Finite Group Databasebeta

← #35375135

Subgroups — #35375135

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#24918029C211yesmaximal, characteristic
2#24916437C211yesmaximal, characteristic, complemented
3#24916435C211yesmaximal, characteristic, complemented
4#24906311C211yesmaximal, characteristic, complemented
5#24906310C211yesmaximal, characteristic, complemented
6#24906308C211yesmaximal, characteristic, complemented
7#24906307C211yesmaximal, characteristic, complemented
8#24906298C211yesmaximal, characteristic, complemented
9#24906295C211yesmaximal, characteristic, complemented
10#24906292C211yesmaximal, characteristic, complemented
11#24906223C211yesmaximal, characteristic, complemented
12#24905922C211yesmaximal, characteristic, complemented
13#24905920C211yesmaximal, characteristic, complemented
14#322×D83C211yesmaximal, characteristic, complemented
15C83×#1582C211yesmaximal, characteristic, complemented
16#19128238C2211yescharacteristic
17#19128233C2211yescharacteristic
18#19128101C411yescharacteristic
19#19128082C411yescharacteristic
20#19128057C411yescharacteristic
21#19128054C411yescharacteristic
22#19127941C411yescharacteristic
23#19127936C411yescharacteristic
24#19127931C411yescharacteristic
25#19127927C411yescharacteristic
26#19127828C2211yescharacteristic
27Q8×C83⋊C8C2211yescharacteristic
28C8×Dic166C2211yescharacteristic
29C4×#13050580C2211yescharacteristic
30C4×#13050579C2211yescharacteristic
31C4×#13050575C2211yescharacteristic
32#19127780C2211yescharacteristic
33#19127779C2211yescharacteristic
34#19127775—21no—
35#19127774—21no—
36#19127766—21no—
37#19127766C2211yescharacteristic
38C8×C22⋊D83—21no—
39#19127761—21no—
40#19127759—21no—
41#19127757C2211yescharacteristic
42#19127757C2211yescharacteristic
43#19127658—21no—
44#19127656—21no—
45C4×C8×D83C2211yescharacteristic
46C4×C8×D83C2211yescharacteristic
47C4×C8×D83C2211yescharacteristic
48#19127453C2211yescharacteristic
49#19127453C2211yescharacteristic
50#19127452C2211yescharacteristic
51#19127433C2211yescharacteristic
52Q8⋊(C83⋊C8)C2211yescharacteristic
53#19127431C2211yescharacteristic
54#19127430C2211yescharacteristic
55D4⋊(C83⋊C8)C2211yescharacteristic
56#19127428C2211yescharacteristic
57#19127423C2211yescharacteristic
58#19127423C2211yescharacteristic
59#19127422C2211yescharacteristic
60#446×C83C2211yescharacteristic
61C4×SD16×C83C2211yescharacteristic
62C8×D4×C83C2211yescharacteristic
63#334×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65D4⋊C8×C83C2211yescharacteristic
66#322×C83C2211yescharacteristic
67C2×#13050580C2×C411yescharacteristic
68C2×#13050579C2×C411yescharacteristic
69C2×#13050575C2×C411yescharacteristic
70C2×#13050574—21no—
71C2×#13050573—21no—
72C2×C8×D83—21no—
73C2×C8×D83—21no—
74C2×C8×D83C2×C411yescharacteristic
75C2×C8×D83C2×C411yescharacteristic
76C2×C8×D83D411yescharacteristic
77C2×C8×D83D411yescharacteristic
78#14581787—21no—
79#14581785—21no—
80#14581783C2×C411yescharacteristic
81#14581783C2×C411yescharacteristic
82#14581781C2×C411yescharacteristic
83#14581779C2×C411yescharacteristic
84#14581777—21no—
85#14581774—21no—
86#14581772C2×C411yescharacteristic
87#14581768C2×C411yescharacteristic
88#14581767C2×C411yescharacteristic
89#14581763C2×C411yescharacteristic
90C4×Dic166C2311yescharacteristic
91C4×D332—21no—
92C4×D332C2311yescharacteristic
93C4×C22⋊D83—21no—
94#14581751—21no—
95#14581749—21no—
96C42×D83C2311yescharacteristic
97#14581725C2×C411yescharacteristic
98#14581725C2×C411yescharacteristic
99#14581724C2×C411yescharacteristic
100C4⋊(C83⋊C8)—21no—
101C4⋊(C83⋊C8)C2311yescharacteristic
102C4⋊(C83⋊C8)C2311yescharacteristic
103Dic83⋊C8—21no—
104Dic83⋊C8—21no—
105#14581717C2×C411yescharacteristic
106#14581716C2×C411yescharacteristic
107#14581715C2×C411yescharacteristic
108#14581714C2×C411yescharacteristic
109#14581713C2×C411yescharacteristic
110#14581712C2×C411yescharacteristic
111C22⋊(C83⋊C8)—21no—
112(C2×D83)⋊C8—21no—
113(C2×D83)⋊C8—21no—
114(C2×D83)⋊C8—21no—
115(C2×D83)⋊C8—21no—
116#14581702—21no—
117#14581702—21no—
118#14581702—21no—
119C4×C83⋊C8—21no—
120C4×C83⋊C8C2311yescharacteristic
121C4×C83⋊C8C2311yescharacteristic
122C4×C83⋊C8C2311yescharacteristic
123C8×Dic83—21no—
124C8×Dic83—21no—
125C8×Dic83C2×C411yescharacteristic
126C8×Dic83C2×C411yescharacteristic
127C8×Dic83D411yescharacteristic
128C8×Dic83D411yescharacteristic
129C2×SD16×C83C2×C411yescharacteristic
130C22×C8×C83—21no—
131C4×Q8×C83C2311yescharacteristic
132C4×D4×C83C2311yescharacteristic
133#106×C83C2×C411yescharacteristic
134C4⋊C8×C83—21no—
135C4⋊C8×C83C2311yescharacteristic
136C4⋊C8×C83C2311yescharacteristic
137#103×C83C2×C411yescharacteristic
138#102×C83C2×C411yescharacteristic
139C22⋊C8×C83—21no—
140#97×C83—21no—
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C2×Dic166C22×C411yescharacteristic
145C2×D332—21no—
146C2×D332C22×C411yescharacteristic
147C2×C22⋊D83—21no—
148C2×C4×D83—21no—
149C2×C4×D83C22×C411yescharacteristic
150C2×C4×D83C2×D411yescharacteristic
151C2×C4×D83#4111yescharacteristic
152#13050580—41no—
153#13050579—41no—
154#13050575—41no—
155#13050574—42no—
156#13050573—42no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8C22×C411yescharacteristic
161C2×C83⋊C8C22×C411yescharacteristic
162C2×C83⋊C8C2×D411yescharacteristic
163C2×C83⋊C8C2×D411yescharacteristic
164C8×D83—22no—
165C8×D83—22no—
166C8×D83—41no—
167C8×D83—41no—
168C8×D83—42no—
169C8×D83—42no—
170C4⋊Dic83—21no—
171C4⋊Dic83—21no—
172C4⋊Dic83—21no—
173C4⋊Dic83C22×C411yescharacteristic
174C4⋊Dic83C22×C411yescharacteristic
175Dic83⋊C4—21no—
176Dic83⋊C4—21no—
177Dic83⋊C4—21no—
178Dic83⋊C4—21no—
179C22⋊Dic83—21no—
180C22⋊Dic83—21no—
181C22⋊Dic83—21no—
182(C2×D83)⋊C4—21no—
183(C2×D83)⋊C4—21no—
184(C2×D83)⋊C4—21no—
185(C2×D83)⋊C4—21no—
186(C2×D83)⋊C4—21no—
187(C2×D83)⋊C4—21no—
188C4×Dic83—21no—
189C4×Dic83C22×C411yescharacteristic
190C4×Dic83C2×D411yescharacteristic
191C4×Dic83#4111yescharacteristic
192C2×Q8×C83C22×C411yescharacteristic
193C2×D4×C83C22×C411yescharacteristic
194C22×C4×C83—21no—
195SD16×C83—41no—
196C2×C8×C83—21no—
197C2×C8×C83—21no—
198C2×C8×C83—21no—
199C2×C8×C83—42no—
200C2×C8×C83C22×C411yescharacteristic
201C2×C8×C83C22×C411yescharacteristic
202C2×C8×C83C2×D411yescharacteristic
203C2×C8×C83C2×D411yescharacteristic
204C4⋊C4×C83—21no—
205C4⋊C4×C83C22×C411yescharacteristic
206C4⋊C4×C83C22×C411yescharacteristic
207C22⋊C4×C83—21no—
208C42×C83—21no—
209C42×C83C2411yescharacteristic
210C23×C83—21no—
211C22×D83—21no—
212C22×D83C4×D411yescharacteristic
213Q8×C83—21no—
214Q8×C83—21no—
215D4×C83—21no—
216D4×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—41no—
221C2×C4×C83—41no—
222C2×C4×C83C23×C411yescharacteristic
223C2×C4×C83C22×D411yescharacteristic
224C2×C4×C83C2×#4111yescharacteristic
225C22⋊D83—42no—
226C2×Dic83—21no—
227C2×Dic83—21no—
228C2×Dic83—21no—
229C2×Dic83C4×D411yescharacteristic
230C2×Dic83C4×D411yescharacteristic
231C2×Dic83C4×D411yescharacteristic
232D332—21no—
233D332—21no—
234D332—42no—
235C4×D83—22no—
236C4×D83—21no—
237C4×D83—21no—
238C4×D83—21no—
239C4×D83—21no—
240C4×D83—41no—
241C4×D83—41no—
242Dic166—21no—
243Dic166—21no—
244C8×C83—21no—
245C8×C83—21no—
246C8×C83—21no—
247C8×C83—41no—
248C8×C83—41no—
249C8×C83—41no—
250C8×C83#13512yes—
251C83⋊C8—21no—
252C83⋊C8—21no—
253C83⋊C8—21no—
254C83⋊C8—41no—
255C83⋊C8—41no—
256C83⋊C8—41no—
257C83⋊C8#13512yes—
258C22×C83—41no—
259C22×C83—41no—
260C22×C83—41no—
261C22×C83C2×C4×D411yescharacteristic
262C2×D83—21no—
263C2×D83—21no—
264C2×D83—41no—
265C2×D83—41no—
266C2×D83—41no—
267C2×D83#44412yes—
268C4×C83—21no—
269C4×C83—41no—
270C4×C83—41no—
271C4×C83—41no—
272C4×C83#56811yescharacteristic
273C4×C83#56811yescharacteristic
274C4×C83C2×#13511yescharacteristic
275C4×C83C2×#13511yescharacteristic
276Dic83—21no—
277Dic83—21no—
278Dic83—21no—
279Dic83—41no—
280Dic83—41no—
281Dic83—41no—
282#17978—831nomaximal, Sylow
283C2×C83—81no—
284C2×C83#293211yescharacteristic
285C2×C83C4×#13511yescharacteristic
286C2×C83C2×#44411yescharacteristic
287D83—22no—
288D83—81no—
289#3168—831no—
290#2966—831no—
291#2966—831no—
292#1584—831no—
293#1584—831no—
294#1583—831no—
295#1583—831no—
296#1582—831no—
297#1582D8311yescharacteristic, complemented
298#1581—831no—
299#1581—831no—
300#1568—831no—
301#1494—831no—
302#1494—831no—
303C2×#322—831no—
304C83#1797811yescharacteristic, complemented, Sylow
305#529—831no—
306#529—831no—
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#446C2×D8311yescharacteristic
317C8×Q8—831no—
318C8×Q8—831no—
319C4×Q16—831no—
320C4×SD16—831no—
321C4×SD16C2×D8311yescharacteristic
322C4×D8—831no—
323#436—831no—
324#436—831no—
325#435—1661no—
326#435—1661no—
327C8×D4—831no—
328C8×D4—1661no—
329C8×D4—1661no—
330C8×D4C2×D8311yescharacteristic
331#433—1661no—
332#433—1661no—
333#432—831no—
334#432—831no—
335#405—1661no—
336#405—1661no—
337C2×C4×C8—831no—
338C2×C4×C8—831no—
339C2×C4×C8—831no—
340#335—831no—
341#335—831no—
342#334—831no—
343#334C2×D8311yescharacteristic
344Q8⋊C8—831no—
345Q8⋊C8—831no—
346Q8⋊C8—831no—
347Q8⋊C8C2×D8311yescharacteristic
348D4⋊C8—831no—
349D4⋊C8—831no—
350D4⋊C8—831no—
351D4⋊C8C2×D8311yescharacteristic
352#322—831no—
353#322—831no—
354#322—831no—
355#322C2×D8311yescharacteristic
356C2×Q16—831no—
357C2×SD16—831no—
358C2×SD16C4×D8311yescharacteristic
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—1661no—
370#126—1661no—
371#125—831no—
372#125—831no—
373#124—831no—
374#124—831no—
375#123—1661no—
376#123—1661no—
377C22⋊Q8—831no—
378C22⋊Q8—831no—
379#121—831no—
380#121—831no—
381C4×Q8—831no—
382C4×Q8C22×D8311yescharacteristic
383C4×D4—831no—
384C4×D4—1661no—
385C4×D4—1661no—
386C4×D4C22×D8311yescharacteristic
387#117—1661no—
388#117—1661no—
389C2×C42—831no—
390#107—831no—
391#107—831no—
392#106—831no—
393#106C4×D8311yescharacteristic
394C4⋊C8—21no—
395C4⋊C8—831no—
396C4⋊C8—831no—
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#103C4×D8311yescharacteristic
406#102—831no—
407#102—831no—
408#102—831no—
409#102C4×D8311yescharacteristic
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—831no—
421C4×C8—831no—
422C4×C8—831no—
423C4×C8—831no—
424C4×C8—831no—
425C4×C8—831no—
426C4×C8—831no—
427C4×C8—1661no—
428C4×C8—1661no—
429C4×C8—1661no—
430C4×C8C22×D8311yescharacteristic
431C4×C8C22×D8311yescharacteristic
432C4×C8C22×D8311yescharacteristic
433C2×Q8—831no—
434C2×Q8C2×C4×D8311yescharacteristic
435C2×D4—831no—
436C2×D4—1661no—
437C2×D4—1661no—
438C2×D4C2×C4×D8311yescharacteristic
439C22×C4—21no—
440C22×C4—831no—
441C22×C4—831no—
442C22×C4—831no—
443C22×C4—1661no—
444Q16—3321no—
445SD16—41no—
446SD16—3321no—
447D8—3321no—
448M16—3322no—
449M16—3322no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—42no—
454C2×C8—3321no—
455C2×C8—3321no—
456C2×C8—3322no—
457C2×C8—3322no—
458C2×C8—831no—
459C2×C8—831no—
460C2×C8—831no—
461C2×C8—831no—
462C2×C8—1662no—
463C2×C8—1661no—
464C2×C8—1661no—
465C2×C8—1661no—
466C2×C8—1662no—
467C2×C8C2×C4×D8311yescharacteristic
468C2×C8C2×C4×D8311yescharacteristic
469C2×C8D4×D8311yescharacteristic
470C2×C8D4×D8311yescharacteristic
471C4⋊C4—21no—
472C4⋊C4—831no—
473C4⋊C4—831no—
474C4⋊C4—1661no—
475C4⋊C4—1661no—
476C4⋊C4—1661no—
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—1661no—
485C22⋊C4—1661no—
486C22⋊C4—1661no—
487C22⋊C4—1661no—
488C22⋊C4—1661no—
489C22⋊C4—1661no—
490C22⋊C4—1661no—
491C22⋊C4—1661no—
492C22⋊C4—1661no—
493C42—21no—
494C42—831no—
495C42—831no—
496C42—831no—
497C42—1661no—
498C42C23×D8311yescharacteristic
499C23—21no—
500C23—831no—
501C23—1661no—
502Q8—21no—
503Q8—21no—
504Q8—1661no—
505Q8—1661no—
506D4—21no—
507D4—21no—
508D4—3322no—
509D4—3322no—
510D4—1661no—
511D4—1661no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—3321no—
518C2×C4—3321no—
519C2×C4—831no—
520C2×C4—831no—
521C2×C4—831no—
522C2×C4—1662no—
523C2×C4—1661no—
524C2×C4—1661no—
525C2×C4—1661no—
526C2×C4—1661no—
527C2×C4—1661no—
528C2×C4—1661no—
529C2×C4—1661no—
530C2×C4C22×C4×D8311yescharacteristic
531C2×C4C2×D4×D8311yescharacteristic
532C2×C4#41×D8311yescharacteristic
533C8—21no—
534C8—21no—
535C8—21no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—3321no—
540C8—3321no—
541C8—3321no—
542C8—832no—
543C8—1661no—
544C8—1661no—
545C8—1661no—
546C8#1458181312yes—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—3321no—
551C22—3321no—
552C22—3321no—
553C22—832no—
554C22—1661no—
555C22—1661no—
556C22C4×D4×D8311yescharacteristic
557C4—21no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—3321no—
562C4—3321no—
563C4—3321no—
564C4—1661no—
565C4—1661no—
566C4—1661no—
567C4#1912846611yescharacteristic
568C4#1912846711yescharacteristic
569C4#135×D8311yescharacteristic
570C4C2×#1458181311yescharacteristic
571C2—81no—
572C2—6641no—
573C2—1662no—
574C2#2491617711yescharacteristic
575C2C4×#1458181311yescharacteristic
576C2#444×D8311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1582C2
socleC22×C83C2×C4×D4
prime radical#19127936C4
cosocleC42×C83C24
hypercenter#1582D83
hypocenterC83#17978
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
2. #24916437C2semidirect
3. #24916435C2semidirect
4. #24906311C2semidirect
5. #24906310C2semidirect
6. #24906308C2semidirect
7. #24906307C2semidirect
8. #24906298C2semidirect
9. #24906295C2semidirect
10. #24906292C2semidirect
11. #24906223C2semidirect
12. #24905922C2semidirect
13. #24905920C2semidirect
14. #322×D83C2semidirect
15. C83×#1582C2semidirect
297. #1582D83semidirect
304. C83#17978semidirect

Maximal subgroups

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

subgroupindex
#249180292
#249164372
#249164352
#249063112
#249063102
#249063082
#249063072
#249062982
#249062952
#249062922
#249062232
#249059222
#249059202
#322×D832
C83×#15822
#1797883