Finite Group Databasebeta

← #35375280

Subgroups — #35375280

Order 21248.

576 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#24918031C211yesmaximal, characteristic
2#24916613C211yesmaximal, characteristic, complemented
3#24916607C211yesmaximal, characteristic, complemented
4#24906336C211yesmaximal, characteristic, complemented
5#24906333C211yesmaximal, characteristic, complemented
6#24906328C211yesmaximal, characteristic, complemented
7#24906309C211yesmaximal, characteristic, complemented
8#24906304C211yesmaximal, characteristic, complemented
9#24906299C211yesmaximal, characteristic, complemented
10#24906296C211yesmaximal, characteristic, complemented
11#24906217C211yesmaximal, characteristic, complemented
12#24905925C211yesmaximal, characteristic, complemented
13#24905925C211yesmaximal, characteristic, complemented
14#24905754C211yesmaximal, characteristic, complemented
15C83×#1586C211yesmaximal, characteristic, complemented
16#19128233C2211yescharacteristic
17#19128233C2211yescharacteristic
18#19128102C411yescharacteristic
19#19128084C411yescharacteristic
20#19128054C411yescharacteristic
21#19128054C411yescharacteristic
22#19127943C411yescharacteristic
23#19127934C411yescharacteristic
24#19127929C411yescharacteristic
25#19127929C411yescharacteristic
26#19127831C2211yescharacteristic
27#19127828C2211yescharacteristic
28C8×Dic166C2211yescharacteristic
29#19127825C2211yescharacteristic
30C4×Dic332C2211yescharacteristic
31C4×#13050578C2211yescharacteristic
32C4×#13050578C2211yescharacteristic
33#19127779C2211yescharacteristic
34#19127777—21no—
35#19127776—21no—
36#19127772—21no—
37#19127769—21no—
38D4×C83⋊C8C2211yescharacteristic
39#19127759—21no—
40#19127759—21no—
41#19127752C2211yescharacteristic
42#19127752C2211yescharacteristic
43#19127729—21no—
44#19127727—21no—
45#19127723C2211yescharacteristic
46#19127723C2211yescharacteristic
47C4×C8×D83C2211yescharacteristic
48#19127452C2211yescharacteristic
49#19127451C2211yescharacteristic
50#19127451C2211yescharacteristic
51#19127433C2211yescharacteristic
52#19127433C2211yescharacteristic
53#19127431C2211yescharacteristic
54#19127431C2211yescharacteristic
55D4⋊(C83⋊C8)C2211yescharacteristic
56D4⋊(C83⋊C8)C2211yescharacteristic
57#19127423C2211yescharacteristic
58#19127423C2211yescharacteristic
59#19127422C2211yescharacteristic
60C4×D8×C83C2211yescharacteristic
61#436×C83C2211yescharacteristic
62C8×D4×C83C2211yescharacteristic
63#334×C83C2211yescharacteristic
64D4⋊C8×C83C2211yescharacteristic
65D4⋊C8×C83C2211yescharacteristic
66#322×C83C2211yescharacteristic
67C2×Dic332C2×C411yescharacteristic
68C2×#13050578C2×C411yescharacteristic
69C2×#13050578C2×C411yescharacteristic
70C2×#13050574—21no—
71C2×#13050573—21no—
72C2×#13050573—21no—
73C22×C83⋊C8—21no—
74C2×C8×D83C2×C411yescharacteristic
75C2×C8×D83C2×C411yescharacteristic
76#14581785—21no—
77#14581785—21no—
78#14581783C2×C411yescharacteristic
79#14581783C2×C411yescharacteristic
80#14581779C2×C411yescharacteristic
81#14581779C2×C411yescharacteristic
82#14581774—21no—
83#14581774—21no—
84#14581772C2×C411yescharacteristic
85#14581772C2×C411yescharacteristic
86#14581763C2×C411yescharacteristic
87#14581763C2×C411yescharacteristic
88C4×Dic166C2311yescharacteristic
89C4×Dic166C2311yescharacteristic
90C4×C22⋊D83—21no—
91C4×C22⋊D83—21no—
92#14581751—21no—
93#14581751—21no—
94C42×D83C2311yescharacteristic
95#14581726C2×C411yescharacteristic
96#14581723C2×C411yescharacteristic
97#14581723C2×C411yescharacteristic
98C4⋊(C83⋊C8)C2311yescharacteristic
99C4⋊(C83⋊C8)C2311yescharacteristic
100Dic83⋊C8—21no—
101Dic83⋊C8—21no—
102Dic83⋊C8—21no—
103Dic83⋊C8—21no—
104Dic83⋊C8—21no—
105Dic83⋊C8—21no—
106Dic83⋊C8—21no—
107Dic83⋊C8D411yescharacteristic
108Dic83⋊C8D411yescharacteristic
109#14581717C2×C411yescharacteristic
110#14581717C2×C411yescharacteristic
111#14581715C2×C411yescharacteristic
112#14581715C2×C411yescharacteristic
113#14581713C2×C411yescharacteristic
114#14581713C2×C411yescharacteristic
115C22⋊(C83⋊C8)—21no—
116C22⋊(C83⋊C8)—21no—
117(C2×D83)⋊C8—21no—
118(C2×D83)⋊C8D411yescharacteristic
119(C2×D83)⋊C8D411yescharacteristic
120#14581702—21no—
121#14581702—21no—
122C4×C83⋊C8C2311yescharacteristic
123C4×C83⋊C8C2311yescharacteristic
124C4×C83⋊C8C2311yescharacteristic
125C8×Dic83—21no—
126C8×Dic83—21no—
127C8×Dic83C2×C411yescharacteristic
128C8×Dic83C2×C411yescharacteristic
129C2×D8×C83C2×C411yescharacteristic
130C2×M16×C83—21no—
131C22×C8×C83—21no—
132C4×D4×C83C2311yescharacteristic
133C4×D4×C83C2311yescharacteristic
134#107×C83C2×C411yescharacteristic
135C4⋊C8×C83C2311yescharacteristic
136C4⋊C8×C83C2311yescharacteristic
137#102×C83C2×C411yescharacteristic
138#102×C83C2×C411yescharacteristic
139C22⋊C8×C83—21no—
140C22⋊C8×C83—21no—
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C2×Dic166C22×C411yescharacteristic
145C2×Dic166C22×C411yescharacteristic
146C2×C22⋊D83—21no—
147C2×C22⋊D83—21no—
148C2×C4×D83C22×C411yescharacteristic
149C2×C4×D83C2×D411yescharacteristic
150C2×C4×D83#4111yescharacteristic
151Dic332—41no—
152#13050578—41no—
153#13050578—41no—
154#13050574—81no—
155#13050573—81no—
156#13050573—81no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8—81no—
161C2×C83⋊C8C22×C411yescharacteristic
162C2×C83⋊C8C22×C411yescharacteristic
163C2×C83⋊C8C2×D411yescharacteristic
164C2×C83⋊C8C2×D411yescharacteristic
165C8×D83—41no—
166C8×D83—41no—
167C4⋊Dic83—21no—
168C4⋊Dic83—21no—
169C4⋊Dic83—21no—
170C4⋊Dic83—21no—
171C4⋊Dic83C22×C411yescharacteristic
172C4⋊Dic83C22×C411yescharacteristic
173Dic83⋊C4—21no—
174Dic83⋊C4—21no—
175Dic83⋊C4—21no—
176Dic83⋊C4—21no—
177C22⋊Dic83—21no—
178C22⋊Dic83—21no—
179C22⋊Dic83—21no—
180C22⋊Dic83—21no—
181C22⋊Dic83—21no—
182C22⋊Dic83—21no—
183(C2×D83)⋊C4—21no—
184(C2×D83)⋊C4—21no—
185C4×Dic83—21no—
186C4×Dic83—21no—
187C4×Dic83C22×C411yescharacteristic
188C4×Dic83C2×D411yescharacteristic
189C4×Dic83#4111yescharacteristic
190C2×D4×C83C22×C411yescharacteristic
191C2×D4×C83C22×C411yescharacteristic
192C22×C4×C83—21no—
193C22×C4×C83—21no—
194D8×C83—41no—
195M16×C83—81no—
196C2×C8×C83—21no—
197C2×C8×C83—21no—
198C2×C8×C83—21no—
199C2×C8×C83—81no—
200C2×C8×C83C22×C411yescharacteristic
201C2×C8×C83C22×C411yescharacteristic
202C2×C8×C83C2×D411yescharacteristic
203C2×C8×C83C2×D411yescharacteristic
204C4⋊C4×C83C22×C411yescharacteristic
205C4⋊C4×C83C22×C411yescharacteristic
206C22⋊C4×C83—21no—
207C22⋊C4×C83—21no—
208C42×C83C2411yescharacteristic
209C23×C83—21no—
210C23×C83—21no—
211C22×D83C4×D411yescharacteristic
212D4×C83—21no—
213D4×C83—21no—
214D4×C83—21no—
215D4×C83—21no—
216C2×C4×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—41no—
219C2×C4×C83—41no—
220C2×C4×C83—41no—
221C2×C4×C83—41no—
222C2×C4×C83C23×C411yescharacteristic
223C2×C4×C83C22×D411yescharacteristic
224C2×C4×C83C2×#4111yescharacteristic
225C22⋊D83—81no—
226C22⋊D83—81no—
227C2×Dic83—21no—
228C2×Dic83—21no—
229C2×Dic83—21no—
230C2×Dic83—21no—
231C2×Dic83C4×D411yescharacteristic
232C2×Dic83C4×D411yescharacteristic
233C2×Dic83C4×D411yescharacteristic
234C4×D83—21no—
235C4×D83—21no—
236C4×D83—21no—
237C4×D83—21no—
238C4×D83—41no—
239Dic166—21no—
240Dic166—21no—
241Dic166—21no—
242Dic166—21no—
243C8×C83—21no—
244C8×C83—21no—
245C8×C83—21no—
246C8×C83—21no—
247C8×C83—41no—
248C8×C83—41no—
249C8×C83—41no—
250C83⋊C8—21no—
251C83⋊C8—21no—
252C83⋊C8—21no—
253C83⋊C8—21no—
254C83⋊C8—41no—
255C83⋊C8—41no—
256C83⋊C8—41no—
257C22×C83—41no—
258C22×C83—41no—
259C22×C83—41no—
260C22×C83—41no—
261C22×C83—41no—
262C22×C83—41no—
263C22×C83C2×C4×D411yescharacteristic
264C2×D83—21no—
265C2×D83—21no—
266C2×D83—21no—
267C4×C83—21no—
268C4×C83—41no—
269C4×C83—41no—
270C4×C83#56811yescharacteristic
271C4×C83#56811yescharacteristic
272C4×C83#57711yescharacteristic
273C4×C83#57711yescharacteristic
274Dic83—21no—
275Dic83—21no—
276Dic83—21no—
277Dic83—41no—
278Dic83—41no—
279Dic83—41no—
280Dic83—41no—
281#17993—831nomaximal, Sylow
282C2×C83—81no—
283C2×C83—81no—
284C2×C83#293211yescharacteristic
285C2×C83#295211yescharacteristic
286C2×C83#295711yescharacteristic
287D83—41no—
288#3168—831no—
289#2993—831no—
290#2993—831no—
291#1587—831no—
292#1587—831no—
293#1586—831no—
294#1586D8311yescharacteristic, complemented
295#1583—831no—
296#1583—831no—
297#1582—831no—
298#1582—831no—
299#1566—831no—
300#1495—831no—
301#1495—831no—
302#1452—831no—
303C83#1799311yescharacteristic, complemented, Sylow
304#529—831no—
305#529—831no—
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#446—831no—
316C8×Q8—831no—
317C8×Q8—831no—
318C4×Q16—831no—
319C4×SD16—831no—
320C4×SD16—831no—
321C4×D8C2×D8311yescharacteristic
322#436—831no—
323#436—1661no—
324#436—1661no—
325#436C2×D8311yescharacteristic
326#435—1661no—
327#435—1661no—
328C8×D4—831no—
329C8×D4C2×D8311yescharacteristic
330#433—1661no—
331#433—1661no—
332#431—831no—
333#431—831no—
334#424—1661no—
335#424—1661no—
336#423—831no—
337#423—831no—
338C2×C4×C8—831no—
339#334—831no—
340#334—831no—
341#334—831no—
342#334C2×D8311yescharacteristic
343Q8⋊C8—831no—
344Q8⋊C8—831no—
345Q8⋊C8—831no—
346Q8⋊C8—831no—
347D4⋊C8—831no—
348D4⋊C8—831no—
349D4⋊C8C2×D8311yescharacteristic
350D4⋊C8C2×D8311yescharacteristic
351#322—831no—
352#322—831no—
353#322—831no—
354#322C2×D8311yescharacteristic
355C2×Q16—831no—
356C2×SD16—831no—
357C2×SD16—831no—
358C2×D8C4×D8311yescharacteristic
359C2×M16—21no—
360C2×M16—1661no—
361C2×M16—1661no—
362C2×M16—1661no—
363C22×C8—21no—
364C22×C8—831no—
365C22×C8—831no—
366C22×C8—1661no—
367#126—1661no—
368#126—1661no—
369#125—831no—
370#125—831no—
371#124—831no—
372#124—831no—
373#123—1661no—
374#123—1661no—
375C22⋊Q8—831no—
376C22⋊Q8—831no—
377#121—831no—
378#121—831no—
379C4×Q8—831no—
380C4×Q8—831no—
381C4×D4—1661no—
382C4×D4—1661no—
383C4×D4C22×D8311yescharacteristic
384C4×D4C22×D8311yescharacteristic
385#117—1661no—
386#117—1661no—
387C2×C42—831no—
388#107—831no—
389#107C4×D8311yescharacteristic
390#106—831no—
391#106—831no—
392C4⋊C8—831no—
393C4⋊C8—831no—
394C4⋊C8—831no—
395C4⋊C8—831no—
396C4⋊C8—1661no—
397C4⋊C8—1661no—
398C4⋊C8—1661no—
399C4⋊C8—1661no—
400C4⋊C8—1661no—
401C4⋊C8—1661no—
402C4⋊C8—1661no—
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#102C4×D8311yescharacteristic
412#102C4×D8311yescharacteristic
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—831no—
416C22⋊C8—831no—
417C22⋊C8—1661no—
418C22⋊C8—1661no—
419C22⋊C8—1661no—
420#97—1661no—
421#97—1661no—
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
432C2×Q8—831no—
433C2×Q8—831no—
434C2×D4—1661no—
435C2×D4—1661no—
436C2×D4C2×C4×D8311yescharacteristic
437C2×D4C2×C4×D8311yescharacteristic
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—831no—
441C22×C4—831no—
442C22×C4—831no—
443Q16—3321no—
444SD16—3321no—
445SD16—3321no—
446D8—41no—
447M16—81no—
448M16—6641no—
449M16—6641no—
450M16—6641no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—81no—
455C2×C8—3321no—
456C2×C8—3321no—
457C2×C8—831no—
458C2×C8—831no—
459C2×C8—831no—
460C2×C8—831no—
461C2×C8—6641no—
462C2×C8—1661no—
463C2×C8—1661no—
464C2×C8—1661no—
465C2×C8C2×C4×D8311yescharacteristic
466C2×C8C2×C4×D8311yescharacteristic
467C2×C8D4×D8311yescharacteristic
468C2×C8D4×D8311yescharacteristic
469C4⋊C4—831no—
470C4⋊C4—831no—
471C4⋊C4—1661no—
472C4⋊C4—1661no—
473C4⋊C4—1661no—
474C4⋊C4—1661no—
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—1661no—
484C22⋊C4—1661no—
485C22⋊C4—1661no—
486C22⋊C4—1661no—
487C22⋊C4—1661no—
488C22⋊C4—1661no—
489C22⋊C4—1661no—
490C22⋊C4—1661no—
491C42—831no—
492C42—831no—
493C42—831no—
494C42—1661no—
495C42—1661no—
496C42C23×D8311yescharacteristic
497C23—21no—
498C23—21no—
499C23—831no—
500Q8—1661no—
501Q8—1661no—
502Q8—1661no—
503Q8—1661no—
504D4—21no—
505D4—21no—
506D4—21no—
507D4—21no—
508D4—6641no—
509D4—6641no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—3321no—
517C2×C4—831no—
518C2×C4—831no—
519C2×C4—831no—
520C2×C4—1661no—
521C2×C4—1661no—
522C2×C4—1661no—
523C2×C4—1661no—
524C2×C4—1661no—
525C2×C4—1661no—
526C2×C4—1661no—
527C2×C4—1661no—
528C2×C4C22×C4×D8311yescharacteristic
529C2×C4C2×D4×D8311yescharacteristic
530C2×C4#41×D8311yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—3321no—
539C8—3321no—
540C8—3321no—
541C8—1661no—
542C8—1661no—
543C8—1661no—
544C8—1661no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—1661no—
552C22—1661no—
553C22—1661no—
554C22C4×D4×D8311yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—3321no—
559C4—3321no—
560C4—3321no—
561C4—3321no—
562C4—1661no—
563C4—1661no—
564C4—1661no—
565C4#1912846611yescharacteristic
566C4#1912846711yescharacteristic
567C4#1912851111yescharacteristic
568C4#1912851111yescharacteristic
569C2—81no—
570C2—81no—
571C2—3321no—
572C2#2491617711yescharacteristic
573C2#2491634511yescharacteristic
574C2#2491637511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1586C2
socleC22×C83C2×C4×D4
prime radical#19127934C4
cosocleC42×C83C24
hypercenter#1586D83
hypocenterC83#17993
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
2. #24916613C2semidirect
3. #24916607C2semidirect
4. #24906336C2semidirect
5. #24906333C2semidirect
6. #24906328C2semidirect
7. #24906309C2semidirect
8. #24906304C2semidirect
9. #24906299C2semidirect
10. #24906296C2semidirect
11. #24906217C2semidirect
12. #24905925C2semidirect
13. #24905925C2semidirect
14. #24905754C2semidirect
15. C83×#1586C2semidirect
294. #1586D83semidirect
303. C83#17993semidirect

Maximal subgroups

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

subgroupindex
#249180312
#249166132
#249166072
#249063362
#249063332
#249063282
#249063092
#249063042
#249062992
#249062962
#249062172
#249059252
#249057542
C83×#15862
#1799383