Finite Group Databasebeta

← #35416733

Subgroups — #35416733

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#24917251C211yesmaximal, characteristic
2#24916403C211yesmaximal, characteristic, complemented
3#24908407C211yesmaximal, characteristic, complemented
4#24908238C211yesmaximal, characteristic, complemented
5#24908213C211yesmaximal, characteristic, complemented
6#24908208C211yesmaximal, characteristic, complemented
7#24908177C211yesmaximal, characteristic
8#24908170C211yesmaximal, characteristic
9#24908108C211yesmaximal, characteristic
10#24908108C211yesmaximal, characteristic
11#24908059C211yesmaximal, characteristic, complemented
12#24908059C211yesmaximal, characteristic, complemented
13#24907483C211yesmaximal, characteristic
14#24907335C211yesmaximal, characteristic, complemented
15C83×#2923C211yesmaximal, characteristic
16#19128258C2211yescharacteristic
17#19128008C411yescharacteristic, complemented
18#19128008C411yescharacteristic, complemented
19#19128001C411yescharacteristic, complemented
20#19128001C411yescharacteristic, complemented
21#19127996C411yescharacteristic, complemented
22#19127991C411yescharacteristic, complemented
23#19127986C411yescharacteristic, complemented
24#19127981C411yescharacteristic, complemented
25#19127829—21no—
26#19127829—21no—
27#19127829—21no—
28#19127829—21no—
29C2×#14581727C2211yescharacteristic
30C2×#14581727C2211yescharacteristic
31#19127737C2211yescharacteristic
32#19127737C2211yescharacteristic
33#19127727C2211yescharacteristic
34#19127727C2211yescharacteristic
35#19127725C2211yescharacteristic
36C2×C4⋊(C83⋊C8)C2211yescharacteristic
37C2×#14581719C2211yescharacteristic
38C2×#14581719C2211yescharacteristic
39#19127697C2211yescharacteristic
40#19127697C2211yescharacteristic
41#19127656C2211yescharacteristic
42#19127656C2211yescharacteristic
43C2×#14581702C2211yescharacteristic
44C2×C8×Dic83C2211yescharacteristic
45C4×C4⋊Dic83C2211yescharacteristic
46#19127465C2211yescharacteristic
47#19127465C2211yescharacteristic
48#19127462C2211yescharacteristic
49#19127462C2211yescharacteristic
50#19127462C2211yescharacteristic
51#19127462C2211yescharacteristic
52#19127460C2211yescharacteristic
53#19127460C2211yescharacteristic
54#19127455C2211yescharacteristic
55#19127455C2211yescharacteristic
56C4×#41×C83C2211yescharacteristic
57#433×C83—21no—
58#433×C83—21no—
59#432×C83—21no—
60#432×C83—21no—
61#424×C83C2211yescharacteristic
62#424×C83C2211yescharacteristic
63#408×C83C2211yescharacteristic
64#408×C83C2211yescharacteristic
65C4×M16×C83C2211yescharacteristic
66C2×#97×C83C2211yescharacteristic
67C2×#13050574C2311yescharacteristic
68C2×#13050574C2311yescharacteristic
69C22×C83⋊C8C2311yescharacteristic
70C22×C83⋊C8C2311yescharacteristic
71#14581792C2×C411yescharacteristic
72#14581792C2×C411yescharacteristic
73#14581784C2×C411yescharacteristic
74#14581784C2×C411yescharacteristic
75#14581771—21no—
76#14581771—21no—
77C4×Dic166—21no—
78C4×Dic166—21no—
79#14581751C2311yescharacteristic
80#14581751C2311yescharacteristic
81C2×C4⋊Dic83—21no—
82C2×C4×Dic83C2311yescharacteristic
83C2×C4×Dic83C2311yescharacteristic
84#14581727—41no—
85#14581727—41no—
86#14581725C2×C411yescharacteristic
87#14581725C2×C411yescharacteristic
88#14581725C2×C411yescharacteristic
89#14581725C2×C411yescharacteristic
90#14581723C2×C411yescharacteristic
91#14581723C2×C411yescharacteristic
92#14581723C2×C411yescharacteristic
93#14581723C2×C411yescharacteristic
94C4⋊(C83⋊C8)—21no—
95C4⋊(C83⋊C8)—21no—
96C4⋊(C83⋊C8)C2×C411yescharacteristic
97C4⋊(C83⋊C8)C2×C411yescharacteristic
98C4⋊(C83⋊C8)C2×C411yescharacteristic
99C4⋊(C83⋊C8)C2×C411yescharacteristic
100Dic83⋊C8—21no—
101Dic83⋊C8—21no—
102Dic83⋊C8—21no—
103Dic83⋊C8—21no—
104#14581719—41no—
105#14581719—41no—
106#14581716C2×C411yescharacteristic
107#14581716C2×C411yescharacteristic
108#14581716C2×C411yescharacteristic
109#14581716C2×C411yescharacteristic
110#14581713C2×C411yescharacteristic
111#14581713C2×C411yescharacteristic
112#14581713C2×C411yescharacteristic
113#14581713C2×C411yescharacteristic
114#14581702—21no—
115#14581702—21no—
116#14581702—41no—
117C8×Dic83—21no—
118C8×Dic83—21no—
119C8×Dic83—41no—
120C83⋊#95—21no—
121C2×#41×C83C2311yescharacteristic
122C2×M16×C83C2311yescharacteristic
123C2×M16×C83C2311yescharacteristic
124C22×C8×C83C2311yescharacteristic
125C22×C8×C83C2311yescharacteristic
126C4×Q8×C83C2×C411yescharacteristic
127C4×Q8×C83C2×C411yescharacteristic
128C4×D4×C83—21no—
129C4×D4×C83—21no—
130C4×D4×C83C2×C411yescharacteristic
131C4×D4×C83C2×C411yescharacteristic
132#117×C83—21no—
133#117×C83C2311yescharacteristic
134C2×C42×C83—21no—
135C2×C42×C83C2311yescharacteristic
136C4⋊C8×C83—21no—
137C4⋊C8×C83—21no—
138C4⋊C8×C83—21no—
139C4⋊C8×C83—21no—
140C22⋊C8×C83—21no—
141C22⋊C8×C83—21no—
142C22⋊C8×C83—21no—
143C22⋊C8×C83—21no—
144#97×C83—21no—
145#97×C83D411yescharacteristic
146#97×C83D411yescharacteristic
147#97×C83D411yescharacteristic
148#97×C83D411yescharacteristic
149C4×C8×C83—21no—
150C2×Dic166—21no—
151C2×Dic166—21no—
152C22×Dic83—21no—
153C22×Dic83—21no—
154#13050574—21no—
155#13050574—21no—
156#13050574—21no—
157#13050574—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8—21no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8—21no—
163C2×C83⋊C8—21no—
164C2×C83⋊C8C22×C411yescharacteristic
165C2×C83⋊C8C22×C411yescharacteristic
166C2×C83⋊C8C22×C411yescharacteristic
167C2×C83⋊C8C22×C411yescharacteristic
168C4⋊Dic83—21no—
169C4⋊Dic83—21no—
170C4⋊Dic83—42no—
171C4⋊Dic83C22×C411yescharacteristic
172C4⋊Dic83C22×C411yescharacteristic
173C4⋊Dic83C22×C411yescharacteristic
174C4⋊Dic83C22×C411yescharacteristic
175Dic83⋊C4—21no—
176Dic83⋊C4—21no—
177Dic83⋊C4—21no—
178Dic83⋊C4—21no—
179C22⋊Dic83—21no—
180C22⋊Dic83—21no—
181C4×Dic83—21no—
182C4×Dic83—21no—
183C4×Dic83—21no—
184C4×Dic83—21no—
185C4×Dic83—21no—
186C4×Dic83—21no—
187#41×C83—21no—
188#41×C83—21no—
189#41×C83—21no—
190#41×C83—21no—
191C2×Q8×C83C22×C411yescharacteristic
192C2×D4×C83—21no—
193C2×D4×C83C22×C411yescharacteristic
194C22×C4×C83—21no—
195C22×C4×C83—21no—
196C22×C4×C83—21no—
197C22×C4×C83#4111yescharacteristic
198C22×C4×C83#4111yescharacteristic
199C22×C4×C83C2411yescharacteristic
200M16×C83—21no—
201M16×C83—21no—
202M16×C83—21no—
203M16×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×C83C2×D411yescharacteristic
211C2×C8×C83C2×D411yescharacteristic
212C2×C8×C83C2×D411yescharacteristic
213C2×C8×C83C2×D411yescharacteristic
214C4⋊C4×C83—21no—
215C4⋊C4×C83—21no—
216C4⋊C4×C83C22×C411yescharacteristic
217C4⋊C4×C83C22×C411yescharacteristic
218C22⋊C4×C83—21no—
219C22⋊C4×C83—21no—
220C22⋊C4×C83—21no—
221C42×C83—21no—
222C42×C83—21no—
223C42×C83—21no—
224C42×C83C22×C411yescharacteristic
225C42×C83C22×C411yescharacteristic
226C42×C83C2×D411yescharacteristic
227C42×C83C2×D411yescharacteristic
228C23×C83—21no—
229C23×C83C2×#4111yescharacteristic
230Q8×C83—21no—
231Q8×C83—21no—
232D4×C83—21no—
233D4×C83—21no—
234D4×C83—41no—
235D4×C83—41no—
236C2×C4×C83—21no—
237C2×C4×C83—21no—
238C2×C4×C83—21no—
239C2×C4×C83—41no—
240C2×C4×C83—41no—
241C2×C4×C83—41no—
242C2×C4×C83—41no—
243C2×C4×C83—81no—
244C2×C4×C83—81no—
245C2×C4×C83C4×D411yescharacteristic
246C2×C4×C83C4×D411yescharacteristic
247C2×C4×C83C4×D411yescharacteristic
248C2×C4×C83C4×D411yescharacteristic
249C2×C4×C83C23×C411yescharacteristic
250C2×C4×C83C22×D411yescharacteristic
251C2×C4×C83H(5,𝔽2)11yescharacteristic
252C2×C4×C832−1+411yescharacteristic
253C2×C4×C832−1+411yescharacteristic
254C2×C4×C832−1+411yescharacteristic
255C2×Dic83—22no—
256C2×Dic83—21no—
257C2×Dic83—21no—
258C2×Dic83—21no—
259C2×Dic83—21no—
260C2×Dic83—41no—
261C2×Dic83—41no—
262C2×Dic83—41no—
263C2×Dic83—41no—
264C2×Dic83—41no—
265Dic166—81no—
266Dic166—81no—
267C8×C83—21no—
268C8×C83—21no—
269C8×C83—21no—
270C8×C83—21no—
271C8×C83—41no—
272C8×C83—41no—
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×C83—41no—
282C22×C83—41no—
283C22×C83—41no—
284C22×C83C2×C4×D411yescharacteristic
285C22×C83#54111yescharacteristic
286C22×C83#54211yescharacteristic
287C4×C83—21no—
288C4×C83—21no—
289C4×C83—21no—
290C4×C83—21no—
291C4×C83—41no—
292C4×C83—41no—
293C4×C83—41no—
294C4×C83#51911yescharacteristic
295C4×C83#52011yescharacteristic
296C4×C83#53611yescharacteristic
297C4×C83#53711yescharacteristic
298Dic83—42no—
299Dic83—41no—
300Dic83—41no—
301Dic83—41no—
302Dic83—41no—
303Dic83—81no—
304#22132—831nomaximal, Sylow
305C2×C83—21no—
306C2×C83—21no—
307C2×C83—81no—
308C2×C83#232311yescharacteristic
309C2×C83#295611yescharacteristic
310C2×C83#295711yescharacteristic
311#3076—831no—
312#2961—831no—
313#2923D8311yescharacteristic
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#1771—831no—
326C83#2213211yescharacteristic, complemented, Sylow
327#533—831no—
328C4×#41C2×D8311yescharacteristic
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—21no—
342#433—21no—
343#432—21no—
344#432—21no—
345C2×#108—831no—
346C2×#108—831no—
347#427—831no—
348#427—831no—
349#424—831no—
350#424—831no—
351#424C2×D8311yescharacteristic
352#424C2×D8311yescharacteristic
353#423—831no—
354C2×C4⋊C8—831no—
355C2×#104—831no—
356C2×#104—831no—
357#416—831no—
358#416—831no—
359#408C2×D8311yescharacteristic
360#408C2×D8311yescharacteristic
361#405—831no—
362#405—831no—
363C4×M16C2×D8311yescharacteristic
364C2×#97—831no—
365C2×#97C2×D8311yescharacteristic
366C2×C4×C8—831no—
367C4×C4⋊C4—831no—
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#336—831no—
377#336—831no—
378C2×#41C22×D8311yescharacteristic
379C2×M16—831no—
380C2×M16—831no—
381C2×M16C22×D8311yescharacteristic
382C2×M16C22×D8311yescharacteristic
383C22×C8—831no—
384C22×C8—831no—
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—1661no—
394C4×Q8—1661no—
395C4×Q8C4×D8311yescharacteristic
396C4×Q8C4×D8311yescharacteristic
397C4×D4—21no—
398C4×D4—21no—
399C4×D4C4×D8311yescharacteristic
400C4×D4C4×D8311yescharacteristic
401#117—21no—
402#117—831no—
403#117—831no—
404#117C22×D8311yescharacteristic
405C2×C4⋊C4—1661no—
406C2×C42—21no—
407C2×C42—831no—
408C2×C42—831no—
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—21no—
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8—831no—
425C4⋊C8—831no—
426C4⋊C8—831no—
427C4⋊C8—831no—
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—21no—
445C22⋊C8—21no—
446C22⋊C8—21no—
447C22⋊C8—21no—
448#97—21no—
449#97—3321no—
450#97—1661no—
451#97—1661no—
452#97C22⋊D8311yescharacteristic
453#97C22⋊D8311yescharacteristic
454#97C22⋊D8311yescharacteristic
455#97C22⋊D8311yescharacteristic
456C4×C8—21no—
457C4×C8—3321no—
458C4×C8—1661no—
459C4×C8—1661no—
460#95—1661no—
461#41—21no—
462#41—21no—
463#41—21no—
464#41—21no—
465C2×Q8—1661no—
466C2×Q8—1661no—
467C2×Q8C2×C4×D8311yescharacteristic
468C2×D4—21no—
469C2×D4C2×C4×D8311yescharacteristic
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—1661no—
474C22×C4—1661no—
475C22×C4#1305059011yescharacteristic
476C22×C4#1305059011yescharacteristic
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—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
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×C8C2×C22⋊D8311yescharacteristic
503C2×C8C2×C22⋊D8311yescharacteristic
504C2×C8C2×C22⋊D8311yescharacteristic
505C2×C8C2×C22⋊D8311yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—3322no—
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⋊C4C2×C4×D8311yescharacteristic
520C4⋊C4C2×C4×D8311yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—1661no—
525C22⋊C4—1661no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—1661no—
530C42—1661no—
531C42—1661no—
532C42—1661no—
533C42—1661no—
534C42—1661no—
535C42C2×C4×D8311yescharacteristic
536C42C2×C4×D8311yescharacteristic
537C42C2×C22⋊D8311yescharacteristic
538C42C2×C22⋊D8311yescharacteristic
539C23—21no—
540C23C2×#1305059011yescharacteristic
541Q8—21no—
542Q8—21no—
543Q8—6641no—
544Q8—6641no—
545D4—21no—
546D4—21no—
547D4—41no—
548D4—41no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4—3321no—
559C2×C4—3321no—
560C2×C4—3321no—
561C2×C4—3321no—
562C2×C4—3321no—
563C2×C4—1662no—
564C2×C4—1661no—
565C2×C4—1661no—
566C2×C4—1661no—
567C2×C4—1661no—
568C2×C4C4×C22⋊D8311yescharacteristic
569C2×C4C4×C22⋊D8311yescharacteristic
570C2×C4C4×C22⋊D8311yescharacteristic
571C2×C4C4×C22⋊D8311yescharacteristic
572C2×C4C22×C4×D8311yescharacteristic
573C2×C4C22×C22⋊D8311yescharacteristic
574C2×C4#1458183811yescharacteristic
575C2×C4#1458183911yescharacteristic
576C2×C4#1458183911yescharacteristic
577C2×C4#1458183911yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—3321no—
585C8—3321no—
586C8—1661no—
587C8—1661no—
588C8—1661no—
589C8—1661no—
590C22—21no—
591C22—21no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22C2×C4×C22⋊D8311yescharacteristic
596C22#1912831311yescharacteristic
597C22#1912832211yescharacteristic
598C4—21no—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—3322no—
606C4—3321no—
607C4—3321no—
608C4—3321no—
609C4—3321no—
610C4—6641no—
611C4#1912817811yescharacteristic
612C4#1912818111yescharacteristic
613C4#1912827211yescharacteristic
614C4#1912827911yescharacteristic
615C2—21no—
616C2—21no—
617C2—81no—
618C2#2491014511yescharacteristic
619C2#2491637011yescharacteristic
620C2#2491637811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#2923C2
socleC22×C83C2×C4×D4
prime radicalC2×#41×C83C23
cosocleC22×C4×C83C24
hypercenter#2923D83
hypocenterC83#22132
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2923

Complements

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

NH ≅ G/Ntype
2. #24916403C2semidirect
3. #24908407C2semidirect
4. #24908238C2semidirect
5. #24908213C2semidirect
6. #24908208C2semidirect
11. #24908059C2semidirect
12. #24908059C2semidirect
14. #24907335C2semidirect
17. #19128008C4semidirect
18. #19128008C4semidirect
19. #19128001C4semidirect
20. #19128001C4semidirect
21. #19127996C4semidirect
22. #19127991C4semidirect
23. #19127986C4semidirect
24. #19127981C4semidirect
326. C83#22132semidirect

Maximal subgroups

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

subgroupindex
#249172512
#249164032
#249084072
#249082382
#249082132
#249082082
#249081772
#249081702
#249081082
#249080592
#249074832
#249073352
C83×#29232
#2213283