Finite Group Databasebeta

← #35374464

Subgroups — #35374464

Order 21248.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917510C211yesmaximal, characteristic
2#24916614C211yesmaximal, characteristic, complemented
3#24906327C211yesmaximal, characteristic, complemented
4#24906320C211yesmaximal, characteristic, complemented
5#24906299C211yesmaximal, characteristic, complemented
6#24906292C211yesmaximal, characteristic, complemented
7#24906285C211yesmaximal, characteristic, complemented
8#24906275C211yesmaximal, characteristic, complemented
9C8×#13050578C211yesmaximal, characteristic, complemented
10C8×#13050575C211yesmaximal, characteristic, complemented
11#24906251C211yesmaximal, characteristic, complemented
12#24905888C211yesmaximal, characteristic, complemented
13#24905869C211yesmaximal, characteristic, complemented
14#24905763C211yesmaximal, characteristic, complemented
15C83×#2972C211yesmaximal, characteristic, complemented
16#19128235C2211yescharacteristic
17#19128036C411yescharacteristic
18#19128019C411yescharacteristic
19#19128001C411yescharacteristic
20#19128001C411yescharacteristic
21#19127916C411yescharacteristic
22#19127916C411yescharacteristic
23#19127852C411yescharacteristic
24#19127835C411yescharacteristic
25#19127831C2211yescharacteristic, complemented
26C8×Dic166C2211yescharacteristic, complemented
27C4×#13050578C2211yescharacteristic
28C4×#13050578C2211yescharacteristic
29C4×#13050575C2211yescharacteristic
30C4×#13050575C2211yescharacteristic
31#19127780C2211yescharacteristic, complemented
32#19127776—21no—
33#19127775—21no—
34C8×D332C2211yescharacteristic, complemented
35#19127761—21no—
36#19127754C2211yescharacteristic
37#19127754C2211yescharacteristic
38#19127726—21no—
39#19127725C2211yescharacteristic
40#19127453C2211yescharacteristic, complemented
41#19127453C2211yescharacteristic, complemented
42#19127451C2211yescharacteristic, complemented
43#19127451C2211yescharacteristic, complemented
44#19127431C2211yescharacteristic, complemented
45#19127431C2211yescharacteristic, complemented
46D4⋊(C83⋊C8)C2211yescharacteristic
47D4⋊(C83⋊C8)C2211yescharacteristic
48D4⋊(C83⋊C8)C2211yescharacteristic
49D4⋊(C83⋊C8)C2211yescharacteristic
50#19127428C2211yescharacteristic, complemented
51#19127428C2211yescharacteristic, complemented
52#19127423C2211yescharacteristic, complemented
53#19127423C2211yescharacteristic, complemented
54#19127422C2211yescharacteristic, complemented
55C8×C83⋊C8C2211yescharacteristic, complemented
56C2×C4×D4×C83C2211yescharacteristic
57C8×D4×C83—21no—
58C8×D4×C83—21no—
59C8×D4×C83C2211yescharacteristic
60C8×D4×C83C2211yescharacteristic
61C8×D4×C83C2211yescharacteristic
62C8×D4×C83C2211yescharacteristic
63#431×C83C2211yescharacteristic
64#431×C83C2211yescharacteristic
65C2×C22⋊C8×C83—21no—
66C2×C22⋊C8×C83—21no—
67C2×#13050578C2×C411yescharacteristic
68C2×#13050578C2×C411yescharacteristic
69C2×#13050575C2×C411yescharacteristic
70C2×#13050575C2×C411yescharacteristic
71C2×#13050574—21no—
72C2×#13050573—21no—
73C2×C8×D83—21no—
74#14581786—21no—
75#14581784C2×C411yescharacteristic
76#14581780C2×C411yescharacteristic
77#14581775—21no—
78#14581771C2×C411yescharacteristic
79#14581766C2×C411yescharacteristic
80C4×Dic166C2311yescharacteristic
81C4×D332C2311yescharacteristic
82C4×C22⋊D83—21no—
83#14581749—21no—
84#14581725C2×C411yescharacteristic
85#14581725C2×C411yescharacteristic
86#14581723C2×C411yescharacteristic
87#14581723C2×C411yescharacteristic
88C4⋊(C83⋊C8)—21no—
89C4⋊(C83⋊C8)—21no—
90C4⋊(C83⋊C8)C2×C411yescharacteristic
91C4⋊(C83⋊C8)C2×C411yescharacteristic
92C4⋊(C83⋊C8)C2311yescharacteristic
93C4⋊(C83⋊C8)C2311yescharacteristic
94Dic83⋊C8—21no—
95Dic83⋊C8—21no—
96#14581715C2×C411yescharacteristic
97#14581715C2×C411yescharacteristic
98#14581713C2×C411yescharacteristic
99#14581713C2×C411yescharacteristic
100#14581713C2×C411yescharacteristic
101#14581713C2×C411yescharacteristic
102#14581712C2×C411yescharacteristic
103#14581712C2×C411yescharacteristic
104C22⋊(C83⋊C8)—21no—
105C22⋊(C83⋊C8)C2×C411yescharacteristic
106C22⋊(C83⋊C8)C2×C411yescharacteristic
107(C2×D83)⋊C8—21no—
108(C2×D83)⋊C8—21no—
109#14581702—21no—
110C4×C83⋊C8C2311yescharacteristic
111C4×C83⋊C8C2311yescharacteristic
112C4×C83⋊C8C2311yescharacteristic
113C4×C83⋊C8C2311yescharacteristic
114C8×Dic83—21no—
115C22×D4×C83C2×C411yescharacteristic
116C23×C4×C83—21no—
117C22×C8×C83—21no—
118C22×C8×C83—21no—
119C22×C8×C83—21no—
120C22×C8×C83—21no—
121C4×D4×C83—21no—
122C4×D4×C83—21no—
123C4×D4×C83C2×C411yescharacteristic
124C4×D4×C83C2×C411yescharacteristic
125C4×D4×C83C2311yescharacteristic
126C4×D4×C83C2311yescharacteristic
127C2×C4⋊C4×C83C2×C411yescharacteristic
128C2×C22⋊C4×C83—21no—
129C2×C42×C83C2311yescharacteristic
130C4⋊C8×C83D411yescharacteristic
131C4⋊C8×C83D411yescharacteristic
132C4⋊C8×C83C2311yescharacteristic
133C4⋊C8×C83C2311yescharacteristic
134C22⋊C8×C83—21no—
135C22⋊C8×C83—21no—
136C22⋊C8×C83—21no—
137C22⋊C8×C83—21no—
138C22⋊C8×C83—21no—
139C22⋊C8×C83D411yescharacteristic
140C22⋊C8×C83D411yescharacteristic
141C4×C8×C83—21no—
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C2×Dic166C22×C411yescharacteristic
145C2×D332C22×C411yescharacteristic
146C2×C22⋊D83—21no—
147C2×C4×D83—21no—
148#13050578—22no—
149#13050578—22no—
150#13050575—22no—
151#13050575—22no—
152#13050574—81no—
153#13050573—81no—
154C2×C83⋊C8—21no—
155C2×C83⋊C8—21no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8C22×C411yescharacteristic
159C2×C83⋊C8C22×C411yescharacteristic
160C2×C83⋊C8C22×C411yescharacteristic
161C2×C83⋊C8C22×C411yescharacteristic
162C8×D83—81no—
163C4⋊Dic83C22×C411yescharacteristic
164C4⋊Dic83C22×C411yescharacteristic
165Dic83⋊C4—21no—
166Dic83⋊C4—21no—
167Dic83⋊C4—21no—
168Dic83⋊C4—21no—
169C22⋊Dic83—21no—
170(C2×D83)⋊C4—21no—
171(C2×D83)⋊C4—21no—
172(C2×D83)⋊C4—21no—
173(C2×D83)⋊C4—21no—
174C4×Dic83—21no—
175C24×C83—21no—
176C2×D4×C83—22no—
177C2×D4×C83—22no—
178C2×D4×C83—21no—
179C2×D4×C83C22×C411yescharacteristic
180C2×D4×C83C22×C411yescharacteristic
181C22×C4×C83—21no—
182C22×C4×C83—21no—
183C22×C4×C83—21no—
184C22×C4×C83—21no—
185C22×C4×C83—21no—
186C22×C4×C83—81no—
187C22×C4×C83—81no—
188C22×C4×C83C22×C411yescharacteristic
189C22×C4×C83C2×D411yescharacteristic
190C22×C4×C83#4111yescharacteristic
191C2×C8×C83—21no—
192C2×C8×C83—21no—
193C2×C8×C83—81no—
194C2×C8×C83—81no—
195C2×C8×C83—81no—
196C2×C8×C83—81no—
197C2×C8×C83C2×D411yescharacteristic
198C2×C8×C83C2×D411yescharacteristic
199C2×C8×C83C2×D411yescharacteristic
200C2×C8×C83C2×D411yescharacteristic
201C4⋊C4×C83—21no—
202C4⋊C4×C83C22×C411yescharacteristic
203C4⋊C4×C83C22×C411yescharacteristic
204C22⋊C4×C83—21no—
205C22⋊C4×C83—21no—
206C22⋊C4×C83—21no—
207C22⋊C4×C83—21no—
208C42×C83C22×C411yescharacteristic
209C42×C83C2×D411yescharacteristic
210C42×C83#4111yescharacteristic
211C42×C83C2411yescharacteristic
212C23×C83—24no—
213C23×C83—21no—
214C23×C83—21no—
215C23×C83—81no—
216C23×C83—81no—
217C23×C83C4×D411yescharacteristic
218C22×D83—21no—
219D4×C83—24no—
220D4×C83—21no—
221D4×C83—21no—
222D4×C83#13112yes—
223D4×C83#13112yes—
224C2×C4×C83—21no—
225C2×C4×C83—21no—
226C2×C4×C83—21no—
227C2×C4×C83—21no—
228C2×C4×C83—21no—
229C2×C4×C83—21no—
230C2×C4×C83—41no—
231C2×C4×C83—41no—
232C2×C4×C83—41no—
233C2×C4×C83—41no—
234C2×C4×C83—41no—
235C2×C4×C83—81no—
236C2×C4×C83—81no—
237C2×C4×C83—81no—
238C2×C4×C83C4×D411yescharacteristic
239C2×C4×C83C4×D411yescharacteristic
240C2×C4×C83C4×D411yescharacteristic
241C2×C4×C83C23×C411yescharacteristic
242C2×C4×C83C22×D411yescharacteristic
243C2×C4×C83C2×#4111yescharacteristic
244C22⋊D83—81no—
245C2×Dic83—21no—
246C2×Dic83—21no—
247C2×Dic83—21no—
248D332—21no—
249D332—21no—
250C4×D83—41no—
251C4×D83—41no—
252Dic166—21no—
253Dic166—21no—
254C8×C83—21no—
255C8×C83—21no—
256C8×C83—21no—
257C8×C83—21no—
258C8×C83—41no—
259C8×C83—41no—
260C83⋊C8—21no—
261C83⋊C8—21no—
262C83⋊C8—21no—
263C83⋊C8—21no—
264C83⋊C8—41no—
265C83⋊C8—41no—
266C83⋊C8—41no—
267C83⋊C8—41no—
268C22×C83—21no—
269C22×C83—22no—
270C22×C83—22no—
271C22×C83—21no—
272C22×C83—21no—
273C22×C83—41no—
274C22×C83—41no—
275C22×C83—41no—
276C22×C83—41no—
277C22×C83—84no—
278C22×C83C2×C4×D411yescharacteristic
279C2×D83—41no—
280C2×D83—41no—
281C2×D83—41no—
282C4×C83—21no—
283C4×C83—21no—
284C4×C83—21no—
285C4×C83—21no—
286C4×C83—41no—
287C4×C83—41no—
288C4×C83C2×#13111yescharacteristic
289C4×C83C2×#13111yescharacteristic
290C4×C83#57611yescharacteristic
291C4×C83#57711yescharacteristic
292Dic83—41no—
293Dic83—41no—
294Dic83—41no—
295#17918—831nomaximal, Sylow
296C2×C83—41no—
297C2×C83—42no—
298C2×C83—42no—
299C2×C83#292911yescharacteristic
300C2×C83#294611yescharacteristic
301C2×C83#295711yescharacteristic
302D83—81no—
303#3105—831no—
304#2993—831no—
305#2972D8311yescharacteristic, complemented
306#1586—831no—
307#1585—831no—
308#1582—831no—
309#1581—831no—
310#1580—831no—
311SD16⋊C8—831no—
312C8×SD16—831no—
313C8×D8—831no—
314#1574—831no—
315#1486—831no—
316#1482—831no—
317#1454—831no—
318C83#1791811yescharacteristic, complemented, Sylow
319#529—831no—
320C2×C4×D4C2×D8311yescharacteristic
321#484—831no—
322#481—831no—
323#478—831no—
324#478—831no—
325#463—831no—
326#463—831no—
327#450—831no—
328#447—831no—
329#446—831no—
330C8×Q8—831no—
331C4×SD16—831no—
332C4×SD16—831no—
333C4×D8—831no—
334C4×D8—831no—
335#436—831no—
336#436—1661no—
337#435—1661no—
338C8×D4—21no—
339C8×D4—21no—
340C8×D4—831no—
341C8×D4C2×D8311yescharacteristic
342C8×D4C2×D8311yescharacteristic
343C8×D4C2×D8311yescharacteristic
344C8×D4C2×D8311yescharacteristic
345#433—1661no—
346#431—831no—
347#431—831no—
348#431C2×D8311yescharacteristic
349#431C2×D8311yescharacteristic
350#424—1661no—
351#423—831no—
352C2×C22⋊C8—21no—
353C2×C22⋊C8—21no—
354#335—831no—
355#335—831no—
356#334—831no—
357#334—831no—
358Q8⋊C8—831no—
359Q8⋊C8—831no—
360D4⋊C8—831no—
361D4⋊C8—831no—
362D4⋊C8—831no—
363D4⋊C8—831no—
364D4⋊C8—831no—
365D4⋊C8—831no—
366#322—831no—
367#322—831no—
368#322—831no—
369C82—831no—
370C22×D4C4×D8311yescharacteristic
371C23×C4—21no—
372C2×SD16—831no—
373C2×SD16—831no—
374C2×D8—831no—
375C2×D8—831no—
376C2×M16—1661no—
377C2×M16—1661no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—1661no—
383#126—1661no—
384#125—831no—
385#124—831no—
386#123—1661no—
387C22⋊Q8—831no—
388#121—831no—
389C4×Q8—831no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—831no—
393C4×D4—1661no—
394C4×D4C4×D8311yescharacteristic
395C4×D4C4×D8311yescharacteristic
396C4×D4C22×D8311yescharacteristic
397C4×D4C22×D8311yescharacteristic
398#117—1661no—
399C2×C4⋊C4C4×D8311yescharacteristic
400C2×C22⋊C4—21no—
401C2×C42C22×D8311yescharacteristic
402#107—831no—
403#107—831no—
404#106—831no—
405#106—831no—
406C4⋊C8—831no—
407C4⋊C8—831no—
408C4⋊C8—831no—
409C4⋊C8—831no—
410C4⋊C8—1661no—
411C4⋊C8—1661no—
412C4⋊C8—1661no—
413C4⋊C8—1661no—
414C4⋊C8C22⋊D8311yescharacteristic
415C4⋊C8C22⋊D8311yescharacteristic
416C4⋊C8C22×D8311yescharacteristic
417C4⋊C8C22×D8311yescharacteristic
418#103—831no—
419#103—831no—
420#102—831no—
421#102—831no—
422#102—831no—
423#102—831no—
424#102—831no—
425#102—831no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—831no—
432C22⋊C8—831no—
433C22⋊C8—1661no—
434C22⋊C8—1661no—
435C22⋊C8—1661no—
436C22⋊C8C22⋊D8311yescharacteristic
437C22⋊C8C22⋊D8311yescharacteristic
438#97—1661no—
439C4×C8—21no—
440C4×C8—831no—
441C4×C8—831no—
442C4×C8—831no—
443C4×C8—831no—
444C4×C8—1661no—
445C4×C8C22×D8311yescharacteristic
446C4×C8C22×D8311yescharacteristic
447C24—21no—
448C2×Q8—831no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—831no—
453C2×D4—1661no—
454C2×D4C2×C4×D8311yescharacteristic
455C2×D4C2×C4×D8311yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—81no—
462C22×C4—81no—
463C22×C4—1661no—
464C22×C4C2×C4×D8311yescharacteristic
465C22×C4C2×C22⋊D8311yescharacteristic
466C22×C4#1305059011yescharacteristic
467SD16—1662no—
468SD16—1662no—
469D8—1662no—
470D8—1662no—
471M16—6641no—
472M16—6641no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—81no—
477C2×C8—81no—
478C2×C8—81no—
479C2×C8—831no—
480C2×C8—831no—
481C2×C8—831no—
482C2×C8—831no—
483C2×C8—6641no—
484C2×C8—1661no—
485C2×C8—1661no—
486C2×C8—1661no—
487C2×C8—1661no—
488C2×C8C2×C22⋊D8311yescharacteristic
489C2×C8C2×C22⋊D8311yescharacteristic
490C2×C8C2×C22⋊D8311yescharacteristic
491C2×C8C2×C22⋊D8311yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—831no—
494C4⋊C4—831no—
495C4⋊C4—1661no—
496C4⋊C4—1661no—
497C4⋊C4—1661no—
498C4⋊C4—1661no—
499C4⋊C4C2×C4×D8311yescharacteristic
500C4⋊C4C2×C4×D8311yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—1661no—
506C22⋊C4—1661no—
507C22⋊C4—1661no—
508C22⋊C4—1661no—
509C22⋊C4—1661no—
510C42—1661no—
511C42C2×C4×D8311yescharacteristic
512C42C2×C22⋊D8311yescharacteristic
513C42#1305059011yescharacteristic
514C42C23×D8311yescharacteristic
515C23—24no—
516C23—21no—
517C23—21no—
518C23—81no—
519C23—81no—
520C23—1661no—
521C23C4×C22⋊D8311yescharacteristic
522Q8—1661no—
523Q8—1661no—
524D4—24no—
525D4—21no—
526D4—21no—
527D4—6641no—
528D4—1661no—
529D4—1661no—
530D4#1458179812yes—
531D4#1458179812yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—3321no—
547C2×C4—3321no—
548C2×C4—1661no—
549C2×C4—1661no—
550C2×C4—1661no—
551C2×C4C4×C22⋊D8311yescharacteristic
552C2×C4C4×C22⋊D8311yescharacteristic
553C2×C4C4×C22⋊D8311yescharacteristic
554C2×C4C22×C4×D8311yescharacteristic
555C2×C4C22×C22⋊D8311yescharacteristic
556C2×C4C2×#1305059011yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—3321no—
564C8—3321no—
565C8—3321no—
566C8—3321no—
567C8—1661no—
568C8—1661no—
569C8—1661no—
570C8—1661no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—22no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—84no—
581C22—3321no—
582C22—3321no—
583C22—3321no—
584C22C2×C4×C22⋊D8311yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—3321no—
592C4—3321no—
593C4—3321no—
594C4C2×#1458179811yescharacteristic
595C4C2×#1458179811yescharacteristic
596C4#1912850411yescharacteristic
597C4#1912851211yescharacteristic
598C2—41no—
599C2—42no—
600C2—42no—
601C2—6641no—
602C2#2491615711yescharacteristic
603C2#2491629511yescharacteristic
604C2#2491637811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#2972C2
socleC22×C83C2×C4×D4
prime radical#19127835C4
cosocleC42×C83C24
hypercenter#2972D83
hypocenterC83#17918
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2972

Complements

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

NH ≅ G/Ntype
2. #24916614C2semidirect
3. #24906327C2semidirect
4. #24906320C2semidirect
5. #24906299C2semidirect
6. #24906292C2semidirect
7. #24906285C2semidirect
8. #24906275C2semidirect
9. C8×#13050578C2semidirect
10. C8×#13050575C2semidirect
11. #24906251C2semidirect
12. #24905888C2semidirect
13. #24905869C2semidirect
14. #24905763C2semidirect
15. C83×#2972C2semidirect
25. #19127831C22semidirect
26. C8×Dic166C22semidirect
31. #19127780C22semidirect
34. C8×D332C22semidirect
40. #19127453C22semidirect
41. #19127453C22semidirect
42. #19127451C22semidirect
43. #19127451C22semidirect
44. #19127431C22semidirect
45. #19127431C22semidirect
50. #19127428C22semidirect
51. #19127428C22semidirect
52. #19127423C22semidirect
53. #19127423C22semidirect
54. #19127422C22semidirect
55. C8×C83⋊C8C22semidirect
305. #2972D83semidirect
318. C83#17918semidirect

Maximal subgroups

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

subgroupindex
#249175102
#249166142
#249063272
#249063202
#249062992
#249062922
#249062852
#249062752
C8×#130505782
C8×#130505752
#249062512
#249058882
#249058692
#249057632
C83×#29722
#1791883