Finite Group Databasebeta

← #35375045

Subgroups — #35375045

Order 21248.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918070C211yesmaximal, characteristic
2#24916557C211yesmaximal, characteristic, complemented
3#24906370C211yesmaximal, characteristic, complemented
4#24906365C211yesmaximal, characteristic, complemented
5#24906358C211yesmaximal, characteristic, complemented
6#24906351C211yesmaximal, characteristic, complemented
7#24906280C211yesmaximal, characteristic, complemented
8#24906275C211yesmaximal, characteristic, complemented
9C8×#13050580C211yesmaximal, characteristic, complemented
10C8×#13050578C211yesmaximal, characteristic, complemented
11#24906228C211yesmaximal, characteristic, complemented
12#24905923C211yesmaximal, characteristic
13#24905917C211yesmaximal, characteristic, complemented
14#24905744C211yesmaximal, characteristic, complemented
15C83×#2993C211yesmaximal, characteristic
16#19128258C2211yescharacteristic
17#19128111C411yescharacteristic
18#19128096C411yescharacteristic
19#19128071C411yescharacteristic
20#19128060C411yescharacteristic
21#19127957C411yescharacteristic
22#19127957C411yescharacteristic
23#19127945C411yescharacteristic
24#19127945C411yescharacteristic
25#19127831C2211yescharacteristic
26#19127831C2211yescharacteristic
27#19127830—21no—
28#19127830—21no—
29C8×Dic166C2211yescharacteristic
30C8×Dic166C2211yescharacteristic
31C4×#13050580C2211yescharacteristic
32C4×#13050580C2211yescharacteristic
33C4×#13050578C2211yescharacteristic
34C4×#13050578C2211yescharacteristic
35#19127759—21no—
36#19127759—21no—
37#19127758C2211yescharacteristic
38C4×#13050574C2211yescharacteristic
39C2×C4×C83⋊C8C2211yescharacteristic
40#19127453C2211yescharacteristic
41#19127453C2211yescharacteristic
42#19127451C2211yescharacteristic
43#19127451C2211yescharacteristic
44Q8⋊(C83⋊C8)C2211yescharacteristic
45Q8⋊(C83⋊C8)C2211yescharacteristic
46#19127431C2211yescharacteristic
47#19127431C2211yescharacteristic
48#19127431C2211yescharacteristic
49#19127431C2211yescharacteristic
50D4⋊(C83⋊C8)C2211yescharacteristic
51D4⋊(C83⋊C8)C2211yescharacteristic
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×#13050580C2×C411yescharacteristic
69C2×#13050578C2×C411yescharacteristic
70C2×#13050578C2×C411yescharacteristic
71C2×#13050574C2×C411yescharacteristic
72C2×#13050574C2×C411yescharacteristic
73C22×C83⋊C8—21no—
74#14581792C2×C411yescharacteristic
75#14581792C2×C411yescharacteristic
76#14581784—21no—
77#14581771—21no—
78#14581771C2×C411yescharacteristic
79#14581771C2×C411yescharacteristic
80C4×Dic166—21no—
81C4×Dic166C2311yescharacteristic
82C4×Dic166C2311yescharacteristic
83#14581751—21no—
84#14581725C2×C411yescharacteristic
85#14581725C2×C411yescharacteristic
86#14581723C2×C411yescharacteristic
87#14581723C2×C411yescharacteristic
88C4⋊(C83⋊C8)C2311yescharacteristic
89C4⋊(C83⋊C8)C2311yescharacteristic
90Dic83⋊C8—21no—
91Dic83⋊C8—21no—
92Dic83⋊C8—21no—
93Dic83⋊C8—21no—
94#14581716C2×C411yescharacteristic
95#14581716C2×C411yescharacteristic
96#14581715C2×C411yescharacteristic
97#14581715C2×C411yescharacteristic
98#14581715C2×C411yescharacteristic
99#14581715C2×C411yescharacteristic
100#14581713C2×C411yescharacteristic
101#14581713C2×C411yescharacteristic
102C22⋊(C83⋊C8)—21no—
103#14581703—21no—
104#14581703C2×C411yescharacteristic
105#14581703C2×C411yescharacteristic
106#14581702—21no—
107#14581702—21no—
108C4×C83⋊C8—21no—
109C4×C83⋊C8C2311yescharacteristic
110C4×C83⋊C8C2311yescharacteristic
111C4×C83⋊C8C2311yescharacteristic
112C4×C83⋊C8C2311yescharacteristic
113C8×Dic83—21no—
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×Dic166—21no—
145C2×Dic166C22×C411yescharacteristic
146C2×Dic166C22×C411yescharacteristic
147#13050580—22no—
148#13050580—22no—
149#13050578—22no—
150#13050578—22no—
151#13050574—22no—
152#13050574—22no—
153C2×C83⋊C8—21no—
154C2×C83⋊C8—21no—
155C2×C83⋊C8—21no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—42no—
158C2×C83⋊C8C22×C411yescharacteristic
159C2×C83⋊C8C22×C411yescharacteristic
160C2×C83⋊C8C22×C411yescharacteristic
161C2×C83⋊C8C22×C411yescharacteristic
162C4⋊Dic83—21no—
163C4⋊Dic83—21no—
164C4⋊Dic83—21no—
165C4⋊Dic83C22×C411yescharacteristic
166C4⋊Dic83C22×C411yescharacteristic
167Dic83⋊C4—21no—
168Dic83⋊C4—21no—
169Dic83⋊C4—21no—
170Dic83⋊C4—21no—
171C22⋊Dic83—21no—
172C22⋊Dic83—21no—
173C4×Dic83—21no—
174C4×Dic83—21no—
175C2×Q8×C83C22×C411yescharacteristic
176C2×D4×C83—21no—
177C2×D4×C83C22×C411yescharacteristic
178C22×C4×C83—21no—
179C22×C4×C83C22×C411yescharacteristic
180C22×C4×C83C2×D411yescharacteristic
181C22×C4×C83#4111yescharacteristic
182M16×C83—81no—
183M16×C83—81no—
184C2×C8×C83—21no—
185C2×C8×C83—21no—
186C2×C8×C83—81no—
187C2×C8×C83C2×D411yescharacteristic
188C2×C8×C83C2×D411yescharacteristic
189C2×C8×C83C2×D411yescharacteristic
190C2×C8×C83C2×D411yescharacteristic
191C4⋊C4×C83—21no—
192C4⋊C4×C83—21no—
193C4⋊C4×C83—21no—
194C4⋊C4×C83—21no—
195C4⋊C4×C83C22×C411yescharacteristic
196C4⋊C4×C83C22×C411yescharacteristic
197C22⋊C4×C83—21no—
198C22⋊C4×C83—21no—
199C22⋊C4×C83—21no—
200C22⋊C4×C83—21no—
201C22⋊C4×C83—21no—
202C42×C83—21no—
203C42×C83C22×C411yescharacteristic
204C42×C83C2×D411yescharacteristic
205C42×C83#4111yescharacteristic
206C42×C83C2411yescharacteristic
207C23×C83—21no—
208C23×C83C4×D411yescharacteristic
209Q8×C83—21no—
210Q8×C83—21no—
211D4×C83—21no—
212D4×C83—21no—
213D4×C83—81no—
214C2×C4×C83—21no—
215C2×C4×C83—21no—
216C2×C4×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83—41no—
222C2×C4×C83—41no—
223C2×C4×C83—41no—
224C2×C4×C83C4×D411yescharacteristic
225C2×C4×C83C4×D411yescharacteristic
226C2×C4×C83C4×D411yescharacteristic
227C2×C4×C83C23×C411yescharacteristic
228C2×C4×C83C22×D411yescharacteristic
229C2×C4×C83C2×#4111yescharacteristic
230C2×Dic83—21no—
231C2×Dic83—21no—
232C2×Dic83—21no—
233C2×Dic83—21no—
234Dic166—21no—
235Dic166—21no—
236Dic166—21no—
237Dic166—21no—
238Dic166—81no—
239C8×C83—21no—
240C8×C83—21no—
241C8×C83—21no—
242C8×C83—21no—
243C8×C83—41no—
244C8×C83—41no—
245C83⋊C8—22no—
246C83⋊C8—21no—
247C83⋊C8—21no—
248C83⋊C8—41no—
249C83⋊C8—41no—
250C83⋊C8—41no—
251C83⋊C8#13112yes—
252C83⋊C8#13112yes—
253C22×C83—21no—
254C22×C83—21no—
255C22×C83—21no—
256C22×C83—41no—
257C22×C83—41no—
258C22×C83—41no—
259C22×C83C2×C4×D411yescharacteristic
260C4×C83—21no—
261C4×C83—21no—
262C4×C83—21no—
263C4×C83—21no—
264C4×C83—41no—
265C4×C83—41no—
266C4×C83—41no—
267C4×C83C2×#13111yescharacteristic
268C4×C83C2×#13111yescharacteristic
269C4×C83#57711yescharacteristic
270C4×C83#57811yescharacteristic
271Dic83—41no—
272Dic83—41no—
273Dic83—41no—
274Dic83—41no—
275#17969—831nomaximal, Sylow
276C2×C83—41no—
277C2×C83—81no—
278C2×C83#293111yescharacteristic
279C2×C83#294711yescharacteristic
280C2×C83#295611yescharacteristic
281#3172—831no—
282#2993D8311yescharacteristic
283#2985—831no—
284#1593—831no—
285#1592—831no—
286#1591—831no—
287#1590—831no—
288#1579—831no—
289SD16⋊C8—831no—
290C8×Q16—831no—
291C8×SD16—831no—
292#1569—831no—
293#1494—831no—
294#1493—831no—
295C8×M16—831no—
296C83#1796911yescharacteristic, complemented, Sylow
297#533—831no—
298#529C2×D8311yescharacteristic
299#501—831no—
300#497—831no—
301#491—831no—
302#489—831no—
303#470—831no—
304#470—831no—
305#468—831no—
306#468—831no—
307#446—831no—
308#446—831no—
309#446—1661no—
310#446—1661no—
311#446C2×D8311yescharacteristic
312C8×Q8—831no—
313C8×Q8—831no—
314C8×Q8C2×D8311yescharacteristic
315C4×Q16—831no—
316C4×Q16—831no—
317C4×SD16—831no—
318C4×SD16—831no—
319#436—21no—
320#436C2×D8311yescharacteristic
321#435—21no—
322C8×D4C2×D8311yescharacteristic
323#433—21no—
324#433—1661no—
325#433—1661no—
326#432—831no—
327#431C2×D8311yescharacteristic
328#424—21no—
329#423C2×D8311yescharacteristic
330C4×M16—831no—
331C2×C4×C8—831no—
332#335—831no—
333#335—831no—
334#334—831no—
335#334—831no—
336Q8⋊C8—831no—
337Q8⋊C8—831no—
338Q8⋊C8—831no—
339Q8⋊C8—831no—
340Q8⋊C8—831no—
341Q8⋊C8—831no—
342D4⋊C8—831no—
343D4⋊C8—831no—
344#322—831no—
345#322—831no—
346C82—831no—
347C82—831no—
348C2×Q16—831no—
349C2×Q16—831no—
350C2×SD16—831no—
351C2×SD16—831no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—831no—
355C2×M16—831no—
356C22×C8—21no—
357C22×C8—1661no—
358C4⋊Q8—831no—
359C4⋊Q8—831no—
360#126—21no—
361#125—1661no—
362#125C4×D8311yescharacteristic
363#124C4×D8311yescharacteristic
364#123—21no—
365C22⋊Q8—831no—
366C22⋊Q8—831no—
367C22⋊Q8—1661no—
368C22⋊Q8C4×D8311yescharacteristic
369#121C4×D8311yescharacteristic
370C4×Q8—831no—
371C4×Q8—831no—
372C4×Q8—1661no—
373C4×Q8C22×D8311yescharacteristic
374C4×D4—21no—
375C4×D4C22×D8311yescharacteristic
376#117—21no—
377#117—1661no—
378C2×C42C22×D8311yescharacteristic
379#107—831no—
380#107—831no—
381#106—831no—
382#106—831no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—831no—
387C4⋊C8—831no—
388C4⋊C8—1661no—
389C4⋊C8—1661no—
390C4⋊C8—1661no—
391C4⋊C8—1661no—
392C4⋊C8C22⋊D8311yescharacteristic
393C4⋊C8C22⋊D8311yescharacteristic
394C4⋊C8C22×D8311yescharacteristic
395C4⋊C8C22×D8311yescharacteristic
396#103—831no—
397#103—831no—
398#103—831no—
399#103—831no—
400#103—831no—
401#103—831no—
402#102—831no—
403#102—831no—
404C22⋊C8—21no—
405C22⋊C8—21no—
406C22⋊C8—1661no—
407C22⋊C8C22⋊D8311yescharacteristic
408C22⋊C8C22⋊D8311yescharacteristic
409#97—21no—
410#97—831no—
411#97—831no—
412#97—1661no—
413#97—1661no—
414#97—1661no—
415C4×C8—21no—
416C4×C8—831no—
417C4×C8—831no—
418C4×C8—831no—
419C4×C8—831no—
420C4×C8—1661no—
421C4×C8—1661no—
422C4×C8—1661no—
423C4×C8C22×D8311yescharacteristic
424C4×C8C22×D8311yescharacteristic
425C2×Q8—831no—
426C2×Q8—831no—
427C2×Q8—1661no—
428C2×Q8C2×C4×D8311yescharacteristic
429C2×D4—21no—
430C2×D4C2×C4×D8311yescharacteristic
431C22×C4—21no—
432C22×C4C2×C4×D8311yescharacteristic
433C22×C4C2×C22⋊D8311yescharacteristic
434C22×C4#1305059011yescharacteristic
435Q16—1662no—
436Q16—1662no—
437SD16—1662no—
438SD16—1662no—
439M16—81no—
440M16—81no—
441M16—1662no—
442M16—1662no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—81no—
446C2×C8—3322no—
447C2×C8—831no—
448C2×C8—831no—
449C2×C8—831no—
450C2×C8—831no—
451C2×C8—1661no—
452C2×C8—1661no—
453C2×C8—1661no—
454C2×C8—1661no—
455C2×C8C2×C22⋊D8311yescharacteristic
456C2×C8C2×C22⋊D8311yescharacteristic
457C2×C8C2×C22⋊D8311yescharacteristic
458C2×C8C2×C22⋊D8311yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—831no—
464C4⋊C4—831no—
465C4⋊C4—1661no—
466C4⋊C4—1661no—
467C4⋊C4—1661no—
468C4⋊C4—1661no—
469C4⋊C4—1661no—
470C4⋊C4—1661no—
471C4⋊C4—1661no—
472C4⋊C4C2×C4×D8311yescharacteristic
473C4⋊C4C2×C4×D8311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—1661no—
480C22⋊C4—1661no—
481C42—21no—
482C42—1661no—
483C42—1661no—
484C42C2×C4×D8311yescharacteristic
485C42C2×C22⋊D8311yescharacteristic
486C42#1305059011yescharacteristic
487C42C23×D8311yescharacteristic
488C23—21no—
489C23C4×C22⋊D8311yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—6641no—
493Q8—1661no—
494Q8—1661no—
495Q8—1661no—
496Q8—1661no—
497D4—21no—
498D4—21no—
499D4—81no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—1661no—
511C2×C4—1661no—
512C2×C4—1661no—
513C2×C4—1661no—
514C2×C4C4×C22⋊D8311yescharacteristic
515C2×C4C4×C22⋊D8311yescharacteristic
516C2×C4C4×C22⋊D8311yescharacteristic
517C2×C4C22×C4×D8311yescharacteristic
518C2×C4C22×C22⋊D8311yescharacteristic
519C2×C4C2×#1305059011yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—3321no—
527C8—3321no—
528C8—3321no—
529C8—832no—
530C8—832no—
531C8—1662no—
532C8—1661no—
533C8—1661no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22C2×C4×C22⋊D8311yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—3321no—
549C4—3321no—
550C4—3321no—
551C4—3321no—
552C4#131×D8311yescharacteristic
553C4#131×D8311yescharacteristic
554C4#1912851211yescharacteristic
555C4#1912851611yescharacteristic
556C2—41no—
557C2—81no—
558C2#2491617311yescharacteristic
559C2#2491630211yescharacteristic
560C2#2491637011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#2993C2
socleC22×C83C2×C4×D4
prime radical#121×C83C2×C4
cosocleC42×C83C24
hypercenter#2993D83
hypocenterC83#17969
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. #24916557C2semidirect
3. #24906370C2semidirect
4. #24906365C2semidirect
5. #24906358C2semidirect
6. #24906351C2semidirect
7. #24906280C2semidirect
8. #24906275C2semidirect
9. C8×#13050580C2semidirect
10. C8×#13050578C2semidirect
11. #24906228C2semidirect
13. #24905917C2semidirect
14. #24905744C2semidirect
296. C83#17969semidirect

Maximal subgroups

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

subgroupindex
#249180702
#249165572
#249063702
#249063652
#249063582
#249063512
#249062802
#249062752
C8×#130505802
C8×#130505782
#249062282
#249059232
#249059172
#249057442
C83×#29932
#1796983