Finite Group Databasebeta

← #35375459

Subgroups — #35375459

Order 21248.

662 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917524C211yesmaximal, characteristic
2#24916478C211yesmaximal, characteristic, complemented
3#24916209C211yesmaximal, characteristic, complemented
4#24906367C211yesmaximal, characteristic, complemented
5#24906355C211yesmaximal, characteristic, complemented
6#24906329C211yesmaximal, characteristic, complemented
7#24906322C211yesmaximal, characteristic, complemented
8#24906301C211yesmaximal, characteristic, complemented
9#24906294C211yesmaximal, characteristic, complemented
10#24906288C211yesmaximal, characteristic, complemented
11C8×D664C211yesmaximal, characteristic, complemented
12#24906248C211yesmaximal, characteristic, complemented
13#24905933C211yesmaximal, characteristic, complemented
14#24905851C211yesmaximal, characteristic, complemented
15C83×#1453C211yesmaximal, characteristic, complemented
16C2×#14581800—21no—
17#19128251C2211yescharacteristic
18C4×#13050590C2211yescharacteristic
19#19128026C411yescharacteristic
20#19128026C411yescharacteristic
21#19127997C411yescharacteristic
22#19127992C411yescharacteristic
23#19127902C411yescharacteristic
24#19127897C411yescharacteristic
25#19127848C411yescharacteristic
26#19127848C411yescharacteristic
27#19127831C2211yescharacteristic
28#19127831C2211yescharacteristic
29C4×#13050579C2211yescharacteristic
30C4×#13050579C2211yescharacteristic
31C4×D664C2211yescharacteristic
32C4×D664C2211yescharacteristic
33#19127780C2211yescharacteristic
34#19127780C2211yescharacteristic
35#19127774—21no—
36#19127774—21no—
37#19127770—21no—
38#19127770—21no—
39C8×D332C2211yescharacteristic
40C8×D332C2211yescharacteristic
41C8×D332C2211yescharacteristic
42C8×D332C2211yescharacteristic
43#19127758C2211yescharacteristic
44#19127756—21no—
45C2×C4⋊(C83⋊C8)C2211yescharacteristic
46#19127669—21no—
47#97×D83—21no—
48#19127454C2211yescharacteristic
49#19127454C2211yescharacteristic
50#19127452C2211yescharacteristic
51#19127452C2211yescharacteristic
52#19127433C2211yescharacteristic
53#19127433C2211yescharacteristic
54#19127430C2211yescharacteristic
55#19127430C2211yescharacteristic
56#19127430C2211yescharacteristic
57#19127430C2211yescharacteristic
58#19127430C2211yescharacteristic
59#19127430C2211yescharacteristic
60#431×C83C2211yescharacteristic
61#431×C83C2211yescharacteristic
62C4×M16×C83C2211yescharacteristic
63#322×C83C2211yescharacteristic
64#322×C83C2211yescharacteristic
65#322×C83C2211yescharacteristic
66C82×C83C2211yescharacteristic
67C2×#13050590—21no—
68C2×#13050590C2×C411yescharacteristic
69C2×#13050579C2×C411yescharacteristic
70C2×#13050579C2×C411yescharacteristic
71C2×D664C2×C411yescharacteristic
72C2×D664C2×C411yescharacteristic
73#14581800—44no—
74C2×#13050573—21no—
75C2×#13050573—21no—
76C22×C83⋊C8—21no—
77C2×C8×D83—21no—
78C2×C8×D83—21no—
79C2×C8×D83—21no—
80C2×C8×D83—21no—
81#14581792C2×C411yescharacteristic
82#14581789C2×C411yescharacteristic
83#14581780—21no—
84#14581766—21no—
85#14581766C2×C411yescharacteristic
86#14581766C2×C411yescharacteristic
87C4×Dic166C2×C411yescharacteristic
88C4×Dic166C2311yescharacteristic
89C4×D332—21no—
90C4×D332C2×C411yescharacteristic
91C4×D332C2311yescharacteristic
92C4×D332C2311yescharacteristic
93C4×D332C2311yescharacteristic
94C4×C22⋊D83—21no—
95C4×C22⋊D83—21no—
96#14581751C2×C411yescharacteristic
97#14581749—21no—
98C42×D83—21no—
99#14581726C2×C411yescharacteristic
100#14581726C2×C411yescharacteristic
101#14581724C2×C411yescharacteristic
102#14581724C2×C411yescharacteristic
103C4⋊(C83⋊C8)—21no—
104C4⋊(C83⋊C8)C2311yescharacteristic
105C4⋊(C83⋊C8)C2311yescharacteristic
106C4⋊(C83⋊C8)C2311yescharacteristic
107C4⋊(C83⋊C8)C2311yescharacteristic
108Dic83⋊C8—21no—
109Dic83⋊C8—21no—
110#14581717C2×C411yescharacteristic
111#14581717C2×C411yescharacteristic
112#14581714C2×C411yescharacteristic
113#14581714C2×C411yescharacteristic
114#14581714C2×C411yescharacteristic
115#14581714C2×C411yescharacteristic
116#14581714C2×C411yescharacteristic
117#14581714C2×C411yescharacteristic
118C22⋊(C83⋊C8)—21no—
119(C2×D83)⋊C8—21no—
120(C2×D83)⋊C8—21no—
121(C2×D83)⋊C8—21no—
122(C2×D83)⋊C8—21no—
123(C2×D83)⋊C8—21no—
124(C2×D83)⋊C8—21no—
125#14581703—21no—
126#14581702—21no—
127#14581702—21no—
128C2×M16×C83D411yescharacteristic
129C2×M16×C83D411yescharacteristic
130C2×C42×C83C2311yescharacteristic
131C4⋊C8×C83—21no—
132C4⋊C8×C83C2×C411yescharacteristic
133C4⋊C8×C83C2×C411yescharacteristic
134C22⋊C8×C83—21no—
135C22⋊C8×C83C2×C411yescharacteristic
136C22⋊C8×C83C2×C411yescharacteristic
137#97×C83D411yescharacteristic
138#97×C83D411yescharacteristic
139C4×C8×C83C2311yescharacteristic
140C4×C8×C83C2311yescharacteristic
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C4×C8×C83C2311yescharacteristic
145#13050590—22no—
146#13050590—41no—
147#13050590—42no—
148#13050590—42no—
149C2×Dic166—21no—
150C2×Dic166C22×C411yescharacteristic
151C2×D332—21no—
152C2×D332—21no—
153C2×D332C22×C411yescharacteristic
154C2×D332C22×C411yescharacteristic
155C2×D332C22×C411yescharacteristic
156C2×C22⋊D83—21no—
157C2×C22⋊D83—21no—
158C2×C22⋊D83—21no—
159C2×C4×D83—21no—
160C2×C4×D83—21no—
161C2×C4×D83—21no—
162C2×C4×D83—21no—
163C2×C4×D83—21no—
164#13050579—41no—
165#13050579—41no—
166D664—22no—
167D664—22no—
168#13050573—42no—
169#13050573—42no—
170C2×C83⋊C8—21no—
171C2×C83⋊C8—21no—
172C2×C83⋊C8—21no—
173C2×C83⋊C8—21no—
174C2×C83⋊C8—42no—
175C8×D83—42no—
176C8×D83—42no—
177C8×D83—42no—
178C8×D83—42no—
179C4⋊Dic83—21no—
180C4⋊Dic83C22×C411yescharacteristic
181C4⋊Dic83C22×C411yescharacteristic
182C4⋊Dic83C22×C411yescharacteristic
183C4⋊Dic83C22×C411yescharacteristic
184Dic83⋊C4—21no—
185Dic83⋊C4—21no—
186C22⋊Dic83—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—
193C4×Dic83—21no—
194C4×Dic83—21no—
195C4×Dic83—21no—
196C22×C4×C83C22×C411yescharacteristic
197C22×C4×C83C2×D411yescharacteristic
198C22×C4×C83#4111yescharacteristic
199M16×C83—22no—
200M16×C83—41no—
201C2×C8×C83—21no—
202C2×C8×C83—21no—
203C2×C8×C83C22×C411yescharacteristic
204C2×C8×C83C22×C411yescharacteristic
205C2×C8×C83C22×C411yescharacteristic
206C2×C8×C83C22×C411yescharacteristic
207C2×C8×C83C2×D411yescharacteristic
208C2×C8×C83C2×D411yescharacteristic
209C2×C8×C83C2×D411yescharacteristic
210C2×C8×C83C2×D411yescharacteristic
211C42×C83C22×C411yescharacteristic
212C42×C83C2×D411yescharacteristic
213C42×C83#4111yescharacteristic
214C42×C83C2411yescharacteristic
215C23×C83C4×D411yescharacteristic
216C22×D83—21no—
217C22×D83—21no—
218C22×D83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83—21no—
222C2×C4×C83—21no—
223C2×C4×C83—41no—
224C2×C4×C83C4×D411yescharacteristic
225C2×C4×C83C4×D411yescharacteristic
226C2×C4×C83C4×D411yescharacteristic
227C2×C4×C83C23×C411yescharacteristic
228C2×C4×C83C22×D411yescharacteristic
229C2×C4×C83C2×#4111yescharacteristic
230C22⋊D83—42no—
231C22⋊D83—42no—
232C22⋊D83—42no—
233C2×Dic83—21no—
234C2×Dic83—21no—
235C2×Dic83—21no—
236C2×Dic83—21no—
237C2×Dic83—21no—
238D332—21no—
239D332—21no—
240D332—21no—
241D332—21no—
242D332—21no—
243D332—42no—
244D332—81no—
245D332#13112yescomplemented
246C4×D83—42no—
247C4×D83—41no—
248C4×D83—41no—
249C4×D83—41no—
250C4×D83—41no—
251C4×D83—41no—
252C4×D83—41no—
253C4×D83—81no—
254Dic166—21no—
255Dic166—21no—
256Dic166—42no—
257C8×C83—21no—
258C8×C83—21no—
259C8×C83—21no—
260C8×C83—21no—
261C8×C83—21no—
262C8×C83—21no—
263C8×C83—21no—
264C8×C83—41no—
265C8×C83—41no—
266C8×C83AGL(1,ℤ/8)12yes—
267C83⋊C8—41no—
268C83⋊C8—41no—
269C83⋊C8—41no—
270C83⋊C8—41no—
271C22×C83—21no—
272C22×C83—21no—
273C22×C83—21no—
274C22×C83C2×C4×D411yescharacteristic
275C2×D83—22no—
276C2×D83—41no—
277C2×D83—41no—
278C2×D83—41no—
279C2×D83—41no—
280C2×D83—41no—
281C2×D83—41no—
282C2×D83—41no—
283C2×D83—41no—
284C4×C83—21no—
285C4×C83—21no—
286C4×C83—21no—
287C4×C83—21no—
288C4×C83C2×#13111yescharacteristic
289C4×C83#56811yescharacteristic
290C4×C83C2×AGL(1,ℤ/8)11yescharacteristic
291C4×C83#57511yescharacteristic
292Dic83—41no—
293Dic83—41no—
294Dic83—41no—
295Dic83—41no—
296Dic83—41no—
297#18007—831nomaximal, Sylow
298C2×C83—41no—
299C2×C83#293311yescharacteristic
300C2×C83C4×AGL(1,ℤ/8)11yescharacteristic
301C2×C83#295711yescharacteristic
302D83—42no—
303D83—81no—
304D83—81no—
305#3106—831no—
306#2970—831no—
307#2935—831no—
308#1592—831no—
309#1590—831no—
310#1586—831no—
311#1585—831no—
312#1582—831no—
313#1581—831no—
314#1580—831no—
315C8×D8—831no—
316#1573—831no—
317#1496—831no—
318#1477—831no—
319#1453D8311yescharacteristic, complemented
320C83#1800711yescharacteristic, complemented, Sylow
321C2×#131—1661no—
322#532—831no—
323C4×#41—831no—
324#482—831no—
325#482—831no—
326#477—831no—
327#476—831no—
328#460—831no—
329#459—831no—
330#449—831no—
331#449—831no—
332#446—831no—
333#446—831no—
334C4×SD16—831no—
335C4×SD16—831no—
336C4×D8—831no—
337C4×D8—831no—
338#436—831no—
339#436—831no—
340#435—1661no—
341#435—1661no—
342#435—1661no—
343#435—1661no—
344C8×D4—831no—
345C8×D4—831no—
346C8×D4—831no—
347C8×D4—831no—
348#432—831no—
349#432—1661no—
350#431C2×D8311yescharacteristic
351#431C2×D8311yescharacteristic
352C2×C4⋊C8—831no—
353#408—1661no—
354C4×M16C2×D8311yescharacteristic
355C2×#97—1661no—
356#335—831no—
357#335—831no—
358#334—831no—
359#334—831no—
360Q8⋊C8—831no—
361Q8⋊C8—831no—
362D4⋊C8—831no—
363D4⋊C8—831no—
364D4⋊C8—831no—
365D4⋊C8—831no—
366D4⋊C8—831no—
367D4⋊C8—831no—
368#322C2×D8311yescharacteristic
369#322C2×D8311yescharacteristic
370#322C2×D8311yescharacteristic
371C82C2×D8311yescharacteristic
372C2×#41—831no—
373C2×#41—1661no—
374C2×SD16—831no—
375C2×SD16—831no—
376C2×D8—831no—
377C2×D8—831no—
378#131—3324no—
379C2×M16—1661no—
380C2×M16—1661no—
381C2×M16D33211yescharacteristic
382C2×M16D33211yescharacteristic
383C22×C8—1661no—
384C22×C8—1661no—
385C22×C8—1661no—
386C22×C8—1661no—
387C22×C8—1661no—
388C4⋊Q8—831no—
389#127—831no—
390#124—1661no—
391#121—831no—
392#121—831no—
393#121—1661no—
394C4×Q8—831no—
395C4×Q8—831no—
396C4×D4—831no—
397C4×D4—831no—
398C4×D4—831no—
399C4×D4—831no—
400C4×D4—1661no—
401C4×D4—1661no—
402C4×D4—1661no—
403#117—831no—
404#117—1661no—
405C2×C42—1661no—
406C2×C42C22×D8311yescharacteristic
407#107—831no—
408#107—831no—
409#106—831no—
410#106—831no—
411C4⋊C8—21no—
412C4⋊C8—831no—
413C4⋊C8—831no—
414C4⋊C8—831no—
415C4⋊C8—831no—
416C4⋊C8—1661no—
417C4⋊C8—1661no—
418C4⋊C8—1661no—
419C4⋊C8C4×D8311yescharacteristic
420C4⋊C8C4×D8311yescharacteristic
421#103—831no—
422#103—831no—
423#102—831no—
424#102—831no—
425#102—831no—
426#102—831no—
427#102—831no—
428#102—831no—
429C22⋊C8—21no—
430C22⋊C8—1661no—
431C22⋊C8—1661no—
432C22⋊C8—1661no—
433C22⋊C8—1661no—
434C22⋊C8—1661no—
435C22⋊C8—1661no—
436C22⋊C8—1661no—
437C22⋊C8C4×D8311yescharacteristic
438C22⋊C8C4×D8311yescharacteristic
439#97—1661no—
440#97—1661no—
441#97—1661no—
442#97D33211yescharacteristic
443#97D33211yescharacteristic
444C4×C8C22×D8311yescharacteristic
445C4×C8C22×D8311yescharacteristic
446C4×C8C22×D8311yescharacteristic
447C4×C8C22×D8311yescharacteristic
448C4×C8C22×D8311yescharacteristic
449C4×C8C22×D8311yescharacteristic
450#41—3322no—
451#41—3322no—
452#41—3321no—
453#41—1662no—
454C2×Q8—831no—
455C2×Q8—1661no—
456C2×D4—831no—
457C2×D4—831no—
458C2×D4—831no—
459C2×D4—1661no—
460C2×D4—1661no—
461C2×D4—1661no—
462C2×D4—1661no—
463C2×D4—1661no—
464C22×C4—1661no—
465C22×C4—1661no—
466C22×C4—1661no—
467C22×C4—1661no—
468C22×C4—1661no—
469C22×C4C2×C4×D8311yescharacteristic
470C22×C4C2×D33211yescharacteristic
471C22×C4#1305059011yescharacteristic
472SD16—3321no—
473SD16—3321no—
474D8—1662no—
475D8—1662no—
476M16—22no—
477M16—41no—
478M16—3322no—
479M16—3322no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—3322no—
483C2×C8—3322no—
484C2×C8—3322no—
485C2×C8—3322no—
486C2×C8—3322no—
487C2×C8—1661no—
488C2×C8—1661no—
489C2×C8—1661no—
490C2×C8—1661no—
491C2×C8C2×C4×D8311yescharacteristic
492C2×C8C2×C4×D8311yescharacteristic
493C2×C8C2×C4×D8311yescharacteristic
494C2×C8C2×C4×D8311yescharacteristic
495C2×C8C2×D33211yescharacteristic
496C2×C8C2×D33211yescharacteristic
497C2×C8C2×D33211yescharacteristic
498C2×C8C2×D33211yescharacteristic
499C4⋊C4—831no—
500C4⋊C4—831no—
501C4⋊C4—831no—
502C4⋊C4—831no—
503C4⋊C4—1661no—
504C4⋊C4—1661no—
505C4⋊C4—1661no—
506C22⋊C4—1661no—
507C22⋊C4—1661no—
508C22⋊C4—1661no—
509C22⋊C4—1661no—
510C22⋊C4—1661no—
511C22⋊C4—1661no—
512C22⋊C4—1661no—
513C42—1661no—
514C42—1661no—
515C42—1661no—
516C42C2×C4×D8311yescharacteristic
517C42C2×D33211yescharacteristic
518C42#1305059011yescharacteristic
519C42C23×D8311yescharacteristic
520C23—1661no—
521C23—1661no—
522C23—1661no—
523C23C4×D33211yescharacteristic
524Q8—3322no—
525Q8—1661no—
526Q8—1661no—
527D4—3322no—
528D4—3322no—
529D4—3322no—
530D4—3322no—
531D4—832no—
532D4—6641no—
533D4—1661no—
534D4—1661no—
535D4—1661no—
536D4—1661no—
537D4—1661no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—3322no—
544C2×C4—3321no—
545C2×C4—3321no—
546C2×C4—3321no—
547C2×C4—3321no—
548C2×C4—3321no—
549C2×C4—3321no—
550C2×C4—6641no—
551C2×C4—1661no—
552C2×C4—1661no—
553C2×C4—1661no—
554C2×C4—1661no—
555C2×C4—1661no—
556C2×C4C4×D33211yescharacteristic
557C2×C4C4×D33211yescharacteristic
558C2×C4C4×D33211yescharacteristic
559C2×C4C22×C4×D8311yescharacteristic
560C2×C4C22×D33211yescharacteristic
561C2×C4C2×#1305059011yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—21no—
568C8—21no—
569C8—41no—
570C8—41no—
571C8—3321no—
572C8—3321no—
573C8—3321no—
574C8—3321no—
575C8#1458182012yes—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—3321no—
580C22—3321no—
581C22—3321no—
582C22—3321no—
583C22—3321no—
584C22—3321no—
585C22—3321no—
586C22—3321no—
587C22—1662no—
588C22C2×C4×D33211yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—21no—
593C4—3321no—
594C4—3321no—
595C4—3321no—
596C4—3321no—
597C4—3321no—
598C4#131×D8311yescharacteristic
599C4#1912846611yescharacteristic
600C4C2×#1458182011yescharacteristic
601C4#1912850111yescharacteristic
602C2—41no—
603C2—3322no—
604C2—6641no—
605C2—6641no—
606C2#2491619111yescharacteristic
607C2C4×#1458182011yescharacteristic
608C2#2491638111yescharacteristic
subgroupG/H
centerC2×C4C22×D332
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1453C2
socleC22×C83C2×C4×D4
prime radical#24917524C2
cosocleC42×C83C24
hypercenter#1453D83
hypocenterC83#18007
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1453

Complements

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

NH ≅ G/Ntype
2. #24916478C2semidirect
3. #24916209C2semidirect
4. #24906367C2semidirect
5. #24906355C2semidirect
6. #24906329C2semidirect
7. #24906322C2semidirect
8. #24906301C2semidirect
9. #24906294C2semidirect
10. #24906288C2semidirect
11. C8×D664C2semidirect
12. #24906248C2semidirect
13. #24905933C2semidirect
14. #24905851C2semidirect
15. C83×#1453C2semidirect
245. D332#131semidirect
319. #1453D83semidirect
320. C83#18007semidirect

Maximal subgroups

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

subgroupindex
#249175242
#249164782
#249162092
#249063672
#249063552
#249063292
#249063222
#249063012
#249062942
#249062882
C8×D6642
#249062482
#249059332
#249058512
C83×#14532
#1800783