Finite Group Databasebeta

← #35376271

Subgroups — #35376271

Order 21248.

588 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#24918069C211yesmaximal, characteristic
2#24916461C211yesmaximal, characteristic
3#24916406C211yesmaximal, characteristic, complemented
4#24906364C211yesmaximal, characteristic, complemented
5#24906359C211yesmaximal, characteristic, complemented
6#24906340C211yesmaximal, characteristic, complemented
7#24906333C211yesmaximal, characteristic, complemented
8#24906312C211yesmaximal, characteristic, complemented
9#24906298C211yesmaximal, characteristic, complemented
10#24906281C211yesmaximal, characteristic, complemented
11#24906262C211yesmaximal, characteristic, complemented
12#24905883C211yesmaximal, characteristic, complemented
13#24905874C211yesmaximal, characteristic
14#24905766C211yesmaximal, characteristic, complemented
15C83×#1565C211yesmaximal, characteristic, complemented
16#19128258C2211yescharacteristic
17#19128235C2211yescharacteristic
18#19128110C411yescharacteristic
19#19128095C411yescharacteristic
20#19128070C411yescharacteristic
21#19128061C411yescharacteristic
22#19127959C411yescharacteristic
23#19127959C411yescharacteristic
24#19127947C411yescharacteristic
25#19127947C411yescharacteristic
26#19127830—21no—
27#19127830—21no—
28#19127828C2211yescharacteristic
29#19127828C2211yescharacteristic
30#19127828C2211yescharacteristic
31#19127825C2211yescharacteristic
32#19127825C2211yescharacteristic
33#19127825C2211yescharacteristic
34C4×Dic332C2211yescharacteristic
35C4×Dic332C2211yescharacteristic
36C4×#13050579C2211yescharacteristic
37C4×#13050579C2211yescharacteristic
38#19127778C2211yescharacteristic
39#19127776—21no—
40#19127775—21no—
41#19127766C2211yescharacteristic
42#19127760—21no—
43#19127727—21no—
44#19127656—21no—
45#19127655—21no—
46C4×#13050574C2211yescharacteristic
47C4×#13050574C2211yescharacteristic
48#19127431C2211yescharacteristic
49#19127431C2211yescharacteristic
50#19127431C2211yescharacteristic
51#19127431C2211yescharacteristic
52#19127431C2211yescharacteristic
53#19127431C2211yescharacteristic
54#19127428C2211yescharacteristic
55#19127428C2211yescharacteristic
56#19127423C2211yescharacteristic
57#19127423C2211yescharacteristic
58#19127422C2211yescharacteristic
59C8×C83⋊C8C2211yescharacteristic
60#431×C83C2211yescharacteristic
61C2×C4⋊C8×C83C2211yescharacteristic
62C4×M16×C83C2211yescharacteristic
63#335×C83C2211yescharacteristic
64#335×C83C2211yescharacteristic
65#334×C83C2211yescharacteristic
66#334×C83C2211yescharacteristic
67C2×Dic332C2×C411yescharacteristic
68C2×Dic332C2×C411yescharacteristic
69C2×#13050579C2×C411yescharacteristic
70C2×#13050579C2×C411yescharacteristic
71C2×#13050574—21no—
72C2×#13050574D411yescharacteristic
73C2×#13050574D411yescharacteristic
74C2×#13050573—21no—
75C2×C8×D83—21no—
76#14581792C2×C411yescharacteristic
77#14581792C2×C411yescharacteristic
78#14581786—21no—
79#14581784—21no—
80#14581784C2×C411yescharacteristic
81#14581780C2×C411yescharacteristic
82#14581775—21no—
83#14581771—21no—
84#14581771C2×C411yescharacteristic
85#14581771C2×C411yescharacteristic
86#14581771C2×C411yescharacteristic
87#14581766C2×C411yescharacteristic
88C4×Dic166—21no—
89C4×Dic166C2311yescharacteristic
90C4×Dic166C2311yescharacteristic
91C4×Dic166C2311yescharacteristic
92C4×D332C2311yescharacteristic
93C4×C22⋊D83—21no—
94#14581751—21no—
95#14581749—21no—
96#14581726C2×C411yescharacteristic
97#14581726C2×C411yescharacteristic
98#14581724C2×C411yescharacteristic
99#14581724C2×C411yescharacteristic
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
114(C2×D83)⋊C8—21no—
115(C2×D83)⋊C8—21no—
116#14581703—21no—
117#14581703D411yescharacteristic
118#14581703D411yescharacteristic
119#14581702—21no—
120#14581702—21no—
121#14581702—21no—
122C4×C83⋊C8C2311yescharacteristic
123C4×C83⋊C8C2311yescharacteristic
124C4×C83⋊C8C2311yescharacteristic
125C4×C83⋊C8C2311yescharacteristic
126C8×Dic83—21no—
127C8×Dic83—21no—
128C8×Dic83—21no—
129C2×M16×C83C2×C411yescharacteristic
130C2×M16×C83C2×C411yescharacteristic
131C22×C8×C83—21no—
132C2×C42×C83C2311yescharacteristic
133C4⋊C8×C83—21no—
134C4⋊C8×C83C2311yescharacteristic
135C4⋊C8×C83C2311yescharacteristic
136C4⋊C8×C83C2311yescharacteristic
137C4⋊C8×C83C2311yescharacteristic
138C22⋊C8×C83—21no—
139#97×C83C2×C411yescharacteristic
140#97×C83C2×C411yescharacteristic
141C4×C8×C83—21no—
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C2×Dic166—21no—
145C2×Dic166C22×C411yescharacteristic
146C2×Dic166C22×C411yescharacteristic
147C2×Dic166C22×C411yescharacteristic
148C2×D332C22×C411yescharacteristic
149C2×C22⋊D83—21no—
150C2×C4×D83—21no—
151Dic332—22no—
152Dic332—41no—
153#13050579—22no—
154#13050579—41no—
155#13050574—22no—
156#13050574—41no—
157#13050574—42no—
158#13050573—42no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8—21no—
161C2×C83⋊C8C2×D411yescharacteristic
162C2×C83⋊C8C2×D411yescharacteristic
163C2×C83⋊C8C2×D411yescharacteristic
164C2×C83⋊C8C2×D411yescharacteristic
165C8×D83—42no—
166C4⋊Dic83—21no—
167C4⋊Dic83—21no—
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—
182C22⋊Dic83—21no—
183C22⋊Dic83—21no—
184(C2×D83)⋊C4—21no—
185(C2×D83)⋊C4—21no—
186(C2×D83)⋊C4—21no—
187(C2×D83)⋊C4—21no—
188C4×Dic83—21no—
189C4×Dic83—21no—
190C4×Dic83—21no—
191C22×C4×C83C22×C411yescharacteristic
192C22×C4×C83C2×D411yescharacteristic
193C22×C4×C83#4111yescharacteristic
194M16×C83—22no—
195M16×C83—41no—
196C2×C8×C83—21no—
197C2×C8×C83—21no—
198C2×C8×C83—21no—
199C2×C8×C83—21no—
200C2×C8×C83—42no—
201C2×C8×C83C22×C411yescharacteristic
202C2×C8×C83C22×C411yescharacteristic
203C2×C8×C83C22×C411yescharacteristic
204C2×C8×C83C22×C411yescharacteristic
205C42×C83C22×C411yescharacteristic
206C42×C83C2×D411yescharacteristic
207C42×C83#4111yescharacteristic
208C42×C83C2411yescharacteristic
209C23×C83C4×D411yescharacteristic
210C22×D83—21no—
211C2×C4×C83—21no—
212C2×C4×C83—21no—
213C2×C4×C83—21no—
214C2×C4×C83—21no—
215C2×C4×C83—41no—
216C2×C4×C83C4×D411yescharacteristic
217C2×C4×C83C4×D411yescharacteristic
218C2×C4×C83C4×D411yescharacteristic
219C2×C4×C83C23×C411yescharacteristic
220C2×C4×C83C22×D411yescharacteristic
221C2×C4×C83C2×#4111yescharacteristic
222C22⋊D83—81no—
223C2×Dic83—21no—
224C2×Dic83—21no—
225C2×Dic83—21no—
226C2×Dic83—21no—
227C2×Dic83—21no—
228C2×Dic83—21no—
229C2×Dic83—21no—
230D332—21no—
231D332—21no—
232C4×D83—41no—
233C4×D83—41no—
234Dic166—21no—
235Dic166—21no—
236Dic166—21no—
237Dic166—21no—
238Dic166—21no—
239Dic166—21no—
240Dic166—81no—
241C8×C83—21no—
242C8×C83—21no—
243C8×C83—21no—
244C8×C83—41no—
245C8×C83—41no—
246C8×C83—41no—
247C8×C83—41no—
248C8×C83#13112yes—
249C83⋊C8—22no—
250C83⋊C8—21no—
251C83⋊C8—21no—
252C83⋊C8—21no—
253C83⋊C8—41no—
254C83⋊C8#13712yes—
255C22×C83—21no—
256C22×C83—21no—
257C22×C83—21no—
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×C83C2×#13711yescharacteristic
269C4×C83#57511yescharacteristic
270Dic83—41no—
271Dic83—41no—
272Dic83—41no—
273Dic83—41no—
274Dic83—41no—
275Dic83—41no—
276Dic83—41no—
277#18077—831nomaximal, Sylow
278C2×C83—41no—
279C2×C83#293511yescharacteristic
280C2×C83C4×#13711yescharacteristic
281C2×C83#295611yescharacteristic
282D83—81no—
283#3172—831no—
284#2969—831no—
285#2962—831no—
286#1592—831no—
287#1591—831no—
288#1588—831no—
289#1587—831no—
290#1584—831no—
291#1582—831no—
292#1579—831no—
293C8×SD16—831no—
294#1565D8311yescharacteristic, complemented
295#1485—831no—
296#1483—831no—
297#1455—831no—
298C83#1807711yescharacteristic, complemented, Sylow
299#533—831no—
300#529—831no—
301#501—831no—
302#497—831no—
303#491—831no—
304#489—831no—
305#470—831no—
306#470—831no—
307#468—831no—
308#468—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#436—1661no—
323#435—1661no—
324C8×D4—831no—
325#433—1661no—
326#431C2×D8311yescharacteristic
327#424—1661no—
328C2×C4⋊C8C2×D8311yescharacteristic
329#405—1661no—
330#405—1661no—
331C4×M16—831no—
332C4×M16—831no—
333C4×M16C2×D8311yescharacteristic
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—
348#322—831no—
349C82—831no—
350C2×Q16—831no—
351C2×Q16—831no—
352C2×SD16—831no—
353C2×SD16—831no—
354C2×M16—831no—
355C2×M16—831no—
356C2×M16—1661no—
357C2×M16—1661no—
358C2×M16C4×D8311yescharacteristic
359C2×M16C4×D8311yescharacteristic
360C22×C8—21no—
361C22×C8—1661no—
362C4⋊Q8—831no—
363C4⋊Q8—831no—
364#126—1661no—
365#125—831no—
366#125—1661no—
367#124—831no—
368#123—1661no—
369C22⋊Q8—831no—
370C22⋊Q8—831no—
371C22⋊Q8—831no—
372C22⋊Q8—1661no—
373#121—831no—
374C4×Q8—831no—
375C4×Q8—831no—
376C4×Q8—831no—
377C4×Q8—1661no—
378C4×D4—831no—
379C4×D4—1661no—
380#117—1661no—
381#117—1661no—
382C2×C42C22×D8311yescharacteristic
383#107—831no—
384#107—831no—
385#106—831no—
386#106—831no—
387C4⋊C8—21no—
388C4⋊C8—1661no—
389C4⋊C8—1661no—
390C4⋊C8—1661no—
391C4⋊C8—1661no—
392C4⋊C8—1661no—
393C4⋊C8—1661no—
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—1661no—
408C22⋊C8—1661no—
409#97—831no—
410#97—831no—
411#97—1661no—
412#97—1661no—
413#97—1661no—
414#97—1661no—
415#97C4×D8311yescharacteristic
416#97C4×D8311yescharacteristic
417C4×C8—21no—
418C4×C8—831no—
419C4×C8—831no—
420C4×C8—831no—
421C4×C8—831no—
422C4×C8—1661no—
423C4×C8—1661no—
424C4×C8—1661no—
425C4×C8C22×D8311yescharacteristic
426C4×C8C22×D8311yescharacteristic
427C2×Q8—831no—
428C2×Q8—831no—
429C2×Q8—831no—
430C2×Q8—1661no—
431C2×D4—831no—
432C2×D4—1661no—
433C22×C4—1661no—
434C22×C4C2×C4×D8311yescharacteristic
435C22×C4D4×D8311yescharacteristic
436C22×C4#1305059111yescharacteristic
437Q16—3321no—
438Q16—1662no—
439SD16—3321no—
440SD16—1662no—
441M16—22no—
442M16—41no—
443M16—3322no—
444M16—3322no—
445M16—3321no—
446M16—1662no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—42no—
452C2×C8—3322no—
453C2×C8—831no—
454C2×C8—831no—
455C2×C8—831no—
456C2×C8—831no—
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—
476C4⋊C4—1661no—
477C4⋊C4—1661no—
478C22⋊C4—1661no—
479C22⋊C4—1661no—
480C22⋊C4—1661no—
481C22⋊C4—1661no—
482C22⋊C4—1661no—
483C22⋊C4—1661no—
484C22⋊C4—1661no—
485C42—1661no—
486C42—1661no—
487C42—1661no—
488C42C2×C4×D8311yescharacteristic
489C42D4×D8311yescharacteristic
490C42#1305059111yescharacteristic
491C42C23×D8311yescharacteristic
492C23—1661no—
493C23#1458175411yescharacteristic
494Q8—6641no—
495Q8—1661no—
496Q8—1661no—
497Q8—1661no—
498Q8—1661no—
499Q8—1661no—
500Q8—1661no—
501D4—6641no—
502D4—1661no—
503D4—1661no—
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—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—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—3321no—
532C8—832no—
533C8—1662no—
534C8—1661no—
535C8—1661no—
536C8—1661no—
537C8#1458179812yes—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—3321no—
542C22—3321no—
543C22—3321no—
544C22C2×#1458175411yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—3321no—
550C4—3321no—
551C4—3321no—
552C4—3321no—
553C4—3321no—
554C4—3321no—
555C4—3321no—
556C4C2×#1458179811yescharacteristic
557C4#1912846711yescharacteristic
558C4#137×D8311yescharacteristic
559C4#1912849711yescharacteristic
560C2—41no—
561C2—6641no—
562C2#2491620611yescharacteristic
563C2#2491628111yescharacteristic
564C2#2491637211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1565C2
socleC22×C83C2×C4×D4
prime radical#14581766C2×C4
cosocleC42×C83C24
hypercenter#1565D83
hypocenterC83#18077
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
3. #24916406C2semidirect
4. #24906364C2semidirect
5. #24906359C2semidirect
6. #24906340C2semidirect
7. #24906333C2semidirect
8. #24906312C2semidirect
9. #24906298C2semidirect
10. #24906281C2semidirect
11. #24906262C2semidirect
12. #24905883C2semidirect
14. #24905766C2semidirect
15. C83×#1565C2semidirect
294. #1565D83semidirect
298. C83#18077semidirect

Maximal subgroups

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

subgroupindex
#249180692
#249164612
#249164062
#249063642
#249063592
#249063402
#249063332
#249063122
#249062982
#249062812
#249062622
#249058832
#249058742
#249057662
C83×#15652
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