4—3328no—
497C2×C4—3328no—
498C2×C4—1664no—
499C2×C4—1664no—
500C2×C4—1668no—
501C2×C4—1668no—
502C2×C4—1664no—
503C2×C4—1668no—
504C22—24no—
505C22—216no—
506C22—24no—
507C22—24no—
508C22—22no—
509C22—416no—
510C22—44no—
511C22—33232no—
512C22—33216no—
513C22—33216no—
514C22—3324no—
515C22—838no—
516C22—8316no—
517C22—834no—
518C22—838no—
519C22—16664no—
520C22—1664no—
521C22—1662no—
522C22—1664no—
523C22—16616no—
524C22—1664no—
525C22#123×D8318yes—
526C22C22×D4×D8311yescharacteristic
527C22C2×#41×D8314yes—
528C22H(5,𝔽2)×D8312yes—
529C4—44no—
530C4—44no—
531C4—44no—
532C4—3324no—
533C4—3324no—
534C4—3324no—
535C2—28no—
536C2—42no—
537C2—3322no—
538C2—838no—
539C2—1668no—
540C2C2×#123×D8312yes—
541C2#534×D8311yescharacteristic
542C2#551×D8314yes—
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2483C2
prime radicalC25×D83C22
hypercenter#2483D83
hypocenterC83C2×#2483
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2483

Complements

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

NH ≅ G/Ntype
2. #24911744C2semidirect
3. #24911743C2semidirect
4. #24911742C2semidirect
5. #24911741C2semidirect
6. #24911740C2semidirect
7. #397×D83C2semidirect
8. #385×D83C2semidirect
9. #381×D83C2semidirect
11. C83×#2483C2semidirect
15. C2×C4⋊C4×D83C22semidirect
26. #19127630C22semidirect
27. #19127629C22semidirect
28. #19127628C22semidirect
29. #19127627C22semidirect
30. #19127626C22semidirect
31. #19127576C22semidirect
32. #19127575C22semidirect
33. #19127574C22semidirect
34. #19127573C22semidirect
35. #19127572C22semidirect
36. #19127564C22semidirect
37. #19127563C22semidirect
38. #19127563C22semidirect
39. #19127562C22semidirect
40. #19127562C22semidirect
44. #95×D83C22semidirect
45. #95×D83C22semidirect
47. #397×C83C22semidirect
48. #385×C83C22semidirect
49. #381×C83C22semidirect
69. C2×C4⋊Dic83C23semidirect
70. C2×Dic83⋊C4C23semidirect
91. C83⋊#95C23semidirect
92. C83⋊#95C23semidirect
93. C83⋊#95C23semidirect
94. C83⋊#95C23semidirect
95. C83⋊#95C23semidirect
99. C2×C4⋊C4×C83C23semidirect
105. #95×C83C23semidirect
106. #95×C83C23semidirect
271. D83#2483direct (N × H)
278. #2483D83direct (N × H)
283. C83C2×#2483semidirect
304. #397C2×D83semidirect
310. #385C2×D83semidirect
316. #381C2×D83semidirect
347. C2×C4⋊C4C22×D83semidirect
377. #95C22×D83semidirect
378. #95C22×D83semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D832
#249117442
#249117432
#249117422
#249117412
#249117402
#397×D832
#385×D832
#381×D832
#379×D832
C83×#24832
C2×#248383