Finite Group Databasebeta

← #35374306

Subgroups — #35374306

Order 21248.

634 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917475C211yesmaximal, characteristic
2C8×#13050590C211yesmaximal, characteristic, complemented
3#24906311C211yesmaximal, characteristic, complemented
4#24906304C211yesmaximal, characteristic, complemented
5#24906297C211yesmaximal, characteristic, complemented
6#24906290C211yesmaximal, characteristic, complemented
7C8×#13050580C211yesmaximal, characteristic, complemented
8C8×#13050577C211yesmaximal, characteristic, complemented
9C8×#13050578C211yesmaximal, characteristic, complemented
10C8×#13050575C211yesmaximal, characteristic, complemented
11#24906244C211yesmaximal, characteristic, complemented
12#24905895C211yesmaximal, characteristic, complemented
13#24905871C211yesmaximal, characteristic, complemented
14#24905746C211yesmaximal, characteristic, complemented
15C83×#2966C211yesmaximal, characteristic, complemented
16C4×#13050590C2211yescharacteristic
17#19128039C411yescharacteristic
18#19128022C411yescharacteristic
19#19128005C411yescharacteristic
20#19127998C411yescharacteristic
21#19127920C411yescharacteristic
22#19127913C411yescharacteristic
23#19127861C411yescharacteristic
24#19127844C411yescharacteristic
25C8×Dic166C2211yescharacteristic
26C8×Dic166C2211yescharacteristic
27C4×#13050580C2211yescharacteristic
28C4×#13050577C2211yescharacteristic
29C4×#13050578C2211yescharacteristic
30C4×#13050575C2211yescharacteristic
31C8×D332C2211yescharacteristic
32C8×D332C2211yescharacteristic
33C8×C22⋊D83—21no—
34C8×C22⋊D83—21no—
35#19127754C2211yescharacteristic
36#19127754C2211yescharacteristic
37#19127754C2211yescharacteristic
38#19127752—21no—
39C4×C8×D83—21no—
40#19127453C2211yescharacteristic
41#19127453C2211yescharacteristic
42#19127451C2211yescharacteristic
43#19127451C2211yescharacteristic
44Q8⋊(C83⋊C8)C2211yescharacteristic
45Q8⋊(C83⋊C8)C2211yescharacteristic
46#19127431C2211yescharacteristic
47#19127431C2211yescharacteristic
48D4⋊(C83⋊C8)C2211yescharacteristic
49D4⋊(C83⋊C8)C2211yescharacteristic
50#19127428C2211yescharacteristic
51#19127428C2211yescharacteristic
52#19127422C2211yescharacteristic
53#19127422C2211yescharacteristic
54C8×C83⋊C8C2211yescharacteristic
55C8×C83⋊C8C2211yescharacteristic
56#529×C83C2211yescharacteristic
57#446×C83C2211yescharacteristic
58C8×Q8×C83C2211yescharacteristic
59#436×C83C2211yescharacteristic
60#435×C83—21no—
61C8×D4×C83—21no—
62C8×D4×C83C2211yescharacteristic
63#433×C83—21no—
64#432×C83C2211yescharacteristic
65#405×C83—21no—
66C2×C4×C8×C83C2211yescharacteristic
67C2×#13050590C2×C411yescharacteristic
68C2×#13050580C2×C411yescharacteristic
69C2×#13050578C2×C411yescharacteristic
70C2×#13050577C2×C411yescharacteristic
71C2×#13050575C2×C411yescharacteristic
72C2×C8×D83—21no—
73C2×C8×D83—21no—
74C4×Dic166C2×C411yescharacteristic
75C4×Dic166C2311yescharacteristic
76C4×D332C2×C411yescharacteristic
77C4×D332C2311yescharacteristic
78C4×C22⋊D83—21no—
79C4×C22⋊D83—21no—
80#14581751C2×C411yescharacteristic
81#14581749—21no—
82C42×D83—21no—
83#14581725C2×C411yescharacteristic
84#14581725C2×C411yescharacteristic
85#14581723C2×C411yescharacteristic
86#14581723C2×C411yescharacteristic
87C4⋊(C83⋊C8)—21no—
88C4⋊(C83⋊C8)C2×C411yescharacteristic
89C4⋊(C83⋊C8)C2×C411yescharacteristic
90C4⋊(C83⋊C8)C2311yescharacteristic
91C4⋊(C83⋊C8)C2311yescharacteristic
92Dic83⋊C8—21no—
93Dic83⋊C8—21no—
94#14581716C2×C411yescharacteristic
95#14581716C2×C411yescharacteristic
96#14581715C2×C411yescharacteristic
97#14581715C2×C411yescharacteristic
98#14581713C2×C411yescharacteristic
99#14581713C2×C411yescharacteristic
100#14581712C2×C411yescharacteristic
101#14581712C2×C411yescharacteristic
102C22⋊(C83⋊C8)—21no—
103C22⋊(C83⋊C8)—21no—
104C22⋊(C83⋊C8)C2×C411yescharacteristic
105C22⋊(C83⋊C8)C2×C411yescharacteristic
106(C2×D83)⋊C8—21no—
107(C2×D83)⋊C8—21no—
108C4×C83⋊C8—21no—
109C4×C83⋊C8C2311yescharacteristic
110C4×C83⋊C8C2311yescharacteristic
111C4×C83⋊C8C2311yescharacteristic
112C4×C83⋊C8C2311yescharacteristic
113C8×Dic83—21no—
114C8×Dic83—21no—
115C2×M16×C83—21no—
116C22×C8×C83—21no—
117C22×C8×C83D411yescharacteristic
118C22×C8×C83D411yescharacteristic
119#126×C83—21no—
120#125×C83C2×C411yescharacteristic
121#124×C83C2×C411yescharacteristic
122#123×C83—21no—
123C22⋊Q8×C83C2×C411yescharacteristic
124#121×C83C2×C411yescharacteristic
125C4×Q8×C83C2311yescharacteristic
126C4×D4×C83—21no—
127C4×D4×C83C2311yescharacteristic
128#117×C83—21no—
129C2×C42×C83C2311yescharacteristic
130C4⋊C8×C83—21no—
131C4⋊C8×C83—21no—
132C4⋊C8×C83C2311yescharacteristic
133C4⋊C8×C83C2311yescharacteristic
134C22⋊C8×C83—21no—
135C22⋊C8×C83—21no—
136C22⋊C8×C83—21no—
137#97×C83—21no—
138#97×C83—21no—
139C4×C8×C83—21no—
140C4×C8×C83D411yescharacteristic
141C4×C8×C83D411yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#13050590—22no—
145#13050590—22no—
146C2×Dic166C22×C411yescharacteristic
147C2×D332C22×C411yescharacteristic
148C2×C22⋊D83—21no—
149C2×C4×D83—21no—
150C2×C4×D83—21no—
151C2×C4×D83—21no—
152#13050580—22no—
153#13050578—22no—
154#13050577—22no—
155#13050575—22no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8C22×C411yescharacteristic
161C2×C83⋊C8C22×C411yescharacteristic
162C2×C83⋊C8C22×C411yescharacteristic
163C2×C83⋊C8C22×C411yescharacteristic
164C8×D83—42no—
165C8×D83—42no—
166C4⋊Dic83C22×C411yescharacteristic
167C4⋊Dic83C22×C411yescharacteristic
168Dic83⋊C4—21no—
169Dic83⋊C4—21no—
170C22⋊Dic83—21no—
171(C2×D83)⋊C4—21no—
172(C2×D83)⋊C4—21no—
173C4×Dic83—21no—
174C4×Dic83—21no—
175C4×Dic83—21no—
176C2×Q8×C83C22×C411yescharacteristic
177C2×D4×C83—21no—
178C2×D4×C83C22×C411yescharacteristic
179C22×C4×C83—21no—
180C22×C4×C83C22×C411yescharacteristic
181C22×C4×C83C2×D411yescharacteristic
182C22×C4×C83#4111yescharacteristic
183M16×C83—42no—
184C2×C8×C83—22no—
185C2×C8×C83—22no—
186C2×C8×C83—21no—
187C2×C8×C83—21no—
188C2×C8×C83—42no—
189C2×C8×C83C2×D411yescharacteristic
190C2×C8×C83C2×D411yescharacteristic
191C2×C8×C83C2×D411yescharacteristic
192C2×C8×C83C2×D411yescharacteristic
193C4⋊C4×C83—21no—
194C4⋊C4×C83—21no—
195C4⋊C4×C83—21no—
196C4⋊C4×C83—21no—
197C4⋊C4×C83C22×C411yescharacteristic
198C4⋊C4×C83C22×C411yescharacteristic
199C22⋊C4×C83—21no—
200C22⋊C4×C83—21no—
201C22⋊C4×C83—21no—
202C22⋊C4×C83—21no—
203C22⋊C4×C83—21no—
204C42×C83—21no—
205C42×C83C22×C411yescharacteristic
206C42×C83C2×D411yescharacteristic
207C42×C83#4111yescharacteristic
208C42×C83C2411yescharacteristic
209C23×C83—21no—
210C23×C83C4×D411yescharacteristic
211C22×D83—21no—
212Q8×C83—21no—
213Q8×C83—21no—
214D4×C83—21no—
215D4×C83—21no—
216D4×C83—42no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83—21no—
222C2×C4×C83—21no—
223C2×C4×C83—21no—
224C2×C4×C83—41no—
225C2×C4×C83—41no—
226C2×C4×C83—41no—
227C2×C4×C83C4×D411yescharacteristic
228C2×C4×C83C4×D411yescharacteristic
229C2×C4×C83C4×D411yescharacteristic
230C2×C4×C83C23×C411yescharacteristic
231C2×C4×C83C22×D411yescharacteristic
232C2×C4×C83C2×#4111yescharacteristic
233C22⋊D83—24no—
234C2×Dic83—21no—
235C2×Dic83—21no—
236C2×Dic83—21no—
237D332—21no—
238D332#13112yes—
239C4×D83—24no—
240C4×D83—42no—
241C4×D83—41no—
242C4×D83—41no—
243Dic166—21no—
244Dic166#13112yes—
245C8×C83—21no—
246C8×C83—21no—
247C8×C83—41no—
248C8×C83—41no—
249C8×C83#13512yes—
250C8×C83#13512yes—
251C83⋊C8—21no—
252C83⋊C8—21no—
253C83⋊C8—21no—
254C83⋊C8—21no—
255C83⋊C8—41no—
256C83⋊C8—41no—
257C83⋊C8—41no—
258C83⋊C8—41no—
259C22×C83—21no—
260C22×C83—21no—
261C22×C83—21no—
262C22×C83—41no—
263C22×C83—41no—
264C22×C83—41no—
265C22×C83C2×C4×D411yescharacteristic
266C2×D83—22no—
267C2×D83—41no—
268C2×D83—41no—
269C4×C83—21no—
270C4×C83—21no—
271C4×C83—21no—
272C4×C83—21no—
273C4×C83—41no—
274C4×C83—41no—
275C4×C83—41no—
276C4×C83C2×#13111yescharacteristic
277C4×C83C2×#13111yescharacteristic
278C4×C83C2×#13511yescharacteristic
279C4×C83C2×#13511yescharacteristic
280Dic83—22no—
281Dic83—41no—
282Dic83—41no—
283#17904—831nomaximal, Sylow
284C2×C83—41no—
285C2×C83—81no—
286C2×C83#292911yescharacteristic
287C2×C83C4×#13511yescharacteristic
288C2×C83#295511yescharacteristic
289D83—42no—
290#3102—831no—
291#2966D8311yescharacteristic, complemented
292C8×#41—831no—
293#1584—831no—
294#1583—831no—
295#1582—831no—
296#1581—831no—
297C8×Q16—831no—
298C8×SD16—831no—
299C8×SD16—831no—
300C8×D8—831no—
301#1572—831no—
302#1488—831no—
303#1482—831no—
304#1450—831no—
305C83#1790411yescharacteristic, complemented, Sylow
306#529C2×D8311yescharacteristic
307C4×#41—831no—
308#485—831no—
309#482—831no—
310#479—831no—
311#478—831no—
312#464—831no—
313#463—831no—
314#452—831no—
315#449—831no—
316#446C2×D8311yescharacteristic
317C8×Q8—831no—
318C8×Q8—831no—
319C8×Q8C2×D8311yescharacteristic
320C4×Q16—831no—
321C4×SD16—831no—
322C4×SD16—831no—
323C4×D8—831no—
324#436C2×D8311yescharacteristic
325#435—21no—
326C8×D4—21no—
327C8×D4—831no—
328C8×D4—831no—
329C8×D4—1661no—
330C8×D4—1661no—
331C8×D4C2×D8311yescharacteristic
332#433—21no—
333#432C2×D8311yescharacteristic
334#431—831no—
335#431—831no—
336#431—831no—
337#431—1661no—
338#405—21no—
339C2×C4×C8—1661no—
340C2×C4×C8C2×D8311yescharacteristic
341#335—831no—
342#335—831no—
343#334—831no—
344#334—831no—
345Q8⋊C8—831no—
346Q8⋊C8—831no—
347Q8⋊C8—831no—
348Q8⋊C8—831no—
349D4⋊C8—831no—
350D4⋊C8—831no—
351D4⋊C8—831no—
352D4⋊C8—831no—
353#322—831no—
354#322—831no—
355C82—831no—
356C82—831no—
357C2×#41—831no—
358C2×Q16—831no—
359C2×SD16—831no—
360C2×SD16—831no—
361C2×D8—831no—
362C2×M16—21no—
363C22×C8—21no—
364C22×C8—1661no—
365C22×C8—1661no—
366C22×C8C22⋊D8311yescharacteristic
367C22×C8C22⋊D8311yescharacteristic
368#126—21no—
369#125C4×D8311yescharacteristic
370#124C4×D8311yescharacteristic
371#123—21no—
372C22⋊Q8C4×D8311yescharacteristic
373#121C4×D8311yescharacteristic
374C4×Q8—831no—
375C4×Q8—831no—
376C4×Q8C22×D8311yescharacteristic
377C4×D4—21no—
378C4×D4—831no—
379C4×D4—831no—
380C4×D4—1661no—
381C4×D4—1661no—
382C4×D4C22×D8311yescharacteristic
383#117—21no—
384#117—831no—
385#117—1661no—
386C2×C42—1661no—
387C2×C42C22×D8311yescharacteristic
388#107—831no—
389#107—831no—
390#106—831no—
391#106—831no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—831no—
395C4⋊C8—831no—
396C4⋊C8—831no—
397C4⋊C8—831no—
398C4⋊C8—1661no—
399C4⋊C8—1661no—
400C4⋊C8—1661no—
401C4⋊C8C22×D8311yescharacteristic
402C4⋊C8C22×D8311yescharacteristic
403#103—831no—
404#103—831no—
405#103—831no—
406#103—831no—
407#102—831no—
408#102—831no—
409#102—831no—
410#102—831no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—831no—
415C22⋊C8—831no—
416C22⋊C8—1661no—
417C22⋊C8—1661no—
418C22⋊C8—1661no—
419C22⋊C8—1661no—
420#97—21no—
421#97—21no—
422C4×C8—21no—
423C4×C8—831no—
424C4×C8—831no—
425C4×C8—831no—
426C4×C8—831no—
427C4×C8—1661no—
428C4×C8—1661no—
429C4×C8—1661no—
430C4×C8C22⋊D8311yescharacteristic
431C4×C8C22⋊D8311yescharacteristic
432C4×C8C22×D8311yescharacteristic
433C4×C8C22×D8311yescharacteristic
434#41—1662no—
435#41—1662no—
436C2×Q8—831no—
437C2×Q8C2×C4×D8311yescharacteristic
438C2×D4—21no—
439C2×D4—831no—
440C2×D4—1661no—
441C2×D4C2×C4×D8311yescharacteristic
442C22×C4—21no—
443C22×C4—1661no—
444C22×C4—1661no—
445C22×C4—1661no—
446C22×C4C2×C4×D8311yescharacteristic
447C22×C4C2×C22⋊D8311yescharacteristic
448C22×C4#1305059011yescharacteristic
449Q16—1662no—
450SD16—1662no—
451SD16—1662no—
452D8—1662no—
453M16—42no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—42no—
459C2×C8—3322no—
460C2×C8—3322no—
461C2×C8—831no—
462C2×C8—831no—
463C2×C8—831no—
464C2×C8—831no—
465C2×C8—1661no—
466C2×C8—1661no—
467C2×C8—1661no—
468C2×C8—1661no—
469C2×C8C2×C22⋊D8311yescharacteristic
470C2×C8C2×C22⋊D8311yescharacteristic
471C2×C8C2×C22⋊D8311yescharacteristic
472C2×C8C2×C22⋊D8311yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—831no—
478C4⋊C4—831no—
479C4⋊C4—1661no—
480C4⋊C4—1661no—
481C4⋊C4C2×C4×D8311yescharacteristic
482C4⋊C4C2×C4×D8311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—1661no—
489C22⋊C4—1661no—
490C22⋊C4—1661no—
491C42—21no—
492C42—1661no—
493C42—1661no—
494C42—1661no—
495C42C2×C4×D8311yescharacteristic
496C42C2×C22⋊D8311yescharacteristic
497C42#1305059011yescharacteristic
498C42C23×D8311yescharacteristic
499C23—21no—
500C23—1661no—
501C23C4×C22⋊D8311yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—832no—
505Q8—1661no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—832no—
510D4—1664no—
511D4—1661no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—3322no—
523C2×C4—3321no—
524C2×C4—3321no—
525C2×C4—1664no—
526C2×C4—1661no—
527C2×C4—1661no—
528C2×C4—1661no—
529C2×C4C4×C22⋊D8311yescharacteristic
530C2×C4C4×C22⋊D8311yescharacteristic
531C2×C4C4×C22⋊D8311yescharacteristic
532C2×C4C22×C4×D8311yescharacteristic
533C2×C4C22×C22⋊D8311yescharacteristic
534C2×C4C2×#1305059011yescharacteristic
535C8—21no—
536C8—21no—
537C8—41no—
538C8—41no—
539C8—3321no—
540C8—3321no—
541C8—3321no—
542C8—3321no—
543C8—1661no—
544C8—1661no—
545C8—1661no—
546C8—1661no—
547C8#1458181212yes—
548C8#1458181212yes—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—3321no—
556C22—3321no—
557C22—1662no—
558C22C2×C4×C22⋊D8311yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—3321no—
567C4—3321no—
568C4—1662no—
569C4#131×D8311yescharacteristic
570C4#131×D8311yescharacteristic
571C4C2×#1458181211yescharacteristic
572C4C2×#1458181211yescharacteristic
573C2—41no—
574C2—81no—
575C2—3322no—
576C2#2491615511yescharacteristic
577C2C4×#1458181211yescharacteristic
578C2#2491636411yescharacteristic
subgroupG/H
centerC2×C8C2×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#2966C2
socleC22×C83C2×C4×D4
prime radical#19127844C4
cosocleC42×C83C24
hypercenter#2966D83
hypocenterC83#17904
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ #2966

Complements

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

NH ≅ G/Ntype
2. C8×#13050590C2semidirect
3. #24906311C2semidirect
4. #24906304C2semidirect
5. #24906297C2semidirect
6. #24906290C2semidirect
7. C8×#13050580C2semidirect
8. C8×#13050577C2semidirect
9. C8×#13050578C2semidirect
10. C8×#13050575C2semidirect
11. #24906244C2semidirect
12. #24905895C2semidirect
13. #24905871C2semidirect
14. #24905746C2semidirect
15. C83×#2966C2semidirect
291. #2966D83semidirect
305. C83#17904semidirect

Maximal subgroups

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

subgroupindex
#249174752
C8×#130505902
#249063112
#249063042
#249062972
#249062902
C8×#130505802
C8×#130505772
C8×#130505782
C8×#130505752
#249062442
#249058952
#249058712
#249057462
C83×#29662
#1790483