Finite Group Databasebeta

← #35375558

Subgroups — #35375558

Order 21248.

650 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917512C211yesmaximal, characteristic
2#24916619C211yesmaximal, characteristic, complemented
3#24916500C211yesmaximal, characteristic, complemented
4#24906352C211yesmaximal, characteristic, complemented
5#24906347C211yesmaximal, characteristic, complemented
6#24906340C211yesmaximal, characteristic, complemented
7#24906326C211yesmaximal, characteristic, complemented
8#24906326C211yesmaximal, characteristic, complemented
9#24906319C211yesmaximal, characteristic, complemented
10#24906262C211yesmaximal, characteristic, complemented
11#24906257C211yesmaximal, characteristic, complemented
12#24905921C211yesmaximal, characteristic, complemented
13C2×#19127428C211yesmaximal, characteristic, complemented
14#24905747C211yesmaximal, characteristic, complemented
15C83×#1573C211yesmaximal, characteristic, complemented
16#19128235C2211yescharacteristic
17C2×C4×D332C2211yescharacteristic
18#19128037C411yescharacteristic
19#19128020C411yescharacteristic
20#19128002C411yescharacteristic
21#19128002C411yescharacteristic
22#19127917C411yescharacteristic
23#19127917C411yescharacteristic
24#19127854C411yescharacteristic
25#19127837C411yescharacteristic
26#19127828C2211yescharacteristic, complemented
27#19127825C2211yescharacteristic, complemented
28C4×#13050579C2211yescharacteristic
29C4×#13050579C2211yescharacteristic
30C4×D664C2211yescharacteristic
31C4×D664C2211yescharacteristic
32#19127778C2211yescharacteristic
33#19127778C2211yescharacteristic
34#19127778C2211yescharacteristic, complemented
35#19127774—21no—
36#19127774—21no—
37#19127772—21no—
38#19127766C2211yescharacteristic
39#19127766C2211yescharacteristic
40#19127766C2211yescharacteristic, complemented
41C8×C22⋊D83—21no—
42#19127761—21no—
43#19127754C2211yescharacteristic
44#19127726—21no—
45#19127663—21no—
46C22⋊C8×D83—21no—
47C2×C4×C83⋊C8C2211yescharacteristic
48#19127431C2211yescharacteristic, complemented
49#19127431C2211yescharacteristic, complemented
50#19127428C2211yescharacteristic
51#19127428C2211yescharacteristic
52#19127428C2211yescharacteristic
53#19127428C2211yescharacteristic
54#19127428C2211yescharacteristic, complemented
55#19127428C2211yescharacteristic, complemented
56#19127423C2211yescharacteristic, complemented
57#19127423C2211yescharacteristic, complemented
58C8×C83⋊C8C2211yescharacteristic, complemented
59C8×C83⋊C8C2211yescharacteristic, complemented
60#432×C83C2211yescharacteristic
61#431×C83C2211yescharacteristic
62C2×C4⋊C8×C83C2211yescharacteristic
63#335×C83C2211yescharacteristic, complemented
64#335×C83C2211yescharacteristic, complemented
65#334×C83C2211yescharacteristic, complemented
66#334×C83C2211yescharacteristic, complemented
67C22×D332C2×C411yescharacteristic
68C22×C4×D83—21no—
69C2×#13050579C2×C411yescharacteristic
70C2×#13050579C2×C411yescharacteristic
71C2×D664C2×C411yescharacteristic
72C2×D664C2×C411yescharacteristic
73C2×#13050573—21no—
74C2×#13050573—21no—
75C2×#13050573—21no—
76C22×C83⋊C8—21no—
77C2×C8×D83—21no—
78C2×C8×D83—21no—
79C2×C8×D83—21no—
80#14581786—21no—
81#14581784C2×C411yescharacteristic
82#14581780C2×C411yescharacteristic
83#14581775—21no—
84#14581771C2×C411yescharacteristic
85#14581766C2×C411yescharacteristic
86C4×Dic166C2311yescharacteristic
87C4×D332—21no—
88C4×D332—21no—
89C4×D332C2×C411yescharacteristic
90C4×D332C2×C411yescharacteristic
91C4×D332C2311yescharacteristic
92C4×D332C2311yescharacteristic
93C4×D332C2311yescharacteristic
94C4×C22⋊D83—21no—
95#14581749—21no—
96C2×C4⋊Dic83C2×C411yescharacteristic
97C2×(C2×D83)⋊C4—21no—
98#14581726C2×C411yescharacteristic
99#14581726C2×C411yescharacteristic
100#14581724C2×C411yescharacteristic
101#14581724C2×C411yescharacteristic
102C4⋊(C83⋊C8)D411yescharacteristic
103C4⋊(C83⋊C8)D411yescharacteristic
104Dic83⋊C8—21no—
105Dic83⋊C8—21no—
106#14581717C2×C411yescharacteristic
107#14581717C2×C411yescharacteristic
108#14581714C2×C411yescharacteristic
109#14581714C2×C411yescharacteristic
110#14581714C2×C411yescharacteristic
111#14581714C2×C411yescharacteristic
112#14581714C2×C411yescharacteristic
113#14581714C2×C411yescharacteristic
114C22⋊(C83⋊C8)D411yescharacteristic
115C22⋊(C83⋊C8)D411yescharacteristic
116(C2×D83)⋊C8—21no—
117(C2×D83)⋊C8—21no—
118(C2×D83)⋊C8—21no—
119(C2×D83)⋊C8—21no—
120(C2×D83)⋊C8—21no—
121(C2×D83)⋊C8—21no—
122#14581702—21no—
123C4×C83⋊C8—21no—
124C4×C83⋊C8C2311yescharacteristic
125C4×C83⋊C8C2311yescharacteristic
126C4×C83⋊C8C2311yescharacteristic
127C4×C83⋊C8C2311yescharacteristic
128C8×Dic83—21no—
129C22×C8×C83—21no—
130C2×C42×C83C2311yescharacteristic
131C4⋊C8×C83—21no—
132C4⋊C8×C83C2×C411yescharacteristic
133C4⋊C8×C83C2×C411yescharacteristic
134C4⋊C8×C83C2311yescharacteristic
135C4⋊C8×C83C2311yescharacteristic
136C4⋊C8×C83C2311yescharacteristic
137C4⋊C8×C83C2311yescharacteristic
138C22⋊C8×C83—21no—
139C22⋊C8×C83C2×C411yescharacteristic
140C22⋊C8×C83C2×C411yescharacteristic
141#97×C83—21no—
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C23×D83—21no—
145C2×Dic166C22×C411yescharacteristic
146C2×D332—22no—
147C2×D332—21no—
148C2×D332—41no—
149C2×D332C22×C411yescharacteristic
150C2×D332C22×C411yescharacteristic
151C2×D332C22×C411yescharacteristic
152C2×C22⋊D83—21no—
153C22×Dic83—21no—
154C2×C4×D83—21no—
155C2×C4×D83—21no—
156C2×C4×D83—21no—
157C2×C4×D83—21no—
158C2×C4×D83—21no—
159C2×C4×D83—81no—
160C2×C4×D83—81no—
161#13050579—22no—
162#13050579—41no—
163D664—22no—
164D664—41no—
165#13050573—81no—
166#13050573—81no—
167#13050573—81no—
168C2×C83⋊C8—24no—
169C2×C83⋊C8—21no—
170C2×C83⋊C8—21no—
171C2×C83⋊C8C2×D411yescharacteristic
172C2×C83⋊C8C2×D411yescharacteristic
173C2×C83⋊C8C2×D411yescharacteristic
174C2×C83⋊C8C2×D411yescharacteristic
175C8×D83—81no—
176C8×D83—81no—
177C8×D83—81no—
178C4⋊Dic83—21no—
179C4⋊Dic83C22×C411yescharacteristic
180C4⋊Dic83C22×C411yescharacteristic
181C4⋊Dic83C22×C411yescharacteristic
182C4⋊Dic83C22×C411yescharacteristic
183Dic83⋊C4—21no—
184Dic83⋊C4—21no—
185Dic83⋊C4—21no—
186Dic83⋊C4—21no—
187C22⋊Dic83—21no—
188(C2×D83)⋊C4—21no—
189(C2×D83)⋊C4—21no—
190(C2×D83)⋊C4—21no—
191(C2×D83)⋊C4—21no—
192(C2×D83)⋊C4—21no—
193(C2×D83)⋊C4—21no—
194(C2×D83)⋊C4—21no—
195(C2×D83)⋊C4—21no—
196C4×Dic83—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—
204C2×C8×C83—81no—
205C2×C8×C83C22×C411yescharacteristic
206C2×C8×C83C22×C411yescharacteristic
207C2×C8×C83C22×C411yescharacteristic
208C2×C8×C83C22×C411yescharacteristic
209C42×C83C22×C411yescharacteristic
210C42×C83C2×D411yescharacteristic
211C42×C83#4111yescharacteristic
212C42×C83C2411yescharacteristic
213C23×C83C4×D411yescharacteristic
214C22×D83—21no—
215C22×D83—21no—
216C22×D83—21no—
217C22×D83—42no—
218C22×D83—42no—
219C22×D83—81no—
220C2×C4×C83—22no—
221C2×C4×C83—21no—
222C2×C4×C83—21no—
223C2×C4×C83—21no—
224C2×C4×C83—21no—
225C2×C4×C83C4×D411yescharacteristic
226C2×C4×C83C4×D411yescharacteristic
227C2×C4×C83C4×D411yescharacteristic
228C2×C4×C83C23×C411yescharacteristic
229C2×C4×C83C22×D411yescharacteristic
230C2×C4×C83C2×#4111yescharacteristic
231C22⋊D83—42no—
232C2×Dic83—21no—
233C2×Dic83—21no—
234C2×Dic83—21no—
235C2×Dic83—21no—
236C2×Dic83—21no—
237C2×Dic83—81no—
238D332—21no—
239D332—21no—
240D332—21no—
241D332—21no—
242D332—21no—
243D332—42no—
244D332#13112yes—
245C4×D83—41no—
246C4×D83—41no—
247C4×D83—41no—
248C4×D83—41no—
249C4×D83—41no—
250C4×D83—41no—
251C4×D83—81no—
252C4×D83—81no—
253Dic166—21no—
254Dic166—21no—
255C8×C83—21no—
256C8×C83—21no—
257C8×C83—21no—
258C8×C83—21no—
259C8×C83—41no—
260C8×C83—41no—
261C8×C83—41no—
262C8×C83—41no—
263C83⋊C8—22no—
264C83⋊C8—22no—
265C83⋊C8—21no—
266C83⋊C8—21no—
267C83⋊C8—21no—
268C83⋊C8—21no—
269C22×C83—21no—
270C22×C83—21no—
271C22×C83#44312yes—
272C22×C83C2×C4×D411yescharacteristic
273C2×D83—22no—
274C2×D83—41no—
275C2×D83—41no—
276C2×D83—41no—
277C2×D83—41no—
278C2×D83—41no—
279C2×D83—41no—
280C2×D83—41no—
281C2×D83—41no—
282C2×D83—84no—
283C4×C83—21no—
284C4×C83—21no—
285C4×C83—21no—
286C4×C83—21no—
287C4×C83C2×#13111yescharacteristic
288C4×C83#56811yescharacteristic
289C4×C83#57611yescharacteristic
290C4×C83#57711yescharacteristic
291Dic83—41no—
292Dic83—41no—
293Dic83—41no—
294Dic83—41no—
295Dic83—41no—
296#18014—831nomaximal, Sylow
297C2×C83—22no—
298C2×C83#293311yescharacteristic
299C2×C83#294611yescharacteristic
300C2×C83C2×#44311yescharacteristic
301D83—42no—
302D83—81no—
303D83—81no—
304#3105—831no—
305#2994—831no—
306#2974—831no—
307#1590—831no—
308#1589—831no—
309#1588—831no—
310#1586—831no—
311#1586—831no—
312#1585—831no—
313C8×SD16—831no—
314C8×D8—831no—
315#1573D8311yescharacteristic, complemented
316#1494—831no—
317C2×D4⋊C8—831no—
318#1450—831no—
319C83#1801411yescharacteristic, complemented, Sylow
320#529—831no—
321C2×C4×D4—831no—
322#484—831no—
323#481—831no—
324#478—831no—
325#478—831no—
326#463—831no—
327#463—831no—
328#450—831no—
329#447—831no—
330#446—831no—
331C8×Q8—831no—
332C4×SD16—831no—
333C4×SD16—831no—
334C4×D8—831no—
335C4×D8—831no—
336#436—831no—
337#436—831no—
338#436—831no—
339#435—1661no—
340#435—1661no—
341#435—1661no—
342C8×D4—831no—
343C8×D4—831no—
344C8×D4—831no—
345C8×D4—1661no—
346#433—1661no—
347#432C2×D8311yescharacteristic
348#431—831no—
349#431C2×D8311yescharacteristic
350#424—1661no—
351C2×C4⋊C8C2×D8311yescharacteristic
352#407—1661no—
353C2×C22⋊C8—1661no—
354C2×C4×C8—831no—
355#335C2×D8311yescharacteristic, complemented
356#335C2×D8311yescharacteristic, complemented
357#334C2×D8311yescharacteristic, complemented
358#334C2×D8311yescharacteristic, complemented
359Q8⋊C8—831no—
360Q8⋊C8—831no—
361D4⋊C8—831no—
362D4⋊C8—831no—
363D4⋊C8—831no—
364D4⋊C8—831no—
365D4⋊C8—831no—
366D4⋊C8—831no—
367#322—831no—
368#322—831no—
369C82—831no—
370C82—831no—
371C22×D4—831no—
372C23×C4—1661no—
373C2×SD16—831no—
374C2×SD16—831no—
375C2×D8—831no—
376C2×D8—831no—
377C2×M16—1661no—
378C2×M16—1661no—
379C2×M16—1661no—
380C22×C8—21no—
381C22×C8—1661no—
382C22×C8—1661no—
383C22×C8—1661no—
384C22×C8—1661no—
385#126—1661no—
386#125—831no—
387#124—831no—
388#123—1661no—
389C22⋊Q8—831no—
390#121—831no—
391C4×Q8—831no—
392C4×D4—831no—
393C4×D4—831no—
394C4×D4—831no—
395C4×D4—831no—
396C4×D4—831no—
397C4×D4—1661no—
398C4×D4—1661no—
399C4×D4—1661no—
400#117—1661no—
401C2×C4⋊C4—831no—
402C2×C22⋊C4—1661no—
403C2×C42C22×D8311yescharacteristic
404#107—831no—
405#107—831no—
406#106—831no—
407#106—831no—
408C4⋊C8—21no—
409C4⋊C8—831no—
410C4⋊C8—831no—
411C4⋊C8—1661no—
412C4⋊C8—1661no—
413C4⋊C8C4×D8311yescharacteristic
414C4⋊C8C4×D8311yescharacteristic
415C4⋊C8C22×D8311yescharacteristic
416C4⋊C8C22×D8311yescharacteristic
417C4⋊C8C22×D8311yescharacteristic
418C4⋊C8C22×D8311yescharacteristic
419#103—831no—
420#103—831no—
421#102—831no—
422#102—831no—
423#102—831no—
424#102—831no—
425#102—831no—
426#102—831no—
427C22⋊C8—21no—
428C22⋊C8—831no—
429C22⋊C8—831no—
430C22⋊C8—1661no—
431C22⋊C8—1661no—
432C22⋊C8—1661no—
433C22⋊C8—1661no—
434C22⋊C8—1661no—
435C22⋊C8—1661no—
436C22⋊C8C4×D8311yescharacteristic
437C22⋊C8C4×D8311yescharacteristic
438#97—21no—
439#97—1661no—
440C4×C8—831no—
441C4×C8—831no—
442C4×C8—831no—
443C4×C8—831no—
444C4×C8—1661no—
445C4×C8—1661no—
446C4×C8C22×D8311yescharacteristic
447C4×C8C22×D8311yescharacteristic
448C24—1661no—
449C2×Q8—831no—
450C2×D4—3321no—
451C2×D4—831no—
452C2×D4—831no—
453C2×D4—831no—
454C2×D4—1662no—
455C2×D4—1661no—
456C2×D4—1661no—
457C22×C4—6641no—
458C22×C4—6641no—
459C22×C4—1661no—
460C22×C4—1661no—
461C22×C4—1661no—
462C22×C4—1661no—
463C22×C4—1661no—
464C22×C4—1661no—
465C22×C4C2×C4×D8311yescharacteristic
466C22×C4D4×D8311yescharacteristic
467C22×C4#1305059111yescharacteristic
468SD16—3321no—
469SD16—1662no—
470D8—3321no—
471D8—1662no—
472M16—6641no—
473M16—6641no—
474M16—6641no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—81no—
480C2×C8—831no—
481C2×C8—831no—
482C2×C8—831no—
483C2×C8—831no—
484C2×C8—6641no—
485C2×C8—6641no—
486C2×C8—6641no—
487C2×C8—1664no—
488C2×C8—1661no—
489C2×C8—1661no—
490C2×C8C2×C4×D8311yescharacteristic
491C2×C8C2×C4×D8311yescharacteristic
492C2×C8C2×C4×D8311yescharacteristic
493C2×C8C2×C4×D8311yescharacteristic
494C4⋊C4—831no—
495C4⋊C4—831no—
496C4⋊C4—831no—
497C4⋊C4—831no—
498C4⋊C4—1661no—
499C4⋊C4—1661no—
500C4⋊C4—1661no—
501C4⋊C4—1661no—
502C4⋊C4—1661no—
503C22⋊C4—1661no—
504C22⋊C4—1661no—
505C22⋊C4—1661no—
506C22⋊C4—1661no—
507C22⋊C4—1661no—
508C22⋊C4—1661no—
509C22⋊C4—1661no—
510C22⋊C4—1661no—
511C22⋊C4—1661no—
512C42—1661no—
513C42C2×C4×D8311yescharacteristic
514C42D4×D8311yescharacteristic
515C42#1305059111yescharacteristic
516C42C23×D8311yescharacteristic
517C23—3322no—
518C23—3322no—
519C23—6641no—
520C23—1661no—
521C23—1661no—
522C23—1661no—
523C23#1458175411yescharacteristic
524Q8—1661no—
525Q8—1661no—
526D4—3322no—
527D4—3322no—
528D4—832no—
529D4—1661no—
530D4—1661no—
531D4—1661no—
532D4—1661no—
533D4—1661no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—3321no—
540C2×C4—3321no—
541C2×C4—3321no—
542C2×C4—3321no—
543C2×C4—3321no—
544C2×C4—3321no—
545C2×C4—6641no—
546C2×C4—6641no—
547C2×C4—6641no—
548C2×C4—1661no—
549C2×C4—1661no—
550C2×C4—1661no—
551C2×C4—1661no—
552C2×C4—1661no—
553C2×C4#1458175411yescharacteristic
554C2×C4#1458175411yescharacteristic
555C2×C4#1458175411yescharacteristic
556C2×C4C22×C4×D8311yescharacteristic
557C2×C4C2×D4×D8311yescharacteristic
558C2×C4C2×#1305059111yescharacteristic
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—1662no—
568C8—1662no—
569C8—1661no—
570C8—1661no—
571C8—1661no—
572C8—1661no—
573C22—21no—
574C22—21no—
575C22—3321no—
576C22—3321no—
577C22—3321no—
578C22—3321no—
579C22—3321no—
580C22—3321no—
581C22—3321no—
582C22—3321no—
583C22—6644no—
584C22—1662no—
585C22#1912781712yes—
586C22C2×#1458175411yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—3321no—
592C4—3321no—
593C4—3321no—
594C4—3321no—
595C4—3321no—
596C4#131×D8311yescharacteristic
597C4#1912846611yescharacteristic
598C4#1912850511yescharacteristic
599C4#1912851011yescharacteristic
600C2—22no—
601C2—3322no—
602C2—6641no—
603C2—6641no—
604C2#2491618711yescharacteristic
605C2#2491629311yescharacteristic
606C2C2×#1912781711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1573C2
socleC22×C83C2×C4×D4
prime radical#19127837C4
cosocleC42×C83C24
hypercenter#1573D83
hypocenterC83#18014
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
2. #24916619C2semidirect
3. #24916500C2semidirect
4. #24906352C2semidirect
5. #24906347C2semidirect
6. #24906340C2semidirect
7. #24906326C2semidirect
8. #24906326C2semidirect
9. #24906319C2semidirect
10. #24906262C2semidirect
11. #24906257C2semidirect
12. #24905921C2semidirect
13. C2×#19127428C2semidirect
14. #24905747C2semidirect
15. C83×#1573C2semidirect
26. #19127828C22semidirect
27. #19127825C22semidirect
34. #19127778C22semidirect
40. #19127766C22semidirect
48. #19127431C22semidirect
49. #19127431C22semidirect
54. #19127428C22semidirect
55. #19127428C22semidirect
56. #19127423C22semidirect
57. #19127423C22semidirect
58. C8×C83⋊C8C22semidirect
59. C8×C83⋊C8C22semidirect
63. #335×C83C22semidirect
64. #335×C83C22semidirect
65. #334×C83C22semidirect
66. #334×C83C22semidirect
315. #1573D83semidirect
319. C83#18014semidirect
355. #335C2×D83semidirect
356. #335C2×D83semidirect
357. #334C2×D83semidirect
358. #334C2×D83semidirect

Maximal subgroups

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

subgroupindex
#249175122
#249166192
#249165002
#249063522
#249063472
#249063402
#249063262
#249063192
#249062622
#249062572
#249059212
C2×#191274282
#249057472
C83×#15732
#1801483