Finite Group Databasebeta

← #35477149

Subgroups — #35477149

Order 21248.

708 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24911896C211yesmaximal, characteristic
2#24910466C211yesmaximal, characteristic
3#24908873C211yesmaximal, characteristic, complemented
4#24908857C211yesmaximal, characteristic, complemented
5#24908667C211yesmaximal, characteristic
6#24908667C211yesmaximal, characteristic
7#24908222C211yesmaximal, characteristic, complemented
8#24908196C211yesmaximal, characteristic, complemented
9#24908056C211yesmaximal, characteristic, complemented
10#24908056C211yesmaximal, characteristic, complemented
11#24907720C211yesmaximal, characteristic, complemented
12#24907653C211yesmaximal, characteristic
13#24907554C211yesmaximal, characteristic
14C4×#14581717C211yesmaximal, characteristic, complemented
15C83×#1923C211yesmaximal, characteristic
16C2×#14581771C2211yescharacteristic
17C2×C4×Dic166C2211yescharacteristic
18C22×C4⋊Dic83C2211yescharacteristic
19C2×#14581726C2211yescharacteristic
20C2×#14581726C2211yescharacteristic
21C2×#14581726C2211yescharacteristic
22C2×#14581726C2211yescharacteristic
23C2×#14581717C2211yescharacteristic
24C2×#14581717C2211yescharacteristic
25C2×#14581717C2211yescharacteristic
26C2×#14581717C2211yescharacteristic
27#19127643—21no—
28#19127624—21no—
29#19127607C2211yescharacteristic
30#19127599C2211yescharacteristic
31#19127599C2211yescharacteristic
32#19127599C2211yescharacteristic
33#19127598—21no—
34#19127594—21no—
35#19127588—21no—
36#19127588—21no—
37#19127573—21no—
38#19127571C2211yescharacteristic
39#19127561C2211yescharacteristic
40#19127561C2211yescharacteristic
41C4×C4⋊Dic83C2211yescharacteristic
42C4×C4⋊Dic83C2211yescharacteristic
43C22⋊C4×Dic83—21no—
44#19127464C2211yescharacteristic
45#19127464C2211yescharacteristic
46#19127464C2211yescharacteristic
47#19127464C2211yescharacteristic
48#19127464C2211yescharacteristic
49#19127464C2211yescharacteristic
50#19127464C2211yescharacteristic
51#19127464C2211yescharacteristic
52C2×C4⋊C8×C83C2211yescharacteristic
53C2×C22⋊C8×C83C2211yescharacteristic
54C2×C22⋊C8×C83C2211yescharacteristic
55C2×C4×C8×C83C2211yescharacteristic
56C4×C22⋊C4×C83C2211yescharacteristic
57#336×C83C2211yescharacteristic
58#336×C83C2211yescharacteristic
59C22×Dic166C2311yescharacteristic
60C23×Dic83—21no—
61#14581771—22no—
62#14581771—22no—
63C4×Dic166—22no—
64C4×Dic166—41no—
65C2×C4⋊Dic83—22no—
66C2×C4⋊Dic83—21no—
67C2×C4⋊Dic83—21no—
68C2×C4⋊Dic83—21no—
69C2×C4⋊Dic83—41no—
70C2×C4⋊Dic83C2311yescharacteristic
71C2×C4⋊Dic83C2311yescharacteristic
72C2×C4⋊Dic83C2311yescharacteristic
73C2×C4⋊Dic83C2311yescharacteristic
74C2×C4⋊Dic83C2311yescharacteristic
75C2×C4⋊Dic83C2311yescharacteristic
76C2×C4⋊Dic83C2311yescharacteristic
77C2×Dic83⋊C4—21no—
78C2×Dic83⋊C4—21no—
79C2×Dic83⋊C4—21no—
80C2×Dic83⋊C4—21no—
81C2×Dic83⋊C4—21no—
82C2×C22⋊Dic83—21no—
83C2×C22⋊Dic83—21no—
84C2×C22⋊Dic83—21no—
85C2×C4×Dic83—21no—
86C2×C4×Dic83—21no—
87C2×C4×Dic83—21no—
88#14581726—22no—
89#14581726—22no—
90#14581726—22no—
91#14581726—41no—
92#14581717—22no—
93#14581717—22no—
94#14581717—22no—
95#14581717—41no—
96C83⋊#95—21no—
97C83⋊#95—21no—
98C83⋊#95—21no—
99C83⋊#95—21no—
100C83⋊#95—21no—
101C83⋊#95—21no—
102C83⋊#95—21no—
103C83⋊#95—21no—
104C83⋊#95—21no—
105C23×C4×C83C2311yescharacteristic
106C22×C8×C83C2311yescharacteristic
107C22×C8×C83C2311yescharacteristic
108C22×C8×C83C2311yescharacteristic
109C22×C8×C83C2311yescharacteristic
110C2×C22⋊C4×C83D411yescharacteristic
111C2×C22⋊C4×C83D411yescharacteristic
112C2×C42×C83C2311yescharacteristic
113C2×C42×C83C2311yescharacteristic
114C4⋊C8×C83—22no—
115C22⋊C8×C83—22no—
116C22⋊C8×C83—41no—
117C4×C8×C83—41no—
118#95×C83D411yescharacteristic
119#95×C83D411yescharacteristic
120C2×Dic166—21no—
121C2×Dic166—21no—
122C2×Dic166—21no—
123C2×Dic166—21no—
124C2×Dic166—21no—
125C2×Dic166#4112yes—
126C22×Dic83—21no—
127C22×Dic83—21no—
128C22×Dic83—21no—
129C22×Dic83—21no—
130C22×Dic83—21no—
131C22×Dic83—21no—
132C22×Dic83—21no—
133C22×Dic83—21no—
134C22×Dic83—42no—
135C22×Dic83—42no—
136C22×Dic83—81no—
137C4⋊Dic83—21no—
138C4⋊Dic83—21no—
139C4⋊Dic83—21no—
140C4⋊Dic83—21no—
141C4⋊Dic83—21no—
142C4⋊Dic83—21no—
143C4⋊Dic83—21no—
144C4⋊Dic83—21no—
145C4⋊Dic83—21no—
146C4⋊Dic83—21no—
147C4⋊Dic83—21no—
148C4⋊Dic83—21no—
149C4⋊Dic83—42no—
150C4⋊Dic83—81no—
151C4⋊Dic83—81no—
152C4⋊Dic83#4112yes—
153C4⋊Dic83#4112yes—
154Dic83⋊C4—24no—
155Dic83⋊C4—42no—
156Dic83⋊C4—42no—
157Dic83⋊C4—81no—
158Dic83⋊C4—81no—
159C22⋊Dic83—24no—
160C22⋊Dic83—81no—
161C22⋊Dic83—81no—
162C4×Dic83—42no—
163C4×Dic83—81no—
164C4×Dic83—81no—
165C24×C83C2×D411yescharacteristic
166C22×C4×C83—21no—
167C22×C4×C83—21no—
168C22×C4×C83—21no—
169C22×C4×C83—21no—
170C22×C4×C83—21no—
171C22×C4×C83—21no—
172C22×C4×C83C2×D411yescharacteristic
173C22×C4×C83C2×D411yescharacteristic
174C22×C4×C83C2×D411yescharacteristic
175C22×C4×C83C2×D411yescharacteristic
176C22×C4×C83C2×D411yescharacteristic
177C22×C4×C83C2411yescharacteristic
178C2×C8×C83—21no—
179C2×C8×C83—21no—
180C2×C8×C83—21no—
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×C83—21no—
188C2×C8×C83—21no—
189C2×C8×C83#4112yes—
190C22⋊C4×C83—41no—
191C22⋊C4×C83Q1614yes—
192C42×C83—21no—
193C42×C83—21no—
194C42×C83—21no—
195C42×C83—21no—
196C23×C83—21no—
197C23×C83—21no—
198C23×C83—21no—
199C23×C83—21no—
200C23×C83—21no—
201C23×C83—21no—
202C23×C83C2×Q1612yes—
203C23×C83C22×D411yescharacteristic
204C2×C4×C83—21no—
205C2×C4×C83—21no—
206C2×C4×C83—21no—
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—41no—
218C2×C4×C83—41no—
219C2×C4×C83—41no—
220C2×C4×C83—41no—
221C2×C4×C83C2×Q1612yes—
222C2×C4×C83C2×Q1612yes—
223C2×C4×C83C2×#4111yescharacteristic
224C2×C4×C83C2×#4111yescharacteristic
225C2×C4×C83C2×#4111yescharacteristic
226C2×C4×C83C2×#4111yescharacteristic
227C2×C4×C83H(5,𝔽2)11yescharacteristic
228C2×C4×C832−1+411yescharacteristic
229C2×Dic83—22no—
230C2×Dic83—22no—
231C2×Dic83—22no—
232C2×Dic83—41no—
233C2×Dic83—41no—
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—
252C2×Dic83—41no—
253C2×Dic83—84no—
254Dic166—22no—
255Dic166—22no—
256Dic166—41no—
257Dic166—41no—
258C8×C83—22no—
259C8×C83—41no—
260C8×C83—41no—
261C8×C83—41no—
262C22×C83—22no—
263C22×C83—22no—
264C22×C83—22no—
265C22×C83—41no—
266C22×C83—41no—
267C22×C83—41no—
268C22×C83—41no—
269C22×C83#52511yescharacteristic
270C22×C83#54611yescharacteristic
271C22×C83#54711yescharacteristic
272C22×C83C22×Q1611yescharacteristic
273C22×C83#57511yescharacteristic
274C22×C83#57611yescharacteristic
275C22×C83#57711yescharacteristic
276C4×C83—22no—
277C4×C83—22no—
278C4×C83—41no—
279C4×C83—41no—
280C4×C83—41no—
281C4×C83#52911yescharacteristic
282C4×C83#53911yescharacteristic
283C4×C83#55311yescharacteristic
284C4×C83#55611yescharacteristic
285Dic83—42no—
286Dic83—42no—
287Dic83—42no—
288Dic83—81no—
289Dic83—81no—
290Dic83—81no—
291Dic83—81no—
292Dic83—81no—
293#27036—831nomaximal, Sylow
294C2×C83—42no—
295C2×C83#246611yescharacteristic
296C2×C83#310411yescharacteristic
297C2×C83#311911yescharacteristic
298C2×C83#329911yescharacteristic
299C2×C83#331911yescharacteristic
300C2×C83#333811yescharacteristic
301C2×C83#335111yescharacteristic
302#2497—831no—
303#2360—831no—
304#2072—831no—
305#2068—831no—
306#2036—831no—
307#2036—831no—
308#1947—831no—
309#1942—831no—
310#1923D8311yescharacteristic
311#1921—831no—
312#1921—831no—
313#1863—831no—
314#1852—831no—
315#1824—831no—
316C4×#103—831no—
317C83#2703611yescharacteristic, complemented, Sylow
318C2×C22⋊Q8—831no—
319C2×C4×Q8—831no—
320C22×C4⋊C4—831no—
321C2×#107—831no—
322C2×#107—831no—
323C2×#107—831no—
324C2×#107—831no—
325C2×C4⋊C8C2×D8311yescharacteristic
326C2×#103—831no—
327C2×#103—831no—
328C2×#103—831no—
329C2×#103—831no—
330C2×C22⋊C8C2×D8311yescharacteristic
331C2×C22⋊C8C2×D8311yescharacteristic
332C2×C4×C8C2×D8311yescharacteristic
333#400—1661no—
334#396—1661no—
335#391—831no—
336#389—831no—
337#389—831no—
338#389—831no—
339#389—1661no—
340#388—1661no—
341#387—1661no—
342#387—1661no—
343#385—1661no—
344#384—831no—
345#380—831no—
346#380—831no—
347C4×C4⋊C4—831no—
348C4×C4⋊C4—831no—
349C4×C22⋊C4—1661no—
350C4×C22⋊C4C2×D8311yescharacteristic
351#340—831no—
352#340—831no—
353#340—831no—
354#340—831no—
355#340—831no—
356#340—831no—
357#340—831no—
358#340—831no—
359#336C2×D8311yescharacteristic
360#336C2×D8311yescharacteristic
361C22×Q8—831no—
362C23×C4—1661no—
363C23×C4C22×D8311yescharacteristic
364C22×C8C22×D8311yescharacteristic
365C22×C8C22×D8311yescharacteristic
366C22×C8C22×D8311yescharacteristic
367C22×C8C22×D8311yescharacteristic
368C22⋊Q8—1662no—
369C22⋊Q8—1662no—
370C4×Q8—3321no—
371C4×Q8—1662no—
372C2×C4⋊C4—3321no—
373C2×C4⋊C4—831no—
374C2×C4⋊C4—831no—
375C2×C4⋊C4—831no—
376C2×C4⋊C4—831no—
377C2×C4⋊C4—831no—
378C2×C4⋊C4—831no—
379C2×C4⋊C4—831no—
380C2×C4⋊C4—1661no—
381C2×C4⋊C4—1661no—
382C2×C4⋊C4—1661no—
383C2×C4⋊C4—1662no—
384C2×C4⋊C4—1661no—
385C2×C4⋊C4—1661no—
386C2×C4⋊C4—1661no—
387C2×C4⋊C4—1661no—
388C2×C4⋊C4—1661no—
389C2×C22⋊C4—1661no—
390C2×C22⋊C4—1661no—
391C2×C22⋊C4—1661no—
392C2×C22⋊C4D33211yescharacteristic
393C2×C22⋊C4D33211yescharacteristic
394C2×C42—1661no—
395C2×C42—1661no—
396C2×C42—1661no—
397C2×C42C22×D8311yescharacteristic
398C2×C42C22×D8311yescharacteristic
399#107—3321no—
400#107—1662no—
401#107—1662no—
402#107—1662no—
403C4⋊C8—22no—
404#103—3321no—
405#103—1662no—
406#103—1662no—
407#103—1662no—
408C22⋊C8—22no—
409C22⋊C8—41no—
410C4×C8—41no—
411#95—1661no—
412#95—1661no—
413#95—1661no—
414#95—1661no—
415#95—1661no—
416#95—1661no—
417#95—1661no—
418#95—1661no—
419#95—1661no—
420#95D33211yescharacteristic
421#95D33211yescharacteristic
422C24C2×D33211yescharacteristic
423C2×Q8—832no—
424C2×Q8—1661no—
425C2×Q8—1661no—
426C2×Q8—1661no—
427C2×Q8—1661no—
428C2×Q8—1661no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—3322no—
436C22×C4—3322no—
437C22×C4—6641no—
438C22×C4—1661no—
439C22×C4—1661no—
440C22×C4—1661no—
441C22×C4—1661no—
442C22×C4—1661no—
443C22×C4—1661no—
444C22×C4—1661no—
445C22×C4—1661no—
446C22×C4C2×D33211yescharacteristic
447C22×C4C2×D33211yescharacteristic
448C22×C4C2×D33211yescharacteristic
449C22×C4C2×D33211yescharacteristic
450C22×C4C2×D33211yescharacteristic
451C22×C4C23×D8311yescharacteristic
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8#1305058912yes—
464C4⋊C4—3322no—
465C4⋊C4—3322no—
466C4⋊C4—3322no—
467C4⋊C4—832no—
468C4⋊C4—832no—
469C4⋊C4—6641no—
470C4⋊C4—6641no—
471C4⋊C4—6641no—
472C4⋊C4—6641no—
473C4⋊C4—1664no—
474C4⋊C4—1661no—
475C4⋊C4—1661no—
476C4⋊C4—1661no—
477C4⋊C4—1661no—
478C4⋊C4—1661no—
479C4⋊C4—1661no—
480C4⋊C4—1661no—
481C4⋊C4—1661no—
482C4⋊C4—1661no—
483C4⋊C4—1661no—
484C4⋊C4—1661no—
485C4⋊C4—1661no—
486C22⋊C4—41no—
487C22⋊C4—6641no—
488C22⋊C4—6641no—
489C22⋊C4—1664no—
490C22⋊C4Dic33214yes—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—3322no—
496C42—6641no—
497C42—6641no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23C2×Dic33212yes—
505C23C22×D33211yescharacteristic
506Q8—3321no—
507Q8—3321no—
508Q8—1662no—
509Q8—1662no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—3321no—
528C2×C4—3321no—
529C2×C4—3321no—
530C2×C4—3321no—
531C2×C4—3321no—
532C2×C4—3321no—
533C2×C4—3321no—
534C2×C4—3321no—
535C2×C4—3321no—
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—6644no—
549C2×C4—1662no—
550C2×C4—1662no—
551C2×C4—1662no—
552C2×C4C2×Dic33212yes—
553C2×C4C2×Dic33212yes—
554C2×C4#41×D8311yescharacteristic
555C2×C4#41×D8311yescharacteristic
556C2×C4#41×D8311yescharacteristic
557C2×C4C2×#1305058911yescharacteristic
558C2×C4#1458183711yescharacteristic
559C2×C4#1458183911yescharacteristic
560C8—22no—
561C8—41no—
562C8—41no—
563C8—41no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22#1912821311yescharacteristic
572C22#1912834611yescharacteristic
573C22#1912835511yescharacteristic
574C22C22×Dic33211yescharacteristic
575C22#1912850111yescharacteristic
576C22#1912850611yescharacteristic
577C22#1912851311yescharacteristic
578C4—22no—
579C4—22no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—3322no—
584C4—3322no—
585C4—3322no—
586C4—6641no—
587C4—6641no—
588C4—6641no—
589C4—6641no—
590C4—6641no—
591C4#1912823011yescharacteristic
592C4#1912829411yescharacteristic
593C4#1912839411yescharacteristic
594C4#1912841811yescharacteristic
595C2—42no—
596C2#2491149711yescharacteristic
597C2#2491750311yescharacteristic
598C2#2491766411yescharacteristic
599C2#2491934011yescharacteristic
600C2#2491962111yescharacteristic
601C2#2491985611yescharacteristic
602C2#2492002511yescharacteristic
subgroupG/H
centerC23C22×D332
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#1923C2
socleC23×C83C22×D4
prime radicalC24×C83C2×D4
hypercenter#1923D83
hypocenterC83#27036
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
3. #24908873C2semidirect
4. #24908857C2semidirect
7. #24908222C2semidirect
8. #24908196C2semidirect
9. #24908056C2semidirect
10. #24908056C2semidirect
11. #24907720C2semidirect
14. C4×#14581717C2semidirect
317. C83#27036semidirect

Maximal subgroups

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

subgroupindex
#249118962
#249104662
#249088732
#249088572
#249086672
#249082222
#249081962
#249080562
#249077202
#249076532
#249075542
C4×#145817172
C83×#19232
#2703683