Finite Group Databasebeta

← #35433332

Subgroups — #35433332

Order 21248.

892 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24916027C211yesmaximal, characteristic, complemented
2C2×#19127719C211yesmaximal, characteristic
3#24915980C211yesmaximal, characteristic
4C2×#19127683C211yesmaximal, characteristic
5#24908915C218yesmaximal, complemented
6C2×#19127471C211yesmaximal, characteristic, complemented
7#24907189C211yesmaximal, characteristic, complemented
8C2×H(3,ℤ/4)×C83C211yesmaximal, characteristic, complemented
9C22×#13050590C2211yescharacteristic
10C22×#13050574C2211yescharacteristic
11C22×#13050574C2211yescharacteristic
12C22×#13050574C2211yescharacteristic
13#19127728—22no—
14#19127728C2214yescomplemented
15#19127725—22no—
16#19127719—22no—
17#19127719C2214yes—
18C2×#14581720—22no—
19#19127709—21no—
20#19127705—21no—
21#19127700—22no—
22#19127695C2214yes—
23#19127683—22no—
24#19127683C2214yes—
25C2×#14581710—21no—
26C2×#14581708—21no—
27#19127471C2214yescomplemented
28#19127465C2214yescomplemented
29C22×M16×C83C2211yescharacteristic
30C2×#117×C83C2211yescharacteristic
31C2×#117×C83C2211yescharacteristic
32H(3,ℤ/4)×C83C2214yescomplemented
33C2×#13050590—21no—
34C2×#13050590—21no—
35C2×#13050590—21no—
36C2×#13050590—21no—
37C2×#13050590—21no—
38C2×#13050590—21no—
39C2×#13050590—21no—
40C2×#13050590—21no—
41C2×#13050590—21no—
42C2×#13050590—21no—
43C2×#13050590D412yes—
44C2×#13050590C2312yes—
45C22×Dic166D411yescharacteristic
46C22×D332D411yescharacteristic
47C22×C22⋊D83—21no—
48C22×C4×D83—21no—
49C2×#13050574—21no—
50C2×#13050574—21no—
51C2×#13050574—21no—
52C2×#13050574—21no—
53C2×#13050574—21no—
54C2×#13050574—21no—
55C2×#13050574—21no—
56C2×#13050574—21no—
57C2×#13050574—21no—
58C2×#13050574—21no—
59C2×#13050574—21no—
60C2×#13050574—21no—
61C2×#13050574—21no—
62C2×#13050574—21no—
63C2×#13050574—21no—
64C2×#13050574—21no—
65C2×#13050574C2312yes—
66C2×#13050574C2312yes—
67C22×C83⋊C8—21no—
68C22×C83⋊C8—21no—
69C22×C83⋊C8C2312yes—
70C4⋊(C83⋊C8)—28no—
71#14581720—28no—
72#14581715—24no—
73#14581712—24no—
74#14581710—24no—
75#14581708—24no—
76C23×C4×C83C2311yescharacteristic
77C2×M16×C83—21no—
78C2×M16×C83—21no—
79C2×M16×C83—21no—
80C2×M16×C83—21no—
81C2×M16×C83—21no—
82C2×M16×C83C2312yes—
83C22×C8×C83—21no—
84#117×C83—21no—
85#117×C83—21no—
86#117×C83—21no—
87#117×C83—21no—
88#117×C83—21no—
89#117×C83D412yes—
90#117×C83C2312yes—
91#117×C83C2312yes—
92C2×C4⋊C4×C83—21no—
93C2×C4⋊C4×C83—21no—
94C2×C22⋊C4×C83—21no—
95C2×C22⋊C4×C83—21no—
96C2×C42×C83—21no—
97C2×C42×C83D412yes—
98C23×D83—21no—
99#13050590—22no—
100#13050590—22no—
101#13050590—22no—
102#13050590—22no—
103#13050590—22no—
104#13050590—22no—
105#13050590—22no—
106#13050590—22no—
107#13050590—41no—
108#13050590—41no—
109#13050590—41no—
110#13050590—41no—
111#13050590—41no—
112#13050590—41no—
113#13050590—41no—
114#13050590—41no—
115C2×Dic166—21no—
116C2×Dic166—21no—
117C2×Dic166—21no—
118C2×Dic166—21no—
119C2×Dic166—21no—
120C2×Dic166C2×D412yes—
121C2×D332—21no—
122C2×D332—21no—
123C2×D332—21no—
124C2×D332—21no—
125C2×D332—21no—
126C2×D332C2×D412yes—
127C2×C22⋊D83—22no—
128C2×C22⋊D83—22no—
129C2×C22⋊D83—41no—
130C2×C22⋊D83—41no—
131C2×C22⋊D83—41no—
132C2×C22⋊D83—41no—
133C22×Dic83—21no—
134C2×C4×D83—22no—
135C2×C4×D83—22no—
136C2×C4×D83—41no—
137C2×C4×D83—41no—
138C2×C4×D83—41no—
139C2×C4×D83—41no—
140#13050574—22no—
141#13050574—22no—
142#13050574—22no—
143#13050574—22no—
144#13050574—41no—
145#13050574—41no—
146#13050574—41no—
147#13050574—41no—
148#13050574—41no—
149#13050574—41no—
150#13050574—41no—
151#13050574—41no—
152C2×C83⋊C8—22no—
153C2×C83⋊C8—22no—
154C2×C83⋊C8—22no—
155C2×C83⋊C8—22no—
156C2×C83⋊C8—22no—
157C2×C83⋊C8—41no—
158C2×C83⋊C8—41no—
159C2×C83⋊C8—41no—
160C2×C83⋊C8—41no—
161C24×C83#4111yescharacteristic
162C22×C4×C83—22no—
163C22×C4×C83—41no—
164C22×C4×C83C2×D411yescharacteristic
165C22×C4×C83C2×D411yescharacteristic
166C22×C4×C83C2×D411yescharacteristic
167C22×C4×C83C2×D411yescharacteristic
168C22×C4×C83#4111yescharacteristic
169C22×C4×C83#4111yescharacteristic
170C22×C4×C83#4111yescharacteristic
171C22×C4×C83#4111yescharacteristic
172C22×C4×C83#4111yescharacteristic
173C22×C4×C83#4111yescharacteristic
174C22×C4×C83#4111yescharacteristic
175C22×C4×C83#4111yescharacteristic
176C22×C4×C83#4111yescharacteristic
177C22×C4×C83C2411yescharacteristic
178M16×C83—22no—
179M16×C83—22no—
180M16×C83—41no—
181M16×C83—41no—
182C2×C8×C83—22no—
183C2×C8×C83—41no—
184C2×C8×C83—41no—
185C4⋊C4×C83—22no—
186C4⋊C4×C83—22no—
187C4⋊C4×C83—22no—
188C4⋊C4×C83—41no—
189C22⋊C4×C83—22no—
190C22⋊C4×C83—22no—
191C22⋊C4×C83—22no—
192C22⋊C4×C83—41no—
193C42×C83—22no—
194C42×C83—22no—
195C42×C83—41no—
196C42×C83C2×D414yes—
197C23×C83—81no—
198C23×C83#12311yescharacteristic
199C23×C83#12311yescharacteristic
200C23×C83#12311yescharacteristic
201C23×C83#12311yescharacteristic
202C23×C83#12611yescharacteristic
203C23×C83#12611yescharacteristic
204C23×C83C2×#4111yescharacteristic
205C22×D83—22no—
206C22×D83—41no—
207C22×D83—41no—
208C22×D83—82no—
209C2×C4×C83—24no—
210C2×C4×C83—42no—
211C2×C4×C83—82no—
212C2×C4×C83—82no—
213C2×C4×C83#12111yescharacteristic
214C2×C4×C83#12111yescharacteristic
215C2×C4×C83#12111yescharacteristic
216C2×C4×C83#12111yescharacteristic
217C2×C4×C83#12311yescharacteristic
218C2×C4×C83#12311yescharacteristic
219C2×C4×C83#12311yescharacteristic
220C2×C4×C83#12311yescharacteristic
221C2×C4×C83#12311yescharacteristic
222C2×C4×C83#12311yescharacteristic
223C2×C4×C83#12311yescharacteristic
224C2×C4×C83#12311yescharacteristic
225C2×C4×C83#12411yescharacteristic
226C2×C4×C83#12411yescharacteristic
227C2×C4×C83#12411yescharacteristic
228C2×C4×C83#12411yescharacteristic
229C2×C4×C83#12611yescharacteristic
230C2×C4×C83#12611yescharacteristic
231C2×C4×C83#12611yescharacteristic
232C2×C4×C83#12611yescharacteristic
233C2×C4×C83#12611yescharacteristic
234C2×C4×C83#12611yescharacteristic
235C2×C4×C83C22×D411yescharacteristic
236C2×C4×C83C22×D411yescharacteristic
237C2×C4×C83C2×#4111yescharacteristic
238C2×C4×C83C2×#4111yescharacteristic
239C2×C4×C83C2×#4111yescharacteristic
240C2×C4×C83C2×#4111yescharacteristic
241C22⋊D83—42no—
242C22⋊D83—42no—
243C22⋊D83—42no—
244C22⋊D83—42no—
245C2×Dic83—22no—
246C2×Dic83—41no—
247C2×Dic83—41no—
248D332—22no—
249D332—22no—
250D332—41no—
251D332—41no—
252C4×D83—42no—
253C4×D83—42no—
254C4×D83—42no—
255C4×D83—42no—
256Dic166—22no—
257Dic166—22no—
258Dic166—41no—
259Dic166—41no—
260C8×C83—42no—
261C83⋊C8—42no—
262C83⋊C8—42no—
263C83⋊C8—42no—
264C22×C83—41no—
265C22×C83—41no—
266C22×C83—41no—
267C22×C83—41no—
268C22×C83—41no—
269C22×C83—41no—
270C22×C83—41no—
271C22×C83#39711yescharacteristic
272C22×C83#39711yescharacteristic
273C22×C83#39711yescharacteristic
274C22×C83#39711yescharacteristic
275C22×C83C2×#12311yescharacteristic
276C22×C83C2×#12311yescharacteristic
277C22×C83C2×#12611yescharacteristic
278C2×D83—42no—
279C2×D83—82no—
280C2×D83—82no—
281C2×D83—82no—
282C4×C83—44no—
283C4×C83—82no—
284C4×C83#39711yescharacteristic
285C4×C83#39711yescharacteristic
286C4×C83#39711yescharacteristic
287C4×C83#39711yescharacteristic
288C4×C83C2×#12111yescharacteristic
289C4×C83C2×#12311yescharacteristic
290C4×C83C2×#12411yescharacteristic
291C4×C83C2×#12611yescharacteristic
292Dic83—42no—
293#23649—831nomaximal, Sylow
294C2×C83—21no—
295C2×C83—21no—
296C2×C83—21no—
297C2×C83—21no—
298C2×C83—21no—
299C2×C83—21no—
300C2×C83—21no—
301C2×C83C2×#39711yescharacteristic
302D83—82no—
303#2905—831no—
304C2×#421—831no—
305#2896—831no—
306C2×#413—831no—
307#2080—838no—
308C2×#344—831no—
309#1738—831no—
310C2×H(3,ℤ/4)D8311yescharacteristic, complemented
311C83#2364911yescharacteristic, complemented, Sylow
312C22×#41—831no—
313C22×M16—831no—
314C22×M16—831no—
315C22×M16—831no—
316C22×M16C2×D8311yescharacteristic
317C2×#117C2×D8311yescharacteristic
318C2×#117C2×D8311yescharacteristic
319#424—834no—
320#424—1662no—
321#423—1662no—
322#421—834no—
323#421—1662no—
324C2×#104—1662no—
325#419—1661no—
326#418—1661no—
327#417—1662no—
328#416—834no—
329#413—834no—
330#413—1662no—
331C2×#101—1661no—
332C2×#100—1661no—
333#344—834no—
334#341—834no—
335H(3,ℤ/4)C2×D8314yescomplemented
336C2×#41—832no—
337C2×#41—832no—
338C2×#41—1661no—
339C2×#41—1661no—
340C2×#41—1661no—
341C2×#41—1661no—
342C2×#41—1661no—
343C2×#41—1661no—
344C2×#41—1661no—
345C2×#41—1661no—
346C2×#41—1661no—
347C2×#41—1661no—
348C22×Q8—831no—
349C22×D4—831no—
350C22×D4—1661no—
351C23×C4—1661no—
352C23×C4C22×D8311yescharacteristic
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—832no—
359C2×M16—832no—
360C2×M16—1661no—
361C2×M16—1661no—
362C2×M16—1661no—
363C2×M16—1661no—
364C2×M16—1661no—
365C2×M16—1661no—
366C2×M16—1661no—
367C2×M16—1661no—
368C2×M16—1661no—
369C2×M16—1661no—
370C2×M16—1661no—
371C2×M16—1661no—
372C2×M16—1661no—
373C2×M16—1661no—
374C2×M16—1661no—
375C2×M16—1661no—
376C2×M16C22×D8312yes—
377C22×C8—21no—
378C22×C8—832no—
379C22×C8—1661no—
380C22×C8—1661no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117D33212yes—
387#117C22×D8312yes—
388#117C22×D8312yes—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C42—21no—
394C2×C42D33212yes—
395C4⋊C8—1668no—
396#104—1668no—
397#103—1664no—
398#102—1664no—
399#101—1664no—
400#100—1664no—
401C24—1661no—
402C24#1305058911yescharacteristic
403#41—3321no—
404#41—3321no—
405#41—3321no—
406#41—3321no—
407#41—3321no—
408#41—3321no—
409#41—3321no—
410#41—3321no—
411#41—1662no—
412#41—1662no—
413#41—1662no—
414#41—1662no—
415#41—1662no—
416#41—1662no—
417#41—1662no—
418#41—1662no—
419C2×Q8—832no—
420C2×Q8—1661no—
421C2×Q8—1661no—
422C2×Q8—1661no—
423C2×Q8—1661no—
424C2×Q8—1661no—
425C2×D4—3321no—
426C2×D4—3321no—
427C2×D4—3321no—
428C2×D4—3321no—
429C2×D4—832no—
430C2×D4—1662no—
431C2×D4—1662no—
432C2×D4—1661no—
433C2×D4—1661no—
434C2×D4—1661no—
435C2×D4—1661no—
436C2×D4—1661no—
437C22×C4—22no—
438C22×C4—41no—
439C22×C4—3321no—
440C22×C4—3321no—
441C22×C4—3321no—
442C22×C4—3321no—
443C22×C4—1661no—
444C22×C4—1662no—
445C22×C4—1662no—
446C22×C4D4×D8311yescharacteristic
447C22×C4D4×D8311yescharacteristic
448C22×C4C2×D33211yescharacteristic
449C22×C4C2×D33211yescharacteristic
450C22×C4#1305058911yescharacteristic
451C22×C4#1305058911yescharacteristic
452C22×C4#1305058911yescharacteristic
453C22×C4#1305059011yescharacteristic
454C22×C4#1305059011yescharacteristic
455C22×C4#1305059011yescharacteristic
456C22×C4#1305059011yescharacteristic
457C22×C4#1305059111yescharacteristic
458C22×C4#1305059111yescharacteristic
459C22×C4C23×D8311yescharacteristic
460M16—22no—
461M16—22no—
462M16—41no—
463M16—41no—
464M16—3321no—
465M16—3321no—
466M16—3321no—
467M16—3321no—
468M16—3321no—
469M16—3321no—
470M16—3321no—
471M16—3321no—
472M16—1662no—
473M16—1662no—
474M16—1662no—
475M16—1662no—
476C2×C8—22no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—3321no—
480C2×C8—3321no—
481C2×C8—3321no—
482C2×C8—3321no—
483C2×C8—1662no—
484C2×C8—1662no—
485C2×C8—1662no—
486C2×C8—1662no—
487C2×C8—1662no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—41no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—41no—
496C42—22no—
497C42—22no—
498C42—41no—
499C42C2×D33214yes—
500C23—81no—
501C23—3321no—
502C23—3321no—
503C23—6642no—
504C23—1662no—
505C23#1458177411yescharacteristic
506C23#1458177411yescharacteristic
507C23#1458177611yescharacteristic
508C23#1458177611yescharacteristic
509C23#1458178711yescharacteristic
510C23#1458178711yescharacteristic
511C23C2×#1305058911yescharacteristic
512Q8—3321no—
513Q8—3321no—
514Q8—1662no—
515Q8—1662no—
516D4—3322no—
517D4—3322no—
518D4—3322no—
519D4—3322no—
520D4—3321no—
521D4—3321no—
522D4—1662no—
523D4—1662no—
524C2×C4—24no—
525C2×C4—42no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—3321no—
529C2×C4—3321no—
530C2×C4—3322no—
531C2×C4—3322no—
532C2×C4—3322no—
533C2×C4—3322no—
534C2×C4—1662no—
535C2×C4#1458176711yescharacteristic
536C2×C4#1458176711yescharacteristic
537C2×C4#1458176711yescharacteristic
538C2×C4#1458176711yescharacteristic
539C2×C4#1458177411yescharacteristic
540C2×C4#1458177411yescharacteristic
541C2×C4#1458177411yescharacteristic
542C2×C4#1458177411yescharacteristic
543C2×C4#1458177411yescharacteristic
544C2×C4#1458177411yescharacteristic
545C2×C4#1458177611yescharacteristic
546C2×C4#1458177611yescharacteristic
547C2×C4#1458178011yescharacteristic
548C2×C4#1458178011yescharacteristic
549C2×C4#1458178011yescharacteristic
550C2×C4#1458178011yescharacteristic
551C2×C4#1458178711yescharacteristic
552C2×C4#1458178711yescharacteristic
553C2×C4#1458178711yescharacteristic
554C2×C4#1458178711yescharacteristic
555C2×C4#1458178711yescharacteristic
556C2×C4#1458178711yescharacteristic
557C2×C4C2×D4×D8311yescharacteristic
558C2×C4C22×D33211yescharacteristic
559C2×C4C2×#1305058911yescharacteristic
560C2×C4C2×#1305059011yescharacteristic
561C2×C4C2×#1305059011yescharacteristic
562C2×C4C2×#1305059111yescharacteristic
563C8—42no—
564C8—3322no—
565C8—3322no—
566C8—3322no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—3322no—
575C22—6642no—
576C22—6642no—
577C22—6642no—
578C22#1912762811yescharacteristic
579C22#1912762811yescharacteristic
580C22#1912762811yescharacteristic
581C22#1912762811yescharacteristic
582C22C2×#1458177411yescharacteristic
583C22C2×#1458177611yescharacteristic
584C22C2×#1458178711yescharacteristic
585C4—44no—
586C4—82no—
587C4—3322no—
588C4#1912762811yescharacteristic
589C4#1912762811yescharacteristic
590C4#1912762811yescharacteristic
591C4#1912762811yescharacteristic
592C4C2×#1458176711yescharacteristic
593C4C2×#1458177411yescharacteristic
594C4C2×#1458178011yescharacteristic
595C4C2×#1458178711yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—21no—
603C2—6642no—
604C2C2×#1912762811yescharacteristic
subgroupG/H
centerC4C2×#14581780
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC2×H(3,ℤ/4)×C83C2
socleC2×C83C2×#397
prime radicalC22×#13050590C22
hypercenterC2×H(3,ℤ/4)D83
hypocenterC83#23649
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #24916027C2semidirect
5. #24908915C2semidirect
6. C2×#19127471C2semidirect
7. #24907189C2semidirect
8. C2×H(3,ℤ/4)×C83C2semidirect
14. #19127728C22semidirect
27. #19127471C22semidirect
28. #19127465C22semidirect
32. H(3,ℤ/4)×C83C22semidirect
310. C2×H(3,ℤ/4)D83semidirect
311. C83#23649semidirect
335. H(3,ℤ/4)C2×D83semidirect

Maximal subgroups

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

subgroupindex
#249160272
C2×#191277192
#249159802
C2×#191276832
#249089152
C2×#191274712
#249071892
C2×H(3,ℤ/4)×C832
#2364983