Finite Group Databasebeta

← #35375134

Subgroups — #35375134

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#24918036C211yesmaximal, characteristic
2#24916440C211yesmaximal, characteristic, complemented
3#24916437C211yesmaximal, characteristic, complemented
4#24906314C211yesmaximal, characteristic, complemented
5#24906306C211yesmaximal, characteristic, complemented
6#24906303C211yesmaximal, characteristic, complemented
7#24906302C211yesmaximal, characteristic, complemented
8#24906297C211yesmaximal, characteristic, complemented
9#24906294C211yesmaximal, characteristic, complemented
10#24906291C211yesmaximal, characteristic, complemented
11#24906225C211yesmaximal, characteristic, complemented
12#24905922C211yesmaximal, characteristic, complemented
13#24905922C211yesmaximal, characteristic, complemented
14#322×D83C211yesmaximal, characteristic, complemented
15C83×#1584C211yesmaximal, characteristic, complemented
16#19128238C2211yescharacteristic
17#19128238C2211yescharacteristic
18#19128102C411yescharacteristic
19#19128086C411yescharacteristic
20#19128057C411yescharacteristic
21#19128057C411yescharacteristic
22#19127939C411yescharacteristic
23#19127938C411yescharacteristic
24#19127933C411yescharacteristic
25#19127933C411yescharacteristic
26#19127832C2211yescharacteristic
27Q8×C83⋊C8C2211yescharacteristic
28C4×#13050577C2211yescharacteristic
29C4×#13050577C2211yescharacteristic
30C4×D664C2211yescharacteristic
31#19127780C2211yescharacteristic
32#19127778C2211yescharacteristic
33#19127774—21no—
34#19127771—21no—
35C8×D332—21no—
36C8×D332C2211yescharacteristic
37#19127766—21no—
38#19127766C2211yescharacteristic
39#19127761—21no—
40#19127761—21no—
41#19127757C2211yescharacteristic
42#19127757C2211yescharacteristic
43#19127658—21no—
44#19127655—21no—
45C4×C8×D83C2211yescharacteristic
46C4×C8×D83C2211yescharacteristic
47C4×C8×D83C2211yescharacteristic
48#19127454C2211yescharacteristic
49#19127451C2211yescharacteristic
50#19127451C2211yescharacteristic
51Q8⋊(C83⋊C8)C2211yescharacteristic
52Q8⋊(C83⋊C8)C2211yescharacteristic
53#19127430C2211yescharacteristic
54#19127430C2211yescharacteristic
55#19127428C2211yescharacteristic
56#19127428C2211yescharacteristic
57#19127423C2211yescharacteristic
58#19127423C2211yescharacteristic
59#19127422C2211yescharacteristic
60#446×C83C2211yescharacteristic
61C8×Q8×C83C2211yescharacteristic
62C4×Q16×C83C2211yescharacteristic
63#335×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65Q8⋊C8×C83C2211yescharacteristic
66#322×C83C2211yescharacteristic
67C2×#13050577C2×C411yescharacteristic
68C2×#13050577C2×C411yescharacteristic
69C2×D664C2×C411yescharacteristic
70C2×#13050573—21no—
71C2×#13050573—21no—
72C2×C8×D83—21no—
73C2×C8×D83—21no—
74C2×C8×D83—21no—
75C2×C8×D83C2×C411yescharacteristic
76C2×C8×D83C2×C411yescharacteristic
77C2×C8×D83D411yescharacteristic
78C2×C8×D83D411yescharacteristic
79#14581787—21no—
80#14581787—21no—
81#14581783C2×C411yescharacteristic
82#14581783C2×C411yescharacteristic
83#14581781C2×C411yescharacteristic
84#14581781C2×C411yescharacteristic
85#14581777—21no—
86#14581777—21no—
87#14581768C2×C411yescharacteristic
88#14581768C2×C411yescharacteristic
89#14581767C2×C411yescharacteristic
90#14581767C2×C411yescharacteristic
91C4×D332—21no—
92C4×D332—21no—
93C4×D332C2311yescharacteristic
94C4×D332C2311yescharacteristic
95#14581749—21no—
96#14581749—21no—
97C42×D83C2311yescharacteristic
98#14581726C2×C411yescharacteristic
99#14581723C2×C411yescharacteristic
100#14581723C2×C411yescharacteristic
101C4⋊(C83⋊C8)—21no—
102C4⋊(C83⋊C8)—21no—
103C4⋊(C83⋊C8)C2311yescharacteristic
104C4⋊(C83⋊C8)C2311yescharacteristic
105#14581716C2×C411yescharacteristic
106#14581716C2×C411yescharacteristic
107#14581714C2×C411yescharacteristic
108#14581714C2×C411yescharacteristic
109#14581712C2×C411yescharacteristic
110#14581712C2×C411yescharacteristic
111(C2×D83)⋊C8—21no—
112(C2×D83)⋊C8—21no—
113(C2×D83)⋊C8—21no—
114(C2×D83)⋊C8—21no—
115(C2×D83)⋊C8—21no—
116(C2×D83)⋊C8—21no—
117#14581703—21no—
118#14581702—21no—
119#14581702—21no—
120C4×C83⋊C8—21no—
121C4×C83⋊C8C2311yescharacteristic
122C4×C83⋊C8C2311yescharacteristic
123C4×C83⋊C8C2311yescharacteristic
124C8×Dic83—21no—
125C8×Dic83C2×C411yescharacteristic
126C8×Dic83C2×C411yescharacteristic
127C8×Dic83D411yescharacteristic
128C8×Dic83D411yescharacteristic
129C2×Q16×C83C2×C411yescharacteristic
130C4×Q8×C83C2311yescharacteristic
131C4×Q8×C83C2311yescharacteristic
132#107×C83C2×C411yescharacteristic
133C4⋊C8×C83—21no—
134C4⋊C8×C83—21no—
135C4⋊C8×C83C2311yescharacteristic
136C4⋊C8×C83C2311yescharacteristic
137#103×C83C2×C411yescharacteristic
138#103×C83C2×C411yescharacteristic
139#97×C83—21no—
140C4×C8×C83—21no—
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C2×D332—21no—
145C2×D332—21no—
146C2×D332C22×C411yescharacteristic
147C2×D332C22×C411yescharacteristic
148C2×C4×D83—21no—
149C2×C4×D83—21no—
150C2×C4×D83C22×C411yescharacteristic
151C2×C4×D83C2×D411yescharacteristic
152C2×C4×D83#4111yescharacteristic
153#13050577—41no—
154#13050577—41no—
155D664—41no—
156#13050573—42no—
157#13050573—42no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8—21no—
161C2×C83⋊C8C22×C411yescharacteristic
162C2×C83⋊C8C22×C411yescharacteristic
163C2×C83⋊C8C2×D411yescharacteristic
164C2×C83⋊C8C2×D411yescharacteristic
165C8×D83—22no—
166C8×D83—22no—
167C8×D83—41no—
168C8×D83—41no—
169C8×D83—42no—
170C8×D83—42no—
171C8×D83—42no—
172C4⋊Dic83—21no—
173C4⋊Dic83—21no—
174C4⋊Dic83C22×C411yescharacteristic
175C4⋊Dic83C22×C411yescharacteristic
176Dic83⋊C4—21no—
177Dic83⋊C4—21no—
178Dic83⋊C4—21no—
179Dic83⋊C4—21no—
180(C2×D83)⋊C4—21no—
181(C2×D83)⋊C4—21no—
182(C2×D83)⋊C4—21no—
183(C2×D83)⋊C4—21no—
184(C2×D83)⋊C4—21no—
185(C2×D83)⋊C4—21no—
186(C2×D83)⋊C4—21no—
187(C2×D83)⋊C4—21no—
188(C2×D83)⋊C4—21no—
189(C2×D83)⋊C4—21no—
190C4×Dic83C22×C411yescharacteristic
191C4×Dic83C2×D411yescharacteristic
192C4×Dic83#4111yescharacteristic
193C2×Q8×C83C22×C411yescharacteristic
194C2×Q8×C83C22×C411yescharacteristic
195Q16×C83—41no—
196C2×C8×C83—21no—
197C2×C8×C83—21no—
198C2×C8×C83—21no—
199C2×C8×C83C22×C411yescharacteristic
200C2×C8×C83C22×C411yescharacteristic
201C2×C8×C83C2×D411yescharacteristic
202C2×C8×C83C2×D411yescharacteristic
203C4⋊C4×C83—21no—
204C4⋊C4×C83—21no—
205C4⋊C4×C83C22×C411yescharacteristic
206C4⋊C4×C83C22×C411yescharacteristic
207C42×C83—21no—
208C42×C83—21no—
209C42×C83C2411yescharacteristic
210C22×D83—21no—
211C22×D83—21no—
212C22×D83C4×D411yescharacteristic
213Q8×C83—21no—
214Q8×C83—21no—
215Q8×C83—21no—
216Q8×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83C23×C411yescharacteristic
222C2×C4×C83C22×D411yescharacteristic
223C2×C4×C83C2×#4111yescharacteristic
224C2×Dic83—21no—
225C2×Dic83—21no—
226C2×Dic83C4×D411yescharacteristic
227C2×Dic83C4×D411yescharacteristic
228C2×Dic83C4×D411yescharacteristic
229D332—21no—
230D332—21no—
231D332—21no—
232D332—21no—
233D332—42no—
234D332—42no—
235C4×D83—22no—
236C4×D83—21no—
237C4×D83—21no—
238C4×D83—21no—
239C4×D83—21no—
240C4×D83—41no—
241C4×D83—41no—
242C4×D83—41no—
243C4×D83—41no—
244C8×C83—21no—
245C8×C83—21no—
246C8×C83—21no—
247C8×C83—41no—
248C8×C83—41no—
249C8×C83—41no—
250C8×C83#13512yes—
251C83⋊C8—21no—
252C83⋊C8—21no—
253C83⋊C8—21no—
254C83⋊C8—41no—
255C83⋊C8—41no—
256C83⋊C8—41no—
257C83⋊C8#13512yes—
258C22×C83C2×C4×D411yescharacteristic
259C2×D83—21no—
260C2×D83—21no—
261C2×D83—41no—
262C2×D83—41no—
263C2×D83—41no—
264C2×D83—41no—
265C2×D83—41no—
266C2×D83—41no—
267C2×D83#44412yes—
268C4×C83—21no—
269C4×C83—41no—
270C4×C83—41no—
271C4×C83—41no—
272C4×C83—41no—
273C4×C83#56811yescharacteristic
274C4×C83#56811yescharacteristic
275C4×C83C2×#13511yescharacteristic
276C4×C83C2×#13511yescharacteristic
277Dic83—21no—
278Dic83—21no—
279Dic83—21no—
280Dic83—41no—
281Dic83—41no—
282#17978—831nomaximal, Sylow
283C2×C83#293211yescharacteristic
284C2×C83C4×#13511yescharacteristic
285C2×C83C2×#44411yescharacteristic
286D83—22no—
287D83—81no—
288D83—81no—
289#3168—831no—
290#2966—831no—
291#2966—831no—
292#1584—831no—
293#1584D8311yescharacteristic, complemented
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#529—831no—
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×Q16C2×D8311yescharacteristic
320C4×SD16—831no—
321C4×SD16—831no—
322C4×D8—831no—
323#436—831no—
324#436—831no—
325#435—1661no—
326#435—1661no—
327C8×D4—831no—
328C8×D4—831no—
329C8×D4—1661no—
330C8×D4—1661no—
331#433—1661no—
332#433—1661no—
333#432—831no—
334#432—831no—
335#405—1661no—
336#405—1661no—
337C2×C4×C8—831no—
338C2×C4×C8—831no—
339C2×C4×C8—831no—
340#335—831no—
341#335C2×D8311yescharacteristic
342#334—831no—
343#334—831no—
344Q8⋊C8—831no—
345Q8⋊C8—831no—
346Q8⋊C8C2×D8311yescharacteristic
347Q8⋊C8C2×D8311yescharacteristic
348D4⋊C8—831no—
349D4⋊C8—831no—
350D4⋊C8—831no—
351D4⋊C8—831no—
352#322—831no—
353#322—831no—
354#322—831no—
355#322C2×D8311yescharacteristic
356C2×Q16C4×D8311yescharacteristic
357C2×SD16—831no—
358C2×SD16—831no—
359C2×D8—831no—
360C2×M16—1661no—
361C2×M16—1661no—
362C22×C8—831no—
363C22×C8—831no—
364C22×C8—831no—
365C22×C8—831no—
366C22×C8—1661no—
367C22×C8—1661no—
368C22×C8—1661no—
369#126—1661no—
370#126—1661no—
371#125—831no—
372#125—831no—
373#124—831no—
374#124—831no—
375#123—1661no—
376#123—1661no—
377C22⋊Q8—831no—
378C22⋊Q8—831no—
379#121—831no—
380#121—831no—
381C4×Q8C22×D8311yescharacteristic
382C4×Q8C22×D8311yescharacteristic
383C4×D4—831no—
384C4×D4—831no—
385C4×D4—1661no—
386C4×D4—1661no—
387#117—1661no—
388#117—1661no—
389C2×C42—831no—
390#107—831no—
391#107C4×D8311yescharacteristic
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#103C4×D8311yescharacteristic
405#103C4×D8311yescharacteristic
406#102—831no—
407#102—831no—
408#102—831no—
409#102—831no—
410C22⋊C8—1661no—
411C22⋊C8—1661no—
412C22⋊C8—1661no—
413C22⋊C8—1661no—
414C22⋊C8—1661no—
415C22⋊C8—1661no—
416#97—21no—
417#97—1661no—
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—831no—
428C4×C8—1661no—
429C4×C8—1661no—
430C4×C8C22×D8311yescharacteristic
431C4×C8C22×D8311yescharacteristic
432C4×C8C22×D8311yescharacteristic
433C2×Q8C2×C4×D8311yescharacteristic
434C2×Q8C2×C4×D8311yescharacteristic
435C2×D4—831no—
436C2×D4—831no—
437C2×D4—1661no—
438C2×D4—1661no—
439C22×C4—831no—
440C22×C4—831no—
441C22×C4—831no—
442C22×C4—1661no—
443C22×C4—1661no—
444Q16—41no—
445SD16—3321no—
446SD16—3321no—
447D8—3321no—
448M16—3322no—
449M16—3322no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—3321no—
454C2×C8—3321no—
455C2×C8—3322no—
456C2×C8—3322no—
457C2×C8—3322no—
458C2×C8—831no—
459C2×C8—831no—
460C2×C8—831no—
461C2×C8—831no—
462C2×C8—1662no—
463C2×C8—1661no—
464C2×C8—1661no—
465C2×C8—1661no—
466C2×C8—1662no—
467C2×C8C2×C4×D8311yescharacteristic
468C2×C8C2×C4×D8311yescharacteristic
469C2×C8D4×D8311yescharacteristic
470C2×C8D4×D8311yescharacteristic
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—831no—
474C4⋊C4—831no—
475C4⋊C4—1661no—
476C4⋊C4—1661no—
477C4⋊C4—1661no—
478C4⋊C4—1661no—
479C4⋊C4—1661no—
480C4⋊C4—1661no—
481C4⋊C4C2×C4×D8311yescharacteristic
482C4⋊C4C2×C4×D8311yescharacteristic
483C22⋊C4—1661no—
484C22⋊C4—1661no—
485C22⋊C4—1661no—
486C22⋊C4—1661no—
487C22⋊C4—1661no—
488C22⋊C4—1661no—
489C22⋊C4—1661no—
490C22⋊C4—1661no—
491C22⋊C4—1661no—
492C22⋊C4—1661no—
493C42—21no—
494C42—21no—
495C42—831no—
496C42—831no—
497C42—831no—
498C42C23×D8311yescharacteristic
499C23—831no—
500C23—1661no—
501C23—1661no—
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8—21no—
506D4—3322no—
507D4—3322no—
508D4—1661no—
509D4—1661no—
510D4—1661no—
511D4—1661no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—3321no—
517C2×C4—3321no—
518C2×C4—3321no—
519C2×C4—3321no—
520C2×C4—831no—
521C2×C4—831no—
522C2×C4—831no—
523C2×C4—1662no—
524C2×C4—1661no—
525C2×C4—1661no—
526C2×C4—1661no—
527C2×C4—1661no—
528C2×C4—1661no—
529C2×C4—1661no—
530C2×C4C22×C4×D8311yescharacteristic
531C2×C4C2×D4×D8311yescharacteristic
532C2×C4#41×D8311yescharacteristic
533C8—21no—
534C8—21no—
535C8—21no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—3321no—
540C8—3321no—
541C8—3321no—
542C8—832no—
543C8—1661no—
544C8—1661no—
545C8—1661no—
546C8#1458181512yes—
547C22—3321no—
548C22—3321no—
549C22—3321no—
550C22—3321no—
551C22—3321no—
552C22—3321no—
553C22—832no—
554C22—1661no—
555C22—1661no—
556C22C4×D4×D8311yescharacteristic
557C4—21no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—3321no—
563C4—3321no—
564C4—1661no—
565C4—1661no—
566C4—1661no—
567C4#1912846611yescharacteristic
568C4#1912846711yescharacteristic
569C4#135×D8311yescharacteristic
570C4C2×#1458181511yescharacteristic
571C2—6641no—
572C2—6641no—
573C2—1662no—
574C2#2491617711yescharacteristic
575C2C4×#1458181511yescharacteristic
576C2#444×D8311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1584C2
socleC22×C83C2×C4×D4
prime radical#19127938C4
cosocleC42×C83C24
hypercenter#1584D83
hypocenterC83#17978
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
2. #24916440C2semidirect
3. #24916437C2semidirect
4. #24906314C2semidirect
5. #24906306C2semidirect
6. #24906303C2semidirect
7. #24906302C2semidirect
8. #24906297C2semidirect
9. #24906294C2semidirect
10. #24906291C2semidirect
11. #24906225C2semidirect
12. #24905922C2semidirect
13. #24905922C2semidirect
14. #322×D83C2semidirect
15. C83×#1584C2semidirect
293. #1584D83semidirect
304. C83#17978semidirect

Maximal subgroups

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

subgroupindex
#249180362
#249164402
#249164372
#249063142
#249063062
#249063032
#249063022
#249062972
#249062942
#249062912
#249062252
#249059222
#322×D832
C83×#15842
#1797883