Finite Group Databasebeta

← #35374498

Subgroups — #35374498

Order 21248.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917524C211yesmaximal, characteristic
2#24916571C211yesmaximal, characteristic, complemented
3#24916538C211yesmaximal, characteristic, complemented
4#24906343C211yesmaximal, characteristic, complemented
5#24906329C211yesmaximal, characteristic, complemented
6#24906308C211yesmaximal, characteristic, complemented
7#24906294C211yesmaximal, characteristic, complemented
8#24906288C211yesmaximal, characteristic, complemented
9#24906277C211yesmaximal, characteristic, complemented
10C8×#13050579C211yesmaximal, characteristic, complemented
11C8×D664C211yesmaximal, characteristic, complemented
12#24906248C211yesmaximal, characteristic, complemented
13#24905898C211yesmaximal, characteristic, complemented
14#24905863C211yesmaximal, characteristic, complemented
15C83×#1454C211yesmaximal, characteristic, complemented
16#19128251C2211yescharacteristic
17C4×#13050590C2211yescharacteristic
18#19128026C411yescharacteristic
19#19128026C411yescharacteristic
20#19127997C411yescharacteristic
21#19127992C411yescharacteristic
22#19127902C411yescharacteristic
23#19127897C411yescharacteristic
24#19127848C411yescharacteristic
25#19127848C411yescharacteristic
26C8×Dic166C2211yescharacteristic
27C8×Dic166C2211yescharacteristic
28C4×#13050579C2211yescharacteristic
29C4×#13050579C2211yescharacteristic
30C4×D664C2211yescharacteristic
31C4×D664C2211yescharacteristic
32#19127780C2211yescharacteristic
33#19127780C2211yescharacteristic
34#19127771—21no—
35#19127771—21no—
36C8×D332C2211yescharacteristic
37C8×D332C2211yescharacteristic
38C8×D332C2211yescharacteristic
39C8×D332C2211yescharacteristic
40(C22⋊D83)⋊C8—21no—
41(C22⋊D83)⋊C8—21no—
42#19127758C2211yescharacteristic
43#19127753—21no—
44C2×C4⋊(C83⋊C8)C2211yescharacteristic
45C4⋊C8×D83—21no—
46#19127666—21no—
47#19127666—21no—
48#19127454C2211yescharacteristic
49#19127454C2211yescharacteristic
50#19127452C2211yescharacteristic
51#19127452C2211yescharacteristic
52#19127433C2211yescharacteristic
53#19127433C2211yescharacteristic
54#19127430C2211yescharacteristic
55#19127430C2211yescharacteristic
56#19127430C2211yescharacteristic
57#19127430C2211yescharacteristic
58#19127430C2211yescharacteristic
59#19127430C2211yescharacteristic
60#431×C83C2211yescharacteristic
61#431×C83C2211yescharacteristic
62#431×C83C2211yescharacteristic
63#322×C83C2211yescharacteristic
64#322×C83C2211yescharacteristic
65#322×C83C2211yescharacteristic
66C82×C83C2211yescharacteristic
67C2×#13050590—21no—
68C2×#13050590C2×C411yescharacteristic
69C2×#13050579C2×C411yescharacteristic
70C2×#13050579C2×C411yescharacteristic
71C2×D664C2×C411yescharacteristic
72C2×D664C2×C411yescharacteristic
73C2×#13050573—21no—
74C2×#13050573—21no—
75C22×C83⋊C8—21no—
76C2×C8×D83—21no—
77C2×C8×D83—21no—
78C2×C8×D83—21no—
79C2×C8×D83—21no—
80#14581792C2×C411yescharacteristic
81#14581789C2×C411yescharacteristic
82#14581780—21no—
83#14581766—21no—
84#14581766C2×C411yescharacteristic
85#14581766C2×C411yescharacteristic
86C4×Dic166C2×C411yescharacteristic
87C4×Dic166C2311yescharacteristic
88C4×D332—21no—
89C4×D332C2×C411yescharacteristic
90C4×D332C2311yescharacteristic
91C4×D332C2311yescharacteristic
92C4×D332C2311yescharacteristic
93C4×C22⋊D83—21no—
94C4×C22⋊D83—21no—
95#14581751C2×C411yescharacteristic
96#14581749—21no—
97C42×D83—21no—
98#14581726C2×C411yescharacteristic
99#14581726C2×C411yescharacteristic
100#14581724C2×C411yescharacteristic
101#14581724C2×C411yescharacteristic
102C4⋊(C83⋊C8)—21no—
103C4⋊(C83⋊C8)C2311yescharacteristic
104C4⋊(C83⋊C8)C2311yescharacteristic
105C4⋊(C83⋊C8)C2311yescharacteristic
106C4⋊(C83⋊C8)C2311yescharacteristic
107Dic83⋊C8—21no—
108Dic83⋊C8—21no—
109#14581717C2×C411yescharacteristic
110#14581717C2×C411yescharacteristic
111#14581714C2×C411yescharacteristic
112#14581714C2×C411yescharacteristic
113#14581714C2×C411yescharacteristic
114#14581714C2×C411yescharacteristic
115#14581714C2×C411yescharacteristic
116#14581714C2×C411yescharacteristic
117C22⋊(C83⋊C8)—21no—
118(C2×D83)⋊C8—21no—
119(C2×D83)⋊C8—21no—
120(C2×D83)⋊C8—21no—
121(C2×D83)⋊C8—21no—
122(C2×D83)⋊C8—21no—
123(C2×D83)⋊C8—21no—
124#14581703—21no—
125C8×Dic83—21no—
126C8×Dic83—21no—
127C2×C42×C83C2311yescharacteristic
128C4⋊C8×C83—21no—
129C4⋊C8×C83C2×C411yescharacteristic
130C4⋊C8×C83C2×C411yescharacteristic
131C4⋊C8×C83D411yescharacteristic
132C4⋊C8×C83D411yescharacteristic
133C22⋊C8×C83—21no—
134C22⋊C8×C83C2×C411yescharacteristic
135C22⋊C8×C83C2×C411yescharacteristic
136C22⋊C8×C83D411yescharacteristic
137C22⋊C8×C83D411yescharacteristic
138C4×C8×C83C2311yescharacteristic
139C4×C8×C83C2311yescharacteristic
140C4×C8×C83C2311yescharacteristic
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#13050590—22no—
145#13050590—22no—
146#13050590—81no—
147#13050590—81no—
148C2×Dic166—21no—
149C2×Dic166C22×C411yescharacteristic
150C2×D332—21no—
151C2×D332—21no—
152C2×D332C22×C411yescharacteristic
153C2×D332C22×C411yescharacteristic
154C2×D332C22×C411yescharacteristic
155C2×C22⋊D83—21no—
156C2×C22⋊D83—21no—
157C2×C22⋊D83—21no—
158C2×C4×D83—21no—
159C2×C4×D83—21no—
160C2×C4×D83—21no—
161C2×C4×D83—21no—
162C2×C4×D83—21no—
163#13050579—22no—
164#13050579—22no—
165D664—22no—
166D664—22no—
167#13050573—81no—
168#13050573—81no—
169C2×C83⋊C8—21no—
170C2×C83⋊C8—21no—
171C2×C83⋊C8—21no—
172C2×C83⋊C8—21no—
173C2×C83⋊C8—81no—
174C8×D83—81no—
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—
185C22⋊Dic83—21no—
186(C2×D83)⋊C4—21no—
187(C2×D83)⋊C4—21no—
188(C2×D83)⋊C4—21no—
189(C2×D83)⋊C4—21no—
190(C2×D83)⋊C4—21no—
191(C2×D83)⋊C4—21no—
192C4×Dic83—21no—
193C4×Dic83—21no—
194C4×Dic83—21no—
195C22×C4×C83C22×C411yescharacteristic
196C22×C4×C83C2×D411yescharacteristic
197C22×C4×C83#4111yescharacteristic
198C2×C8×C83—21no—
199C2×C8×C83—21no—
200C2×C8×C83C22×C411yescharacteristic
201C2×C8×C83C22×C411yescharacteristic
202C2×C8×C83C22×C411yescharacteristic
203C2×C8×C83C22×C411yescharacteristic
204C2×C8×C83C2×D411yescharacteristic
205C2×C8×C83C2×D411yescharacteristic
206C2×C8×C83C2×D411yescharacteristic
207C2×C8×C83C2×D411yescharacteristic
208C42×C83C22×C411yescharacteristic
209C42×C83C2×D411yescharacteristic
210C42×C83#4111yescharacteristic
211C42×C83C2411yescharacteristic
212C23×C83C4×D411yescharacteristic
213C22×D83—21no—
214C22×D83—21no—
215C22×D83—21no—
216C2×C4×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—41no—
221C2×C4×C83C4×D411yescharacteristic
222C2×C4×C83C4×D411yescharacteristic
223C2×C4×C83C4×D411yescharacteristic
224C2×C4×C83C23×C411yescharacteristic
225C2×C4×C83C22×D411yescharacteristic
226C2×C4×C83C2×#4111yescharacteristic
227C22⋊D83—24no—
228C22⋊D83—81no—
229C22⋊D83—81no—
230C2×Dic83—21no—
231C2×Dic83—21no—
232C2×Dic83—21no—
233C2×Dic83—21no—
234C2×Dic83—21no—
235D332—21no—
236D332—21no—
237D332—21no—
238D332—21no—
239D332—21no—
240D332—81no—
241D332—81no—
242D332#13112yes—
243C4×D83—24no—
244C4×D83—41no—
245C4×D83—41no—
246C4×D83—41no—
247C4×D83—41no—
248C4×D83—41no—
249C4×D83—41no—
250C4×D83—81no—
251Dic166—21no—
252Dic166—81no—
253Dic166#13112yes—
254C8×C83—21no—
255C8×C83—21no—
256C8×C83—21no—
257C8×C83—21no—
258C8×C83—21no—
259C8×C83—21no—
260C8×C83—21no—
261C8×C83—21no—
262C8×C83—41no—
263C8×C83—41no—
264C83⋊C8—41no—
265C83⋊C8—41no—
266C83⋊C8—41no—
267C83⋊C8—41no—
268C22×C83—21no—
269C22×C83—21no—
270C22×C83—21no—
271C22×C83C2×C4×D411yescharacteristic
272C2×D83—22no—
273C2×D83—41no—
274C2×D83—41no—
275C2×D83—41no—
276C2×D83—41no—
277C2×D83—41no—
278C2×D83—41no—
279C2×D83—41no—
280C2×D83—41no—
281C4×C83—21no—
282C4×C83—21no—
283C4×C83—21no—
284C4×C83—21no—
285C4×C83C2×#13111yescharacteristic
286C4×C83C2×#13111yescharacteristic
287C4×C83#57611yescharacteristic
288C4×C83#57711yescharacteristic
289Dic83—22no—
290Dic83—41no—
291Dic83—41no—
292Dic83—41no—
293Dic83—41no—
294#17920—831nomaximal, Sylow
295C2×C83—41no—
296C2×C83#292911yescharacteristic
297C2×C83#294611yescharacteristic
298C2×C83#295711yescharacteristic
299D83—42no—
300D83—81no—
301D83—81no—
302#3106—831no—
303#2988—831no—
304#2981—831no—
305#1588—831no—
306#1586—831no—
307#1583—831no—
308#1581—831no—
309#1580—831no—
310SD16⋊C8—831no—
311C8×SD16—831no—
312C8×D8—831no—
313#1573—831no—
314#1488—831no—
315#1480—831no—
316#1454D8311yescharacteristic, complemented
317C83#1792011yescharacteristic, complemented, Sylow
318#532—831no—
319C4×#41—831no—
320#482—831no—
321#482—831no—
322#477—831no—
323#476—831no—
324#460—831no—
325#459—831no—
326#449—831no—
327#449—831no—
328C8×Q8—831no—
329C8×Q8—831no—
330C4×SD16—831no—
331C4×SD16—831no—
332C4×D8—831no—
333C4×D8—831no—
334#436—831no—
335#436—831no—
336#435—1661no—
337#435—1661no—
338C8×D4—831no—
339C8×D4—831no—
340C8×D4—831no—
341C8×D4—831no—
342C8×D4—1661no—
343C8×D4—1661no—
344#432—831no—
345#431—1661no—
346#431C2×D8311yescharacteristic
347#431C2×D8311yescharacteristic
348#431C2×D8311yescharacteristic
349C2×C4⋊C8—831no—
350C2×C4⋊C8—1661no—
351#408—1661no—
352#408—1661no—
353#335—831no—
354#335—831no—
355#334—831no—
356#334—831no—
357Q8⋊C8—831no—
358Q8⋊C8—831no—
359D4⋊C8—831no—
360D4⋊C8—831no—
361D4⋊C8—831no—
362D4⋊C8—831no—
363D4⋊C8—831no—
364D4⋊C8—831no—
365#322C2×D8311yescharacteristic
366#322C2×D8311yescharacteristic
367#322C2×D8311yescharacteristic
368C82C2×D8311yescharacteristic
369C2×#41—831no—
370C2×#41—1661no—
371C2×SD16—831no—
372C2×SD16—831no—
373C2×D8—831no—
374C2×D8—831no—
375C2×M16—1661no—
376C2×M16—1661no—
377C22×C8—1661no—
378C22×C8—1661no—
379C22×C8—1661no—
380C22×C8—1661no—
381C22×C8—1661no—
382C4⋊Q8—831no—
383#127—831no—
384#124—1661no—
385#121—831no—
386#121—831no—
387#121—1661no—
388C4×Q8—831no—
389C4×Q8—831no—
390C4×D4—831no—
391C4×D4—831no—
392C4×D4—831no—
393C4×D4—831no—
394C4×D4—1661no—
395C4×D4—1661no—
396C4×D4—1661no—
397#117—831no—
398#117—1661no—
399C2×C42—1661no—
400C2×C42C22×D8311yescharacteristic
401#107—831no—
402#107—831no—
403#106—831no—
404#106—831no—
405C4⋊C8—21no—
406C4⋊C8—831no—
407C4⋊C8—831no—
408C4⋊C8—831no—
409C4⋊C8—831no—
410C4⋊C8—1661no—
411C4⋊C8—1661no—
412C4⋊C8—1661no—
413C4⋊C8C4×D8311yescharacteristic
414C4⋊C8C4×D8311yescharacteristic
415C4⋊C8D33211yescharacteristic
416C4⋊C8D33211yescharacteristic
417#103—831no—
418#103—831no—
419#102—831no—
420#102—831no—
421#102—831no—
422#102—831no—
423#102—831no—
424#102—831no—
425C22⋊C8—21no—
426C22⋊C8—1661no—
427C22⋊C8—1661no—
428C22⋊C8—1661no—
429C22⋊C8—1661no—
430C22⋊C8—1661no—
431C22⋊C8—1661no—
432C22⋊C8—1661no—
433C22⋊C8C4×D8311yescharacteristic
434C22⋊C8C4×D8311yescharacteristic
435C22⋊C8D33211yescharacteristic
436C22⋊C8D33211yescharacteristic
437#97—1661no—
438C4×C8—1661no—
439C4×C8—1661no—
440C4×C8C22×D8311yescharacteristic
441C4×C8C22×D8311yescharacteristic
442C4×C8C22×D8311yescharacteristic
443C4×C8C22×D8311yescharacteristic
444C4×C8C22×D8311yescharacteristic
445C4×C8C22×D8311yescharacteristic
446#41—6641no—
447#41—6641no—
448#41—1662no—
449#41—1662no—
450C2×Q8—831no—
451C2×Q8—1661no—
452C2×D4—831no—
453C2×D4—831no—
454C2×D4—831no—
455C2×D4—1661no—
456C2×D4—1661no—
457C2×D4—1661no—
458C2×D4—1661no—
459C2×D4—1661no—
460C22×C4—1661no—
461C22×C4—1661no—
462C22×C4—1661no—
463C22×C4—1661no—
464C22×C4—1661no—
465C22×C4C2×C4×D8311yescharacteristic
466C22×C4C2×D33211yescharacteristic
467C22×C4#1305059011yescharacteristic
468SD16—1662no—
469SD16—1662no—
470D8—1662no—
471D8—1662no—
472M16—6641no—
473M16—6641no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—6641no—
477C2×C8—6641no—
478C2×C8—6641no—
479C2×C8—6641no—
480C2×C8—6641no—
481C2×C8—1661no—
482C2×C8—1661no—
483C2×C8—1661no—
484C2×C8—1661no—
485C2×C8C2×C4×D8311yescharacteristic
486C2×C8C2×C4×D8311yescharacteristic
487C2×C8C2×C4×D8311yescharacteristic
488C2×C8C2×C4×D8311yescharacteristic
489C2×C8C2×D33211yescharacteristic
490C2×C8C2×D33211yescharacteristic
491C2×C8C2×D33211yescharacteristic
492C2×C8C2×D33211yescharacteristic
493C4⋊C4—831no—
494C4⋊C4—831no—
495C4⋊C4—831no—
496C4⋊C4—831no—
497C4⋊C4—1661no—
498C4⋊C4—1661no—
499C4⋊C4—1661no—
500C22⋊C4—1661no—
501C22⋊C4—1661no—
502C22⋊C4—1661no—
503C22⋊C4—1661no—
504C22⋊C4—1661no—
505C22⋊C4—1661no—
506C22⋊C4—1661no—
507C42—1661no—
508C42—1661no—
509C42—1661no—
510C42C2×C4×D8311yescharacteristic
511C42C2×D33211yescharacteristic
512C42#1305059011yescharacteristic
513C42C23×D8311yescharacteristic
514C23—1661no—
515C23—1661no—
516C23—1661no—
517C23C4×D33211yescharacteristic
518Q8—832no—
519Q8—6641no—
520Q8—1661no—
521D4—832no—
522D4—6641no—
523D4—6641no—
524D4—6641no—
525D4—6641no—
526D4—1664no—
527D4—1661no—
528D4—1661no—
529D4—1661no—
530D4—1661no—
531D4—1661no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—3321no—
538C2×C4—3321no—
539C2×C4—3321no—
540C2×C4—3321no—
541C2×C4—3321no—
542C2×C4—3321no—
543C2×C4—6641no—
544C2×C4—1664no—
545C2×C4—1661no—
546C2×C4—1661no—
547C2×C4—1661no—
548C2×C4—1661no—
549C2×C4—1661no—
550C2×C4C4×D33211yescharacteristic
551C2×C4C4×D33211yescharacteristic
552C2×C4C4×D33211yescharacteristic
553C2×C4C22×C4×D8311yescharacteristic
554C2×C4C22×D33211yescharacteristic
555C2×C4C2×#1305059011yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—21no—
564C8—41no—
565C8—41no—
566C8—3321no—
567C8—3321no—
568C8—3321no—
569C8—3321no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—3321no—
574C22—3321no—
575C22—3321no—
576C22—3321no—
577C22—3321no—
578C22—3321no—
579C22—3321no—
580C22—3321no—
581C22—1662no—
582C22C2×C4×D33211yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—3321no—
588C4—3321no—
589C4—3321no—
590C4—3321no—
591C4—1662no—
592C4#131×D8311yescharacteristic
593C4#131×D8311yescharacteristic
594C4#1912850611yescharacteristic
595C4#1912851311yescharacteristic
596C2—41no—
597C2—3322no—
598C2—6641no—
599C2—6641no—
600C2#2491615911yescharacteristic
601C2#2491629711yescharacteristic
602C2#2491638111yescharacteristic
subgroupG/H
centerC2×C4C22×D332
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1454C2
socleC22×C83C2×C4×D4
prime radical#24917524C2
cosocleC42×C83C24
hypercenter#1454D83
hypocenterC83#17920
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
2. #24916571C2semidirect
3. #24916538C2semidirect
4. #24906343C2semidirect
5. #24906329C2semidirect
6. #24906308C2semidirect
7. #24906294C2semidirect
8. #24906288C2semidirect
9. #24906277C2semidirect
10. C8×#13050579C2semidirect
11. C8×D664C2semidirect
12. #24906248C2semidirect
13. #24905898C2semidirect
14. #24905863C2semidirect
15. C83×#1454C2semidirect
316. #1454D83semidirect
317. C83#17920semidirect

Maximal subgroups

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

subgroupindex
#249175242
#249165712
#249165382
#249063432
#249063292
#249063082
#249062942
#249062882
#249062772
C8×#130505792
C8×D6642
#249062482
#249058982
#249058632
C83×#14542
#1792083