Finite Group Databasebeta

← #35416739

Subgroups — #35416739

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#24917245C211yesmaximal, characteristic
2#24916404C211yesmaximal, characteristic, complemented
3#24916115C211yesmaximal, characteristic
4#24908238C211yesmaximal, characteristic, complemented
5#24908215C211yesmaximal, characteristic, complemented
6#24908210C211yesmaximal, characteristic, complemented
7#24908175C211yesmaximal, characteristic
8#24908168C211yesmaximal, characteristic
9#24908109C211yesmaximal, characteristic
10#24908109C211yesmaximal, characteristic
11#24908060C211yesmaximal, characteristic, complemented
12#24908060C211yesmaximal, characteristic, complemented
13#24907484C211yesmaximal, characteristic
14#24907338C211yesmaximal, characteristic, complemented
15C83×#1986C211yesmaximal, characteristic, complemented
16C4×#13050590C2211yescharacteristic
17#19128005C411yescharacteristic, complemented
18#19128005C411yescharacteristic, complemented
19#19127998C411yescharacteristic, complemented
20#19127998C411yescharacteristic, complemented
21#19127993C411yescharacteristic, complemented
22#19127988C411yescharacteristic, complemented
23#19127983C411yescharacteristic, complemented
24#19127978C411yescharacteristic, complemented
25#19127832—21no—
26#19127832—21no—
27#19127832—21no—
28#19127832—21no—
29#19127760—21no—
30#19127760—21no—
31#19127756—21no—
32#19127756—21no—
33C2×#14581727C2211yescharacteristic
34C2×#14581727C2211yescharacteristic
35#19127737C2211yescharacteristic
36#19127737C2211yescharacteristic
37#19127729C2211yescharacteristic
38#19127729C2211yescharacteristic
39#19127728C2211yescharacteristic
40#19127728C2211yescharacteristic
41#19127725C2211yescharacteristic
42C2×C4⋊(C83⋊C8)C2211yescharacteristic
43C2×#14581720C2211yescharacteristic
44C2×#14581720C2211yescharacteristic
45#19127695C2211yescharacteristic
46#19127695C2211yescharacteristic
47#19127669C2211yescharacteristic
48#19127669C2211yescharacteristic
49#19127657C2211yescharacteristic
50#19127657C2211yescharacteristic
51C2×#14581703C2211yescharacteristic
52C2×#14581703C2211yescharacteristic
53C2×C4×C83⋊C8C2211yescharacteristic
54#19127465C2211yescharacteristic
55#19127465C2211yescharacteristic
56#19127461C2211yescharacteristic
57#19127461C2211yescharacteristic
58#19127456C2211yescharacteristic
59#19127456C2211yescharacteristic
60#533×C83C2211yescharacteristic
61C4×M16×C83C2211yescharacteristic
62C4×C4⋊C4×C83C2211yescharacteristic
63#339×C83C2211yescharacteristic
64#339×C83C2211yescharacteristic
65#339×C83C2211yescharacteristic
66#339×C83C2211yescharacteristic
67C2×#13050590C2311yescharacteristic
68C2×#13050574C2311yescharacteristic
69C2×#13050574C2311yescharacteristic
70C22×C83⋊C8C2311yescharacteristic
71C22×C83⋊C8C2311yescharacteristic
72C22×C83⋊C8C2311yescharacteristic
73C22×C83⋊C8C2311yescharacteristic
74C4×Dic166C2×C411yescharacteristic
75C4×Dic166C2×C411yescharacteristic
76C4×D332C2×C411yescharacteristic
77C4×D332C2×C411yescharacteristic
78C4×C22⋊D83—21no—
79C4×C22⋊D83—21no—
80#14581751C2311yescharacteristic
81#14581749—21no—
82C42×D83—21no—
83#14581727—41no—
84#14581727—41no—
85#14581725C2×C411yescharacteristic
86#14581725C2×C411yescharacteristic
87#14581725C2×C411yescharacteristic
88#14581725C2×C411yescharacteristic
89#14581723C2×C411yescharacteristic
90#14581723C2×C411yescharacteristic
91#14581723C2×C411yescharacteristic
92#14581723C2×C411yescharacteristic
93C4⋊(C83⋊C8)—21no—
94C4⋊(C83⋊C8)—21no—
95C4⋊(C83⋊C8)—21no—
96C4⋊(C83⋊C8)—21no—
97C4⋊(C83⋊C8)—21no—
98C4⋊(C83⋊C8)—21no—
99C4⋊(C83⋊C8)C2×C411yescharacteristic
100C4⋊(C83⋊C8)C2×C411yescharacteristic
101C4⋊(C83⋊C8)C2×C411yescharacteristic
102C4⋊(C83⋊C8)C2×C411yescharacteristic
103Dic83⋊C8—21no—
104Dic83⋊C8—21no—
105Dic83⋊C8—21no—
106Dic83⋊C8—21no—
107#14581720—41no—
108#14581720—41no—
109#14581715C2×C411yescharacteristic
110#14581715C2×C411yescharacteristic
111#14581715C2×C411yescharacteristic
112#14581715C2×C411yescharacteristic
113#14581712C2×C411yescharacteristic
114#14581712C2×C411yescharacteristic
115#14581712C2×C411yescharacteristic
116#14581712C2×C411yescharacteristic
117(C2×D83)⋊C8—21no—
118(C2×D83)⋊C8—21no—
119(C2×D83)⋊C8—21no—
120(C2×D83)⋊C8—21no—
121#14581703—21no—
122#14581703—21no—
123#14581703—41no—
124#14581703D411yescharacteristic
125#14581703D411yescharacteristic
126#14581703D411yescharacteristic
127#14581703D411yescharacteristic
128C4×C83⋊C8—21no—
129C4×C83⋊C8—21no—
130C4×C83⋊C8—41no—
131C2×M16×C83C2311yescharacteristic
132C2×M16×C83C2311yescharacteristic
133C4⋊Q8×C83C2×C411yescharacteristic
134C4⋊Q8×C83C2×C411yescharacteristic
135#125×C83C2×C411yescharacteristic
136#125×C83C2×C411yescharacteristic
137C22⋊Q8×C83—21no—
138C22⋊Q8×C83—21no—
139C4×Q8×C83—21no—
140C4×Q8×C83—21no—
141#117×C83C2311yescharacteristic
142#117×C83C2311yescharacteristic
143C2×C4⋊C4×C83—21no—
144C2×C42×C83C2311yescharacteristic
145C2×C42×C83C2311yescharacteristic
146C2×C42×C83C2311yescharacteristic
147#97×C83—21no—
148C4×C8×C83—21no—
149#95×C83—21no—
150#13050590—21no—
151#13050590—21no—
152#13050590—21no—
153#13050590—21no—
154C2×Dic166C22×C411yescharacteristic
155C2×D332C22×C411yescharacteristic
156C2×C22⋊D83—21no—
157C2×C4×D83—21no—
158C2×C4×D83—21no—
159C2×C4×D83—21no—
160#13050574—21no—
161#13050574—21no—
162#13050574—21no—
163#13050574—21no—
164C2×C83⋊C8—21no—
165C2×C83⋊C8—21no—
166C2×C83⋊C8—21no—
167C2×C83⋊C8—21no—
168C2×C83⋊C8—21no—
169C2×C83⋊C8—21no—
170C2×C83⋊C8—21no—
171C2×C83⋊C8—21no—
172C2×C83⋊C8—21no—
173C2×C83⋊C8—21no—
174C2×C83⋊C8C22×C411yescharacteristic
175C2×C83⋊C8C22×C411yescharacteristic
176C2×C83⋊C8C22×C411yescharacteristic
177C2×C83⋊C8C22×C411yescharacteristic
178C2×C83⋊C8C2×D411yescharacteristic
179C2×C83⋊C8C2×D411yescharacteristic
180C2×C83⋊C8C2×D411yescharacteristic
181C2×C83⋊C8C2×D411yescharacteristic
182C4⋊Dic83C22×C411yescharacteristic
183C4⋊Dic83C22×C411yescharacteristic
184Dic83⋊C4—21no—
185Dic83⋊C4—21no—
186C22⋊Dic83—21no—
187(C2×D83)⋊C4—21no—
188(C2×D83)⋊C4—21no—
189C4×Dic83—21no—
190C4×Dic83—21no—
191C4×Dic83—21no—
192C2×Q8×C83—21no—
193C2×Q8×C83—21no—
194C22×C4×C83—21no—
195C22×C4×C83—21no—
196C22×C4×C83#4111yescharacteristic
197C22×C4×C83#4111yescharacteristic
198C22×C4×C83C2411yescharacteristic
199M16×C83—21no—
200M16×C83—21no—
201M16×C83—21no—
202M16×C83—21no—
203C2×C8×C83—21no—
204C2×C8×C83—21no—
205C4⋊C4×C83—21no—
206C4⋊C4×C83—21no—
207C4⋊C4×C83—21no—
208C4⋊C4×C83—21no—
209C4⋊C4×C83—21no—
210C4⋊C4×C83—21no—
211C4⋊C4×C83—42no—
212C4⋊C4×C83C22×C411yescharacteristic
213C4⋊C4×C83C22×C411yescharacteristic
214C4⋊C4×C83C22×C411yescharacteristic
215C4⋊C4×C83C22×C411yescharacteristic
216C22⋊C4×C83—21no—
217C22⋊C4×C83—21no—
218C42×C83—21no—
219C42×C83—21no—
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—
230Q8×C83—81no—
231Q8×C83—81no—
232C2×C4×C83—22no—
233C2×C4×C83—21no—
234C2×C4×C83—21no—
235C2×C4×C83—21no—
236C2×C4×C83—21no—
237C2×C4×C83—41no—
238C2×C4×C83—41no—
239C2×C4×C83—41no—
240C2×C4×C83—41no—
241C2×C4×C83—41no—
242C2×C4×C83—41no—
243C2×C4×C83—41no—
244C2×C4×C83C4×D411yescharacteristic
245C2×C4×C83C4×D411yescharacteristic
246C2×C4×C83C4×D411yescharacteristic
247C2×C4×C83C4×D411yescharacteristic
248C2×C4×C83C23×C411yescharacteristic
249C2×C4×C83C22×D411yescharacteristic
250C2×C4×C83H(5,𝔽2)11yescharacteristic
251C2×C4×C832−1+411yescharacteristic
252C2×C4×C832−1+411yescharacteristic
253C2×C4×C832−1+411yescharacteristic
254C22⋊D83—41no—
255C22⋊D83—41no—
256C2×Dic83—21no—
257C2×Dic83—21no—
258C2×Dic83—21no—
259D332—21no—
260D332—21no—
261C4×D83—41no—
262C4×D83—41no—
263C4×D83—81no—
264C4×D83—81no—
265Dic166—21no—
266Dic166—21no—
267C8×C83—41no—
268C8×C83—41no—
269C83⋊C8—21no—
270C83⋊C8—21no—
271C83⋊C8—21no—
272C83⋊C8—21no—
273C83⋊C8—21no—
274C83⋊C8—21no—
275C83⋊C8—21no—
276C83⋊C8—21no—
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—41no—
293C4×C83—41no—
294C4×C83—41no—
295C4×C83—41no—
296C4×C83—81no—
297C4×C83#51911yescharacteristic
298C4×C83#52011yescharacteristic
299C4×C83#53611yescharacteristic
300C4×C83#53711yescharacteristic
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#1986D8311yescharacteristic, complemented
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#1771—831no—
326C83#2213211yescharacteristic, complemented, Sylow
327#533C2×D8311yescharacteristic
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⋊C8—831no—
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×M16C2×D8311yescharacteristic
364C2×#97—831no—
365C2×#97—831no—
366C2×C4×C8—831no—
367C4×C4⋊C4C2×D8311yescharacteristic
368#341—831no—
369#341—831no—
370#339—831no—
371#339—831no—
372#339C2×D8311yescharacteristic
373#339C2×D8311yescharacteristic
374#339C2×D8311yescharacteristic
375#339C2×D8311yescharacteristic
376#336—831no—
377#336—831no—
378C2×#41—831no—
379C2×M16—831no—
380C2×M16—831no—
381C2×M16C22×D8311yescharacteristic
382C2×M16C22×D8311yescharacteristic
383C22×C8—831no—
384C22×C8—831no—
385C22×C8—831no—
386C22×C8—831no—
387C4⋊Q8C4×D8311yescharacteristic
388C4⋊Q8C4×D8311yescharacteristic
389#125C4×D8311yescharacteristic
390#125C4×D8311yescharacteristic
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—831no—
396C4×Q8—831no—
397C4×D4—831no—
398C4×D4—831no—
399C4×D4—1661no—
400C4×D4—1661no—
401#117—831no—
402#117—1661no—
403#117C22×D8311yescharacteristic
404#117C22×D8311yescharacteristic
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—831no—
421C4⋊C8—831no—
422C4⋊C8—831no—
423C4⋊C8—831no—
424C4⋊C8—1661no—
425C4⋊C8—1661no—
426C4⋊C8—1661no—
427C4⋊C8—1661no—
428C4⋊C8—1661no—
429C4⋊C8—1661no—
430C4⋊C8—1661no—
431C4⋊C8—1661no—
432C4⋊C8—1661no—
433C4⋊C8—1661no—
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—21no—
449#97—3321no—
450#97—831no—
451#97—831no—
452#97—831no—
453#97—831no—
454#97—1661no—
455#97—1661no—
456C4×C8—21no—
457C4×C8—3321no—
458C4×C8—1661no—
459C4×C8—1661no—
460#95—21no—
461#41—1661no—
462#41—1661no—
463#41—1661no—
464#41—1661no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—831no—
468C2×D4—831no—
469C2×D4—1661no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—1661no—
473C22×C4—1661no—
474C22×C4—1661no—
475C22×C4#1305058911yescharacteristic
476C22×C4#1305058911yescharacteristic
477C22×C4C23×D8311yescharacteristic
478M16—21no—
479M16—21no—
480M16—21no—
481M16—21no—
482M16—1661no—
483M16—1661no—
484M16—1661no—
485M16—1661no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—831no—
489C2×C8—831no—
490C2×C8—831no—
491C2×C8—831no—
492C2×C8—831no—
493C2×C8—831no—
494C2×C8—831no—
495C2×C8—831no—
496C2×C8—1661no—
497C2×C8—1661no—
498C2×C8—1661no—
499C2×C8—1661no—
500C2×C8—1661no—
501C2×C8—1661no—
502C2×C8—1661no—
503C2×C8—1661no—
504C2×C8—1661no—
505C2×C8—1661no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—42no—
513C4⋊C4—831no—
514C4⋊C4—831no—
515C4⋊C4—1661no—
516C4⋊C4—1661no—
517C4⋊C4C2×C4×D8311yescharacteristic
518C4⋊C4C2×C4×D8311yescharacteristic
519C4⋊C4C2×C4×D8311yescharacteristic
520C4⋊C4C2×C4×D8311yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—1661no—
524C22⋊C4—1661no—
525C22⋊C4—1661no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—1661no—
533C42—1661no—
534C42—1661no—
535C42C2×C4×D8311yescharacteristic
536C42C2×C4×D8311yescharacteristic
537C42D4×D8311yescharacteristic
538C42D4×D8311yescharacteristic
539C23—1661no—
540C23C2×#1305058911yescharacteristic
541Q8—81no—
542Q8—81no—
543Q8—1661no—
544Q8—1661no—
545D4—3321no—
546D4—3321no—
547D4—1661no—
548D4—1661no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—3321no—
562C2×C4—3321no—
563C2×C4—6641no—
564C2×C4—6641no—
565C2×C4—1661no—
566C2×C4—1661no—
567C2×C4—1661no—
568C2×C4(C22⋊D83)⋊C411yescharacteristic
569C2×C4(C22⋊D83)⋊C411yescharacteristic
570C2×C4(C22⋊D83)⋊C411yescharacteristic
571C2×C4(C22⋊D83)⋊C411yescharacteristic
572C2×C4C22×C4×D8311yescharacteristic
573C2×C4C2×D4×D8311yescharacteristic
574C2×C4#1458183811yescharacteristic
575C2×C4#1458183911yescharacteristic
576C2×C4#1458184011yescharacteristic
577C2×C4#1458184011yescharacteristic
578C8—41no—
579C8—41no—
580C8—3321no—
581C8—3321no—
582C8—1661no—
583C8—1661no—
584C8—1661no—
585C8—1661no—
586C8—1661no—
587C8—1661no—
588C8—1661no—
589C8—1661no—
590C22—21no—
591C22—21no—
592C22—3321no—
593C22—3321no—
594C22—3321no—
595C22C2×(C22⋊D83)⋊C411yescharacteristic
596C22#1912831211yescharacteristic
597C22#1912832011yescharacteristic
598C4—21no—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—42no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—81no—
608C4—3321no—
609C4—3321no—
610C4—3321no—
611C4#1912817711yescharacteristic
612C4#1912818311yescharacteristic
613C4#1912827411yescharacteristic
614C4#1912828111yescharacteristic
615C2—21no—
616C2—21no—
617C2—6641no—
618C2#2491014811yescharacteristic
619C2#2491636911yescharacteristic
620C2#2491637611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#1986C2
socleC22×C83C2×C4×D4
prime radicalC2×#13050590C23
cosocleC22×C4×C83C24
hypercenter#1986D83
hypocenterC83#22132
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
2. #24916404C2semidirect
4. #24908238C2semidirect
5. #24908215C2semidirect
6. #24908210C2semidirect
11. #24908060C2semidirect
12. #24908060C2semidirect
14. #24907338C2semidirect
15. C83×#1986C2semidirect
17. #19128005C4semidirect
18. #19128005C4semidirect
19. #19127998C4semidirect
20. #19127998C4semidirect
21. #19127993C4semidirect
22. #19127988C4semidirect
23. #19127983C4semidirect
24. #19127978C4semidirect
314. #1986D83semidirect
326. C83#22132semidirect

Maximal subgroups

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

subgroupindex
#249172452
#249164042
#249161152
#249082382
#249082152
#249082102
#249081752
#249081682
#249081092
#249080602
#249074842
#249073382
C83×#19862
#2213283