Finite Group Databasebeta

← #35374367

Subgroups — #35374367

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#24917475C211yesmaximal, characteristic
2#24916439C211yesmaximal, characteristic, complemented
3#24916419C211yesmaximal, characteristic, complemented
4#24906344C211yesmaximal, characteristic, complemented
5#24906337C211yesmaximal, characteristic, complemented
6#24906330C211yesmaximal, characteristic, complemented
7#24906323C211yesmaximal, characteristic, complemented
8#24906284C211yesmaximal, characteristic, complemented
9#24906279C211yesmaximal, characteristic, complemented
10#24906278C211yesmaximal, characteristic, complemented
11#24906272C211yesmaximal, characteristic, complemented
12#24906241C211yesmaximal, characteristic, complemented
13#24905898C211yesmaximal, characteristic, complemented
14#24905756C211yesmaximal, characteristic, complemented
15C83×#1482C211yesmaximal, characteristic, complemented
16C4×#13050590C2211yescharacteristic
17#19128039C411yescharacteristic
18#19128022C411yescharacteristic
19#19128005C411yescharacteristic
20#19127998C411yescharacteristic
21#19127920C411yescharacteristic
22#19127913C411yescharacteristic
23#19127861C411yescharacteristic
24#19127844C411yescharacteristic
25#19127832C2211yescharacteristic
26Q8×C83⋊C8C2211yescharacteristic
27#19127825C2211yescharacteristic
28#19127825C2211yescharacteristic
29C4×#13050580C2211yescharacteristic
30C4×#13050577C2211yescharacteristic
31C4×#13050578C2211yescharacteristic
32C4×#13050575C2211yescharacteristic
33#19127779C2211yescharacteristic
34#19127773—21no—
35D4×C83⋊C8—21no—
36D4×C83⋊C8C2211yescharacteristic
37#19127766C2211yescharacteristic
38#19127766C2211yescharacteristic
39(C22⋊D83)⋊C8—21no—
40(C22⋊D83)⋊C8—21no—
41#19127762—21no—
42#19127758C2211yescharacteristic
43#19127754C2211yescharacteristic
44#19127752—21no—
45#19127657—21no—
46C2×C4×C83⋊C8C2211yescharacteristic
47C4×C8×D83—21no—
48#19127453C2211yescharacteristic
49#19127453C2211yescharacteristic
50#19127451C2211yescharacteristic
51#19127451C2211yescharacteristic
52#19127433C2211yescharacteristic
53#19127433C2211yescharacteristic
54#19127430C2211yescharacteristic
55#19127430C2211yescharacteristic
56#19127423C2211yescharacteristic
57#19127423C2211yescharacteristic
58#19127422C2211yescharacteristic
59#19127422C2211yescharacteristic
60#529×C83C2211yescharacteristic
61#431×C83C2211yescharacteristic
62#431×C83C2211yescharacteristic
63Q8⋊C8×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65D4⋊C8×C83C2211yescharacteristic
66D4⋊C8×C83C2211yescharacteristic
67C2×#13050590C2×C411yescharacteristic
68C2×#13050580C2×C411yescharacteristic
69C2×#13050578C2×C411yescharacteristic
70C2×#13050577C2×C411yescharacteristic
71C2×#13050575C2×C411yescharacteristic
72C2×#13050574—21no—
73C22×C83⋊C8—21no—
74C22×C83⋊C8D411yescharacteristic
75C22×C83⋊C8D411yescharacteristic
76C2×C8×D83—21no—
77C2×C8×D83—21no—
78C4×Dic166C2×C411yescharacteristic
79C4×Dic166C2311yescharacteristic
80C4×D332C2×C411yescharacteristic
81C4×D332C2311yescharacteristic
82C4×C22⋊D83—21no—
83C4×C22⋊D83—21no—
84#14581751C2×C411yescharacteristic
85#14581749—21no—
86C42×D83—21no—
87#14581725C2×C411yescharacteristic
88#14581725C2×C411yescharacteristic
89#14581723C2×C411yescharacteristic
90#14581723C2×C411yescharacteristic
91C4⋊(C83⋊C8)—21no—
92C4⋊(C83⋊C8)—21no—
93C4⋊(C83⋊C8)C2×C411yescharacteristic
94C4⋊(C83⋊C8)C2×C411yescharacteristic
95C4⋊(C83⋊C8)C2311yescharacteristic
96C4⋊(C83⋊C8)C2311yescharacteristic
97Dic83⋊C8—21no—
98Dic83⋊C8—21no—
99#14581716C2×C411yescharacteristic
100#14581716C2×C411yescharacteristic
101#14581715C2×C411yescharacteristic
102#14581715C2×C411yescharacteristic
103#14581713C2×C411yescharacteristic
104#14581713C2×C411yescharacteristic
105#14581712C2×C411yescharacteristic
106#14581712C2×C411yescharacteristic
107C22⋊(C83⋊C8)—21no—
108C22⋊(C83⋊C8)—21no—
109C22⋊(C83⋊C8)—21no—
110C22⋊(C83⋊C8)C2×C411yescharacteristic
111C22⋊(C83⋊C8)C2×C411yescharacteristic
112(C2×D83)⋊C8—21no—
113(C2×D83)⋊C8—21no—
114#14581703—21no—
115#14581703—21no—
116C4×C83⋊C8—21no—
117C4×C83⋊C8D411yescharacteristic
118C4×C83⋊C8D411yescharacteristic
119C4×C83⋊C8C2311yescharacteristic
120C4×C83⋊C8C2311yescharacteristic
121C4×C83⋊C8C2311yescharacteristic
122C4×C83⋊C8C2311yescharacteristic
123C8×Dic83—21no—
124C8×Dic83—21no—
125#126×C83—21no—
126#125×C83C2×C411yescharacteristic
127#124×C83C2×C411yescharacteristic
128#123×C83—21no—
129C22⋊Q8×C83C2×C411yescharacteristic
130#121×C83C2×C411yescharacteristic
131C4×Q8×C83C2311yescharacteristic
132C4×D4×C83—21no—
133C4×D4×C83C2311yescharacteristic
134#117×C83—21no—
135C2×C42×C83C2311yescharacteristic
136C4⋊C8×C83—21no—
137C4⋊C8×C83C2311yescharacteristic
138C4⋊C8×C83C2311yescharacteristic
139C22⋊C8×C83—21no—
140C22⋊C8×C83—21no—
141C4×C8×C83—21no—
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#13050590—22no—
145#13050590—22no—
146C2×Dic166C22×C411yescharacteristic
147C2×D332C22×C411yescharacteristic
148C2×C22⋊D83—21no—
149C2×C4×D83—21no—
150C2×C4×D83—21no—
151C2×C4×D83—21no—
152#13050580—22no—
153#13050578—22no—
154#13050577—22no—
155#13050575—22no—
156#13050574—42no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—41no—
160C2×C83⋊C8—41no—
161C2×C83⋊C8—42no—
162C2×C83⋊C8C22×C411yescharacteristic
163C2×C83⋊C8C22×C411yescharacteristic
164C2×C83⋊C8C22×C411yescharacteristic
165C2×C83⋊C8C22×C411yescharacteristic
166C2×C83⋊C8C2×D411yescharacteristic
167C2×C83⋊C8C2×D411yescharacteristic
168C2×C83⋊C8C2×D411yescharacteristic
169C2×C83⋊C8C2×D411yescharacteristic
170C8×D83—42no—
171C8×D83—42no—
172C4⋊Dic83C22×C411yescharacteristic
173C4⋊Dic83C22×C411yescharacteristic
174Dic83⋊C4—21no—
175Dic83⋊C4—21no—
176C22⋊Dic83—21no—
177(C2×D83)⋊C4—21no—
178(C2×D83)⋊C4—21no—
179C4×Dic83—21no—
180C4×Dic83—21no—
181C4×Dic83—21no—
182C2×Q8×C83C22×C411yescharacteristic
183C2×D4×C83—21no—
184C2×D4×C83C22×C411yescharacteristic
185C22×C4×C83—21no—
186C22×C4×C83C22×C411yescharacteristic
187C22×C4×C83C2×D411yescharacteristic
188C22×C4×C83#4111yescharacteristic
189C2×C8×C83—21no—
190C2×C8×C83—21no—
191C2×C8×C83—21no—
192C2×C8×C83—21no—
193C4⋊C4×C83—21no—
194C4⋊C4×C83—21no—
195C4⋊C4×C83—21no—
196C4⋊C4×C83—21no—
197C4⋊C4×C83C22×C411yescharacteristic
198C4⋊C4×C83C22×C411yescharacteristic
199C22⋊C4×C83—21no—
200C22⋊C4×C83—21no—
201C22⋊C4×C83—21no—
202C22⋊C4×C83—21no—
203C22⋊C4×C83—21no—
204C42×C83—21no—
205C42×C83C22×C411yescharacteristic
206C42×C83C2×D411yescharacteristic
207C42×C83#4111yescharacteristic
208C42×C83C2411yescharacteristic
209C23×C83—21no—
210C23×C83C4×D411yescharacteristic
211C22×D83—21no—
212Q8×C83—21no—
213Q8×C83—21no—
214D4×C83—21no—
215D4×C83—21no—
216D4×C83—42no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83—21no—
222C2×C4×C83—21no—
223C2×C4×C83—21no—
224C2×C4×C83—41no—
225C2×C4×C83—41no—
226C2×C4×C83—41no—
227C2×C4×C83C4×D411yescharacteristic
228C2×C4×C83C4×D411yescharacteristic
229C2×C4×C83C4×D411yescharacteristic
230C2×C4×C83C23×C411yescharacteristic
231C2×C4×C83C22×D411yescharacteristic
232C2×C4×C83C2×#4111yescharacteristic
233C22⋊D83—24no—
234C2×Dic83—21no—
235C2×Dic83—21no—
236C2×Dic83—21no—
237D332—21no—
238D332#13112yes—
239C4×D83—24no—
240C4×D83—42no—
241C4×D83—41no—
242C4×D83—41no—
243Dic166—21no—
244Dic166#13112yes—
245C8×C83—41no—
246C8×C83—41no—
247C8×C83—41no—
248C8×C83—41no—
249C83⋊C8—21no—
250C83⋊C8—21no—
251C83⋊C8—21no—
252C83⋊C8—21no—
253C83⋊C8—21no—
254C83⋊C8—21no—
255C83⋊C8—21no—
256C83⋊C8—21no—
257C83⋊C8—41no—
258C83⋊C8—41no—
259C22×C83—21no—
260C22×C83—21no—
261C22×C83—21no—
262C22×C83—41no—
263C22×C83—41no—
264C22×C83—41no—
265C22×C83C2×C4×D411yescharacteristic
266C2×D83—22no—
267C2×D83—41no—
268C2×D83—41no—
269C4×C83—21no—
270C4×C83—21no—
271C4×C83—21no—
272C4×C83—21no—
273C4×C83—41no—
274C4×C83—41no—
275C4×C83—41no—
276C4×C83C2×#13111yescharacteristic
277C4×C83C2×#13111yescharacteristic
278C4×C83#57511yescharacteristic
279C4×C83#57511yescharacteristic
280Dic83—22no—
281Dic83—41no—
282Dic83—41no—
283#17909—831nomaximal, Sylow
284C2×C83—41no—
285C2×C83—81no—
286C2×C83#292911yescharacteristic
287C2×C83#294311yescharacteristic
288C2×C83#295511yescharacteristic
289D83—42no—
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#1482D8311yescharacteristic, complemented
304#1452—831no—
305C83#1790911yescharacteristic, complemented, Sylow
306#529C2×D8311yescharacteristic
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—831no—
340C2×C4×C8—1661no—
341#335—831no—
342#335—831no—
343#334—831no—
344#334—831no—
345Q8⋊C8—831no—
346Q8⋊C8—831no—
347Q8⋊C8C2×D8311yescharacteristic
348Q8⋊C8C2×D8311yescharacteristic
349D4⋊C8—831no—
350D4⋊C8—831no—
351D4⋊C8C2×D8311yescharacteristic
352D4⋊C8C2×D8311yescharacteristic
353#322—831no—
354#322—831no—
355#322—831no—
356#322—831no—
357C2×#41—831no—
358C2×Q16—831no—
359C2×SD16—831no—
360C2×SD16—831no—
361C2×D8—831no—
362C2×M16—1661no—
363C22×C8—831no—
364C22×C8—831no—
365C22×C8—1661no—
366C22×C8—1661no—
367C22×C8—1661no—
368#126—21no—
369#125C4×D8311yescharacteristic
370#124C4×D8311yescharacteristic
371#123—21no—
372C22⋊Q8C4×D8311yescharacteristic
373#121C4×D8311yescharacteristic
374C4×Q8—831no—
375C4×Q8—831no—
376C4×Q8C22×D8311yescharacteristic
377C4×D4—21no—
378C4×D4—831no—
379C4×D4—831no—
380C4×D4—1661no—
381C4×D4—1661no—
382C4×D4C22×D8311yescharacteristic
383#117—21no—
384#117—831no—
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⋊C8C22×D8311yescharacteristic
402C4⋊C8C22×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—21no—
413C22⋊C8—831no—
414C22⋊C8—831no—
415C22⋊C8—1661no—
416C22⋊C8—1661no—
417C22⋊C8—1661no—
418C22⋊C8—1661no—
419C22⋊C8—1661no—
420#97—1661no—
421#97—1661no—
422C4×C8—21no—
423C4×C8—831no—
424C4×C8—831no—
425C4×C8—831no—
426C4×C8—831no—
427C4×C8—831no—
428C4×C8—831no—
429C4×C8—1661no—
430C4×C8—1661no—
431C4×C8—1661no—
432C4×C8C22×D8311yescharacteristic
433C4×C8C22×D8311yescharacteristic
434#41—1662no—
435#41—1662no—
436C2×Q8—831no—
437C2×Q8C2×C4×D8311yescharacteristic
438C2×D4—21no—
439C2×D4—831no—
440C2×D4—1661no—
441C2×D4C2×C4×D8311yescharacteristic
442C22×C4—21no—
443C22×C4—1661no—
444C22×C4—1661no—
445C22×C4—1661no—
446C22×C4C2×C4×D8311yescharacteristic
447C22×C4D4×D8311yescharacteristic
448C22×C4#1305058911yescharacteristic
449Q16—1662no—
450SD16—1662no—
451SD16—1662no—
452D8—1662no—
453M16—3322no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—3322no—
459C2×C8—3322no—
460C2×C8—3322no—
461C2×C8—3321no—
462C2×C8—3321no—
463C2×C8—831no—
464C2×C8—831no—
465C2×C8—831no—
466C2×C8—831no—
467C2×C8—831no—
468C2×C8—831no—
469C2×C8—831no—
470C2×C8—831no—
471C2×C8—1661no—
472C2×C8—1661no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—831no—
478C4⋊C4—831no—
479C4⋊C4—1661no—
480C4⋊C4—1661no—
481C4⋊C4C2×C4×D8311yescharacteristic
482C4⋊C4C2×C4×D8311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—1661no—
489C22⋊C4—1661no—
490C22⋊C4—1661no—
491C42—21no—
492C42—1661no—
493C42—1661no—
494C42—1661no—
495C42C2×C4×D8311yescharacteristic
496C42D4×D8311yescharacteristic
497C42#1305058911yescharacteristic
498C42C23×D8311yescharacteristic
499C23—21no—
500C23—1661no—
501C23(C22⋊D83)⋊C411yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—832no—
505Q8—1661no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—832no—
510D4—1664no—
511D4—1661no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—3322no—
523C2×C4—3321no—
524C2×C4—3321no—
525C2×C4—1664no—
526C2×C4—1661no—
527C2×C4—1661no—
528C2×C4—1661no—
529C2×C4(C22⋊D83)⋊C411yescharacteristic
530C2×C4(C22⋊D83)⋊C411yescharacteristic
531C2×C4(C22⋊D83)⋊C411yescharacteristic
532C2×C4C22×C4×D8311yescharacteristic
533C2×C4C2×D4×D8311yescharacteristic
534C2×C4C2×#1305058911yescharacteristic
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—3321no—
540C8—3321no—
541C8—1661no—
542C8—1661no—
543C8—1661no—
544C8—1661no—
545C8—1661no—
546C8—1661no—
547C8—1661no—
548C8—1661no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—3321no—
556C22—3321no—
557C22—1662no—
558C22C2×(C22⋊D83)⋊C411yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—3321no—
567C4—3321no—
568C4—1662no—
569C4#131×D8311yescharacteristic
570C4#131×D8311yescharacteristic
571C4#1912849811yescharacteristic
572C4#1912849811yescharacteristic
573C2—41no—
574C2—81no—
575C2—3322no—
576C2#2491616011yescharacteristic
577C2#2491625911yescharacteristic
578C2#2491636211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1482C2
socleC22×C83C2×C4×D4
prime radical#19127844C4
cosocleC42×C83C24
hypercenter#1482D83
hypocenterC83#17909
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1482

Complements

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

NH ≅ G/Ntype
2. #24916439C2semidirect
3. #24916419C2semidirect
4. #24906344C2semidirect
5. #24906337C2semidirect
6. #24906330C2semidirect
7. #24906323C2semidirect
8. #24906284C2semidirect
9. #24906279C2semidirect
10. #24906278C2semidirect
11. #24906272C2semidirect
12. #24906241C2semidirect
13. #24905898C2semidirect
14. #24905756C2semidirect
15. C83×#1482C2semidirect
303. #1482D83semidirect
305. C83#17909semidirect

Maximal subgroups

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

subgroupindex
#249174752
#249164392
#249164192
#249063442
#249063372
#249063302
#249063232
#249062842
#249062792
#249062782
#249062722
#249062412
#249058982
#249057562
C83×#14822
#1790983