Finite Group Databasebeta

← #35404979

Subgroups — #35404979

Order 21248.

810 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127657C211yesmaximal, characteristic
2#24910072C211yesmaximal, characteristic
3#24907632C211yesmaximal, characteristic, complemented
4#24907629C211yesmaximal, characteristic, complemented
5#24907593C211yesmaximal, characteristic, complemented
6#24907590C211yesmaximal, characteristic, complemented
7#24907494C211yesmaximal, characteristic
8#24907494C211yesmaximal, characteristic
9#24907490C211yesmaximal, characteristic
10#24907486C211yesmaximal, characteristic
11#24907361C211yesmaximal, characteristic, complemented
12#24907361C211yesmaximal, characteristic, complemented
13C4×#14581725C211yesmaximal, characteristic, complemented
14C4×#14581723C211yesmaximal, characteristic, complemented
15C83×#2314C211yesmaximal, characteristic
16C22×#13050574C2211yescharacteristic
17C23×C83⋊C8C2211yescharacteristic
18C2×#14581725C2211yescharacteristic
19C2×#14581725C2211yescharacteristic
20C2×#14581725C2211yescharacteristic
21C2×#14581725C2211yescharacteristic
22C2×#14581723C2211yescharacteristic
23C2×#14581723C2211yescharacteristic
24C2×#14581723C2211yescharacteristic
25C2×#14581723C2211yescharacteristic
26#19127657C418yescomplemented
27C2×#14581703C2211yescharacteristic
28C2×#14581703C2211yescharacteristic
29C2×C4×C83⋊C8C2211yescharacteristic
30C2×C4×C83⋊C8C2211yescharacteristic
31#19127594—21no—
32#19127594—21no—
33#19127587—21no—
34#19127587—21no—
35#19127571C2211yescharacteristic
36#19127567C2211yescharacteristic
37#19127561C2211yescharacteristic
38#19127561C2211yescharacteristic
39C4×C4⋊Dic83C2211yescharacteristic
40C4×C4⋊Dic83C2211yescharacteristic
41#19127463C2211yescharacteristic
42#19127463C2211yescharacteristic
43#19127463C2211yescharacteristic
44#19127463C2211yescharacteristic
45#19127463C2211yescharacteristic
46#19127463C2211yescharacteristic
47#19127463C2211yescharacteristic
48#19127463C2211yescharacteristic
49C2×#117×C83C2211yescharacteristic
50#388×C83—21no—
51#388×C83—21no—
52#387×C83—21no—
53#387×C83—21no—
54#384×C83C2211yescharacteristic
55#382×C83C2211yescharacteristic
56#380×C83C2211yescharacteristic
57#380×C83C2211yescharacteristic
58C4×C4⋊C4×C83C2211yescharacteristic
59C4×C4⋊C4×C83C2211yescharacteristic
60C2×#13050574—22no—
61C2×#13050574—22no—
62C2×#13050574C2×C414yes—
63C22×C83⋊C8—22no—
64C22×C83⋊C8—22no—
65C22×C83⋊C8C2×C414yes—
66C22×C83⋊C8C2311yescharacteristic
67C22×C83⋊C8C2311yescharacteristic
68C22×C83⋊C8C2311yescharacteristic
69C22×C83⋊C8C2311yescharacteristic
70C2×C4⋊Dic83—21no—
71C2×C4⋊Dic83—21no—
72C2×C4⋊Dic83C2311yescharacteristic
73C2×C4⋊Dic83C2311yescharacteristic
74C2×C4⋊Dic83C2311yescharacteristic
75C2×C4⋊Dic83C2311yescharacteristic
76C2×C22⋊Dic83—21no—
77C2×C22⋊Dic83—21no—
78C2×C4×Dic83—21no—
79C2×C4×Dic83—21no—
80#14581725—22no—
81#14581725—22no—
82#14581725—22no—
83#14581725—22no—
84#14581723—22no—
85#14581723—22no—
86#14581723—22no—
87#14581723—22no—
88#14581703C2×C414yes—
89#14581703C2×C414yes—
90C4×C83⋊C8C2×C414yes—
91C4×C83⋊C8C2×C414yes—
92C83⋊#95—21no—
93C83⋊#95—21no—
94C83⋊#95—21no—
95C83⋊#95—21no—
96C83⋊#95—21no—
97C83⋊#95—21no—
98C23×C4×C83C2311yescharacteristic
99#117×C83C2×C414yes—
100#117×C83Q814yes—
101C2×C4⋊C4×C83—21no—
102C2×C4⋊C4×C83—21no—
103C2×C4⋊C4×C83D411yescharacteristic
104C2×C4⋊C4×C83D411yescharacteristic
105C2×C4⋊C4×C83C2311yescharacteristic
106C2×C4⋊C4×C83C2311yescharacteristic
107C2×C4⋊C4×C83C2311yescharacteristic
108C2×C4⋊C4×C83C2311yescharacteristic
109C2×C22⋊C4×C83—21no—
110C2×C22⋊C4×C83—21no—
111C2×C22⋊C4×C83D411yescharacteristic
112C2×C22⋊C4×C83D411yescharacteristic
113C2×C42×C83—21no—
114C2×C42×C83—21no—
115C2×C42×C83C2311yescharacteristic
116C2×C42×C83C2311yescharacteristic
117#95×C83—21no—
118#95×C83—21no—
119#95×C83—21no—
120#95×C83—21no—
121#95×C83—21no—
122#95×C83—21no—
123C22×Dic83—21no—
124C22×Dic83—21no—
125C22×Dic83—21no—
126C22×Dic83—21no—
127#13050574—28no—
128C2×C83⋊C8—21no—
129C2×C83⋊C8—21no—
130C2×C83⋊C8—21no—
131C2×C83⋊C8—21no—
132C2×C83⋊C8—28no—
133C2×C83⋊C8C22×C412yes—
134C2×C83⋊C8C22×C412yes—
135C2×C83⋊C8C22×C412yes—
136C2×C83⋊C8C22×C412yes—
137C2×C83⋊C8#4112yes—
138C2×C83⋊C8#4112yes—
139C2×C83⋊C8#4112yes—
140C2×C83⋊C8#4112yes—
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—81no—
150C4⋊Dic83—81no—
151C22⋊Dic83—81no—
152C22⋊Dic83—81no—
153C4×Dic83—81no—
154C4×Dic83—81no—
155C24×C83C2×D411yescharacteristic
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×C83C22×C412yes—
165C22×C4×C83C2×D411yescharacteristic
166C22×C4×C83C2×D411yescharacteristic
167C22×C4×C83C2×D411yescharacteristic
168C22×C4×C83C2×D411yescharacteristic
169C22×C4×C83C2×D411yescharacteristic
170C22×C4×C83C2×Q812yes—
171C22×C4×C83C2411yescharacteristic
172C4⋊C4×C83—21no—
173C4⋊C4×C83—21no—
174C4⋊C4×C83—21no—
175C4⋊C4×C83—21no—
176C4⋊C4×C83—21no—
177C4⋊C4×C83—21no—
178C4⋊C4×C83—21no—
179C4⋊C4×C83—21no—
180C4⋊C4×C83—81no—
181C4⋊C4×C83—81no—
182C4⋊C4×C83C4⋊C414yes—
183C4⋊C4×C83C4⋊C414yes—
184C22⋊C4×C83—81no—
185C22⋊C4×C83—81no—
186C22⋊C4×C83C4⋊C414yes—
187C22⋊C4×C83C4⋊C414yes—
188C42×C83—81no—
189C42×C83—81no—
190C42×C83C22×C412yes—
191C42×C83C22×C412yes—
192C42×C83C2×Q812yes—
193C42×C83C2×Q812yes—
194C23×C83—21no—
195C23×C83—21no—
196C23×C83—21no—
197C23×C83—21no—
198C23×C83—21no—
199C23×C83—21no—
200C23×C83C2×C4⋊C412yes—
201C23×C83C22×D411yescharacteristic
202C2×C4×C83—21no—
203C2×C4×C83—21no—
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—22no—
214C2×C4×C83—22no—
215C2×C4×C83—22no—
216C2×C4×C83—41no—
217C2×C4×C83—41no—
218C2×C4×C83—41no—
219C2×C4×C83—41no—
220C2×C4×C83—41no—
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×C83C2×C4⋊C412yes—
229C2×C4×C83C2×C4⋊C412yes—
230C2×C4×C83C2×C4⋊C412yes—
231C2×C4×C83C2×C4⋊C412yes—
232C2×C4×C83C2×C4⋊C412yes—
233C2×C4×C83C23×C411yescharacteristic
234C2×C4×C83C22×Q811yescharacteristic
235C2×C4×C83C2×#4111yescharacteristic
236C2×C4×C83C2×#4111yescharacteristic
237C2×C4×C83C2×#4111yescharacteristic
238C2×C4×C83C2×#4111yescharacteristic
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—
251C83⋊C8—22no—
252C83⋊C8—22no—
253C83⋊C8#11714yes—
254C83⋊C8#11714yes—
255C22×C83—22no—
256C22×C83—22no—
257C22×C83—22no—
258C22×C83—41no—
259C22×C83—41no—
260C22×C83—41no—
261C22×C83—41no—
262C22×C83C22×C4⋊C411yescharacteristic
263C22×C83#53211yescharacteristic
264C22×C83#53211yescharacteristic
265C22×C83#57611yescharacteristic
266C22×C83#57711yescharacteristic
267C22×C83#57711yescharacteristic
268C22×C83#57811yescharacteristic
269C4×C83—22no—
270C4×C83—22no—
271C4×C83—22no—
272C4×C83—22no—
273C4×C83—22no—
274C4×C83—81no—
275C4×C83—81no—
276C4×C83—81no—
277C4×C83—81no—
278C4×C83C2×#11711yescharacteristic
279C4×C83C2×#11711yescharacteristic
280C4×C83#53311yescharacteristic
281C4×C83#53311yescharacteristic
282Dic83—81no—
283Dic83—81no—
284Dic83—81no—
285Dic83—81no—
286#20822—831nomaximal, Sylow
287C2×C83—42no—
288C2×C83#228511yescharacteristic
289C2×C83#291211yescharacteristic
290C2×C83#291311yescharacteristic
291C2×C83#317811yescharacteristic
292C2×C83#317811yescharacteristic
293C2×C83#317911yescharacteristic
294C2×C83#317911yescharacteristic
295C2×#405—831no—
296#2314—831no—
297#2314D8311yescharacteristic
298#1847—831no—
299#1847—831no—
300#1835—831no—
301#1834—831no—
302#1809—831no—
303#1809—831no—
304#1808—831no—
305#1807—831no—
306#1776—831no—
307#1776—831no—
308C4×#107—831no—
309C4×#106—831no—
310C83#2082211yescharacteristic, complemented, Sylow
311C22×M16—831no—
312C23×C8—831no—
313C2×#117C2×D8311yescharacteristic
314C2×#107—831no—
315C2×#107—831no—
316C2×#107—831no—
317C2×#107—831no—
318C2×#106—831no—
319C2×#106—831no—
320C2×#106—831no—
321C2×#106—831no—
322#405—838no—
323C2×#97—831no—
324C2×#97—831no—
325C2×C4×C8—831no—
326C2×C4×C8—831no—
327#388—21no—
328#388—21no—
329#388—1661no—
330#388—1661no—
331#387—21no—
332#387—21no—
333#387—1661no—
334#387—1661no—
335#384—831no—
336#384C2×D8311yescharacteristic
337#382—831no—
338#382C2×D8311yescharacteristic
339#380—831no—
340#380—831no—
341#380C2×D8311yescharacteristic
342#380C2×D8311yescharacteristic
343C4×C4⋊C4—831no—
344C4×C4⋊C4—831no—
345C4×C4⋊C4C2×D8311yescharacteristic
346C4×C4⋊C4C2×D8311yescharacteristic
347#340—831no—
348#340—831no—
349#340—831no—
350#340—831no—
351#340—831no—
352#340—831no—
353#340—831no—
354#340—831no—
355C23×C4C22×D8311yescharacteristic
356C2×M16—834no—
357C2×M16—1662no—
358C2×M16—1662no—
359C22×C8—831no—
360C22×C8—831no—
361C22×C8—834no—
362C22×C8—831no—
363C22×C8—831no—
364C22×C8—1662no—
365C22×C8—1662no—
366#117Dic16614yes—
367#117C4×D8314yes—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—831no—
371C2×C4⋊C4—831no—
372C2×C4⋊C4—831no—
373C2×C4⋊C4—831no—
374C2×C4⋊C4—1661no—
375C2×C4⋊C4—1661no—
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—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—1661no—
385C2×C22⋊C4—1661no—
386C2×C22⋊C4C22⋊D8311yescharacteristic
387C2×C22⋊C4C22⋊D8311yescharacteristic
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—1661no—
391C2×C42—1661no—
392C2×C42C22×D8311yescharacteristic
393C2×C42C22×D8311yescharacteristic
394#107—1662no—
395#107—1662no—
396#107—1662no—
397#107—1662no—
398#106—1662no—
399#106—1662no—
400#106—1662no—
401#106—1662no—
402#97—834no—
403#97—834no—
404C4×C8—834no—
405C4×C8—834no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—1661no—
413#95—1661no—
414#95—1661no—
415#95—1661no—
416#95—1661no—
417#95—1661no—
418C24C2×C22⋊D8311yescharacteristic
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—1661no—
428C22×C4—1661no—
429C22×C4—1661no—
430C22×C4—1661no—
431C22×C4C2×C4×D8312yes—
432C22×C4C2×C22⋊D8311yescharacteristic
433C22×C4C2×C22⋊D8311yescharacteristic
434C22×C4C2×C22⋊D8311yescharacteristic
435C22×C4C2×C22⋊D8311yescharacteristic
436C22×C4C2×C22⋊D8311yescharacteristic
437C22×C4C2×Dic16612yes—
438C22×C4C23×D8311yescharacteristic
439M16—1668no—
440C2×C8—832no—
441C2×C8—832no—
442C2×C8—832no—
443C2×C8—832no—
444C2×C8—832no—
445C2×C8—832no—
446C2×C8—832no—
447C2×C8—832no—
448C2×C8—1668no—
449C2×C8—1661no—
450C2×C8—1661no—
451C2×C8—1661no—
452C2×C8—1661no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—81no—
462C4⋊C4—81no—
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⋊C4Dic83⋊C414yes—
474C4⋊C4Dic83⋊C414yes—
475C22⋊C4—81no—
476C22⋊C4—81no—
477C22⋊C4—6641no—
478C22⋊C4—6641no—
479C22⋊C4Dic83⋊C414yes—
480C22⋊C4Dic83⋊C414yes—
481C42—81no—
482C42—81no—
483C42—6641no—
484C42—6641no—
485C42C2×C4×D8312yes—
486C42C2×C4×D8312yes—
487C42C2×Dic16612yes—
488C42C2×Dic16612yes—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23C2×Dic83⋊C412yes—
496C23C22×C22⋊D8311yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—3321no—
524C2×C4—3321no—
525C2×C4—3321no—
526C2×C4—3321no—
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×C4C2×Dic83⋊C412yes—
536C2×C4C2×Dic83⋊C412yes—
537C2×C4C2×Dic83⋊C412yes—
538C2×C4C2×Dic83⋊C412yes—
539C2×C4C2×Dic83⋊C412yes—
540C2×C4C22×C4×D8311yescharacteristic
541C2×C4C22×Dic16611yescharacteristic
542C2×C4#41×D8311yescharacteristic
543C2×C4#41×D8311yescharacteristic
544C2×C4#41×D8311yescharacteristic
545C2×C4#41×D8311yescharacteristic
546C8—834no—
547C8—834no—
548C8—1662no—
549C8—1662no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22C22×Dic83⋊C411yescharacteristic
558C22#1912824711yescharacteristic
559C22#1912824711yescharacteristic
560C22#1912850411yescharacteristic
561C22#1912850911yescharacteristic
562C22#1912851211yescharacteristic
563C22#1912851611yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—22no—
568C4—22no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—6641no—
574C4—6641no—
575C4—6641no—
576C4—6641no—
577C4#117×D8311yescharacteristic
578C4#117×D8311yescharacteristic
579C4#1912825411yescharacteristic
580C4#1912825411yescharacteristic
581C2—42no—
582C2#2490986611yescharacteristic
583C2#2491605611yescharacteristic
584C2#2491606111yescharacteristic
585C2#2491812511yescharacteristic
586C2#2491813311yescharacteristic
587C2#2491814011yescharacteristic
588C2#2491814811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#2314C2
socleC23×C83C22×D4
prime radicalC24×C83C2×D4
cosocleC22×C4×C83C24
hypercenter#2314D83
hypocenterC83#20822
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
3. #24907632C2semidirect
4. #24907629C2semidirect
5. #24907593C2semidirect
6. #24907590C2semidirect
11. #24907361C2semidirect
12. #24907361C2semidirect
13. C4×#14581725C2semidirect
14. C4×#14581723C2semidirect
26. #19127657C4semidirect
310. C83#20822semidirect

Maximal subgroups

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

subgroupindex
C2×#191276572
#249100722
#249076322
#249076292
#249075932
#249075902
#249074942
#249074902
#249074862
#249073612
C4×#145817252
C4×#145817232
C83×#23142
#2082283