Finite Group Databasebeta

← #35375461

Subgroups — #35375461

Order 21248.

662 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917517C211yesmaximal, characteristic
2#24916475C211yesmaximal, characteristic, complemented
3#24916207C211yesmaximal, characteristic, complemented
4#24906362C211yesmaximal, characteristic, complemented
5#24906356C211yesmaximal, characteristic, complemented
6#24906330C211yesmaximal, characteristic, complemented
7#24906317C211yesmaximal, characteristic, complemented
8#24906296C211yesmaximal, characteristic, complemented
9#24906295C211yesmaximal, characteristic, complemented
10#24906284C211yesmaximal, characteristic, complemented
11#24906255C211yesmaximal, characteristic, complemented
12#24906249C211yesmaximal, characteristic, complemented
13#24905851C211yesmaximal, characteristic, complemented
14#24905758C211yesmaximal, characteristic, complemented
15C83×#1496C211yesmaximal, characteristic, complemented
16C2×#14581799—21no—
17C4×#13050590C2211yescharacteristic
18#19128022C411yescharacteristic
19#19128022C411yescharacteristic
20#19127993C411yescharacteristic
21#19127988C411yescharacteristic
22#19127898C411yescharacteristic
23#19127893C411yescharacteristic
24#19127844C411yescharacteristic
25#19127844C411yescharacteristic
26#19127828C2211yescharacteristic
27#19127828C2211yescharacteristic
28C4×#13050578C2211yescharacteristic
29C4×#13050578C2211yescharacteristic
30C4×#13050575C2211yescharacteristic
31C4×#13050575C2211yescharacteristic
32#19127779C2211yescharacteristic
33#19127779C2211yescharacteristic
34#19127775—21no—
35#19127775—21no—
36#19127773—21no—
37#19127773—21no—
38D4×C83⋊C8C2211yescharacteristic
39D4×C83⋊C8C2211yescharacteristic
40#19127766C2211yescharacteristic
41#19127766C2211yescharacteristic
42#19127756—21no—
43#19127754C2211yescharacteristic
44C2×C4⋊(C83⋊C8)C2211yescharacteristic
45#19127668—21no—
46C4×#13050574C2211yescharacteristic
47#97×D83—21no—
48#19127453C2211yescharacteristic
49#19127453C2211yescharacteristic
50#19127451C2211yescharacteristic
51#19127451C2211yescharacteristic
52#19127433C2211yescharacteristic
53#19127433C2211yescharacteristic
54#19127430C2211yescharacteristic
55#19127430C2211yescharacteristic
56#19127423C2211yescharacteristic
57#19127423C2211yescharacteristic
58#19127422C2211yescharacteristic
59C8×C83⋊C8C2211yescharacteristic
60#532×C83C2211yescharacteristic
61#432×C83C2211yescharacteristic
62#431×C83C2211yescharacteristic
63D4⋊C8×C83C2211yescharacteristic
64D4⋊C8×C83C2211yescharacteristic
65D4⋊C8×C83C2211yescharacteristic
66D4⋊C8×C83C2211yescharacteristic
67C2×#13050590C2×C411yescharacteristic
68C2×#13050578C2×C411yescharacteristic
69C2×#13050578C2×C411yescharacteristic
70C2×#13050575C2×C411yescharacteristic
71C2×#13050575C2×C411yescharacteristic
72#14581799—44no—
73C2×#13050574—21no—
74C2×#13050574—21no—
75C2×#13050574D411yescharacteristic
76C2×#13050574D411yescharacteristic
77C22×C83⋊C8—21no—
78C22×C83⋊C8—21no—
79C22×C83⋊C8—21no—
80C2×C8×D83—21no—
81C2×C8×D83—21no—
82C4×Dic166C2×C411yescharacteristic
83C4×Dic166C2311yescharacteristic
84C4×D332C2×C411yescharacteristic
85C4×D332C2311yescharacteristic
86C4×C22⋊D83—21no—
87C4×C22⋊D83—21no—
88#14581751C2×C411yescharacteristic
89#14581749—21no—
90C42×D83—21no—
91#14581725C2×C411yescharacteristic
92#14581725C2×C411yescharacteristic
93#14581723C2×C411yescharacteristic
94#14581723C2×C411yescharacteristic
95C4⋊(C83⋊C8)—21no—
96C4⋊(C83⋊C8)C2×C411yescharacteristic
97C4⋊(C83⋊C8)C2×C411yescharacteristic
98C4⋊(C83⋊C8)C2311yescharacteristic
99C4⋊(C83⋊C8)C2311yescharacteristic
100Dic83⋊C8—21no—
101Dic83⋊C8—21no—
102#14581715C2×C411yescharacteristic
103#14581715C2×C411yescharacteristic
104#14581713C2×C411yescharacteristic
105#14581713C2×C411yescharacteristic
106#14581713C2×C411yescharacteristic
107#14581713C2×C411yescharacteristic
108#14581712C2×C411yescharacteristic
109#14581712C2×C411yescharacteristic
110C22⋊(C83⋊C8)—21no—
111C22⋊(C83⋊C8)—21no—
112C22⋊(C83⋊C8)—21no—
113C22⋊(C83⋊C8)—21no—
114C22⋊(C83⋊C8)C2×C411yescharacteristic
115C22⋊(C83⋊C8)C2×C411yescharacteristic
116(C2×D83)⋊C8—21no—
117(C2×D83)⋊C8—21no—
118#14581703D411yescharacteristic
119#14581703D411yescharacteristic
120#14581702—21no—
121#14581702—21no—
122C4×C83⋊C8C2311yescharacteristic
123C4×C83⋊C8C2311yescharacteristic
124C4×C83⋊C8C2311yescharacteristic
125C4×C83⋊C8C2311yescharacteristic
126C2×#41×C83—21no—
127C4⋊Q8×C83C2×C411yescharacteristic
128#127×C83C2×C411yescharacteristic
129#124×C83—21no—
130#121×C83—21no—
131#121×C83C2×C411yescharacteristic
132#121×C83C2×C411yescharacteristic
133C4×D4×C83—21no—
134C4×D4×C83C2311yescharacteristic
135C4×D4×C83C2311yescharacteristic
136C2×C42×C83C2311yescharacteristic
137C4⋊C8×C83—21no—
138C4⋊C8×C83C2311yescharacteristic
139C4⋊C8×C83C2311yescharacteristic
140C22⋊C8×C83—21no—
141C22⋊C8×C83—21no—
142#97×C83—21no—
143C4×C8×C83C2311yescharacteristic
144C4×C8×C83C2311yescharacteristic
145#13050590—22no—
146#13050590—41no—
147C2×Dic166C22×C411yescharacteristic
148C2×D332C22×C411yescharacteristic
149C2×C22⋊D83—21no—
150C2×C4×D83—21no—
151C2×C4×D83—21no—
152C2×C4×D83—21no—
153#13050578—41no—
154#13050578—41no—
155#13050575—22no—
156#13050575—22no—
157#13050574—22no—
158#13050574—41no—
159#13050574—42no—
160#13050574—42no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8—21no—
163C2×C83⋊C8—42no—
164C2×C83⋊C8—42no—
165C2×C83⋊C8—42no—
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—42no—
175C8×D83—42no—
176C4⋊Dic83C22×C411yescharacteristic
177C4⋊Dic83C22×C411yescharacteristic
178Dic83⋊C4—21no—
179Dic83⋊C4—21no—
180C22⋊Dic83—21no—
181(C2×D83)⋊C4—21no—
182(C2×D83)⋊C4—21no—
183C4×Dic83—21no—
184C4×Dic83—21no—
185C4×Dic83—21no—
186#41×C83—42no—
187#41×C83—42no—
188C2×Q8×C83—21no—
189C2×D4×C83—21no—
190C2×D4×C83—21no—
191C2×D4×C83—21no—
192C2×D4×C83—21no—
193C2×D4×C83C22×C411yescharacteristic
194C2×D4×C83C22×C411yescharacteristic
195C22×C4×C83—21no—
196C22×C4×C83—21no—
197C22×C4×C83C22×C411yescharacteristic
198C22×C4×C83C2×D411yescharacteristic
199C22×C4×C83#4111yescharacteristic
200C2×C8×C83—21no—
201C2×C8×C83—21no—
202C2×C8×C83—21no—
203C2×C8×C83—21no—
204C4⋊C4×C83—21no—
205C4⋊C4×C83C22×C411yescharacteristic
206C4⋊C4×C83C22×C411yescharacteristic
207C22⋊C4×C83—21no—
208C22⋊C4×C83—21no—
209C22⋊C4×C83—21no—
210C22⋊C4×C83—21no—
211C42×C83C22×C411yescharacteristic
212C42×C83C2×D411yescharacteristic
213C42×C83#4111yescharacteristic
214C42×C83C2411yescharacteristic
215C23×C83—21no—
216C23×C83—21no—
217C23×C83C4×D411yescharacteristic
218C22×D83—21no—
219Q8×C83—42no—
220D4×C83—21no—
221D4×C83—21no—
222D4×C83—21no—
223D4×C83—21no—
224D4×C83—42no—
225D4×C83—42no—
226D4×C83—42no—
227D4×C83—81no—
228C2×C4×C83—21no—
229C2×C4×C83—21no—
230C2×C4×C83—21no—
231C2×C4×C83—21no—
232C2×C4×C83—21no—
233C2×C4×C83—21no—
234C2×C4×C83—41no—
235C2×C4×C83—41no—
236C2×C4×C83—41no—
237C2×C4×C83—41no—
238C2×C4×C83—41no—
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#13112yescomplemented
251C4×D83—42no—
252C4×D83—41no—
253C4×D83—41no—
254C4×D83—81no—
255Dic166—21no—
256Dic166—21no—
257C8×C83—41no—
258C8×C83—41no—
259C8×C83—41no—
260C8×C83—41no—
261C83⋊C8—21no—
262C83⋊C8—21no—
263C83⋊C8—21no—
264C83⋊C8—21no—
265C83⋊C8—21no—
266C83⋊C8—21no—
267C83⋊C8—21no—
268C83⋊C8—41no—
269C83⋊C8—41no—
270C83⋊C8AGL(1,ℤ/8)12yes—
271C22×C83—21no—
272C22×C83—21no—
273C22×C83—21no—
274C22×C83—41no—
275C22×C83—41no—
276C22×C83—41no—
277C22×C83—41no—
278C22×C83—41no—
279C22×C83—41no—
280C22×C83C2×C4×D411yescharacteristic
281C2×D83—22no—
282C2×D83—41no—
283C2×D83—41no—
284C4×C83—21no—
285C4×C83—21no—
286C4×C83—21no—
287C4×C83—21no—
288C4×C83—41no—
289C4×C83—41no—
290C4×C83C2×#13111yescharacteristic
291C4×C83#56811yescharacteristic
292C4×C83C2×AGL(1,ℤ/8)11yescharacteristic
293C4×C83#57511yescharacteristic
294Dic83—41no—
295Dic83—41no—
296Dic83—41no—
297#18007—831nomaximal, Sylow
298C2×C83—41no—
299C2×C83—81no—
300C2×C83—81no—
301C2×C83#293311yescharacteristic
302C2×C83C4×AGL(1,ℤ/8)11yescharacteristic
303C2×C83#295711yescharacteristic
304D83—42no—
305#3106—831no—
306#2970—831no—
307#2935—831no—
308#1592—831no—
309#1590—831no—
310#1586—831no—
311#1585—831no—
312#1582—831no—
313#1581—831no—
314#1580—831no—
315C8×D8—831no—
316#1573—831no—
317#1496D8311yescharacteristic, complemented
318#1477—831no—
319#1453—831no—
320C83#1800711yescharacteristic, complemented, Sylow
321C2×#131—1661no—
322#532C2×D8311yescharacteristic
323C4×#41—831no—
324#482—831no—
325#482—831no—
326#477—831no—
327#476—831no—
328#460—831no—
329#459—831no—
330#449—831no—
331#449—831no—
332#446—831no—
333#446—831no—
334C4×SD16—831no—
335C4×SD16—831no—
336C4×D8—831no—
337C4×D8—831no—
338#436—831no—
339#436—831no—
340#435—1661no—
341#435—1661no—
342#435—1661no—
343#435—1661no—
344C8×D4—831no—
345C8×D4—831no—
346C8×D4—831no—
347C8×D4—831no—
348#432—1661no—
349#432C2×D8311yescharacteristic
350#431—831no—
351#431C2×D8311yescharacteristic
352C2×C4⋊C8—831no—
353#408—1661no—
354C4×M16—831no—
355C2×#97—1661no—
356#335—831no—
357#335—831no—
358#334—831no—
359#334—831no—
360Q8⋊C8—831no—
361Q8⋊C8—831no—
362D4⋊C8—831no—
363D4⋊C8—831no—
364D4⋊C8C2×D8311yescharacteristic
365D4⋊C8C2×D8311yescharacteristic
366D4⋊C8C2×D8311yescharacteristic
367D4⋊C8C2×D8311yescharacteristic
368#322—831no—
369#322—831no—
370#322—831no—
371C82—831no—
372C2×#41—21no—
373C2×#41—831no—
374C2×SD16—831no—
375C2×SD16—831no—
376C2×D8—831no—
377C2×D8—831no—
378#131—3324no—
379C2×M16—831no—
380C2×M16—831no—
381C2×M16—1661no—
382C2×M16—1661no—
383C22×C8—1661no—
384C22×C8—1661no—
385C22×C8—1661no—
386C22×C8—1661no—
387C22×C8—1661no—
388C4⋊Q8C4×D8311yescharacteristic
389#127C4×D8311yescharacteristic
390#124—21no—
391#121—21no—
392#121C4×D8311yescharacteristic
393#121C4×D8311yescharacteristic
394C4×Q8—831no—
395C4×Q8—831no—
396C4×D4—21no—
397C4×D4—831no—
398C4×D4—831no—
399C4×D4—1661no—
400C4×D4—1661no—
401C4×D4C22×D8311yescharacteristic
402C4×D4C22×D8311yescharacteristic
403#117—831no—
404#117—1661no—
405C2×C42—1661no—
406C2×C42C22×D8311yescharacteristic
407#107—831no—
408#107—831no—
409#106—831no—
410#106—831no—
411C4⋊C8—21no—
412C4⋊C8—831no—
413C4⋊C8—831no—
414C4⋊C8—831no—
415C4⋊C8—831no—
416C4⋊C8—1661no—
417C4⋊C8—1661no—
418C4⋊C8—1661no—
419C4⋊C8C22×D8311yescharacteristic
420C4⋊C8C22×D8311yescharacteristic
421#103—831no—
422#103—831no—
423#102—831no—
424#102—831no—
425#102—831no—
426#102—831no—
427#102—831no—
428#102—831no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—831no—
432C22⋊C8—831no—
433C22⋊C8—1661no—
434C22⋊C8—1661no—
435C22⋊C8—1661no—
436C22⋊C8—1661no—
437C22⋊C8—1661no—
438C22⋊C8—1661no—
439#97—21no—
440#97—831no—
441#97—831no—
442#97—1661no—
443#97—1661no—
444C4×C8—831no—
445C4×C8—831no—
446C4×C8—831no—
447C4×C8—831no—
448C4×C8C22×D8311yescharacteristic
449C4×C8C22×D8311yescharacteristic
450#41—42no—
451#41—42no—
452#41—3321no—
453#41—1662no—
454C2×Q8—21no—
455C2×Q8—831no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—831no—
461C2×D4—1661no—
462C2×D4C2×C4×D8311yescharacteristic
463C2×D4C2×C4×D8311yescharacteristic
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—1661no—
467C22×C4—1661no—
468C22×C4—1661no—
469C22×C4C2×C4×D8311yescharacteristic
470C22×C4D4×D8311yescharacteristic
471C22×C4#1305058911yescharacteristic
472SD16—3321no—
473SD16—3321no—
474D8—1662no—
475D8—1662no—
476M16—3322no—
477M16—3322no—
478M16—3321no—
479M16—1662no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—3322no—
485C2×C8—3322no—
486C2×C8—3322no—
487C2×C8—3322no—
488C2×C8—3322no—
489C2×C8—831no—
490C2×C8—831no—
491C2×C8—831no—
492C2×C8—831no—
493C2×C8—831no—
494C2×C8—831no—
495C2×C8—831no—
496C2×C8—831no—
497C2×C8—1661no—
498C2×C8—1661no—
499C4⋊C4—21no—
500C4⋊C4—831no—
501C4⋊C4—831no—
502C4⋊C4—1661no—
503C4⋊C4—1661no—
504C4⋊C4C2×C4×D8311yescharacteristic
505C4⋊C4C2×C4×D8311yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—1661no—
511C22⋊C4—1661no—
512C22⋊C4—1661no—
513C42—1661no—
514C42—1661no—
515C42—1661no—
516C42C2×C4×D8311yescharacteristic
517C42D4×D8311yescharacteristic
518C42#1305058911yescharacteristic
519C42C23×D8311yescharacteristic
520C23—21no—
521C23—21no—
522C23—1661no—
523C23(C22⋊D83)⋊C411yescharacteristic
524Q8—42no—
525Q8—1661no—
526Q8—1661no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—42no—
532D4—42no—
533D4—42no—
534D4—81no—
535D4—3322no—
536D4—832no—
537D4—1661no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—3322no—
550C2×C4—3321no—
551C2×C4—3321no—
552C2×C4—6641no—
553C2×C4—1661no—
554C2×C4—1661no—
555C2×C4—1661no—
556C2×C4(C22⋊D83)⋊C411yescharacteristic
557C2×C4(C22⋊D83)⋊C411yescharacteristic
558C2×C4(C22⋊D83)⋊C411yescharacteristic
559C2×C4C22×C4×D8311yescharacteristic
560C2×C4C2×D4×D8311yescharacteristic
561C2×C4C2×#1305058911yescharacteristic
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—3321no—
567C8—3321no—
568C8—832no—
569C8—1661no—
570C8—1661no—
571C8—1661no—
572C8—1661no—
573C8—1661no—
574C8—1661no—
575C8—1661no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—3321no—
586C22—3321no—
587C22—1662no—
588C22C2×(C22⋊D83)⋊C411yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—21no—
593C4—41no—
594C4—41no—
595C4—3321no—
596C4—3321no—
597C4—3321no—
598C4#131×D8311yescharacteristic
599C4#1912846611yescharacteristic
600C4AGL(1,ℤ/8)×D8311yescharacteristic
601C4#1912849711yescharacteristic
602C2—41no—
603C2—81no—
604C2—81no—
605C2—3322no—
606C2#2491619311yescharacteristic
607C2#2491626711yescharacteristic
608C2#2491637611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1496C2
socleC22×C83C2×C4×D4
prime radical#24917517C2
cosocleC42×C83C24
hypercenter#1496D83
hypocenterC83#18007
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1496

Complements

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

NH ≅ G/Ntype
2. #24916475C2semidirect
3. #24916207C2semidirect
4. #24906362C2semidirect
5. #24906356C2semidirect
6. #24906330C2semidirect
7. #24906317C2semidirect
8. #24906296C2semidirect
9. #24906295C2semidirect
10. #24906284C2semidirect
11. #24906255C2semidirect
12. #24906249C2semidirect
13. #24905851C2semidirect
14. #24905758C2semidirect
15. C83×#1496C2semidirect
250. D332#131semidirect
317. #1496D83semidirect
320. C83#18007semidirect

Maximal subgroups

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

subgroupindex
#249175172
#249164752
#249162072
#249063622
#249063562
#249063302
#249063172
#249062962
#249062952
#249062842
#249062552
#249062492
#249058512
#249057582
C83×#14962
#1800783