Finite Group Databasebeta

← #35408737

Subgroups — #35408737

Order 21248.

874 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127801C211yesmaximal, characteristic
2#24909940C211yesmaximal, characteristic, complemented
3#24908343C211yesmaximal, characteristic
4#24908316C211yesmaximal, characteristic
5#24908198C211yesmaximal, characteristic, complemented
6#24908193C211yesmaximal, characteristic, complemented
7#24908163C211yesmaximal, characteristic
8#24908152C211yesmaximal, characteristic, complemented
9#24908149C211yesmaximal, characteristic
10#24908138C211yesmaximal, characteristic, complemented
11#24907361C211yesmaximal, characteristic, complemented
12#24907296C211yesmaximal, characteristic, complemented
13#24907288C211yesmaximal, characteristic
14C4×#14581703C211yesmaximal, characteristic, complemented
15C83×#2293C211yesmaximal, characteristic
16C22×#13050578C2211yescharacteristic
17C2×C4×Dic166C2211yescharacteristic
18#19127801C418yescomplemented
19C2×#14581725C2211yescharacteristic
20C2×#14581725C2211yescharacteristic
21C2×#14581723C2211yescharacteristic
22C2×#14581715C2211yescharacteristic
23C2×#14581715C2211yescharacteristic
24C2×#14581715C2211yescharacteristic
25C2×#14581713C2211yescharacteristic
26C2×#14581713C2211yescharacteristic
27C2×#14581713C2211yescharacteristic
28C2×#14581703C2211yescharacteristic
29C2×#14581703C2211yescharacteristic
30C2×#14581703C2211yescharacteristic
31C2×#14581703C2211yescharacteristic
32C2×C4×C83⋊C8C2211yescharacteristic
33C2×C4×C83⋊C8C2211yescharacteristic
34#19127607C2211yescharacteristic
35#19127607C2211yescharacteristic
36#19127599C2211yescharacteristic
37#19127599C2211yescharacteristic
38#19127585—21no—
39#19127585—21no—
40C4×Dic83⋊C4—21no—
41C4×C4⋊Dic83C2211yescharacteristic
42#19127547—21no—
43#19127463C2211yescharacteristic
44#19127463C2211yescharacteristic
45#19127463C2211yescharacteristic
46#19127463C2211yescharacteristic
47#19127463C2211yescharacteristic
48#19127463C2211yescharacteristic
49C2×C4×D4×C83C2211yescharacteristic
50C2×#117×C83—21no—
51#390×C83C2211yescharacteristic
52#390×C83C2211yescharacteristic
53#389×C83C2211yescharacteristic
54#389×C83C2211yescharacteristic
55#388×C83—21no—
56#388×C83—21no—
57C4×C4⋊C4×C83C2211yescharacteristic
58C4×C22⋊C4×C83—21no—
59C43×C83C2211yescharacteristic
60C22×Dic166C2311yescharacteristic
61C2×#13050578—22no—
62C2×#13050578—22no—
63C2×#13050578C2×C414yes—
64C22×C83⋊C8C2311yescharacteristic
65C22×C83⋊C8C2311yescharacteristic
66C22×C83⋊C8C2311yescharacteristic
67C22×C83⋊C8C2311yescharacteristic
68C4×Dic166—22no—
69C4×Dic166C2×C414yes—
70C2×C4⋊Dic83C2311yescharacteristic
71C2×C4⋊Dic83C2311yescharacteristic
72C2×C4⋊Dic83C2311yescharacteristic
73C2×Dic83⋊C4—21no—
74C2×Dic83⋊C4—21no—
75C2×Dic83⋊C4—21no—
76C2×C4×Dic83—21no—
77C2×C4×Dic83—21no—
78#14581725—22no—
79#14581725C2×C414yes—
80#14581723—22no—
81#14581715—22no—
82#14581715—22no—
83#14581715C2×C414yes—
84#14581713—22no—
85#14581713—22no—
86#14581713C2×C414yes—
87#14581703—22no—
88#14581703—22no—
89#14581703—22no—
90#14581703C2×C414yes—
91C4×C83⋊C8—22no—
92C4×C83⋊C8—22no—
93C83⋊#95—21no—
94C83⋊#95—21no—
95C83⋊#95—21no—
96C83⋊#95—21no—
97C83⋊#95—21no—
98C83⋊#95—21no—
99C83⋊#95—21no—
100C22×D4×C83C2311yescharacteristic
101C23×C4×C83—21no—
102C4×D4×C83—22no—
103C4×D4×C83C2×C414yes—
104#117×C83—44no—
105C2×C4⋊C4×C83—21no—
106C2×C4⋊C4×C83—21no—
107C2×C4⋊C4×C83C2311yescharacteristic
108C2×C4⋊C4×C83C2311yescharacteristic
109C2×C4⋊C4×C83C2311yescharacteristic
110C2×C22⋊C4×C83—21no—
111C2×C22⋊C4×C83—21no—
112C2×C22⋊C4×C83—21no—
113C2×C22⋊C4×C83—21no—
114C2×C22⋊C4×C83—21no—
115C2×C42×C83—21no—
116C2×C42×C83D411yescharacteristic
117C2×C42×C83D411yescharacteristic
118C2×C42×C83D411yescharacteristic
119C2×C42×C83D411yescharacteristic
120C2×C42×C83C2311yescharacteristic
121C2×C42×C83C2311yescharacteristic
122C2×C42×C83C2311yescharacteristic
123#95×C83—21no—
124#95×C83—21no—
125#95×C83—21no—
126C2×Dic166—21no—
127C2×Dic166—21no—
128C2×Dic166—21no—
129C2×Dic166—21no—
130C2×Dic166—21no—
131C2×Dic166C22×C412yes—
132C22×Dic83—21no—
133C22×Dic83—21no—
134C22×Dic83—21no—
135C22×Dic83—21no—
136#13050578—28no—
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⋊C8C22×C412yes—
144C2×C83⋊C8C22×C412yes—
145C2×C83⋊C8#4112yes—
146C2×C83⋊C8#4112yes—
147C2×C83⋊C8#4112yes—
148C2×C83⋊C8#4112yes—
149C4⋊Dic83—21no—
150C4⋊Dic83—21no—
151C4⋊Dic83—21no—
152C4⋊Dic83—21no—
153C4⋊Dic83—21no—
154C4⋊Dic83C22×C412yes—
155Dic83⋊C4—24no—
156Dic83⋊C4—42no—
157Dic83⋊C4—42no—
158C4×Dic83—24no—
159C4×Dic83—42no—
160C24×C83—21no—
161C2×D4×C83—21no—
162C2×D4×C83—21no—
163C2×D4×C83—21no—
164C2×D4×C83—21no—
165C2×D4×C83—21no—
166C2×D4×C83C22×C412yes—
167C22×C4×C83—21no—
168C22×C4×C83—24no—
169C22×C4×C83—21no—
170C22×C4×C83—21no—
171C22×C4×C83—42no—
172C22×C4×C83—42no—
173C22×C4×C83C2×D411yescharacteristic
174C22×C4×C83C2×D411yescharacteristic
175C22×C4×C83C2×D411yescharacteristic
176C22×C4×C83C2×D411yescharacteristic
177C22×C4×C83C2×D411yescharacteristic
178C22×C4×C83C2×D411yescharacteristic
179C22×C4×C83C2411yescharacteristic
180C4⋊C4×C83—21no—
181C4⋊C4×C83—21no—
182C4⋊C4×C83—21no—
183C4⋊C4×C83—21no—
184C4⋊C4×C83—21no—
185C4⋊C4×C83—42no—
186C4⋊C4×C83—42no—
187C4⋊C4×C83C22×C412yes—
188C22⋊C4×C83—24no—
189C22⋊C4×C83—42no—
190C22⋊C4×C83—42no—
191C22⋊C4×C83—42no—
192C22⋊C4×C83—42no—
193C42×C83—22no—
194C42×C83—22no—
195C42×C83—21no—
196C42×C83—21no—
197C42×C83—21no—
198C42×C83—21no—
199C42×C83—41no—
200C42×C83—41no—
201C42×C83—42no—
202C42×C83C22×C412yes—
203C42×C83#4112yes—
204C23×C83—22no—
205C23×C83—41no—
206C23×C83—41no—
207C23×C83—41no—
208C23×C83—41no—
209C23×C83—41no—
210C23×C83—41no—
211C23×C83C22×D411yescharacteristic
212D4×C83—22no—
213D4×C83—22no—
214D4×C83—41no—
215D4×C83—41no—
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×C83—21no—
224C2×C4×C83—22no—
225C2×C4×C83—21no—
226C2×C4×C83—21no—
227C2×C4×C83—21no—
228C2×C4×C83—21no—
229C2×C4×C83—21no—
230C2×C4×C83—21no—
231C2×C4×C83—48no—
232C2×C4×C83—41no—
233C2×C4×C83—41no—
234C2×C4×C83—41no—
235C2×C4×C83—41no—
236C2×C4×C83—41no—
237C2×C4×C83—41no—
238C2×C4×C83—41no—
239C2×C4×C83—41no—
240C2×C4×C83C4×D412yes—
241C2×C4×C83C4×D412yes—
242C2×C4×C83AGL(1,ℤ/8)12yes—
243C2×C4×C83#13712yes—
244C2×C4×C83C23×C411yescharacteristic
245C2×C4×C83C2×#4111yescharacteristic
246C2×C4×C83C2×#4111yescharacteristic
247C2×C4×C83C2×#4111yescharacteristic
248C2×C4×C83C2×#4111yescharacteristic
249C2×C4×C83C2×#4111yescharacteristic
250C2×Dic83—22no—
251C2×Dic83—22no—
252C2×Dic83—41no—
253C2×Dic83—41no—
254C2×Dic83—41no—
255C2×Dic83—41no—
256C2×Dic83—41no—
257C2×Dic83—41no—
258C2×Dic83—41no—
259C2×Dic83—41no—
260C2×Dic83—41no—
261C2×Dic83—41no—
262Dic166—22no—
263Dic166—22no—
264Dic166—41no—
265Dic166—41no—
266C83⋊C8—22no—
267C83⋊C8—22no—
268C83⋊C8—22no—
269C83⋊C8#11714yescomplemented
270C22×C83—42no—
271C22×C83—42no—
272C22×C83—42no—
273C22×C83—81no—
274C22×C83—81no—
275C22×C83—81no—
276C22×C83—81no—
277C22×C83C2×C4×D411yescharacteristic
278C22×C83#53211yescharacteristic
279C22×C83#53211yescharacteristic
280C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C83C2×#13711yescharacteristic
282C22×C83#57511yescharacteristic
283C22×C83#57511yescharacteristic
284C4×C83—22no—
285C4×C83—22no—
286C4×C83—22no—
287C4×C83—22no—
288C4×C83—41no—
289C4×C83—41no—
290C4×C83—42no—
291C4×C83—81no—
292C4×C83—81no—
293C4×C83C2×#11711yescharacteristic
294C4×C83C4×#4111yescharacteristic
295C4×C83#52911yescharacteristic
296C4×C83#52911yescharacteristic
297Dic83—42no—
298Dic83—42no—
299Dic83—81no—
300Dic83—81no—
301#21288—831nomaximal, Sylow
302C2×C83—82no—
303C2×C83#229311yescharacteristic
304C2×C83C4×AGL(1,ℤ/8)11yescharacteristic
305C2×C83C4×#13711yescharacteristic
306C2×C83#318011yescharacteristic
307C2×C83#318111yescharacteristic
308C2×C83#318211yescharacteristic
309C2×C83#318311yescharacteristic
310C2×#440—831no—
311#2295—831no—
312#2293D8311yescharacteristic
313#1973—831no—
314#1968—831no—
315#1943—831no—
316#1942—831no—
317#1936—831no—
318#1935—831no—
319#1934—831no—
320#1933—831no—
321#1776—831no—
322#1763—831no—
323#1762—831no—
324C4×#97—831no—
325C83#2128811yescharacteristic, complemented, Sylow
326C22×SD16—831no—
327C2×C4×Q8—831no—
328C2×C4×D4C2×D8311yescharacteristic
329C2×#117—21no—
330#440—838no—
331C2×#107—831no—
332C2×#107—831no—
333C2×#106—831no—
334C2×#103—831no—
335C2×#103—831no—
336C2×#103—831no—
337C2×#102—831no—
338C2×#102—831no—
339C2×#102—831no—
340C2×#97—831no—
341C2×#97—831no—
342C2×#97—831no—
343C2×#97—831no—
344C2×C4×C8—831no—
345C2×C4×C8—831no—
346#391—831no—
347#391—831no—
348#390C2×D8311yescharacteristic
349#390C2×D8311yescharacteristic
350#389—831no—
351#389—831no—
352#389C2×D8311yescharacteristic
353#389C2×D8311yescharacteristic
354#388—21no—
355#388—21no—
356#387—1661no—
357#387—1661no—
358C4×C4⋊C4—831no—
359C4×C4⋊C4—1661no—
360C4×C4⋊C4C2×D8311yescharacteristic
361C4×C22⋊C4—21no—
362#376—1661no—
363C43C2×D8311yescharacteristic
364#340—831no—
365#340—831no—
366#340—831no—
367#340—831no—
368#340—831no—
369#340—831no—
370C22×Q8—831no—
371C22×D4C22×D8311yescharacteristic
372C23×C4—21no—
373C2×SD16—834no—
374C2×SD16—1662no—
375C2×SD16—1662no—
376C22×C8—831no—
377C22×C8—831no—
378C22×C8—831no—
379C22×C8—831no—
380C4×Q8—834no—
381C4×Q8—1662no—
382C4×D4—22no—
383C4×D4C4×D8314yes—
384#117—44no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—831no—
388C2×C4⋊C4—831no—
389C2×C4⋊C4—831no—
390C2×C4⋊C4—1661no—
391C2×C4⋊C4—1661no—
392C2×C4⋊C4—1661no—
393C2×C4⋊C4C22×D8311yescharacteristic
394C2×C4⋊C4C22×D8311yescharacteristic
395C2×C4⋊C4C22×D8311yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C42—21no—
402C2×C42—1661no—
403C2×C42—1661no—
404C2×C42C22⋊D8311yescharacteristic
405C2×C42C22⋊D8311yescharacteristic
406C2×C42C22⋊D8311yescharacteristic
407C2×C42C22⋊D8311yescharacteristic
408C2×C42C22×D8311yescharacteristic
409C2×C42C22×D8311yescharacteristic
410C2×C42C22×D8311yescharacteristic
411#107—834no—
412#107—1662no—
413#106—1662no—
414#103—834no—
415#103—1662no—
416#103—1662no—
417#102—834no—
418#102—1662no—
419#102—1662no—
420#97—834no—
421#97—1662no—
422#97—1662no—
423#97—1662no—
424C4×C8—1662no—
425C4×C8—1662no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—1661no—
430#95—1661no—
431#95—1661no—
432#95—1661no—
433#95—1661no—
434#95—1661no—
435#95—1661no—
436C24—21no—
437C2×Q8—832no—
438C2×Q8—1661no—
439C2×Q8—1661no—
440C2×Q8—1661no—
441C2×Q8—1661no—
442C2×Q8—1661no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4C2×C4×D8312yes—
449C22×C4—21no—
450C22×C4—24no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—1661no—
456C22×C4—1661no—
457C22×C4—1661no—
458C22×C4—1661no—
459C22×C4C2×C22⋊D8311yescharacteristic
460C22×C4C2×C22⋊D8311yescharacteristic
461C22×C4C2×C22⋊D8311yescharacteristic
462C22×C4C2×C22⋊D8311yescharacteristic
463C22×C4C2×C22⋊D8311yescharacteristic
464C22×C4C2×C22⋊D8311yescharacteristic
465C22×C4C23×D8311yescharacteristic
466SD16—1668no—
467C2×C8—832no—
468C2×C8—832no—
469C2×C8—832no—
470C2×C8—832no—
471C2×C8—832no—
472C2×C8—832no—
473C2×C8—1661no—
474C2×C8—1661no—
475C2×C8—1661no—
476C2×C8—1661no—
477C2×C8—1661no—
478C2×C8—1661no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—42no—
485C4⋊C4—42no—
486C4⋊C4—3322no—
487C4⋊C4—3322no—
488C4⋊C4—832no—
489C4⋊C4—1661no—
490C4⋊C4—1661no—
491C4⋊C4—1661no—
492C4⋊C4—1661no—
493C4⋊C4—1661no—
494C4⋊C4—1664no—
495C4⋊C4C2×C4×D8312yes—
496C22⋊C4—24no—
497C22⋊C4—42no—
498C22⋊C4—42no—
499C22⋊C4—42no—
500C22⋊C4—42no—
501C42—22no—
502C42—22no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—41no—
508C42—41no—
509C42—42no—
510C42—3322no—
511C42—1664no—
512C42C2×C4×D8312yes—
513C42#1305059012yes—
514C23—22no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23C22×C22⋊D8311yescharacteristic
522Q8—3321no—
523Q8—3321no—
524Q8—1662no—
525Q8—1662no—
526D4—22no—
527D4—22no—
528D4—41no—
529D4—41no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—48no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—3321no—
555C2×C4—3321no—
556C2×C4—3321no—
557C2×C4—3321no—
558C2×C4—3321no—
559C2×C4—3321no—
560C2×C4—3321no—
561C2×C4—3321no—
562C2×C4—3321no—
563C2×C4—3321no—
564C2×C4—1662no—
565C2×C4—1662no—
566C2×C4C4×C22⋊D8312yes—
567C2×C4C4×C22⋊D8312yes—
568C2×C4#1458181812yes—
569C2×C4#1458182212yes—
570C2×C4C22×C4×D8311yescharacteristic
571C2×C4#41×D8311yescharacteristic
572C2×C4#41×D8311yescharacteristic
573C2×C4#41×D8311yescharacteristic
574C2×C4#41×D8311yescharacteristic
575C2×C4C2×#1305059011yescharacteristic
576C8—834no—
577C8—1662no—
578C8—1662no—
579C8—1662no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22C2×C4×C22⋊D8311yescharacteristic
588C22#1912824711yescharacteristic
589C22#1912824711yescharacteristic
590C22C2×#1458181811yescharacteristic
591C22C2×#1458182211yescharacteristic
592C22#1912849911yescharacteristic
593C22#1912849911yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—42no—
599C4—41no—
600C4—41no—
601C4—81no—
602C4—81no—
603C4—3322no—
604C4—3322no—
605C4—6641no—
606C4—6641no—
607C4#117×D8311yescharacteristic
608C4#1912816911yescharacteristic
609C4#1912822911yescharacteristic
610C4#1912822911yescharacteristic
611C2—82no—
612C2#2490992211yescharacteristic
613C2C4×#1458181811yescharacteristic
614C2C4×#1458182211yescharacteristic
615C2#2491815511yescharacteristic
616C2#2491817311yescharacteristic
617C2#2491817711yescharacteristic
618C2#2491818611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#2293C2
socleC23×C83C22×D4
prime radicalC22×D4×C83C23
cosocleC22×C4×C83C24
hypercenter#2293D83
hypocenterC83#21288
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C43 ◁ #2293

Complements

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

NH ≅ G/Ntype
2. #24909940C2semidirect
5. #24908198C2semidirect
6. #24908193C2semidirect
8. #24908152C2semidirect
10. #24908138C2semidirect
11. #24907361C2semidirect
12. #24907296C2semidirect
14. C4×#14581703C2semidirect
18. #19127801C4semidirect
269. C83⋊C8#117semidirect
325. C83#21288semidirect

Maximal subgroups

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

subgroupindex
C2×#191278012
#249099402
#249083432
#249083162
#249081982
#249081932
#249081632
#249081522
#249081492
#249081382
#249073612
#249072962
#249072882
C4×#145817032
C83×#22932
#2128883