Finite Group Databasebeta

← #35375628

Subgroups — #35375628

Order 21248.

642 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917510C211yesmaximal, characteristic
2#24916619C211yesmaximal, characteristic, complemented
3#24916498C211yesmaximal, characteristic, complemented
4#24906374C211yesmaximal, characteristic, complemented
5#24906362C211yesmaximal, characteristic, complemented
6#24906309C211yesmaximal, characteristic, complemented
7#24906296C211yesmaximal, characteristic, complemented
8#24906295C211yesmaximal, characteristic, complemented
9#24906289C211yesmaximal, characteristic, complemented
10#24906284C211yesmaximal, characteristic, complemented
11#24906272C211yesmaximal, characteristic, complemented
12#24906246C211yesmaximal, characteristic, complemented
13#24905924C211yesmaximal, characteristic, complemented
14#24905755C211yesmaximal, characteristic, complemented
15C2×D4⋊C8×C83C211yesmaximal, characteristic, complemented
16#19128235C2211yescharacteristic
17#19128036C411yescharacteristic
18#19128019C411yescharacteristic
19#19128001C411yescharacteristic
20#19128001C411yescharacteristic
21#19127916C411yescharacteristic
22#19127916C411yescharacteristic
23#19127852C411yescharacteristic
24#19127835C411yescharacteristic
25#19127828C2211yescharacteristic, complemented
26#19127825C2211yescharacteristic, complemented
27C4×#13050578C2211yescharacteristic
28C4×#13050578C2211yescharacteristic
29C4×#13050575C2211yescharacteristic
30C4×#13050575C2211yescharacteristic
31#19127779C2211yescharacteristic
32#19127779C2211yescharacteristic
33#19127778C2211yescharacteristic, complemented
34#19127773—21no—
35#19127773—21no—
36#19127772—21no—
37D4×C83⋊C8C2211yescharacteristic
38D4×C83⋊C8C2211yescharacteristic
39#19127766C2211yescharacteristic, complemented
40C8×C22⋊D83—21no—
41#19127761—21no—
42#19127758C2211yescharacteristic
43#19127754C2211yescharacteristic
44#19127754C2211yescharacteristic
45#19127726—21no—
46#19127665—21no—
47C2×C22⋊(C83⋊C8)—21no—
48#19127453C2211yescharacteristic, complemented
49#19127453C2211yescharacteristic, complemented
50#19127451C2211yescharacteristic, complemented
51#19127451C2211yescharacteristic, complemented
52#19127433C2211yescharacteristic, complemented
53#19127433C2211yescharacteristic, complemented
54#19127430C2211yescharacteristic, complemented
55#19127430C2211yescharacteristic, complemented
56#19127423C2211yescharacteristic, complemented
57#19127423C2211yescharacteristic, complemented
58#19127423C2211yescharacteristic, complemented
59#19127423C2211yescharacteristic, complemented
60C2×C4×D4×C83C2211yescharacteristic
61C2×C4⋊C8×C83C2211yescharacteristic
62C2×C4×C8×C83C2211yescharacteristic
63D4⋊C8×C83C2211yescharacteristic
64D4⋊C8×C83C2211yescharacteristic
65D4⋊C8×C83C2211yescharacteristic
66D4⋊C8×C83C2211yescharacteristic
67C2×#13050578C2×C411yescharacteristic
68C2×#13050578C2×C411yescharacteristic
69C2×#13050575C2×C411yescharacteristic
70C2×#13050575C2×C411yescharacteristic
71C2×#13050574—21no—
72C2×#13050574—21no—
73C2×#13050573—21no—
74C22×C83⋊C8—21no—
75C22×C83⋊C8—21no—
76C2×C8×D83—21no—
77#14581786—21no—
78#14581784C2×C411yescharacteristic
79#14581780C2×C411yescharacteristic
80#14581775—21no—
81#14581771C2×C411yescharacteristic
82#14581766C2×C411yescharacteristic
83C4×Dic166C2311yescharacteristic
84C4×D332C2311yescharacteristic
85C4×C22⋊D83—21no—
86#14581749—21no—
87#14581725C2×C411yescharacteristic
88#14581725C2×C411yescharacteristic
89#14581723C2×C411yescharacteristic
90#14581723C2×C411yescharacteristic
91C4⋊(C83⋊C8)C2×C411yescharacteristic
92C4⋊(C83⋊C8)C2×C411yescharacteristic
93C4⋊(C83⋊C8)D411yescharacteristic
94C4⋊(C83⋊C8)D411yescharacteristic
95C4⋊(C83⋊C8)C2311yescharacteristic
96C4⋊(C83⋊C8)C2311yescharacteristic
97Dic83⋊C8—21no—
98Dic83⋊C8—21no—
99#14581715C2×C411yescharacteristic
100#14581715C2×C411yescharacteristic
101#14581713C2×C411yescharacteristic
102#14581713C2×C411yescharacteristic
103#14581713C2×C411yescharacteristic
104#14581713C2×C411yescharacteristic
105#14581712C2×C411yescharacteristic
106#14581712C2×C411yescharacteristic
107C22⋊(C83⋊C8)—21no—
108C22⋊(C83⋊C8)—21no—
109C22⋊(C83⋊C8)—21no—
110C22⋊(C83⋊C8)—21no—
111C22⋊(C83⋊C8)—21no—
112C22⋊(C83⋊C8)C2×C411yescharacteristic
113C22⋊(C83⋊C8)C2×C411yescharacteristic
114C22⋊(C83⋊C8)D411yescharacteristic
115C22⋊(C83⋊C8)D411yescharacteristic
116(C2×D83)⋊C8—21no—
117(C2×D83)⋊C8—21no—
118#14581703—21no—
119#14581702—21no—
120C4×C83⋊C8C2311yescharacteristic
121C4×C83⋊C8C2311yescharacteristic
122C4×C83⋊C8C2311yescharacteristic
123C4×C83⋊C8C2311yescharacteristic
124C8×Dic83—21no—
125C22×D4×C83C2×C411yescharacteristic
126C23×C4×C83—21no—
127C22×C8×C83—21no—
128C22×C8×C83—21no—
129C4×D4×C83—21no—
130C4×D4×C83—21no—
131C4×D4×C83C2×C411yescharacteristic
132C4×D4×C83C2×C411yescharacteristic
133C4×D4×C83C2311yescharacteristic
134C4×D4×C83C2311yescharacteristic
135C2×C4⋊C4×C83C2×C411yescharacteristic
136C2×C22⋊C4×C83—21no—
137C2×C42×C83C2311yescharacteristic
138C4⋊C8×C83—21no—
139C4⋊C8×C83C2311yescharacteristic
140C4⋊C8×C83C2311yescharacteristic
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—41no—
150#13050575—22no—
151#13050575—41no—
152#13050574—81no—
153#13050574—81no—
154#13050573—81no—
155C2×C83⋊C8—21no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—81no—
158C2×C83⋊C8—81no—
159C2×C83⋊C8C22×C411yescharacteristic
160C2×C83⋊C8C22×C411yescharacteristic
161C2×C83⋊C8C22×C411yescharacteristic
162C2×C83⋊C8C22×C411yescharacteristic
163C2×C83⋊C8C2×D411yescharacteristic
164C2×C83⋊C8C2×D411yescharacteristic
165C2×C83⋊C8C2×D411yescharacteristic
166C2×C83⋊C8C2×D411yescharacteristic
167C8×D83—81no—
168C4⋊Dic83C22×C411yescharacteristic
169C4⋊Dic83C22×C411yescharacteristic
170Dic83⋊C4—21no—
171Dic83⋊C4—21no—
172Dic83⋊C4—21no—
173Dic83⋊C4—21no—
174C22⋊Dic83—21no—
175(C2×D83)⋊C4—21no—
176(C2×D83)⋊C4—21no—
177(C2×D83)⋊C4—21no—
178(C2×D83)⋊C4—21no—
179C4×Dic83—21no—
180C24×C83—21no—
181C2×D4×C83—22no—
182C2×D4×C83—21no—
183C2×D4×C83—41no—
184C2×D4×C83C22×C411yescharacteristic
185C2×D4×C83C22×C411yescharacteristic
186C22×C4×C83—21no—
187C22×C4×C83—21no—
188C22×C4×C83—21no—
189C22×C4×C83—21no—
190C22×C4×C83—21no—
191C22×C4×C83—81no—
192C22×C4×C83—81no—
193C22×C4×C83C22×C411yescharacteristic
194C22×C4×C83C2×D411yescharacteristic
195C22×C4×C83#4111yescharacteristic
196C2×C8×C83—21no—
197C2×C8×C83—21no—
198C2×C8×C83—21no—
199C2×C8×C83—21no—
200C2×C8×C83—42no—
201C2×C8×C83—81no—
202C4⋊C4×C83—21no—
203C4⋊C4×C83C22×C411yescharacteristic
204C4⋊C4×C83C22×C411yescharacteristic
205C22⋊C4×C83—21no—
206C22⋊C4×C83—21no—
207C22⋊C4×C83—21no—
208C22⋊C4×C83—21no—
209C42×C83C22×C411yescharacteristic
210C42×C83C2×D411yescharacteristic
211C42×C83#4111yescharacteristic
212C42×C83C2411yescharacteristic
213C23×C83—21no—
214C23×C83—21no—
215C23×C83—42no—
216C23×C83—42no—
217C23×C83—81no—
218C23×C83C4×D411yescharacteristic
219C22×D83—21no—
220D4×C83—21no—
221D4×C83—21no—
222D4×C83—21no—
223D4×C83—42no—
224D4×C83#13112yes—
225C2×C4×C83—22no—
226C2×C4×C83—21no—
227C2×C4×C83—21no—
228C2×C4×C83—21no—
229C2×C4×C83—21no—
230C2×C4×C83—21no—
231C2×C4×C83—21no—
232C2×C4×C83—41no—
233C2×C4×C83—41no—
234C2×C4×C83—41no—
235C2×C4×C83—41no—
236C2×C4×C83—81no—
237C2×C4×C83—81no—
238C2×C4×C83—81no—
239C2×C4×C83C4×D411yescharacteristic
240C2×C4×C83C4×D411yescharacteristic
241C2×C4×C83C4×D411yescharacteristic
242C2×C4×C83C23×C411yescharacteristic
243C2×C4×C83C22×D411yescharacteristic
244C2×C4×C83C2×#4111yescharacteristic
245C22⋊D83—42no—
246C2×Dic83—21no—
247C2×Dic83—21no—
248C2×Dic83—21no—
249D332—21no—
250D332—21no—
251C4×D83—41no—
252C4×D83—41no—
253Dic166—21no—
254Dic166—21no—
255C8×C83—41no—
256C8×C83—41no—
257C8×C83—41no—
258C8×C83—41no—
259C83⋊C8—21no—
260C83⋊C8—21no—
261C83⋊C8—21no—
262C83⋊C8—21no—
263C83⋊C8—21no—
264C83⋊C8—21no—
265C83⋊C8—21no—
266C83⋊C8—21no—
267C83⋊C8—41no—
268C83⋊C8—41no—
269C22×C83—21no—
270C22×C83—21no—
271C22×C83—22no—
272C22×C83—41no—
273C22×C83—41no—
274C22×C83—41no—
275C22×C83—41no—
276C22×C83—41no—
277C22×C83—84no—
278C22×C83#44412yes—
279C22×C83C2×C4×D411yescharacteristic
280C2×D83—41no—
281C2×D83—41no—
282C2×D83—41no—
283C4×C83—21no—
284C4×C83—21no—
285C4×C83—21no—
286C4×C83—21no—
287C4×C83—41no—
288C4×C83—41no—
289C4×C83C2×#13111yescharacteristic
290C4×C83#56811yescharacteristic
291C4×C83#57611yescharacteristic
292C4×C83#57711yescharacteristic
293Dic83—41no—
294Dic83—41no—
295Dic83—41no—
296#18020—831nomaximal, Sylow
297C2×C83—22no—
298C2×C83—42no—
299C2×C83—81no—
300C2×C83#293311yescharacteristic
301C2×C83#294611yescharacteristic
302C2×C83C2×#44411yescharacteristic
303D83—81no—
304#3105—831no—
305#2994—831no—
306#2974—831no—
307#1594—831no—
308#1592—831no—
309#1583—831no—
310#1582—831no—
311#1581—831no—
312#1581—831no—
313#1580—831no—
314SD16⋊C8—831no—
315#1573—831no—
316#1494—831no—
317C2×D4⋊C8D8311yescharacteristic, complemented
318#1452—831no—
319C83#1802011yescharacteristic, complemented, Sylow
320#529—831no—
321C2×C4×D4C2×D8311yescharacteristic
322#484—831no—
323#481—831no—
324#478—831no—
325#478—831no—
326#463—831no—
327#463—831no—
328#450—831no—
329#447—831no—
330#446—831no—
331C8×Q8—831no—
332C4×SD16—831no—
333C4×SD16—831no—
334C4×D8—831no—
335C4×D8—831no—
336#436—831no—
337#436—831no—
338#436—831no—
339#435—1661no—
340#435—1661no—
341#435—1661no—
342C8×D4—831no—
343C8×D4—831no—
344C8×D4—831no—
345C8×D4—1661no—
346#433—1661no—
347#432—831no—
348#431—831no—
349#431—831no—
350#424—1661no—
351C2×C4⋊C8C2×D8311yescharacteristic
352#407—1661no—
353C2×C22⋊C8—1661no—
354C2×C4×C8C2×D8311yescharacteristic
355#335—831no—
356#335—831no—
357#334—831no—
358#334—831no—
359Q8⋊C8—831no—
360Q8⋊C8—831no—
361D4⋊C8—831no—
362D4⋊C8—831no—
363D4⋊C8C2×D8311yescharacteristic
364D4⋊C8C2×D8311yescharacteristic
365D4⋊C8C2×D8311yescharacteristic
366D4⋊C8C2×D8311yescharacteristic
367#322—831no—
368#322—831no—
369#322—831no—
370#322—831no—
371C22×D4C4×D8311yescharacteristic
372C23×C4—21no—
373C2×SD16—831no—
374C2×SD16—831no—
375C2×D8—831no—
376C2×D8—831no—
377C2×M16—1661no—
378C2×M16—1661no—
379C2×M16—1661no—
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—1661no—
383C22×C8—1661no—
384C22×C8—1661no—
385#126—1661no—
386#125—831no—
387#124—831no—
388#123—1661no—
389C22⋊Q8—831no—
390#121—831no—
391C4×Q8—831no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—831no—
395C4×D4—1661no—
396C4×D4C4×D8311yescharacteristic
397C4×D4C4×D8311yescharacteristic
398C4×D4C22×D8311yescharacteristic
399C4×D4C22×D8311yescharacteristic
400#117—1661no—
401C2×C4⋊C4C4×D8311yescharacteristic
402C2×C22⋊C4—21no—
403C2×C42C22×D8311yescharacteristic
404#107—831no—
405#107—831no—
406#106—831no—
407#106—831no—
408C4⋊C8—21no—
409C4⋊C8—831no—
410C4⋊C8—831no—
411C4⋊C8—831no—
412C4⋊C8—831no—
413C4⋊C8—831no—
414C4⋊C8—831no—
415C4⋊C8—1661no—
416C4⋊C8—1661no—
417C4⋊C8C22×D8311yescharacteristic
418C4⋊C8C22×D8311yescharacteristic
419#103—831no—
420#103—831no—
421#102—831no—
422#102—831no—
423#102—831no—
424#102—831no—
425#102—831no—
426#102—831no—
427C22⋊C8—831no—
428C22⋊C8—831no—
429C22⋊C8—831no—
430C22⋊C8—831no—
431C22⋊C8—1661no—
432C22⋊C8—1661no—
433C22⋊C8—1661no—
434C22⋊C8—1661no—
435C22⋊C8—1661no—
436C22⋊C8—1661no—
437C22⋊C8—1661no—
438#97—1661no—
439#97—1661no—
440C4×C8—21no—
441C4×C8—831no—
442C4×C8—831no—
443C4×C8—831no—
444C4×C8—831no—
445C4×C8—1661no—
446C4×C8C22×D8311yescharacteristic
447C4×C8C22×D8311yescharacteristic
448C24—21no—
449C2×Q8—831no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—831no—
454C2×D4—1661no—
455C2×D4C2×C4×D8311yescharacteristic
456C2×D4C2×C4×D8311yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—81no—
463C22×C4—81no—
464C22×C4—1661no—
465C22×C4C2×C4×D8311yescharacteristic
466C22×C4D4×D8311yescharacteristic
467C22×C4#1305058911yescharacteristic
468SD16—3321no—
469SD16—1662no—
470D8—3321no—
471D8—1662no—
472M16—6641no—
473M16—6641no—
474M16—6641no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—42no—
480C2×C8—81no—
481C2×C8—831no—
482C2×C8—831no—
483C2×C8—831no—
484C2×C8—831no—
485C2×C8—831no—
486C2×C8—831no—
487C2×C8—831no—
488C2×C8—831no—
489C2×C8—6641no—
490C2×C8—6641no—
491C2×C8—6641no—
492C2×C8—1661no—
493C2×C8—1661no—
494C4⋊C4—21no—
495C4⋊C4—831no—
496C4⋊C4—831no—
497C4⋊C4—1661no—
498C4⋊C4—1661no—
499C4⋊C4—1661no—
500C4⋊C4—1661no—
501C4⋊C4C2×C4×D8311yescharacteristic
502C4⋊C4C2×C4×D8311yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—1661no—
508C22⋊C4—1661no—
509C22⋊C4—1661no—
510C22⋊C4—1661no—
511C22⋊C4—1661no—
512C42—1661no—
513C42C2×C4×D8311yescharacteristic
514C42D4×D8311yescharacteristic
515C42#1305058911yescharacteristic
516C42C23×D8311yescharacteristic
517C23—21no—
518C23—21no—
519C23—42no—
520C23—42no—
521C23—81no—
522C23—1661no—
523C23(C22⋊D83)⋊C411yescharacteristic
524Q8—1661no—
525Q8—1661no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—42no—
530D4—3322no—
531D4—1661no—
532D4—1661no—
533D4#1458179812yes—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4—3321no—
549C2×C4—3321no—
550C2×C4—1661no—
551C2×C4—1661no—
552C2×C4—1661no—
553C2×C4(C22⋊D83)⋊C411yescharacteristic
554C2×C4(C22⋊D83)⋊C411yescharacteristic
555C2×C4(C22⋊D83)⋊C411yescharacteristic
556C2×C4C22×C4×D8311yescharacteristic
557C2×C4C2×D4×D8311yescharacteristic
558C2×C4C2×#1305058911yescharacteristic
559C8—41no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—3321no—
564C8—3321no—
565C8—1661no—
566C8—1661no—
567C8—1661no—
568C8—1661no—
569C8—1661no—
570C8—1661no—
571C8—1661no—
572C8—1661no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—84no—
582C22—3321no—
583C22—3321no—
584C22—3321no—
585C22#1912782012yes—
586C22C2×(C22⋊D83)⋊C411yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—3321no—
594C4—3321no—
595C4—3321no—
596C4C2×#1458179811yescharacteristic
597C4#1912846711yescharacteristic
598C4#1912850211yescharacteristic
599C4#1912850711yescharacteristic
600C2—22no—
601C2—42no—
602C2—81no—
603C2—6641no—
604C2#2491618411yescharacteristic
605C2#2491628911yescharacteristic
606C2C2×#1912782011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC2×D4⋊C8×C83C2
socleC22×C83C2×C4×D4
prime radical#19127835C4
cosocleC42×C83C24
hypercenterC2×D4⋊C8D83
hypocenterC83#18020
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #24916619C2semidirect
3. #24916498C2semidirect
4. #24906374C2semidirect
5. #24906362C2semidirect
6. #24906309C2semidirect
7. #24906296C2semidirect
8. #24906295C2semidirect
9. #24906289C2semidirect
10. #24906284C2semidirect
11. #24906272C2semidirect
12. #24906246C2semidirect
13. #24905924C2semidirect
14. #24905755C2semidirect
15. C2×D4⋊C8×C83C2semidirect
25. #19127828C22semidirect
26. #19127825C22semidirect
33. #19127778C22semidirect
39. #19127766C22semidirect
48. #19127453C22semidirect
49. #19127453C22semidirect
50. #19127451C22semidirect
51. #19127451C22semidirect
52. #19127433C22semidirect
53. #19127433C22semidirect
54. #19127430C22semidirect
55. #19127430C22semidirect
56. #19127423C22semidirect
57. #19127423C22semidirect
58. #19127423C22semidirect
59. #19127423C22semidirect
317. C2×D4⋊C8D83semidirect
319. C83#18020semidirect

Maximal subgroups

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

subgroupindex
#249175102
#249166192
#249164982
#249063742
#249063622
#249063092
#249062962
#249062952
#249062892
#249062842
#249062722
#249062462
#249059242
#249057552
C2×D4⋊C8×C832
#1802083