Finite Group Databasebeta

← #35416729

Subgroups — #35416729

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#24916400C211yesmaximal, characteristic, complemented
3#24916114C211yesmaximal, characteristic
4#24908406C211yesmaximal, characteristic, complemented
5#24908236C211yesmaximal, characteristic, complemented
6#24908215C211yesmaximal, characteristic, complemented
7#24908210C211yesmaximal, characteristic, complemented
8#24908171C211yesmaximal, characteristic
9#24908164C211yesmaximal, characteristic
10#24908114C211yesmaximal, characteristic
11#24908114C211yesmaximal, characteristic
12#24908065C211yesmaximal, characteristic, complemented
13#24908065C211yesmaximal, characteristic, complemented
14#24907338C211yesmaximal, characteristic, complemented
15C83×#1806C211yesmaximal, 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#19127830—21no—
26#19127830—21no—
27#19127830—21no—
28#19127830—21no—
29#19127762—21no—
30#19127762—21no—
31#19127758—21no—
32#19127758—21no—
33C2×#14581727C2211yescharacteristic
34C2×#14581727C2211yescharacteristic
35#19127737C2211yescharacteristic
36#19127737C2211yescharacteristic
37#19127729C2211yescharacteristic
38#19127729C2211yescharacteristic
39#19127728C2211yescharacteristic
40#19127728C2211yescharacteristic
41C2×C4⋊(C83⋊C8)C2211yescharacteristic
42#19127697C2211yescharacteristic
43#19127697C2211yescharacteristic
44#19127668C2211yescharacteristic
45#19127668C2211yescharacteristic
46#19127659C2211yescharacteristic
47#19127659C2211yescharacteristic
48C4×#13050574C2211yescharacteristic
49C2×#14581703C2211yescharacteristic
50C2×#14581703C2211yescharacteristic
51C2×C4×C83⋊C8C2211yescharacteristic
52#19127465C2211yescharacteristic
53#19127465C2211yescharacteristic
54#19127461C2211yescharacteristic
55#19127461C2211yescharacteristic
56#19127461C2211yescharacteristic
57#19127461C2211yescharacteristic
58#19127456C2211yescharacteristic
59#19127456C2211yescharacteristic
60C4×#41×C83C2211yescharacteristic
61#423×C83C2211yescharacteristic
62C2×#104×C83C2211yescharacteristic
63C2×#104×C83C2211yescharacteristic
64C4×C4⋊C4×C83C2211yescharacteristic
65#339×C83C2211yescharacteristic
66#339×C83C2211yescharacteristic
67C2×#13050574C2311yescharacteristic
68C2×#13050574C2311yescharacteristic
69C22×C83⋊C8C2311yescharacteristic
70C22×C83⋊C8C2311yescharacteristic
71C22×C83⋊C8C2311yescharacteristic
72C22×C83⋊C8C2311yescharacteristic
73#14581792C2×C411yescharacteristic
74#14581792C2×C411yescharacteristic
75#14581784C2×C411yescharacteristic
76#14581784C2×C411yescharacteristic
77#14581771—21no—
78#14581771—21no—
79C4×Dic166—21no—
80C4×Dic166—21no—
81#14581751C2311yescharacteristic
82#14581751C2311yescharacteristic
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)C2×C411yescharacteristic
98C4⋊(C83⋊C8)C2×C411yescharacteristic
99C4⋊(C83⋊C8)C2×C411yescharacteristic
100C4⋊(C83⋊C8)C2×C411yescharacteristic
101Dic83⋊C8—21no—
102Dic83⋊C8—21no—
103Dic83⋊C8—21no—
104Dic83⋊C8—21no—
105#14581716C2×C411yescharacteristic
106#14581716C2×C411yescharacteristic
107#14581716C2×C411yescharacteristic
108#14581716C2×C411yescharacteristic
109#14581713C2×C411yescharacteristic
110#14581713C2×C411yescharacteristic
111#14581713C2×C411yescharacteristic
112#14581713C2×C411yescharacteristic
113C22⋊(C83⋊C8)—21no—
114C22⋊(C83⋊C8)—21no—
115C22⋊(C83⋊C8)—21no—
116C22⋊(C83⋊C8)—21no—
117#14581703—21no—
118#14581703—41no—
119#14581703D411yescharacteristic
120#14581703D411yescharacteristic
121#14581703D411yescharacteristic
122#14581703D411yescharacteristic
123#14581702—21no—
124#14581702—21no—
125C4×C83⋊C8—21no—
126C4×C83⋊C8—41no—
127C8×Dic83—21no—
128C8×Dic83—21no—
129C2×#41×C83C2311yescharacteristic
130C2×M16×C83C2311yescharacteristic
131C2×M16×C83C2311yescharacteristic
132C4×Q8×C83C2×C411yescharacteristic
133C4×Q8×C83C2×C411yescharacteristic
134C4×D4×C83—21no—
135C4×D4×C83—21no—
136C4×D4×C83C2×C411yescharacteristic
137C4×D4×C83C2×C411yescharacteristic
138#117×C83—21no—
139#117×C83C2311yescharacteristic
140C2×C4⋊C4×C83—21no—
141C2×C42×C83—21no—
142C2×C42×C83C2311yescharacteristic
143C2×C42×C83C2311yescharacteristic
144C2×C42×C83C2311yescharacteristic
145C4⋊C8×C83—21no—
146C4⋊C8×C83—21no—
147#104×C83—41no—
148#104×C83—41no—
149#95×C83—21no—
150C2×Dic166—21no—
151C2×Dic166—21no—
152#13050574—21no—
153#13050574—21no—
154#13050574—21no—
155#13050574—21no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—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⋊C8—21no—
165C2×C83⋊C8—21no—
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
174C4⋊Dic83—21no—
175C4⋊Dic83—21no—
176C4⋊Dic83C22×C411yescharacteristic
177C4⋊Dic83C22×C411yescharacteristic
178C4⋊Dic83C22×C411yescharacteristic
179C4⋊Dic83C22×C411yescharacteristic
180Dic83⋊C4—21no—
181Dic83⋊C4—21no—
182Dic83⋊C4—21no—
183Dic83⋊C4—21no—
184C22⋊Dic83—21no—
185C22⋊Dic83—21no—
186C4×Dic83—21no—
187C4×Dic83—21no—
188#41×C83—21no—
189#41×C83—21no—
190#41×C83—21no—
191#41×C83—21no—
192C2×Q8×C83C22×C411yescharacteristic
193C2×D4×C83—21no—
194C2×D4×C83C22×C411yescharacteristic
195C22×C4×C83—21no—
196C22×C4×C83—21no—
197C22×C4×C83—21no—
198C22×C4×C83—21no—
199C22×C4×C83—21no—
200C22×C4×C83#4111yescharacteristic
201C22×C4×C83#4111yescharacteristic
202C22×C4×C83C2411yescharacteristic
203M16×C83—21no—
204M16×C83—21no—
205M16×C83—21no—
206M16×C83—21no—
207C2×C8×C83—21no—
208C2×C8×C83—21no—
209C4⋊C4×C83—21no—
210C4⋊C4×C83—21no—
211C4⋊C4×C83—42no—
212C4⋊C4×C83C22×C411yescharacteristic
213C4⋊C4×C83C22×C411yescharacteristic
214C22⋊C4×C83—21no—
215C22⋊C4×C83—21no—
216C22⋊C4×C83—21no—
217C42×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×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—22no—
237C2×C4×C83—21no—
238C2×C4×C83—21no—
239C2×C4×C83—21no—
240C2×C4×C83—41no—
241C2×C4×C83—41no—
242C2×C4×C83—41no—
243C2×C4×C83—41no—
244C2×C4×C83—41no—
245C2×C4×C83—41no—
246C2×C4×C83—41no—
247C2×C4×C83—41no—
248C2×C4×C83—41no—
249C2×C4×C83—81no—
250C2×C4×C83—81no—
251C2×C4×C83C4×D411yescharacteristic
252C2×C4×C83C4×D411yescharacteristic
253C2×C4×C83C4×D411yescharacteristic
254C2×C4×C83C4×D411yescharacteristic
255C2×C4×C83C23×C411yescharacteristic
256C2×C4×C83C22×D411yescharacteristic
257C2×C4×C83H(5,𝔽2)11yescharacteristic
258C2×C4×C832−1+411yescharacteristic
259C2×C4×C832−1+411yescharacteristic
260C2×C4×C832−1+411yescharacteristic
261C2×Dic83—21no—
262C2×Dic83—21no—
263C2×Dic83—21no—
264C2×Dic83—21no—
265Dic166—81no—
266Dic166—81no—
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×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—42no—
292C4×C83—41no—
293C4×C83—41no—
294C4×C83—41no—
295C4×C83—81no—
296C4×C83#51911yescharacteristic
297C4×C83#52011yescharacteristic
298C4×C83#53611yescharacteristic
299C4×C83#53711yescharacteristic
300Dic83—41no—
301Dic83—41no—
302Dic83—41no—
303Dic83—41no—
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#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#1806D8311yescharacteristic
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—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#423C2×D8311yescharacteristic
354C2×C4⋊C8—831no—
355C2×#104C2×D8311yescharacteristic
356C2×#104C2×D8311yescharacteristic
357#416—831no—
358#416—831no—
359#408—831no—
360#408—831no—
361#405—831no—
362#405—831no—
363C4×M16—831no—
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#339—831no—
373#339—831no—
374#339C2×D8311yescharacteristic
375#339C2×D8311yescharacteristic
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×C8—831no—
386C22×C8—831no—
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—21no—
406C2×C42—21no—
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—21no—
421C4⋊C8—21no—
422C4⋊C8—831no—
423C4⋊C8—831no—
424C4⋊C8—831no—
425C4⋊C8—831no—
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—41no—
435#104—41no—
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—3321no—
449#97—831no—
450#97—831no—
451#97—831no—
452#97—831no—
453#97—1661no—
454#97—1661no—
455#97—1661no—
456C4×C8—3321no—
457C4×C8—1661no—
458C4×C8—1661no—
459C4×C8—1661no—
460#95—21no—
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—21no—
474C22×C4—21no—
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—42no—
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—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—1661no—
534C42—1661no—
535C42C2×C4×D8311yescharacteristic
536C42C2×C4×D8311yescharacteristic
537C42D4×D8311yescharacteristic
538C42D4×D8311yescharacteristic
539C23—21no—
540C23C2×#1305058911yescharacteristic
541Q8—21no—
542Q8—21no—
543Q8—6641no—
544Q8—6641no—
545D4—21no—
546D4—21no—
547D4—41no—
548D4—41no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—1661no—
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#1458183711yescharacteristic
575C2×C4#1458183911yescharacteristic
576C2×C4#1458183911yescharacteristic
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—41no—
593C22—41no—
594C22—41no—
595C22C2×(C22⋊D83)⋊C411yescharacteristic
596C22#1912831111yescharacteristic
597C22#1912831811yescharacteristic
598C4—21no—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—42no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—81no—
607C4—3321no—
608C4—3321no—
609C4—3321no—
610C4—3321no—
611C4#1912817811yescharacteristic
612C4#1912818211yescharacteristic
613C4#1912827411yescharacteristic
614C4#1912828011yescharacteristic
615C2—21no—
616C2—21no—
617C2—81no—
618C2#2491014111yescharacteristic
619C2#2491636911yescharacteristic
620C2#2491637611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#1806C2
socleC22×C83C2×C4×D4
prime radicalC2×#41×C83C23
cosocleC22×C4×C83C24
hypercenter#1806D83
hypocenterC83#22132
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #24916400C2semidirect
4. #24908406C2semidirect
5. #24908236C2semidirect
6. #24908215C2semidirect
7. #24908210C2semidirect
12. #24908065C2semidirect
13. #24908065C2semidirect
14. #24907338C2semidirect
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
#249164002
#249161142
#249084062
#249082362
#249082152
#249082102
#249081712
#249081642
#249081142
#249080652
#249073382
C83×#18062
#2213283