Finite Group Databasebeta

← #35375262

Subgroups — #35375262

Order 21248.

544 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918046C211yesmaximal, characteristic
2#24916559C211yesmaximal, characteristic
3#24916554C211yesmaximal, characteristic
4#24906336C211yesmaximal, characteristic, complemented
5#24906335C211yesmaximal, characteristic, complemented
6#24906333C211yesmaximal, characteristic, complemented
7#24906316C211yesmaximal, characteristic, complemented
8#24906313C211yesmaximal, characteristic, complemented
9#24906311C211yesmaximal, characteristic, complemented
10#24906310C211yesmaximal, characteristic, complemented
11#24906223C211yesmaximal, characteristic
12#24905934C211yesmaximal, characteristic
13#24905934C211yesmaximal, characteristic
14#24905754C211yesmaximal, characteristic
15C83×#1587C211yesmaximal, characteristic, complemented
16#19128255C2211yescharacteristic
17#19128255C2211yescharacteristic
18#19128105C411yescharacteristic
19#19128079C411yescharacteristic
20#19128050C411yescharacteristic
21#19128050C411yescharacteristic
22#19127943C411yescharacteristic
23#19127941C411yescharacteristic
24#19127941C411yescharacteristic
25#19127939C411yescharacteristic
26#19127832C2211yescharacteristic
27#19127831—21no—
28#19127831C2211yescharacteristic
29#19127830—21no—
30#19127829—21no—
31#19127828—21no—
32#19127828C2211yescharacteristic
33Q8×C83⋊C8C2211yescharacteristic
34C8×Dic166C2211yescharacteristic
35#19127825C2211yescharacteristic
36C4×Dic332C2211yescharacteristic
37C4×#13050580C2211yescharacteristic
38C4×#13050580C2211yescharacteristic
39#19127763—21no—
40#19127761—21no—
41#19127761—21no—
42#19127760—21no—
43#19127757C2211yescharacteristic
44#19127757C2211yescharacteristic
45#19127752C2211yescharacteristic
46#19127752C2211yescharacteristic
47C4×C8×D83C2211yescharacteristic
48#19127453C2211yescharacteristic
49#19127453C2211yescharacteristic
50#19127452C2211yescharacteristic
51#19127433C2211yescharacteristic
52#19127433C2211yescharacteristic
53Q8⋊(C83⋊C8)C2211yescharacteristic
54Q8⋊(C83⋊C8)C2211yescharacteristic
55#19127431C2211yescharacteristic
56#19127431C2211yescharacteristic
57#19127423C2211yescharacteristic
58#19127423C2211yescharacteristic
59#19127422C2211yescharacteristic
60#446×C83C2211yescharacteristic
61C8×Q8×C83C2211yescharacteristic
62C4×Q16×C83C2211yescharacteristic
63#334×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65Q8⋊C8×C83C2211yescharacteristic
66#322×C83C2211yescharacteristic
67C2×Dic332C2×C411yescharacteristic
68C2×#13050580C2×C411yescharacteristic
69C2×#13050580C2×C411yescharacteristic
70C2×C8×D83C2×C411yescharacteristic
71C2×C8×D83C2×C411yescharacteristic
72#14581791C2×C411yescharacteristic
73#14581791C2×C411yescharacteristic
74#14581790C2×C411yescharacteristic
75#14581790C2×C411yescharacteristic
76#14581782—21no—
77#14581782—21no—
78#14581772C2×C411yescharacteristic
79#14581772C2×C411yescharacteristic
80#14581770—21no—
81#14581770—21no—
82#14581768C2×C411yescharacteristic
83#14581768C2×C411yescharacteristic
84C4×Dic166—21no—
85C4×Dic166—21no—
86C4×Dic166C2311yescharacteristic
87C4×Dic166C2311yescharacteristic
88#14581749—21no—
89#14581749—21no—
90C42×D83C2311yescharacteristic
91#14581726C2×C411yescharacteristic
92#14581725C2×C411yescharacteristic
93#14581725C2×C411yescharacteristic
94C4⋊(C83⋊C8)—21no—
95C4⋊(C83⋊C8)—21no—
96C4⋊(C83⋊C8)C2311yescharacteristic
97C4⋊(C83⋊C8)C2311yescharacteristic
98Dic83⋊C8—21no—
99Dic83⋊C8—21no—
100Dic83⋊C8—21no—
101Dic83⋊C8—21no—
102Dic83⋊C8—21no—
103Dic83⋊C8D411yescharacteristic
104Dic83⋊C8D411yescharacteristic
105#14581717C2×C411yescharacteristic
106#14581717C2×C411yescharacteristic
107#14581716C2×C411yescharacteristic
108#14581716C2×C411yescharacteristic
109#14581715C2×C411yescharacteristic
110#14581715C2×C411yescharacteristic
111(C2×D83)⋊C8—21no—
112(C2×D83)⋊C8—21no—
113(C2×D83)⋊C8—21no—
114(C2×D83)⋊C8D411yescharacteristic
115(C2×D83)⋊C8D411yescharacteristic
116#14581703—21no—
117#14581702—21no—
118#14581702—21no—
119#14581702—21no—
120#14581702—21no—
121C4×C83⋊C8—21no—
122C4×C83⋊C8C2311yescharacteristic
123C4×C83⋊C8C2311yescharacteristic
124C4×C83⋊C8C2311yescharacteristic
125C8×Dic83—21no—
126C8×Dic83—21no—
127C8×Dic83C2×C411yescharacteristic
128C8×Dic83C2×C411yescharacteristic
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
139#97×C83—21no—
140C4×C8×C83—21no—
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C2×Dic166—21no—
145C2×Dic166—21no—
146C2×Dic166C22×C411yescharacteristic
147C2×Dic166C22×C411yescharacteristic
148C2×C4×D83C22×C411yescharacteristic
149C2×C4×D83C2×D411yescharacteristic
150C2×C4×D83#4111yescharacteristic
151Dic332—41no—
152#13050580—41no—
153#13050580—41no—
154C2×C83⋊C8—21no—
155C2×C83⋊C8—21no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8C22×C411yescharacteristic
158C2×C83⋊C8C22×C411yescharacteristic
159C2×C83⋊C8C2×D411yescharacteristic
160C2×C83⋊C8C2×D411yescharacteristic
161C8×D83—41no—
162C8×D83—41no—
163C4⋊Dic83—21no—
164C4⋊Dic83—21no—
165C4⋊Dic83C22×C411yescharacteristic
166C4⋊Dic83C22×C411yescharacteristic
167Dic83⋊C4—21no—
168Dic83⋊C4—21no—
169Dic83⋊C4—21no—
170Dic83⋊C4—21no—
171Dic83⋊C4—21no—
172Dic83⋊C4—21no—
173Dic83⋊C4—21no—
174Dic83⋊C4—21no—
175Dic83⋊C4—21no—
176Dic83⋊C4—21no—
177(C2×D83)⋊C4—21no—
178(C2×D83)⋊C4—21no—
179(C2×D83)⋊C4—21no—
180(C2×D83)⋊C4—21no—
181C4×Dic83—21no—
182C4×Dic83—21no—
183C4×Dic83C22×C411yescharacteristic
184C4×Dic83C2×D411yescharacteristic
185C4×Dic83#4111yescharacteristic
186C2×Q8×C83C22×C411yescharacteristic
187C2×Q8×C83C22×C411yescharacteristic
188Q16×C83—41no—
189C2×C8×C83—21no—
190C2×C8×C83—21no—
191C2×C8×C83—21no—
192C2×C8×C83C22×C411yescharacteristic
193C2×C8×C83C22×C411yescharacteristic
194C2×C8×C83C2×D411yescharacteristic
195C2×C8×C83C2×D411yescharacteristic
196C4⋊C4×C83—21no—
197C4⋊C4×C83—21no—
198C4⋊C4×C83C22×C411yescharacteristic
199C4⋊C4×C83C22×C411yescharacteristic
200C42×C83—21no—
201C42×C83—21no—
202C42×C83C2411yescharacteristic
203C22×D83C4×D411yescharacteristic
204Q8×C83—21no—
205Q8×C83—21no—
206Q8×C83—21no—
207Q8×C83—21no—
208C2×C4×C83—21no—
209C2×C4×C83—21no—
210C2×C4×C83—21no—
211C2×C4×C83—21no—
212C2×C4×C83C23×C411yescharacteristic
213C2×C4×C83C22×D411yescharacteristic
214C2×C4×C83C2×#4111yescharacteristic
215C2×Dic83—21no—
216C2×Dic83—21no—
217C2×Dic83—21no—
218C2×Dic83—21no—
219C2×Dic83C4×D411yescharacteristic
220C2×Dic83C4×D411yescharacteristic
221C2×Dic83C4×D411yescharacteristic
222C4×D83—21no—
223C4×D83—21no—
224C4×D83—21no—
225C4×D83—21no—
226C4×D83—41no—
227Dic166—21no—
228Dic166—21no—
229Dic166—21no—
230Dic166—21no—
231Dic166—81no—
232Dic166—81no—
233C8×C83—21no—
234C8×C83—21no—
235C8×C83—21no—
236C8×C83—21no—
237C8×C83—41no—
238C8×C83—41no—
239C8×C83—41no—
240C83⋊C8—21no—
241C83⋊C8—21no—
242C83⋊C8—21no—
243C83⋊C8—21no—
244C83⋊C8—41no—
245C83⋊C8—41no—
246C83⋊C8—41no—
247C22×C83C2×C4×D411yescharacteristic
248C2×D83—21no—
249C2×D83—21no—
250C2×D83—21no—
251C4×C83—21no—
252C4×C83—41no—
253C4×C83—41no—
254C4×C83—41no—
255C4×C83—41no—
256C4×C83#56811yescharacteristic
257C4×C83#56811yescharacteristic
258C4×C83#57811yescharacteristic
259C4×C83#57811yescharacteristic
260Dic83—21no—
261Dic83—21no—
262Dic83—21no—
263Dic83—41no—
264Dic83—41no—
265Dic83—41no—
266Dic83—41no—
267#17991—831nomaximal, Sylow
268C2×C83#293211yescharacteristic
269C2×C83#295011yescharacteristic
270C2×C83#295711yescharacteristic
271D83—41no—
272#3170—831no—
273#2985—831no—
274#2985—831no—
275#1587—831no—
276#1587—831no—
277#1587—831no—
278#1587D8311yescharacteristic, complemented
279#1584—831no—
280#1584—831no—
281#1584—831no—
282#1584—831no—
283#1568—831no—
284#1497—831no—
285#1497—831no—
286#1452—831no—
287C83#1799111yescharacteristic, complemented, Sylow
288#533—831no—
289#533—831no—
290#500—831no—
291#494—831no—
292#487—831no—
293#487—831no—
294#467—831no—
295#467—831no—
296#467—831no—
297#467—831no—
298#446—831no—
299#446—831no—
300#446—831no—
301#446—1661no—
302#446—1661no—
303#446—1661no—
304#446—1661no—
305#446C2×D8311yescharacteristic
306C8×Q8—831no—
307C8×Q8—831no—
308C8×Q8—831no—
309C8×Q8C2×D8311yescharacteristic
310C4×Q16—831no—
311C4×Q16—831no—
312C4×Q16—831no—
313C4×Q16C2×D8311yescharacteristic
314#433—1661no—
315#433—1661no—
316#433—1661no—
317#433—1661no—
318#432—831no—
319#432—831no—
320#431—831no—
321#431—831no—
322C2×C4×C8—831no—
323#335—831no—
324#335—831no—
325#334—831no—
326#334C2×D8311yescharacteristic
327Q8⋊C8—831no—
328Q8⋊C8—831no—
329Q8⋊C8—831no—
330Q8⋊C8—831no—
331Q8⋊C8—831no—
332Q8⋊C8—831no—
333Q8⋊C8C2×D8311yescharacteristic
334Q8⋊C8C2×D8311yescharacteristic
335#322—831no—
336#322—831no—
337#322—831no—
338#322C2×D8311yescharacteristic
339C2×Q16—831no—
340C2×Q16—831no—
341C2×Q16—831no—
342C2×Q16C4×D8311yescharacteristic
343C22×C8—831no—
344C22×C8—831no—
345C4⋊Q8—831no—
346C4⋊Q8—831no—
347C4⋊Q8—831no—
348C4⋊Q8—831no—
349#125—1661no—
350#125—1661no—
351C22⋊Q8—831no—
352C22⋊Q8—831no—
353C22⋊Q8—831no—
354C22⋊Q8—831no—
355C22⋊Q8—1661no—
356C22⋊Q8—1661no—
357C4×Q8—831no—
358C4×Q8—831no—
359C4×Q8—1661no—
360C4×Q8—1661no—
361C4×Q8C22×D8311yescharacteristic
362C4×Q8C22×D8311yescharacteristic
363#117—1661no—
364#117—1661no—
365C2×C42—831no—
366#107—831no—
367#107—831no—
368#107—831no—
369#107C4×D8311yescharacteristic
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8—831no—
373C4⋊C8—831no—
374C4⋊C8—831no—
375C4⋊C8—831no—
376C4⋊C8—1661no—
377C4⋊C8—1661no—
378C4⋊C8—1661no—
379C4⋊C8—1661no—
380C4⋊C8—1661no—
381C4⋊C8—1661no—
382C4⋊C8—1661no—
383C4⋊C8C22×D8311yescharacteristic
384C4⋊C8C22×D8311yescharacteristic
385#103—831no—
386#103—831no—
387#103—831no—
388#103—831no—
389#103—831no—
390#103—831no—
391#103C4×D8311yescharacteristic
392#103C4×D8311yescharacteristic
393C22⋊C8—831no—
394C22⋊C8—831no—
395C22⋊C8—1661no—
396C22⋊C8—1661no—
397C22⋊C8—1661no—
398#97—21no—
399#97—1661no—
400#97—1661no—
401#97—1661no—
402#97—1661no—
403#97—1661no—
404C4×C8—21no—
405C4×C8—831no—
406C4×C8—831no—
407C4×C8—831no—
408C4×C8—831no—
409C4×C8—831no—
410C4×C8—1661no—
411C4×C8—1661no—
412C4×C8—1661no—
413C4×C8C22×D8311yescharacteristic
414C4×C8C22×D8311yescharacteristic
415C4×C8C22×D8311yescharacteristic
416C2×Q8—831no—
417C2×Q8—831no—
418C2×Q8—1661no—
419C2×Q8—1661no—
420C2×Q8C2×C4×D8311yescharacteristic
421C2×Q8C2×C4×D8311yescharacteristic
422C22×C4—831no—
423C22×C4—831no—
424C22×C4—831no—
425Q16—41no—
426Q16—3321no—
427Q16—3321no—
428Q16—3321no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—3321no—
433C2×C8—3321no—
434C2×C8—831no—
435C2×C8—831no—
436C2×C8—831no—
437C2×C8—831no—
438C2×C8—1661no—
439C2×C8—1661no—
440C2×C8—1661no—
441C2×C8C2×C4×D8311yescharacteristic
442C2×C8C2×C4×D8311yescharacteristic
443C2×C8D4×D8311yescharacteristic
444C2×C8D4×D8311yescharacteristic
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—831no—
448C4⋊C4—831no—
449C4⋊C4—1661no—
450C4⋊C4—1661no—
451C4⋊C4—1661no—
452C4⋊C4—1661no—
453C4⋊C4—1661no—
454C4⋊C4—1661no—
455C4⋊C4—1661no—
456C4⋊C4—1661no—
457C4⋊C4—1661no—
458C4⋊C4—1661no—
459C4⋊C4—1661no—
460C4⋊C4—1661no—
461C4⋊C4C2×C4×D8311yescharacteristic
462C4⋊C4C2×C4×D8311yescharacteristic
463C22⋊C4—1661no—
464C22⋊C4—1661no—
465C22⋊C4—1661no—
466C22⋊C4—1661no—
467C42—21no—
468C42—21no—
469C42—831no—
470C42—831no—
471C42—831no—
472C42—1661no—
473C42—1661no—
474C42C23×D8311yescharacteristic
475C23—831no—
476Q8—21no—
477Q8—21no—
478Q8—21no—
479Q8—21no—
480Q8—6641no—
481Q8—6641no—
482Q8—1661no—
483Q8—1661no—
484Q8—1661no—
485Q8—1661no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—3321no—
491C2×C4—831no—
492C2×C4—831no—
493C2×C4—831no—
494C2×C4—1661no—
495C2×C4—1661no—
496C2×C4—1661no—
497C2×C4—1661no—
498C2×C4—1661no—
499C2×C4—1661no—
500C2×C4—1661no—
501C2×C4—1661no—
502C2×C4C22×C4×D8311yescharacteristic
503C2×C4C2×D4×D8311yescharacteristic
504C2×C4#41×D8311yescharacteristic
505C8—21no—
506C8—21no—
507C8—21no—
508C8—21no—
509C8—41no—
510C8—41no—
511C8—41no—
512C8—3321no—
513C8—3321no—
514C8—3321no—
515C8—1661no—
516C8—1661no—
517C8—1661no—
518C8—1661no—
519C22—1661no—
520C22—1661no—
521C22—1661no—
522C22C4×D4×D8311yescharacteristic
523C4—21no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—41no—
528C4—3321no—
529C4—3321no—
530C4—3321no—
531C4—3321no—
532C4—1661no—
533C4—1661no—
534C4—1661no—
535C4#1912846611yescharacteristic
536C4#1912846711yescharacteristic
537C4#1912851711yescharacteristic
538C4#1912851711yescharacteristic
539C2—3321no—
540C2#2491617711yescharacteristic
541C2#2491632811yescharacteristic
542C2#2491637511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1587C2
socleC22×C83C2×C4×D4
prime radicalC22×D83C4×D4
cosocleC42×C83C24
hypercenter#1587D83
hypocenterC83#17991
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
4. #24906336C2semidirect
5. #24906335C2semidirect
6. #24906333C2semidirect
7. #24906316C2semidirect
8. #24906313C2semidirect
9. #24906311C2semidirect
10. #24906310C2semidirect
15. C83×#1587C2semidirect
278. #1587D83semidirect
287. C83#17991semidirect

Maximal subgroups

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

subgroupindex
#249180462
#249165592
#249165542
#249063362
#249063352
#249063332
#249063162
#249063132
#249063112
#249063102
#249062232
#249059342
#249057542
C83×#15872
#1799183