Finite Group Databasebeta

← #35375355

Subgroups — #35375355

Order 21248.

616 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917483C211yesmaximal, characteristic
2#24916481C211yesmaximal, characteristic, complemented
3#24916467C211yesmaximal, characteristic, complemented
4#24906355C211yesmaximal, characteristic, complemented
5#24906349C211yesmaximal, characteristic, complemented
6#24906315C211yesmaximal, characteristic, complemented
7#24906308C211yesmaximal, characteristic, complemented
8#24906308C211yesmaximal, characteristic, complemented
9#24906294C211yesmaximal, characteristic, complemented
10C8×Dic332C211yesmaximal, characteristic, complemented
11C8×#13050579C211yesmaximal, characteristic, complemented
12#24906243C211yesmaximal, characteristic, complemented
13#24905924C211yesmaximal, characteristic, complemented
14#24905846C211yesmaximal, characteristic, complemented
15C8×M16×C83C211yesmaximal, characteristic, complemented
16#19128235C2211yescharacteristic
17C4×#13050590C2211yescharacteristic
18#19128043C411yescharacteristic
19#19128026C411yescharacteristic
20#19128009C411yescharacteristic
21#19128002C411yescharacteristic
22#19127924C411yescharacteristic
23#19127917C411yescharacteristic
24#19127865C411yescharacteristic
25#19127848C411yescharacteristic
26#19127831C2211yescharacteristic
27C8×Dic166C2211yescharacteristic
28C8×Dic166C2211yescharacteristic
29C8×Dic166C2211yescharacteristic
30C4×Dic332C2211yescharacteristic
31C4×#13050579C2211yescharacteristic
32C4×#13050579C2211yescharacteristic
33C4×D664C2211yescharacteristic
34#19127780C2211yescharacteristic
35#19127780C2211yescharacteristic
36#19127780C2211yescharacteristic
37#19127777—21no—
38#19127777—21no—
39#19127777—21no—
40#19127770—21no—
41C8×D332C2211yescharacteristic
42#19127763—21no—
43#19127758C2211yescharacteristic
44#19127756—21no—
45#19127754C2211yescharacteristic
46#19127658—21no—
47#19127653—21no—
48#19127454C2211yescharacteristic
49#19127454C2211yescharacteristic
50#19127452C2211yescharacteristic
51#19127452C2211yescharacteristic
52#19127433C2211yescharacteristic
53#19127433C2211yescharacteristic
54#19127433C2211yescharacteristic
55#19127433C2211yescharacteristic
56#19127430C2211yescharacteristic
57#19127430C2211yescharacteristic
58#19127430C2211yescharacteristic
59#19127430C2211yescharacteristic
60#431×C83C2211yescharacteristic
61C4×M16×C83C2211yescharacteristic
62C2×C4×C8×C83C2211yescharacteristic
63#322×C83C2211yescharacteristic
64#322×C83C2211yescharacteristic
65C82×C83C2211yescharacteristic
66C82×C83C2211yescharacteristic
67C2×#13050590C2×C411yescharacteristic
68C2×Dic332C2×C411yescharacteristic
69C2×#13050579C2×C411yescharacteristic
70C2×#13050579C2×C411yescharacteristic
71C2×D664C2×C411yescharacteristic
72C2×#13050573—21no—
73C2×#13050573—21no—
74C2×#13050573—21no—
75C2×C8×D83—21no—
76#14581786—21no—
77#14581784C2×C411yescharacteristic
78#14581780C2×C411yescharacteristic
79#14581775—21no—
80#14581771C2×C411yescharacteristic
81#14581766C2×C411yescharacteristic
82C4×Dic166C2×C411yescharacteristic
83C4×Dic166C2311yescharacteristic
84C4×Dic166C2311yescharacteristic
85C4×D332C2×C411yescharacteristic
86C4×D332C2311yescharacteristic
87C4×D332C2311yescharacteristic
88C4×C22⋊D83—21no—
89C4×C22⋊D83—21no—
90C4×C22⋊D83—21no—
91#14581751C2×C411yescharacteristic
92#14581749—21no—
93#14581749—21no—
94C42×D83—21no—
95#14581726C2×C411yescharacteristic
96#14581726C2×C411yescharacteristic
97#14581724C2×C411yescharacteristic
98#14581724C2×C411yescharacteristic
99C4⋊(C83⋊C8)C2311yescharacteristic
100C4⋊(C83⋊C8)C2311yescharacteristic
101C4⋊(C83⋊C8)C2311yescharacteristic
102C4⋊(C83⋊C8)C2311yescharacteristic
103Dic83⋊C8—21no—
104Dic83⋊C8—21no—
105Dic83⋊C8—21no—
106Dic83⋊C8—21no—
107#14581717C2×C411yescharacteristic
108#14581717C2×C411yescharacteristic
109#14581717C2×C411yescharacteristic
110#14581717C2×C411yescharacteristic
111#14581714C2×C411yescharacteristic
112#14581714C2×C411yescharacteristic
113#14581714C2×C411yescharacteristic
114#14581714C2×C411yescharacteristic
115C22⋊(C83⋊C8)—21no—
116C22⋊(C83⋊C8)—21no—
117(C2×D83)⋊C8—21no—
118(C2×D83)⋊C8—21no—
119(C2×D83)⋊C8—21no—
120(C2×D83)⋊C8—21no—
121#14581703—21no—
122#14581702—21no—
123C4×C83⋊C8—21no—
124C8×Dic83—21no—
125C8×Dic83—21no—
126C8×Dic83—21no—
127C2×M16×C83D411yescharacteristic
128C2×M16×C83D411yescharacteristic
129C22×C8×C83—21no—
130C2×C42×C83C2311yescharacteristic
131C4⋊C8×C83C2×C411yescharacteristic
132C4⋊C8×C83C2×C411yescharacteristic
133C22⋊C8×C83C2×C411yescharacteristic
134C22⋊C8×C83C2×C411yescharacteristic
135#97×C83D411yescharacteristic
136#97×C83D411yescharacteristic
137C4×C8×C83—21no—
138C4×C8×C83C2311yescharacteristic
139C4×C8×C83C2311yescharacteristic
140C4×C8×C83C2311yescharacteristic
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#13050590—22no—
145#13050590—41no—
146C2×Dic166C22×C411yescharacteristic
147C2×Dic166C22×C411yescharacteristic
148C2×D332C22×C411yescharacteristic
149C2×D332C22×C411yescharacteristic
150C2×C22⋊D83—21no—
151C2×C22⋊D83—21no—
152C2×C4×D83—21no—
153C2×C4×D83—21no—
154C2×C4×D83—21no—
155C2×C4×D83—21no—
156Dic332—22no—
157#13050579—22no—
158#13050579—41no—
159D664—41no—
160#13050573—42no—
161#13050573—42no—
162#13050573—42no—
163C2×C83⋊C8—21no—
164C2×C83⋊C8—21no—
165C2×C83⋊C8—21no—
166C2×C83⋊C8—21no—
167C8×D83—42no—
168C4⋊Dic83C22×C411yescharacteristic
169C4⋊Dic83C22×C411yescharacteristic
170C4⋊Dic83C22×C411yescharacteristic
171C4⋊Dic83C22×C411yescharacteristic
172Dic83⋊C4—21no—
173Dic83⋊C4—21no—
174Dic83⋊C4—21no—
175Dic83⋊C4—21no—
176Dic83⋊C4—21no—
177Dic83⋊C4—21no—
178C22⋊Dic83—21no—
179C22⋊Dic83—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—
186C4×Dic83—21no—
187C4×Dic83—21no—
188C4×Dic83—21no—
189C4×Dic83—21no—
190C22×C4×C83C22×C411yescharacteristic
191C22×C4×C83C2×D411yescharacteristic
192C22×C4×C83#4111yescharacteristic
193M16×C83—22no—
194M16×C83—22no—
195C2×C8×C83—21no—
196C2×C8×C83—21no—
197C2×C8×C83—42no—
198C2×C8×C83C22×C411yescharacteristic
199C2×C8×C83C22×C411yescharacteristic
200C2×C8×C83C22×C411yescharacteristic
201C2×C8×C83C22×C411yescharacteristic
202C2×C8×C83C2×D411yescharacteristic
203C2×C8×C83C2×D411yescharacteristic
204C2×C8×C83C2×D411yescharacteristic
205C2×C8×C83C2×D411yescharacteristic
206C42×C83C22×C411yescharacteristic
207C42×C83C2×D411yescharacteristic
208C42×C83#4111yescharacteristic
209C42×C83C2411yescharacteristic
210C23×C83C4×D411yescharacteristic
211C22×D83—21no—
212C22×D83—21no—
213C2×C4×C83—21no—
214C2×C4×C83—21no—
215C2×C4×C83—21no—
216C2×C4×C83—21no—
217C2×C4×C83—41no—
218C2×C4×C83C4×D411yescharacteristic
219C2×C4×C83C4×D411yescharacteristic
220C2×C4×C83C4×D411yescharacteristic
221C2×C4×C83C23×C411yescharacteristic
222C2×C4×C83C22×D411yescharacteristic
223C2×C4×C83C2×#4111yescharacteristic
224C22⋊D83—42no—
225C22⋊D83—81no—
226C2×Dic83—21no—
227C2×Dic83—21no—
228C2×Dic83—21no—
229C2×Dic83—21no—
230C2×Dic83—21no—
231C2×Dic83—21no—
232D332—21no—
233D332—21no—
234D332—21no—
235D332—21no—
236C4×D83—42no—
237C4×D83—41no—
238C4×D83—41no—
239C4×D83—41no—
240C4×D83—41no—
241C4×D83—81no—
242Dic166—21no—
243Dic166—21no—
244Dic166—21no—
245Dic166#13112yes—
246C8×C83—22no—
247C8×C83—21no—
248C8×C83—21no—
249C8×C83—21no—
250C8×C83—21no—
251C8×C83—21no—
252C8×C83—21no—
253C8×C83—41no—
254C8×C83#13512yes—
255C8×C83#13512yes—
256C83⋊C8—41no—
257C83⋊C8—41no—
258C83⋊C8—41no—
259C83⋊C8—41no—
260C22×C83—21no—
261C22×C83—21no—
262C22×C83—21no—
263C22×C83C2×C4×D411yescharacteristic
264C2×D83—41no—
265C2×D83—41no—
266C2×D83—41no—
267C2×D83—41no—
268C2×D83—41no—
269C2×D83—41no—
270C4×C83—21no—
271C4×C83—21no—
272C4×C83—21no—
273C4×C83—21no—
274C4×C83C2×#13111yescharacteristic
275C4×C83#56811yescharacteristic
276C4×C83C2×#13511yescharacteristic
277C4×C83C2×#13511yescharacteristic
278Dic83—22no—
279Dic83—41no—
280Dic83—41no—
281Dic83—41no—
282Dic83—41no—
283Dic83—41no—
284#17999—831nomaximal, Sylow
285C2×C83—41no—
286C2×C83#293311yescharacteristic
287C2×C83C4×#13511yescharacteristic
288C2×C83#295611yescharacteristic
289D83—81no—
290D83—81no—
291#3102—831no—
292#2971—831no—
293#2969—831no—
294#1590—831no—
295#1589—831no—
296#1584—831no—
297#1583—831no—
298#1583—831no—
299#1581—831no—
300C8×Q16—831no—
301C8×SD16—831no—
302#1572—831no—
303#1494—831no—
304#1476—831no—
305C8×M16D8311yescharacteristic, complemented
306C83#1799911yescharacteristic, complemented, Sylow
307#529—831no—
308C4×#41—831no—
309#485—831no—
310#482—831no—
311#479—831no—
312#478—831no—
313#464—831no—
314#463—831no—
315#452—831no—
316#449—831no—
317#446—831no—
318C8×Q8—831no—
319C8×Q8—831no—
320C8×Q8—831no—
321C4×Q16—831no—
322C4×SD16—831no—
323C4×SD16—831no—
324C4×D8—831no—
325#436—831no—
326#436—831no—
327#436—831no—
328#436—1661no—
329#436—1661no—
330#436—1661no—
331#435—1661no—
332C8×D4—831no—
333#433—1661no—
334#432—831no—
335#432—1661no—
336#431—831no—
337#431C2×D8311yescharacteristic
338#405—1661no—
339C4×M16—1661no—
340C4×M16C2×D8311yescharacteristic
341C2×C4×C8C2×D8311yescharacteristic
342#335—831no—
343#335—831no—
344#334—831no—
345#334—831no—
346Q8⋊C8—831no—
347Q8⋊C8—831no—
348Q8⋊C8—831no—
349Q8⋊C8—831no—
350D4⋊C8—831no—
351D4⋊C8—831no—
352D4⋊C8—831no—
353D4⋊C8—831no—
354#322C2×D8311yescharacteristic
355#322C2×D8311yescharacteristic
356C82C2×D8311yescharacteristic
357C82C2×D8311yescharacteristic
358C2×#41—831no—
359C2×Q16—831no—
360C2×SD16—831no—
361C2×SD16—831no—
362C2×D8—831no—
363C2×M16—1661no—
364C2×M16—1661no—
365C2×M16—1661no—
366C2×M16D33211yescharacteristic
367C2×M16D33211yescharacteristic
368C22×C8—21no—
369C22×C8—1661no—
370#126—1661no—
371#125—831no—
372#124—831no—
373#123—1661no—
374C22⋊Q8—831no—
375#121—831no—
376C4×Q8—831no—
377C4×Q8—831no—
378C4×Q8—831no—
379C4×D4—831no—
380C4×D4—831no—
381C4×D4—831no—
382C4×D4—1661no—
383C4×D4—1661no—
384C4×D4—1661no—
385#117—831no—
386#117—1661no—
387#117—1661no—
388C2×C42—1661no—
389C2×C42C22×D8311yescharacteristic
390#107—831no—
391#107—831no—
392#106—831no—
393#106—831no—
394C4⋊C8—831no—
395C4⋊C8—831no—
396C4⋊C8—831no—
397C4⋊C8—831no—
398C4⋊C8—1661no—
399C4⋊C8—1661no—
400C4⋊C8—1661no—
401C4⋊C8—1661no—
402C4⋊C8C4×D8311yescharacteristic
403C4⋊C8C4×D8311yescharacteristic
404#103—831no—
405#103—831no—
406#103—831no—
407#103—831no—
408#102—831no—
409#102—831no—
410#102—831no—
411#102—831no—
412C22⋊C8—1661no—
413C22⋊C8—1661no—
414C22⋊C8—1661no—
415C22⋊C8—1661no—
416C22⋊C8—1661no—
417C22⋊C8—1661no—
418C22⋊C8C4×D8311yescharacteristic
419C22⋊C8C4×D8311yescharacteristic
420#97—1661no—
421#97—1661no—
422#97D33211yescharacteristic
423#97D33211yescharacteristic
424C4×C8—21no—
425C4×C8—1661no—
426C4×C8—1661no—
427C4×C8—1661no—
428C4×C8—1661no—
429C4×C8C22×D8311yescharacteristic
430C4×C8C22×D8311yescharacteristic
431C4×C8C22×D8311yescharacteristic
432C4×C8C22×D8311yescharacteristic
433C4×C8C22×D8311yescharacteristic
434C4×C8C22×D8311yescharacteristic
435#41—3321no—
436#41—1662no—
437C2×Q8—831no—
438C2×Q8—831no—
439C2×D4—831no—
440C2×D4—831no—
441C2×D4—1661no—
442C2×D4—1661no—
443C22×C4—1661no—
444C22×C4—1661no—
445C22×C4—1661no—
446C22×C4—1661no—
447C22×C4C2×C4×D8311yescharacteristic
448C22×C4C2×D33211yescharacteristic
449C22×C4#1305059011yescharacteristic
450Q16—1662no—
451SD16—3321no—
452SD16—1662no—
453D8—3321no—
454M16—22no—
455M16—22no—
456M16—3322no—
457M16—3322no—
458M16—3322no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—42no—
462C2×C8—3322no—
463C2×C8—1661no—
464C2×C8—1661no—
465C2×C8—1661no—
466C2×C8—1661no—
467C2×C8C2×C4×D8311yescharacteristic
468C2×C8C2×C4×D8311yescharacteristic
469C2×C8C2×C4×D8311yescharacteristic
470C2×C8C2×C4×D8311yescharacteristic
471C2×C8C2×D33211yescharacteristic
472C2×C8C2×D33211yescharacteristic
473C2×C8C2×D33211yescharacteristic
474C2×C8C2×D33211yescharacteristic
475C4⋊C4—831no—
476C4⋊C4—831no—
477C4⋊C4—831no—
478C4⋊C4—831no—
479C4⋊C4—1661no—
480C4⋊C4—1661no—
481C4⋊C4—1661no—
482C4⋊C4—1661no—
483C4⋊C4—1661no—
484C4⋊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—1661no—
494C42—1661no—
495C42—1661no—
496C42—1661no—
497C42C2×C4×D8311yescharacteristic
498C42C2×D33211yescharacteristic
499C42#1305059011yescharacteristic
500C42C23×D8311yescharacteristic
501C23—1661no—
502C23—1661no—
503C23C4×D33211yescharacteristic
504Q8—832no—
505Q8—1661no—
506Q8—1661no—
507Q8—1661no—
508D4—3322no—
509D4—6641no—
510D4—1661no—
511D4—1661no—
512D4—1661no—
513D4—1661no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—3322no—
520C2×C4—3321no—
521C2×C4—3321no—
522C2×C4—3321no—
523C2×C4—3321no—
524C2×C4—6641no—
525C2×C4—1661no—
526C2×C4—1661no—
527C2×C4—1661no—
528C2×C4—1661no—
529C2×C4—1661no—
530C2×C4—1661no—
531C2×C4C4×D33211yescharacteristic
532C2×C4C4×D33211yescharacteristic
533C2×C4C4×D33211yescharacteristic
534C2×C4C22×C4×D8311yescharacteristic
535C2×C4C22×D33211yescharacteristic
536C2×C4C2×#1305059011yescharacteristic
537C8—22no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—21no—
543C8—21no—
544C8—41no—
545C8—3321no—
546C8—3321no—
547C8—3321no—
548C8—3321no—
549C8#1458181412yes—
550C8#1458181412yes—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—3321no—
555C22—3321no—
556C22—3321no—
557C22—3321no—
558C22—3321no—
559C22—3321no—
560C22C2×C4×D33211yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—3321no—
566C4—3321no—
567C4—3321no—
568C4—3321no—
569C4—3321no—
570C4—1662no—
571C4#131×D8311yescharacteristic
572C4#1912846611yescharacteristic
573C4C2×#1458181411yescharacteristic
574C4C2×#1458181411yescharacteristic
575C2—41no—
576C2—6641no—
577C2—6641no—
578C2#2491619111yescharacteristic
579C2C4×#1458181411yescharacteristic
580C2#2491637411yescharacteristic
subgroupG/H
centerC2×C4C22×D332
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC8×M16×C83C2
socleC22×C83C2×C4×D4
prime radical#19127848C4
cosocleC42×C83C24
hypercenterC8×M16D83
hypocenterC83#17999
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ C8×M16

Complements

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

NH ≅ G/Ntype
2. #24916481C2semidirect
3. #24916467C2semidirect
4. #24906355C2semidirect
5. #24906349C2semidirect
6. #24906315C2semidirect
7. #24906308C2semidirect
8. #24906308C2semidirect
9. #24906294C2semidirect
10. C8×Dic332C2semidirect
11. C8×#13050579C2semidirect
12. #24906243C2semidirect
13. #24905924C2semidirect
14. #24905846C2semidirect
15. C8×M16×C83C2semidirect
305. C8×M16D83semidirect
306. C83#17999semidirect

Maximal subgroups

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

subgroupindex
#249174832
#249164812
#249164672
#249063552
#249063492
#249063152
#249063082
#249062942
C8×Dic3322
C8×#130505792
#249062432
#249059242
#249058462
C8×M16×C832
#1799983