Finite Group Databasebeta

← #35375047

Subgroups — #35375047

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#24918069C211yesmaximal, characteristic
2#24916608C211yesmaximal, characteristic
3#24916560C211yesmaximal, characteristic, complemented
4#24906371C211yesmaximal, characteristic, complemented
5#24906364C211yesmaximal, characteristic, complemented
6#24906359C211yesmaximal, characteristic, complemented
7#24906352C211yesmaximal, characteristic, complemented
8#24906281C211yesmaximal, characteristic, complemented
9#24906274C211yesmaximal, characteristic, complemented
10#24906269C211yesmaximal, characteristic, complemented
11#24906262C211yesmaximal, characteristic, complemented
12#24905921C211yesmaximal, characteristic
13#24905917C211yesmaximal, characteristic, complemented
14M16×C83⋊C8C211yesmaximal, characteristic, complemented
15C83×#1569C211yesmaximal, characteristic, complemented
16#19128258C2211yescharacteristic
17#19128235C2211yescharacteristic
18#19128110C411yescharacteristic
19#19128095C411yescharacteristic
20#19128070C411yescharacteristic
21#19128061C411yescharacteristic
22#19127959C411yescharacteristic
23#19127959C411yescharacteristic
24#19127947C411yescharacteristic
25#19127947C411yescharacteristic
26#19127829—21no—
27#19127829—21no—
28#19127828C2211yescharacteristic
29#19127828C2211yescharacteristic
30#19127828C2211yescharacteristic
31#19127825C2211yescharacteristic
32#19127825C2211yescharacteristic
33#19127825C2211yescharacteristic
34C4×Dic332C2211yescharacteristic
35C4×Dic332C2211yescharacteristic
36C4×#13050579C2211yescharacteristic
37C4×#13050579C2211yescharacteristic
38#19127778C2211yescharacteristic
39#19127777—21no—
40#19127770—21no—
41#19127766C2211yescharacteristic
42#19127761—21no—
43#19127759—21no—
44#19127759—21no—
45#19127754C2211yescharacteristic
46#19127726—21no—
47C2×C4×C83⋊C8C2211yescharacteristic
48#19127431C2211yescharacteristic
49#19127431C2211yescharacteristic
50#19127431C2211yescharacteristic
51#19127431C2211yescharacteristic
52#19127431C2211yescharacteristic
53#19127431C2211yescharacteristic
54#19127428C2211yescharacteristic
55#19127428C2211yescharacteristic
56#19127422C2211yescharacteristic
57#19127422C2211yescharacteristic
58C8×C83⋊C8C2211yescharacteristic
59C8×C83⋊C8C2211yescharacteristic
60#432×C83C2211yescharacteristic
61#423×C83C2211yescharacteristic
62C4×M16×C83C2211yescharacteristic
63#335×C83C2211yescharacteristic
64#335×C83C2211yescharacteristic
65#334×C83C2211yescharacteristic
66#334×C83C2211yescharacteristic
67C2×Dic332C2×C411yescharacteristic
68C2×Dic332C2×C411yescharacteristic
69C2×#13050579C2×C411yescharacteristic
70C2×#13050579C2×C411yescharacteristic
71C2×#13050573—21no—
72C22×C83⋊C8—21no—
73C2×C8×D83—21no—
74#14581792C2×C411yescharacteristic
75#14581792C2×C411yescharacteristic
76#14581786—21no—
77#14581784—21no—
78#14581784C2×C411yescharacteristic
79#14581780C2×C411yescharacteristic
80#14581775—21no—
81#14581771—21no—
82#14581771C2×C411yescharacteristic
83#14581771C2×C411yescharacteristic
84#14581771C2×C411yescharacteristic
85#14581766C2×C411yescharacteristic
86C4×Dic166—21no—
87C4×Dic166C2311yescharacteristic
88C4×Dic166C2311yescharacteristic
89C4×Dic166C2311yescharacteristic
90C4×D332C2311yescharacteristic
91C4×C22⋊D83—21no—
92#14581751—21no—
93#14581749—21no—
94#14581726C2×C411yescharacteristic
95#14581726C2×C411yescharacteristic
96#14581724C2×C411yescharacteristic
97#14581724C2×C411yescharacteristic
98C4⋊(C83⋊C8)D411yescharacteristic
99C4⋊(C83⋊C8)D411yescharacteristic
100Dic83⋊C8—21no—
101Dic83⋊C8—21no—
102Dic83⋊C8—21no—
103Dic83⋊C8—21no—
104Dic83⋊C8—21no—
105Dic83⋊C8—21no—
106#14581717C2×C411yescharacteristic
107#14581717C2×C411yescharacteristic
108#14581717C2×C411yescharacteristic
109#14581717C2×C411yescharacteristic
110#14581717C2×C411yescharacteristic
111#14581717C2×C411yescharacteristic
112#14581714C2×C411yescharacteristic
113#14581714C2×C411yescharacteristic
114C22⋊(C83⋊C8)D411yescharacteristic
115C22⋊(C83⋊C8)D411yescharacteristic
116(C2×D83)⋊C8—21no—
117(C2×D83)⋊C8—21no—
118#14581702—21no—
119#14581702—21no—
120#14581702—21no—
121C4×C83⋊C8—21no—
122C4×C83⋊C8C2311yescharacteristic
123C4×C83⋊C8C2311yescharacteristic
124C4×C83⋊C8C2311yescharacteristic
125C4×C83⋊C8C2311yescharacteristic
126C8×Dic83—21no—
127C8×Dic83—21no—
128C8×Dic83—21no—
129C2×M16×C83—21no—
130C2×M16×C83C2×C411yescharacteristic
131C2×M16×C83C2×C411yescharacteristic
132C2×C42×C83C2311yescharacteristic
133C4⋊C8×C83—21no—
134C4⋊C8×C83C2311yescharacteristic
135C4⋊C8×C83C2311yescharacteristic
136C4⋊C8×C83C2311yescharacteristic
137C4⋊C8×C83C2311yescharacteristic
138C22⋊C8×C83—21no—
139#97×C83—21no—
140#97×C83C2×C411yescharacteristic
141#97×C83C2×C411yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C2×Dic166—21no—
145C2×Dic166C22×C411yescharacteristic
146C2×Dic166C22×C411yescharacteristic
147C2×Dic166C22×C411yescharacteristic
148C2×D332C22×C411yescharacteristic
149C2×C22⋊D83—21no—
150C2×C4×D83—21no—
151Dic332—22no—
152Dic332—22no—
153#13050579—22no—
154#13050579—22no—
155#13050573—81no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—42no—
159C2×C83⋊C8C2×D411yescharacteristic
160C2×C83⋊C8C2×D411yescharacteristic
161C2×C83⋊C8C2×D411yescharacteristic
162C2×C83⋊C8C2×D411yescharacteristic
163C8×D83—81no—
164C4⋊Dic83—21no—
165C4⋊Dic83—21no—
166C4⋊Dic83—21no—
167C4⋊Dic83C22×C411yescharacteristic
168C4⋊Dic83C22×C411yescharacteristic
169C4⋊Dic83C22×C411yescharacteristic
170C4⋊Dic83C22×C411yescharacteristic
171Dic83⋊C4—21no—
172Dic83⋊C4—21no—
173Dic83⋊C4—21no—
174Dic83⋊C4—21no—
175Dic83⋊C4—21no—
176Dic83⋊C4—21no—
177Dic83⋊C4—21no—
178Dic83⋊C4—21no—
179C22⋊Dic83—21no—
180C22⋊Dic83—21no—
181C22⋊Dic83—21no—
182(C2×D83)⋊C4—21no—
183(C2×D83)⋊C4—21no—
184(C2×D83)⋊C4—21no—
185(C2×D83)⋊C4—21no—
186C4×Dic83—21no—
187C4×Dic83—21no—
188C4×Dic83—21no—
189C22×C4×C83C22×C411yescharacteristic
190C22×C4×C83C2×D411yescharacteristic
191C22×C4×C83#4111yescharacteristic
192M16×C83—22no—
193M16×C83—22no—
194M16×C83—81no—
195C2×C8×C83—21no—
196C2×C8×C83—21no—
197C2×C8×C83—21no—
198C2×C8×C83—21no—
199C2×C8×C83C22×C411yescharacteristic
200C2×C8×C83C22×C411yescharacteristic
201C2×C8×C83C22×C411yescharacteristic
202C2×C8×C83C22×C411yescharacteristic
203C42×C83C22×C411yescharacteristic
204C42×C83C2×D411yescharacteristic
205C42×C83#4111yescharacteristic
206C42×C83C2411yescharacteristic
207C23×C83C4×D411yescharacteristic
208C22×D83—21no—
209C2×C4×C83—21no—
210C2×C4×C83—21no—
211C2×C4×C83—21no—
212C2×C4×C83—21no—
213C2×C4×C83—41no—
214C2×C4×C83C4×D411yescharacteristic
215C2×C4×C83C4×D411yescharacteristic
216C2×C4×C83C4×D411yescharacteristic
217C2×C4×C83C23×C411yescharacteristic
218C2×C4×C83C22×D411yescharacteristic
219C2×C4×C83C2×#4111yescharacteristic
220C22⋊D83—81no—
221C2×Dic83—21no—
222C2×Dic83—21no—
223C2×Dic83—21no—
224C2×Dic83—21no—
225C2×Dic83—21no—
226C2×Dic83—21no—
227C2×Dic83—21no—
228D332—21no—
229D332—21no—
230C4×D83—41no—
231C4×D83—41no—
232Dic166—21no—
233Dic166—21no—
234Dic166—21no—
235Dic166—21no—
236Dic166—21no—
237Dic166—21no—
238Dic166—81no—
239C8×C83—21no—
240C8×C83—21no—
241C8×C83—41no—
242C8×C83—41no—
243C8×C83—41no—
244C8×C83—41no—
245C8×C83#13112yes—
246C8×C83#13112yes—
247C83⋊C8—22no—
248C83⋊C8—21no—
249C83⋊C8—21no—
250C83⋊C8—21no—
251C83⋊C8—21no—
252C83⋊C8—41no—
253C22×C83—21no—
254C22×C83—21no—
255C22×C83—21no—
256C22×C83C2×C4×D411yescharacteristic
257C2×D83—41no—
258C2×D83—41no—
259C2×D83—41no—
260C4×C83—21no—
261C4×C83—21no—
262C4×C83—21no—
263C4×C83—21no—
264C4×C83C2×#13111yescharacteristic
265C4×C83C2×#13111yescharacteristic
266C4×C83#57711yescharacteristic
267C4×C83#57811yescharacteristic
268Dic83—41no—
269Dic83—41no—
270Dic83—41no—
271Dic83—41no—
272Dic83—41no—
273Dic83—41no—
274Dic83—41no—
275#17969—831nomaximal, Sylow
276C2×C83—41no—
277C2×C83#293111yescharacteristic
278C2×C83#294711yescharacteristic
279C2×C83#295611yescharacteristic
280D83—81no—
281#3172—831no—
282#2993—831no—
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#1569D8311yescharacteristic, complemented
293#1494—831no—
294#1493—831no—
295C8×M16—831no—
296C83#1796911yescharacteristic, complemented, Sylow
297#533—831no—
298#529—831no—
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—831no—
310#446—1661no—
311#446—1661no—
312C8×Q8—831no—
313C8×Q8—831no—
314C8×Q8—831no—
315C4×Q16—831no—
316C4×Q16—831no—
317C4×SD16—831no—
318C4×SD16—831no—
319#436—831no—
320#436—1661no—
321#435—1661no—
322C8×D4—831no—
323#433—1661no—
324#433—1661no—
325#433—1661no—
326#432C2×D8311yescharacteristic
327#431—831no—
328#424—1661no—
329#423C2×D8311yescharacteristic
330C4×M16C2×D8311yescharacteristic
331C2×C4×C8—831no—
332#335C2×D8311yescharacteristic
333#335C2×D8311yescharacteristic
334#334C2×D8311yescharacteristic
335#334C2×D8311yescharacteristic
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—1661no—
354C2×M16C4×D8311yescharacteristic
355C2×M16C4×D8311yescharacteristic
356C22×C8—1661no—
357C22×C8—1661no—
358C4⋊Q8—831no—
359C4⋊Q8—831no—
360#126—1661no—
361#125—831no—
362#125—1661no—
363#124—831no—
364#123—1661no—
365C22⋊Q8—831no—
366C22⋊Q8—831no—
367C22⋊Q8—831no—
368C22⋊Q8—1661no—
369#121—831no—
370C4×Q8—831no—
371C4×Q8—831no—
372C4×Q8—831no—
373C4×Q8—1661no—
374C4×D4—831no—
375C4×D4—1661no—
376#117—1661no—
377#117—1661no—
378C2×C42C22×D8311yescharacteristic
379#107—831no—
380#107—831no—
381#106—831no—
382#106—831no—
383C4⋊C8—21no—
384C4⋊C8—831no—
385C4⋊C8—831no—
386C4⋊C8—1661no—
387C4⋊C8—1661no—
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—831no—
406C22⋊C8—831no—
407C22⋊C8—1661no—
408C22⋊C8—1661no—
409#97—21no—
410#97—1661no—
411#97—1661no—
412#97—1661no—
413#97C4×D8311yescharacteristic
414#97C4×D8311yescharacteristic
415C4×C8—831no—
416C4×C8—831no—
417C4×C8—831no—
418C4×C8—831no—
419C4×C8—1661no—
420C4×C8—1661no—
421C4×C8—1661no—
422C4×C8—1661no—
423C4×C8C22×D8311yescharacteristic
424C4×C8C22×D8311yescharacteristic
425C2×Q8—831no—
426C2×Q8—831no—
427C2×Q8—831no—
428C2×Q8—1661no—
429C2×D4—831no—
430C2×D4—1661no—
431C22×C4—1661no—
432C22×C4C2×C4×D8311yescharacteristic
433C22×C4D4×D8311yescharacteristic
434C22×C4#1305059111yescharacteristic
435Q16—1662no—
436Q16—1662no—
437SD16—1662no—
438SD16—1662no—
439M16—22no—
440M16—22no—
441M16—81no—
442M16—6641no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—3322no—
448C2×C8—831no—
449C2×C8—831no—
450C2×C8—831no—
451C2×C8—831no—
452C2×C8—6641no—
453C2×C8—1661no—
454C2×C8—1661no—
455C2×C8C2×C4×D8311yescharacteristic
456C2×C8C2×C4×D8311yescharacteristic
457C2×C8C2×C4×D8311yescharacteristic
458C2×C8C2×C4×D8311yescharacteristic
459C4⋊C4—831no—
460C4⋊C4—831no—
461C4⋊C4—831no—
462C4⋊C4—831no—
463C4⋊C4—1661no—
464C4⋊C4—1661no—
465C4⋊C4—1661no—
466C4⋊C4—1661no—
467C4⋊C4—1661no—
468C4⋊C4—1661no—
469C4⋊C4—1661no—
470C4⋊C4—1661no—
471C4⋊C4—1661no—
472C4⋊C4—1661no—
473C4⋊C4—1661no—
474C22⋊C4—1661no—
475C22⋊C4—1661no—
476C22⋊C4—1661no—
477C22⋊C4—1661no—
478C22⋊C4—1661no—
479C22⋊C4—1661no—
480C22⋊C4—1661no—
481C42—1661no—
482C42—1661no—
483C42—1661no—
484C42C2×C4×D8311yescharacteristic
485C42D4×D8311yescharacteristic
486C42#1305059111yescharacteristic
487C42C23×D8311yescharacteristic
488C23—1661no—
489C23#1458175411yescharacteristic
490Q8—6641no—
491Q8—1661no—
492Q8—1661no—
493Q8—1661no—
494Q8—1661no—
495Q8—1661no—
496Q8—1661no—
497D4—6641no—
498D4—1661no—
499D4—1661no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—3321no—
506C2×C4—3321no—
507C2×C4—1661no—
508C2×C4—1661no—
509C2×C4—1661no—
510C2×C4—1661no—
511C2×C4—1661no—
512C2×C4—1661no—
513C2×C4—1661no—
514C2×C4#1458175411yescharacteristic
515C2×C4#1458175411yescharacteristic
516C2×C4#1458175411yescharacteristic
517C2×C4C22×C4×D8311yescharacteristic
518C2×C4C2×D4×D8311yescharacteristic
519C2×C4C2×#1305059111yescharacteristic
520C8—21no—
521C8—21no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—3321no—
527C8—1662no—
528C8—1661no—
529C8—1661no—
530C8—1661no—
531C8—1661no—
532C8#1458180012yes—
533C8#1458180012yes—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—3321no—
538C22—3321no—
539C22—3321no—
540C22C2×#1458175411yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—3321no—
546C4—3321no—
547C4—3321no—
548C4—3321no—
549C4—3321no—
550C4—3321no—
551C4—3321no—
552C4C2×#1458180011yescharacteristic
553C4C2×#1458180011yescharacteristic
554C4#1912851111yescharacteristic
555C4#1912851711yescharacteristic
556C2—41no—
557C2—6641no—
558C2#2491617411yescharacteristic
559C2#2491630411yescharacteristic
560C2#2491637211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1569C2
socleC22×C83C2×C4×D4
prime radical#14581766C2×C4
cosocleC42×C83C24
hypercenter#1569D83
hypocenterC83#17969
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
3. #24916560C2semidirect
4. #24906371C2semidirect
5. #24906364C2semidirect
6. #24906359C2semidirect
7. #24906352C2semidirect
8. #24906281C2semidirect
9. #24906274C2semidirect
10. #24906269C2semidirect
11. #24906262C2semidirect
13. #24905917C2semidirect
14. M16×C83⋊C8C2semidirect
15. C83×#1569C2semidirect
292. #1569D83semidirect
296. C83#17969semidirect

Maximal subgroups

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

subgroupindex
#249180692
#249166082
#249165602
#249063712
#249063642
#249063592
#249063522
#249062812
#249062742
#249062692
#249062622
#249059212
#249059172
M16×C83⋊C82
C83×#15692
#1796983