Finite Group Databasebeta

← #35375132

Subgroups — #35375132

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#24916438C211yesmaximal, characteristic, complemented
3#24906313C211yesmaximal, characteristic, complemented
4#24906311C211yesmaximal, characteristic, complemented
5#24906306C211yesmaximal, characteristic, complemented
6#24906304C211yesmaximal, characteristic, complemented
7#24906299C211yesmaximal, characteristic, complemented
8#24906297C211yesmaximal, characteristic, complemented
9#24906292C211yesmaximal, characteristic, complemented
10#24906290C211yesmaximal, characteristic, complemented
11#24906224C211yesmaximal, characteristic, complemented
12#24905923C211yesmaximal, characteristic, complemented
13#24905921C211yesmaximal, characteristic, complemented
14C2×#19127422C211yesmaximal, characteristic, complemented
15C83×#2966C211yesmaximal, 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#19127772—21no—
33C8×D332C2211yescharacteristic
34C8×C22⋊D83—21no—
35#19127760—21no—
36#19127758C2211yescharacteristic
37#19127655—21no—
38C2×C4×C83⋊C8C2211yescharacteristic
39C2×C4×C83⋊C8C2211yescharacteristic
40#19127453C2211yescharacteristic
41#19127453C2211yescharacteristic
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#19127422C2211yescharacteristic
53#19127422C2211yescharacteristic
54#19127422C2211yescharacteristic
55#19127422C2211yescharacteristic
56#529×C83C2211yescharacteristic
57#446×C83C2211yescharacteristic
58C8×Q8×C83C2211yescharacteristic
59#436×C83C2211yescharacteristic
60#435×C83—21no—
61C8×D4×C83—21no—
62C8×D4×C83C2211yescharacteristic
63#433×C83—21no—
64#432×C83C2211yescharacteristic
65#405×C83—21no—
66C2×C4×C8×C83C2211yescharacteristic
67C2×#13050580C2×C411yescharacteristic
68C2×#13050578C2×C411yescharacteristic
69C2×#13050577C2×C411yescharacteristic
70C2×#13050575C2×C411yescharacteristic
71C2×#13050573—21no—
72C22×C83⋊C8—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)C2311yescharacteristic
91C4⋊(C83⋊C8)C2311yescharacteristic
92Dic83⋊C8—21no—
93Dic83⋊C8—21no—
94#14581716C2×C411yescharacteristic
95#14581716C2×C411yescharacteristic
96#14581715C2×C411yescharacteristic
97#14581715C2×C411yescharacteristic
98#14581713C2×C411yescharacteristic
99#14581713C2×C411yescharacteristic
100#14581712C2×C411yescharacteristic
101#14581712C2×C411yescharacteristic
102C22⋊(C83⋊C8)—21no—
103(C2×D83)⋊C8—21no—
104(C2×D83)⋊C8—21no—
105#14581703—21no—
106#14581702—21no—
107C4×C83⋊C8—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—
116C22×C8×C83—21no—
117C22×C8×C83D411yescharacteristic
118C22×C8×C83D411yescharacteristic
119#126×C83—21no—
120#125×C83C2×C411yescharacteristic
121#124×C83C2×C411yescharacteristic
122#123×C83—21no—
123C22⋊Q8×C83C2×C411yescharacteristic
124#121×C83C2×C411yescharacteristic
125C4×Q8×C83C2311yescharacteristic
126C4×D4×C83—21no—
127C4×D4×C83C2311yescharacteristic
128#117×C83—21no—
129C2×C42×C83C2311yescharacteristic
130C4⋊C8×C83—21no—
131C4⋊C8×C83—21no—
132C4⋊C8×C83C2311yescharacteristic
133C4⋊C8×C83C2311yescharacteristic
134C22⋊C8×C83—21no—
135C22⋊C8×C83—21no—
136C22⋊C8×C83—21no—
137#97×C83—21no—
138#97×C83—21no—
139C4×C8×C83—21no—
140C4×C8×C83D411yescharacteristic
141C4×C8×C83D411yescharacteristic
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#13050573—42no—
153C2×C83⋊C8—21no—
154C2×C83⋊C8—21no—
155C2×C83⋊C8—21no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—41no—
158C2×C83⋊C8—41no—
159C2×C83⋊C8—42no—
160C2×C83⋊C8C22×C411yescharacteristic
161C2×C83⋊C8C22×C411yescharacteristic
162C2×C83⋊C8C22×C411yescharacteristic
163C2×C83⋊C8C22×C411yescharacteristic
164C8×D83—42no—
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—42no—
185C2×C8×C83—22no—
186C2×C8×C83—22no—
187C2×C8×C83—21no—
188C2×C8×C83—21no—
189C2×C8×C83—42no—
190C2×C8×C83C2×D411yescharacteristic
191C2×C8×C83C2×D411yescharacteristic
192C2×C8×C83C2×D411yescharacteristic
193C2×C8×C83C2×D411yescharacteristic
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—21no—
245C8×C83—21no—
246C8×C83—41no—
247C8×C83—41no—
248C8×C83#13512yes—
249C8×C83#13512yes—
250C83⋊C8—21no—
251C83⋊C8—21no—
252C83⋊C8—21no—
253C83⋊C8—21no—
254C83⋊C8—41no—
255C83⋊C8—41no—
256C83⋊C8—41no—
257C83⋊C8—41no—
258C22×C83—21no—
259C22×C83—21no—
260C22×C83—41no—
261C22×C83—41no—
262C22×C83—41no—
263C22×C83#44412yes—
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×C83C2×#13511yescharacteristic
278C4×C83C2×#13511yescharacteristic
279Dic83—41no—
280Dic83—41no—
281Dic83—41no—
282#17978—831nomaximal, Sylow
283C2×C83—22no—
284C2×C83—81no—
285C2×C83#293211yescharacteristic
286C2×C83C4×#13511yescharacteristic
287C2×C83C2×#44411yescharacteristic
288D83—81no—
289#3168—831no—
290#2966—831no—
291#2966D8311yescharacteristic, complemented
292#1584—831no—
293#1584—831no—
294#1583—831no—
295#1583—831no—
296#1582—831no—
297#1582—831no—
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#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#446C2×D8311yescharacteristic
317C8×Q8—831no—
318C8×Q8C2×D8311yescharacteristic
319C4×Q16—831no—
320C4×SD16—831no—
321C4×SD16—831no—
322C4×D8—831no—
323#436—831no—
324#436C2×D8311yescharacteristic
325#435—21no—
326#435—1661no—
327C8×D4—21no—
328C8×D4—831no—
329C8×D4—1661no—
330C8×D4C2×D8311yescharacteristic
331#433—21no—
332#433—1661no—
333#432—831no—
334#432C2×D8311yescharacteristic
335#405—21no—
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⋊C8—831no—
347Q8⋊C8—831no—
348D4⋊C8—831no—
349D4⋊C8—831no—
350D4⋊C8—831no—
351D4⋊C8—831no—
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—21no—
361C2×M16—1661no—
362C22×C8—21no—
363C22×C8—831no—
364C22×C8—831no—
365C22×C8—1661no—
366C22×C8—1661no—
367C22×C8C22⋊D8311yescharacteristic
368C22×C8C22⋊D8311yescharacteristic
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—21no—
395C4⋊C8—21no—
396C4⋊C8—831no—
397C4⋊C8—831no—
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—21no—
412C22⋊C8—21no—
413C22⋊C8—1661no—
414C22⋊C8—1661no—
415C22⋊C8—1661no—
416#97—21no—
417#97—21no—
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—1661no—
428C4×C8—1661no—
429C4×C8C22⋊D8311yescharacteristic
430C4×C8C22⋊D8311yescharacteristic
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×C4C2×C22⋊D8311yescharacteristic
443C22×C4#1305059011yescharacteristic
444Q16—3321no—
445SD16—3321no—
446SD16—3321no—
447D8—3321no—
448M16—42no—
449M16—3322no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—42no—
455C2×C8—3322no—
456C2×C8—3322no—
457C2×C8—3321no—
458C2×C8—3321no—
459C2×C8—831no—
460C2×C8—831no—
461C2×C8—831no—
462C2×C8—831no—
463C2×C8—1661no—
464C2×C8—1661no—
465C2×C8—1661no—
466C2×C8—1661no—
467C2×C8C2×C22⋊D8311yescharacteristic
468C2×C8C2×C22⋊D8311yescharacteristic
469C2×C8C2×C22⋊D8311yescharacteristic
470C2×C8C2×C22⋊D8311yescharacteristic
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
496C42C2×C22⋊D8311yescharacteristic
497C42#1305059011yescharacteristic
498C42C23×D8311yescharacteristic
499C23—21no—
500C23—1661no—
501C23C4×C22⋊D8311yescharacteristic
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×C4C4×C22⋊D8311yescharacteristic
528C2×C4C4×C22⋊D8311yescharacteristic
529C2×C4C4×C22⋊D8311yescharacteristic
530C2×C4C22×C4×D8311yescharacteristic
531C2×C4C22×C22⋊D8311yescharacteristic
532C2×C4C2×#1305059011yescharacteristic
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—3321no—
538C8—3321no—
539C8—3321no—
540C8—3321no—
541C8—1661no—
542C8—1661no—
543C8—1661no—
544C8—1661no—
545C8#1458181212yes—
546C8#1458181212yes—
547C22—21no—
548C22—21no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—3321no—
553C22—3321no—
554C22—3321no—
555C22#1912782112yes—
556C22C2×C4×C22⋊D8311yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—3321no—
565C4—3321no—
566C4—3321no—
567C4#1912846611yescharacteristic
568C4#1912846611yescharacteristic
569C4C2×#1458181211yescharacteristic
570C4C2×#1458181211yescharacteristic
571C2—22no—
572C2—81no—
573C2—6641no—
574C2#2491617911yescharacteristic
575C2C4×#1458181211yescharacteristic
576C2C2×#1912782111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#2966C2
socleC22×C83C2×C4×D4
prime radical#19127935C4
cosocleC42×C83C24
hypercenter#2966D83
hypocenterC83#17978
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #2966

Complements

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

NH ≅ G/Ntype
2. #24916438C2semidirect
3. #24906313C2semidirect
4. #24906311C2semidirect
5. #24906306C2semidirect
6. #24906304C2semidirect
7. #24906299C2semidirect
8. #24906297C2semidirect
9. #24906292C2semidirect
10. #24906290C2semidirect
11. #24906224C2semidirect
12. #24905923C2semidirect
13. #24905921C2semidirect
14. C2×#19127422C2semidirect
15. C83×#2966C2semidirect
291. #2966D83semidirect
304. C83#17978semidirect

Maximal subgroups

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

subgroupindex
#249180272
#249164382
#249063132
#249063112
#249063062
#249063042
#249062992
#249062972
#249062922
#249062902
#249062242
#249059232
#249059212
C2×#191274222
C83×#29662
#1797883