Finite Group Databasebeta

← #35376269

Subgroups — #35376269

Order 21248.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918070C211yesmaximal, characteristic
2#24916410C211yesmaximal, characteristic, complemented
3#24906365C211yesmaximal, characteristic, complemented
4#24906358C211yesmaximal, characteristic, complemented
5#24906339C211yesmaximal, characteristic, complemented
6#24906334C211yesmaximal, characteristic, complemented
7#24906311C211yesmaximal, characteristic, complemented
8#24906299C211yesmaximal, characteristic, complemented
9#24906280C211yesmaximal, characteristic, complemented
10C8×#13050578C211yesmaximal, characteristic, complemented
11#24906216C211yesmaximal, characteristic, complemented
12#24905883C211yesmaximal, characteristic, complemented
13#24905876C211yesmaximal, characteristic
14#24905766C211yesmaximal, characteristic, complemented
15C83×#2969C211yesmaximal, characteristic
16#19128258C2211yescharacteristic
17#19128111C411yescharacteristic
18#19128096C411yescharacteristic
19#19128071C411yescharacteristic
20#19128060C411yescharacteristic
21#19127957C411yescharacteristic
22#19127957C411yescharacteristic
23#19127945C411yescharacteristic
24#19127945C411yescharacteristic
25#19127831C2211yescharacteristic
26#19127831C2211yescharacteristic
27#19127829—21no—
28#19127829—21no—
29C8×Dic166C2211yescharacteristic
30C8×Dic166C2211yescharacteristic
31C4×#13050580C2211yescharacteristic
32C4×#13050580C2211yescharacteristic
33C4×#13050578C2211yescharacteristic
34C4×#13050578C2211yescharacteristic
35#19127729—21no—
36C2×C4⋊(C83⋊C8)C2211yescharacteristic
37#19127659—21no—
38C4×#13050574C2211yescharacteristic
39C4×#13050574C2211yescharacteristic
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
54#19127422C2211yescharacteristic
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#405×C83—21no—
66C4×M16×C83C2211yescharacteristic
67C2×#13050580C2×C411yescharacteristic
68C2×#13050580C2×C411yescharacteristic
69C2×#13050578C2×C411yescharacteristic
70C2×#13050578C2×C411yescharacteristic
71C2×#13050574—21no—
72C2×#13050574C2×C411yescharacteristic
73C2×#13050574C2×C411yescharacteristic
74C22×C83⋊C8—21no—
75#14581792C2×C411yescharacteristic
76#14581792C2×C411yescharacteristic
77#14581784—21no—
78#14581771—21no—
79#14581771C2×C411yescharacteristic
80#14581771C2×C411yescharacteristic
81C4×Dic166—21no—
82C4×Dic166C2311yescharacteristic
83C4×Dic166C2311yescharacteristic
84#14581751—21no—
85#14581725C2×C411yescharacteristic
86#14581725C2×C411yescharacteristic
87#14581723C2×C411yescharacteristic
88#14581723C2×C411yescharacteristic
89C4⋊(C83⋊C8)—21no—
90C4⋊(C83⋊C8)C2311yescharacteristic
91C4⋊(C83⋊C8)C2311yescharacteristic
92Dic83⋊C8—21no—
93Dic83⋊C8—21no—
94Dic83⋊C8—21no—
95Dic83⋊C8—21no—
96#14581716C2×C411yescharacteristic
97#14581716C2×C411yescharacteristic
98#14581715C2×C411yescharacteristic
99#14581715C2×C411yescharacteristic
100#14581715C2×C411yescharacteristic
101#14581715C2×C411yescharacteristic
102#14581713C2×C411yescharacteristic
103#14581713C2×C411yescharacteristic
104#14581703—21no—
105#14581703C2×C411yescharacteristic
106#14581703C2×C411yescharacteristic
107#14581702—21no—
108#14581702—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×C83D411yescharacteristic
117C2×M16×C83D411yescharacteristic
118C22×C8×C83—21no—
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×C83D411yescharacteristic
139#97×C83D411yescharacteristic
140C4×C8×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—41no—
149#13050578—22no—
150#13050578—41no—
151#13050574—22no—
152#13050574—41no—
153#13050574—42no—
154C2×C83⋊C8—21no—
155C2×C83⋊C8—21no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—42no—
159C2×C83⋊C8C22×C411yescharacteristic
160C2×C83⋊C8C22×C411yescharacteristic
161C2×C83⋊C8C22×C411yescharacteristic
162C2×C83⋊C8C22×C411yescharacteristic
163C4⋊Dic83—21no—
164C4⋊Dic83—21no—
165C4⋊Dic83—21no—
166C4⋊Dic83C22×C411yescharacteristic
167C4⋊Dic83C22×C411yescharacteristic
168Dic83⋊C4—21no—
169Dic83⋊C4—21no—
170Dic83⋊C4—21no—
171Dic83⋊C4—21no—
172C22⋊Dic83—21no—
173C22⋊Dic83—21no—
174C4×Dic83—21no—
175C4×Dic83—21no—
176C2×Q8×C83C22×C411yescharacteristic
177C2×D4×C83—21no—
178C2×D4×C83C22×C411yescharacteristic
179C22×C4×C83—21no—
180C22×C4×C83C22×C411yescharacteristic
181C22×C4×C83C2×D411yescharacteristic
182C22×C4×C83#4111yescharacteristic
183M16×C83—22no—
184M16×C83—41no—
185M16×C83—42no—
186C2×C8×C83—21no—
187C2×C8×C83—21no—
188C2×C8×C83—42no—
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
211Q8×C83—21no—
212Q8×C83—21no—
213D4×C83—21no—
214D4×C83—21no—
215D4×C83—81no—
216C2×C4×C83—21no—
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—41no—
224C2×C4×C83—41no—
225C2×C4×C83—41no—
226C2×C4×C83C4×D411yescharacteristic
227C2×C4×C83C4×D411yescharacteristic
228C2×C4×C83C4×D411yescharacteristic
229C2×C4×C83C23×C411yescharacteristic
230C2×C4×C83C22×D411yescharacteristic
231C2×C4×C83C2×#4111yescharacteristic
232C2×Dic83—21no—
233C2×Dic83—21no—
234C2×Dic83—21no—
235C2×Dic83—21no—
236Dic166—21no—
237Dic166—21no—
238Dic166—21no—
239Dic166—21no—
240Dic166—81no—
241C8×C83—21no—
242C8×C83—21no—
243C8×C83—21no—
244C8×C83—41no—
245C8×C83—41no—
246C8×C83#13712yes—
247C83⋊C8—22no—
248C83⋊C8—21no—
249C83⋊C8—21no—
250C83⋊C8—21no—
251C83⋊C8—41no—
252C83⋊C8—41no—
253C83⋊C8—41no—
254C83⋊C8#13112yes—
255C22×C83—21no—
256C22×C83—21no—
257C22×C83—21no—
258C22×C83—41no—
259C22×C83—41no—
260C22×C83—41no—
261C22×C83C2×C4×D411yescharacteristic
262C4×C83—21no—
263C4×C83—21no—
264C4×C83—21no—
265C4×C83—21no—
266C4×C83—41no—
267C4×C83—41no—
268C4×C83—41no—
269C4×C83C2×#13111yescharacteristic
270C4×C83#56811yescharacteristic
271C4×C83C2×#13711yescharacteristic
272C4×C83#57511yescharacteristic
273Dic83—41no—
274Dic83—41no—
275Dic83—41no—
276Dic83—41no—
277#18077—831nomaximal, Sylow
278C2×C83—41no—
279C2×C83—81no—
280C2×C83#293511yescharacteristic
281C2×C83C4×#13711yescharacteristic
282C2×C83#295611yescharacteristic
283#3172—831no—
284#2969D8311yescharacteristic
285#2962—831no—
286#1592—831no—
287#1591—831no—
288#1588—831no—
289#1587—831no—
290#1584—831no—
291#1582—831no—
292#1579—831no—
293C8×SD16—831no—
294#1565—831no—
295#1485—831no—
296#1483—831no—
297#1455—831no—
298C83#1807711yescharacteristic, complemented, Sylow
299#533—831no—
300#529C2×D8311yescharacteristic
301#501—831no—
302#497—831no—
303#491—831no—
304#489—831no—
305#470—831no—
306#470—831no—
307#468—831no—
308#468—831no—
309#446—831no—
310#446—831no—
311#446—1661no—
312#446—1661no—
313#446C2×D8311yescharacteristic
314C8×Q8—831no—
315C8×Q8—831no—
316C8×Q8C2×D8311yescharacteristic
317C4×Q16—831no—
318C4×Q16—831no—
319C4×SD16—831no—
320C4×SD16—831no—
321#436—21no—
322#436C2×D8311yescharacteristic
323#435—21no—
324C8×D4C2×D8311yescharacteristic
325#433—21no—
326#431C2×D8311yescharacteristic
327#424—1661no—
328C2×C4⋊C8—831no—
329#405—21no—
330#405—1661no—
331C4×M16—831no—
332C4×M16—831no—
333C4×M16C2×D8311yescharacteristic
334#335—831no—
335#335—831no—
336#334—831no—
337#334—831no—
338Q8⋊C8—831no—
339Q8⋊C8—831no—
340Q8⋊C8—831no—
341Q8⋊C8—831no—
342Q8⋊C8—831no—
343Q8⋊C8—831no—
344D4⋊C8—831no—
345D4⋊C8—831no—
346#322—831no—
347#322—831no—
348#322—831no—
349C82—831no—
350C2×Q16—831no—
351C2×Q16—831no—
352C2×SD16—831no—
353C2×SD16—831no—
354C2×M16—21no—
355C2×M16—831no—
356C2×M16—831no—
357C2×M16—1661no—
358C2×M16C22⋊D8311yescharacteristic
359C2×M16C22⋊D8311yescharacteristic
360C22×C8—21no—
361C22×C8—1661no—
362C4⋊Q8—831no—
363C4⋊Q8—831no—
364#126—21no—
365#125—1661no—
366#125C4×D8311yescharacteristic
367#124C4×D8311yescharacteristic
368#123—21no—
369C22⋊Q8—831no—
370C22⋊Q8—831no—
371C22⋊Q8—1661no—
372C22⋊Q8C4×D8311yescharacteristic
373#121C4×D8311yescharacteristic
374C4×Q8—831no—
375C4×Q8—831no—
376C4×Q8—1661no—
377C4×Q8C22×D8311yescharacteristic
378C4×D4—21no—
379C4×D4C22×D8311yescharacteristic
380#117—21no—
381#117—1661no—
382C2×C42C22×D8311yescharacteristic
383#107—831no—
384#107—831no—
385#106—831no—
386#106—831no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—831no—
390C4⋊C8—831no—
391C4⋊C8—1661no—
392C4⋊C8—1661no—
393C4⋊C8—1661no—
394C4⋊C8—1661no—
395C4⋊C8—1661no—
396C4⋊C8C22×D8311yescharacteristic
397C4⋊C8C22×D8311yescharacteristic
398#103—831no—
399#103—831no—
400#103—831no—
401#103—831no—
402#103—831no—
403#103—831no—
404#102—831no—
405#102—831no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409#97—21no—
410#97—831no—
411#97—831no—
412#97—1661no—
413#97—1661no—
414#97—1661no—
415#97C22⋊D8311yescharacteristic
416#97C22⋊D8311yescharacteristic
417C4×C8—21no—
418C4×C8—21no—
419C4×C8—831no—
420C4×C8—831no—
421C4×C8—831no—
422C4×C8—831no—
423C4×C8—1661no—
424C4×C8—1661no—
425C4×C8C22×D8311yescharacteristic
426C4×C8C22×D8311yescharacteristic
427C2×Q8—831no—
428C2×Q8—831no—
429C2×Q8—1661no—
430C2×Q8C2×C4×D8311yescharacteristic
431C2×D4—21no—
432C2×D4C2×C4×D8311yescharacteristic
433C22×C4—21no—
434C22×C4C2×C4×D8311yescharacteristic
435C22×C4C2×C22⋊D8311yescharacteristic
436C22×C4#1305059011yescharacteristic
437Q16—3321no—
438Q16—1662no—
439SD16—3321no—
440SD16—1662no—
441M16—22no—
442M16—41no—
443M16—42no—
444M16—3322no—
445M16—3321no—
446M16—1662no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—42no—
450C2×C8—3322no—
451C2×C8—831no—
452C2×C8—831no—
453C2×C8—831no—
454C2×C8—831no—
455C2×C8—1661no—
456C2×C8—1661no—
457C2×C8—1661no—
458C2×C8—1661no—
459C2×C8C2×C22⋊D8311yescharacteristic
460C2×C8C2×C22⋊D8311yescharacteristic
461C2×C8C2×C22⋊D8311yescharacteristic
462C2×C8C2×C22⋊D8311yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—831no—
468C4⋊C4—831no—
469C4⋊C4—1661no—
470C4⋊C4—1661no—
471C4⋊C4—1661no—
472C4⋊C4—1661no—
473C4⋊C4—1661no—
474C4⋊C4—1661no—
475C4⋊C4—1661no—
476C4⋊C4C2×C4×D8311yescharacteristic
477C4⋊C4C2×C4×D8311yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—1661no—
484C22⋊C4—1661no—
485C42—21no—
486C42—1661no—
487C42—1661no—
488C42C2×C4×D8311yescharacteristic
489C42C2×C22⋊D8311yescharacteristic
490C42#1305059011yescharacteristic
491C42C23×D8311yescharacteristic
492C23—21no—
493C23C4×C22⋊D8311yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—6641no—
497Q8—1661no—
498Q8—1661no—
499Q8—1661no—
500Q8—1661no—
501D4—21no—
502D4—21no—
503D4—81no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—1661no—
515C2×C4—1661no—
516C2×C4—1661no—
517C2×C4—1661no—
518C2×C4C4×C22⋊D8311yescharacteristic
519C2×C4C4×C22⋊D8311yescharacteristic
520C2×C4C4×C22⋊D8311yescharacteristic
521C2×C4C22×C4×D8311yescharacteristic
522C2×C4C22×C22⋊D8311yescharacteristic
523C2×C4C2×#1305059011yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—41no—
528C8—41no—
529C8—3321no—
530C8—3321no—
531C8—3321no—
532C8—832no—
533C8—1662no—
534C8—1661no—
535C8—1661no—
536C8—1661no—
537C8#1458182212yes—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22C2×C4×C22⋊D8311yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—3321no—
553C4—3321no—
554C4—3321no—
555C4—3321no—
556C4#131×D8311yescharacteristic
557C4#1912846611yescharacteristic
558C4C2×#1458182211yescharacteristic
559C4#1912849911yescharacteristic
560C2—41no—
561C2—81no—
562C2#2491620511yescharacteristic
563C2C4×#1458182211yescharacteristic
564C2#2491637011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#2969C2
socleC22×C83C2×C4×D4
prime radical#121×C83C2×C4
cosocleC42×C83C24
hypercenter#2969D83
hypocenterC83#18077
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. #24916410C2semidirect
3. #24906365C2semidirect
4. #24906358C2semidirect
5. #24906339C2semidirect
6. #24906334C2semidirect
7. #24906311C2semidirect
8. #24906299C2semidirect
9. #24906280C2semidirect
10. C8×#13050578C2semidirect
11. #24906216C2semidirect
12. #24905883C2semidirect
14. #24905766C2semidirect
298. C83#18077semidirect

Maximal subgroups

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

subgroupindex
#249180702
#249164102
#249063652
#249063582
#249063392
#249063342
#249063112
#249062992
#249062802
C8×#130505782
#249062162
#249058832
#249058762
#249057662
C83×#29692
#1807783