Finite Group Databasebeta

← #35375100

Subgroups — #35375100

Order 21248.

592 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918027C211yesmaximal, characteristic
2#24916614C211yesmaximal, characteristic, complemented
3#24906375C211yesmaximal, characteristic, complemented
4#24906370C211yesmaximal, characteristic, complemented
5#24906353C211yesmaximal, characteristic, complemented
6#24906351C211yesmaximal, characteristic, complemented
7#24906285C211yesmaximal, characteristic, complemented
8#24906280C211yesmaximal, characteristic, complemented
9C8×#13050577C211yesmaximal, characteristic, complemented
10C8×#13050578C211yesmaximal, characteristic, complemented
11#24906218C211yesmaximal, characteristic, complemented
12#24905928C211yesmaximal, characteristic, complemented
13#24905926C211yesmaximal, characteristic, complemented
14#24905747C211yesmaximal, characteristic, complemented
15C83×#2993C211yesmaximal, characteristic, complemented
16#19128235C2211yescharacteristic
17#19128100C411yescharacteristic
18#19128083C411yescharacteristic
19#19128058C411yescharacteristic
20#19128055C411yescharacteristic
21#19127940C411yescharacteristic
22#19127935C411yescharacteristic
23#19127932C411yescharacteristic
24#19127928C411yescharacteristic
25#19127831C2211yescharacteristic
26C8×Dic166C2211yescharacteristic
27C4×#13050580C2211yescharacteristic
28C4×#13050577C2211yescharacteristic
29C4×#13050578C2211yescharacteristic
30C4×#13050575C2211yescharacteristic
31#19127780C2211yescharacteristic
32#19127776—21no—
33#19127775—21no—
34C8×D332C2211yescharacteristic
35#19127761—21no—
36#19127754C2211yescharacteristic
37#19127726—21no—
38#19127725C2211yescharacteristic
39C2×C4×C83⋊C8C2211yescharacteristic
40#19127451C2211yescharacteristic
41#19127451C2211yescharacteristic
42#19127451C2211yescharacteristic
43#19127451C2211yescharacteristic
44Q8⋊(C83⋊C8)C2211yescharacteristic
45Q8⋊(C83⋊C8)C2211yescharacteristic
46#19127431C2211yescharacteristic
47#19127431C2211yescharacteristic
48D4⋊(C83⋊C8)C2211yescharacteristic
49D4⋊(C83⋊C8)C2211yescharacteristic
50#19127428C2211yescharacteristic
51#19127428C2211yescharacteristic
52#19127423C2211yescharacteristic
53#19127423C2211yescharacteristic
54C8×C83⋊C8C2211yescharacteristic
55C8×C83⋊C8C2211yescharacteristic
56#529×C83C2211yescharacteristic
57#446×C83C2211yescharacteristic
58C8×Q8×C83C2211yescharacteristic
59#436×C83—21no—
60#436×C83C2211yescharacteristic
61#435×C83—21no—
62C8×D4×C83C2211yescharacteristic
63#433×C83—21no—
64#431×C83C2211yescharacteristic
65#424×C83—21no—
66#423×C83C2211yescharacteristic
67C2×#13050580C2×C411yescharacteristic
68C2×#13050578C2×C411yescharacteristic
69C2×#13050577C2×C411yescharacteristic
70C2×#13050575C2×C411yescharacteristic
71C2×#13050574—21no—
72C2×#13050573—21no—
73C22×C83⋊C8C2×C411yescharacteristic
74C22×C83⋊C8C2×C411yescharacteristic
75C2×C8×D83—21no—
76#14581786—21no—
77#14581784C2×C411yescharacteristic
78#14581780C2×C411yescharacteristic
79#14581775—21no—
80#14581771C2×C411yescharacteristic
81#14581766C2×C411yescharacteristic
82C4×Dic166C2311yescharacteristic
83C4×D332C2311yescharacteristic
84C4×C22⋊D83—21no—
85#14581749—21no—
86#14581725C2×C411yescharacteristic
87#14581725C2×C411yescharacteristic
88#14581723C2×C411yescharacteristic
89#14581723C2×C411yescharacteristic
90C4⋊(C83⋊C8)—21no—
91C4⋊(C83⋊C8)—21no—
92C4⋊(C83⋊C8)C2311yescharacteristic
93C4⋊(C83⋊C8)C2311yescharacteristic
94Dic83⋊C8—21no—
95Dic83⋊C8—21no—
96#14581716C2×C411yescharacteristic
97#14581716C2×C411yescharacteristic
98#14581715C2×C411yescharacteristic
99#14581715C2×C411yescharacteristic
100#14581713C2×C411yescharacteristic
101#14581713C2×C411yescharacteristic
102#14581712C2×C411yescharacteristic
103#14581712C2×C411yescharacteristic
104C22⋊(C83⋊C8)—21no—
105(C2×D83)⋊C8—21no—
106(C2×D83)⋊C8—21no—
107#14581702—21no—
108C4×C83⋊C8C2×C411yescharacteristic
109C4×C83⋊C8C2×C411yescharacteristic
110C4×C83⋊C8C2311yescharacteristic
111C4×C83⋊C8C2311yescharacteristic
112C4×C83⋊C8C2311yescharacteristic
113C4×C83⋊C8C2311yescharacteristic
114C8×Dic83—21no—
115C2×M16×C83—21no—
116C2×M16×C83—21no—
117C22×C8×C83—21no—
118#126×C83—21no—
119#125×C83C2×C411yescharacteristic
120#124×C83C2×C411yescharacteristic
121#123×C83—21no—
122C22⋊Q8×C83C2×C411yescharacteristic
123#121×C83C2×C411yescharacteristic
124C4×Q8×C83C2311yescharacteristic
125C4×D4×C83—21no—
126C4×D4×C83C2311yescharacteristic
127#117×C83—21no—
128C2×C42×C83C2311yescharacteristic
129C4⋊C8×C83—21no—
130C4⋊C8×C83—21no—
131C4⋊C8×C83—21no—
132C4⋊C8×C83D411yescharacteristic
133C4⋊C8×C83D411yescharacteristic
134C4⋊C8×C83C2311yescharacteristic
135C4⋊C8×C83C2311yescharacteristic
136C22⋊C8×C83—21no—
137C22⋊C8×C83—21no—
138C22⋊C8×C83D411yescharacteristic
139C22⋊C8×C83D411yescharacteristic
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#13050578—22no—
150#13050577—22no—
151#13050575—22no—
152#13050574—81no—
153#13050573—81no—
154C2×C83⋊C8—22no—
155C2×C83⋊C8—22no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8C22×C411yescharacteristic
161C2×C83⋊C8C22×C411yescharacteristic
162C2×C83⋊C8C22×C411yescharacteristic
163C2×C83⋊C8C22×C411yescharacteristic
164C8×D83—81no—
165C4⋊Dic83C22×C411yescharacteristic
166C4⋊Dic83C22×C411yescharacteristic
167Dic83⋊C4—21no—
168Dic83⋊C4—21no—
169Dic83⋊C4—21no—
170Dic83⋊C4—21no—
171C22⋊Dic83—21no—
172(C2×D83)⋊C4—21no—
173(C2×D83)⋊C4—21no—
174(C2×D83)⋊C4—21no—
175(C2×D83)⋊C4—21no—
176C4×Dic83—21no—
177C2×Q8×C83C22×C411yescharacteristic
178C2×D4×C83—21no—
179C2×D4×C83C22×C411yescharacteristic
180C22×C4×C83—21no—
181C22×C4×C83C22×C411yescharacteristic
182C22×C4×C83C2×D411yescharacteristic
183C22×C4×C83#4111yescharacteristic
184M16×C83—81no—
185M16×C83—81no—
186C2×C8×C83—21no—
187C2×C8×C83—21no—
188C2×C8×C83—81no—
189C2×C8×C83C2×D411yescharacteristic
190C2×C8×C83C2×D411yescharacteristic
191C2×C8×C83C2×D411yescharacteristic
192C2×C8×C83C2×D411yescharacteristic
193C4⋊C4×C83—21no—
194C4⋊C4×C83—21no—
195C4⋊C4×C83—21no—
196C4⋊C4×C83—21no—
197C4⋊C4×C83C22×C411yescharacteristic
198C4⋊C4×C83C22×C411yescharacteristic
199C22⋊C4×C83—21no—
200C22⋊C4×C83—21no—
201C22⋊C4×C83—21no—
202C22⋊C4×C83—21no—
203C22⋊C4×C83—21no—
204C42×C83—21no—
205C42×C83C22×C411yescharacteristic
206C42×C83C2×D411yescharacteristic
207C42×C83#4111yescharacteristic
208C42×C83C2411yescharacteristic
209C23×C83—21no—
210C23×C83C4×D411yescharacteristic
211C22×D83—21no—
212Q8×C83—21no—
213Q8×C83—21no—
214D4×C83—21no—
215D4×C83—21no—
216D4×C83—81no—
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×C83—41no—
226C2×C4×C83—41no—
227C2×C4×C83C4×D411yescharacteristic
228C2×C4×C83C4×D411yescharacteristic
229C2×C4×C83C4×D411yescharacteristic
230C2×C4×C83C23×C411yescharacteristic
231C2×C4×C83C22×D411yescharacteristic
232C2×C4×C83C2×#4111yescharacteristic
233C22⋊D83—81no—
234C2×Dic83—21no—
235C2×Dic83—21no—
236C2×Dic83—21no—
237D332—21no—
238D332—21no—
239C4×D83—41no—
240C4×D83—41no—
241Dic166—21no—
242Dic166—21no—
243C8×C83—21no—
244C8×C83—21no—
245C8×C83—21no—
246C8×C83—21no—
247C8×C83—41no—
248C8×C83—41no—
249C83⋊C8—21no—
250C83⋊C8—21no—
251C83⋊C8—41no—
252C83⋊C8—41no—
253C83⋊C8—41no—
254C83⋊C8—41no—
255C83⋊C8#13112yes—
256C83⋊C8#13112yes—
257C22×C83—21no—
258C22×C83—21no—
259C22×C83—21no—
260C22×C83—41no—
261C22×C83—41no—
262C22×C83—41no—
263C22×C83C2×C4×D411yescharacteristic
264C2×D83—41no—
265C2×D83—41no—
266C2×D83—41no—
267C4×C83—21no—
268C4×C83—21no—
269C4×C83—21no—
270C4×C83—21no—
271C4×C83—41no—
272C4×C83—41no—
273C4×C83—41no—
274C4×C83C2×#13111yescharacteristic
275C4×C83C2×#13111yescharacteristic
276C4×C83#57711yescharacteristic
277C4×C83#57711yescharacteristic
278Dic83—41no—
279Dic83—41no—
280Dic83—41no—
281#17974—831nomaximal, Sylow
282C2×C83—41no—
283C2×C83—81no—
284C2×C83#293111yescharacteristic
285C2×C83#295211yescharacteristic
286C2×C83#295711yescharacteristic
287D83—81no—
288#3168—831no—
289#2993—831no—
290#2993D8311yescharacteristic, complemented
291#1594—831no—
292#1593—831no—
293#1590—831no—
294#1590—831no—
295#1580—831no—
296#1579—831no—
297C8×SD16—831no—
298C8×SD16—831no—
299#1566—831no—
300#1495—831no—
301#1495—831no—
302#1450—831no—
303C83#1797411yescharacteristic, complemented, Sylow
304#529—831no—
305#529C2×D8311yescharacteristic
306#499—831no—
307#495—831no—
308#488—831no—
309#488—831no—
310#467—831no—
311#466—831no—
312#465—831no—
313#465—831no—
314#446—831no—
315#446C2×D8311yescharacteristic
316C8×Q8—831no—
317C8×Q8C2×D8311yescharacteristic
318C4×Q16—831no—
319C4×SD16—831no—
320C4×SD16—831no—
321C4×D8—831no—
322#436—21no—
323#436—831no—
324#436—1661no—
325#436C2×D8311yescharacteristic
326#435—21no—
327#435—1661no—
328C8×D4—831no—
329C8×D4C2×D8311yescharacteristic
330#433—21no—
331#433—1661no—
332#431—831no—
333#431C2×D8311yescharacteristic
334#424—21no—
335#424—1661no—
336#423—831no—
337#423C2×D8311yescharacteristic
338C2×C4×C8—831no—
339#334—831no—
340#334—831no—
341#334—831no—
342#334—831no—
343Q8⋊C8—831no—
344Q8⋊C8—831no—
345Q8⋊C8—831no—
346Q8⋊C8—831no—
347D4⋊C8—831no—
348D4⋊C8—831no—
349D4⋊C8—831no—
350D4⋊C8—831no—
351#322—831no—
352#322—831no—
353C82—831no—
354C82—831no—
355C2×Q16—831no—
356C2×SD16—831no—
357C2×SD16—831no—
358C2×D8—831no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—1661no—
362C2×M16—1661no—
363C22×C8—21no—
364C22×C8—831no—
365C22×C8—831no—
366C22×C8—1661no—
367#126—21no—
368#126—1661no—
369#125—831no—
370#125C4×D8311yescharacteristic
371#124—831no—
372#124C4×D8311yescharacteristic
373#123—21no—
374#123—1661no—
375C22⋊Q8—831no—
376C22⋊Q8C4×D8311yescharacteristic
377#121—831no—
378#121C4×D8311yescharacteristic
379C4×Q8—831no—
380C4×Q8C22×D8311yescharacteristic
381C4×D4—21no—
382C4×D4—831no—
383C4×D4—1661no—
384C4×D4C22×D8311yescharacteristic
385#117—21no—
386#117—1661no—
387C2×C42C22×D8311yescharacteristic
388#107—831no—
389#107—831no—
390#106—831no—
391#106—831no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8—831no—
396C4⋊C8—831no—
397C4⋊C8—1661no—
398C4⋊C8—1661no—
399C4⋊C8—1661no—
400C4⋊C8—1661no—
401C4⋊C8C22⋊D8311yescharacteristic
402C4⋊C8C22⋊D8311yescharacteristic
403C4⋊C8C22×D8311yescharacteristic
404C4⋊C8C22×D8311yescharacteristic
405#103—831no—
406#103—831no—
407#103—831no—
408#103—831no—
409#102—831no—
410#102—831no—
411#102—831no—
412#102—831no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—1661no—
416C22⋊C8—1661no—
417C22⋊C8—1661no—
418C22⋊C8C22⋊D8311yescharacteristic
419C22⋊C8C22⋊D8311yescharacteristic
420#97—21no—
421#97—1661no—
422C4×C8—21no—
423C4×C8—831no—
424C4×C8—831no—
425C4×C8—831no—
426C4×C8—831no—
427C4×C8—831no—
428C4×C8—831no—
429C4×C8—1661no—
430C4×C8C22×D8311yescharacteristic
431C4×C8C22×D8311yescharacteristic
432C2×Q8—831no—
433C2×Q8C2×C4×D8311yescharacteristic
434C2×D4—21no—
435C2×D4—831no—
436C2×D4—1661no—
437C2×D4C2×C4×D8311yescharacteristic
438C22×C4—21no—
439C22×C4—1661no—
440C22×C4C2×C4×D8311yescharacteristic
441C22×C4C2×C22⋊D8311yescharacteristic
442C22×C4#1305059011yescharacteristic
443Q16—1662no—
444SD16—1662no—
445SD16—1662no—
446D8—1662no—
447M16—81no—
448M16—81no—
449M16—6641no—
450M16—6641no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—81no—
454C2×C8—831no—
455C2×C8—831no—
456C2×C8—831no—
457C2×C8—831no—
458C2×C8—6641no—
459C2×C8—1661no—
460C2×C8—1661no—
461C2×C8—1661no—
462C2×C8—1661no—
463C2×C8—1662no—
464C2×C8—1662no—
465C2×C8C2×C22⋊D8311yescharacteristic
466C2×C8C2×C22⋊D8311yescharacteristic
467C2×C8C2×C22⋊D8311yescharacteristic
468C2×C8C2×C22⋊D8311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—831no—
474C4⋊C4—831no—
475C4⋊C4—1661no—
476C4⋊C4—1661no—
477C4⋊C4—1661no—
478C4⋊C4—1661no—
479C4⋊C4C2×C4×D8311yescharacteristic
480C4⋊C4C2×C4×D8311yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—1661no—
487C22⋊C4—1661no—
488C22⋊C4—1661no—
489C22⋊C4—1661no—
490C22⋊C4—1661no—
491C42—21no—
492C42—1661no—
493C42C2×C4×D8311yescharacteristic
494C42C2×C22⋊D8311yescharacteristic
495C42#1305059011yescharacteristic
496C42C23×D8311yescharacteristic
497C23—21no—
498C23—1661no—
499C23C4×C22⋊D8311yescharacteristic
500Q8—21no—
501Q8—21no—
502Q8—1661no—
503Q8—1661no—
504D4—21no—
505D4—21no—
506D4—81no—
507D4—6641no—
508D4—1661no—
509D4—1661no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—3321no—
521C2×C4—3321no—
522C2×C4—1661no—
523C2×C4—1661no—
524C2×C4—1661no—
525C2×C4C4×C22⋊D8311yescharacteristic
526C2×C4C4×C22⋊D8311yescharacteristic
527C2×C4C4×C22⋊D8311yescharacteristic
528C2×C4C22×C4×D8311yescharacteristic
529C2×C4C22×C22⋊D8311yescharacteristic
530C2×C4C2×#1305059011yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—3321no—
538C8—3321no—
539C8—3321no—
540C8—3321no—
541C8—832no—
542C8—832no—
543C8—1661no—
544C8—1661no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—3321no—
552C22—3321no—
553C22—3321no—
554C22C2×C4×C22⋊D8311yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—3321no—
563C4—3321no—
564C4—3321no—
565C4#131×D8311yescharacteristic
566C4#131×D8311yescharacteristic
567C4#1912850911yescharacteristic
568C4#1912851211yescharacteristic
569C2—41no—
570C2—81no—
571C2—6641no—
572C2#2491617311yescharacteristic
573C2#2491634411yescharacteristic
574C2#2491637811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#2993C2
socleC22×C83C2×C4×D4
prime radical#19127935C4
cosocleC42×C83C24
hypercenter#2993D83
hypocenterC83#17974
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #24916614C2semidirect
3. #24906375C2semidirect
4. #24906370C2semidirect
5. #24906353C2semidirect
6. #24906351C2semidirect
7. #24906285C2semidirect
8. #24906280C2semidirect
9. C8×#13050577C2semidirect
10. C8×#13050578C2semidirect
11. #24906218C2semidirect
12. #24905928C2semidirect
13. #24905926C2semidirect
14. #24905747C2semidirect
15. C83×#2993C2semidirect
290. #2993D83semidirect
303. C83#17974semidirect

Maximal subgroups

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

subgroupindex
#249180272
#249166142
#249063752
#249063702
#249063532
#249063512
#249062852
#249062802
C8×#130505772
C8×#130505782
#249062182
#249059282
#249059262
#249057472
C83×#29932
#1797483