Finite Group Databasebeta

← #35375595

Subgroups — #35375595

Order 21248.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917545C211yesmaximal, characteristic
2#24916619C211yesmaximal, characteristic
3#24916553C211yesmaximal, characteristic, complemented
4#24906359C211yesmaximal, characteristic, complemented
5#24906352C211yesmaximal, characteristic, complemented
6#24906340C211yesmaximal, characteristic, complemented
7#24906333C211yesmaximal, characteristic, complemented
8#24906333C211yesmaximal, characteristic, complemented
9#24906319C211yesmaximal, characteristic, complemented
10#24906269C211yesmaximal, characteristic, complemented
11#24906262C211yesmaximal, characteristic, complemented
12#24905921C211yesmaximal, characteristic
13C2×#19127431C211yesmaximal, characteristic, complemented
14#24905747C211yesmaximal, characteristic, complemented
15C83×#1573C211yesmaximal, characteristic, complemented
16#19128235C2211yescharacteristic
17C2×C4×Dic166C2211yescharacteristic
18#19128032C411yescharacteristic
19#19128015C411yescharacteristic
20#19128009C411yescharacteristic
21#19128009C411yescharacteristic
22#19127924C411yescharacteristic
23#19127924C411yescharacteristic
24#19127859C411yescharacteristic
25#19127842C411yescharacteristic
26#19127829—21no—
27#19127829—21no—
28#19127828C2211yescharacteristic
29#19127828C2211yescharacteristic
30#19127828C2211yescharacteristic
31#19127825C2211yescharacteristic
32#19127825C2211yescharacteristic
33#19127825C2211yescharacteristic
34C4×Dic332C2211yescharacteristic
35C4×Dic332C2211yescharacteristic
36C4×#13050579C2211yescharacteristic
37C4×#13050579C2211yescharacteristic
38#19127778C2211yescharacteristic
39#19127772—21no—
40#19127766C2211yescharacteristic
41C8×C22⋊D83—21no—
42#19127761—21no—
43#19127755—21no—
44#19127754C2211yescharacteristic
45#19127751—21no—
46#19127726—21no—
47C2×C4×C83⋊C8C2211yescharacteristic
48#19127431C2211yescharacteristic
49#19127431C2211yescharacteristic
50#19127431C2211yescharacteristic
51#19127431C2211yescharacteristic
52#19127431C2211yescharacteristic
53#19127431C2211yescharacteristic
54#19127428C2211yescharacteristic
55#19127428C2211yescharacteristic
56#19127423C2211yescharacteristic
57#19127423C2211yescharacteristic
58C8×C83⋊C8C2211yescharacteristic
59C8×C83⋊C8C2211yescharacteristic
60#432×C83C2211yescharacteristic
61#431×C83C2211yescharacteristic
62C2×C4⋊C8×C83C2211yescharacteristic
63#335×C83C2211yescharacteristic
64#335×C83C2211yescharacteristic
65#334×C83C2211yescharacteristic
66#334×C83C2211yescharacteristic
67C22×Dic166C2×C411yescharacteristic
68C2×Dic332C2×C411yescharacteristic
69C2×Dic332C2×C411yescharacteristic
70C2×#13050579C2×C411yescharacteristic
71C2×#13050579C2×C411yescharacteristic
72C2×#13050573—21no—
73C22×C83⋊C8—21no—
74C2×C8×D83—21no—
75#14581786—21no—
76#14581784C2×C411yescharacteristic
77#14581780C2×C411yescharacteristic
78#14581775—21no—
79#14581771C2×C411yescharacteristic
80#14581766C2×C411yescharacteristic
81C4×Dic166—21no—
82C4×Dic166—21no—
83C4×Dic166C2×C411yescharacteristic
84C4×Dic166C2×C411yescharacteristic
85C4×Dic166C2311yescharacteristic
86C4×Dic166C2311yescharacteristic
87C4×Dic166C2311yescharacteristic
88C4×D332C2311yescharacteristic
89C4×C22⋊D83—21no—
90#14581749—21no—
91C2×C4⋊Dic83C2×C411yescharacteristic
92C2×Dic83⋊C4—21no—
93C2×C4×Dic83—21no—
94#14581726C2×C411yescharacteristic
95#14581726C2×C411yescharacteristic
96#14581724C2×C411yescharacteristic
97#14581724C2×C411yescharacteristic
98C4⋊(C83⋊C8)D411yescharacteristic
99C4⋊(C83⋊C8)D411yescharacteristic
100Dic83⋊C8—21no—
101Dic83⋊C8—21no—
102Dic83⋊C8—21no—
103Dic83⋊C8—21no—
104Dic83⋊C8—21no—
105Dic83⋊C8—21no—
106#14581717C2×C411yescharacteristic
107#14581717C2×C411yescharacteristic
108#14581717C2×C411yescharacteristic
109#14581717C2×C411yescharacteristic
110#14581717C2×C411yescharacteristic
111#14581717C2×C411yescharacteristic
112#14581714C2×C411yescharacteristic
113#14581714C2×C411yescharacteristic
114C22⋊(C83⋊C8)D411yescharacteristic
115C22⋊(C83⋊C8)D411yescharacteristic
116(C2×D83)⋊C8—21no—
117(C2×D83)⋊C8—21no—
118#14581702—21no—
119#14581702—21no—
120#14581702—21no—
121C4×C83⋊C8—21no—
122C4×C83⋊C8C2311yescharacteristic
123C4×C83⋊C8C2311yescharacteristic
124C4×C83⋊C8C2311yescharacteristic
125C4×C83⋊C8C2311yescharacteristic
126C8×Dic83—21no—
127C8×Dic83—21no—
128C8×Dic83—21no—
129C22×C8×C83—21no—
130C2×C42×C83C2311yescharacteristic
131C4⋊C8×C83—21no—
132C4⋊C8×C83C2×C411yescharacteristic
133C4⋊C8×C83C2×C411yescharacteristic
134C4⋊C8×C83C2311yescharacteristic
135C4⋊C8×C83C2311yescharacteristic
136C4⋊C8×C83C2311yescharacteristic
137C4⋊C8×C83C2311yescharacteristic
138C22⋊C8×C83—21no—
139C22⋊C8×C83C2×C411yescharacteristic
140C22⋊C8×C83C2×C411yescharacteristic
141#97×C83—21no—
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C2×Dic166—22no—
145C2×Dic166—21no—
146C2×Dic166—41no—
147C2×Dic166C22×C411yescharacteristic
148C2×Dic166C22×C411yescharacteristic
149C2×Dic166C22×C411yescharacteristic
150C2×D332C22×C411yescharacteristic
151C2×C22⋊D83—21no—
152C22×Dic83—21no—
153C22×Dic83—21no—
154C2×C4×D83—21no—
155Dic332—22no—
156Dic332—41no—
157#13050579—22no—
158#13050579—41no—
159#13050573—81no—
160C2×C83⋊C8—24no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8—21no—
163C2×C83⋊C8C2×D411yescharacteristic
164C2×C83⋊C8C2×D411yescharacteristic
165C2×C83⋊C8C2×D411yescharacteristic
166C2×C83⋊C8C2×D411yescharacteristic
167C8×D83—81no—
168C4⋊Dic83—21no—
169C4⋊Dic83C22×C411yescharacteristic
170C4⋊Dic83C22×C411yescharacteristic
171C4⋊Dic83C22×C411yescharacteristic
172C4⋊Dic83C22×C411yescharacteristic
173Dic83⋊C4—21no—
174Dic83⋊C4—21no—
175Dic83⋊C4—21no—
176Dic83⋊C4—21no—
177Dic83⋊C4—21no—
178Dic83⋊C4—21no—
179Dic83⋊C4—21no—
180Dic83⋊C4—21no—
181C22⋊Dic83—21no—
182(C2×D83)⋊C4—21no—
183(C2×D83)⋊C4—21no—
184(C2×D83)⋊C4—21no—
185(C2×D83)⋊C4—21no—
186C4×Dic83—21no—
187C4×Dic83—21no—
188C4×Dic83—21no—
189C4×Dic83—21no—
190C4×Dic83—21no—
191C22×C4×C83C22×C411yescharacteristic
192C22×C4×C83C2×D411yescharacteristic
193C22×C4×C83#4111yescharacteristic
194C2×C8×C83—21no—
195C2×C8×C83—21no—
196C2×C8×C83—21no—
197C2×C8×C83—21no—
198C2×C8×C83—81no—
199C2×C8×C83C22×C411yescharacteristic
200C2×C8×C83C22×C411yescharacteristic
201C2×C8×C83C22×C411yescharacteristic
202C2×C8×C83C22×C411yescharacteristic
203C42×C83C22×C411yescharacteristic
204C42×C83C2×D411yescharacteristic
205C42×C83#4111yescharacteristic
206C42×C83C2411yescharacteristic
207C23×C83C4×D411yescharacteristic
208C22×D83—21no—
209C2×C4×C83—22no—
210C2×C4×C83—21no—
211C2×C4×C83—21no—
212C2×C4×C83—21no—
213C2×C4×C83—21no—
214C2×C4×C83C4×D411yescharacteristic
215C2×C4×C83C4×D411yescharacteristic
216C2×C4×C83C4×D411yescharacteristic
217C2×C4×C83C23×C411yescharacteristic
218C2×C4×C83C22×D411yescharacteristic
219C2×C4×C83C2×#4111yescharacteristic
220C22⋊D83—42no—
221C2×Dic83—21no—
222C2×Dic83—21no—
223C2×Dic83—21no—
224C2×Dic83—21no—
225C2×Dic83—21no—
226C2×Dic83—21no—
227C2×Dic83—21no—
228C2×Dic83—42no—
229C2×Dic83—42no—
230D332—21no—
231D332—21no—
232C4×D83—41no—
233C4×D83—41no—
234Dic166—21no—
235Dic166—21no—
236Dic166—21no—
237Dic166—21no—
238Dic166—21no—
239Dic166—42no—
240Dic166#13112yes—
241C8×C83—21no—
242C8×C83—21no—
243C8×C83—21no—
244C8×C83—21no—
245C8×C83—41no—
246C8×C83—41no—
247C8×C83—41no—
248C8×C83—41no—
249C83⋊C8—22no—
250C83⋊C8—22no—
251C83⋊C8—21no—
252C83⋊C8—21no—
253C83⋊C8—21no—
254C83⋊C8—21no—
255C22×C83—21no—
256C22×C83—21no—
257C22×C83#44312yes—
258C22×C83C2×C4×D411yescharacteristic
259C2×D83—41no—
260C2×D83—41no—
261C2×D83—41no—
262C4×C83—21no—
263C4×C83—21no—
264C4×C83—21no—
265C4×C83—21no—
266C4×C83C2×#13111yescharacteristic
267C4×C83#56811yescharacteristic
268C4×C83#57711yescharacteristic
269C4×C83#57811yescharacteristic
270Dic83—22no—
271Dic83—41no—
272Dic83—41no—
273Dic83—41no—
274Dic83—41no—
275Dic83—41no—
276Dic83—41no—
277#18017—831nomaximal, Sylow
278C2×C83—22no—
279C2×C83#293311yescharacteristic
280C2×C83#294711yescharacteristic
281C2×C83C2×#44311yescharacteristic
282D83—81no—
283#3108—831no—
284#2994—831no—
285#2984—831no—
286#1591—831no—
287#1590—831no—
288#1588—831no—
289#1587—831no—
290#1587—831no—
291#1585—831no—
292C8×Q16—831no—
293C8×SD16—831no—
294#1573D8311yescharacteristic, complemented
295#1494—831no—
296C2×Q8⋊C8—831no—
297#1450—831no—
298C83#1801711yescharacteristic, complemented, Sylow
299#529—831no—
300C2×C4×Q8—831no—
301#483—831no—
302#480—831no—
303#479—831no—
304#479—831no—
305#464—831no—
306#464—831no—
307#451—831no—
308#448—831no—
309#446—831no—
310#446—831no—
311#446—831no—
312#446—1661no—
313#446—1661no—
314C8×Q8—831no—
315C8×Q8—831no—
316C8×Q8—831no—
317C4×Q16—831no—
318C4×Q16—831no—
319C4×SD16—831no—
320C4×SD16—831no—
321#436—831no—
322#435—1661no—
323C8×D4—831no—
324C8×D4—1661no—
325#433—1661no—
326#432—1661no—
327#432C2×D8311yescharacteristic
328#431—831no—
329#431—1661no—
330#431C2×D8311yescharacteristic
331#424—1661no—
332C2×C4⋊C8C2×D8311yescharacteristic
333C2×C4×C8—831no—
334#335C2×D8311yescharacteristic
335#335C2×D8311yescharacteristic
336#334C2×D8311yescharacteristic
337#334C2×D8311yescharacteristic
338Q8⋊C8—831no—
339Q8⋊C8—831no—
340Q8⋊C8—831no—
341Q8⋊C8—831no—
342Q8⋊C8—831no—
343Q8⋊C8—831no—
344D4⋊C8—831no—
345D4⋊C8—831no—
346#322—831no—
347#322—831no—
348C82—831no—
349C82—831no—
350C22×Q8—831no—
351C2×Q16—831no—
352C2×Q16—831no—
353C2×SD16—831no—
354C2×SD16—831no—
355C2×M16—1661no—
356C22×C8—21no—
357C22×C8—1661no—
358C22×C8—1661no—
359#126—1661no—
360#125—831no—
361#124—831no—
362#123—1661no—
363C22⋊Q8—831no—
364#121—831no—
365C4×Q8—831no—
366C4×Q8—831no—
367C4×Q8—831no—
368C4×Q8—831no—
369C4×Q8—831no—
370C4×Q8—1661no—
371C4×Q8—1661no—
372C4×D4—831no—
373C4×D4—1661no—
374#117—1661no—
375C2×C4⋊C4—831no—
376C2×C4⋊C4—1661no—
377C2×C42—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—1661no—
387C4⋊C8—1661no—
388C4⋊C8—1661no—
389C4⋊C8—1661no—
390C4⋊C8—1661no—
391C4⋊C8—1661no—
392C4⋊C8C4×D8311yescharacteristic
393C4⋊C8C4×D8311yescharacteristic
394C4⋊C8C22×D8311yescharacteristic
395C4⋊C8C22×D8311yescharacteristic
396C4⋊C8C22×D8311yescharacteristic
397C4⋊C8C22×D8311yescharacteristic
398#103—831no—
399#103—831no—
400#103—831no—
401#103—831no—
402#103—831no—
403#103—831no—
404#102—831no—
405#102—831no—
406C22⋊C8—21no—
407C22⋊C8—831no—
408C22⋊C8—831no—
409C22⋊C8—1661no—
410C22⋊C8—1661no—
411C22⋊C8C4×D8311yescharacteristic
412C22⋊C8C4×D8311yescharacteristic
413#97—21no—
414#97—1661no—
415#97—1661no—
416#97—1661no—
417C4×C8—831no—
418C4×C8—831no—
419C4×C8—831no—
420C4×C8—831no—
421C4×C8—1661no—
422C4×C8—1661no—
423C4×C8—1661no—
424C4×C8—1661no—
425C4×C8C22×D8311yescharacteristic
426C4×C8C22×D8311yescharacteristic
427C2×Q8—3321no—
428C2×Q8—831no—
429C2×Q8—831no—
430C2×Q8—831no—
431C2×Q8—1662no—
432C2×Q8—1661no—
433C2×D4—831no—
434C2×D4—1661no—
435C22×C4—1661no—
436C22×C4—1661no—
437C22×C4—1661no—
438C22×C4C2×C4×D8311yescharacteristic
439C22×C4D4×D8311yescharacteristic
440C22×C4#1305059111yescharacteristic
441Q16—3321no—
442Q16—1662no—
443SD16—3321no—
444SD16—1662no—
445M16—6641no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—81no—
451C2×C8—831no—
452C2×C8—831no—
453C2×C8—831no—
454C2×C8—831no—
455C2×C8—6641no—
456C2×C8—1664no—
457C2×C8—1661no—
458C2×C8—1661no—
459C2×C8C2×C4×D8311yescharacteristic
460C2×C8C2×C4×D8311yescharacteristic
461C2×C8C2×C4×D8311yescharacteristic
462C2×C8C2×C4×D8311yescharacteristic
463C4⋊C4—831no—
464C4⋊C4—831no—
465C4⋊C4—831no—
466C4⋊C4—831no—
467C4⋊C4—1661no—
468C4⋊C4—1661no—
469C4⋊C4—1661no—
470C4⋊C4—1661no—
471C4⋊C4—1661no—
472C4⋊C4—1661no—
473C4⋊C4—1661no—
474C4⋊C4—1661no—
475C4⋊C4—1661no—
476C22⋊C4—1661no—
477C22⋊C4—1661no—
478C22⋊C4—1661no—
479C22⋊C4—1661no—
480C22⋊C4—1661no—
481C42—1661no—
482C42—1661no—
483C42—1661no—
484C42—1661no—
485C42—1661no—
486C42C2×C4×D8311yescharacteristic
487C42D4×D8311yescharacteristic
488C42#1305059111yescharacteristic
489C42C23×D8311yescharacteristic
490C23—1661no—
491C23#1458175411yescharacteristic
492Q8—3322no—
493Q8—832no—
494Q8—1661no—
495Q8—1661no—
496Q8—1661no—
497Q8—1661no—
498Q8—1661no—
499D4—3322no—
500D4—1661no—
501D4—1661no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—3322no—
508C2×C4—3322no—
509C2×C4—3321no—
510C2×C4—3321no—
511C2×C4—1661no—
512C2×C4—1661no—
513C2×C4—1661no—
514C2×C4—1661no—
515C2×C4—1661no—
516C2×C4—1661no—
517C2×C4—1661no—
518C2×C4#1458175411yescharacteristic
519C2×C4#1458175411yescharacteristic
520C2×C4#1458175411yescharacteristic
521C2×C4C22×C4×D8311yescharacteristic
522C2×C4C2×D4×D8311yescharacteristic
523C2×C4C2×#1305059111yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—1662no—
533C8—1662no—
534C8—1661no—
535C8—1661no—
536C8—1661no—
537C8—1661no—
538C22—21no—
539C22—21no—
540C22—3321no—
541C22—3321no—
542C22—3321no—
543C22#1912781712yes—
544C22C2×#1458175411yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—3321no—
550C4—3321no—
551C4—3321no—
552C4—3321no—
553C4—3321no—
554C4—3321no—
555C4—1662no—
556C4#131×D8311yescharacteristic
557C4#1912846611yescharacteristic
558C4#1912851111yescharacteristic
559C4#1912851711yescharacteristic
560C2—22no—
561C2—6641no—
562C2#2491618711yescharacteristic
563C2#2491630411yescharacteristic
564C2C2×#1912781711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1573C2
socleC22×C83C2×C4×D4
prime radical#14581766C2×C4
cosocleC42×C83C24
hypercenter#1573D83
hypocenterC83#18017
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
3. #24916553C2semidirect
4. #24906359C2semidirect
5. #24906352C2semidirect
6. #24906340C2semidirect
7. #24906333C2semidirect
8. #24906333C2semidirect
9. #24906319C2semidirect
10. #24906269C2semidirect
11. #24906262C2semidirect
13. C2×#19127431C2semidirect
14. #24905747C2semidirect
15. C83×#1573C2semidirect
294. #1573D83semidirect
298. C83#18017semidirect

Maximal subgroups

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

subgroupindex
#249175452
#249166192
#249165532
#249063592
#249063522
#249063402
#249063332
#249063192
#249062692
#249062622
#249059212
C2×#191274312
#249057472
C83×#15732
#1801783