Finite Group Databasebeta

← #35414933

Subgroups — #35414933

Order 21248.

834 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
1C2×#19127753C211yesmaximal, characteristic
2#24909859C211yesmaximal, characteristic
3#382×D83C211yesmaximal, characteristic
4#24908233C211yesmaximal, characteristic, complemented
5#24908231C211yesmaximal, characteristic, complemented
6#24908229C211yesmaximal, characteristic, complemented
7#24907657C211yesmaximal, characteristic
8#24907654C211yesmaximal, characteristic
9#24907652C211yesmaximal, characteristic
10#24907649C211yesmaximal, characteristic
11#24907626C211yesmaximal, characteristic, complemented
12#24907624C211yesmaximal, characteristic, complemented
13#24907592C211yesmaximal, characteristic, complemented
14#24907592C211yesmaximal, characteristic, complemented
15C83×#1949C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×D83C2211yescharacteristic
17C2×C4⋊C4×D83C2211yescharacteristic
18C2×C42×D83C2211yescharacteristic
19#19127753C418yescomplemented
20C2×#14581726C2211yescharacteristic
21C2×#14581725C2211yescharacteristic
22C2×#14581725C2211yescharacteristic
23C2×#14581724C2211yescharacteristic
24C2×#14581723C2211yescharacteristic
25C2×#14581723C2211yescharacteristic
26C2×C4⋊(C83⋊C8)C2211yescharacteristic
27C2×(C2×D83)⋊C8C2211yescharacteristic
28C2×(C2×D83)⋊C8C2211yescharacteristic
29C2×C8×Dic83C2211yescharacteristic
30C2×C8×Dic83C2211yescharacteristic
31#19127568—21no—
32#19127567C2211yescharacteristic
33#19127566C2211yescharacteristic
34#19127566C2211yescharacteristic
35#19127566C2211yescharacteristic
36#19127566C2211yescharacteristic
37#19127565—21no—
38#19127565—21no—
39#19127563—21no—
40#19127558C2211yescharacteristic
41#19127558C2211yescharacteristic
42C4×C4⋊Dic83C2211yescharacteristic
43C4×(C2×D83)⋊C4—21no—
44#19127547—21no—
45#95×D83—21no—
46#95×D83—21no—
47#19127464C2211yescharacteristic
48#19127464C2211yescharacteristic
49#19127463C2211yescharacteristic
50#19127463C2211yescharacteristic
51#19127463C2211yescharacteristic
52#19127463C2211yescharacteristic
53C2×#107×C83C2211yescharacteristic
54C2×#106×C83C2211yescharacteristic
55C2×C4⋊C8×C83C2211yescharacteristic
56#382×C83C2211yescharacteristic
57C4×C4⋊C4×C83C2211yescharacteristic
58#340×C83C2211yescharacteristic
59#340×C83C2211yescharacteristic
60C22×C4×D83—21no—
61C22×C4×D83—21no—
62C22×C4×D83D411yescharacteristic
63C22×C4×D83D411yescharacteristic
64C22×C4×D83C2311yescharacteristic
65C22×C83⋊C8C2311yescharacteristic
66C22×C83⋊C8C2311yescharacteristic
67C2×C4⋊Dic83C2311yescharacteristic
68C2×C4⋊Dic83C2311yescharacteristic
69C2×C4⋊Dic83C2311yescharacteristic
70C2×C4⋊Dic83C2311yescharacteristic
71C2×Dic83⋊C4—21no—
72C2×Dic83⋊C4—21no—
73C4⋊C4×D83—41no—
74C4⋊C4×D83—41no—
75C4⋊C4×D83—41no—
76C4⋊C4×D83—41no—
77C2×(C2×D83)⋊C4—21no—
78C2×(C2×D83)⋊C4—21no—
79C2×C4×Dic83—21no—
80C2×C4×Dic83D411yescharacteristic
81C2×C4×Dic83D411yescharacteristic
82C2×C4×Dic83C2311yescharacteristic
83C42×D83C2×C414yes—
84C42×D83Q814yes—
85#14581726—41no—
86#14581725—41no—
87#14581725—41no—
88#14581724—41no—
89#14581723—41no—
90#14581723—41no—
91C4⋊(C83⋊C8)C2×C414yescomplemented
92(C2×D83)⋊C8C2×C414yes—
93(C2×D83)⋊C8C2×C414yes—
94C8×Dic83C2×C414yescomplemented
95C8×Dic83C2×C414yescomplemented
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—
105C83⋊#95—21no—
106C83⋊#95—21no—
107C83⋊#95—21no—
108C83⋊#95—21no—
109C22×C8×C83C2311yescharacteristic
110C22×C8×C83C2311yescharacteristic
111C2×C4⋊C4×C83C2311yescharacteristic
112C2×C4⋊C4×C83C2311yescharacteristic
113C2×C4⋊C4×C83C2311yescharacteristic
114C2×C4⋊C4×C83C2311yescharacteristic
115C2×C42×C83—21no—
116C2×C42×C83C2311yescharacteristic
117#107×C83—41no—
118#106×C83—41no—
119C4⋊C8×C83C2×C414yescomplemented
120#95×C83—21no—
121#95×C83—21no—
122#95×C83—21no—
123C23×D83C2×D411yescharacteristic
124C22×Dic83—21no—
125C22×Dic83—21no—
126C22×Dic83—21no—
127C22×Dic83—21no—
128C22×Dic83C2×D411yescharacteristic
129C22×Dic83C2×D411yescharacteristic
130C22×Dic83C2×D411yescharacteristic
131C2×C4×D83—22no—
132C2×C4×D83—22no—
133C2×C4×D83—21no—
134C2×C4×D83—21no—
135C2×C4×D83—21no—
136C2×C4×D83—21no—
137C2×C4×D83—41no—
138C2×C4×D83—41no—
139C2×C4×D83—42no—
140C2×C4×D83—42no—
141C2×C4×D83—42no—
142C2×C4×D83—42no—
143C2×C4×D83—42no—
144C2×C4×D83—42no—
145C2×C4×D83C4⋊C414yes—
146C2×C4×D83C4⋊C414yes—
147C2×C4×D83C22×C412yes—
148C2×C4×D83C2×Q812yes—
149C2×C83⋊C8—21no—
150C2×C83⋊C8—21no—
151C2×C83⋊C8—21no—
152C2×C83⋊C8—21no—
153C2×C83⋊C8C22×C412yes—
154C2×C83⋊C8C22×C412yes—
155C4⋊Dic83—21no—
156C4⋊Dic83—21no—
157C4⋊Dic83—21no—
158C4⋊Dic83—21no—
159C4⋊Dic83—21no—
160C4⋊Dic83—21no—
161C4⋊Dic83—21no—
162C4⋊Dic83—21no—
163Dic83⋊C4—42no—
164Dic83⋊C4—42no—
165(C2×D83)⋊C4—42no—
166(C2×D83)⋊C4—42no—
167C4×Dic83—42no—
168C4×Dic83C4⋊C414yes—
169C4×Dic83C4⋊C414yes—
170C4×Dic83C22×C412yes—
171C4×Dic83C2×Q812yes—
172C22×C4×C83—21no—
173C22×C4×C83—21no—
174C22×C4×C83—21no—
175C22×C4×C83—21no—
176C22×C4×C83C2×D411yescharacteristic
177C22×C4×C83C2×D411yescharacteristic
178C22×C4×C83C2411yescharacteristic
179C2×C8×C83—21no—
180C2×C8×C83—21no—
181C2×C8×C83—21no—
182C2×C8×C83—21no—
183C2×C8×C83C22×C412yes—
184C2×C8×C83C22×C412yes—
185C4⋊C4×C83—21no—
186C4⋊C4×C83—21no—
187C4⋊C4×C83—21no—
188C4⋊C4×C83—21no—
189C4⋊C4×C83—21no—
190C4⋊C4×C83—21no—
191C4⋊C4×C83—21no—
192C4⋊C4×C83—21no—
193C42×C83—42no—
194C42×C83C22×C412yes—
195C42×C83C2×Q812yes—
196C23×C83C22×D411yescharacteristic
197C22×D83—21no—
198C22×D83—21no—
199C22×D83—21no—
200C22×D83—21no—
201C22×D83C2×C4⋊C412yes—
202C22×D83#13512yes—
203C22×D83#13512yes—
204C2×C4×C83—21no—
205C2×C4×C83—21no—
206C2×C4×C83—21no—
207C2×C4×C83—21no—
208C2×C4×C83—41no—
209C2×C4×C83—41no—
210C2×C4×C83—41no—
211C2×C4×C83—41no—
212C2×C4×C83—41no—
213C2×C4×C83—41no—
214C2×C4×C83—41no—
215C2×C4×C83—41no—
216C2×C4×C83—41no—
217C2×C4×C83—41no—
218C2×C4×C83—41no—
219C2×C4×C83—41no—
220C2×C4×C83C2×C4⋊C412yes—
221C2×C4×C83C2×C4⋊C412yes—
222C2×C4×C83C23×C411yescharacteristic
223C2×C4×C83C22×Q811yescharacteristic
224C2×C4×C83H(5,𝔽2)11yescharacteristic
225C2×C4×C83H(5,𝔽2)11yescharacteristic
226C2×C4×C832−1+411yescharacteristic
227C2×C4×C832−1+411yescharacteristic
228C2×Dic83—21no—
229C2×Dic83—21no—
230C2×Dic83—21no—
231C2×Dic83—21no—
232C2×Dic83—21no—
233C2×Dic83—21no—
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×Dic83C2×C4⋊C412yes—
247C2×Dic83C2×C4⋊C412yes—
248C2×Dic83C2×C4⋊C412yes—
249C4×D83—28no—
250C4×D83—22no—
251C4×D83—22no—
252C4×D83—22no—
253C4×D83—22no—
254C4×D83—44no—
255C4×D83—84no—
256C4×D83—84no—
257C8×C83—22no—
258C8×C83—22no—
259C83⋊C8—22no—
260C83⋊C8—22no—
261C22×C83C22×C4⋊C411yescharacteristic
262C22×C83#53511yescharacteristic
263C22×C83#53611yescharacteristic
264C22×C83C2×#13511yescharacteristic
265C22×C83C2×#13511yescharacteristic
266C22×C83#57511yescharacteristic
267C22×C83#57511yescharacteristic
268C2×D83—22no—
269C2×D83—22no—
270C2×D83—22no—
271C2×D83—22no—
272C2×D83—22no—
273C2×D83—22no—
274C2×D83#42714yes—
275C4×C83—22no—
276C4×C83—22no—
277C4×C83—81no—
278C4×C83—81no—
279C4×C83—81no—
280C4×C83—81no—
281C4×C83#52011yescharacteristic
282C4×C83#52011yescharacteristic
283C4×C83#54411yescharacteristic
284C4×C83#54411yescharacteristic
285Dic83—22no—
286Dic83—22no—
287Dic83—22no—
288Dic83—81no—
289Dic83—81no—
290Dic83—81no—
291Dic83—81no—
292#21983—831nomaximal, Sylow
293C2×C83#231711yescharacteristic
294C2×C83C2×#42711yescharacteristic
295C2×C83#291111yescharacteristic
296C2×C83#321111yescharacteristic
297C2×C83#321111yescharacteristic
298C2×C83#323211yescharacteristic
299C2×C83#323211yescharacteristic
300D83—24no—
301C2×#431—831no—
302#2283—831no—
303C2×#382—831no—
304#1949—831no—
305#1949—831no—
306#1949—831no—
307#1949D8311yescharacteristic, complemented
308#1853—831no—
309#1853—831no—
310#1852—831no—
311#1852—831no—
312#1846—831no—
313#1846—831no—
314#1835—831no—
315#1835—831no—
316C83#2198311yescharacteristic, complemented, Sylow
317C22×C4⋊C4—831no—
318C22×C4⋊C4—831no—
319C22×C42—831no—
320#431—838no—
321C2×#107—831no—
322C2×#107—831no—
323C2×#107—831no—
324C2×#107C2×D8311yescharacteristic
325C2×#106—831no—
326C2×#106—831no—
327C2×#106—831no—
328C2×#106C2×D8311yescharacteristic
329C2×C4⋊C8—831no—
330C2×C4⋊C8C2×D8311yescharacteristic
331C2×C22⋊C8—831no—
332C2×C22⋊C8—831no—
333C2×C4×C8—831no—
334C2×C4×C8—831no—
335#383—1661no—
336#382—831no—
337#382—831no—
338#382—831no—
339#382—831no—
340#382—831no—
341#382—1661no—
342#382—1661no—
343#382C2×D8311yescharacteristic
344#381—1661no—
345#380—831no—
346#380—831no—
347C4×C4⋊C4—831no—
348C4×C4⋊C4C2×D8311yescharacteristic
349C4×C22⋊C4—1661no—
350#376—1661no—
351C2×#95—1661no—
352C2×#95—1661no—
353#340—831no—
354#340—831no—
355#340—831no—
356#340—831no—
357#340—831no—
358#340—831no—
359#340C2×D8311yescharacteristic
360#340C2×D8311yescharacteristic
361C23×C4—831no—
362C23×C4—831no—
363C23×C4—831no—
364C23×C4—1661no—
365C23×C4—1661no—
366C22×C8—831no—
367C22×C8—831no—
368C22×C8C22×D8311yescharacteristic
369C22×C8C22×D8311yescharacteristic
370C2×C4⋊C4—3321no—
371C2×C4⋊C4—3321no—
372C2×C4⋊C4—3321no—
373C2×C4⋊C4—3321no—
374C2×C4⋊C4—831no—
375C2×C4⋊C4—831no—
376C2×C4⋊C4—831no—
377C2×C4⋊C4—831no—
378C2×C4⋊C4—1661no—
379C2×C4⋊C4—1661no—
380C2×C4⋊C4C22×D8311yescharacteristic
381C2×C4⋊C4C22×D8311yescharacteristic
382C2×C4⋊C4C22×D8311yescharacteristic
383C2×C4⋊C4C22×D8311yescharacteristic
384C2×C22⋊C4—1661no—
385C2×C22⋊C4—1661no—
386C2×C42—21no—
387C2×C42—831no—
388C2×C42—831no—
389C2×C42—831no—
390C2×C42—834no—
391C2×C42—834no—
392C2×C42—1661no—
393C2×C42C22×D8311yescharacteristic
394#107—41no—
395#107—3321no—
396#107—3321no—
397#107—3321no—
398#106—41no—
399#106—3321no—
400#106—3321no—
401#106—3321no—
402C4⋊C8—834no—
403C4⋊C8C4×D8314yescomplemented
404C22⋊C8—834no—
405C22⋊C8—834no—
406C4×C8—834no—
407C4×C8—834no—
408#95—21no—
409#95—21no—
410#95—21no—
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#95—1661no—
421#95—1661no—
422#95—1661no—
423#95—1661no—
424C24—831no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—3321no—
430C22×C4—3321no—
431C22×C4—3322no—
432C22×C4—3322no—
433C22×C4—3322no—
434C22×C4—3322no—
435C22×C4—3322no—
436C22×C4—3322no—
437C22×C4—834no—
438C22×C4—831no—
439C22×C4—831no—
440C22×C4—831no—
441C22×C4—832no—
442C22×C4—832no—
443C22×C4—834no—
444C22×C4—1662no—
445C22×C4—1662no—
446C22×C4—1661no—
447C22×C4—1661no—
448C22×C4—1661no—
449C22×C4—1661no—
450C22×C4—1661no—
451C22×C4—1661no—
452C22×C4—1661no—
453C22×C4—1661no—
454C22×C4D4×D8311yescharacteristic
455C22×C4D4×D8311yescharacteristic
456C22×C4C23×D8311yescharacteristic
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—832no—
462C2×C8—832no—
463C2×C8—1661no—
464C2×C8—1661no—
465C2×C8—1661no—
466C2×C8—1661no—
467C2×C8C2×C4×D8312yes—
468C2×C8C2×C4×D8312yes—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—3322no—
478C4⋊C4—3322no—
479C4⋊C4—1661no—
480C4⋊C4—1661no—
481C4⋊C4—1661no—
482C4⋊C4—1661no—
483C4⋊C4—1661no—
484C4⋊C4—1661no—
485C4⋊C4—1661no—
486C4⋊C4—1661no—
487C22⋊C4—3322no—
488C22⋊C4—3322no—
489C42—42no—
490C42—3322no—
491C42—832no—
492C42—832no—
493C42—834no—
494C42—834no—
495C42C2×C4×D8312yes—
496C42Q8×D8312yes—
497C23—832no—
498C23—832no—
499C23—832no—
500C23—1661no—
501C23—1661no—
502C23—1661no—
503C23—1661no—
504C23C2×D4×D8311yescharacteristic
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
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—3324no—
522C2×C4—3321no—
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—832no—
535C2×C4—832no—
536C2×C4—832no—
537C2×C4—6644no—
538C2×C4—6644no—
539C2×C4—1668no—
540C2×C4—1661no—
541C2×C4—1661no—
542C2×C4—1661no—
543C2×C4—1661no—
544C2×C4—1661no—
545C2×C4—1661no—
546C2×C4—1662no—
547C2×C4—1662no—
548C2×C4—1662no—
549C2×C4—1662no—
550C2×C4C4⋊C4×D8312yes—
551C2×C4C4⋊C4×D8312yes—
552C2×C4C22×C4×D8311yescharacteristic
553C2×C4C2×Q8×D8311yescharacteristic
554C2×C4#1458183711yescharacteristic
555C2×C4#1458183811yescharacteristic
556C2×C4#1458183911yescharacteristic
557C2×C4#1458184011yescharacteristic
558C8—22no—
559C8—22no—
560C8—1662no—
561C8—1662no—
562C22—834no—
563C22—1662no—
564C22—1662no—
565C22—1662no—
566C22—1662no—
567C22—1662no—
568C22—1662no—
569C22C2×C4⋊C4×D8311yescharacteristic
570C22#1912826711yescharacteristic
571C22#1912827411yescharacteristic
572C22#135×D8311yescharacteristic
573C22#135×D8311yescharacteristic
574C22#1912849711yescharacteristic
575C22#1912850011yescharacteristic
576C4—22no—
577C4—22no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—6641no—
583C4—6641no—
584C4—6641no—
585C4—6641no—
586C4—1662no—
587C4—1662no—
588C4—1662no—
589C4#1912818011yescharacteristic
590C4#1912818311yescharacteristic
591C4#1912832811yescharacteristic
592C4#1912833111yescharacteristic
593C2—1664no—
594C2#2491008511yescharacteristic
595C2#427×D8311yescharacteristic
596C2#2491605011yescharacteristic
597C2#2491842611yescharacteristic
598C2#2491843211yescharacteristic
599C2#2491862911yescharacteristic
600C2#2491863511yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#1949C2
socleC23×C83C22×D4
prime radicalC23×D83C2×D4
cosocleC22×C4×C83C24
hypercenter#1949D83
hypocenterC83#21983
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #24908233C2semidirect
5. #24908231C2semidirect
6. #24908229C2semidirect
11. #24907626C2semidirect
12. #24907624C2semidirect
13. #24907592C2semidirect
14. #24907592C2semidirect
15. C83×#1949C2semidirect
19. #19127753C4semidirect
91. C4⋊(C83⋊C8)C2×C4semidirect
94. C8×Dic83C2×C4semidirect
95. C8×Dic83C2×C4semidirect
119. C4⋊C8×C83C2×C4semidirect
307. #1949D83semidirect
316. C83#21983semidirect
403. C4⋊C8C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191277532
#249098592
#382×D832
#249082332
#249082312
#249082292
#249076572
#249076542
#249076522
#249076492
#249076262
#249076242
#249075922
C83×#19492
#2198383