Finite Group Databasebeta

← #35477235

Subgroups — #35477235

Order 21248.

678 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24911874C211yesmaximal, characteristic
2#24908881C211yesmaximal, characteristic, complemented
3#24908844C211yesmaximal, characteristic, complemented
4#24908663C211yesmaximal, characteristic
5#24908656C211yesmaximal, characteristic
6#24908231C211yesmaximal, characteristic, complemented
7#24908188C211yesmaximal, characteristic, complemented
8#24908071C211yesmaximal, characteristic
9#24908055C211yesmaximal, characteristic, complemented
10#24908031C211yesmaximal, characteristic, complemented
11#24907717C211yesmaximal, characteristic, complemented
12#24907662C211yesmaximal, characteristic
13#24907558C211yesmaximal, characteristic
14C4×#14581716C211yesmaximal, characteristic, complemented
15C83×#2362C211yesmaximal, characteristic
16C2×#14581725C2211yescharacteristic
17C2×#14581725C2211yescharacteristic
18C2×#14581723C2211yescharacteristic
19C2×#14581723C2211yescharacteristic
20C2×C4⋊(C83⋊C8)C2211yescharacteristic
21C2×#14581716C2211yescharacteristic
22C2×#14581716C2211yescharacteristic
23C2×#14581716C2211yescharacteristic
24C2×#14581716C2211yescharacteristic
25C2×C22⋊(C83⋊C8)C2211yescharacteristic
26C2×C22⋊(C83⋊C8)C2211yescharacteristic
27C2×C4×C83⋊C8C2211yescharacteristic
28#19127642—21no—
29#19127629—21no—
30#19127599C2211yescharacteristic
31#19127599C2211yescharacteristic
32#19127589—21no—
33#19127568—21no—
34#19127567C2211yescharacteristic
35#19127561C2211yescharacteristic
36#19127561C2211yescharacteristic
37C4×C4⋊Dic83C2211yescharacteristic
38#19127463C2211yescharacteristic
39#19127463C2211yescharacteristic
40#19127463C2211yescharacteristic
41#19127463C2211yescharacteristic
42#19127463C2211yescharacteristic
43#19127463C2211yescharacteristic
44#19127463C2211yescharacteristic
45#19127463C2211yescharacteristic
46#19127456C2211yescharacteristic
47#19127456C2211yescharacteristic
48C2×C22⋊Q8×C83C2211yescharacteristic
49C2×C4×Q8×C83C2211yescharacteristic
50C2×#117×C83C2211yescharacteristic
51#391×C83C2211yescharacteristic
52#389×C83C2211yescharacteristic
53#388×C83—21no—
54#388×C83—21no—
55#387×C83—21no—
56C4×C4⋊C4×C83—21no—
57C4×C4⋊C4×C83C2211yescharacteristic
58C4×C22⋊C4×C83C2211yescharacteristic
59C22×C83⋊C8C2311yescharacteristic
60C22×C83⋊C8C2311yescharacteristic
61C22×C83⋊C8C2311yescharacteristic
62C22×C83⋊C8C2311yescharacteristic
63C2×C4⋊Dic83C2311yescharacteristic
64C2×C4⋊Dic83C2311yescharacteristic
65C2×C4⋊Dic83C2311yescharacteristic
66C2×C4⋊Dic83C2311yescharacteristic
67C2×Dic83⋊C4—21no—
68C2×Dic83⋊C4—21no—
69C2×C22⋊Dic83—21no—
70C2×C22⋊Dic83—21no—
71C2×C4×Dic83—21no—
72#14581725—22no—
73#14581725—22no—
74#14581723—22no—
75#14581723—41no—
76C4⋊(C83⋊C8)—22no—
77#14581716—22no—
78#14581716—22no—
79#14581716—22no—
80#14581716—41no—
81C22⋊(C83⋊C8)—22no—
82C22⋊(C83⋊C8)—41no—
83C4×C83⋊C8—41no—
84C83⋊#95—21no—
85C83⋊#95—21no—
86C83⋊#95—21no—
87C83⋊#95—21no—
88C83⋊#95—21no—
89C83⋊#95—21no—
90C83⋊#95—21no—
91C22×Q8×C83C2311yescharacteristic
92C23×C4×C83C2311yescharacteristic
93C22⋊Q8×C83—22no—
94C22⋊Q8×C83—22no—
95C4×Q8×C83—22no—
96C4×Q8×C83—41no—
97#117×C83—22no—
98#117×C83—41no—
99C2×C4⋊C4×C83—21no—
100C2×C4⋊C4×C83—21no—
101C2×C4⋊C4×C83—21no—
102C2×C4⋊C4×C83C2311yescharacteristic
103C2×C4⋊C4×C83C2311yescharacteristic
104C2×C4⋊C4×C83C2311yescharacteristic
105C2×C22⋊C4×C83—21no—
106C2×C22⋊C4×C83—21no—
107C2×C22⋊C4×C83D411yescharacteristic
108C2×C22⋊C4×C83D411yescharacteristic
109C2×C42×C83—21no—
110C2×C42×C83—21no—
111C2×C42×C83—21no—
112C2×C42×C83C2311yescharacteristic
113C2×C42×C83C2311yescharacteristic
114#95×C83—21no—
115#95×C83—21no—
116#95×C83—21no—
117#95×C83—21no—
118#95×C83D411yescharacteristic
119#95×C83D411yescharacteristic
120C22×Dic83—21no—
121C22×Dic83—21no—
122C22×Dic83—21no—
123C22×Dic83—21no—
124C2×C83⋊C8—21no—
125C2×C83⋊C8—21no—
126C2×C83⋊C8—21no—
127C2×C83⋊C8—21no—
128C2×C83⋊C8—21no—
129C2×C83⋊C8—21no—
130C2×C83⋊C8—21no—
131C2×C83⋊C8—21no—
132C2×C83⋊C8—21no—
133C2×C83⋊C8—21no—
134C2×C83⋊C8—21no—
135C2×C83⋊C8#4112yes—
136C4⋊Dic83—21no—
137C4⋊Dic83—21no—
138C4⋊Dic83—21no—
139C4⋊Dic83—21no—
140C4⋊Dic83—21no—
141C4⋊Dic83—21no—
142C4⋊Dic83—21no—
143C4⋊Dic83—21no—
144Dic83⋊C4—81no—
145Dic83⋊C4—81no—
146C22⋊Dic83—42no—
147C22⋊Dic83—81no—
148C4×Dic83—42no—
149C24×C83C2×D411yescharacteristic
150C2×Q8×C83—21no—
151C2×Q8×C83—21no—
152C2×Q8×C83—21no—
153C2×Q8×C83—21no—
154C2×Q8×C83—21no—
155C2×Q8×C83#4112yes—
156C22×C4×C83—21no—
157C22×C4×C83—21no—
158C22×C4×C83—21no—
159C22×C4×C83—21no—
160C22×C4×C83—21no—
161C22×C4×C83—21no—
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×C83C2411yescharacteristic
172C4⋊C4×C83—24no—
173C4⋊C4×C83—21no—
174C4⋊C4×C83—21no—
175C4⋊C4×C83—21no—
176C4⋊C4×C83—21no—
177C4⋊C4×C83—42no—
178C4⋊C4×C83—42no—
179C4⋊C4×C83#4112yes—
180C4⋊C4×C83#4112yes—
181C22⋊C4×C83—24no—
182C22⋊C4×C83—22no—
183C22⋊C4×C83—41no—
184C22⋊C4×C83—42no—
185C42×C83—21no—
186C42×C83—21no—
187C42×C83—21no—
188C42×C83—21no—
189C42×C83—42no—
190C42×C83—42no—
191C42×C83—42no—
192C23×C83—21no—
193C23×C83—21no—
194C23×C83—21no—
195C23×C83—21no—
196C23×C83—21no—
197C23×C83—21no—
198C23×C83—21no—
199C23×C83C22×D411yescharacteristic
200Q8×C83—22no—
201Q8×C83—22no—
202Q8×C83—41no—
203Q8×C83—41no—
204C2×C4×C83—21no—
205C2×C4×C83—21no—
206C2×C4×C83—22no—
207C2×C4×C83—22no—
208C2×C4×C83—21no—
209C2×C4×C83—21no—
210C2×C4×C83—22no—
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—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—41no—
233C2×C4×C83—41no—
234C2×C4×C83#13512yes—
235C2×C4×C83C2×#4111yescharacteristic
236C2×C4×C83C2×#4111yescharacteristic
237C2×C4×C83C2×#4111yescharacteristic
238C2×C4×C83C2×#4111yescharacteristic
239C2×C4×C83H(5,𝔽2)11yescharacteristic
240C2×C4×C832−1+411yescharacteristic
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—
253C83⋊C8—22no—
254C83⋊C8—41no—
255C83⋊C8—41no—
256C83⋊C8—41no—
257C22×C83—41no—
258C22×C83—41no—
259C22×C83—41no—
260C22×C83—41no—
261C22×C83—41no—
262C22×C83—41no—
263C22×C83—41no—
264C22×C83#52511yescharacteristic
265C22×C83#54611yescharacteristic
266C22×C83#54711yescharacteristic
267C22×C83C2×#13511yescharacteristic
268C22×C83#57511yescharacteristic
269C22×C83#57711yescharacteristic
270C22×C83#57811yescharacteristic
271C4×C83—22no—
272C4×C83—41no—
273C4×C83—41no—
274C4×C83—42no—
275C4×C83—41no—
276C4×C83—42no—
277C4×C83—41no—
278C4×C83—42no—
279C4×C83—81no—
280C4×C83#52911yescharacteristic
281C4×C83#53911yescharacteristic
282C4×C83#55311yescharacteristic
283C4×C83#55611yescharacteristic
284Dic83—81no—
285Dic83—81no—
286Dic83—81no—
287Dic83—81no—
288#27042—831nomaximal, Sylow
289C2×C83—81no—
290C2×C83#246611yescharacteristic
291C2×C83#310211yescharacteristic
292C2×C83#312111yescharacteristic
293C2×C83#330011yescharacteristic
294C2×C83#330711yescharacteristic
295C2×C83#334011yescharacteristic
296C2×C83#335211yescharacteristic
297#2495—831no—
298#2362D8311yescharacteristic
299#2074—831no—
300#2066—831no—
301#2036—831no—
302#2035—831no—
303#1949—831no—
304#1941—831no—
305#1923—831no—
306#1921—831no—
307#1918—831no—
308#1863—831no—
309#1854—831no—
310#1825—831no—
311C4×#103—831no—
312C83#2704211yescharacteristic, complemented, Sylow
313C2×C22⋊Q8C2×D8311yescharacteristic
314C2×C4×Q8C2×D8311yescharacteristic
315C2×#117C2×D8311yescharacteristic
316C2×#107—831no—
317C2×#107—831no—
318C2×#106—831no—
319C2×#106—831no—
320C2×C4⋊C8—831no—
321C2×#103—831no—
322C2×#103—831no—
323C2×#103—831no—
324C2×#103—831no—
325C2×C22⋊C8—831no—
326C2×C22⋊C8—831no—
327C2×C4×C8—831no—
328#400—1661no—
329#397—1661no—
330#391C2×D8311yescharacteristic
331#389—831no—
332#389—831no—
333#389C2×D8311yescharacteristic
334#388—21no—
335#388—21no—
336#388—1661no—
337#387—21no—
338#383—1661no—
339#382—831no—
340#380—831no—
341#380—831no—
342C4×C4⋊C4—21no—
343C4×C4⋊C4—831no—
344C4×C4⋊C4C2×D8311yescharacteristic
345C4×C22⋊C4C2×D8311yescharacteristic
346#340—831no—
347#340—831no—
348#340—831no—
349#340—831no—
350#340—831no—
351#340—831no—
352#340—831no—
353#340—831no—
354#336—831no—
355#336—831no—
356C22×Q8C22×D8311yescharacteristic
357C23×C4C22×D8311yescharacteristic
358C22×C8—831no—
359C22×C8—831no—
360C22×C8—831no—
361C22×C8—831no—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C4×Q8—22no—
365C4×Q8—41no—
366#117—22no—
367#117—41no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—831no—
372C2×C4⋊C4—831no—
373C2×C4⋊C4—831no—
374C2×C4⋊C4—831no—
375C2×C4⋊C4—1661no—
376C2×C4⋊C4—1661no—
377C2×C4⋊C4C22×D8311yescharacteristic
378C2×C4⋊C4C22×D8311yescharacteristic
379C2×C4⋊C4C22×D8311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—1661no—
383C2×C22⋊C4—1661no—
384C2×C22⋊C4C22⋊D8311yescharacteristic
385C2×C22⋊C4C22⋊D8311yescharacteristic
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—1661no—
390C2×C42C22×D8311yescharacteristic
391C2×C42C22×D8311yescharacteristic
392#107—1662no—
393#107—1662no—
394#106—3321no—
395#106—1662no—
396C4⋊C8—1662no—
397#103—3321no—
398#103—1662no—
399#103—1662no—
400#103—1662no—
401C22⋊C8—3321no—
402C22⋊C8—1662no—
403C4×C8—3321no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—1661no—
409#95—1661no—
410#95—1661no—
411#95—1661no—
412#95—1661no—
413#95—1661no—
414#95—1661no—
415#95C22⋊D8311yescharacteristic
416#95C22⋊D8311yescharacteristic
417C24C2×C22⋊D8311yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8#1305059012yes—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—1661no—
435C22×C4—1661no—
436C22×C4—1661no—
437C22×C4—1661no—
438C22×C4C2×C22⋊D8311yescharacteristic
439C22×C4C2×C22⋊D8311yescharacteristic
440C22×C4C2×C22⋊D8311yescharacteristic
441C22×C4C2×C22⋊D8311yescharacteristic
442C22×C4C2×C22⋊D8311yescharacteristic
443C22×C4C23×D8311yescharacteristic
444C2×C8—832no—
445C2×C8—1661no—
446C2×C8—1661no—
447C2×C8—1661no—
448C2×C8—1661no—
449C2×C8—1661no—
450C2×C8—1661no—
451C2×C8—1661no—
452C2×C8—1661no—
453C2×C8—1661no—
454C2×C8—1661no—
455C2×C8—1661no—
456C4⋊C4—24no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—42no—
462C4⋊C4—42no—
463C4⋊C4—6641no—
464C4⋊C4—6641no—
465C4⋊C4—1661no—
466C4⋊C4—1661no—
467C4⋊C4—1661no—
468C4⋊C4—1661no—
469C4⋊C4—1661no—
470C4⋊C4—1661no—
471C4⋊C4—1661no—
472C4⋊C4—1661no—
473C4⋊C4#1305058912yes—
474C4⋊C4#1305059012yes—
475C22⋊C4—24no—
476C22⋊C4—22no—
477C22⋊C4—41no—
478C22⋊C4—42no—
479C22⋊C4—3322no—
480C22⋊C4—6641no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—42no—
486C42—42no—
487C42—42no—
488C42—3322no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23C22×C22⋊D8311yescharacteristic
497Q8—22no—
498Q8—22no—
499Q8—41no—
500Q8—41no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
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#1458181212yes—
544C2×C4#41×D8311yescharacteristic
545C2×C4C2×#1305058911yescharacteristic
546C2×C4C2×#1305059011yescharacteristic
547C2×C4C2×#1305059011yescharacteristic
548C2×C4#1458183711yescharacteristic
549C2×C4#1458183911yescharacteristic
550C8—3321no—
551C8—3321no—
552C8—3321no—
553C8—1662no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22#1912821211yescharacteristic
562C22#1912834511yescharacteristic
563C22#1912835011yescharacteristic
564C22C2×#1458181211yescharacteristic
565C22#1912849911yescharacteristic
566C22#1912850911yescharacteristic
567C22#1912851611yescharacteristic
568C4—22no—
569C4—41no—
570C4—41no—
571C4—42no—
572C4—41no—
573C4—42no—
574C4—41no—
575C4—42no—
576C4—81no—
577C4—6641no—
578C4—6641no—
579C4—6641no—
580C4—6641no—
581C4#1912823111yescharacteristic
582C4#1912829311yescharacteristic
583C4#1912840111yescharacteristic
584C4#1912842111yescharacteristic
585C2—81no—
586C2#2491149311yescharacteristic
587C2#2491748111yescharacteristic
588C2#2491769211yescharacteristic
589C2#2491935011yescharacteristic
590C2#2491943911yescharacteristic
591C2#2491987011yescharacteristic
592C2#2492003211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#2362C2
socleC23×C83C22×D4
prime radicalC24×C83C2×D4
hypercenter#2362D83
hypocenterC83#27042
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2362

Complements

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

NH ≅ G/Ntype
2. #24908881C2semidirect
3. #24908844C2semidirect
6. #24908231C2semidirect
7. #24908188C2semidirect
9. #24908055C2semidirect
10. #24908031C2semidirect
11. #24907717C2semidirect
14. C4×#14581716C2semidirect
312. C83#27042semidirect

Maximal subgroups

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

subgroupindex
#249118742
#249088812
#249088442
#249086632
#249086562
#249082312
#249081882
#249080712
#249080552
#249080312
#249077172
#249076622
#249075582
C4×#145817162
C83×#23622
#2704283