Finite Group Databasebeta

← #35374470

Subgroups — #35374470

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#24917506C211yesmaximal, characteristic
2#24916612C211yesmaximal, characteristic, complemented
3#24916486C211yesmaximal, characteristic, complemented
4#24906330C211yesmaximal, characteristic, complemented
5#24906323C211yesmaximal, characteristic, complemented
6#24906302C211yesmaximal, characteristic, complemented
7#24906295C211yesmaximal, characteristic, complemented
8#24906284C211yesmaximal, characteristic, complemented
9#24906278C211yesmaximal, characteristic, complemented
10#24906260C211yesmaximal, characteristic, complemented
11#24906255C211yesmaximal, characteristic, complemented
12#24906251C211yesmaximal, characteristic, complemented
13#24905889C211yesmaximal, characteristic, complemented
14#24905763C211yesmaximal, characteristic, complemented
15C83×#1482C211yesmaximal, characteristic, complemented
16C2×C4×D332C2211yescharacteristic
17#19128034C411yescharacteristic
18#19128017C411yescharacteristic
19#19127998C411yescharacteristic
20#19127998C411yescharacteristic
21#19127913C411yescharacteristic
22#19127913C411yescharacteristic
23#19127851C411yescharacteristic
24#19127834C411yescharacteristic
25#19127832C2211yescharacteristic, complemented
26Q8×C83⋊C8C2211yescharacteristic, complemented
27C4×#13050577C2211yescharacteristic
28C4×#13050577C2211yescharacteristic
29C4×#13050575C2211yescharacteristic
30C4×#13050575C2211yescharacteristic
31#19127779—21no—
32#19127779C2211yescharacteristic, complemented
33#19127773—21no—
34C8×D332—21no—
35C8×D332—21no—
36D4×C83⋊C8C2211yescharacteristic, complemented
37#19127766C2211yescharacteristic
38#19127766C2211yescharacteristic
39#19127766C2211yescharacteristic
40#19127766C2211yescharacteristic
41#19127762—21no—
42#19127754C2211yescharacteristic
43#19127754C2211yescharacteristic
44#19127728—21no—
45#19127725C2211yescharacteristic
46C22⋊C8×D83—21no—
47C22⋊C8×D83—21no—
48#19127453C2211yescharacteristic, complemented
49#19127453C2211yescharacteristic, complemented
50#19127451C2211yescharacteristic, complemented
51#19127451C2211yescharacteristic, complemented
52#19127430C2211yescharacteristic
53#19127430C2211yescharacteristic
54#19127430C2211yescharacteristic
55#19127430C2211yescharacteristic
56#19127423C2211yescharacteristic, complemented
57#19127423C2211yescharacteristic, complemented
58#19127422C2211yescharacteristic, complemented
59C8×C83⋊C8C2211yescharacteristic, complemented
60#529×C83C2211yescharacteristic
61#431×C83C2211yescharacteristic
62#431×C83C2211yescharacteristic
63Q8⋊C8×C83C2211yescharacteristic, complemented
64Q8⋊C8×C83C2211yescharacteristic, complemented
65D4⋊C8×C83C2211yescharacteristic, complemented
66D4⋊C8×C83C2211yescharacteristic, complemented
67C22×D332C2×C411yescharacteristic
68C22×C4×D83—21no—
69C2×#13050577C2×C411yescharacteristic
70C2×#13050577C2×C411yescharacteristic
71C2×#13050575C2×C411yescharacteristic
72C2×#13050575C2×C411yescharacteristic
73C2×#13050574—21no—
74C2×#13050574—21no—
75C22×C83⋊C8—21no—
76C2×C8×D83—21no—
77C2×C8×D83—21no—
78C2×C8×D83—21no—
79C2×C8×D83—21no—
80C4×D332—21no—
81C4×D332—21no—
82C4×D332C2×C411yescharacteristic
83C4×D332C2×C411yescharacteristic
84C4×D332C2311yescharacteristic
85C4×D332C2311yescharacteristic
86C2×C4⋊Dic83C2×C411yescharacteristic
87C2×(C2×D83)⋊C4—21no—
88#14581725C2×C411yescharacteristic
89#14581725C2×C411yescharacteristic
90#14581723C2×C411yescharacteristic
91#14581723C2×C411yescharacteristic
92C4⋊(C83⋊C8)—21no—
93C4⋊(C83⋊C8)—21no—
94C4⋊(C83⋊C8)—21no—
95C4⋊(C83⋊C8)C2×C411yescharacteristic
96C4⋊(C83⋊C8)C2×C411yescharacteristic
97C4⋊(C83⋊C8)D411yescharacteristic
98C4⋊(C83⋊C8)D411yescharacteristic
99C4⋊(C83⋊C8)C2311yescharacteristic
100C4⋊(C83⋊C8)C2311yescharacteristic
101#14581716C2×C411yescharacteristic
102#14581716C2×C411yescharacteristic
103#14581713C2×C411yescharacteristic
104#14581713C2×C411yescharacteristic
105#14581712C2×C411yescharacteristic
106#14581712C2×C411yescharacteristic
107#14581712C2×C411yescharacteristic
108#14581712C2×C411yescharacteristic
109C22⋊(C83⋊C8)—21no—
110C22⋊(C83⋊C8)—21no—
111C22⋊(C83⋊C8)C2×C411yescharacteristic
112C22⋊(C83⋊C8)C2×C411yescharacteristic
113C22⋊(C83⋊C8)D411yescharacteristic
114C22⋊(C83⋊C8)D411yescharacteristic
115(C2×D83)⋊C8—21no—
116(C2×D83)⋊C8—21no—
117(C2×D83)⋊C8—21no—
118(C2×D83)⋊C8—21no—
119#14581703—21no—
120C4×C83⋊C8—21no—
121C4×C83⋊C8C2311yescharacteristic
122C4×C83⋊C8C2311yescharacteristic
123C4×C83⋊C8C2311yescharacteristic
124C4×C83⋊C8C2311yescharacteristic
125#126×C83—21no—
126#125×C83C2×C411yescharacteristic
127#124×C83C2×C411yescharacteristic
128#123×C83—21no—
129C22⋊Q8×C83C2×C411yescharacteristic
130#121×C83C2×C411yescharacteristic
131C4×Q8×C83C2311yescharacteristic
132C4×D4×C83—21no—
133C4×D4×C83C2311yescharacteristic
134#117×C83—21no—
135C2×C42×C83C2311yescharacteristic
136C4⋊C8×C83—21no—
137C4⋊C8×C83C2311yescharacteristic
138C4⋊C8×C83C2311yescharacteristic
139C22⋊C8×C83—21no—
140C22⋊C8×C83—21no—
141C4×C8×C83—21no—
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C23×D83—21no—
145C2×D332—21no—
146C2×D332—22no—
147C2×D332—22no—
148C2×D332C22×C411yescharacteristic
149C2×D332C22×C411yescharacteristic
150C22×Dic83—21no—
151C2×C4×D83—21no—
152C2×C4×D83—21no—
153C2×C4×D83—21no—
154C2×C4×D83—21no—
155C2×C4×D83—81no—
156C2×C4×D83—81no—
157#13050577—22no—
158#13050577—22no—
159#13050575—22no—
160#13050575—22no—
161#13050574—81no—
162#13050574—81no—
163C2×C83⋊C8—21no—
164C2×C83⋊C8—21no—
165C2×C83⋊C8—81no—
166C2×C83⋊C8C22×C411yescharacteristic
167C2×C83⋊C8C22×C411yescharacteristic
168C2×C83⋊C8C22×C411yescharacteristic
169C2×C83⋊C8C22×C411yescharacteristic
170C2×C83⋊C8C2×D411yescharacteristic
171C2×C83⋊C8C2×D411yescharacteristic
172C2×C83⋊C8C2×D411yescharacteristic
173C2×C83⋊C8C2×D411yescharacteristic
174C8×D83—81no—
175C8×D83—81no—
176C8×D83—81no—
177C8×D83—81no—
178C4⋊Dic83—21no—
179C4⋊Dic83C22×C411yescharacteristic
180C4⋊Dic83C22×C411yescharacteristic
181(C2×D83)⋊C4—21no—
182(C2×D83)⋊C4—21no—
183(C2×D83)⋊C4—21no—
184(C2×D83)⋊C4—21no—
185C2×Q8×C83C22×C411yescharacteristic
186C2×D4×C83—21no—
187C2×D4×C83C22×C411yescharacteristic
188C22×C4×C83—21no—
189C22×C4×C83C22×C411yescharacteristic
190C22×C4×C83C2×D411yescharacteristic
191C22×C4×C83#4111yescharacteristic
192C2×C8×C83—21no—
193C2×C8×C83—21no—
194C2×C8×C83—21no—
195C2×C8×C83—21no—
196C4⋊C4×C83—21no—
197C4⋊C4×C83—21no—
198C4⋊C4×C83—21no—
199C4⋊C4×C83—21no—
200C4⋊C4×C83C22×C411yescharacteristic
201C4⋊C4×C83C22×C411yescharacteristic
202C22⋊C4×C83—21no—
203C22⋊C4×C83—21no—
204C22⋊C4×C83—21no—
205C22⋊C4×C83—21no—
206C22⋊C4×C83—21no—
207C42×C83—21no—
208C42×C83C22×C411yescharacteristic
209C42×C83C2×D411yescharacteristic
210C42×C83#4111yescharacteristic
211C42×C83C2411yescharacteristic
212C23×C83—21no—
213C23×C83C4×D411yescharacteristic
214C22×D83—21no—
215C22×D83—21no—
216C22×D83—24no—
217C22×D83—81no—
218C22×D83—81no—
219Q8×C83—21no—
220Q8×C83—21no—
221D4×C83—21no—
222D4×C83—21no—
223D4×C83—81no—
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—21no—
231C2×C4×C83—41no—
232C2×C4×C83—41no—
233C2×C4×C83—41no—
234C2×C4×C83C4×D411yescharacteristic
235C2×C4×C83C4×D411yescharacteristic
236C2×C4×C83C4×D411yescharacteristic
237C2×C4×C83C23×C411yescharacteristic
238C2×C4×C83C22×D411yescharacteristic
239C2×C4×C83C2×#4111yescharacteristic
240C2×Dic83—21no—
241C2×Dic83—21no—
242C2×Dic83—81no—
243D332—24no—
244D332—21no—
245D332—21no—
246D332#13112yes—
247D332#13112yes—
248C4×D83—41no—
249C4×D83—41no—
250C4×D83—41no—
251C4×D83—41no—
252C4×D83—81no—
253C4×D83—81no—
254C8×C83—41no—
255C8×C83—41no—
256C8×C83—41no—
257C8×C83—41no—
258C83⋊C8—21no—
259C83⋊C8—21no—
260C83⋊C8—21no—
261C83⋊C8—21no—
262C83⋊C8—21no—
263C83⋊C8—21no—
264C83⋊C8—21no—
265C83⋊C8—21no—
266C83⋊C8—41no—
267C83⋊C8—41no—
268C22×C83—21no—
269C22×C83—21no—
270C22×C83—21no—
271C22×C83—41no—
272C22×C83—41no—
273C22×C83—41no—
274C22×C83C2×C4×D411yescharacteristic
275C2×D83—22no—
276C2×D83—22no—
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×C83—41no—
287C4×C83—41no—
288C4×C83—41no—
289C4×C83C2×#13111yescharacteristic
290C4×C83C2×#13111yescharacteristic
291C4×C83#57611yescharacteristic
292C4×C83#57711yescharacteristic
293Dic83—41no—
294Dic83—41no—
295#17918—831nomaximal, Sylow
296C2×C83—41no—
297C2×C83—81no—
298C2×C83#292911yescharacteristic
299C2×C83#294611yescharacteristic
300C2×C83#295711yescharacteristic
301D83—42no—
302D83—42no—
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#1482D8311yescharacteristic, complemented
317#1454—831no—
318C83#1791811yescharacteristic, complemented, Sylow
319#529C2×D8311yescharacteristic
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#431—831no—
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⋊C8C2×D8311yescharacteristic, complemented
359Q8⋊C8C2×D8311yescharacteristic, complemented
360D4⋊C8—831no—
361D4⋊C8—831no—
362D4⋊C8—831no—
363D4⋊C8—831no—
364D4⋊C8C2×D8311yescharacteristic, complemented
365D4⋊C8C2×D8311yescharacteristic, complemented
366#322—831no—
367#322—831no—
368#322—831no—
369C82—831no—
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—21no—
384#125C4×D8311yescharacteristic
385#124C4×D8311yescharacteristic
386#123—21no—
387C22⋊Q8C4×D8311yescharacteristic
388#121C4×D8311yescharacteristic
389C4×Q8C22×D8311yescharacteristic
390C4×D4—21no—
391C4×D4—831no—
392C4×D4—831no—
393C4×D4—831no—
394C4×D4—831no—
395C4×D4—1661no—
396C4×D4—1661no—
397C4×D4C22×D8311yescharacteristic
398#117—21no—
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—831no—
412C4⋊C8—831no—
413C4⋊C8—1661no—
414C4⋊C8—1661no—
415C4⋊C8—1661no—
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—831no—
429C22⋊C8—831no—
430C22⋊C8—831no—
431C22⋊C8—831no—
432C22⋊C8—1661no—
433C22⋊C8—1661no—
434C22⋊C8—1661no—
435C22⋊C8—1661no—
436C22⋊C8—1661no—
437C22⋊C8—1661no—
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—1661no—
448C2×Q8C2×C4×D8311yescharacteristic
449C2×D4—21no—
450C2×D4—831no—
451C2×D4—831no—
452C2×D4—1662no—
453C2×D4—1662no—
454C2×D4—1661no—
455C2×D4C2×C4×D8311yescharacteristic
456C22×C4—21no—
457C22×C4—6641no—
458C22×C4—6641no—
459C22×C4—1661no—
460C22×C4—1661no—
461C22×C4—1661no—
462C22×C4—1661no—
463C22×C4—1661no—
464C22×C4C2×C4×D8311yescharacteristic
465C22×C4D4×D8311yescharacteristic
466C22×C4#1305058911yescharacteristic
467SD16—1662no—
468SD16—1662no—
469D8—1662no—
470D8—1662no—
471M16—6641no—
472M16—6641no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—831no—
478C2×C8—831no—
479C2×C8—831no—
480C2×C8—831no—
481C2×C8—831no—
482C2×C8—831no—
483C2×C8—831no—
484C2×C8—831no—
485C2×C8—6641no—
486C2×C8—6641no—
487C2×C8—6641no—
488C2×C8—6641no—
489C2×C8—6641no—
490C2×C8—1661no—
491C2×C8—1661no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—831no—
497C4⋊C4—831no—
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—21no—
506C22⋊C4—1661no—
507C22⋊C4—1661no—
508C22⋊C4—1661no—
509C22⋊C4—1661no—
510C42—21no—
511C42C2×C4×D8311yescharacteristic
512C42D4×D8311yescharacteristic
513C42#1305058911yescharacteristic
514C42C23×D8311yescharacteristic
515C23—21no—
516C23—6641no—
517C23—6641no—
518C23—1664no—
519C23—1661no—
520C23—1661no—
521C23(C22⋊D83)⋊C411yescharacteristic
522Q8—21no—
523Q8—21no—
524D4—21no—
525D4—21no—
526D4—81no—
527D4—832no—
528D4—832no—
529D4—1664no—
530D4—1661no—
531D4—1661no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—3321no—
543C2×C4—3321no—
544C2×C4—3321no—
545C2×C4—3321no—
546C2×C4—6641no—
547C2×C4—6641no—
548C2×C4—6641no—
549C2×C4—1661no—
550C2×C4—1661no—
551C2×C4(C22⋊D83)⋊C411yescharacteristic
552C2×C4(C22⋊D83)⋊C411yescharacteristic
553C2×C4(C22⋊D83)⋊C411yescharacteristic
554C2×C4C22×C4×D8311yescharacteristic
555C2×C4C2×D4×D8311yescharacteristic
556C2×C4C2×#1305058911yescharacteristic
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—3321no—
562C8—3321no—
563C8—1661no—
564C8—1661no—
565C8—1661no—
566C8—1661no—
567C8—1661no—
568C8—1661no—
569C8—1661no—
570C8—1661no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—3321no—
578C22—3321no—
579C22—3321no—
580C22—3321no—
581C22—6644no—
582C22—1662no—
583C22—1662no—
584C22C2×(C22⋊D83)⋊C411yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—3321no—
593C4—3321no—
594C4#131×D8311yescharacteristic
595C4#131×D8311yescharacteristic
596C4#1912850311yescharacteristic
597C4#1912850811yescharacteristic
598C2—41no—
599C2—81no—
600C2—3322no—
601C2—3322no—
602C2#2491616011yescharacteristic
603C2#2491629811yescharacteristic
604C2#2491637611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1482C2
socleC22×C83C2×C4×D4
prime radical#19127834C4
cosocleC42×C83C24
hypercenter#1482D83
hypocenterC83#17918
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1482

Complements

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

NH ≅ G/Ntype
2. #24916612C2semidirect
3. #24916486C2semidirect
4. #24906330C2semidirect
5. #24906323C2semidirect
6. #24906302C2semidirect
7. #24906295C2semidirect
8. #24906284C2semidirect
9. #24906278C2semidirect
10. #24906260C2semidirect
11. #24906255C2semidirect
12. #24906251C2semidirect
13. #24905889C2semidirect
14. #24905763C2semidirect
15. C83×#1482C2semidirect
25. #19127832C22semidirect
26. Q8×C83⋊C8C22semidirect
32. #19127779C22semidirect
36. D4×C83⋊C8C22semidirect
48. #19127453C22semidirect
49. #19127453C22semidirect
50. #19127451C22semidirect
51. #19127451C22semidirect
56. #19127423C22semidirect
57. #19127423C22semidirect
58. #19127422C22semidirect
59. C8×C83⋊C8C22semidirect
63. Q8⋊C8×C83C22semidirect
64. Q8⋊C8×C83C22semidirect
65. D4⋊C8×C83C22semidirect
66. D4⋊C8×C83C22semidirect
316. #1482D83semidirect
318. C83#17918semidirect
358. Q8⋊C8C2×D83semidirect
359. Q8⋊C8C2×D83semidirect
364. D4⋊C8C2×D83semidirect
365. D4⋊C8C2×D83semidirect

Maximal subgroups

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

subgroupindex
#249175062
#249166122
#249164862
#249063302
#249063232
#249063022
#249062952
#249062842
#249062782
#249062602
#249062552
#249062512
#249058892
#249057632
C83×#14822
#1791883