Finite Group Databasebeta

← #35374358

Subgroups — #35374358

Order 21248.

626 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#24917487C211yesmaximal, characteristic
2#24916440C211yesmaximal, characteristic, complemented
3C8×#13050591C211yesmaximal, characteristic, complemented
4#24906338C211yesmaximal, characteristic, complemented
5#24906335C211yesmaximal, characteristic, complemented
6#24906326C211yesmaximal, characteristic, complemented
7#24906323C211yesmaximal, characteristic, complemented
8#24906288C211yesmaximal, characteristic, complemented
9#24906273C211yesmaximal, characteristic, complemented
10#24906273C211yesmaximal, characteristic, complemented
11#24906240C211yesmaximal, characteristic, complemented
12#24905896C211yesmaximal, characteristic, complemented
13#24905870C211yesmaximal, characteristic, complemented
14#24905754C211yesmaximal, characteristic, complemented
15C83×#1579C211yesmaximal, characteristic, complemented
16#19128238C2211yescharacteristic
17C4×#13050591C2211yescharacteristic
18#19128041C411yescharacteristic
19#19128028C411yescharacteristic
20#19128010C411yescharacteristic
21#19128004C411yescharacteristic
22#19127925C411yescharacteristic
23#19127919C411yescharacteristic
24#19127862C411yescharacteristic
25#19127849C411yescharacteristic
26#19127832C2211yescharacteristic
27Q8×C83⋊C8C2211yescharacteristic
28C4×#13050577C2211yescharacteristic
29C4×#13050577C2211yescharacteristic
30C4×D664C2211yescharacteristic
31#19127778C2211yescharacteristic
32#19127771—21no—
33C8×D332—21no—
34C8×D332—21no—
35C8×D332C2211yescharacteristic
36C8×D332C2211yescharacteristic
37#19127766—21no—
38#19127766C2211yescharacteristic
39#19127761—21no—
40#19127757C2211yescharacteristic
41#19127753—21no—
42#19127753C2211yescharacteristic
43#19127752C2211yescharacteristic
44#19127752C2211yescharacteristic
45#19127655—21no—
46C4×C8×D83—21no—
47C4×C8×D83C2211yescharacteristic
48#19127453C2211yescharacteristic
49#19127453C2211yescharacteristic
50#19127452C2211yescharacteristic
51Q8⋊(C83⋊C8)C2211yescharacteristic
52Q8⋊(C83⋊C8)C2211yescharacteristic
53#19127430C2211yescharacteristic
54#19127430C2211yescharacteristic
55#19127428C2211yescharacteristic
56#19127428C2211yescharacteristic
57#19127423C2211yescharacteristic
58#19127423C2211yescharacteristic
59#19127422C2211yescharacteristic
60C8×Q8×C83C2211yescharacteristic
61C8×Q8×C83C2211yescharacteristic
62C4×Q16×C83C2211yescharacteristic
63#334×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65Q8⋊C8×C83C2211yescharacteristic
66#322×C83C2211yescharacteristic
67C2×#13050591C2×C411yescharacteristic
68C2×#13050577C2×C411yescharacteristic
69C2×#13050577C2×C411yescharacteristic
70C2×D664C2×C411yescharacteristic
71C2×#13050573—21no—
72C2×C8×D83—21no—
73C2×C8×D83—21no—
74C2×C8×D83—21no—
75C2×C8×D83D411yescharacteristic
76C2×C8×D83D411yescharacteristic
77#14581787—21no—
78#14581783C2×C411yescharacteristic
79#14581781C2×C411yescharacteristic
80#14581777—21no—
81#14581768C2×C411yescharacteristic
82#14581767C2×C411yescharacteristic
83Q8×Dic83C2×C411yescharacteristic
84C4×D332—21no—
85C4×D332—21no—
86C4×D332C2311yescharacteristic
87C4×D332C2311yescharacteristic
88#14581754—21no—
89#14581754C2×C411yescharacteristic
90#14581750—21no—
91#14581750C2×C411yescharacteristic
92#14581749—21no—
93C42×D83—21no—
94C42×D83C2311yescharacteristic
95#14581726C2×C411yescharacteristic
96#14581723C2×C411yescharacteristic
97#14581723C2×C411yescharacteristic
98C4⋊(C83⋊C8)—21no—
99C4⋊(C83⋊C8)—21no—
100C4⋊(C83⋊C8)C2311yescharacteristic
101C4⋊(C83⋊C8)C2311yescharacteristic
102Dic83⋊C8—21no—
103Dic83⋊C8C2×C411yescharacteristic
104Dic83⋊C8C2×C411yescharacteristic
105#14581716C2×C411yescharacteristic
106#14581716C2×C411yescharacteristic
107#14581714C2×C411yescharacteristic
108#14581714C2×C411yescharacteristic
109#14581712C2×C411yescharacteristic
110#14581712C2×C411yescharacteristic
111(C2×D83)⋊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)⋊C8—21no—
118(C2×D83)⋊C8C2×C411yescharacteristic
119(C2×D83)⋊C8C2×C411yescharacteristic
120#14581703—21no—
121#14581702—21no—
122C4×C83⋊C8—21no—
123C4×C83⋊C8C2311yescharacteristic
124C4×C83⋊C8C2311yescharacteristic
125C4×C83⋊C8C2311yescharacteristic
126C8×Dic83—21no—
127C8×Dic83D411yescharacteristic
128C8×Dic83D411yescharacteristic
129C2×Q16×C83C2×C411yescharacteristic
130C4×Q8×C83C2311yescharacteristic
131C4×Q8×C83C2311yescharacteristic
132#107×C83C2×C411yescharacteristic
133C4⋊C8×C83—21no—
134C4⋊C8×C83—21no—
135C4⋊C8×C83C2311yescharacteristic
136C4⋊C8×C83C2311yescharacteristic
137#103×C83C2×C411yescharacteristic
138#103×C83C2×C411yescharacteristic
139C4×C8×C83—21no—
140C4×C8×C83—21no—
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#13050591—22no—
145#13050591—22no—
146C2×D332—21no—
147C2×D332—21no—
148C2×D332C22×C411yescharacteristic
149C2×D332C22×C411yescharacteristic
150C2×C4×D83—21no—
151C2×C4×D83—21no—
152C2×C4×D83—21no—
153C2×C4×D83—21no—
154C2×C4×D83C22×C411yescharacteristic
155C2×C4×D83C2×D411yescharacteristic
156C2×C4×D83#4111yescharacteristic
157#13050577—22no—
158#13050577—22no—
159D664—22no—
160#13050573—42no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8—21no—
163C2×C83⋊C8—21no—
164C2×C83⋊C8C22×C411yescharacteristic
165C2×C83⋊C8C22×C411yescharacteristic
166C2×C83⋊C8C2×D411yescharacteristic
167C2×C83⋊C8C2×D411yescharacteristic
168C8×D83—41no—
169C8×D83—41no—
170C8×D83—42no—
171C8×D83—42no—
172C8×D83—42no—
173C4⋊Dic83—21no—
174C4⋊Dic83—21no—
175C4⋊Dic83C22×C411yescharacteristic
176C4⋊Dic83C22×C411yescharacteristic
177Dic83⋊C4—21no—
178Dic83⋊C4—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—
185(C2×D83)⋊C4—21no—
186(C2×D83)⋊C4—21no—
187C4×Dic83—21no—
188C4×Dic83—21no—
189C4×Dic83C22×C411yescharacteristic
190C4×Dic83C2×D411yescharacteristic
191C4×Dic83#4111yescharacteristic
192C2×Q8×C83C22×C411yescharacteristic
193C2×Q8×C83C22×C411yescharacteristic
194Q16×C83—22no—
195C2×C8×C83—21no—
196C2×C8×C83—21no—
197C2×C8×C83—21no—
198C2×C8×C83C22×C411yescharacteristic
199C2×C8×C83C22×C411yescharacteristic
200C2×C8×C83C2×D411yescharacteristic
201C2×C8×C83C2×D411yescharacteristic
202C4⋊C4×C83—21no—
203C4⋊C4×C83—21no—
204C4⋊C4×C83C22×C411yescharacteristic
205C4⋊C4×C83C22×C411yescharacteristic
206C42×C83—21no—
207C42×C83—21no—
208C42×C83C2411yescharacteristic
209C22×D83—21no—
210C22×D83—21no—
211C22×D83C4×D411yescharacteristic
212Q8×C83—21no—
213Q8×C83—21no—
214Q8×C83—21no—
215Q8×C83#13112yes—
216C2×C4×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83C23×C411yescharacteristic
221C2×C4×C83C22×D411yescharacteristic
222C2×C4×C83C2×#4111yescharacteristic
223C2×Dic83—21no—
224C2×Dic83—21no—
225C2×Dic83C4×D411yescharacteristic
226C2×Dic83C4×D411yescharacteristic
227C2×Dic83C4×D411yescharacteristic
228D332—24no—
229D332—21no—
230D332—21no—
231D332—21no—
232D332—42no—
233D332#13112yes—
234C4×D83—24no—
235C4×D83—21no—
236C4×D83—21no—
237C4×D83—21no—
238C4×D83—21no—
239C4×D83—41no—
240C4×D83—42no—
241C4×D83—41no—
242C4×D83—41no—
243C4×D83—41no—
244C4×D83—41no—
245C8×C83—21no—
246C8×C83—21no—
247C8×C83—21no—
248C8×C83—21no—
249C8×C83—41no—
250C8×C83—41no—
251C8×C83—41no—
252C83⋊C8—21no—
253C83⋊C8—21no—
254C83⋊C8—21no—
255C83⋊C8—21no—
256C83⋊C8—41no—
257C83⋊C8—41no—
258C83⋊C8—41no—
259C22×C83C2×C4×D411yescharacteristic
260C2×D83—21no—
261C2×D83—22no—
262C2×D83—21no—
263C2×D83—21no—
264C2×D83—41no—
265C2×D83—41no—
266C2×D83—41no—
267C2×D83—41no—
268C2×D83—41no—
269C4×C83—22no—
270C4×C83—21no—
271C4×C83—41no—
272C4×C83—41no—
273C4×C83—41no—
274C4×C83C2×#13111yescharacteristic
275C4×C83C2×#13111yescharacteristic
276C4×C83#57511yescharacteristic
277C4×C83#57511yescharacteristic
278Dic83—21no—
279Dic83—21no—
280Dic83—21no—
281Dic83—41no—
282Dic83—41no—
283#17909—831nomaximal, Sylow
284C2×C83#292911yescharacteristic
285C2×C83#294311yescharacteristic
286C2×C83#295511yescharacteristic
287D83—41no—
288D83—42no—
289D83—81no—
290#3102—831no—
291#2966—831no—
292C8×#41—831no—
293#1588—831no—
294#1587—831no—
295#1586—831no—
296#1585—831no—
297#1580—831no—
298#1579D8311yescharacteristic, complemented
299SD16⋊C8—831no—
300SD16⋊C8—831no—
301#1572—831no—
302#1488—831no—
303#1482—831no—
304#1452—831no—
305C83#1790911yescharacteristic, 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×Q8C2×D8311yescharacteristic
319C8×Q8C2×D8311yescharacteristic
320C4×Q16C2×D8311yescharacteristic
321C4×SD16—831no—
322C4×SD16—831no—
323C4×D8—831no—
324#436—831no—
325#435—1661no—
326C8×D4—831no—
327C8×D4—831no—
328C8×D4—831no—
329C8×D4—1661no—
330C8×D4—1661no—
331C8×D4—1661no—
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⋊C8C2×D8311yescharacteristic
348Q8⋊C8C2×D8311yescharacteristic
349D4⋊C8—831no—
350D4⋊C8—831no—
351D4⋊C8—831no—
352D4⋊C8—831no—
353#322—831no—
354#322—831no—
355#322—831no—
356#322C2×D8311yescharacteristic
357C2×#41—831no—
358C2×Q16C4×D8311yescharacteristic
359C2×SD16—831no—
360C2×SD16—831no—
361C2×D8—831no—
362C2×M16—1661no—
363C22×C8—831no—
364C22×C8—831no—
365C22×C8—1661no—
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×Q8C22×D8311yescharacteristic
376C4×Q8C22×D8311yescharacteristic
377C4×D4—831no—
378C4×D4—831no—
379C4×D4—831no—
380C4×D4—1661no—
381C4×D4—1661no—
382C4×D4—1661no—
383#117—831no—
384#117—1661no—
385#117—1661no—
386C2×C42—831no—
387C2×C42—1661no—
388#107—831no—
389#107C4×D8311yescharacteristic
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#103C4×D8311yescharacteristic
406#103C4×D8311yescharacteristic
407#102—831no—
408#102—831no—
409#102—831no—
410#102—831no—
411C22⋊C8—831no—
412C22⋊C8—831no—
413C22⋊C8—1661no—
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—21no—
424C4×C8—831no—
425C4×C8—831no—
426C4×C8—831no—
427C4×C8—831no—
428C4×C8—831no—
429C4×C8—1661no—
430C4×C8—1661no—
431C4×C8C22×D8311yescharacteristic
432C4×C8C22×D8311yescharacteristic
433C4×C8C22×D8311yescharacteristic
434#41—1662no—
435#41—1662no—
436C2×Q8C2×C4×D8311yescharacteristic
437C2×Q8C2×C4×D8311yescharacteristic
438C2×D4—831no—
439C2×D4—831no—
440C2×D4—1661no—
441C2×D4—1661no—
442C22×C4—831no—
443C22×C4—831no—
444C22×C4—831no—
445C22×C4—1661no—
446C22×C4—1661no—
447C22×C4—1661no—
448C22×C4—1661no—
449Q16—22no—
450SD16—1662no—
451SD16—1662no—
452D8—1662no—
453M16—3322no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—3322no—
458C2×C8—3322no—
459C2×C8—3321no—
460C2×C8—3321no—
461C2×C8—3322no—
462C2×C8—831no—
463C2×C8—831no—
464C2×C8—831no—
465C2×C8—831no—
466C2×C8—1661no—
467C2×C8—1661no—
468C2×C8—1661no—
469C2×C8C2×C4×D8311yescharacteristic
470C2×C8C2×C4×D8311yescharacteristic
471C2×C8D4×D8311yescharacteristic
472C2×C8D4×D8311yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—831no—
476C4⋊C4—831no—
477C4⋊C4—1661no—
478C4⋊C4—1661no—
479C4⋊C4—1661no—
480C4⋊C4—1661no—
481C4⋊C4C2×C4×D8311yescharacteristic
482C4⋊C4C2×C4×D8311yescharacteristic
483C22⋊C4—1661no—
484C22⋊C4—1661no—
485C22⋊C4—1661no—
486C22⋊C4—1661no—
487C22⋊C4—1661no—
488C22⋊C4—1661no—
489C22⋊C4—1661no—
490C22⋊C4—1661no—
491C42—21no—
492C42—21no—
493C42—831no—
494C42—831no—
495C42—831no—
496C42—1661no—
497C42—1661no—
498C42C23×D8311yescharacteristic
499C23—831no—
500C23—1661no—
501C23—1661no—
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8#1458179812yes—
506D4—3322no—
507D4—832no—
508D4—1664no—
509D4—1661no—
510D4—1661no—
511D4—1661no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—3321no—
517C2×C4—3322no—
518C2×C4—3321no—
519C2×C4—3321no—
520C2×C4—3321no—
521C2×C4—3321no—
522C2×C4—831no—
523C2×C4—831no—
524C2×C4—831no—
525C2×C4—1664no—
526C2×C4—1661no—
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—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—3321no—
543C8—3321no—
544C8—3321no—
545C8—1661no—
546C8—1661no—
547C8—1661no—
548C8—1661no—
549C22—3321no—
550C22—3321no—
551C22—3321no—
552C22—3321no—
553C22—3321no—
554C22—1661no—
555C22—1661no—
556C22—1662no—
557C22—1661no—
558C22C4×D4×D8311yescharacteristic
559C4—21no—
560C4—22no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—3321no—
565C4—3321no—
566C4—1661no—
567C4—1661no—
568C4—1661no—
569C4#131×D8311yescharacteristic
570C4C2×#1458179811yescharacteristic
571C4#1912850011yescharacteristic
572C4#1912850011yescharacteristic
573C2—3322no—
574C2—3321no—
575C2—6641no—
576C2#2491615211yescharacteristic
577C2#2491626211yescharacteristic
578C2#2491636311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1579C2
socleC22×C83C2×C4×D4
prime radical#19127849C4
cosocleC42×C83C24
hypercenter#1579D83
hypocenterC83#17909
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1579

Complements

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

NH ≅ G/Ntype
2. #24916440C2semidirect
3. C8×#13050591C2semidirect
4. #24906338C2semidirect
5. #24906335C2semidirect
6. #24906326C2semidirect
7. #24906323C2semidirect
8. #24906288C2semidirect
9. #24906273C2semidirect
10. #24906273C2semidirect
11. #24906240C2semidirect
12. #24905896C2semidirect
13. #24905870C2semidirect
14. #24905754C2semidirect
15. C83×#1579C2semidirect
298. #1579D83semidirect
305. C83#17909semidirect

Maximal subgroups

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

subgroupindex
#249174872
#249164402
C8×#130505912
#249063382
#249063352
#249063262
#249063232
#249062882
#249062732
#249062402
#249058962
#249058702
#249057542
C83×#15792
#1790983