Finite Group Databasebeta

← #35375278

Subgroups — #35375278

Order 21248.

576 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918036C211yesmaximal, characteristic
2#24916615C211yesmaximal, characteristic, complemented
3#24916611C211yesmaximal, characteristic, complemented
4#24906335C211yesmaximal, characteristic, complemented
5#24906329C211yesmaximal, characteristic, complemented
6#24906326C211yesmaximal, characteristic, complemented
7#24906306C211yesmaximal, characteristic, complemented
8#24906303C211yesmaximal, characteristic, complemented
9#24906302C211yesmaximal, characteristic, complemented
10#24906297C211yesmaximal, characteristic, complemented
11#24906217C211yesmaximal, characteristic, complemented
12#24905927C211yesmaximal, characteristic, complemented
13#24905927C211yesmaximal, characteristic, complemented
14#24905754C211yesmaximal, characteristic, complemented
15C83×#1587C211yesmaximal, 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#19127780—21no—
32#19127780C2211yescharacteristic
33#19127778—21no—
34#19127778C2211yescharacteristic
35#19127774—21no—
36#19127771—21no—
37C8×D332C2211yescharacteristic
38#19127766C2211yescharacteristic
39#19127763—21no—
40#19127760—21no—
41#19127752C2211yescharacteristic
42#19127752C2211yescharacteristic
43#19127726—21no—
44#19127726—21no—
45#19127723C2211yescharacteristic
46#19127723C2211yescharacteristic
47C4×C8×D83C2211yescharacteristic
48#19127452C2211yescharacteristic
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#334×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×#13050573—21no—
73C2×#13050573—21no—
74C2×C8×D83—21no—
75C2×C8×D83—21no—
76C2×C8×D83C2×C411yescharacteristic
77C2×C8×D83C2×C411yescharacteristic
78#14581787—21no—
79#14581787—21no—
80#14581783C2×C411yescharacteristic
81#14581783C2×C411yescharacteristic
82#14581781C2×C411yescharacteristic
83#14581781C2×C411yescharacteristic
84#14581777—21no—
85#14581777—21no—
86#14581768C2×C411yescharacteristic
87#14581768C2×C411yescharacteristic
88#14581767C2×C411yescharacteristic
89#14581767C2×C411yescharacteristic
90C4×D332—21no—
91C4×D332—21no—
92C4×D332C2311yescharacteristic
93C4×D332C2311yescharacteristic
94#14581749—21no—
95#14581749—21no—
96C42×D83C2311yescharacteristic
97#14581726C2×C411yescharacteristic
98#14581723C2×C411yescharacteristic
99#14581723C2×C411yescharacteristic
100C4⋊(C83⋊C8)—21no—
101C4⋊(C83⋊C8)—21no—
102C4⋊(C83⋊C8)C2311yescharacteristic
103C4⋊(C83⋊C8)C2311yescharacteristic
104Dic83⋊C8—21no—
105Dic83⋊C8—21no—
106Dic83⋊C8—21no—
107Dic83⋊C8D411yescharacteristic
108Dic83⋊C8D411yescharacteristic
109#14581716C2×C411yescharacteristic
110#14581716C2×C411yescharacteristic
111#14581714C2×C411yescharacteristic
112#14581714C2×C411yescharacteristic
113#14581712C2×C411yescharacteristic
114#14581712C2×C411yescharacteristic
115(C2×D83)⋊C8—21no—
116(C2×D83)⋊C8—21no—
117(C2×D83)⋊C8—21no—
118(C2×D83)⋊C8—21no—
119(C2×D83)⋊C8—21no—
120(C2×D83)⋊C8D411yescharacteristic
121(C2×D83)⋊C8D411yescharacteristic
122#14581703—21no—
123C4×C83⋊C8—21no—
124C4×C83⋊C8C2311yescharacteristic
125C4×C83⋊C8C2311yescharacteristic
126C4×C83⋊C8C2311yescharacteristic
127C8×Dic83C2×C411yescharacteristic
128C8×Dic83C2×C411yescharacteristic
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—81no—
157#13050573—81no—
158#13050573—81no—
159#13050573—81no—
160C2×C83⋊C8—21no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8—21no—
163C2×C83⋊C8C22×C411yescharacteristic
164C2×C83⋊C8C22×C411yescharacteristic
165C2×C83⋊C8C2×D411yescharacteristic
166C2×C83⋊C8C2×D411yescharacteristic
167C8×D83—41no—
168C8×D83—41no—
169C8×D83—81no—
170C8×D83—81no—
171C4⋊Dic83—21no—
172C4⋊Dic83—21no—
173C4⋊Dic83C22×C411yescharacteristic
174C4⋊Dic83C22×C411yescharacteristic
175Dic83⋊C4—21no—
176Dic83⋊C4—21no—
177Dic83⋊C4—21no—
178Dic83⋊C4—21no—
179(C2×D83)⋊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—
189C4×Dic83C22×C411yescharacteristic
190C4×Dic83C2×D411yescharacteristic
191C4×Dic83#4111yescharacteristic
192C2×Q8×C83C22×C411yescharacteristic
193C2×Q8×C83C22×C411yescharacteristic
194Q16×C83—41no—
195C2×C8×C83—21no—
196C2×C8×C83—21no—
197C2×C8×C83—21no—
198C2×C8×C83C22×C411yescharacteristic
199C2×C8×C83C22×C411yescharacteristic
200C2×C8×C83C2×D411yescharacteristic
201C2×C8×C83C2×D411yescharacteristic
202C4⋊C4×C83—21no—
203C4⋊C4×C83—21no—
204C4⋊C4×C83C22×C411yescharacteristic
205C4⋊C4×C83C22×C411yescharacteristic
206C42×C83—21no—
207C42×C83—21no—
208C42×C83C2411yescharacteristic
209C22×D83—21no—
210C22×D83—21no—
211C22×D83C4×D411yescharacteristic
212Q8×C83—21no—
213Q8×C83—21no—
214Q8×C83—21no—
215Q8×C83—21no—
216C2×C4×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83C23×C411yescharacteristic
221C2×C4×C83C22×D411yescharacteristic
222C2×C4×C83C2×#4111yescharacteristic
223C2×Dic83—21no—
224C2×Dic83—21no—
225C2×Dic83C4×D411yescharacteristic
226C2×Dic83C4×D411yescharacteristic
227C2×Dic83C4×D411yescharacteristic
228D332—21no—
229D332—21no—
230D332—21no—
231D332—21no—
232D332—81no—
233D332—81no—
234C4×D83—21no—
235C4×D83—21no—
236C4×D83—21no—
237C4×D83—21no—
238C4×D83—41no—
239C4×D83—41no—
240C4×D83—41no—
241C4×D83—41no—
242C4×D83—41no—
243C8×C83—21no—
244C8×C83—21no—
245C8×C83—21no—
246C8×C83—21no—
247C8×C83—41no—
248C8×C83—41no—
249C8×C83—41no—
250C83⋊C8—21no—
251C83⋊C8—21no—
252C83⋊C8—21no—
253C83⋊C8—21no—
254C83⋊C8—41no—
255C83⋊C8—41no—
256C83⋊C8—41no—
257C22×C83C2×C4×D411yescharacteristic
258C2×D83—21no—
259C2×D83—21no—
260C2×D83—21no—
261C2×D83—41no—
262C2×D83—41no—
263C2×D83—41no—
264C2×D83—41no—
265C2×D83—41no—
266C2×D83—41no—
267C4×C83—21no—
268C4×C83—41no—
269C4×C83—41no—
270C4×C83—41no—
271C4×C83—41no—
272C4×C83#56811yescharacteristic
273C4×C83#56811yescharacteristic
274C4×C83#57711yescharacteristic
275C4×C83#57711yescharacteristic
276Dic83—21no—
277Dic83—21no—
278Dic83—21no—
279Dic83—41no—
280Dic83—41no—
281#17993—831nomaximal, Sylow
282C2×C83#293211yescharacteristic
283C2×C83#295211yescharacteristic
284C2×C83#295711yescharacteristic
285D83—41no—
286D83—81no—
287D83—81no—
288#3168—831no—
289#2993—831no—
290#2993—831no—
291#1587—831no—
292#1587D8311yescharacteristic, complemented
293#1586—831no—
294#1586—831no—
295#1583—831no—
296#1583—831no—
297#1582—831no—
298#1582—831no—
299#1566—831no—
300#1495—831no—
301#1495—831no—
302#1452—831no—
303C83#1799311yescharacteristic, complemented, Sylow
304#529—831no—
305#529—831no—
306#499—831no—
307#495—831no—
308#488—831no—
309#488—831no—
310#467—831no—
311#466—831no—
312#465—831no—
313#465—831no—
314#446—831no—
315#446C2×D8311yescharacteristic
316C8×Q8—831no—
317C8×Q8C2×D8311yescharacteristic
318C4×Q16C2×D8311yescharacteristic
319C4×SD16—831no—
320C4×SD16—831no—
321C4×D8—831no—
322#436—831no—
323#436—831no—
324#436—1661no—
325#436—1661no—
326#435—1661no—
327#435—1661no—
328C8×D4—831no—
329C8×D4—831no—
330#433—1661no—
331#433—1661no—
332#431—831no—
333#431—831no—
334#424—1661no—
335#424—1661no—
336#423—831no—
337#423—831no—
338C2×C4×C8—831no—
339#334—831no—
340#334—831no—
341#334—831no—
342#334C2×D8311yescharacteristic
343Q8⋊C8—831no—
344Q8⋊C8—831no—
345Q8⋊C8C2×D8311yescharacteristic
346Q8⋊C8C2×D8311yescharacteristic
347D4⋊C8—831no—
348D4⋊C8—831no—
349D4⋊C8—831no—
350D4⋊C8—831no—
351#322—831no—
352#322—831no—
353#322—831no—
354#322C2×D8311yescharacteristic
355C2×Q16C4×D8311yescharacteristic
356C2×SD16—831no—
357C2×SD16—831no—
358C2×D8—831no—
359C2×M16—1661no—
360C2×M16—1661no—
361C2×M16—1661no—
362C2×M16—1661no—
363C22×C8—831no—
364C22×C8—831no—
365C22×C8—1661no—
366C22×C8—1661no—
367#126—1661no—
368#126—1661no—
369#125—831no—
370#125—831no—
371#124—831no—
372#124—831no—
373#123—1661no—
374#123—1661no—
375C22⋊Q8—831no—
376C22⋊Q8—831no—
377#121—831no—
378#121—831no—
379C4×Q8C22×D8311yescharacteristic
380C4×Q8C22×D8311yescharacteristic
381C4×D4—831no—
382C4×D4—831no—
383C4×D4—1661no—
384C4×D4—1661no—
385#117—1661no—
386#117—1661no—
387C2×C42—831no—
388#107—831no—
389#107C4×D8311yescharacteristic
390#106—831no—
391#106—831no—
392C4⋊C8—21no—
393C4⋊C8—21no—
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⋊C8—1661no—
403C4⋊C8C22×D8311yescharacteristic
404C4⋊C8C22×D8311yescharacteristic
405#103—831no—
406#103—831no—
407#103C4×D8311yescharacteristic
408#103C4×D8311yescharacteristic
409#102—831no—
410#102—831no—
411#102—831no—
412#102—831no—
413C22⋊C8—831no—
414C22⋊C8—831no—
415C22⋊C8—1661no—
416C22⋊C8—1661no—
417C22⋊C8—1661no—
418C22⋊C8—1661no—
419C22⋊C8—1661no—
420#97—21no—
421#97—1661no—
422C4×C8—21no—
423C4×C8—831no—
424C4×C8—831no—
425C4×C8—831no—
426C4×C8—831no—
427C4×C8—831no—
428C4×C8—1661no—
429C4×C8C22×D8311yescharacteristic
430C4×C8C22×D8311yescharacteristic
431C4×C8C22×D8311yescharacteristic
432C2×Q8C2×C4×D8311yescharacteristic
433C2×Q8C2×C4×D8311yescharacteristic
434C2×D4—831no—
435C2×D4—831no—
436C2×D4—1661no—
437C2×D4—1661no—
438C22×C4—831no—
439C22×C4—831no—
440C22×C4—831no—
441C22×C4—1661no—
442C22×C4—1661no—
443Q16—41no—
444SD16—3321no—
445SD16—3321no—
446D8—3321no—
447M16—6641no—
448M16—6641no—
449M16—6641no—
450M16—6641no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—3321no—
455C2×C8—3321no—
456C2×C8—831no—
457C2×C8—831no—
458C2×C8—831no—
459C2×C8—831no—
460C2×C8—6641no—
461C2×C8—6641no—
462C2×C8—1661no—
463C2×C8—1661no—
464C2×C8—1661no—
465C2×C8C2×C4×D8311yescharacteristic
466C2×C8C2×C4×D8311yescharacteristic
467C2×C8D4×D8311yescharacteristic
468C2×C8D4×D8311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—831no—
472C4⋊C4—831no—
473C4⋊C4—1661no—
474C4⋊C4—1661no—
475C4⋊C4—1661no—
476C4⋊C4—1661no—
477C4⋊C4—1661no—
478C4⋊C4—1661no—
479C4⋊C4C2×C4×D8311yescharacteristic
480C4⋊C4C2×C4×D8311yescharacteristic
481C22⋊C4—1661no—
482C22⋊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—21no—
492C42—21no—
493C42—831no—
494C42—831no—
495C42—831no—
496C42C23×D8311yescharacteristic
497C23—831no—
498C23—1661no—
499C23—1661no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—21no—
504D4—6641no—
505D4—6641no—
506D4—1661no—
507D4—1661no—
508D4—1661no—
509D4—1661no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—3321no—
515C2×C4—3321no—
516C2×C4—3321no—
517C2×C4—3321no—
518C2×C4—3321no—
519C2×C4—831no—
520C2×C4—831no—
521C2×C4—831no—
522C2×C4—1661no—
523C2×C4—1661no—
524C2×C4—1661no—
525C2×C4—1661no—
526C2×C4—1661no—
527C2×C4—1661no—
528C2×C4C22×C4×D8311yescharacteristic
529C2×C4C2×D4×D8311yescharacteristic
530C2×C4#41×D8311yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—3321no—
539C8—3321no—
540C8—3321no—
541C8—1661no—
542C8—1661no—
543C8—1661no—
544C8—1661no—
545C22—3321no—
546C22—3321no—
547C22—3321no—
548C22—3321no—
549C22—3321no—
550C22—3321no—
551C22—1661no—
552C22—1661no—
553C22—1661no—
554C22C4×D4×D8311yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—3321no—
561C4—3321no—
562C4—1661no—
563C4—1661no—
564C4—1661no—
565C4#1912846611yescharacteristic
566C4#1912846711yescharacteristic
567C4#1912851011yescharacteristic
568C4#1912851011yescharacteristic
569C2—3321no—
570C2—6641no—
571C2—6641no—
572C2#2491617711yescharacteristic
573C2#2491634311yescharacteristic
574C2#2491637511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1587C2
socleC22×C83C2×C4×D4
prime radical#19127938C4
cosocleC42×C83C24
hypercenter#1587D83
hypocenterC83#17993
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
2. #24916615C2semidirect
3. #24916611C2semidirect
4. #24906335C2semidirect
5. #24906329C2semidirect
6. #24906326C2semidirect
7. #24906306C2semidirect
8. #24906303C2semidirect
9. #24906302C2semidirect
10. #24906297C2semidirect
11. #24906217C2semidirect
12. #24905927C2semidirect
13. #24905927C2semidirect
14. #24905754C2semidirect
15. C83×#1587C2semidirect
292. #1587D83semidirect
303. C83#17993semidirect

Maximal subgroups

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

subgroupindex
#249180362
#249166152
#249166112
#249063352
#249063292
#249063262
#249063062
#249063032
#249063022
#249062972
#249062172
#249059272
#249057542
C83×#15872
#1799383