Finite Group Databasebeta

← #35375043

Subgroups — #35375043

Order 21248.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918063C211yesmaximal, characteristic
2#24916608C211yesmaximal, characteristic
3#24916558C211yesmaximal, characteristic, complemented
4#24906369C211yesmaximal, characteristic, complemented
5#24906368C211yesmaximal, characteristic, complemented
6#24906357C211yesmaximal, characteristic, complemented
7#24906350C211yesmaximal, characteristic, complemented
8#24906279C211yesmaximal, characteristic, complemented
9#24906278C211yesmaximal, characteristic, complemented
10#24906267C211yesmaximal, characteristic, complemented
11#24906260C211yesmaximal, characteristic, complemented
12#24906228C211yesmaximal, characteristic, complemented
13#24905924C211yesmaximal, characteristic
14C8×#13050574C211yesmaximal, characteristic, complemented
15C83×#1493C211yesmaximal, characteristic, complemented
16#19128235C2211yescharacteristic
17#19128107C411yescharacteristic
18#19128093C411yescharacteristic
19#19128069C411yescharacteristic
20#19128063C411yescharacteristic
21#19127957C411yescharacteristic
22#19127957C411yescharacteristic
23#19127949C411yescharacteristic
24#19127949C411yescharacteristic
25#19127832—21no—
26#19127832—21no—
27#19127832C2211yescharacteristic
28#19127832C2211yescharacteristic
29#19127828C2211yescharacteristic
30Q8×C83⋊C8C2211yescharacteristic
31Q8×C83⋊C8C2211yescharacteristic
32#19127825C2211yescharacteristic
33C4×#13050580C2211yescharacteristic
34C4×#13050580C2211yescharacteristic
35C4×#13050577C2211yescharacteristic
36C4×#13050577C2211yescharacteristic
37#19127778C2211yescharacteristic
38#19127777—21no—
39#19127770—21no—
40#19127766C2211yescharacteristic
41#19127762—21no—
42#19127762—21no—
43#19127761—21no—
44#19127758C2211yescharacteristic
45#19127754C2211yescharacteristic
46#19127726—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
60#533×C83C2211yescharacteristic
61#423×C83C2211yescharacteristic
62C2×C4×C8×C83C2211yescharacteristic
63Q8⋊C8×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65Q8⋊C8×C83C2211yescharacteristic
66Q8⋊C8×C83C2211yescharacteristic
67C2×#13050580C2×C411yescharacteristic
68C2×#13050580C2×C411yescharacteristic
69C2×#13050577C2×C411yescharacteristic
70C2×#13050577C2×C411yescharacteristic
71C2×#13050574C2×C411yescharacteristic
72C2×#13050574C2×C411yescharacteristic
73C2×#13050573—21no—
74C2×C8×D83—21no—
75#14581786—21no—
76#14581784C2×C411yescharacteristic
77#14581780C2×C411yescharacteristic
78#14581775—21no—
79#14581771C2×C411yescharacteristic
80#14581766C2×C411yescharacteristic
81C4×Dic166C2311yescharacteristic
82C4×D332C2311yescharacteristic
83C4×C22⋊D83—21no—
84#14581749—21no—
85#14581725C2×C411yescharacteristic
86#14581725C2×C411yescharacteristic
87#14581723C2×C411yescharacteristic
88#14581723C2×C411yescharacteristic
89C4⋊(C83⋊C8)—21no—
90C4⋊(C83⋊C8)—21no—
91C4⋊(C83⋊C8)—21no—
92C4⋊(C83⋊C8)—21no—
93C4⋊(C83⋊C8)D411yescharacteristic
94C4⋊(C83⋊C8)D411yescharacteristic
95C4⋊(C83⋊C8)C2311yescharacteristic
96C4⋊(C83⋊C8)C2311yescharacteristic
97Dic83⋊C8—21no—
98Dic83⋊C8—21no—
99#14581716C2×C411yescharacteristic
100#14581716C2×C411yescharacteristic
101#14581716C2×C411yescharacteristic
102#14581716C2×C411yescharacteristic
103#14581715C2×C411yescharacteristic
104#14581715C2×C411yescharacteristic
105#14581712C2×C411yescharacteristic
106#14581712C2×C411yescharacteristic
107C22⋊(C83⋊C8)—21no—
108C22⋊(C83⋊C8)D411yescharacteristic
109C22⋊(C83⋊C8)D411yescharacteristic
110(C2×D83)⋊C8—21no—
111(C2×D83)⋊C8—21no—
112#14581703—21no—
113#14581703—21no—
114#14581703—21no—
115#14581703C2×C411yescharacteristic
116#14581703C2×C411yescharacteristic
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×M16×C83—21no—
126C22×C8×C83—21no—
127C4⋊Q8×C83C2×C411yescharacteristic
128C4⋊Q8×C83C2×C411yescharacteristic
129#125×C83—21no—
130C22⋊Q8×C83—21no—
131C22⋊Q8×C83C2×C411yescharacteristic
132C22⋊Q8×C83C2×C411yescharacteristic
133C4×Q8×C83—21no—
134C4×Q8×C83C2311yescharacteristic
135C4×Q8×C83C2311yescharacteristic
136#117×C83—21no—
137C2×C42×C83C2311yescharacteristic
138C4⋊C8×C83—21no—
139C4⋊C8×C83C2311yescharacteristic
140C4⋊C8×C83C2311yescharacteristic
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#13050580—22no—
150#13050577—22no—
151#13050577—22no—
152#13050574—22no—
153#13050574—22no—
154#13050573—81no—
155C2×C83⋊C8—21no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8C22×C411yescharacteristic
158C2×C83⋊C8C22×C411yescharacteristic
159C2×C83⋊C8C22×C411yescharacteristic
160C2×C83⋊C8C22×C411yescharacteristic
161C2×C83⋊C8C2×D411yescharacteristic
162C2×C83⋊C8C2×D411yescharacteristic
163C2×C83⋊C8C2×D411yescharacteristic
164C2×C83⋊C8C2×D411yescharacteristic
165C8×D83—81no—
166C4⋊Dic83C22×C411yescharacteristic
167C4⋊Dic83C22×C411yescharacteristic
168Dic83⋊C4—21no—
169Dic83⋊C4—21no—
170Dic83⋊C4—21no—
171Dic83⋊C4—21no—
172C22⋊Dic83—21no—
173(C2×D83)⋊C4—21no—
174(C2×D83)⋊C4—21no—
175(C2×D83)⋊C4—21no—
176(C2×D83)⋊C4—21no—
177C4×Dic83—21no—
178C2×Q8×C83—21no—
179C2×Q8×C83C22×C411yescharacteristic
180C2×Q8×C83C22×C411yescharacteristic
181C22×C4×C83C22×C411yescharacteristic
182C22×C4×C83C2×D411yescharacteristic
183C22×C4×C83#4111yescharacteristic
184M16×C83—81no—
185C2×C8×C83—21no—
186C2×C8×C83—21no—
187C2×C8×C83—21no—
188C2×C8×C83—21no—
189C2×C8×C83—42no—
190C4⋊C4×C83—21no—
191C4⋊C4×C83—21no—
192C4⋊C4×C83—21no—
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—
201C42×C83—21no—
202C42×C83—21no—
203C42×C83C22×C411yescharacteristic
204C42×C83C2×D411yescharacteristic
205C42×C83#4111yescharacteristic
206C42×C83C2411yescharacteristic
207C23×C83C4×D411yescharacteristic
208C22×D83—21no—
209Q8×C83—21no—
210Q8×C83—21no—
211Q8×C83—21no—
212Q8×C83—21no—
213Q8×C83—81no—
214C2×C4×C83—21no—
215C2×C4×C83—21no—
216C2×C4×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83—21no—
222C2×C4×C83—41no—
223C2×C4×C83C4×D411yescharacteristic
224C2×C4×C83C4×D411yescharacteristic
225C2×C4×C83C4×D411yescharacteristic
226C2×C4×C83C23×C411yescharacteristic
227C2×C4×C83C22×D411yescharacteristic
228C2×C4×C83C2×#4111yescharacteristic
229C22⋊D83—81no—
230C2×Dic83—21no—
231C2×Dic83—21no—
232C2×Dic83—21no—
233D332—21no—
234D332—21no—
235C4×D83—41no—
236C4×D83—41no—
237Dic166—21no—
238Dic166—21no—
239C8×C83—22no—
240C8×C83—41no—
241C8×C83—41no—
242C8×C83—41no—
243C83⋊C8—21no—
244C83⋊C8—21no—
245C83⋊C8—21no—
246C83⋊C8—21no—
247C83⋊C8—21no—
248C83⋊C8—21no—
249C83⋊C8—41no—
250C83⋊C8—41no—
251C83⋊C8#13112yes—
252C83⋊C8#13112yes—
253C22×C83—21no—
254C22×C83—21no—
255C22×C83—21no—
256C22×C83C2×C4×D411yescharacteristic
257C2×D83—41no—
258C2×D83—41no—
259C2×D83—41no—
260C4×C83—21no—
261C4×C83—21no—
262C4×C83—21no—
263C4×C83—21no—
264C4×C83—41no—
265C4×C83—41no—
266C4×C83—41no—
267C4×C83—41no—
268C4×C83C2×#13111yescharacteristic
269C4×C83C2×#13111yescharacteristic
270C4×C83#57711yescharacteristic
271C4×C83#57811yescharacteristic
272Dic83—41no—
273Dic83—41no—
274Dic83—41no—
275#17969—831nomaximal, Sylow
276C2×C83—41no—
277C2×C83#293111yescharacteristic
278C2×C83#294711yescharacteristic
279C2×C83#295611yescharacteristic
280D83—81no—
281#3172—831no—
282#2993—831no—
283#2985—831no—
284#1593—831no—
285#1592—831no—
286#1591—831no—
287#1590—831no—
288#1579—831no—
289SD16⋊C8—831no—
290C8×Q16—831no—
291C8×SD16—831no—
292#1569—831no—
293#1494—831no—
294#1493D8311yescharacteristic, complemented
295C8×M16—831no—
296C83#1796911yescharacteristic, complemented, Sylow
297#533C2×D8311yescharacteristic
298#529—831no—
299#501—831no—
300#497—831no—
301#491—831no—
302#489—831no—
303#470—831no—
304#470—831no—
305#468—831no—
306#468—831no—
307#446—831no—
308#446—831no—
309#446—831no—
310#446—1661no—
311#446—1661no—
312C8×Q8—831no—
313C8×Q8—831no—
314C8×Q8—831no—
315C4×Q16—831no—
316C4×Q16—831no—
317C4×SD16—831no—
318C4×SD16—831no—
319#436—831no—
320#436—1661no—
321#435—1661no—
322C8×D4—831no—
323#433—1661no—
324#433—1661no—
325#433—1661no—
326#432—831no—
327#431—831no—
328#424—1661no—
329#423C2×D8311yescharacteristic
330C4×M16—831no—
331C2×C4×C8C2×D8311yescharacteristic
332#335—831no—
333#335—831no—
334#334—831no—
335#334—831no—
336Q8⋊C8—831no—
337Q8⋊C8—831no—
338Q8⋊C8C2×D8311yescharacteristic
339Q8⋊C8C2×D8311yescharacteristic
340Q8⋊C8C2×D8311yescharacteristic
341Q8⋊C8C2×D8311yescharacteristic
342D4⋊C8—831no—
343D4⋊C8—831no—
344#322—831no—
345#322—831no—
346C82—831no—
347C82—831no—
348C2×Q16—831no—
349C2×Q16—831no—
350C2×SD16—831no—
351C2×SD16—831no—
352C2×M16—21no—
353C2×M16—831no—
354C2×M16—831no—
355C2×M16—1661no—
356C22×C8—21no—
357C22×C8—1661no—
358C4⋊Q8C4×D8311yescharacteristic
359C4⋊Q8C4×D8311yescharacteristic
360#126—1661no—
361#125—21no—
362#125—831no—
363#124—831no—
364#123—1661no—
365C22⋊Q8—21no—
366C22⋊Q8—831no—
367C22⋊Q8C4×D8311yescharacteristic
368C22⋊Q8C4×D8311yescharacteristic
369#121—831no—
370C4×Q8—21no—
371C4×Q8—831no—
372C4×Q8C22×D8311yescharacteristic
373C4×Q8C22×D8311yescharacteristic
374C4×D4—831no—
375C4×D4—1661no—
376#117—21no—
377#117—1661no—
378C2×C42C22×D8311yescharacteristic
379#107—831no—
380#107—831no—
381#106—831no—
382#106—831no—
383C4⋊C8—21no—
384C4⋊C8—831no—
385C4⋊C8—831no—
386C4⋊C8—831no—
387C4⋊C8—831no—
388C4⋊C8—1661no—
389C4⋊C8—1661no—
390C4⋊C8—1661no—
391C4⋊C8—1661no—
392C4⋊C8—1661no—
393C4⋊C8—1661no—
394C4⋊C8C22×D8311yescharacteristic
395C4⋊C8C22×D8311yescharacteristic
396#103—831no—
397#103—831no—
398#103—831no—
399#103—831no—
400#103—831no—
401#103—831no—
402#102—831no—
403#102—831no—
404C22⋊C8—831no—
405C22⋊C8—831no—
406C22⋊C8—1661no—
407C22⋊C8—1661no—
408C22⋊C8—1661no—
409#97—831no—
410#97—831no—
411#97—1661no—
412#97—1661no—
413#97—1661no—
414#97—1661no—
415C4×C8—21no—
416C4×C8—831no—
417C4×C8—831no—
418C4×C8—831no—
419C4×C8—831no—
420C4×C8—1661no—
421C4×C8—1661no—
422C4×C8—1661no—
423C4×C8C22×D8311yescharacteristic
424C4×C8C22×D8311yescharacteristic
425C2×Q8—21no—
426C2×Q8—831no—
427C2×Q8C2×C4×D8311yescharacteristic
428C2×Q8C2×C4×D8311yescharacteristic
429C2×D4—831no—
430C2×D4—1661no—
431C22×C4—1661no—
432C22×C4C2×C4×D8311yescharacteristic
433C22×C4D4×D8311yescharacteristic
434C22×C4#1305058911yescharacteristic
435Q16—1662no—
436Q16—1662no—
437SD16—1662no—
438SD16—1662no—
439M16—81no—
440M16—6641no—
441M16—1662no—
442M16—1662no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—42no—
448C2×C8—831no—
449C2×C8—831no—
450C2×C8—831no—
451C2×C8—831no—
452C2×C8—831no—
453C2×C8—831no—
454C2×C8—831no—
455C2×C8—831no—
456C2×C8—6641no—
457C2×C8—1661no—
458C2×C8—1661no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—831no—
467C4⋊C4—831no—
468C4⋊C4—1661no—
469C4⋊C4—1661no—
470C4⋊C4—1661no—
471C4⋊C4—1661no—
472C4⋊C4C2×C4×D8311yescharacteristic
473C4⋊C4C2×C4×D8311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—1661no—
477C22⋊C4—1661no—
478C22⋊C4—1661no—
479C22⋊C4—1661no—
480C22⋊C4—1661no—
481C42—21no—
482C42—21no—
483C42—1661no—
484C42C2×C4×D8311yescharacteristic
485C42D4×D8311yescharacteristic
486C42#1305058911yescharacteristic
487C42C23×D8311yescharacteristic
488C23—1661no—
489C23(C22⋊D83)⋊C411yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—81no—
495Q8—1661no—
496Q8—1661no—
497D4—6641no—
498D4—1661no—
499D4—1661no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—3321no—
510C2×C4—3321no—
511C2×C4—1661no—
512C2×C4—1661no—
513C2×C4—1661no—
514C2×C4(C22⋊D83)⋊C411yescharacteristic
515C2×C4(C22⋊D83)⋊C411yescharacteristic
516C2×C4(C22⋊D83)⋊C411yescharacteristic
517C2×C4C22×C4×D8311yescharacteristic
518C2×C4C2×D4×D8311yescharacteristic
519C2×C4C2×#1305058911yescharacteristic
520C8—22no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—3321no—
525C8—3321no—
526C8—832no—
527C8—832no—
528C8—1661no—
529C8—1661no—
530C8—1661no—
531C8—1661no—
532C8—1661no—
533C8—1661no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—3321no—
538C22—3321no—
539C22—3321no—
540C22C2×(C22⋊D83)⋊C411yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—3321no—
550C4—3321no—
551C4—3321no—
552C4#131×D8311yescharacteristic
553C4#131×D8311yescharacteristic
554C4#1912850711yescharacteristic
555C4#1912851411yescharacteristic
556C2—41no—
557C2—6641no—
558C2#2491617111yescharacteristic
559C2#2491630011yescharacteristic
560C2#2491636911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1493C2
socleC22×C83C2×C4×D4
prime radical#14581766C2×C4
cosocleC42×C83C24
hypercenter#1493D83
hypocenterC83#17969
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
3. #24916558C2semidirect
4. #24906369C2semidirect
5. #24906368C2semidirect
6. #24906357C2semidirect
7. #24906350C2semidirect
8. #24906279C2semidirect
9. #24906278C2semidirect
10. #24906267C2semidirect
11. #24906260C2semidirect
12. #24906228C2semidirect
14. C8×#13050574C2semidirect
15. C83×#1493C2semidirect
294. #1493D83semidirect
296. C83#17969semidirect

Maximal subgroups

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

subgroupindex
#249180632
#249166082
#249165582
#249063692
#249063682
#249063572
#249063502
#249062792
#249062782
#249062672
#249062602
#249062282
#249059242
C8×#130505742
C83×#14932
#1796983