Finite Group Databasebeta

← #35375032

Subgroups — #35375032

Order 21248.

622 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918058C211yesmaximal, characteristic
2#24916608C211yesmaximal, characteristic, complemented
3#24916541C211yesmaximal, characteristic, complemented
4#24906376C211yesmaximal, characteristic, complemented
5#24906364C211yesmaximal, characteristic, complemented
6#24906352C211yesmaximal, characteristic, complemented
7#24906347C211yesmaximal, characteristic, complemented
8#24906286C211yesmaximal, characteristic, complemented
9#24906274C211yesmaximal, characteristic, complemented
10#24906262C211yesmaximal, characteristic, complemented
11#24906257C211yesmaximal, characteristic, complemented
12#24905921C211yesmaximal, characteristic, complemented
13#24905913C211yesmaximal, characteristic, complemented
14M16×C83⋊C8C211yesmaximal, characteristic, complemented
15C83×#1569C211yesmaximal, characteristic, complemented
16#19128251C2211yescharacteristic
17#19128235C2211yescharacteristic
18#19128110C411yescharacteristic
19#19128090C411yescharacteristic
20#19128066C411yescharacteristic
21#19128061C411yescharacteristic
22#19127954C411yescharacteristic
23#19127954C411yescharacteristic
24#19127947C411yescharacteristic
25#19127947C411yescharacteristic
26#19127828C2211yescharacteristic
27#19127825C2211yescharacteristic
28C4×#13050579C2211yescharacteristic
29C4×#13050579C2211yescharacteristic
30C4×D664C2211yescharacteristic
31C4×D664C2211yescharacteristic
32#19127778C2211yescharacteristic
33#19127778C2211yescharacteristic
34#19127778C2211yescharacteristic
35#19127777—21no—
36#19127774—21no—
37#19127774—21no—
38#19127770—21no—
39#19127766C2211yescharacteristic
40#19127766C2211yescharacteristic
41#19127766C2211yescharacteristic
42#19127761—21no—
43#19127754C2211yescharacteristic
44#19127726—21no—
45#19127666—21no—
46#19127666—21no—
47C2×C4×C83⋊C8C2211yescharacteristic
48#19127431C2211yescharacteristic
49#19127431C2211yescharacteristic
50#19127428C2211yescharacteristic
51#19127428C2211yescharacteristic
52#19127428C2211yescharacteristic
53#19127428C2211yescharacteristic
54#19127428C2211yescharacteristic
55#19127428C2211yescharacteristic
56#19127422C2211yescharacteristic
57#19127422C2211yescharacteristic
58C8×C83⋊C8C2211yescharacteristic
59C8×C83⋊C8C2211yescharacteristic
60#432×C83C2211yescharacteristic
61#423×C83C2211yescharacteristic
62C4×M16×C83C2211yescharacteristic
63#335×C83C2211yescharacteristic
64#335×C83C2211yescharacteristic
65#334×C83C2211yescharacteristic
66#334×C83C2211yescharacteristic
67C2×#13050590—21no—
68C2×#13050579C2×C411yescharacteristic
69C2×#13050579C2×C411yescharacteristic
70C2×D664C2×C411yescharacteristic
71C2×D664C2×C411yescharacteristic
72C2×#13050573—21no—
73C2×#13050573—21no—
74C2×#13050573—21no—
75C22×C83⋊C8—21no—
76C2×C8×D83—21no—
77C2×C8×D83—21no—
78C2×C8×D83—21no—
79#14581792C2×C411yescharacteristic
80#14581789C2×C411yescharacteristic
81#14581786—21no—
82#14581784C2×C411yescharacteristic
83#14581780—21no—
84#14581780C2×C411yescharacteristic
85#14581775—21no—
86#14581771C2×C411yescharacteristic
87#14581766—21no—
88#14581766C2×C411yescharacteristic
89#14581766C2×C411yescharacteristic
90#14581766C2×C411yescharacteristic
91C4×Dic166C2311yescharacteristic
92C4×D332—21no—
93C4×D332C2311yescharacteristic
94C4×D332C2311yescharacteristic
95C4×D332C2311yescharacteristic
96C4×C22⋊D83—21no—
97#14581749—21no—
98#14581726C2×C411yescharacteristic
99#14581726C2×C411yescharacteristic
100#14581724C2×C411yescharacteristic
101#14581724C2×C411yescharacteristic
102C4⋊(C83⋊C8)D411yescharacteristic
103C4⋊(C83⋊C8)D411yescharacteristic
104Dic83⋊C8—21no—
105Dic83⋊C8—21no—
106#14581717C2×C411yescharacteristic
107#14581717C2×C411yescharacteristic
108#14581714C2×C411yescharacteristic
109#14581714C2×C411yescharacteristic
110#14581714C2×C411yescharacteristic
111#14581714C2×C411yescharacteristic
112#14581714C2×C411yescharacteristic
113#14581714C2×C411yescharacteristic
114C22⋊(C83⋊C8)D411yescharacteristic
115C22⋊(C83⋊C8)D411yescharacteristic
116(C2×D83)⋊C8—21no—
117(C2×D83)⋊C8—21no—
118(C2×D83)⋊C8—21no—
119(C2×D83)⋊C8—21no—
120(C2×D83)⋊C8—21no—
121(C2×D83)⋊C8—21no—
122#14581702—21no—
123C4×C83⋊C8—21no—
124C4×C83⋊C8C2311yescharacteristic
125C4×C83⋊C8C2311yescharacteristic
126C4×C83⋊C8C2311yescharacteristic
127C4×C83⋊C8C2311yescharacteristic
128C8×Dic83—21no—
129C2×M16×C83—21no—
130C2×M16×C83C2×C411yescharacteristic
131C2×M16×C83C2×C411yescharacteristic
132C2×C42×C83C2311yescharacteristic
133C4⋊C8×C83—21no—
134C4⋊C8×C83C2311yescharacteristic
135C4⋊C8×C83C2311yescharacteristic
136C4⋊C8×C83C2311yescharacteristic
137C4⋊C8×C83C2311yescharacteristic
138C22⋊C8×C83—21no—
139#97×C83—21no—
140#97×C83C2×C411yescharacteristic
141#97×C83C2×C411yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#13050590—81no—
145#13050590—81no—
146C2×Dic166—21no—
147C2×Dic166C22×C411yescharacteristic
148C2×D332—21no—
149C2×D332—21no—
150C2×D332C22×C411yescharacteristic
151C2×D332C22×C411yescharacteristic
152C2×D332C22×C411yescharacteristic
153C2×C22⋊D83—21no—
154C2×C22⋊D83—21no—
155C2×C22⋊D83—21no—
156C2×C4×D83—21no—
157C2×C4×D83—21no—
158C2×C4×D83—21no—
159#13050579—22no—
160#13050579—22no—
161D664—22no—
162D664—22no—
163#13050573—81no—
164#13050573—81no—
165#13050573—81no—
166C2×C83⋊C8—21no—
167C2×C83⋊C8—21no—
168C2×C83⋊C8—42no—
169C2×C83⋊C8C2×D411yescharacteristic
170C2×C83⋊C8C2×D411yescharacteristic
171C2×C83⋊C8C2×D411yescharacteristic
172C2×C83⋊C8C2×D411yescharacteristic
173C8×D83—81no—
174C8×D83—81no—
175C8×D83—81no—
176C4⋊Dic83—21no—
177C4⋊Dic83C22×C411yescharacteristic
178C4⋊Dic83C22×C411yescharacteristic
179C4⋊Dic83C22×C411yescharacteristic
180C4⋊Dic83C22×C411yescharacteristic
181Dic83⋊C4—21no—
182Dic83⋊C4—21no—
183Dic83⋊C4—21no—
184Dic83⋊C4—21no—
185C22⋊Dic83—21no—
186(C2×D83)⋊C4—21no—
187(C2×D83)⋊C4—21no—
188(C2×D83)⋊C4—21no—
189(C2×D83)⋊C4—21no—
190(C2×D83)⋊C4—21no—
191(C2×D83)⋊C4—21no—
192(C2×D83)⋊C4—21no—
193(C2×D83)⋊C4—21no—
194C4×Dic83—21no—
195C22×C4×C83C22×C411yescharacteristic
196C22×C4×C83C2×D411yescharacteristic
197C22×C4×C83#4111yescharacteristic
198M16×C83—22no—
199M16×C83—22no—
200M16×C83—81no—
201C2×C8×C83—21no—
202C2×C8×C83—21no—
203C2×C8×C83—21no—
204C2×C8×C83—21no—
205C2×C8×C83C22×C411yescharacteristic
206C2×C8×C83C22×C411yescharacteristic
207C2×C8×C83C22×C411yescharacteristic
208C2×C8×C83C22×C411yescharacteristic
209C42×C83C22×C411yescharacteristic
210C42×C83C2×D411yescharacteristic
211C42×C83#4111yescharacteristic
212C42×C83C2411yescharacteristic
213C23×C83C4×D411yescharacteristic
214C22×D83—21no—
215C22×D83—21no—
216C22×D83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83—41no—
222C2×C4×C83C4×D411yescharacteristic
223C2×C4×C83C4×D411yescharacteristic
224C2×C4×C83C4×D411yescharacteristic
225C2×C4×C83C23×C411yescharacteristic
226C2×C4×C83C22×D411yescharacteristic
227C2×C4×C83C2×#4111yescharacteristic
228C22⋊D83—81no—
229C22⋊D83—81no—
230C22⋊D83—81no—
231C2×Dic83—21no—
232C2×Dic83—21no—
233C2×Dic83—21no—
234C2×Dic83—21no—
235C2×Dic83—21no—
236D332—21no—
237D332—21no—
238D332—21no—
239D332—21no—
240D332—21no—
241D332—21no—
242D332—81no—
243D332—81no—
244C4×D83—41no—
245C4×D83—41no—
246C4×D83—41no—
247C4×D83—41no—
248C4×D83—41no—
249C4×D83—41no—
250Dic166—21no—
251Dic166—21no—
252Dic166—81no—
253C8×C83—21no—
254C8×C83—21no—
255C8×C83—41no—
256C8×C83—41no—
257C8×C83—41no—
258C8×C83—41no—
259C8×C83#13112yes—
260C8×C83#13112yes—
261C83⋊C8—22no—
262C83⋊C8—21no—
263C83⋊C8—21no—
264C83⋊C8—21no—
265C83⋊C8—21no—
266C83⋊C8—41no—
267C22×C83—21no—
268C22×C83—21no—
269C22×C83—21no—
270C22×C83C2×C4×D411yescharacteristic
271C2×D83—41no—
272C2×D83—41no—
273C2×D83—41no—
274C2×D83—41no—
275C2×D83—41no—
276C2×D83—41no—
277C2×D83—41no—
278C2×D83—41no—
279C2×D83—41no—
280C4×C83—21no—
281C4×C83—21no—
282C4×C83—21no—
283C4×C83—21no—
284C4×C83C2×#13111yescharacteristic
285C4×C83C2×#13111yescharacteristic
286C4×C83#57611yescharacteristic
287C4×C83#57711yescharacteristic
288Dic83—41no—
289Dic83—41no—
290Dic83—41no—
291Dic83—41no—
292Dic83—41no—
293#17968—831nomaximal, Sylow
294C2×C83—41no—
295C2×C83#293111yescharacteristic
296C2×C83#294611yescharacteristic
297C2×C83#295611yescharacteristic
298D83—81no—
299D83—81no—
300D83—81no—
301#3171—831no—
302#2993—831no—
303#2981—831no—
304#1594—831no—
305#1592—831no—
306#1590—831no—
307#1589—831no—
308#1580—831no—
309SD16⋊C8—831no—
310C8×SD16—831no—
311C8×D8—831no—
312#1569D8311yescharacteristic, complemented
313#1494—831no—
314#1492—831no—
315C8×M16—831no—
316C83#1796811yescharacteristic, complemented, Sylow
317#532—831no—
318#529—831no—
319#501—831no—
320#496—831no—
321#490—831no—
322#489—831no—
323#469—831no—
324#469—831no—
325#468—831no—
326#468—831no—
327#446—831no—
328C8×Q8—831no—
329C4×SD16—831no—
330C4×SD16—831no—
331C4×D8—831no—
332C4×D8—831no—
333#436—831no—
334#436—831no—
335#436—831no—
336#436—1661no—
337#435—1661no—
338#435—1661no—
339#435—1661no—
340C8×D4—831no—
341C8×D4—831no—
342C8×D4—831no—
343#433—1661no—
344#432C2×D8311yescharacteristic
345#431—831no—
346#424—1661no—
347#423C2×D8311yescharacteristic
348#408—1661no—
349#408—1661no—
350C4×M16C2×D8311yescharacteristic
351C2×C4×C8—831no—
352#335C2×D8311yescharacteristic
353#335C2×D8311yescharacteristic
354#334C2×D8311yescharacteristic
355#334C2×D8311yescharacteristic
356Q8⋊C8—831no—
357Q8⋊C8—831no—
358D4⋊C8—831no—
359D4⋊C8—831no—
360D4⋊C8—831no—
361D4⋊C8—831no—
362D4⋊C8—831no—
363D4⋊C8—831no—
364#322—831no—
365#322—831no—
366C82—831no—
367C82—831no—
368C2×#41—1661no—
369C2×SD16—831no—
370C2×SD16—831no—
371C2×D8—831no—
372C2×D8—831no—
373C2×M16—21no—
374C2×M16—1661no—
375C2×M16—1661no—
376C2×M16—1661no—
377C2×M16C4×D8311yescharacteristic
378C2×M16C4×D8311yescharacteristic
379C22×C8—1661no—
380C22×C8—1661no—
381C22×C8—1661no—
382C22×C8—1661no—
383C4⋊Q8—831no—
384#127—831no—
385#126—1661no—
386#125—831no—
387#124—831no—
388#124—1661no—
389#123—1661no—
390C22⋊Q8—831no—
391#121—831no—
392#121—831no—
393#121—831no—
394#121—1661no—
395C4×Q8—831no—
396C4×D4—831no—
397C4×D4—831no—
398C4×D4—831no—
399C4×D4—1661no—
400C4×D4—1661no—
401#117—1661no—
402C2×C42C22×D8311yescharacteristic
403#107—831no—
404#107—831no—
405#106—831no—
406#106—831no—
407C4⋊C8—21no—
408C4⋊C8—831no—
409C4⋊C8—831no—
410C4⋊C8—1661no—
411C4⋊C8—1661no—
412C4⋊C8C22×D8311yescharacteristic
413C4⋊C8C22×D8311yescharacteristic
414C4⋊C8C22×D8311yescharacteristic
415C4⋊C8C22×D8311yescharacteristic
416#103—831no—
417#103—831no—
418#102—831no—
419#102—831no—
420#102—831no—
421#102—831no—
422#102—831no—
423#102—831no—
424C22⋊C8—21no—
425C22⋊C8—831no—
426C22⋊C8—831no—
427C22⋊C8—1661no—
428C22⋊C8—1661no—
429C22⋊C8—1661no—
430C22⋊C8—1661no—
431C22⋊C8—1661no—
432C22⋊C8—1661no—
433#97—21no—
434#97—1661no—
435#97C4×D8311yescharacteristic
436#97C4×D8311yescharacteristic
437C4×C8—831no—
438C4×C8—831no—
439C4×C8—831no—
440C4×C8—831no—
441C4×C8—1661no—
442C4×C8—1661no—
443C4×C8C22×D8311yescharacteristic
444C4×C8C22×D8311yescharacteristic
445#41—6641no—
446#41—6641no—
447C2×Q8—831no—
448C2×Q8—1661no—
449C2×D4—831no—
450C2×D4—831no—
451C2×D4—831no—
452C2×D4—1661no—
453C2×D4—1661no—
454C2×D4—1661no—
455C2×D4—1661no—
456C2×D4—1661no—
457C22×C4—1661no—
458C22×C4—1661no—
459C22×C4—1661no—
460C22×C4C2×C4×D8311yescharacteristic
461C22×C4D4×D8311yescharacteristic
462C22×C4#1305059111yescharacteristic
463SD16—1662no—
464SD16—1662no—
465D8—1662no—
466D8—1662no—
467M16—22no—
468M16—22no—
469M16—81no—
470M16—6641no—
471M16—6641no—
472M16—6641no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—3322no—
478C2×C8—831no—
479C2×C8—831no—
480C2×C8—831no—
481C2×C8—831no—
482C2×C8—6641no—
483C2×C8—6641no—
484C2×C8—6641no—
485C2×C8—1661no—
486C2×C8—1661no—
487C2×C8C2×C4×D8311yescharacteristic
488C2×C8C2×C4×D8311yescharacteristic
489C2×C8C2×C4×D8311yescharacteristic
490C2×C8C2×C4×D8311yescharacteristic
491C4⋊C4—831no—
492C4⋊C4—831no—
493C4⋊C4—831no—
494C4⋊C4—831no—
495C4⋊C4—1661no—
496C4⋊C4—1661no—
497C4⋊C4—1661no—
498C4⋊C4—1661no—
499C4⋊C4—1661no—
500C22⋊C4—1661no—
501C22⋊C4—1661no—
502C22⋊C4—1661no—
503C22⋊C4—1661no—
504C22⋊C4—1661no—
505C22⋊C4—1661no—
506C22⋊C4—1661no—
507C22⋊C4—1661no—
508C22⋊C4—1661no—
509C42—1661no—
510C42C2×C4×D8311yescharacteristic
511C42D4×D8311yescharacteristic
512C42#1305059111yescharacteristic
513C42C23×D8311yescharacteristic
514C23—1661no—
515C23—1661no—
516C23—1661no—
517C23#1458175411yescharacteristic
518Q8—6641no—
519Q8—1661no—
520Q8—1661no—
521D4—6641no—
522D4—6641no—
523D4—6641no—
524D4—6641no—
525D4—6641no—
526D4—1661no—
527D4—1661no—
528D4—1661no—
529D4—1661no—
530D4—1661no—
531D4—1661no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—3321no—
538C2×C4—3321no—
539C2×C4—3321no—
540C2×C4—3321no—
541C2×C4—3321no—
542C2×C4—3321no—
543C2×C4—1661no—
544C2×C4—1661no—
545C2×C4—1661no—
546C2×C4—1661no—
547C2×C4—1661no—
548C2×C4#1458175411yescharacteristic
549C2×C4#1458175411yescharacteristic
550C2×C4#1458175411yescharacteristic
551C2×C4C22×C4×D8311yescharacteristic
552C2×C4C2×D4×D8311yescharacteristic
553C2×C4C2×#1305059111yescharacteristic
554C8—21no—
555C8—21no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—3321no—
561C8—1662no—
562C8—1661no—
563C8—1661no—
564C8—1661no—
565C8—1661no—
566C8#1458180012yes—
567C8#1458180012yes—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—3321no—
572C22—3321no—
573C22—3321no—
574C22—3321no—
575C22—3321no—
576C22—3321no—
577C22—3321no—
578C22—3321no—
579C22—3321no—
580C22C2×#1458175411yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—3321no—
586C4—3321no—
587C4—3321no—
588C4—3321no—
589C4—3321no—
590C4C2×#1458180011yescharacteristic
591C4C2×#1458180011yescharacteristic
592C4#1912850511yescharacteristic
593C4#1912851011yescharacteristic
594C2—41no—
595C2—6641no—
596C2—6641no—
597C2—6641no—
598C2#2491617411yescharacteristic
599C2#2491629311yescharacteristic
600C2#2491637211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1569C2
socleC22×C83C2×C4×D4
prime radical#24918058C2
cosocleC42×C83C24
hypercenter#1569D83
hypocenterC83#17968
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
2. #24916608C2semidirect
3. #24916541C2semidirect
4. #24906376C2semidirect
5. #24906364C2semidirect
6. #24906352C2semidirect
7. #24906347C2semidirect
8. #24906286C2semidirect
9. #24906274C2semidirect
10. #24906262C2semidirect
11. #24906257C2semidirect
12. #24905921C2semidirect
13. #24905913C2semidirect
14. M16×C83⋊C8C2semidirect
15. C83×#1569C2semidirect
312. #1569D83semidirect
316. C83#17968semidirect

Maximal subgroups

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

subgroupindex
#249180582
#249166082
#249165412
#249063762
#249063642
#249063522
#249063472
#249062862
#249062742
#249062622
#249062572
#249059212
#249059132
M16×C83⋊C82
C83×#15692
#1796883