Finite Group Databasebeta

← #35374365

Subgroups — #35374365

Order 21248.

626 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917483C211yesmaximal, characteristic
2#24916438C211yesmaximal, characteristic, complemented
3C8×#13050590C211yesmaximal, characteristic, complemented
4#24906343C211yesmaximal, characteristic, complemented
5#24906336C211yesmaximal, characteristic, complemented
6#24906329C211yesmaximal, characteristic, complemented
7#24906322C211yesmaximal, characteristic, complemented
8#24906288C211yesmaximal, characteristic, complemented
9#24906283C211yesmaximal, characteristic, complemented
10#24906277C211yesmaximal, characteristic, complemented
11#24906277C211yesmaximal, characteristic, complemented
12#24906243C211yesmaximal, characteristic, complemented
13#24905898C211yesmaximal, characteristic, complemented
14#24905872C211yesmaximal, characteristic, complemented
15C83×#1452C211yesmaximal, 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#19127772—21no—
36C8×D332C2211yescharacteristic
37C8×D332C2211yescharacteristic
38C8×D332C2211yescharacteristic
39C8×C22⋊D83—21no—
40C8×C22⋊D83—21no—
41C8×C22⋊D83—21no—
42#19127760—21no—
43#19127758C2211yescharacteristic
44#19127754C2211yescharacteristic
45#19127752—21no—
46#19127655—21no—
47C4×C8×D83—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
61#431×C83C2211yescharacteristic
62C2×C4×C8×C83C2211yescharacteristic
63#322×C83C2211yescharacteristic
64#322×C83C2211yescharacteristic
65#322×C83C2211yescharacteristic
66#322×C83C2211yescharacteristic
67C2×#13050590C2×C411yescharacteristic
68C2×Dic332C2×C411yescharacteristic
69C2×#13050579C2×C411yescharacteristic
70C2×#13050579C2×C411yescharacteristic
71C2×D664C2×C411yescharacteristic
72C2×#13050573—21no—
73C2×C8×D83—21no—
74C2×C8×D83—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—
127C22×C8×C83D411yescharacteristic
128C22×C8×C83D411yescharacteristic
129C2×C42×C83C2311yescharacteristic
130C4⋊C8×C83—21no—
131C4⋊C8×C83C2×C411yescharacteristic
132C4⋊C8×C83C2×C411yescharacteristic
133C22⋊C8×C83—21no—
134C22⋊C8×C83C2×C411yescharacteristic
135C22⋊C8×C83C2×C411yescharacteristic
136C4×C8×C83D411yescharacteristic
137C4×C8×C83D411yescharacteristic
138C4×C8×C83C2311yescharacteristic
139C4×C8×C83C2311yescharacteristic
140C4×C8×C83C2311yescharacteristic
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#13050590—22no—
145#13050590—22no—
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—22no—
159D664—22no—
160#13050573—42no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8—21no—
163C2×C83⋊C8—21no—
164C2×C83⋊C8—21no—
165C8×D83—42no—
166C8×D83—42no—
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
193C2×C8×C83—21no—
194C2×C8×C83—21no—
195C2×C8×C83—41no—
196C2×C8×C83—41no—
197C2×C8×C83C22×C411yescharacteristic
198C2×C8×C83C22×C411yescharacteristic
199C2×C8×C83C22×C411yescharacteristic
200C2×C8×C83C22×C411yescharacteristic
201C2×C8×C83C2×D411yescharacteristic
202C2×C8×C83C2×D411yescharacteristic
203C2×C8×C83C2×D411yescharacteristic
204C2×C8×C83C2×D411yescharacteristic
205C42×C83C22×C411yescharacteristic
206C42×C83C2×D411yescharacteristic
207C42×C83#4111yescharacteristic
208C42×C83C2411yescharacteristic
209C23×C83C4×D411yescharacteristic
210C22×D83—21no—
211C22×D83—21no—
212C2×C4×C83—21no—
213C2×C4×C83—21no—
214C2×C4×C83—21no—
215C2×C4×C83—21no—
216C2×C4×C83—41no—
217C2×C4×C83C4×D411yescharacteristic
218C2×C4×C83C4×D411yescharacteristic
219C2×C4×C83C4×D411yescharacteristic
220C2×C4×C83C23×C411yescharacteristic
221C2×C4×C83C22×D411yescharacteristic
222C2×C4×C83C2×#4111yescharacteristic
223C22⋊D83—24no—
224C22⋊D83—42no—
225C2×Dic83—21no—
226C2×Dic83—21no—
227C2×Dic83—21no—
228C2×Dic83—21no—
229C2×Dic83—21no—
230C2×Dic83—21no—
231D332—21no—
232D332—21no—
233D332—21no—
234D332#13112yes—
235C4×D83—24no—
236C4×D83—42no—
237C4×D83—41no—
238C4×D83—41no—
239C4×D83—41no—
240C4×D83—41no—
241Dic166—21no—
242Dic166—21no—
243Dic166—21no—
244Dic166#13112yes—
245C8×C83—21no—
246C8×C83—21no—
247C8×C83—21no—
248C8×C83—21no—
249C8×C83—21no—
250C8×C83—21no—
251C8×C83—21no—
252C8×C83—21no—
253C8×C83—41no—
254C8×C83—41no—
255C83⋊C8—41no—
256C83⋊C8—41no—
257C83⋊C8—41no—
258C83⋊C8—41no—
259C22×C83—21no—
260C22×C83—21no—
261C22×C83—21no—
262C22×C83C2×C4×D411yescharacteristic
263C2×D83—22no—
264C2×D83—41no—
265C2×D83—41no—
266C2×D83—41no—
267C2×D83—41no—
268C2×D83—41no—
269C4×C83—21no—
270C4×C83—21no—
271C4×C83—21no—
272C4×C83—21no—
273C4×C83C2×#13111yescharacteristic
274C4×C83C2×#13111yescharacteristic
275C4×C83#57511yescharacteristic
276C4×C83#57511yescharacteristic
277Dic83—22no—
278Dic83—41no—
279Dic83—41no—
280Dic83—41no—
281Dic83—41no—
282Dic83—41no—
283#17909—831nomaximal, Sylow
284C2×C83—41no—
285C2×C83#292911yescharacteristic
286C2×C83#294311yescharacteristic
287C2×C83#295511yescharacteristic
288D83—42no—
289D83—81no—
290#3102—831no—
291#2966—831no—
292C8×#41—831no—
293#1588—831no—
294#1587—831no—
295#1586—831no—
296#1585—831no—
297#1580—831no—
298#1579—831no—
299SD16⋊C8—831no—
300SD16⋊C8—831no—
301#1572—831no—
302#1488—831no—
303#1482—831no—
304#1452D8311yescharacteristic, complemented
305C83#1790911yescharacteristic, complemented, Sylow
306#529—831no—
307C4×#41—831no—
308#485—831no—
309#482—831no—
310#479—831no—
311#478—831no—
312#464—831no—
313#463—831no—
314#452—831no—
315#449—831no—
316#446—831no—
317C8×Q8—831no—
318C8×Q8—831no—
319C8×Q8—831no—
320C4×Q16—831no—
321C4×SD16—831no—
322C4×SD16—831no—
323C4×D8—831no—
324#436—831no—
325#435—1661no—
326C8×D4—831no—
327C8×D4—831no—
328C8×D4—831no—
329C8×D4—1661no—
330C8×D4—1661no—
331C8×D4—1661no—
332#433—1661no—
333#432—831no—
334#431—831no—
335#431—1661no—
336#431C2×D8311yescharacteristic
337#431C2×D8311yescharacteristic
338#405—1661no—
339C2×C4×C8—1661no—
340C2×C4×C8C2×D8311yescharacteristic
341#335—831no—
342#335—831no—
343#334—831no—
344#334—831no—
345Q8⋊C8—831no—
346Q8⋊C8—831no—
347Q8⋊C8—831no—
348Q8⋊C8—831no—
349D4⋊C8—831no—
350D4⋊C8—831no—
351D4⋊C8—831no—
352D4⋊C8—831no—
353#322C2×D8311yescharacteristic
354#322C2×D8311yescharacteristic
355#322C2×D8311yescharacteristic
356#322C2×D8311yescharacteristic
357C2×#41—831no—
358C2×Q16—831no—
359C2×SD16—831no—
360C2×SD16—831no—
361C2×D8—831no—
362C2×M16—1661no—
363C22×C8—1661no—
364C22×C8—1661no—
365C22×C8—1661no—
366C22×C8D33211yescharacteristic
367C22×C8D33211yescharacteristic
368#126—1661no—
369#125—831no—
370#124—831no—
371#123—1661no—
372C22⋊Q8—831no—
373#121—831no—
374C4×Q8—831no—
375C4×Q8—831no—
376C4×Q8—831no—
377C4×D4—831no—
378C4×D4—831no—
379C4×D4—831no—
380C4×D4—1661no—
381C4×D4—1661no—
382C4×D4—1661no—
383#117—831no—
384#117—1661no—
385#117—1661no—
386C2×C42—1661no—
387C2×C42C22×D8311yescharacteristic
388#107—831no—
389#107—831no—
390#106—831no—
391#106—831no—
392C4⋊C8—21no—
393C4⋊C8—831no—
394C4⋊C8—831no—
395C4⋊C8—831no—
396C4⋊C8—831no—
397C4⋊C8—1661no—
398C4⋊C8—1661no—
399C4⋊C8—1661no—
400C4⋊C8—1661no—
401C4⋊C8C4×D8311yescharacteristic
402C4⋊C8C4×D8311yescharacteristic
403#103—831no—
404#103—831no—
405#103—831no—
406#103—831no—
407#102—831no—
408#102—831no—
409#102—831no—
410#102—831no—
411C22⋊C8—21no—
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—
422C4×C8—1661no—
423C4×C8—1661no—
424C4×C8—1661no—
425C4×C8—1661no—
426C4×C8D33211yescharacteristic
427C4×C8D33211yescharacteristic
428C4×C8C22×D8311yescharacteristic
429C4×C8C22×D8311yescharacteristic
430C4×C8C22×D8311yescharacteristic
431C4×C8C22×D8311yescharacteristic
432C4×C8C22×D8311yescharacteristic
433C4×C8C22×D8311yescharacteristic
434#41—1662no—
435#41—1662no—
436C2×Q8—831no—
437C2×Q8—831no—
438C2×D4—831no—
439C2×D4—831no—
440C2×D4—1661no—
441C2×D4—1661no—
442C22×C4—1661no—
443C22×C4—1661no—
444C22×C4—1661no—
445C22×C4—1661no—
446C22×C4C2×C4×D8311yescharacteristic
447C22×C4C2×D33211yescharacteristic
448C22×C4#1305059011yescharacteristic
449Q16—1662no—
450SD16—1662no—
451SD16—1662no—
452D8—1662no—
453M16—3322no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—41no—
457C2×C8—41no—
458C2×C8—3322no—
459C2×C8—3322no—
460C2×C8—3322no—
461C2×C8—1661no—
462C2×C8—1661no—
463C2×C8—1661no—
464C2×C8—1661no—
465C2×C8C2×C4×D8311yescharacteristic
466C2×C8C2×C4×D8311yescharacteristic
467C2×C8C2×C4×D8311yescharacteristic
468C2×C8C2×C4×D8311yescharacteristic
469C2×C8C2×D33211yescharacteristic
470C2×C8C2×D33211yescharacteristic
471C2×C8C2×D33211yescharacteristic
472C2×C8C2×D33211yescharacteristic
473C4⋊C4—831no—
474C4⋊C4—831no—
475C4⋊C4—831no—
476C4⋊C4—831no—
477C4⋊C4—1661no—
478C4⋊C4—1661no—
479C4⋊C4—1661no—
480C4⋊C4—1661no—
481C4⋊C4—1661no—
482C4⋊C4—1661no—
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—1661no—
492C42—1661no—
493C42—1661no—
494C42—1661no—
495C42C2×C4×D8311yescharacteristic
496C42C2×D33211yescharacteristic
497C42#1305059011yescharacteristic
498C42C23×D8311yescharacteristic
499C23—1661no—
500C23—1661no—
501C23C4×D33211yescharacteristic
502Q8—832no—
503Q8—1661no—
504Q8—1661no—
505Q8—1661no—
506D4—3322no—
507D4—832no—
508D4—1664no—
509D4—1661no—
510D4—1661no—
511D4—1661no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—3322no—
518C2×C4—3321no—
519C2×C4—3321no—
520C2×C4—3321no—
521C2×C4—3321no—
522C2×C4—1664no—
523C2×C4—1661no—
524C2×C4—1661no—
525C2×C4—1661no—
526C2×C4—1661no—
527C2×C4—1661no—
528C2×C4—1661no—
529C2×C4C4×D33211yescharacteristic
530C2×C4C4×D33211yescharacteristic
531C2×C4C4×D33211yescharacteristic
532C2×C4C22×C4×D8311yescharacteristic
533C2×C4C22×D33211yescharacteristic
534C2×C4C2×#1305059011yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—21no—
543C8—41no—
544C8—41no—
545C8—3321no—
546C8—3321no—
547C8—3321no—
548C8—3321no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—3321no—
553C22—3321no—
554C22—3321no—
555C22—3321no—
556C22—3321no—
557C22—1662no—
558C22C2×C4×D33211yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—3321no—
564C4—3321no—
565C4—3321no—
566C4—3321no—
567C4—3321no—
568C4—1662no—
569C4#131×D8311yescharacteristic
570C4#131×D8311yescharacteristic
571C4#1912850111yescharacteristic
572C4#1912850111yescharacteristic
573C2—41no—
574C2—3322no—
575C2—6641no—
576C2#2491615911yescharacteristic
577C2#2491626511yescharacteristic
578C2#2491636711yescharacteristic
subgroupG/H
centerC2×C4C22×D332
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1452C2
socleC22×C83C2×C4×D4
prime radical#19127848C4
cosocleC42×C83C24
hypercenter#1452D83
hypocenterC83#17909
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #1452

Complements

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

NH ≅ G/Ntype
2. #24916438C2semidirect
3. C8×#13050590C2semidirect
4. #24906343C2semidirect
5. #24906336C2semidirect
6. #24906329C2semidirect
7. #24906322C2semidirect
8. #24906288C2semidirect
9. #24906283C2semidirect
10. #24906277C2semidirect
11. #24906277C2semidirect
12. #24906243C2semidirect
13. #24905898C2semidirect
14. #24905872C2semidirect
15. C83×#1452C2semidirect
304. #1452D83semidirect
305. C83#17909semidirect

Maximal subgroups

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

subgroupindex
#249174832
#249164382
C8×#130505902
#249063432
#249063362
#249063292
#249063222
#249062882
#249062832
#249062772
#249062432
#249058982
#249058722
C83×#14522
#1790983