Finite Group Databasebeta

← #35376267

Subgroups — #35376267

Order 21248.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918063C211yesmaximal, characteristic
2#24916461C211yesmaximal, characteristic
3#24916412C211yesmaximal, characteristic, complemented
4#24906368C211yesmaximal, characteristic, complemented
5#24906357C211yesmaximal, characteristic, complemented
6#24906338C211yesmaximal, characteristic, complemented
7#24906337C211yesmaximal, characteristic, complemented
8#24906310C211yesmaximal, characteristic, complemented
9#24906302C211yesmaximal, characteristic, complemented
10#24906279C211yesmaximal, characteristic, complemented
11#24906260C211yesmaximal, characteristic, complemented
12#24906216C211yesmaximal, characteristic, complemented
13#24905877C211yesmaximal, characteristic
14#24905766C211yesmaximal, characteristic, complemented
15C83×#1485C211yesmaximal, characteristic, complemented
16#19128235C2211yescharacteristic
17#19128107C411yescharacteristic
18#19128093C411yescharacteristic
19#19128069C411yescharacteristic
20#19128063C411yescharacteristic
21#19127957C411yescharacteristic
22#19127957C411yescharacteristic
23#19127949C411yescharacteristic
24#19127949C411yescharacteristic
25#19127832—21no—
26#19127832—21no—
27#19127832C2211yescharacteristic
28#19127832C2211yescharacteristic
29#19127828C2211yescharacteristic
30Q8×C83⋊C8C2211yescharacteristic
31Q8×C83⋊C8C2211yescharacteristic
32#19127825C2211yescharacteristic
33C4×#13050580C2211yescharacteristic
34C4×#13050580C2211yescharacteristic
35C4×#13050577C2211yescharacteristic
36C4×#13050577C2211yescharacteristic
37#19127778C2211yescharacteristic
38#19127776—21no—
39#19127775—21no—
40#19127766C2211yescharacteristic
41#19127760—21no—
42#19127728—21no—
43C2×C4⋊(C83⋊C8)C2211yescharacteristic
44#19127657—21no—
45#19127655—21no—
46C4×#13050574C2211yescharacteristic
47C4×#13050574C2211yescharacteristic
48#19127453C2211yescharacteristic
49#19127453C2211yescharacteristic
50#19127451C2211yescharacteristic
51#19127451C2211yescharacteristic
52#19127433C2211yescharacteristic
53#19127433C2211yescharacteristic
54#19127430C2211yescharacteristic
55#19127430C2211yescharacteristic
56#19127423C2211yescharacteristic
57#19127423C2211yescharacteristic
58#19127422C2211yescharacteristic
59C8×C83⋊C8C2211yescharacteristic
60#533×C83C2211yescharacteristic
61#431×C83C2211yescharacteristic
62C4×M16×C83C2211yescharacteristic
63Q8⋊C8×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65Q8⋊C8×C83C2211yescharacteristic
66Q8⋊C8×C83C2211yescharacteristic
67C2×#13050580C2×C411yescharacteristic
68C2×#13050580C2×C411yescharacteristic
69C2×#13050577C2×C411yescharacteristic
70C2×#13050577C2×C411yescharacteristic
71C2×#13050574C2×C411yescharacteristic
72C2×#13050574C2×C411yescharacteristic
73C2×#13050574D411yescharacteristic
74C2×#13050574D411yescharacteristic
75C2×#13050573—21no—
76C22×C83⋊C8—21no—
77C2×C8×D83—21no—
78#14581786—21no—
79#14581784C2×C411yescharacteristic
80#14581780C2×C411yescharacteristic
81#14581775—21no—
82#14581771C2×C411yescharacteristic
83#14581766C2×C411yescharacteristic
84C4×Dic166C2311yescharacteristic
85C4×D332C2311yescharacteristic
86C4×C22⋊D83—21no—
87#14581749—21no—
88#14581725C2×C411yescharacteristic
89#14581725C2×C411yescharacteristic
90#14581723C2×C411yescharacteristic
91#14581723C2×C411yescharacteristic
92C4⋊(C83⋊C8)—21no—
93C4⋊(C83⋊C8)—21no—
94C4⋊(C83⋊C8)—21no—
95C4⋊(C83⋊C8)—21no—
96C4⋊(C83⋊C8)—21no—
97C4⋊(C83⋊C8)C2311yescharacteristic
98C4⋊(C83⋊C8)C2311yescharacteristic
99Dic83⋊C8—21no—
100Dic83⋊C8—21no—
101#14581716C2×C411yescharacteristic
102#14581716C2×C411yescharacteristic
103#14581716C2×C411yescharacteristic
104#14581716C2×C411yescharacteristic
105#14581715C2×C411yescharacteristic
106#14581715C2×C411yescharacteristic
107#14581712C2×C411yescharacteristic
108#14581712C2×C411yescharacteristic
109(C2×D83)⋊C8—21no—
110(C2×D83)⋊C8—21no—
111#14581703—21no—
112#14581703—21no—
113#14581703C2×C411yescharacteristic
114#14581703C2×C411yescharacteristic
115#14581703D411yescharacteristic
116#14581703D411yescharacteristic
117#14581702—21no—
118C4×C83⋊C8—21no—
119C4×C83⋊C8—21no—
120C4×C83⋊C8C2311yescharacteristic
121C4×C83⋊C8C2311yescharacteristic
122C4×C83⋊C8C2311yescharacteristic
123C4×C83⋊C8C2311yescharacteristic
124C8×Dic83—21no—
125C2×M16×C83—21no—
126C4⋊Q8×C83C2×C411yescharacteristic
127C4⋊Q8×C83C2×C411yescharacteristic
128#125×C83—21no—
129C22⋊Q8×C83—21no—
130C22⋊Q8×C83C2×C411yescharacteristic
131C22⋊Q8×C83C2×C411yescharacteristic
132C4×Q8×C83—21no—
133C4×Q8×C83C2311yescharacteristic
134C4×Q8×C83C2311yescharacteristic
135#117×C83—21no—
136C2×C42×C83C2311yescharacteristic
137C4⋊C8×C83C2311yescharacteristic
138C4⋊C8×C83C2311yescharacteristic
139C22⋊C8×C83—21no—
140#97×C83—21no—
141C4×C8×C83—21no—
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C2×Dic166C22×C411yescharacteristic
145C2×D332C22×C411yescharacteristic
146C2×C22⋊D83—21no—
147C2×C4×D83—21no—
148#13050580—22no—
149#13050580—41no—
150#13050577—22no—
151#13050577—41no—
152#13050574—22no—
153#13050574—22no—
154#13050574—41no—
155#13050574—41no—
156#13050573—42no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—42no—
160C2×C83⋊C8C22×C411yescharacteristic
161C2×C83⋊C8C22×C411yescharacteristic
162C2×C83⋊C8C22×C411yescharacteristic
163C2×C83⋊C8C22×C411yescharacteristic
164C2×C83⋊C8C2×D411yescharacteristic
165C2×C83⋊C8C2×D411yescharacteristic
166C2×C83⋊C8C2×D411yescharacteristic
167C2×C83⋊C8C2×D411yescharacteristic
168C8×D83—42no—
169C4⋊Dic83C22×C411yescharacteristic
170C4⋊Dic83C22×C411yescharacteristic
171Dic83⋊C4—21no—
172Dic83⋊C4—21no—
173Dic83⋊C4—21no—
174Dic83⋊C4—21no—
175C22⋊Dic83—21no—
176(C2×D83)⋊C4—21no—
177(C2×D83)⋊C4—21no—
178(C2×D83)⋊C4—21no—
179(C2×D83)⋊C4—21no—
180C4×Dic83—21no—
181C2×Q8×C83—21no—
182C2×Q8×C83C22×C411yescharacteristic
183C2×Q8×C83C22×C411yescharacteristic
184C22×C4×C83C22×C411yescharacteristic
185C22×C4×C83C2×D411yescharacteristic
186C22×C4×C83#4111yescharacteristic
187M16×C83—42no—
188C2×C8×C83—21no—
189C2×C8×C83—21no—
190C2×C8×C83—21no—
191C2×C8×C83—21no—
192C4⋊C4×C83—21no—
193C4⋊C4×C83—21no—
194C4⋊C4×C83—21no—
195C4⋊C4×C83—21no—
196C4⋊C4×C83—21no—
197C4⋊C4×C83—21no—
198C4⋊C4×C83—21no—
199C4⋊C4×C83C22×C411yescharacteristic
200C4⋊C4×C83C22×C411yescharacteristic
201C22⋊C4×C83—21no—
202C22⋊C4×C83—21no—
203C42×C83—21no—
204C42×C83—21no—
205C42×C83C22×C411yescharacteristic
206C42×C83C2×D411yescharacteristic
207C42×C83#4111yescharacteristic
208C42×C83C2411yescharacteristic
209C23×C83C4×D411yescharacteristic
210C22×D83—21no—
211Q8×C83—21no—
212Q8×C83—21no—
213Q8×C83—21no—
214Q8×C83—21no—
215Q8×C83—81no—
216C2×C4×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83—21no—
222C2×C4×C83—21no—
223C2×C4×C83—21no—
224C2×C4×C83—41no—
225C2×C4×C83C4×D411yescharacteristic
226C2×C4×C83C4×D411yescharacteristic
227C2×C4×C83C4×D411yescharacteristic
228C2×C4×C83C23×C411yescharacteristic
229C2×C4×C83C22×D411yescharacteristic
230C2×C4×C83C2×#4111yescharacteristic
231C22⋊D83—81no—
232C2×Dic83—21no—
233C2×Dic83—21no—
234C2×Dic83—21no—
235D332—21no—
236D332—21no—
237C4×D83—41no—
238C4×D83—41no—
239Dic166—21no—
240Dic166—21no—
241C8×C83—22no—
242C8×C83—41no—
243C8×C83—41no—
244C8×C83—41no—
245C83⋊C8—21no—
246C83⋊C8—21no—
247C83⋊C8—21no—
248C83⋊C8—21no—
249C83⋊C8—21no—
250C83⋊C8—21no—
251C83⋊C8—41no—
252C83⋊C8—41no—
253C83⋊C8#13112yes—
254C83⋊C8#13712yes—
255C22×C83—21no—
256C22×C83—21no—
257C22×C83—21no—
258C22×C83C2×C4×D411yescharacteristic
259C2×D83—41no—
260C2×D83—41no—
261C2×D83—41no—
262C4×C83—21no—
263C4×C83—21no—
264C4×C83—21no—
265C4×C83—21no—
266C4×C83—41no—
267C4×C83—41no—
268C4×C83—41no—
269C4×C83—41no—
270C4×C83C2×#13111yescharacteristic
271C4×C83#56811yescharacteristic
272C4×C83C2×#13711yescharacteristic
273C4×C83#57511yescharacteristic
274Dic83—41no—
275Dic83—41no—
276Dic83—41no—
277#18077—831nomaximal, Sylow
278C2×C83—41no—
279C2×C83#293511yescharacteristic
280C2×C83C4×#13711yescharacteristic
281C2×C83#295611yescharacteristic
282D83—81no—
283#3172—831no—
284#2969—831no—
285#2962—831no—
286#1592—831no—
287#1591—831no—
288#1588—831no—
289#1587—831no—
290#1584—831no—
291#1582—831no—
292#1579—831no—
293C8×SD16—831no—
294#1565—831no—
295#1485D8311yescharacteristic, complemented
296#1483—831no—
297#1455—831no—
298C83#1807711yescharacteristic, complemented, Sylow
299#533C2×D8311yescharacteristic
300#529—831no—
301#501—831no—
302#497—831no—
303#491—831no—
304#489—831no—
305#470—831no—
306#470—831no—
307#468—831no—
308#468—831no—
309#446—831no—
310#446—831no—
311#446—831no—
312#446—1661no—
313#446—1661no—
314C8×Q8—831no—
315C8×Q8—831no—
316C8×Q8—831no—
317C4×Q16—831no—
318C4×Q16—831no—
319C4×SD16—831no—
320C4×SD16—831no—
321#436—831no—
322#436—1661no—
323#435—1661no—
324C8×D4—831no—
325#433—1661no—
326#431C2×D8311yescharacteristic
327#424—1661no—
328C2×C4⋊C8—831no—
329#405—1661no—
330#405—1661no—
331C4×M16—831no—
332C4×M16—831no—
333C4×M16C2×D8311yescharacteristic
334#335—831no—
335#335—831no—
336#334—831no—
337#334—831no—
338Q8⋊C8—831no—
339Q8⋊C8—831no—
340Q8⋊C8C2×D8311yescharacteristic
341Q8⋊C8C2×D8311yescharacteristic
342Q8⋊C8C2×D8311yescharacteristic
343Q8⋊C8C2×D8311yescharacteristic
344D4⋊C8—831no—
345D4⋊C8—831no—
346#322—831no—
347#322—831no—
348#322—831no—
349C82—831no—
350C2×Q16—831no—
351C2×Q16—831no—
352C2×SD16—831no—
353C2×SD16—831no—
354C2×M16—21no—
355C2×M16—831no—
356C2×M16—831no—
357C2×M16—831no—
358C2×M16—831no—
359C2×M16—1661no—
360C22×C8—1661no—
361C22×C8—1661no—
362C4⋊Q8C4×D8311yescharacteristic
363C4⋊Q8C4×D8311yescharacteristic
364#126—1661no—
365#125—21no—
366#125—831no—
367#124—831no—
368#123—1661no—
369C22⋊Q8—21no—
370C22⋊Q8—831no—
371C22⋊Q8C4×D8311yescharacteristic
372C22⋊Q8C4×D8311yescharacteristic
373#121—831no—
374C4×Q8—21no—
375C4×Q8—831no—
376C4×Q8C22×D8311yescharacteristic
377C4×Q8C22×D8311yescharacteristic
378C4×D4—831no—
379C4×D4—1661no—
380#117—21no—
381#117—1661no—
382C2×C42C22×D8311yescharacteristic
383#107—831no—
384#107—831no—
385#106—831no—
386#106—831no—
387C4⋊C8—831no—
388C4⋊C8—831no—
389C4⋊C8—1661no—
390C4⋊C8—1661no—
391C4⋊C8—1661no—
392C4⋊C8—1661no—
393C4⋊C8—1661no—
394C4⋊C8—1661no—
395C4⋊C8—1661no—
396C4⋊C8C22×D8311yescharacteristic
397C4⋊C8C22×D8311yescharacteristic
398#103—831no—
399#103—831no—
400#103—831no—
401#103—831no—
402#103—831no—
403#103—831no—
404#102—831no—
405#102—831no—
406C22⋊C8—21no—
407C22⋊C8—1661no—
408C22⋊C8—1661no—
409#97—21no—
410#97—831no—
411#97—831no—
412#97—831no—
413#97—831no—
414#97—1661no—
415#97—1661no—
416#97—1661no—
417C4×C8—21no—
418C4×C8—831no—
419C4×C8—831no—
420C4×C8—831no—
421C4×C8—831no—
422C4×C8—1661no—
423C4×C8—1661no—
424C4×C8—1661no—
425C4×C8C22×D8311yescharacteristic
426C4×C8C22×D8311yescharacteristic
427C2×Q8—21no—
428C2×Q8—831no—
429C2×Q8C2×C4×D8311yescharacteristic
430C2×Q8C2×C4×D8311yescharacteristic
431C2×D4—831no—
432C2×D4—1661no—
433C22×C4—1661no—
434C22×C4C2×C4×D8311yescharacteristic
435C22×C4D4×D8311yescharacteristic
436C22×C4#1305058911yescharacteristic
437Q16—3321no—
438Q16—1662no—
439SD16—3321no—
440SD16—1662no—
441M16—42no—
442M16—3322no—
443M16—3321no—
444M16—3321no—
445M16—1662no—
446M16—1662no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—3322no—
452C2×C8—3322no—
453C2×C8—831no—
454C2×C8—831no—
455C2×C8—831no—
456C2×C8—831no—
457C2×C8—831no—
458C2×C8—831no—
459C2×C8—831no—
460C2×C8—831no—
461C2×C8—1661no—
462C2×C8—1661no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—831no—
471C4⋊C4—831no—
472C4⋊C4—1661no—
473C4⋊C4—1661no—
474C4⋊C4—1661no—
475C4⋊C4—1661no—
476C4⋊C4C2×C4×D8311yescharacteristic
477C4⋊C4C2×C4×D8311yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—1661no—
481C22⋊C4—1661no—
482C22⋊C4—1661no—
483C22⋊C4—1661no—
484C22⋊C4—1661no—
485C42—21no—
486C42—21no—
487C42—1661no—
488C42C2×C4×D8311yescharacteristic
489C42D4×D8311yescharacteristic
490C42#1305058911yescharacteristic
491C42C23×D8311yescharacteristic
492C23—1661no—
493C23(C22⋊D83)⋊C411yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—81no—
499Q8—1661no—
500Q8—1661no—
501D4—6641no—
502D4—1661no—
503D4—1661no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—3321no—
514C2×C4—3321no—
515C2×C4—1661no—
516C2×C4—1661no—
517C2×C4—1661no—
518C2×C4(C22⋊D83)⋊C411yescharacteristic
519C2×C4(C22⋊D83)⋊C411yescharacteristic
520C2×C4(C22⋊D83)⋊C411yescharacteristic
521C2×C4C22×C4×D8311yescharacteristic
522C2×C4C2×D4×D8311yescharacteristic
523C2×C4C2×#1305058911yescharacteristic
524C8—22no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—3321no—
529C8—3321no—
530C8—832no—
531C8—832no—
532C8—1661no—
533C8—1661no—
534C8—1661no—
535C8—1661no—
536C8—1661no—
537C8—1661no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—3321no—
542C22—3321no—
543C22—3321no—
544C22C2×(C22⋊D83)⋊C411yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—3321no—
554C4—3321no—
555C4—3321no—
556C4#131×D8311yescharacteristic
557C4#1912846611yescharacteristic
558C4#137×D8311yescharacteristic
559C4#1912850011yescharacteristic
560C2—41no—
561C2—6641no—
562C2#2491620311yescharacteristic
563C2#2491627811yescharacteristic
564C2#2491636911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1485C2
socleC22×C83C2×C4×D4
prime radical#14581766C2×C4
cosocleC42×C83C24
hypercenter#1485D83
hypocenterC83#18077
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1485

Complements

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

NH ≅ G/Ntype
3. #24916412C2semidirect
4. #24906368C2semidirect
5. #24906357C2semidirect
6. #24906338C2semidirect
7. #24906337C2semidirect
8. #24906310C2semidirect
9. #24906302C2semidirect
10. #24906279C2semidirect
11. #24906260C2semidirect
12. #24906216C2semidirect
14. #24905766C2semidirect
15. C83×#1485C2semidirect
295. #1485D83semidirect
298. C83#18077semidirect

Maximal subgroups

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

subgroupindex
#249180632
#249164612
#249164122
#249063682
#249063572
#249063382
#249063372
#249063102
#249063022
#249062792
#249062602
#249062162
#249058772
#249057662
C83×#14852
#1807783