Finite Group Databasebeta

← #35374311

Subgroups — #35374311

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#24917485C211yesmaximal, characteristic
2#24916440C211yesmaximal, characteristic, complemented
3C8×#13050589C211yesmaximal, characteristic, complemented
4#24906316C211yesmaximal, characteristic, complemented
5#24906305C211yesmaximal, characteristic, complemented
6#24906300C211yesmaximal, characteristic, complemented
7#24906289C211yesmaximal, characteristic, complemented
8C8×#13050580C211yesmaximal, characteristic, complemented
9C8×#13050579C211yesmaximal, characteristic, complemented
10C8×#13050575C211yesmaximal, characteristic, complemented
11#24906240C211yesmaximal, characteristic, complemented
12#24905894C211yesmaximal, characteristic, complemented
13#24905870C211yesmaximal, characteristic, complemented
14#24905745C211yesmaximal, characteristic, complemented
15C8×SD16×C83C211yesmaximal, characteristic, complemented
16#19128238C2211yescharacteristic
17C4×#13050589C2211yescharacteristic
18#19128040C411yescharacteristic
19#19128027C411yescharacteristic
20#19128011C411yescharacteristic
21#19128003C411yescharacteristic
22#19127926C411yescharacteristic
23#19127918C411yescharacteristic
24#19127860C411yescharacteristic
25#19127847C411yescharacteristic
26#19127832C2211yescharacteristic
27C8×Dic166C2211yescharacteristic
28#19127825C2211yescharacteristic
29C4×#13050580C2211yescharacteristic
30C4×#13050579C2211yescharacteristic
31C4×#13050575C2211yescharacteristic
32#19127778C2211yescharacteristic
33#19127771—21no—
34C8×D332—21no—
35C8×D332C2211yescharacteristic
36D4×C83⋊C8C2211yescharacteristic
37C8×C22⋊D83—21no—
38(C22⋊D83)⋊C8—21no—
39#19127761—21no—
40#19127757C2211yescharacteristic
41#19127753C2211yescharacteristic
42#19127752C2211yescharacteristic
43#19127752C2211yescharacteristic
44#19127751—21no—
45#19127655—21no—
46C2×C8×Dic83—21no—
47C4×C8×D83C2211yescharacteristic
48#19127453C2211yescharacteristic
49#19127453C2211yescharacteristic
50#19127452C2211yescharacteristic
51#19127433C2211yescharacteristic
52Q8⋊(C83⋊C8)C2211yescharacteristic
53#19127431C2211yescharacteristic
54#19127430C2211yescharacteristic
55D4⋊(C83⋊C8)C2211yescharacteristic
56#19127428C2211yescharacteristic
57#19127423C2211yescharacteristic
58#19127423C2211yescharacteristic
59C8×C83⋊C8C2211yescharacteristic
60C8×Q8×C83C2211yescharacteristic
61C4×SD16×C83C2211yescharacteristic
62C8×D4×C83C2211yescharacteristic
63#334×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65D4⋊C8×C83C2211yescharacteristic
66C82×C83C2211yescharacteristic
67C2×#13050589C2×C411yescharacteristic
68C2×#13050580C2×C411yescharacteristic
69C2×#13050579C2×C411yescharacteristic
70C2×#13050575C2×C411yescharacteristic
71C2×#13050573—21no—
72C22×C83⋊C8—21no—
73C2×C8×D83—21no—
74C2×C8×D83D411yescharacteristic
75C2×C8×D83D411yescharacteristic
76#14581787—21no—
77#14581783C2×C411yescharacteristic
78#14581781C2×C411yescharacteristic
79#14581777—21no—
80#14581768C2×C411yescharacteristic
81#14581767C2×C411yescharacteristic
82C4×Dic166C2311yescharacteristic
83#14581757C2×C411yescharacteristic
84C4×D332—21no—
85C4×D332C2311yescharacteristic
86D4×Dic83C2×C411yescharacteristic
87C4×C22⋊D83—21no—
88(C22⋊D83)⋊C4—21no—
89#14581750C2×C411yescharacteristic
90#14581749—21no—
91#14581748—21no—
92C2×C4×Dic83—21no—
93C42×D83C2311yescharacteristic
94#14581725C2×C411yescharacteristic
95#14581725C2×C411yescharacteristic
96#14581724C2×C411yescharacteristic
97C4⋊(C83⋊C8)—21no—
98C4⋊(C83⋊C8)C2311yescharacteristic
99C4⋊(C83⋊C8)C2311yescharacteristic
100Dic83⋊C8—21no—
101Dic83⋊C8—21no—
102Dic83⋊C8—21no—
103Dic83⋊C8C2×C411yescharacteristic
104Dic83⋊C8C2×C411yescharacteristic
105#14581717C2×C411yescharacteristic
106#14581716C2×C411yescharacteristic
107#14581715C2×C411yescharacteristic
108#14581714C2×C411yescharacteristic
109#14581713C2×C411yescharacteristic
110#14581712C2×C411yescharacteristic
111C22⋊(C83⋊C8)—21no—
112(C2×D83)⋊C8—21no—
113(C2×D83)⋊C8—21no—
114(C2×D83)⋊C8—21no—
115(C2×D83)⋊C8—21no—
116(C2×D83)⋊C8—21no—
117(C2×D83)⋊C8C2×C411yescharacteristic
118(C2×D83)⋊C8C2×C411yescharacteristic
119#14581703—21no—
120#14581702—21no—
121C4×C83⋊C8C2311yescharacteristic
122C4×C83⋊C8C2311yescharacteristic
123C4×C83⋊C8C2311yescharacteristic
124C8×Dic83—21no—
125C8×Dic83—21no—
126C8×Dic83—21no—
127C8×Dic83D411yescharacteristic
128C8×Dic83D411yescharacteristic
129C2×SD16×C83C2×C411yescharacteristic
130C22×C8×C83—21no—
131C4×Q8×C83C2311yescharacteristic
132C4×D4×C83C2311yescharacteristic
133#106×C83C2×C411yescharacteristic
134C4⋊C8×C83—21no—
135C4⋊C8×C83C2311yescharacteristic
136C4⋊C8×C83C2311yescharacteristic
137#103×C83C2×C411yescharacteristic
138#102×C83C2×C411yescharacteristic
139C22⋊C8×C83—21no—
140C4×C8×C83—21no—
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#13050589—22no—
145#13050589—22no—
146C2×Dic166C22×C411yescharacteristic
147C2×D332—21no—
148C2×D332C22×C411yescharacteristic
149C2×C22⋊D83—21no—
150C22×Dic83—21no—
151C22×Dic83—21no—
152C2×C4×D83—21no—
153C2×C4×D83C22×C411yescharacteristic
154C2×C4×D83C2×D411yescharacteristic
155C2×C4×D83#4111yescharacteristic
156#13050580—22no—
157#13050579—22no—
158#13050575—22no—
159#13050573—42no—
160C2×C83⋊C8—21no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8—21no—
163C2×C83⋊C8—42no—
164C2×C83⋊C8C22×C411yescharacteristic
165C2×C83⋊C8C22×C411yescharacteristic
166C2×C83⋊C8C2×D411yescharacteristic
167C2×C83⋊C8C2×D411yescharacteristic
168C8×D83—22no—
169C8×D83—22no—
170C8×D83—42no—
171C4⋊Dic83—21no—
172C4⋊Dic83C22×C411yescharacteristic
173C4⋊Dic83C22×C411yescharacteristic
174Dic83⋊C4—21no—
175Dic83⋊C4—21no—
176Dic83⋊C4—21no—
177Dic83⋊C4—21no—
178C22⋊Dic83—21no—
179(C2×D83)⋊C4—21no—
180(C2×D83)⋊C4—21no—
181(C2×D83)⋊C4—21no—
182(C2×D83)⋊C4—21no—
183(C2×D83)⋊C4—21no—
184(C2×D83)⋊C4—21no—
185C4×Dic83—21no—
186C4×Dic83—21no—
187C4×Dic83—21no—
188C4×Dic83C22×C411yescharacteristic
189C4×Dic83C2×D411yescharacteristic
190C4×Dic83#4111yescharacteristic
191C2×Q8×C83C22×C411yescharacteristic
192C2×D4×C83C22×C411yescharacteristic
193C22×C4×C83—21no—
194SD16×C83—22no—
195C2×C8×C83—21no—
196C2×C8×C83—21no—
197C2×C8×C83—21no—
198C2×C8×C83—42no—
199C2×C8×C83C22×C411yescharacteristic
200C2×C8×C83C22×C411yescharacteristic
201C2×C8×C83C2×D411yescharacteristic
202C2×C8×C83C2×D411yescharacteristic
203C4⋊C4×C83—21no—
204C4⋊C4×C83C22×C411yescharacteristic
205C4⋊C4×C83C22×C411yescharacteristic
206C22⋊C4×C83—21no—
207C42×C83—21no—
208C42×C83C2411yescharacteristic
209C23×C83—21no—
210C22×D83—21no—
211C22×D83C4×D411yescharacteristic
212Q8×C83—21no—
213Q8×C83—21no—
214D4×C83—21no—
215D4×C83#13112yes—
216C2×C4×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—41no—
220C2×C4×C83—41no—
221C2×C4×C83C23×C411yescharacteristic
222C2×C4×C83C22×D411yescharacteristic
223C2×C4×C83C2×#4111yescharacteristic
224C22⋊D83—24no—
225C2×Dic83—24no—
226C2×Dic83—21no—
227C2×Dic83—21no—
228C2×Dic83—21no—
229C2×Dic83—42no—
230C2×Dic83C4×D411yescharacteristic
231C2×Dic83C4×D411yescharacteristic
232C2×Dic83C4×D411yescharacteristic
233D332—21no—
234D332—21no—
235D332—42no—
236C4×D83—21no—
237C4×D83—21no—
238C4×D83—21no—
239C4×D83—21no—
240C4×D83—41no—
241C4×D83—41no—
242C4×D83—41no—
243Dic166—21no—
244Dic166#13112yes—
245C8×C83—21no—
246C8×C83—21no—
247C8×C83—21no—
248C8×C83—41no—
249C8×C83—41no—
250C8×C83—41no—
251C8×C83#13512yes—
252C83⋊C8—21no—
253C83⋊C8—21no—
254C83⋊C8—21no—
255C83⋊C8—41no—
256C83⋊C8—41no—
257C83⋊C8—41no—
258C83⋊C8#13512yes—
259C22×C83—22no—
260C22×C83—41no—
261C22×C83—41no—
262C22×C83C2×C4×D411yescharacteristic
263C2×D83—21no—
264C2×D83—21no—
265C2×D83—21no—
266C2×D83—41no—
267C2×D83—41no—
268C2×D83—41no—
269C4×C83—21no—
270C4×C83—41no—
271C4×C83—41no—
272C4×C83—41no—
273C4×C83C2×#13111yescharacteristic
274C4×C83C2×#13111yescharacteristic
275C4×C83C2×#13511yescharacteristic
276C4×C83C2×#13511yescharacteristic
277Dic83—22no—
278Dic83—21no—
279Dic83—21no—
280Dic83—21no—
281Dic83—41no—
282Dic83—41no—
283#17904—831nomaximal, Sylow
284C2×C83—42no—
285C2×C83#292911yescharacteristic
286C2×C83C4×#13511yescharacteristic
287C2×C83#295511yescharacteristic
288D83—41no—
289D83—81no—
290#3102—831no—
291#2966—831no—
292C8×#41—831no—
293#1584—831no—
294#1583—831no—
295#1582—831no—
296#1581—831no—
297C8×Q16—831no—
298C8×SD16—831no—
299C8×SD16D8311yescharacteristic, complemented
300C8×D8—831no—
301#1572—831no—
302#1488—831no—
303#1482—831no—
304#1450—831no—
305C83#1790411yescharacteristic, complemented, Sylow
306#529—831no—
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#446—831no—
317C8×Q8—831no—
318C8×Q8—831no—
319C8×Q8C2×D8311yescharacteristic
320C4×Q16—831no—
321C4×SD16—831no—
322C4×SD16C2×D8311yescharacteristic
323C4×D8—831no—
324#436—831no—
325#435—1661no—
326C8×D4—831no—
327C8×D4—831no—
328C8×D4—1661no—
329C8×D4—1661no—
330C8×D4—1661no—
331C8×D4C2×D8311yescharacteristic
332#433—1661no—
333#432—831no—
334#431—831no—
335#431—831no—
336#431—831no—
337#431—1661no—
338#405—1661no—
339C2×C4×C8—831no—
340C2×C4×C8—1661no—
341#335—831no—
342#335—831no—
343#334—831no—
344#334C2×D8311yescharacteristic
345Q8⋊C8—831no—
346Q8⋊C8—831no—
347Q8⋊C8—831no—
348Q8⋊C8C2×D8311yescharacteristic
349D4⋊C8—831no—
350D4⋊C8—831no—
351D4⋊C8—831no—
352D4⋊C8C2×D8311yescharacteristic
353#322—831no—
354#322—831no—
355C82—831no—
356C82C2×D8311yescharacteristic
357C2×#41—831no—
358C2×Q16—831no—
359C2×SD16—831no—
360C2×SD16C4×D8311yescharacteristic
361C2×D8—831no—
362C2×M16—1661no—
363C22×C8—21no—
364C22×C8—831no—
365C22×C8—831no—
366C22×C8—1661no—
367C22×C8—1661no—
368#126—1661no—
369#125—831no—
370#124—831no—
371#123—1661no—
372C22⋊Q8—831no—
373#121—831no—
374C4×Q8—831no—
375C4×Q8—831no—
376C4×Q8C22×D8311yescharacteristic
377C4×D4—831no—
378C4×D4—831no—
379C4×D4—1661no—
380C4×D4—1661no—
381C4×D4—1661no—
382C4×D4C22×D8311yescharacteristic
383#117—831no—
384#117—1661no—
385#117—1661no—
386C2×C42—831no—
387C2×C42—1661no—
388#107—831no—
389#107—831no—
390#106—831no—
391#106C4×D8311yescharacteristic
392C4⋊C8—21no—
393C4⋊C8—831no—
394C4⋊C8—831no—
395C4⋊C8—831no—
396C4⋊C8—831no—
397C4⋊C8—1661no—
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#103C4×D8311yescharacteristic
407#102—831no—
408#102—831no—
409#102—831no—
410#102C4×D8311yescharacteristic
411C22⋊C8—21no—
412C22⋊C8—831no—
413C22⋊C8—831no—
414C22⋊C8—1661no—
415C22⋊C8—1661no—
416C22⋊C8—1661no—
417C22⋊C8—1661no—
418C22⋊C8—1661no—
419C22⋊C8—1661no—
420#97—1661no—
421#97—1661no—
422C4×C8—21no—
423C4×C8—831no—
424C4×C8—831no—
425C4×C8—831no—
426C4×C8—831no—
427C4×C8—831no—
428C4×C8—1661no—
429C4×C8—1661no—
430C4×C8—1661no—
431C4×C8C22×D8311yescharacteristic
432C4×C8C22×D8311yescharacteristic
433C4×C8C22×D8311yescharacteristic
434#41—1662no—
435#41—1662no—
436C2×Q8—831no—
437C2×Q8C2×C4×D8311yescharacteristic
438C2×D4—831no—
439C2×D4—1661no—
440C2×D4—1661no—
441C2×D4C2×C4×D8311yescharacteristic
442C22×C4—21no—
443C22×C4—831no—
444C22×C4—831no—
445C22×C4—831no—
446C22×C4—1661no—
447C22×C4—1661no—
448C22×C4—1661no—
449Q16—1662no—
450SD16—22no—
451SD16—1662no—
452D8—1662no—
453M16—3322no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—42no—
458C2×C8—3322no—
459C2×C8—3322no—
460C2×C8—831no—
461C2×C8—831no—
462C2×C8—831no—
463C2×C8—831no—
464C2×C8—1662no—
465C2×C8—1661no—
466C2×C8—1661no—
467C2×C8—1661no—
468C2×C8—1662no—
469C2×C8C2×C4×D8311yescharacteristic
470C2×C8C2×C4×D8311yescharacteristic
471C2×C8D4×D8311yescharacteristic
472C2×C8D4×D8311yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—831no—
475C4⋊C4—831no—
476C4⋊C4—1661no—
477C4⋊C4—1661no—
478C4⋊C4—1661no—
479C4⋊C4—1661no—
480C4⋊C4—1661no—
481C4⋊C4C2×C4×D8311yescharacteristic
482C4⋊C4C2×C4×D8311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—1661no—
485C22⋊C4—1661no—
486C22⋊C4—1661no—
487C22⋊C4—1661no—
488C22⋊C4—1661no—
489C22⋊C4—1661no—
490C22⋊C4—1661no—
491C42—21no—
492C42—831no—
493C42—831no—
494C42—831no—
495C42—1661no—
496C42—1661no—
497C42—1661no—
498C42C23×D8311yescharacteristic
499C23—21no—
500C23—831no—
501C23—1661no—
502Q8—21no—
503Q8—21no—
504Q8—832no—
505Q8—1661no—
506D4—21no—
507D4—3322no—
508D4—1664no—
509D4—1661no—
510D4—1661no—
511D4#1458179812yes—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—3321no—
518C2×C4—3322no—
519C2×C4—3321no—
520C2×C4—3321no—
521C2×C4—831no—
522C2×C4—831no—
523C2×C4—831no—
524C2×C4—1661no—
525C2×C4—1661no—
526C2×C4—1664no—
527C2×C4—1661no—
528C2×C4—1661no—
529C2×C4—1661no—
530C2×C4—1661no—
531C2×C4—1661no—
532C2×C4C22×C4×D8311yescharacteristic
533C2×C4C2×D4×D8311yescharacteristic
534C2×C4#41×D8311yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—3321no—
542C8—3321no—
543C8—3321no—
544C8—832no—
545C8—1661no—
546C8—1661no—
547C8—1661no—
548C8#1458181312yes—
549C22—22no—
550C22—41no—
551C22—41no—
552C22—3321no—
553C22—3321no—
554C22—3321no—
555C22—1661no—
556C22—1661no—
557C22—1661no—
558C22C4×D4×D8311yescharacteristic
559C4—21no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—3321no—
564C4—3321no—
565C4—1661no—
566C4—1661no—
567C4—1661no—
568C4—1662no—
569C4#131×D8311yescharacteristic
570C4C2×#1458179811yescharacteristic
571C4#135×D8311yescharacteristic
572C4C2×#1458181311yescharacteristic
573C2—42no—
574C2—3321no—
575C2—6641no—
576C2#2491615211yescharacteristic
577C2C4×#1458181311yescharacteristic
578C2#2491636111yescharacteristic
subgroupG/H
centerC2×C8D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC8×SD16×C83C2
socleC22×C83C2×C4×D4
prime radical#19127847C4
cosocleC42×C83C24
hypercenterC8×SD16D83
hypocenterC83#17904
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
2. #24916440C2semidirect
3. C8×#13050589C2semidirect
4. #24906316C2semidirect
5. #24906305C2semidirect
6. #24906300C2semidirect
7. #24906289C2semidirect
8. C8×#13050580C2semidirect
9. C8×#13050579C2semidirect
10. C8×#13050575C2semidirect
11. #24906240C2semidirect
12. #24905894C2semidirect
13. #24905870C2semidirect
14. #24905745C2semidirect
15. C8×SD16×C83C2semidirect
299. C8×SD16D83semidirect
305. C83#17904semidirect

Maximal subgroups

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

subgroupindex
#249174852
#249164402
C8×#130505892
#249063162
#249063052
#249063002
#249062892
C8×#130505802
C8×#130505792
C8×#130505752
#249062402
#249058942
#249058702
#249057452
C8×SD16×C832
#1790483