Finite Group Databasebeta

← #35375345

Subgroups — #35375345

Order 21248.

616 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917481C211yesmaximal, characteristic
2#24916483C211yesmaximal, characteristic, complemented
3#24916461C211yesmaximal, characteristic, complemented
4#24906356C211yesmaximal, characteristic, complemented
5#24906345C211yesmaximal, characteristic, complemented
6#24906310C211yesmaximal, characteristic, complemented
7#24906309C211yesmaximal, characteristic, complemented
8#24906303C211yesmaximal, characteristic, complemented
9#24906295C211yesmaximal, characteristic, complemented
10#24906267C211yesmaximal, characteristic, complemented
11#24906260C211yesmaximal, characteristic, complemented
12#24906241C211yesmaximal, characteristic, complemented
13#24905924C211yesmaximal, characteristic, complemented
14C8×#13050574C211yesmaximal, characteristic, complemented
15C83×#1476C211yesmaximal, characteristic, complemented
16#19128235C2211yescharacteristic
17#19128042C411yescharacteristic
18#19128025C411yescharacteristic
19#19128008C411yescharacteristic
20#19128001C411yescharacteristic
21#19127923C411yescharacteristic
22#19127916C411yescharacteristic
23#19127863C411yescharacteristic
24#19127846C411yescharacteristic
25#19127828C2211yescharacteristic
26Q8×C83⋊C8C2211yescharacteristic
27Q8×C83⋊C8C2211yescharacteristic
28#19127825C2211yescharacteristic
29C4×#13050580C2211yescharacteristic
30C4×#13050577C2211yescharacteristic
31C4×#13050578C2211yescharacteristic
32C4×#13050575C2211yescharacteristic
33#19127779—21no—
34#19127779—21no—
35#19127779C2211yescharacteristic
36#19127779C2211yescharacteristic
37#19127778C2211yescharacteristic
38#19127776—21no—
39#19127775—21no—
40#19127766C2211yescharacteristic
41#19127760—21no—
42#19127758—21no—
43#19127758C2211yescharacteristic
44#19127754C2211yescharacteristic
45#19127655—21no—
46C4×#13050574—21no—
47C4×#13050574C2211yescharacteristic
48#19127453C2211yescharacteristic
49#19127453C2211yescharacteristic
50#19127451C2211yescharacteristic
51#19127451C2211yescharacteristic
52#19127433C2211yescharacteristic
53#19127433C2211yescharacteristic
54#19127430C2211yescharacteristic
55#19127430C2211yescharacteristic
56#19127423C2211yescharacteristic
57#19127423C2211yescharacteristic
58C8×C83⋊C8C2211yescharacteristic
59C8×C83⋊C8C2211yescharacteristic
60C4×#41×C83C2211yescharacteristic
61#431×C83C2211yescharacteristic
62C2×C4×C8×C83C2211yescharacteristic
63Q8⋊C8×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65D4⋊C8×C83C2211yescharacteristic
66D4⋊C8×C83C2211yescharacteristic
67C2×#13050580C2×C411yescharacteristic
68C2×#13050578C2×C411yescharacteristic
69C2×#13050577C2×C411yescharacteristic
70C2×#13050575C2×C411yescharacteristic
71C2×#13050574—21no—
72C2×#13050574—21no—
73C2×#13050574D411yescharacteristic
74C2×#13050574D411yescharacteristic
75C2×#13050573—21no—
76C2×C8×D83—21no—
77#14581786—21no—
78#14581784C2×C411yescharacteristic
79#14581780C2×C411yescharacteristic
80#14581775—21no—
81#14581771C2×C411yescharacteristic
82#14581766C2×C411yescharacteristic
83C4×Dic166C2311yescharacteristic
84C4×D332C2311yescharacteristic
85C4×C22⋊D83—21no—
86#14581749—21no—
87#14581725C2×C411yescharacteristic
88#14581725C2×C411yescharacteristic
89#14581723C2×C411yescharacteristic
90#14581723C2×C411yescharacteristic
91C4⋊(C83⋊C8)—21no—
92C4⋊(C83⋊C8)—21no—
93C4⋊(C83⋊C8)C2×C411yescharacteristic
94C4⋊(C83⋊C8)C2×C411yescharacteristic
95C4⋊(C83⋊C8)C2311yescharacteristic
96C4⋊(C83⋊C8)C2311yescharacteristic
97Dic83⋊C8—21no—
98Dic83⋊C8—21no—
99#14581716C2×C411yescharacteristic
100#14581716C2×C411yescharacteristic
101#14581715C2×C411yescharacteristic
102#14581715C2×C411yescharacteristic
103#14581713C2×C411yescharacteristic
104#14581713C2×C411yescharacteristic
105#14581712C2×C411yescharacteristic
106#14581712C2×C411yescharacteristic
107C22⋊(C83⋊C8)—21no—
108C22⋊(C83⋊C8)—21no—
109C22⋊(C83⋊C8)—21no—
110C22⋊(C83⋊C8)C2×C411yescharacteristic
111C22⋊(C83⋊C8)C2×C411yescharacteristic
112(C2×D83)⋊C8—21no—
113(C2×D83)⋊C8—21no—
114#14581703—21no—
115#14581703D411yescharacteristic
116#14581703D411yescharacteristic
117#14581702—21no—
118C4×C83⋊C8—21no—
119C4×C83⋊C8—21no—
120C4×C83⋊C8C2311yescharacteristic
121C4×C83⋊C8C2311yescharacteristic
122C4×C83⋊C8C2311yescharacteristic
123C4×C83⋊C8C2311yescharacteristic
124C8×Dic83—21no—
125C2×#41×C83C2×C411yescharacteristic
126C22×C8×C83—21no—
127C4×Q8×C83C2×C411yescharacteristic
128C4×Q8×C83C2311yescharacteristic
129C4×D4×C83—21no—
130C4×D4×C83—21no—
131C4×D4×C83C2×C411yescharacteristic
132C4×D4×C83C2311yescharacteristic
133#117×C83—21no—
134#117×C83C2×C411yescharacteristic
135C2×C42×C83—21no—
136C2×C42×C83C2311yescharacteristic
137C4⋊C8×C83C2311yescharacteristic
138C4⋊C8×C83C2311yescharacteristic
139C22⋊C8×C83—21no—
140C4×C8×C83—21no—
141C4×C8×C83—21no—
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C2×Dic166C22×C411yescharacteristic
145C2×D332C22×C411yescharacteristic
146C2×C22⋊D83—21no—
147C2×C4×D83—21no—
148#13050580—22no—
149#13050578—41no—
150#13050577—22no—
151#13050575—41no—
152#13050574—22no—
153#13050574—22no—
154#13050574—42no—
155#13050574—42no—
156#13050573—42no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8C22×C411yescharacteristic
160C2×C83⋊C8C22×C411yescharacteristic
161C2×C83⋊C8C22×C411yescharacteristic
162C2×C83⋊C8C22×C411yescharacteristic
163C2×C83⋊C8C2×D411yescharacteristic
164C2×C83⋊C8C2×D411yescharacteristic
165C2×C83⋊C8C2×D411yescharacteristic
166C2×C83⋊C8C2×D411yescharacteristic
167C8×D83—42no—
168C4⋊Dic83C22×C411yescharacteristic
169C4⋊Dic83C22×C411yescharacteristic
170Dic83⋊C4—21no—
171Dic83⋊C4—21no—
172Dic83⋊C4—21no—
173Dic83⋊C4—21no—
174C22⋊Dic83—21no—
175(C2×D83)⋊C4—21no—
176(C2×D83)⋊C4—21no—
177(C2×D83)⋊C4—21no—
178(C2×D83)⋊C4—21no—
179C4×Dic83—21no—
180#41×C83—22no—
181#41×C83—41no—
182C2×Q8×C83C22×C411yescharacteristic
183C2×D4×C83—21no—
184C2×D4×C83C22×C411yescharacteristic
185C22×C4×C83—21no—
186C22×C4×C83—21no—
187C22×C4×C83—21no—
188C22×C4×C83C22×C411yescharacteristic
189C22×C4×C83C2×D411yescharacteristic
190C22×C4×C83#4111yescharacteristic
191C2×C8×C83—21no—
192C2×C8×C83—21no—
193C2×C8×C83—21no—
194C2×C8×C83—21no—
195C2×C8×C83—42no—
196C4⋊C4×C83—21no—
197C4⋊C4×C83—21no—
198C4⋊C4×C83C22×C411yescharacteristic
199C4⋊C4×C83C22×C411yescharacteristic
200C22⋊C4×C83—21no—
201C22⋊C4×C83—21no—
202C22⋊C4×C83—21no—
203C42×C83—21no—
204C42×C83—21no—
205C42×C83—21no—
206C42×C83C22×C411yescharacteristic
207C42×C83C2×D411yescharacteristic
208C42×C83#4111yescharacteristic
209C42×C83C2411yescharacteristic
210C23×C83—21no—
211C23×C83C4×D411yescharacteristic
212C22×D83—21no—
213Q8×C83—21no—
214Q8×C83#13112yes—
215D4×C83—21no—
216D4×C83—21no—
217D4×C83—42no—
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—21no—
225C2×C4×C83—41no—
226C2×C4×C83—42no—
227C2×C4×C83—41no—
228C2×C4×C83—41no—
229C2×C4×C83—81no—
230C2×C4×C83C4×D411yescharacteristic
231C2×C4×C83C4×D411yescharacteristic
232C2×C4×C83C4×D411yescharacteristic
233C2×C4×C83C23×C411yescharacteristic
234C2×C4×C83C22×D411yescharacteristic
235C2×C4×C83C2×#4111yescharacteristic
236C22⋊D83—81no—
237C2×Dic83—21no—
238C2×Dic83—21no—
239C2×Dic83—21no—
240D332—21no—
241D332—21no—
242C4×D83—41no—
243C4×D83—41no—
244Dic166—21no—
245Dic166—21no—
246C8×C83—22no—
247C8×C83—41no—
248C8×C83—41no—
249C8×C83—41no—
250C83⋊C8—21no—
251C83⋊C8—21no—
252C83⋊C8—21no—
253C83⋊C8—21no—
254C83⋊C8—21no—
255C83⋊C8—21no—
256C83⋊C8—41no—
257C83⋊C8—41no—
258C83⋊C8#13512yes—
259C83⋊C8#13512yes—
260C22×C83—21no—
261C22×C83—21no—
262C22×C83—21no—
263C22×C83—41no—
264C22×C83—41no—
265C22×C83—41no—
266C22×C83C2×C4×D411yescharacteristic
267C2×D83—41no—
268C2×D83—41no—
269C2×D83—41no—
270C4×C83—21no—
271C4×C83—22no—
272C4×C83—21no—
273C4×C83—21no—
274C4×C83—21no—
275C4×C83—41no—
276C4×C83—41no—
277C4×C83C2×#13111yescharacteristic
278C4×C83#56811yescharacteristic
279C4×C83C2×#13511yescharacteristic
280C4×C83C2×#13511yescharacteristic
281Dic83—41no—
282Dic83—41no—
283Dic83—41no—
284#17999—831nomaximal, Sylow
285C2×C83—41no—
286C2×C83—81no—
287C2×C83#293311yescharacteristic
288C2×C83C4×#13511yescharacteristic
289C2×C83#295611yescharacteristic
290D83—81no—
291#3102—831no—
292#2971—831no—
293#2969—831no—
294#1590—831no—
295#1589—831no—
296#1584—831no—
297#1583—831no—
298#1583—831no—
299#1581—831no—
300C8×Q16—831no—
301C8×SD16—831no—
302#1572—831no—
303#1494—831no—
304#1476D8311yescharacteristic, complemented
305C8×M16—831no—
306C83#1799911yescharacteristic, complemented, Sylow
307#529—831no—
308C4×#41C2×D8311yescharacteristic
309#485—831no—
310#482—831no—
311#479—831no—
312#478—831no—
313#464—831no—
314#463—831no—
315#452—831no—
316#449—831no—
317#446—831no—
318C8×Q8—831no—
319C8×Q8—831no—
320C8×Q8—831no—
321C4×Q16—831no—
322C4×SD16—831no—
323C4×SD16—831no—
324C4×D8—831no—
325#436—831no—
326#436—831no—
327#436—831no—
328#436—1661no—
329#436—1661no—
330#436—1661no—
331#435—1661no—
332C8×D4—831no—
333#433—1661no—
334#432—831no—
335#432—1661no—
336#431—831no—
337#431C2×D8311yescharacteristic
338#405—1661no—
339C4×M16—831no—
340C4×M16—1661no—
341C2×C4×C8C2×D8311yescharacteristic
342#335—831no—
343#335—831no—
344#334—831no—
345#334—831no—
346Q8⋊C8—831no—
347Q8⋊C8—831no—
348Q8⋊C8C2×D8311yescharacteristic
349Q8⋊C8C2×D8311yescharacteristic
350D4⋊C8—831no—
351D4⋊C8—831no—
352D4⋊C8C2×D8311yescharacteristic
353D4⋊C8C2×D8311yescharacteristic
354#322—831no—
355#322—831no—
356C82—831no—
357C82—831no—
358C2×#41C4×D8311yescharacteristic
359C2×Q16—831no—
360C2×SD16—831no—
361C2×SD16—831no—
362C2×D8—831no—
363C2×M16—831no—
364C2×M16—831no—
365C2×M16—1661no—
366C2×M16—1661no—
367C2×M16—1661no—
368C22×C8—21no—
369C22×C8—1661no—
370#126—1661no—
371#125—831no—
372#124—831no—
373#123—1661no—
374C22⋊Q8—831no—
375#121—831no—
376C4×Q8—831no—
377C4×Q8C4×D8311yescharacteristic
378C4×Q8C22×D8311yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—831no—
382C4×D4—1661no—
383C4×D4C4×D8311yescharacteristic
384C4×D4C22×D8311yescharacteristic
385#117—21no—
386#117—1661no—
387#117C4×D8311yescharacteristic
388C2×C42—21no—
389C2×C42C22×D8311yescharacteristic
390#107—831no—
391#107—831no—
392#106—831no—
393#106—831no—
394C4⋊C8—831no—
395C4⋊C8—831no—
396C4⋊C8—831no—
397C4⋊C8—831no—
398C4⋊C8—1661no—
399C4⋊C8—1661no—
400C4⋊C8—1661no—
401C4⋊C8—1661no—
402C4⋊C8C22×D8311yescharacteristic
403C4⋊C8C22×D8311yescharacteristic
404#103—831no—
405#103—831no—
406#103—831no—
407#103—831no—
408#102—831no—
409#102—831no—
410#102—831no—
411#102—831no—
412C22⋊C8—21no—
413C22⋊C8—831no—
414C22⋊C8—831no—
415C22⋊C8—1661no—
416C22⋊C8—1661no—
417C22⋊C8—1661no—
418C22⋊C8—1661no—
419C22⋊C8—1661no—
420#97—831no—
421#97—831no—
422#97—1661no—
423#97—1661no—
424C4×C8—21no—
425C4×C8—21no—
426C4×C8—831no—
427C4×C8—831no—
428C4×C8—831no—
429C4×C8—831no—
430C4×C8—1661no—
431C4×C8—1661no—
432C4×C8—1661no—
433C4×C8C22×D8311yescharacteristic
434C4×C8C22×D8311yescharacteristic
435#41—22no—
436#41—41no—
437C2×Q8—831no—
438C2×Q8C2×C4×D8311yescharacteristic
439C2×D4—21no—
440C2×D4—831no—
441C2×D4—1661no—
442C2×D4C2×C4×D8311yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—1661no—
447C22×C4C2×C4×D8311yescharacteristic
448C22×C4D4×D8311yescharacteristic
449C22×C4#1305058911yescharacteristic
450Q16—1662no—
451SD16—3321no—
452SD16—1662no—
453D8—3321no—
454M16—3322no—
455M16—3322no—
456M16—3322no—
457M16—1662no—
458M16—1662no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—42no—
464C2×C8—3322no—
465C2×C8—831no—
466C2×C8—831no—
467C2×C8—831no—
468C2×C8—831no—
469C2×C8—831no—
470C2×C8—831no—
471C2×C8—831no—
472C2×C8—831no—
473C2×C8—1661no—
474C2×C8—1661no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—831no—
478C4⋊C4—831no—
479C4⋊C4—1661no—
480C4⋊C4—1661no—
481C4⋊C4—1661no—
482C4⋊C4—1661no—
483C4⋊C4C2×C4×D8311yescharacteristic
484C4⋊C4C2×C4×D8311yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—1661no—
489C22⋊C4—1661no—
490C22⋊C4—1661no—
491C22⋊C4—1661no—
492C22⋊C4—1661no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—1661no—
497C42C2×C4×D8311yescharacteristic
498C42D4×D8311yescharacteristic
499C42#1305058911yescharacteristic
500C42C23×D8311yescharacteristic
501C23—21no—
502C23—1661no—
503C23(C22⋊D83)⋊C411yescharacteristic
504Q8—21no—
505Q8—1661no—
506Q8—1661no—
507Q8#1458179812yes—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—6641no—
512D4—1661no—
513D4—1661no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—81no—
526C2×C4—3321no—
527C2×C4—3321no—
528C2×C4—1661no—
529C2×C4—1661no—
530C2×C4—1661no—
531C2×C4(C22⋊D83)⋊C411yescharacteristic
532C2×C4(C22⋊D83)⋊C411yescharacteristic
533C2×C4(C22⋊D83)⋊C411yescharacteristic
534C2×C4C22×C4×D8311yescharacteristic
535C2×C4C2×D4×D8311yescharacteristic
536C2×C4C2×#1305058911yescharacteristic
537C8—22no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—3321no—
542C8—3321no—
543C8—832no—
544C8—832no—
545C8—1661no—
546C8—1661no—
547C8—1661no—
548C8—1661no—
549C8—1661no—
550C8—1661no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—3321no—
558C22—3321no—
559C22—3321no—
560C22C2×(C22⋊D83)⋊C411yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—22no—
566C4—41no—
567C4—41no—
568C4—3321no—
569C4—3321no—
570C4—3321no—
571C4C2×#1458179811yescharacteristic
572C4#1912846711yescharacteristic
573C4#135×D8311yescharacteristic
574C4#135×D8311yescharacteristic
575C2—41no—
576C2—81no—
577C2—6641no—
578C2#2491618411yescharacteristic
579C2#2491623111yescharacteristic
580C2#2491636911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1476C2
socleC22×C83C2×C4×D4
prime radical#19127846C4
cosocleC42×C83C24
hypercenter#1476D83
hypocenterC83#17999
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
2. #24916483C2semidirect
3. #24916461C2semidirect
4. #24906356C2semidirect
5. #24906345C2semidirect
6. #24906310C2semidirect
7. #24906309C2semidirect
8. #24906303C2semidirect
9. #24906295C2semidirect
10. #24906267C2semidirect
11. #24906260C2semidirect
12. #24906241C2semidirect
13. #24905924C2semidirect
14. C8×#13050574C2semidirect
15. C83×#1476C2semidirect
304. #1476D83semidirect
306. C83#17999semidirect

Maximal subgroups

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

subgroupindex
#249174812
#249164832
#249164612
#249063562
#249063452
#249063102
#249063092
#249063032
#249062952
#249062672
#249062602
#249062412
#249059242
C8×#130505742
C83×#14762
#1799983