Finite Group Databasebeta

← #35416735

Subgroups — #35416735

Order 21248.

628 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917253C211yesmaximal, characteristic
2#24916403C211yesmaximal, characteristic, complemented
3#24916112C211yesmaximal, characteristic
4#24908406C211yesmaximal, characteristic, complemented
5#24908239C211yesmaximal, characteristic, complemented
6#24908216C211yesmaximal, characteristic, complemented
7#24908211C211yesmaximal, characteristic, complemented
8#24908174C211yesmaximal, characteristic
9#24908167C211yesmaximal, characteristic
10#24908112C211yesmaximal, characteristic
11#24908112C211yesmaximal, characteristic
12#24908063C211yesmaximal, characteristic, complemented
13#24908063C211yesmaximal, characteristic, complemented
14#24907484C211yesmaximal, characteristic
15C83×#1771C211yesmaximal, characteristic, complemented
16#19128258C2211yescharacteristic
17C4×#13050590C2211yescharacteristic
18#19128009C411yescharacteristic, complemented
19#19128009C411yescharacteristic, complemented
20#19128002C411yescharacteristic, complemented
21#19128002C411yescharacteristic, complemented
22#19127997C411yescharacteristic, complemented
23#19127992C411yescharacteristic, complemented
24#19127987C411yescharacteristic, complemented
25#19127982C411yescharacteristic, complemented
26#19127829—21no—
27#19127829—21no—
28#19127829—21no—
29#19127829—21no—
30#19127763—21no—
31#19127763—21no—
32#19127756—21no—
33#19127756—21no—
34C2×#14581728C2211yescharacteristic
35C2×#14581728C2211yescharacteristic
36#19127739C2211yescharacteristic
37#19127739C2211yescharacteristic
38#19127727C2211yescharacteristic
39#19127727C2211yescharacteristic
40#19127727C2211yescharacteristic
41#19127727C2211yescharacteristic
42#19127725C2211yescharacteristic
43C2×#14581720C2211yescharacteristic
44C2×#14581720C2211yescharacteristic
45#19127698C2211yescharacteristic
46#19127698C2211yescharacteristic
47#19127667C2211yescharacteristic
48#19127667C2211yescharacteristic
49#19127656C2211yescharacteristic
50#19127656C2211yescharacteristic
51C4×#13050574C2211yescharacteristic
52#19127466C2211yescharacteristic
53#19127466C2211yescharacteristic
54#19127461C2211yescharacteristic
55#19127461C2211yescharacteristic
56#19127461C2211yescharacteristic
57#19127461C2211yescharacteristic
58#19127461C2211yescharacteristic
59#19127461C2211yescharacteristic
60C2×C4⋊C8×C83C2211yescharacteristic
61C2×#97×C83C2211yescharacteristic
62C2×#97×C83C2211yescharacteristic
63C2×C4×C8×C83C2211yescharacteristic
64C4×C4⋊C4×C83C2211yescharacteristic
65#336×C83C2211yescharacteristic
66#336×C83C2211yescharacteristic
67C2×#13050590C2311yescharacteristic
68C2×#13050574C2311yescharacteristic
69C2×#13050574C2311yescharacteristic
70C2×#13050574C2311yescharacteristic
71C2×#13050574C2311yescharacteristic
72#14581792C2×C411yescharacteristic
73#14581792C2×C411yescharacteristic
74#14581784C2×C411yescharacteristic
75#14581784C2×C411yescharacteristic
76#14581771—21no—
77#14581771—21no—
78C4×Dic166—21no—
79C4×Dic166—21no—
80C4×Dic166C2×C411yescharacteristic
81C4×Dic166C2×C411yescharacteristic
82C4×D332C2×C411yescharacteristic
83C4×D332C2×C411yescharacteristic
84C4×C22⋊D83—21no—
85C4×C22⋊D83—21no—
86#14581751C2311yescharacteristic
87#14581751C2311yescharacteristic
88#14581751C2311yescharacteristic
89#14581749—21no—
90C42×D83—21no—
91#14581728—41no—
92#14581728—41no—
93#14581726C2×C411yescharacteristic
94#14581726C2×C411yescharacteristic
95#14581726C2×C411yescharacteristic
96#14581726C2×C411yescharacteristic
97#14581724C2×C411yescharacteristic
98#14581724C2×C411yescharacteristic
99#14581724C2×C411yescharacteristic
100#14581724C2×C411yescharacteristic
101C4⋊(C83⋊C8)—21no—
102C4⋊(C83⋊C8)—21no—
103Dic83⋊C8—21no—
104Dic83⋊C8—21no—
105Dic83⋊C8—21no—
106Dic83⋊C8—21no—
107Dic83⋊C8—21no—
108Dic83⋊C8—21no—
109Dic83⋊C8—21no—
110Dic83⋊C8—21no—
111#14581720—41no—
112#14581720—41no—
113#14581717C2×C411yescharacteristic
114#14581717C2×C411yescharacteristic
115#14581717C2×C411yescharacteristic
116#14581717C2×C411yescharacteristic
117#14581714C2×C411yescharacteristic
118#14581714C2×C411yescharacteristic
119#14581714C2×C411yescharacteristic
120#14581714C2×C411yescharacteristic
121(C2×D83)⋊C8—21no—
122(C2×D83)⋊C8—21no—
123(C2×D83)⋊C8—21no—
124(C2×D83)⋊C8—21no—
125#14581703—21no—
126#14581702—21no—
127#14581702—21no—
128C4×C83⋊C8—21no—
129C8×Dic83—21no—
130C8×Dic83—21no—
131C22×C8×C83C2311yescharacteristic
132C22×C8×C83C2311yescharacteristic
133C22×C8×C83C2311yescharacteristic
134C22×C8×C83C2311yescharacteristic
135C2×C4⋊C4×C83—21no—
136C2×C42×C83C2311yescharacteristic
137C2×C42×C83C2311yescharacteristic
138C2×C42×C83C2311yescharacteristic
139C4⋊C8×C83C2×C411yescharacteristic
140C4⋊C8×C83C2×C411yescharacteristic
141C4⋊C8×C83C2×C411yescharacteristic
142C4⋊C8×C83C2×C411yescharacteristic
143#97×C83—41no—
144#97×C83D411yescharacteristic
145#97×C83D411yescharacteristic
146#97×C83D411yescharacteristic
147#97×C83D411yescharacteristic
148C4×C8×C83—41no—
149#95×C83—21no—
150#13050590—21no—
151#13050590—21no—
152#13050590—21no—
153#13050590—21no—
154C2×Dic166—21no—
155C2×Dic166—21no—
156C2×Dic166C22×C411yescharacteristic
157C2×D332C22×C411yescharacteristic
158C2×C22⋊D83—21no—
159C2×C4×D83—21no—
160C2×C4×D83—21no—
161C2×C4×D83—21no—
162#13050574—21no—
163#13050574—21no—
164#13050574—21no—
165#13050574—21no—
166#13050574—21no—
167#13050574—21no—
168#13050574—21no—
169#13050574—21no—
170C2×C83⋊C8—21no—
171C2×C83⋊C8—21no—
172C2×C83⋊C8—21no—
173C2×C83⋊C8—21no—
174C4⋊Dic83—21no—
175C4⋊Dic83—21no—
176C4⋊Dic83C22×C411yescharacteristic
177C4⋊Dic83C22×C411yescharacteristic
178C4⋊Dic83C22×C411yescharacteristic
179C4⋊Dic83C22×C411yescharacteristic
180C4⋊Dic83C22×C411yescharacteristic
181C4⋊Dic83C22×C411yescharacteristic
182Dic83⋊C4—21no—
183Dic83⋊C4—21no—
184Dic83⋊C4—21no—
185Dic83⋊C4—21no—
186Dic83⋊C4—21no—
187Dic83⋊C4—21no—
188C22⋊Dic83—21no—
189C22⋊Dic83—21no—
190C22⋊Dic83—21no—
191(C2×D83)⋊C4—21no—
192(C2×D83)⋊C4—21no—
193C4×Dic83—21no—
194C4×Dic83—21no—
195C4×Dic83—21no—
196C4×Dic83—21no—
197C4×Dic83—21no—
198C22×C4×C83—21no—
199C22×C4×C83—21no—
200C22×C4×C83#4111yescharacteristic
201C22×C4×C83#4111yescharacteristic
202C22×C4×C83C2411yescharacteristic
203C2×C8×C83—21no—
204C2×C8×C83—21no—
205C2×C8×C83—21no—
206C2×C8×C83—21no—
207C2×C8×C83—21no—
208C2×C8×C83—21no—
209C2×C8×C83—21no—
210C2×C8×C83—21no—
211C2×C8×C83C22×C411yescharacteristic
212C2×C8×C83C22×C411yescharacteristic
213C2×C8×C83C22×C411yescharacteristic
214C2×C8×C83C22×C411yescharacteristic
215C2×C8×C83C2×D411yescharacteristic
216C2×C8×C83C2×D411yescharacteristic
217C2×C8×C83C2×D411yescharacteristic
218C2×C8×C83C2×D411yescharacteristic
219C4⋊C4×C83—42no—
220C42×C83—21no—
221C42×C83—21no—
222C42×C83—21no—
223C42×C83—21no—
224C42×C83C22×C411yescharacteristic
225C42×C83C22×C411yescharacteristic
226C42×C83C2×D411yescharacteristic
227C42×C83C2×D411yescharacteristic
228C23×C83C2×#4111yescharacteristic
229C22×D83—21no—
230C2×C4×C83—22no—
231C2×C4×C83—41no—
232C2×C4×C83—41no—
233C2×C4×C83—41no—
234C2×C4×C83—41no—
235C2×C4×C83—41no—
236C2×C4×C83—41no—
237C2×C4×C83—41no—
238C2×C4×C83C4×D411yescharacteristic
239C2×C4×C83C4×D411yescharacteristic
240C2×C4×C83C4×D411yescharacteristic
241C2×C4×C83C4×D411yescharacteristic
242C2×C4×C83C23×C411yescharacteristic
243C2×C4×C83C22×D411yescharacteristic
244C2×C4×C83H(5,𝔽2)11yescharacteristic
245C2×C4×C832−1+411yescharacteristic
246C2×C4×C832−1+411yescharacteristic
247C2×C4×C832−1+411yescharacteristic
248C22⋊D83—41no—
249C22⋊D83—41no—
250C2×Dic83—21no—
251C2×Dic83—21no—
252C2×Dic83—21no—
253C2×Dic83—21no—
254C2×Dic83—21no—
255C2×Dic83—21no—
256C2×Dic83—21no—
257D332—21no—
258D332—21no—
259C4×D83—41no—
260C4×D83—41no—
261C4×D83—81no—
262C4×D83—81no—
263Dic166—21no—
264Dic166—21no—
265Dic166—81no—
266Dic166—81no—
267C8×C83—21no—
268C8×C83—21no—
269C8×C83—21no—
270C8×C83—21no—
271C8×C83—21no—
272C8×C83—21no—
273C8×C83—21no—
274C8×C83—21no—
275C83⋊C8—41no—
276C83⋊C8—41no—
277C83⋊C8—41no—
278C83⋊C8—41no—
279C22×C83—21no—
280C22×C83—21no—
281C22×C83C2×C4×D411yescharacteristic
282C22×C83#54111yescharacteristic
283C22×C83#54211yescharacteristic
284C2×D83—41no—
285C2×D83—41no—
286C2×D83—41no—
287C4×C83—21no—
288C4×C83—21no—
289C4×C83—21no—
290C4×C83—21no—
291C4×C83—42no—
292C4×C83—81no—
293C4×C83#51911yescharacteristic
294C4×C83#52011yescharacteristic
295C4×C83#53611yescharacteristic
296C4×C83#53711yescharacteristic
297Dic83—41no—
298Dic83—41no—
299Dic83—41no—
300Dic83—41no—
301Dic83—41no—
302Dic83—41no—
303Dic83—41no—
304#22132—831nomaximal, Sylow
305C2×C83—21no—
306C2×C83—21no—
307C2×C83#232311yescharacteristic
308C2×C83#295611yescharacteristic
309C2×C83#295711yescharacteristic
310D83—81no—
311#3076—831no—
312#2961—831no—
313#2923—831no—
314#1986—831no—
315#1950—831no—
316#1946—831no—
317#1945—831no—
318#1938—831no—
319#1937—831no—
320#1929—831no—
321#1929—831no—
322#1922—831no—
323#1922—831no—
324#1806—831no—
325#1771D8311yescharacteristic, complemented
326C83#2213211yescharacteristic, complemented, Sylow
327#533—831no—
328C4×#41—831no—
329#479—831no—
330#479—831no—
331#478—831no—
332#478—831no—
333#477—831no—
334#476—831no—
335#475—831no—
336#474—831no—
337#446—1661no—
338#446—1661no—
339#446—1661no—
340#446—1661no—
341#433—1661no—
342#433—1661no—
343#432—1661no—
344#432—1661no—
345C2×#108—831no—
346C2×#108—831no—
347#427—831no—
348#427—831no—
349#424—831no—
350#424—831no—
351#424—831no—
352#424—831no—
353#423—831no—
354C2×C4⋊C8C2×D8311yescharacteristic
355C2×#104—831no—
356C2×#104—831no—
357#416—831no—
358#416—831no—
359#408—831no—
360#408—831no—
361#405—831no—
362#405—831no—
363C4×M16—831no—
364C2×#97C2×D8311yescharacteristic
365C2×#97C2×D8311yescharacteristic
366C2×C4×C8C2×D8311yescharacteristic
367C4×C4⋊C4C2×D8311yescharacteristic
368#341—831no—
369#341—831no—
370#339—831no—
371#339—831no—
372#339—831no—
373#339—831no—
374#339—831no—
375#339—831no—
376#336C2×D8311yescharacteristic
377#336C2×D8311yescharacteristic
378C2×#41—831no—
379C2×M16—831no—
380C2×M16—831no—
381C2×M16—831no—
382C2×M16—831no—
383C22×C8C22×D8311yescharacteristic
384C22×C8C22×D8311yescharacteristic
385C22×C8C22×D8311yescharacteristic
386C22×C8C22×D8311yescharacteristic
387C4⋊Q8—831no—
388C4⋊Q8—831no—
389#125—831no—
390#125—831no—
391C22⋊Q8—1661no—
392C22⋊Q8—1661no—
393C4×Q8—831no—
394C4×Q8—831no—
395C4×Q8—1661no—
396C4×Q8—1661no—
397C4×D4—831no—
398C4×D4—831no—
399C4×D4—1661no—
400C4×D4—1661no—
401#117—831no—
402#117—831no—
403#117—831no—
404#117—1661no—
405C2×C4⋊C4—21no—
406C2×C42—1661no—
407C2×C42C22×D8311yescharacteristic
408C2×C42C22×D8311yescharacteristic
409C2×C42C22×D8311yescharacteristic
410#108—3321no—
411#108—3321no—
412#107—831no—
413#107—831no—
414#107—831no—
415#107—831no—
416#106—831no—
417#106—831no—
418#106—831no—
419#106—831no—
420C4⋊C8—1661no—
421C4⋊C8—1661no—
422C4⋊C8—1661no—
423C4⋊C8—1661no—
424C4⋊C8—1661no—
425C4⋊C8—1661no—
426C4⋊C8—1661no—
427C4⋊C8—1661no—
428C4⋊C8—1661no—
429C4⋊C8—1661no—
430C4⋊C8C4×D8311yescharacteristic
431C4⋊C8C4×D8311yescharacteristic
432C4⋊C8C4×D8311yescharacteristic
433C4⋊C8C4×D8311yescharacteristic
434#104—3321no—
435#104—3321no—
436#103—831no—
437#103—831no—
438#103—831no—
439#103—831no—
440#102—831no—
441#102—831no—
442#102—831no—
443#102—831no—
444C22⋊C8—1661no—
445C22⋊C8—1661no—
446C22⋊C8—1661no—
447C22⋊C8—1661no—
448#97—41no—
449#97—1661no—
450#97—1661no—
451#97—1661no—
452#97D33211yescharacteristic
453#97D33211yescharacteristic
454#97D33211yescharacteristic
455#97D33211yescharacteristic
456C4×C8—41no—
457C4×C8—1661no—
458C4×C8—1661no—
459C4×C8—1661no—
460#95—21no—
461#41—1661no—
462#41—1661no—
463#41—1661no—
464#41—1661no—
465C2×Q8—831no—
466C2×Q8—1661no—
467C2×Q8—1661no—
468C2×D4—831no—
469C2×D4—1661no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—1661no—
473C22×C4—1661no—
474C22×C4—1661no—
475C22×C4#1305059011yescharacteristic
476C22×C4#1305059011yescharacteristic
477C22×C4C23×D8311yescharacteristic
478M16—1661no—
479M16—1661no—
480M16—1661no—
481M16—1661no—
482M16—1661no—
483M16—1661no—
484M16—1661no—
485M16—1661no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—1661no—
495C2×C8—1661no—
496C2×C8—1661no—
497C2×C8—1661no—
498C2×C8C2×C4×D8311yescharacteristic
499C2×C8C2×C4×D8311yescharacteristic
500C2×C8C2×C4×D8311yescharacteristic
501C2×C8C2×C4×D8311yescharacteristic
502C2×C8C2×D33211yescharacteristic
503C2×C8C2×D33211yescharacteristic
504C2×C8C2×D33211yescharacteristic
505C2×C8C2×D33211yescharacteristic
506C4⋊C4—42no—
507C4⋊C4—831no—
508C4⋊C4—831no—
509C4⋊C4—831no—
510C4⋊C4—831no—
511C4⋊C4—831no—
512C4⋊C4—831no—
513C4⋊C4—1661no—
514C4⋊C4—1661no—
515C4⋊C4—1661no—
516C4⋊C4—1661no—
517C4⋊C4—1661no—
518C4⋊C4—1661no—
519C4⋊C4—1661no—
520C4⋊C4—1661no—
521C22⋊C4—1661no—
522C22⋊C4—1661no—
523C22⋊C4—1661no—
524C22⋊C4—1661no—
525C22⋊C4—1661no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—1661no—
531C42—1661no—
532C42—1661no—
533C42—1661no—
534C42—1661no—
535C42C2×C4×D8311yescharacteristic
536C42C2×C4×D8311yescharacteristic
537C42C2×D33211yescharacteristic
538C42C2×D33211yescharacteristic
539C23—1661no—
540C23C2×#1305059011yescharacteristic
541Q8—6641no—
542Q8—6641no—
543Q8—1661no—
544Q8—1661no—
545D4—3321no—
546D4—3321no—
547D4—1661no—
548D4—1661no—
549C2×C4—22no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—3321no—
558C2×C4—3321no—
559C2×C4—6641no—
560C2×C4—6641no—
561C2×C4—1661no—
562C2×C4—1661no—
563C2×C4—1661no—
564C2×C4—1661no—
565C2×C4—1661no—
566C2×C4—1661no—
567C2×C4—1661no—
568C2×C4C4×D33211yescharacteristic
569C2×C4C4×D33211yescharacteristic
570C2×C4C4×D33211yescharacteristic
571C2×C4C4×D33211yescharacteristic
572C2×C4C22×C4×D8311yescharacteristic
573C2×C4C22×D33211yescharacteristic
574C2×C4#1458183711yescharacteristic
575C2×C4#1458183911yescharacteristic
576C2×C4#1458183911yescharacteristic
577C2×C4#1458184011yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—21no—
586C8—3321no—
587C8—3321no—
588C8—3321no—
589C8—3321no—
590C22—21no—
591C22—21no—
592C22—3321no—
593C22—3321no—
594C22—3321no—
595C22C2×C4×D33211yescharacteristic
596C22#1912830911yescharacteristic
597C22#1912831611yescharacteristic
598C4—21no—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—42no—
603C4—81no—
604C4—3321no—
605C4—3321no—
606C4—3321no—
607C4—3321no—
608C4—3321no—
609C4—3321no—
610C4—3321no—
611C4#1912817711yescharacteristic
612C4#1912818011yescharacteristic
613C4#1912827711yescharacteristic
614C4#1912828211yescharacteristic
615C2—21no—
616C2—21no—
617C2—6641no—
618C2#2491014611yescharacteristic
619C2#2491637411yescharacteristic
620C2#2491638111yescharacteristic
subgroupG/H
centerC2×C4C22×D332
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#1771C2
socleC22×C83C2×C4×D4
prime radicalC2×#13050590C23
cosocleC22×C4×C83C24
hypercenter#1771D83
hypocenterC83#22132
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #1771

Complements

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

NH ≅ G/Ntype
2. #24916403C2semidirect
4. #24908406C2semidirect
5. #24908239C2semidirect
6. #24908216C2semidirect
7. #24908211C2semidirect
12. #24908063C2semidirect
13. #24908063C2semidirect
15. C83×#1771C2semidirect
18. #19128009C4semidirect
19. #19128009C4semidirect
20. #19128002C4semidirect
21. #19128002C4semidirect
22. #19127997C4semidirect
23. #19127992C4semidirect
24. #19127987C4semidirect
25. #19127982C4semidirect
325. #1771D83semidirect
326. C83#22132semidirect

Maximal subgroups

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

subgroupindex
#249172532
#249164032
#249161122
#249084062
#249082392
#249082162
#249082112
#249081742
#249081672
#249081122
#249080632
#249074842
C83×#17712
#2213283