Finite Group Databasebeta

← #35408780

Subgroups — #35408780

Order 21248.

814 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
1C2×#19127803C211yesmaximal, characteristic
2#24910115C211yesmaximal, characteristic, complemented
3#24910107C211yesmaximal, characteristic
4#24908344C211yesmaximal, characteristic
5#24908317C211yesmaximal, characteristic
6#24908201C211yesmaximal, characteristic, complemented
7#24908196C211yesmaximal, characteristic, complemented
8#24908160C211yesmaximal, characteristic
9#24908153C211yesmaximal, characteristic, complemented
10#24908146C211yesmaximal, characteristic
11#24908139C211yesmaximal, characteristic, complemented
12#24907360C211yesmaximal, characteristic, complemented
13C4×#14581717C211yesmaximal, characteristic, complemented
14C4×#14581714C211yesmaximal, characteristic
15C83×#1726C211yesmaximal, characteristic, complemented
16C22×#13050579C2211yescharacteristic
17C2×C4×Dic166C2211yescharacteristic
18C2×C4×D332C2211yescharacteristic
19#19127803C418yescomplemented
20C2×#14581726C2211yescharacteristic
21C2×#14581726C2211yescharacteristic
22C2×#14581724C2211yescharacteristic
23C2×#14581717C2211yescharacteristic
24C2×#14581717C2211yescharacteristic
25C2×#14581717C2211yescharacteristic
26C2×#14581714C2211yescharacteristic
27C2×#14581714C2211yescharacteristic
28C2×#14581714C2211yescharacteristic
29#19127607C2211yescharacteristic
30#19127607C2211yescharacteristic
31#19127603C2211yescharacteristic
32#19127603C2211yescharacteristic
33#19127599C2211yescharacteristic
34#19127599C2211yescharacteristic
35#19127599C2211yescharacteristic
36#19127599C2211yescharacteristic
37#19127590—21no—
38#19127590—21no—
39#19127583—21no—
40#19127583—21no—
41#19127568—21no—
42#19127565—21no—
43#19127563—21no—
44#19127560—21no—
45C4×C4⋊Dic83C2211yescharacteristic
46C4×C4⋊Dic83C2211yescharacteristic
47#19127464C2211yescharacteristic
48#19127464C2211yescharacteristic
49#19127464C2211yescharacteristic
50#19127464C2211yescharacteristic
51#19127464C2211yescharacteristic
52#19127464C2211yescharacteristic
53C2×#97×C83C2211yescharacteristic
54C2×#97×C83C2211yescharacteristic
55C2×#97×C83C2211yescharacteristic
56C2×C4×C8×C83C2211yescharacteristic
57C2×C4×C8×C83C2211yescharacteristic
58C2×C4×C8×C83C2211yescharacteristic
59#376×C83C2211yescharacteristic
60C22×Dic166C2311yescharacteristic
61C22×D332C2311yescharacteristic
62C22×C4×D83—21no—
63C2×#13050579—22no—
64C2×#13050579—22no—
65C2×#13050579C2×C414yes—
66C4×Dic166—22no—
67C4×Dic166C2×C414yes—
68C4×D332—22no—
69C4×D332C2×C414yes—
70C2×C4⋊Dic83C2311yescharacteristic
71C2×C4⋊Dic83C2311yescharacteristic
72C2×C4⋊Dic83C2311yescharacteristic
73C2×C4⋊Dic83C2311yescharacteristic
74C2×C4⋊Dic83C2311yescharacteristic
75C2×C4⋊Dic83C2311yescharacteristic
76C2×Dic83⋊C4—21no—
77C2×Dic83⋊C4—21no—
78C2×Dic83⋊C4—21no—
79C2×Dic83⋊C4—21no—
80C2×Dic83⋊C4—21no—
81C2×(C2×D83)⋊C4—21no—
82C2×(C2×D83)⋊C4—21no—
83C2×(C2×D83)⋊C4—21no—
84C2×(C2×D83)⋊C4—21no—
85C2×(C2×D83)⋊C4—21no—
86C2×C4×Dic83—21no—
87C2×C4×Dic83—21no—
88C2×C4×Dic83—21no—
89#14581726—22no—
90#14581726C2×C414yes—
91#14581724—22no—
92#14581717—22no—
93#14581717—22no—
94#14581717C2×C414yes—
95#14581714—22no—
96#14581714—22no—
97#14581714C2×C414yes—
98C83⋊#95—21no—
99C83⋊#95—21no—
100C83⋊#95—21no—
101C83⋊#95—21no—
102C83⋊#95—21no—
103C83⋊#95—21no—
104C83⋊#95—21no—
105C83⋊#95—21no—
106C83⋊#95—21no—
107C83⋊#95—21no—
108C22×C8×C83C2311yescharacteristic
109C22×C8×C83C2311yescharacteristic
110C22×C8×C83C2311yescharacteristic
111C22×C8×C83C2311yescharacteristic
112C2×C42×C83C2311yescharacteristic
113C2×C42×C83C2311yescharacteristic
114C2×C42×C83C2311yescharacteristic
115#97×C83—22no—
116#97×C83—22no—
117#97×C83C2×C414yes—
118C4×C8×C83—22no—
119C4×C8×C83—22no—
120C4×C8×C83—22no—
121#95×C83D411yescharacteristic
122#95×C83D411yescharacteristic
123#95×C83D411yescharacteristic
124#95×C83D411yescharacteristic
125C23×D83—21no—
126C2×Dic166—21no—
127C2×Dic166—21no—
128C2×Dic166—21no—
129C2×Dic166—21no—
130C2×Dic166—21no—
131C2×Dic166C22×C412yes—
132C2×D332—21no—
133C2×D332—21no—
134C2×D332—21no—
135C2×D332—21no—
136C2×D332—21no—
137C2×D332C22×C412yes—
138C22×Dic83—21no—
139C22×Dic83—21no—
140C22×Dic83—21no—
141C22×Dic83—21no—
142C22×Dic83—21no—
143C22×Dic83—21no—
144C22×Dic83—21no—
145C2×C4×D83—24no—
146C2×C4×D83—81no—
147C2×C4×D83—81no—
148#13050579—28no—
149C4⋊Dic83—21no—
150C4⋊Dic83—21no—
151C4⋊Dic83—21no—
152C4⋊Dic83—21no—
153C4⋊Dic83—21no—
154C4⋊Dic83—21no—
155C4⋊Dic83—21no—
156C4⋊Dic83—21no—
157C4⋊Dic83—21no—
158C4⋊Dic83—21no—
159C4⋊Dic83C22×C412yes—
160C4⋊Dic83C22×C412yes—
161Dic83⋊C4—24no—
162Dic83⋊C4—81no—
163Dic83⋊C4—81no—
164Dic83⋊C4—81no—
165Dic83⋊C4—81no—
166(C2×D83)⋊C4—24no—
167(C2×D83)⋊C4—81no—
168(C2×D83)⋊C4—81no—
169(C2×D83)⋊C4—81no—
170(C2×D83)⋊C4—81no—
171C4×Dic83—24no—
172C4×Dic83—81no—
173C4×Dic83—81no—
174C22×C4×C83C2×D411yescharacteristic
175C22×C4×C83C2×D411yescharacteristic
176C22×C4×C83C2×D411yescharacteristic
177C22×C4×C83C2×D411yescharacteristic
178C22×C4×C83C2×D411yescharacteristic
179C22×C4×C83C2×D411yescharacteristic
180C22×C4×C83C2411yescharacteristic
181C2×C8×C83—21no—
182C2×C8×C83—21no—
183C2×C8×C83—21no—
184C2×C8×C83—21no—
185C2×C8×C83—21no—
186C2×C8×C83—21no—
187C2×C8×C83C22×C412yes—
188C2×C8×C83C22×C412yes—
189C2×C8×C83#4112yes—
190C2×C8×C83#4112yes—
191C2×C8×C83#4112yes—
192C2×C8×C83#4112yes—
193C42×C83—21no—
194C42×C83—21no—
195C42×C83—21no—
196C42×C83—21no—
197C42×C83C22×C412yes—
198C42×C83#4112yes—
199C23×C83C22×D411yescharacteristic
200C22×D83—22no—
201C22×D83—41no—
202C22×D83—41no—
203C22×D83—41no—
204C22×D83—41no—
205C22×D83—41no—
206C22×D83—41no—
207C2×C4×C83—21no—
208C2×C4×C83—21no—
209C2×C4×C83—21no—
210C2×C4×C83—21no—
211C2×C4×C83—21no—
212C2×C4×C83—21no—
213C2×C4×C83—21no—
214C2×C4×C83—21no—
215C2×C4×C83—21no—
216C2×C4×C83—21no—
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×C83C4×D412yes—
224C2×C4×C83C4×D412yes—
225C2×C4×C83C23×C411yescharacteristic
226C2×C4×C83C2×#4111yescharacteristic
227C2×C4×C83C2×#4111yescharacteristic
228C2×C4×C83C2×#4111yescharacteristic
229C2×C4×C83C2×#4111yescharacteristic
230C2×C4×C83C2×#4111yescharacteristic
231C2×Dic83—22no—
232C2×Dic83—22no—
233C2×Dic83—22no—
234C2×Dic83—41no—
235C2×Dic83—41no—
236C2×Dic83—41no—
237C2×Dic83—41no—
238C2×Dic83—41no—
239C2×Dic83—41no—
240C2×Dic83—41no—
241C2×Dic83—41no—
242C2×Dic83—41no—
243C2×Dic83—41no—
244C2×Dic83—41no—
245C2×Dic83—41no—
246C2×Dic83—41no—
247C2×Dic83—41no—
248C2×Dic83—41no—
249C2×Dic83—41no—
250C2×Dic83—41no—
251C2×Dic83—41no—
252D332—22no—
253D332—22no—
254D332—41no—
255D332—41no—
256C4×D83—84no—
257Dic166—22no—
258Dic166—22no—
259Dic166—41no—
260Dic166—41no—
261C8×C83—22no—
262C8×C83—22no—
263C8×C83—22no—
264C8×C83#11714yes—
265C22×C83C2×C4×D411yescharacteristic
266C22×C83#53211yescharacteristic
267C22×C83#53211yescharacteristic
268C22×C83#57611yescharacteristic
269C22×C83#57711yescharacteristic
270C22×C83#57711yescharacteristic
271C22×C83#57811yescharacteristic
272C2×D83—42no—
273C2×D83—42no—
274C2×D83—42no—
275C2×D83—81no—
276C2×D83—81no—
277C2×D83—81no—
278C2×D83—81no—
279C4×C83—22no—
280C4×C83—22no—
281C4×C83—41no—
282C4×C83—41no—
283C4×C83—41no—
284C4×C83—41no—
285C4×C83C2×#11711yescharacteristic
286C4×C83C4×#4111yescharacteristic
287C4×C83#52911yescharacteristic
288C4×C83#52911yescharacteristic
289Dic83—42no—
290Dic83—42no—
291Dic83—42no—
292Dic83—81no—
293Dic83—81no—
294Dic83—81no—
295Dic83—81no—
296#21291—831nomaximal, Sylow
297C2×C83#229311yescharacteristic
298C2×C83#294611yescharacteristic
299C2×C83#294711yescharacteristic
300C2×C83#317411yescharacteristic
301C2×C83#317511yescharacteristic
302C2×C83#317811yescharacteristic
303C2×C83#317911yescharacteristic
304D83—82no—
305C2×#440—831no—
306#2320—831no—
307#2319—831no—
308#1973—831no—
309#1968—831no—
310#1943—831no—
311#1942—831no—
312#1936—831no—
313#1935—831no—
314#1934—831no—
315#1933—831no—
316#1776—831no—
317C4×#103—831no—
318C4×#102—831no—
319#1726D8311yescharacteristic, complemented
320C83#2129111yescharacteristic, complemented, Sylow
321C22×SD16—831no—
322C2×C4×Q8—831no—
323C2×C4×D4—831no—
324#440—838no—
325C2×#107—831no—
326C2×#107—831no—
327C2×#106—831no—
328C2×#103—831no—
329C2×#103—831no—
330C2×#103—831no—
331C2×#102—831no—
332C2×#102—831no—
333C2×#102—831no—
334C2×#97C2×D8311yescharacteristic
335C2×#97C2×D8311yescharacteristic
336C2×#97C2×D8311yescharacteristic
337C2×C4×C8C2×D8311yescharacteristic
338C2×C4×C8C2×D8311yescharacteristic
339C2×C4×C8C2×D8311yescharacteristic
340#391—831no—
341#391—831no—
342#390—831no—
343#390—831no—
344#389—831no—
345#389—831no—
346#389—831no—
347#389—831no—
348#388—1661no—
349#388—1661no—
350#387—1661no—
351#387—1661no—
352#383—1661no—
353#382—1661no—
354#381—1661no—
355#380—1661no—
356C4×C4⋊C4—831no—
357C4×C4⋊C4—831no—
358#376C2×D8311yescharacteristic
359#340—831no—
360#340—831no—
361#340—831no—
362#340—831no—
363#340—831no—
364#340—831no—
365C22×Q8—831no—
366C22×D4—831no—
367C23×C4—1661no—
368C2×SD16—834no—
369C2×SD16—1662no—
370C2×SD16—1662no—
371C22×C8C22×D8311yescharacteristic
372C22×C8C22×D8311yescharacteristic
373C22×C8C22×D8311yescharacteristic
374C22×C8C22×D8311yescharacteristic
375C4×Q8—834no—
376C4×Q8—1662no—
377C4×D4—834no—
378C4×D4—1662no—
379C2×C4⋊C4—831no—
380C2×C4⋊C4—831no—
381C2×C4⋊C4—831no—
382C2×C4⋊C4—831no—
383C2×C4⋊C4—831no—
384C2×C4⋊C4—831no—
385C2×C4⋊C4—1661no—
386C2×C4⋊C4—1661no—
387C2×C4⋊C4—1661no—
388C2×C4⋊C4—1661no—
389C2×C4⋊C4—1661no—
390C2×C22⋊C4—1661no—
391C2×C22⋊C4—1661no—
392C2×C22⋊C4—1661no—
393C2×C22⋊C4—1661no—
394C2×C22⋊C4—1661no—
395C2×C42—1661no—
396C2×C42—1661no—
397C2×C42—1661no—
398C2×C42C22×D8311yescharacteristic
399C2×C42C22×D8311yescharacteristic
400C2×C42C22×D8311yescharacteristic
401#107—834no—
402#107—1662no—
403#106—1662no—
404#103—834no—
405#103—1662no—
406#103—1662no—
407#102—834no—
408#102—1662no—
409#102—1662no—
410#97—22no—
411#97—22no—
412#97C4×D8314yes—
413C4×C8—22no—
414C4×C8—22no—
415C4×C8—22no—
416#95—1661no—
417#95—1661no—
418#95—1661no—
419#95—1661no—
420#95—1661no—
421#95—1661no—
422#95—1661no—
423#95—1661no—
424#95—1661no—
425#95—1661no—
426#95D33211yescharacteristic
427#95D33211yescharacteristic
428#95D33211yescharacteristic
429#95D33211yescharacteristic
430C24—1661no—
431C2×Q8—832no—
432C2×Q8—1661no—
433C2×Q8—1661no—
434C2×Q8—1661no—
435C2×Q8—1661no—
436C2×Q8—1661no—
437C2×D4—832no—
438C2×D4—1661no—
439C2×D4—1661no—
440C2×D4—1661no—
441C2×D4—1661no—
442C2×D4—1661no—
443C22×C4—6641no—
444C22×C4—6641no—
445C22×C4—1661no—
446C22×C4—1661no—
447C22×C4—1661no—
448C22×C4—1661no—
449C22×C4—1661no—
450C22×C4—1661no—
451C22×C4—1661no—
452C22×C4—1664no—
453C22×C4C2×D33211yescharacteristic
454C22×C4C2×D33211yescharacteristic
455C22×C4C2×D33211yescharacteristic
456C22×C4C2×D33211yescharacteristic
457C22×C4C2×D33211yescharacteristic
458C22×C4C2×D33211yescharacteristic
459C22×C4C23×D8311yescharacteristic
460SD16—1668no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8C2×C4×D8312yes—
468C2×C8C2×C4×D8312yes—
469C2×C8#1305059012yes—
470C2×C8#1305059012yes—
471C2×C8#1305059012yes—
472C2×C8#1305059012yes—
473C4⋊C4—832no—
474C4⋊C4—832no—
475C4⋊C4—6641no—
476C4⋊C4—6641no—
477C4⋊C4—6641no—
478C4⋊C4—6641no—
479C4⋊C4—1661no—
480C4⋊C4—1661no—
481C4⋊C4—1661no—
482C4⋊C4—1661no—
483C4⋊C4—1661no—
484C4⋊C4—1661no—
485C4⋊C4—1661no—
486C4⋊C4—1661no—
487C4⋊C4—1661no—
488C4⋊C4—1661no—
489C4⋊C4—1664no—
490C22⋊C4—6641no—
491C22⋊C4—6641no—
492C22⋊C4—6641no—
493C22⋊C4—6641no—
494C22⋊C4—1664no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—6641no—
500C42—6641no—
501C42—1664no—
502C42C2×C4×D8312yes—
503C42#1305059012yes—
504C23—3321no—
505C23—3321no—
506C23—3321no—
507C23—3321no—
508C23—3321no—
509C23—3321no—
510C23—1662no—
511C23C22×D33211yescharacteristic
512Q8—3321no—
513Q8—3321no—
514Q8—1662no—
515Q8—1662no—
516D4—3321no—
517D4—3321no—
518D4—1662no—
519D4—1662no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—3321no—
537C2×C4—3321no—
538C2×C4—3321no—
539C2×C4—3321no—
540C2×C4—3321no—
541C2×C4—3321no—
542C2×C4—3321no—
543C2×C4—3321no—
544C2×C4—3321no—
545C2×C4—3321no—
546C2×C4—3321no—
547C2×C4—3321no—
548C2×C4—3321no—
549C2×C4—3321no—
550C2×C4—3321no—
551C2×C4—3321no—
552C2×C4—3321no—
553C2×C4—3321no—
554C2×C4—6644no—
555C2×C4—1662no—
556C2×C4—1662no—
557C2×C4—1662no—
558C2×C4C4×D33212yes—
559C2×C4C4×D33212yes—
560C2×C4C22×C4×D8311yescharacteristic
561C2×C4C2×#1305059011yescharacteristic
562C2×C4C2×#1305059011yescharacteristic
563C2×C4C2×#1305059011yescharacteristic
564C2×C4C2×#1305059011yescharacteristic
565C2×C4C2×#1305059011yescharacteristic
566C8—22no—
567C8—22no—
568C8—22no—
569C8#1458174914yes—
570C22—3322no—
571C22—3322no—
572C22—3322no—
573C22—6641no—
574C22—6641no—
575C22—6641no—
576C22—6641no—
577C22C2×C4×D33211yescharacteristic
578C22#1912825111yescharacteristic
579C22#1912825111yescharacteristic
580C22#1912850611yescharacteristic
581C22#1912851311yescharacteristic
582C22#1912851311yescharacteristic
583C22#1912851811yescharacteristic
584C4—22no—
585C4—22no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—3322no—
591C4—3322no—
592C4—3322no—
593C4—6641no—
594C4—6641no—
595C4—6641no—
596C4—6641no—
597C4C2×#1458174911yescharacteristic
598C4C4×#1305059011yescharacteristic
599C4#1912823511yescharacteristic
600C4#1912823511yescharacteristic
601C2—6642no—
602C2#2490992711yescharacteristic
603C2#2491629711yescharacteristic
604C2#2491630811yescharacteristic
605C2#2491809111yescharacteristic
606C2#2491810211yescharacteristic
607C2#2491813111yescharacteristic
608C2#2491814611yescharacteristic
subgroupG/H
centerC23C22×D332
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#1726C2
socleC23×C83C22×D4
prime radicalC22×D332C23
cosocleC22×C4×C83C24
hypercenter#1726D83
hypocenterC83#21291
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ #376 ◁ #1726

Complements

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

NH ≅ G/Ntype
2. #24910115C2semidirect
6. #24908201C2semidirect
7. #24908196C2semidirect
9. #24908153C2semidirect
11. #24908139C2semidirect
12. #24907360C2semidirect
13. C4×#14581717C2semidirect
15. C83×#1726C2semidirect
19. #19127803C4semidirect
319. #1726D83semidirect
320. C83#21291semidirect

Maximal subgroups

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

subgroupindex
C2×#191278032
#249101152
#249101072
#249083442
#249083172
#249082012
#249081962
#249081602
#249081532
#249081462
#249081392
#249073602
C4×#145817172
C4×#145817142
C83×#17262
#2129183