Finite Group Databasebeta

← #35466794

Subgroups — #35466794

Order 21248.

674 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#24912951C211yesmaximal, characteristic
2#24909014C211yesmaximal, characteristic, complemented
3#24908987C211yesmaximal, characteristic
4#24908882C211yesmaximal, characteristic, complemented
5#24908877C211yesmaximal, characteristic
6#24908404C211yesmaximal, characteristic, complemented
7#24908395C211yesmaximal, characteristic
8#24908277C211yesmaximal, characteristic
9#24908224C211yesmaximal, characteristic, complemented
10#24908097C211yesmaximal, characteristic, complemented
11#24908097C211yesmaximal, characteristic, complemented
12#24908090C211yesmaximal, characteristic
13#24908090C211yesmaximal, characteristic
14#24907361C211yesmaximal, characteristic, complemented
15C83×#2355C211yesmaximal, characteristic, complemented
16C2×#14581780C2211yescharacteristic
17C2×#14581725C2211yescharacteristic
18C2×#14581723C2211yescharacteristic
19C2×#14581723C2211yescharacteristic
20C2×#14581723C2211yescharacteristic
21C2×C4⋊(C83⋊C8)C2211yescharacteristic
22C2×#14581715C2211yescharacteristic
23C2×#14581715C2211yescharacteristic
24C2×#14581715C2211yescharacteristic
25C2×#14581715C2211yescharacteristic
26C2×#14581712C2211yescharacteristic
27C2×#14581712C2211yescharacteristic
28C2×#14581712C2211yescharacteristic
29C2×#14581712C2211yescharacteristic
30C2×#14581703C2211yescharacteristic
31#19127627—21no—
32#19127612—21no—
33#19127607C2211yescharacteristic
34#19127607C2211yescharacteristic
35#19127603C2211yescharacteristic
36#19127603C2211yescharacteristic
37#19127591—21no—
38#19127591—21no—
39C4×C4⋊Dic83C2211yescharacteristic
40#19127463C2211yescharacteristic
41#19127463C2211yescharacteristic
42#19127463C2211yescharacteristic
43#19127463C2211yescharacteristic
44#19127456C2211yescharacteristic
45#19127456C2211yescharacteristic
46#19127456C2211yescharacteristic
47#19127456C2211yescharacteristic
48C2×C4×Q8×C83C2211yescharacteristic
49#391×C83—21no—
50#387×C83—21no—
51#387×C83—21no—
52#384×C83C2211yescharacteristic
53#382×C83C2211yescharacteristic
54#382×C83C2211yescharacteristic
55C4×C4⋊C4×C83—21no—
56C4×C4⋊C4×C83C2211yescharacteristic
57C4×C4⋊C4×C83C2211yescharacteristic
58C4×C4⋊C4×C83C2211yescharacteristic
59C22×Dic166C2311yescharacteristic
60C22×D332C2311yescharacteristic
61C22×C83⋊C8C2311yescharacteristic
62C22×C83⋊C8C2311yescharacteristic
63C22×C83⋊C8C2311yescharacteristic
64C22×C83⋊C8C2311yescharacteristic
65#14581780—22no—
66#14581780—22no—
67C2×C4⋊Dic83C2311yescharacteristic
68C2×C4⋊Dic83C2311yescharacteristic
69C2×(C2×D83)⋊C4—21no—
70C2×(C2×D83)⋊C4—21no—
71C2×(C2×D83)⋊C4—21no—
72C2×(C2×D83)⋊C4—21no—
73C2×(C2×D83)⋊C4—21no—
74C2×(C2×D83)⋊C4—21no—
75C2×C4×Dic83—21no—
76#14581725—22no—
77#14581723—22no—
78#14581723—41no—
79#14581723—41no—
80C4⋊(C83⋊C8)—22no—
81#14581715—22no—
82#14581715—22no—
83#14581715—41no—
84#14581715—41no—
85#14581712—22no—
86#14581712—22no—
87#14581712—41no—
88#14581712—41no—
89#14581703—22no—
90C83⋊#95—21no—
91C83⋊#95—21no—
92C83⋊#95—21no—
93C83⋊#95—21no—
94C83⋊#95—21no—
95C22×Q8×C83D411yescharacteristic
96C4×Q8×C83—22no—
97C4×Q8×C83—22no—
98C2×C4⋊C4×C83—21no—
99C2×C4⋊C4×C83—21no—
100C2×C4⋊C4×C83D411yescharacteristic
101C2×C4⋊C4×C83D411yescharacteristic
102C2×C4⋊C4×C83D411yescharacteristic
103C2×C4⋊C4×C83C2311yescharacteristic
104C2×C4⋊C4×C83C2311yescharacteristic
105C2×C4⋊C4×C83C2311yescharacteristic
106C2×C4⋊C4×C83C2311yescharacteristic
107C2×C42×C83—21no—
108C2×C42×C83—21no—
109C2×C42×C83—21no—
110C2×C42×C83C2311yescharacteristic
111C2×C42×C83C2311yescharacteristic
112C2×C42×C83C2311yescharacteristic
113#95×C83—21no—
114#95×C83—21no—
115#95×C83—21no—
116#95×C83—21no—
117#95×C83—21no—
118#95×C83—21no—
119#95×C83—21no—
120C23×D83—21no—
121C2×Dic166—21no—
122C2×Dic166—21no—
123C2×Dic166—21no—
124C2×Dic166—21no—
125C2×Dic166—21no—
126C2×Dic166—21no—
127C2×D332—21no—
128C2×D332—21no—
129C2×D332—21no—
130C2×D332—21no—
131C2×D332—21no—
132C2×D332—21no—
133C22×Dic83—21no—
134C22×Dic83—21no—
135C22×Dic83—21no—
136C2×C83⋊C8—21no—
137C2×C83⋊C8—21no—
138C2×C83⋊C8—21no—
139C2×C83⋊C8—21no—
140C2×C83⋊C8—21no—
141C2×C83⋊C8—21no—
142C2×C83⋊C8—21no—
143C2×C83⋊C8—21no—
144C2×C83⋊C8—21no—
145C2×C83⋊C8—21no—
146C2×C83⋊C8—21no—
147C2×C83⋊C8#4112yes—
148C4⋊Dic83—21no—
149C4⋊Dic83—21no—
150C4⋊Dic83—21no—
151C4⋊Dic83—21no—
152(C2×D83)⋊C4—42no—
153(C2×D83)⋊C4—42no—
154(C2×D83)⋊C4—42no—
155(C2×D83)⋊C4—42no—
156(C2×D83)⋊C4—81no—
157(C2×D83)⋊C4—81no—
158C4×Dic83—81no—
159C2×Q8×C83—22no—
160C2×Q8×C83—41no—
161C2×Q8×C83—41no—
162C22×C4×C83—21no—
163C22×C4×C83—21no—
164C22×C4×C83—21no—
165C22×C4×C83—21no—
166C22×C4×C83C2×D411yescharacteristic
167C22×C4×C83C2×D411yescharacteristic
168C22×C4×C83C2×D411yescharacteristic
169C22×C4×C83C2×D411yescharacteristic
170C22×C4×C83C2×D411yescharacteristic
171C22×C4×C83C2×D411yescharacteristic
172C22×C4×C83C2411yescharacteristic
173C4⋊C4×C83—22no—
174C4⋊C4×C83—22no—
175C4⋊C4×C83—22no—
176C4⋊C4×C83—21no—
177C4⋊C4×C83—21no—
178C4⋊C4×C83—21no—
179C4⋊C4×C83—21no—
180C4⋊C4×C83—21no—
181C4⋊C4×C83—21no—
182C4⋊C4×C83—21no—
183C4⋊C4×C83—42no—
184C4⋊C4×C83—81no—
185C4⋊C4×C83#4112yes—
186C42×C83—21no—
187C42×C83—21no—
188C42×C83—21no—
189C42×C83—21no—
190C42×C83—42no—
191C42×C83—81no—
192C42×C83—81no—
193C42×C83#4112yes—
194C42×C83#4112yes—
195C23×C83C22×D411yescharacteristic
196C22×D83—41no—
197C22×D83—41no—
198C22×D83—41no—
199C22×D83—41no—
200C22×D83—41no—
201C22×D83—41no—
202C22×D83—41no—
203Q8×C83—44no—
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—22no—
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—41no—
222C2×C4×C83—41no—
223C2×C4×C83—41no—
224C2×C4×C83—41no—
225C2×C4×C83—41no—
226C2×C4×C83—41no—
227C2×C4×C83—41no—
228C2×C4×C83—41no—
229C2×C4×C83—41no—
230C2×C4×C83—41no—
231C2×C4×C83—41no—
232C2×C4×C83#12312yes—
233C2×C4×C83#12312yes—
234C2×C4×C83C2×#4111yescharacteristic
235C2×C4×C83C2×#4111yescharacteristic
236C2×C4×C83C2×#4111yescharacteristic
237C2×C4×C83C2×#4111yescharacteristic
238C2×C4×C83H(5,𝔽2)11yescharacteristic
239C2×C4×C832−1+411yescharacteristic
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—
249D332—41no—
250D332—41no—
251D332—41no—
252D332—41no—
253Dic166—41no—
254Dic166—41no—
255Dic166—41no—
256Dic166—41no—
257C83⋊C8—22no—
258C83⋊C8—41no—
259C83⋊C8—41no—
260C83⋊C8—41no—
261C22×C83C2×#12311yescharacteristic
262C22×C83#54811yescharacteristic
263C22×C83#55011yescharacteristic
264C22×C83#57511yescharacteristic
265C22×C83#57511yescharacteristic
266C22×C83#57711yescharacteristic
267C22×C83#57711yescharacteristic
268C2×D83—81no—
269C2×D83—81no—
270C2×D83—81no—
271C2×D83—81no—
272C2×D83—81no—
273C2×D83—81no—
274C2×D83—81no—
275C4×C83—22no—
276C4×C83—22no—
277C4×C83—41no—
278C4×C83—41no—
279C4×C83—41no—
280C4×C83—41no—
281C4×C83—42no—
282C4×C83—81no—
283C4×C83—81no—
284C4×C83—81no—
285C4×C83#52911yescharacteristic
286C4×C83#54211yescharacteristic
287C4×C83#55611yescharacteristic
288C4×C83#55911yescharacteristic
289Dic83—81no—
290Dic83—81no—
291Dic83—81no—
292#26331—831nomaximal, Sylow
293C2×C83#244811yescharacteristic
294C2×C83#309311yescharacteristic
295C2×C83#309911yescharacteristic
296C2×C83#337111yescharacteristic
297C2×C83#337611yescharacteristic
298C2×C83#340111yescharacteristic
299C2×C83#340111yescharacteristic
300D83—161no—
301#2592—831no—
302#2355D8311yescharacteristic, complemented
303#2097—831no—
304#2092—831no—
305#2074—831no—
306#2073—831no—
307#1985—831no—
308#1983—831no—
309#1959—831no—
310#1948—831no—
311#1927—831no—
312#1927—831no—
313#1926—831no—
314#1926—831no—
315#1776—831no—
316C83#2633111yescharacteristic, complemented, Sylow
317C2×#124—831no—
318C2×C4×Q8C2×D8311yescharacteristic
319C2×#107—831no—
320C2×#106—831no—
321C2×#106—831no—
322C2×#106—831no—
323C2×C4⋊C8—831no—
324C2×#103—831no—
325C2×#103—831no—
326C2×#103—831no—
327C2×#103—831no—
328C2×#102—831no—
329C2×#102—831no—
330C2×#102—831no—
331C2×#102—831no—
332C2×#97—831no—
333#397—1661no—
334#393—1661no—
335#391—21no—
336#391—831no—
337#391—831no—
338#390—831no—
339#390—831no—
340#388—1661no—
341#388—1661no—
342#387—21no—
343#387—21no—
344#384C2×D8311yescharacteristic
345#382C2×D8311yescharacteristic
346#382C2×D8311yescharacteristic
347C4×C4⋊C4—21no—
348C4×C4⋊C4—831no—
349C4×C4⋊C4C2×D8311yescharacteristic
350C4×C4⋊C4C2×D8311yescharacteristic
351C4×C4⋊C4C2×D8311yescharacteristic
352#340—831no—
353#340—831no—
354#340—831no—
355#340—831no—
356#336—831no—
357#336—831no—
358#336—831no—
359#336—831no—
360C22×Q8—831no—
361C22×Q8C22⋊D8311yescharacteristic
362C22×D4—831no—
363C22×C8—831no—
364C22×C8—831no—
365C22×C8—831no—
366C22×C8—831no—
367#124—1662no—
368#124—1662no—
369C4×Q8—22no—
370C4×Q8—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—831no—
374C2×C4⋊C4—831no—
375C2×C4⋊C4C22⋊D8311yescharacteristic
376C2×C4⋊C4C22⋊D8311yescharacteristic
377C2×C4⋊C4C22⋊D8311yescharacteristic
378C2×C4⋊C4C22×D8311yescharacteristic
379C2×C4⋊C4C22×D8311yescharacteristic
380C2×C4⋊C4C22×D8311yescharacteristic
381C2×C4⋊C4C22×D8311yescharacteristic
382C2×C22⋊C4—1661no—
383C2×C22⋊C4—1661no—
384C2×C22⋊C4—1661no—
385C2×C22⋊C4—1661no—
386C2×C22⋊C4—1661no—
387C2×C22⋊C4—1661no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—1661no—
392C2×C42C22×D8311yescharacteristic
393C2×C42C22×D8311yescharacteristic
394C2×C42C22×D8311yescharacteristic
395#107—1662no—
396#106—3321no—
397#106—3321no—
398#106—1662no—
399C4⋊C8—1662no—
400#103—3321no—
401#103—3321no—
402#103—1662no—
403#103—1662no—
404#102—3321no—
405#102—3321no—
406#102—1662no—
407#102—1662no—
408#97—1662no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—1661no—
417#95—1661no—
418#95—1661no—
419#95—1661no—
420#95—1661no—
421C24—1661no—
422C2×Q8—22no—
423C2×Q8—41no—
424C2×Q8—41no—
425C2×Q8—1661no—
426C2×Q8—1661no—
427C2×Q8—1661no—
428C2×Q8—1661no—
429C2×Q8—1661no—
430C2×Q8—1661no—
431C2×D4—1661no—
432C2×D4—1661no—
433C2×D4—1661no—
434C2×D4—1661no—
435C2×D4—1661no—
436C2×D4—1661no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—1661no—
442C22×C4—1661no—
443C22×C4—1661no—
444C22×C4C2×C22⋊D8311yescharacteristic
445C22×C4C2×C22⋊D8311yescharacteristic
446C22×C4C2×C22⋊D8311yescharacteristic
447C22×C4C2×C22⋊D8311yescharacteristic
448C22×C4C2×C22⋊D8311yescharacteristic
449C22×C4C2×C22⋊D8311yescharacteristic
450C22×C4C23×D8311yescharacteristic
451C2×C8—832no—
452C2×C8—1661no—
453C2×C8—1661no—
454C2×C8—1661no—
455C2×C8—1661no—
456C2×C8—1661no—
457C2×C8—1661no—
458C2×C8—1661no—
459C2×C8—1661no—
460C2×C8—1661no—
461C2×C8—1661no—
462C2×C8—1661no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—42no—
474C4⋊C4—81no—
475C4⋊C4—1661no—
476C4⋊C4—1661no—
477C4⋊C4—1661no—
478C4⋊C4—1661no—
479C4⋊C4#1305059112yes—
480C22⋊C4—3322no—
481C22⋊C4—3322no—
482C22⋊C4—3322no—
483C22⋊C4—3322no—
484C22⋊C4—6641no—
485C22⋊C4—6641no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—42no—
491C42—81no—
492C42—81no—
493C42—6641no—
494C42#1305059012yes—
495C42#1305059012yes—
496C23—3321no—
497C23—3321no—
498C23—3321no—
499C23—3321no—
500C23—3321no—
501C23—3321no—
502C23—3321no—
503C23C22×C22⋊D8311yescharacteristic
504Q8—44no—
505Q8—3321no—
506Q8—3321no—
507Q8—3321no—
508Q8—3321no—
509D4—3321no—
510D4—3321no—
511D4—3321no—
512D4—3321no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
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—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
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#1458177512yes—
551C2×C4#1458177512yes—
552C2×C4#41×D8311yescharacteristic
553C2×C4C2×#1305059011yescharacteristic
554C2×C4C2×#1305059011yescharacteristic
555C2×C4C2×#1305059111yescharacteristic
556C2×C4#1458183811yescharacteristic
557C2×C4#1458184011yescharacteristic
558C8—3321no—
559C8—3321no—
560C8—3321no—
561C8—1662no—
562C22—6641no—
563C22—6641no—
564C22—6641no—
565C22—6641no—
566C22—6641no—
567C22—6641no—
568C22—6641no—
569C22C2×#1458177511yescharacteristic
570C22#1912836211yescharacteristic
571C22#1912837011yescharacteristic
572C22#1912849911yescharacteristic
573C22#1912849911yescharacteristic
574C22#1912850911yescharacteristic
575C22#1912851211yescharacteristic
576C4—22no—
577C4—22no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—42no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—6641no—
587C4—6641no—
588C4—6641no—
589C4#1912823811yescharacteristic
590C4#1912832311yescharacteristic
591C4#1912842311yescharacteristic
592C4#1912843611yescharacteristic
593C2—13281no—
594C2#2491125511yescharacteristic
595C2#2491739411yescharacteristic
596C2#2491745211yescharacteristic
597C2#2492023111yescharacteristic
598C2#2492029011yescharacteristic
599C2#2492052311yescharacteristic
600C2#2492052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#2355C2
socleC23×C83C22×D4
prime radicalC22×D332C23
hypercenter#2355D83
hypocenterC83#26331
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2355

Complements

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

NH ≅ G/Ntype
2. #24909014C2semidirect
4. #24908882C2semidirect
6. #24908404C2semidirect
9. #24908224C2semidirect
10. #24908097C2semidirect
11. #24908097C2semidirect
14. #24907361C2semidirect
15. C83×#2355C2semidirect
302. #2355D83semidirect
316. C83#26331semidirect

Maximal subgroups

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

subgroupindex
#249129512
#249090142
#249089872
#249088822
#249088772
#249084042
#249083952
#249082772
#249082242
#249080972
#249080902
#249073612
C83×#23552
#2633183