Finite Group Databasebeta

← #35375160

Subgroups — #35375160

Order 21248.

606 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918027C211yesmaximal, characteristic
2#24916439C211yesmaximal, characteristic, complemented
3#24916432C211yesmaximal, characteristic, complemented
4#24906344C211yesmaximal, characteristic, complemented
5#24906338C211yesmaximal, characteristic, complemented
6#24906337C211yesmaximal, characteristic, complemented
7#24906331C211yesmaximal, characteristic, complemented
8#24906330C211yesmaximal, characteristic, complemented
9#24906324C211yesmaximal, characteristic, complemented
10#24906323C211yesmaximal, characteristic, complemented
11#24906317C211yesmaximal, characteristic, complemented
12#24906224C211yesmaximal, characteristic, complemented
13#24905924C211yesmaximal, characteristic, complemented
14C2×#19127422C211yesmaximal, characteristic, complemented
15C83×#1494C211yesmaximal, characteristic, complemented
16#19128235C2211yescharacteristic
17#19128100C411yescharacteristic
18#19128083C411yescharacteristic
19#19128058C411yescharacteristic
20#19128055C411yescharacteristic
21#19127940C411yescharacteristic
22#19127935C411yescharacteristic
23#19127932C411yescharacteristic
24#19127928C411yescharacteristic
25#19127832C2211yescharacteristic
26#19127828C2211yescharacteristic
27Q8×C83⋊C8C2211yescharacteristic
28#19127825C2211yescharacteristic
29C4×#13050580C2211yescharacteristic
30C4×#13050577C2211yescharacteristic
31C4×#13050578C2211yescharacteristic
32C4×#13050575C2211yescharacteristic
33#19127779C2211yescharacteristic
34#19127778C2211yescharacteristic
35#19127773—21no—
36#19127769—21no—
37D4×C83⋊C8—21no—
38D4×C83⋊C8C2211yescharacteristic
39#19127766C2211yescharacteristic
40(C22⋊D83)⋊C8—21no—
41#19127763—21no—
42#19127762—21no—
43#19127758C2211yescharacteristic
44#19127658—21no—
45#19127657—21no—
46C2×C4×C83⋊C8C2211yescharacteristic
47C2×C4×C83⋊C8C2211yescharacteristic
48#19127453C2211yescharacteristic
49#19127453C2211yescharacteristic
50#19127451C2211yescharacteristic
51#19127451C2211yescharacteristic
52#19127433C2211yescharacteristic
53#19127433C2211yescharacteristic
54#19127430C2211yescharacteristic
55#19127430C2211yescharacteristic
56#19127422C2211yescharacteristic
57#19127422C2211yescharacteristic
58#19127422C2211yescharacteristic
59#19127422C2211yescharacteristic
60#529×C83C2211yescharacteristic
61#432×C83C2211yescharacteristic
62C2×C4×C8×C83C2211yescharacteristic
63Q8⋊C8×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65D4⋊C8×C83C2211yescharacteristic
66D4⋊C8×C83C2211yescharacteristic
67C2×#13050580C2×C411yescharacteristic
68C2×#13050578C2×C411yescharacteristic
69C2×#13050577C2×C411yescharacteristic
70C2×#13050575C2×C411yescharacteristic
71C2×#13050574—21no—
72C2×#13050573—21no—
73C22×C83⋊C8—21no—
74C22×C83⋊C8C2×C411yescharacteristic
75C22×C83⋊C8C2×C411yescharacteristic
76C22×C83⋊C8D411yescharacteristic
77C22×C83⋊C8D411yescharacteristic
78C2×C8×D83—21no—
79#14581786—21no—
80#14581784C2×C411yescharacteristic
81#14581780C2×C411yescharacteristic
82#14581775—21no—
83#14581771C2×C411yescharacteristic
84#14581766C2×C411yescharacteristic
85C4×Dic166C2311yescharacteristic
86C4×D332C2311yescharacteristic
87C4×C22⋊D83—21no—
88#14581749—21no—
89#14581725C2×C411yescharacteristic
90#14581725C2×C411yescharacteristic
91#14581723C2×C411yescharacteristic
92#14581723C2×C411yescharacteristic
93C4⋊(C83⋊C8)—21no—
94C4⋊(C83⋊C8)—21no—
95C4⋊(C83⋊C8)C2311yescharacteristic
96C4⋊(C83⋊C8)C2311yescharacteristic
97Dic83⋊C8—21no—
98Dic83⋊C8—21no—
99#14581716C2×C411yescharacteristic
100#14581716C2×C411yescharacteristic
101#14581715C2×C411yescharacteristic
102#14581715C2×C411yescharacteristic
103#14581713C2×C411yescharacteristic
104#14581713C2×C411yescharacteristic
105#14581712C2×C411yescharacteristic
106#14581712C2×C411yescharacteristic
107C22⋊(C83⋊C8)—21no—
108C22⋊(C83⋊C8)—21no—
109C22⋊(C83⋊C8)—21no—
110(C2×D83)⋊C8—21no—
111(C2×D83)⋊C8—21no—
112#14581703—21no—
113#14581703—21no—
114#14581702—21no—
115C4×C83⋊C8—21no—
116C4×C83⋊C8C2×C411yescharacteristic
117C4×C83⋊C8C2×C411yescharacteristic
118C4×C83⋊C8D411yescharacteristic
119C4×C83⋊C8D411yescharacteristic
120C4×C83⋊C8C2311yescharacteristic
121C4×C83⋊C8C2311yescharacteristic
122C4×C83⋊C8C2311yescharacteristic
123C4×C83⋊C8C2311yescharacteristic
124C8×Dic83—21no—
125C22×C8×C83—21no—
126#126×C83—21no—
127#125×C83C2×C411yescharacteristic
128#124×C83C2×C411yescharacteristic
129#123×C83—21no—
130C22⋊Q8×C83C2×C411yescharacteristic
131#121×C83C2×C411yescharacteristic
132C4×Q8×C83C2311yescharacteristic
133C4×D4×C83—21no—
134C4×D4×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—41no—
149#13050578—41no—
150#13050577—41no—
151#13050575—41no—
152#13050574—42no—
153#13050573—42no—
154C2×C83⋊C8—21no—
155C2×C83⋊C8—21no—
156C2×C83⋊C8—41no—
157C2×C83⋊C8—41no—
158C2×C83⋊C8—41no—
159C2×C83⋊C8—41no—
160C2×C83⋊C8—42no—
161C2×C83⋊C8C22×C411yescharacteristic
162C2×C83⋊C8C22×C411yescharacteristic
163C2×C83⋊C8C22×C411yescharacteristic
164C2×C83⋊C8C22×C411yescharacteristic
165C2×C83⋊C8C2×D411yescharacteristic
166C2×C83⋊C8C2×D411yescharacteristic
167C2×C83⋊C8C2×D411yescharacteristic
168C2×C83⋊C8C2×D411yescharacteristic
169C8×D83—42no—
170C4⋊Dic83C22×C411yescharacteristic
171C4⋊Dic83C22×C411yescharacteristic
172Dic83⋊C4—21no—
173Dic83⋊C4—21no—
174Dic83⋊C4—21no—
175Dic83⋊C4—21no—
176C22⋊Dic83—21no—
177(C2×D83)⋊C4—21no—
178(C2×D83)⋊C4—21no—
179(C2×D83)⋊C4—21no—
180(C2×D83)⋊C4—21no—
181C4×Dic83—21no—
182C2×Q8×C83C22×C411yescharacteristic
183C2×D4×C83—21no—
184C2×D4×C83C22×C411yescharacteristic
185C22×C4×C83—21no—
186C22×C4×C83C22×C411yescharacteristic
187C22×C4×C83C2×D411yescharacteristic
188C22×C4×C83#4111yescharacteristic
189C2×C8×C83—24no—
190C2×C8×C83—21no—
191C2×C8×C83—21no—
192C2×C8×C83—21no—
193C2×C8×C83—21no—
194C4⋊C4×C83—21no—
195C4⋊C4×C83—21no—
196C4⋊C4×C83—21no—
197C4⋊C4×C83—21no—
198C4⋊C4×C83C22×C411yescharacteristic
199C4⋊C4×C83C22×C411yescharacteristic
200C22⋊C4×C83—21no—
201C22⋊C4×C83—21no—
202C22⋊C4×C83—21no—
203C22⋊C4×C83—21no—
204C22⋊C4×C83—21no—
205C42×C83—21no—
206C42×C83C22×C411yescharacteristic
207C42×C83C2×D411yescharacteristic
208C42×C83#4111yescharacteristic
209C42×C83C2411yescharacteristic
210C23×C83—21no—
211C23×C83C4×D411yescharacteristic
212C22×D83—21no—
213Q8×C83—21no—
214Q8×C83—21no—
215D4×C83—21no—
216D4×C83—21no—
217D4×C83—42no—
218C2×C4×C83—22no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83—21no—
222C2×C4×C83—21no—
223C2×C4×C83—21no—
224C2×C4×C83—21no—
225C2×C4×C83—21no—
226C2×C4×C83—41no—
227C2×C4×C83—41no—
228C2×C4×C83C4×D411yescharacteristic
229C2×C4×C83C4×D411yescharacteristic
230C2×C4×C83C4×D411yescharacteristic
231C2×C4×C83C23×C411yescharacteristic
232C2×C4×C83C22×D411yescharacteristic
233C2×C4×C83C2×#4111yescharacteristic
234C22⋊D83—42no—
235C2×Dic83—21no—
236C2×Dic83—21no—
237C2×Dic83—21no—
238D332—21no—
239D332—21no—
240C4×D83—41no—
241C4×D83—41no—
242Dic166—21no—
243Dic166—21no—
244C8×C83—22no—
245C8×C83—22no—
246C8×C83—41no—
247C8×C83—41no—
248C83⋊C8—21no—
249C83⋊C8—21no—
250C83⋊C8—21no—
251C83⋊C8—21no—
252C83⋊C8—21no—
253C83⋊C8—21no—
254C83⋊C8—21no—
255C83⋊C8—21no—
256C83⋊C8—41no—
257C83⋊C8—41no—
258C22×C83—21no—
259C22×C83—21no—
260C22×C83—41no—
261C22×C83—41no—
262C22×C83—41no—
263C22×C83#44312yes—
264C22×C83C2×C4×D411yescharacteristic
265C2×D83—41no—
266C2×D83—41no—
267C2×D83—41no—
268C4×C83—21no—
269C4×C83—21no—
270C4×C83—21no—
271C4×C83—21no—
272C4×C83—41no—
273C4×C83—41no—
274C4×C83—41no—
275C4×C83#56811yescharacteristic
276C4×C83#56811yescharacteristic
277C4×C83#57511yescharacteristic
278C4×C83#57511yescharacteristic
279Dic83—41no—
280Dic83—41no—
281Dic83—41no—
282#17982—831nomaximal, Sylow
283C2×C83—22no—
284C2×C83—81no—
285C2×C83#293211yescharacteristic
286C2×C83#294311yescharacteristic
287C2×C83C2×#44311yescharacteristic
288D83—81no—
289#3168—831no—
290#2966—831no—
291#2966—831no—
292#1588—831no—
293#1588—831no—
294#1587—831no—
295#1587—831no—
296#1586—831no—
297#1586—831no—
298#1585—831no—
299#1585—831no—
300#1568—831no—
301#1494—831no—
302#1494D8311yescharacteristic, complemented
303C2×#322—831no—
304C83#1798211yescharacteristic, complemented, Sylow
305#529—831no—
306#529C2×D8311yescharacteristic
307#499—831no—
308#495—831no—
309#488—831no—
310#488—831no—
311#467—831no—
312#466—831no—
313#465—831no—
314#465—831no—
315#446—831no—
316#446—831no—
317C8×Q8—831no—
318C8×Q8—831no—
319C4×Q16—831no—
320C4×SD16—831no—
321C4×SD16—831no—
322C4×D8—831no—
323#436—831no—
324#436—831no—
325#435—1661no—
326#435—1661no—
327C8×D4—831no—
328C8×D4—831no—
329C8×D4—1661no—
330C8×D4—1661no—
331#433—1661no—
332#433—1661no—
333#432—831no—
334#432C2×D8311yescharacteristic
335#405—1661no—
336#405—1661no—
337C2×C4×C8—831no—
338C2×C4×C8—831no—
339C2×C4×C8C2×D8311yescharacteristic
340#335—831no—
341#335—831no—
342#334—831no—
343#334—831no—
344Q8⋊C8—831no—
345Q8⋊C8—831no—
346Q8⋊C8C2×D8311yescharacteristic
347Q8⋊C8C2×D8311yescharacteristic
348D4⋊C8—831no—
349D4⋊C8—831no—
350D4⋊C8C2×D8311yescharacteristic
351D4⋊C8C2×D8311yescharacteristic
352#322—831no—
353#322—831no—
354#322—831no—
355#322—831no—
356C2×Q16—831no—
357C2×SD16—831no—
358C2×SD16—831no—
359C2×D8—831no—
360C2×M16—1661no—
361C2×M16—1661no—
362C22×C8—21no—
363C22×C8—831no—
364C22×C8—831no—
365C22×C8—831no—
366C22×C8—831no—
367C22×C8—1661no—
368C22×C8—1661no—
369#126—21no—
370#126—1661no—
371#125—831no—
372#125C4×D8311yescharacteristic
373#124—831no—
374#124C4×D8311yescharacteristic
375#123—21no—
376#123—1661no—
377C22⋊Q8—831no—
378C22⋊Q8C4×D8311yescharacteristic
379#121—831no—
380#121C4×D8311yescharacteristic
381C4×Q8—831no—
382C4×Q8C22×D8311yescharacteristic
383C4×D4—21no—
384C4×D4—831no—
385C4×D4—1661no—
386C4×D4C22×D8311yescharacteristic
387#117—21no—
388#117—1661no—
389C2×C42C22×D8311yescharacteristic
390#107—831no—
391#107—831no—
392#106—831no—
393#106—831no—
394C4⋊C8—831no—
395C4⋊C8—831no—
396C4⋊C8—1661no—
397C4⋊C8—1661no—
398C4⋊C8—1661no—
399C4⋊C8—1661no—
400C4⋊C8C22×D8311yescharacteristic
401C4⋊C8C22×D8311yescharacteristic
402#103—831no—
403#103—831no—
404#103—831no—
405#103—831no—
406#102—831no—
407#102—831no—
408#102—831no—
409#102—831no—
410C22⋊C8—21no—
411C22⋊C8—1661no—
412C22⋊C8—1661no—
413C22⋊C8—1661no—
414C22⋊C8—1661no—
415C22⋊C8—1661no—
416#97—21no—
417#97—1661no—
418#97—1661no—
419#97—1661no—
420C4×C8—21no—
421C4×C8—831no—
422C4×C8—831no—
423C4×C8—831no—
424C4×C8—831no—
425C4×C8—831no—
426C4×C8—831no—
427C4×C8—831no—
428C4×C8—831no—
429C4×C8—1661no—
430C4×C8—1661no—
431C4×C8C22×D8311yescharacteristic
432C4×C8C22×D8311yescharacteristic
433C2×Q8—831no—
434C2×Q8C2×C4×D8311yescharacteristic
435C2×D4—21no—
436C2×D4—831no—
437C2×D4—1661no—
438C2×D4C2×C4×D8311yescharacteristic
439C22×C4—21no—
440C22×C4—1661no—
441C22×C4C2×C4×D8311yescharacteristic
442C22×C4D4×D8311yescharacteristic
443C22×C4#1305058911yescharacteristic
444Q16—3321no—
445SD16—3321no—
446SD16—3321no—
447D8—3321no—
448M16—3322no—
449M16—3322no—
450C2×C8—24no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—3322no—
456C2×C8—3322no—
457C2×C8—3321no—
458C2×C8—3321no—
459C2×C8—3321no—
460C2×C8—3321no—
461C2×C8—831no—
462C2×C8—831no—
463C2×C8—831no—
464C2×C8—831no—
465C2×C8—831no—
466C2×C8—831no—
467C2×C8—831no—
468C2×C8—831no—
469C2×C8—1661no—
470C2×C8—1661no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—831no—
476C4⋊C4—831no—
477C4⋊C4—1661no—
478C4⋊C4—1661no—
479C4⋊C4—1661no—
480C4⋊C4—1661no—
481C4⋊C4C2×C4×D8311yescharacteristic
482C4⋊C4C2×C4×D8311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—1661no—
489C22⋊C4—1661no—
490C22⋊C4—1661no—
491C22⋊C4—1661no—
492C22⋊C4—1661no—
493C42—21no—
494C42—1661no—
495C42C2×C4×D8311yescharacteristic
496C42D4×D8311yescharacteristic
497C42#1305058911yescharacteristic
498C42C23×D8311yescharacteristic
499C23—21no—
500C23—1661no—
501C23(C22⋊D83)⋊C411yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—1661no—
505Q8—1661no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—3322no—
510D4—1661no—
511D4—1661no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—3321no—
523C2×C4—3321no—
524C2×C4—1661no—
525C2×C4—1661no—
526C2×C4—1661no—
527C2×C4(C22⋊D83)⋊C411yescharacteristic
528C2×C4(C22⋊D83)⋊C411yescharacteristic
529C2×C4(C22⋊D83)⋊C411yescharacteristic
530C2×C4C22×C4×D8311yescharacteristic
531C2×C4C2×D4×D8311yescharacteristic
532C2×C4C2×#1305058911yescharacteristic
533C8—22no—
534C8—22no—
535C8—41no—
536C8—41no—
537C8—3321no—
538C8—3321no—
539C8—1661no—
540C8—1661no—
541C8—1661no—
542C8—1661no—
543C8—1661no—
544C8—1661no—
545C8—1661no—
546C8—1661no—
547C22—21no—
548C22—21no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—3321no—
553C22—3321no—
554C22—3321no—
555C22#1912781512yes—
556C22C2×(C22⋊D83)⋊C411yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—3321no—
565C4—3321no—
566C4—3321no—
567C4#1912846611yescharacteristic
568C4#1912846611yescharacteristic
569C4#1912849811yescharacteristic
570C4#1912849811yescharacteristic
571C2—22no—
572C2—81no—
573C2—6641no—
574C2#2491617811yescharacteristic
575C2#2491625911yescharacteristic
576C2C2×#1912781511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1494C2
socleC22×C83C2×C4×D4
prime radical#19127935C4
cosocleC42×C83C24
hypercenter#1494D83
hypocenterC83#17982
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #24916439C2semidirect
3. #24916432C2semidirect
4. #24906344C2semidirect
5. #24906338C2semidirect
6. #24906337C2semidirect
7. #24906331C2semidirect
8. #24906330C2semidirect
9. #24906324C2semidirect
10. #24906323C2semidirect
11. #24906317C2semidirect
12. #24906224C2semidirect
13. #24905924C2semidirect
14. C2×#19127422C2semidirect
15. C83×#1494C2semidirect
302. #1494D83semidirect
304. C83#17982semidirect

Maximal subgroups

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

subgroupindex
#249180272
#249164392
#249164322
#249063442
#249063382
#249063372
#249063312
#249063302
#249063242
#249063232
#249063172
#249062242
#249059242
C2×#191274222
C83×#14942
#1798283