Finite Group Databasebeta

← #35374468

Subgroups — #35374468

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#24917512C211yesmaximal, characteristic
2#24916614C211yesmaximal, characteristic, complemented
3#24916486C211yesmaximal, characteristic, complemented
4#24906329C211yesmaximal, characteristic, complemented
5#24906322C211yesmaximal, characteristic, complemented
6#24906301C211yesmaximal, characteristic, complemented
7#24906294C211yesmaximal, characteristic, complemented
8#24906288C211yesmaximal, characteristic, complemented
9#24906277C211yesmaximal, characteristic, complemented
10C8×#13050579C211yesmaximal, characteristic, complemented
11C8×D664C211yesmaximal, characteristic, complemented
12#24906252C211yesmaximal, characteristic, complemented
13#24905889C211yesmaximal, characteristic, complemented
14#24905872C211yesmaximal, characteristic, complemented
15C83×#1454C211yesmaximal, characteristic, complemented
16#19128235C2211yescharacteristic
17C2×C4×D332C2211yescharacteristic
18#19128037C411yescharacteristic
19#19128020C411yescharacteristic
20#19128002C411yescharacteristic
21#19128002C411yescharacteristic
22#19127917C411yescharacteristic
23#19127917C411yescharacteristic
24#19127854C411yescharacteristic
25#19127837C411yescharacteristic
26#19127831C2211yescharacteristic, complemented
27C8×Dic166C2211yescharacteristic, complemented
28C4×#13050579C2211yescharacteristic
29C4×#13050579C2211yescharacteristic
30C4×D664C2211yescharacteristic
31C4×D664C2211yescharacteristic
32#19127780C2211yescharacteristic, complemented
33#19127776—21no—
34#19127775—21no—
35C8×D332C2211yescharacteristic
36C8×D332C2211yescharacteristic
37C8×D332C2211yescharacteristic
38C8×D332C2211yescharacteristic
39C8×D332C2211yescharacteristic, complemented
40#19127766—21no—
41#19127766—21no—
42#19127761—21no—
43#19127754C2211yescharacteristic
44#19127726—21no—
45#19127725C2211yescharacteristic
46C22⋊C8×D83—21no—
47C22⋊C8×D83—21no—
48#19127454C2211yescharacteristic, complemented
49#19127454C2211yescharacteristic, complemented
50#19127452C2211yescharacteristic, complemented
51#19127452C2211yescharacteristic, complemented
52#19127433C2211yescharacteristic, complemented
53#19127433C2211yescharacteristic, complemented
54#19127430C2211yescharacteristic
55#19127430C2211yescharacteristic
56#19127430C2211yescharacteristic
57#19127430C2211yescharacteristic
58#19127430C2211yescharacteristic, complemented
59#19127430C2211yescharacteristic, complemented
60#431×C83C2211yescharacteristic
61#431×C83C2211yescharacteristic
62#431×C83C2211yescharacteristic
63#322×C83C2211yescharacteristic, complemented
64#322×C83C2211yescharacteristic, complemented
65#322×C83C2211yescharacteristic, complemented
66C82×C83C2211yescharacteristic, complemented
67C22×D332C2×C411yescharacteristic
68C22×C4×D83—21no—
69C2×#13050579C2×C411yescharacteristic
70C2×#13050579C2×C411yescharacteristic
71C2×D664C2×C411yescharacteristic
72C2×D664C2×C411yescharacteristic
73C2×#13050574—21no—
74C2×#13050573—21no—
75C2×C8×D83—21no—
76C2×C8×D83—21no—
77C2×C8×D83—21no—
78C2×C8×D83—21no—
79C2×C8×D83—21no—
80#14581786—21no—
81#14581784C2×C411yescharacteristic
82#14581780C2×C411yescharacteristic
83#14581775—21no—
84#14581771C2×C411yescharacteristic
85#14581766C2×C411yescharacteristic
86C4×Dic166C2311yescharacteristic
87C4×D332—21no—
88C4×D332—21no—
89C4×D332C2×C411yescharacteristic
90C4×D332C2×C411yescharacteristic
91C4×D332C2311yescharacteristic
92C4×D332C2311yescharacteristic
93C4×D332C2311yescharacteristic
94C4×C22⋊D83—21no—
95#14581749—21no—
96C2×C4⋊Dic83C2×C411yescharacteristic
97C2×(C2×D83)⋊C4—21no—
98#14581726C2×C411yescharacteristic
99#14581726C2×C411yescharacteristic
100#14581724C2×C411yescharacteristic
101#14581724C2×C411yescharacteristic
102C4⋊(C83⋊C8)—21no—
103C4⋊(C83⋊C8)C2311yescharacteristic
104C4⋊(C83⋊C8)C2311yescharacteristic
105C4⋊(C83⋊C8)C2311yescharacteristic
106C4⋊(C83⋊C8)C2311yescharacteristic
107Dic83⋊C8—21no—
108Dic83⋊C8—21no—
109#14581717C2×C411yescharacteristic
110#14581717C2×C411yescharacteristic
111#14581714C2×C411yescharacteristic
112#14581714C2×C411yescharacteristic
113#14581714C2×C411yescharacteristic
114#14581714C2×C411yescharacteristic
115#14581714C2×C411yescharacteristic
116#14581714C2×C411yescharacteristic
117C22⋊(C83⋊C8)—21no—
118(C2×D83)⋊C8—21no—
119(C2×D83)⋊C8—21no—
120(C2×D83)⋊C8—21no—
121(C2×D83)⋊C8—21no—
122(C2×D83)⋊C8—21no—
123(C2×D83)⋊C8—21no—
124#14581702—21no—
125C4×C83⋊C8—21no—
126C8×Dic83—21no—
127C2×C42×C83C2311yescharacteristic
128C4⋊C8×C83—21no—
129C4⋊C8×C83C2×C411yescharacteristic
130C4⋊C8×C83C2×C411yescharacteristic
131C4⋊C8×C83D411yescharacteristic
132C4⋊C8×C83D411yescharacteristic
133C22⋊C8×C83—21no—
134C22⋊C8×C83C2×C411yescharacteristic
135C22⋊C8×C83C2×C411yescharacteristic
136C22⋊C8×C83D411yescharacteristic
137C22⋊C8×C83D411yescharacteristic
138C4×C8×C83C2311yescharacteristic
139C4×C8×C83C2311yescharacteristic
140C4×C8×C83C2311yescharacteristic
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C23×D83—21no—
145C2×Dic166C22×C411yescharacteristic
146C2×D332—21no—
147C2×D332—22no—
148C2×D332—22no—
149C2×D332C22×C411yescharacteristic
150C2×D332C22×C411yescharacteristic
151C2×D332C22×C411yescharacteristic
152C2×C22⋊D83—21no—
153C22×Dic83—21no—
154C2×C4×D83—21no—
155C2×C4×D83—21no—
156C2×C4×D83—21no—
157C2×C4×D83—21no—
158C2×C4×D83—21no—
159C2×C4×D83—81no—
160C2×C4×D83—81no—
161#13050579—22no—
162#13050579—22no—
163D664—22no—
164D664—22no—
165#13050574—81no—
166#13050573—81no—
167C2×C83⋊C8—21no—
168C2×C83⋊C8—21no—
169C2×C83⋊C8—21no—
170C2×C83⋊C8—21no—
171C8×D83—81no—
172C8×D83—81no—
173C8×D83—81no—
174C8×D83—81no—
175C8×D83—81no—
176C4⋊Dic83—21no—
177C4⋊Dic83C22×C411yescharacteristic
178C4⋊Dic83C22×C411yescharacteristic
179C4⋊Dic83C22×C411yescharacteristic
180C4⋊Dic83C22×C411yescharacteristic
181Dic83⋊C4—21no—
182Dic83⋊C4—21no—
183Dic83⋊C4—21no—
184Dic83⋊C4—21no—
185C22⋊Dic83—21no—
186(C2×D83)⋊C4—21no—
187(C2×D83)⋊C4—21no—
188(C2×D83)⋊C4—21no—
189(C2×D83)⋊C4—21no—
190(C2×D83)⋊C4—21no—
191(C2×D83)⋊C4—21no—
192(C2×D83)⋊C4—21no—
193(C2×D83)⋊C4—21no—
194C4×Dic83—21no—
195C22×C4×C83C22×C411yescharacteristic
196C22×C4×C83C2×D411yescharacteristic
197C22×C4×C83#4111yescharacteristic
198C2×C8×C83—21no—
199C2×C8×C83—21no—
200C2×C8×C83C22×C411yescharacteristic
201C2×C8×C83C22×C411yescharacteristic
202C2×C8×C83C22×C411yescharacteristic
203C2×C8×C83C22×C411yescharacteristic
204C2×C8×C83C2×D411yescharacteristic
205C2×C8×C83C2×D411yescharacteristic
206C2×C8×C83C2×D411yescharacteristic
207C2×C8×C83C2×D411yescharacteristic
208C42×C83C22×C411yescharacteristic
209C42×C83C2×D411yescharacteristic
210C42×C83#4111yescharacteristic
211C42×C83C2411yescharacteristic
212C23×C83C4×D411yescharacteristic
213C22×D83—21no—
214C22×D83—21no—
215C22×D83—24no—
216C22×D83—21no—
217C22×D83—81no—
218C22×D83—81no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83—21no—
222C2×C4×C83—21no—
223C2×C4×C83—41no—
224C2×C4×C83C4×D411yescharacteristic
225C2×C4×C83C4×D411yescharacteristic
226C2×C4×C83C4×D411yescharacteristic
227C2×C4×C83C23×C411yescharacteristic
228C2×C4×C83C22×D411yescharacteristic
229C2×C4×C83C2×#4111yescharacteristic
230C22⋊D83—81no—
231C2×Dic83—21no—
232C2×Dic83—21no—
233C2×Dic83—21no—
234C2×Dic83—21no—
235C2×Dic83—21no—
236C2×Dic83—81no—
237D332—24no—
238D332—21no—
239D332—21no—
240D332—21no—
241D332—21no—
242D332#13112yes—
243D332#13112yes—
244C4×D83—41no—
245C4×D83—41no—
246C4×D83—41no—
247C4×D83—41no—
248C4×D83—41no—
249C4×D83—41no—
250C4×D83—81no—
251C4×D83—81no—
252Dic166—21no—
253Dic166—21no—
254C8×C83—21no—
255C8×C83—21no—
256C8×C83—21no—
257C8×C83—21no—
258C8×C83—21no—
259C8×C83—21no—
260C8×C83—21no—
261C8×C83—21no—
262C8×C83—41no—
263C8×C83—41no—
264C83⋊C8—41no—
265C83⋊C8—41no—
266C83⋊C8—41no—
267C83⋊C8—41no—
268C22×C83—21no—
269C22×C83—21no—
270C22×C83—21no—
271C22×C83C2×C4×D411yescharacteristic
272C2×D83—22no—
273C2×D83—22no—
274C2×D83—41no—
275C2×D83—41no—
276C2×D83—41no—
277C2×D83—41no—
278C2×D83—41no—
279C2×D83—41no—
280C2×D83—41no—
281C2×D83—84no—
282C4×C83—21no—
283C4×C83—21no—
284C4×C83—21no—
285C4×C83—21no—
286C4×C83C2×#13111yescharacteristic
287C4×C83C2×#13111yescharacteristic
288C4×C83#57611yescharacteristic
289C4×C83#57711yescharacteristic
290Dic83—41no—
291Dic83—41no—
292Dic83—41no—
293Dic83—41no—
294Dic83—41no—
295#17918—831nomaximal, Sylow
296C2×C83—41no—
297C2×C83#292911yescharacteristic
298C2×C83#294611yescharacteristic
299C2×C83#295711yescharacteristic
300D83—42no—
301D83—42no—
302D83—81no—
303#3105—831no—
304#2993—831no—
305#2972—831no—
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#1454D8311yescharacteristic, complemented
318C83#1791811yescharacteristic, complemented, Sylow
319#529—831no—
320C2×C4×D4—831no—
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—831no—
339C8×D4—831no—
340C8×D4—831no—
341C8×D4—831no—
342C8×D4—831no—
343C8×D4—1661no—
344C8×D4—1661no—
345#433—1661no—
346#431—831no—
347#431C2×D8311yescharacteristic
348#431C2×D8311yescharacteristic
349#431C2×D8311yescharacteristic
350#424—1661no—
351#423—831no—
352C2×C22⋊C8—1661no—
353C2×C22⋊C8—1661no—
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#322C2×D8311yescharacteristic, complemented
367#322C2×D8311yescharacteristic, complemented
368#322C2×D8311yescharacteristic, complemented
369C82C2×D8311yescharacteristic, complemented
370C22×D4—831no—
371C23×C4—1661no—
372C2×SD16—831no—
373C2×SD16—831no—
374C2×D8—831no—
375C2×D8—831no—
376C2×M16—1661no—
377C2×M16—1661no—
378C22×C8—1661no—
379C22×C8—1661no—
380C22×C8—1661no—
381C22×C8—1661no—
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—831no—
391C4×D4—831no—
392C4×D4—831no—
393C4×D4—831no—
394C4×D4—831no—
395C4×D4—1661no—
396C4×D4—1661no—
397C4×D4—1661no—
398#117—1661no—
399C2×C4⋊C4—831no—
400C2×C22⋊C4—1661no—
401C2×C42C22×D8311yescharacteristic
402#107—831no—
403#107—831no—
404#106—831no—
405#106—831no—
406C4⋊C8—21no—
407C4⋊C8—831no—
408C4⋊C8—831no—
409C4⋊C8—831no—
410C4⋊C8—831no—
411C4⋊C8—1661no—
412C4⋊C8—1661no—
413C4⋊C8—1661no—
414C4⋊C8C4×D8311yescharacteristic
415C4⋊C8C4×D8311yescharacteristic
416C4⋊C8D33211yescharacteristic
417C4⋊C8D33211yescharacteristic
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—1661no—
428C22⋊C8—1661no—
429C22⋊C8—1661no—
430C22⋊C8—1661no—
431C22⋊C8—1661no—
432C22⋊C8—1661no—
433C22⋊C8—1661no—
434C22⋊C8C4×D8311yescharacteristic
435C22⋊C8C4×D8311yescharacteristic
436C22⋊C8D33211yescharacteristic
437C22⋊C8D33211yescharacteristic
438#97—1661no—
439C4×C8—1661no—
440C4×C8—1661no—
441C4×C8C22×D8311yescharacteristic
442C4×C8C22×D8311yescharacteristic
443C4×C8C22×D8311yescharacteristic
444C4×C8C22×D8311yescharacteristic
445C4×C8C22×D8311yescharacteristic
446C4×C8C22×D8311yescharacteristic
447C24—1661no—
448C2×Q8—831no—
449C2×D4—831no—
450C2×D4—831no—
451C2×D4—831no—
452C2×D4—1662no—
453C2×D4—1662no—
454C2×D4—1661no—
455C2×D4—1661no—
456C22×C4—6641no—
457C22×C4—6641no—
458C22×C4—1661no—
459C22×C4—1661no—
460C22×C4—1661no—
461C22×C4—1661no—
462C22×C4—1661no—
463C22×C4—1661no—
464C22×C4C2×C4×D8311yescharacteristic
465C22×C4C2×D33211yescharacteristic
466C22×C4#1305059011yescharacteristic
467SD16—1662no—
468SD16—1662no—
469D8—1662no—
470D8—1662no—
471M16—6641no—
472M16—6641no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—6641no—
476C2×C8—6641no—
477C2×C8—6641no—
478C2×C8—6641no—
479C2×C8—6641no—
480C2×C8—1661no—
481C2×C8—1661no—
482C2×C8—1661no—
483C2×C8—1661no—
484C2×C8C2×C4×D8311yescharacteristic
485C2×C8C2×C4×D8311yescharacteristic
486C2×C8C2×C4×D8311yescharacteristic
487C2×C8C2×C4×D8311yescharacteristic
488C2×C8C2×D33211yescharacteristic
489C2×C8C2×D33211yescharacteristic
490C2×C8C2×D33211yescharacteristic
491C2×C8C2×D33211yescharacteristic
492C4⋊C4—831no—
493C4⋊C4—831no—
494C4⋊C4—831no—
495C4⋊C4—831no—
496C4⋊C4—1661no—
497C4⋊C4—1661no—
498C4⋊C4—1661no—
499C4⋊C4—1661no—
500C4⋊C4—1661no—
501C22⋊C4—1661no—
502C22⋊C4—1661no—
503C22⋊C4—1661no—
504C22⋊C4—1661no—
505C22⋊C4—1661no—
506C22⋊C4—1661no—
507C22⋊C4—1661no—
508C22⋊C4—1661no—
509C22⋊C4—1661no—
510C42—1661no—
511C42C2×C4×D8311yescharacteristic
512C42C2×D33211yescharacteristic
513C42#1305059011yescharacteristic
514C42C23×D8311yescharacteristic
515C23—6641no—
516C23—6641no—
517C23—1664no—
518C23—1661no—
519C23—1661no—
520C23—1661no—
521C23C4×D33211yescharacteristic
522Q8—1661no—
523Q8—1661no—
524D4—832no—
525D4—832no—
526D4—6641no—
527D4—1664no—
528D4—1661no—
529D4—1661no—
530D4—1661no—
531D4—1661no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—3321no—
538C2×C4—3321no—
539C2×C4—3321no—
540C2×C4—3321no—
541C2×C4—3321no—
542C2×C4—3321no—
543C2×C4—6641no—
544C2×C4—6641no—
545C2×C4—6641no—
546C2×C4—1661no—
547C2×C4—1661no—
548C2×C4—1661no—
549C2×C4—1661no—
550C2×C4—1661no—
551C2×C4C4×D33211yescharacteristic
552C2×C4C4×D33211yescharacteristic
553C2×C4C4×D33211yescharacteristic
554C2×C4C22×C4×D8311yescharacteristic
555C2×C4C22×D33211yescharacteristic
556C2×C4C2×#1305059011yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—21no—
564C8—21no—
565C8—41no—
566C8—41no—
567C8—3321no—
568C8—3321no—
569C8—3321no—
570C8—3321no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—3321no—
575C22—3321no—
576C22—3321no—
577C22—3321no—
578C22—3321no—
579C22—3321no—
580C22—3321no—
581C22—6644no—
582C22—1662no—
583C22—1662no—
584C22C2×C4×D33211yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—3321no—
590C4—3321no—
591C4—3321no—
592C4—3321no—
593C4—3321no—
594C4#131×D8311yescharacteristic
595C4#131×D8311yescharacteristic
596C4#1912850611yescharacteristic
597C4#1912851311yescharacteristic
598C2—41no—
599C2—3322no—
600C2—3322no—
601C2—6641no—
602C2#2491615911yescharacteristic
603C2#2491629711yescharacteristic
604C2#2491638111yescharacteristic
subgroupG/H
centerC2×C4C22×D332
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1454C2
socleC22×C83C2×C4×D4
prime radical#19127837C4
cosocleC42×C83C24
hypercenter#1454D83
hypocenterC83#17918
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
2. #24916614C2semidirect
3. #24916486C2semidirect
4. #24906329C2semidirect
5. #24906322C2semidirect
6. #24906301C2semidirect
7. #24906294C2semidirect
8. #24906288C2semidirect
9. #24906277C2semidirect
10. C8×#13050579C2semidirect
11. C8×D664C2semidirect
12. #24906252C2semidirect
13. #24905889C2semidirect
14. #24905872C2semidirect
15. C83×#1454C2semidirect
26. #19127831C22semidirect
27. C8×Dic166C22semidirect
32. #19127780C22semidirect
39. C8×D332C22semidirect
48. #19127454C22semidirect
49. #19127454C22semidirect
50. #19127452C22semidirect
51. #19127452C22semidirect
52. #19127433C22semidirect
53. #19127433C22semidirect
58. #19127430C22semidirect
59. #19127430C22semidirect
63. #322×C83C22semidirect
64. #322×C83C22semidirect
65. #322×C83C22semidirect
66. C82×C83C22semidirect
317. #1454D83semidirect
318. C83#17918semidirect
366. #322C2×D83semidirect
367. #322C2×D83semidirect
368. #322C2×D83semidirect
369. C82C2×D83semidirect

Maximal subgroups

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

subgroupindex
#249175122
#249166142
#249164862
#249063292
#249063222
#249063012
#249062942
#249062882
#249062772
C8×#130505792
C8×D6642
#249062522
#249058892
#249058722
C83×#14542
#1791883