Finite Group Databasebeta

← #35375536

Subgroups — #35375536

Order 21248.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917539C211yesmaximal, characteristic
2#24916468C211yesmaximal, characteristic
3#24916414C211yesmaximal, characteristic, complemented
4#24906369C211yesmaximal, characteristic, complemented
5#24906356C211yesmaximal, characteristic, complemented
6#24906337C211yesmaximal, characteristic, complemented
7#24906317C211yesmaximal, characteristic, complemented
8#24906310C211yesmaximal, characteristic, complemented
9#24906309C211yesmaximal, characteristic, complemented
10#24906272C211yesmaximal, characteristic, complemented
11#24906267C211yesmaximal, characteristic, complemented
12#24906254C211yesmaximal, characteristic, complemented
13#24905859C211yesmaximal, characteristic, complemented
14#24905758C211yesmaximal, characteristic, complemented
15C83×#1495C211yesmaximal, characteristic
16C2×C4×Dic166C2211yescharacteristic
17#19128029C411yescharacteristic
18#19128012C411yescharacteristic
19#19128005C411yescharacteristic
20#19128005C411yescharacteristic
21#19127920C411yescharacteristic
22#19127920C411yescharacteristic
23#19127856C411yescharacteristic
24#19127839C411yescharacteristic
25#19127832C2211yescharacteristic
26#19127830—21no—
27#19127830—21no—
28#19127828C2211yescharacteristic
29#19127828C2211yescharacteristic
30Q8×C83⋊C8C2211yescharacteristic
31#19127825C2211yescharacteristic
32#19127825C2211yescharacteristic
33C4×#13050580C2211yescharacteristic
34C4×#13050580C2211yescharacteristic
35C4×#13050578C2211yescharacteristic
36C4×#13050578C2211yescharacteristic
37#19127779—21no—
38#19127779C2211yescharacteristic
39#19127773—21no—
40D4×C83⋊C8C2211yescharacteristic
41#19127762—21no—
42#19127754C2211yescharacteristic
43#19127754C2211yescharacteristic
44#19127724—21no—
45#19127657—21no—
46C4×#13050574C2211yescharacteristic
47M16×Dic83—21no—
48#19127453C2211yescharacteristic
49#19127453C2211yescharacteristic
50#19127451C2211yescharacteristic
51#19127451C2211yescharacteristic
52#19127433C2211yescharacteristic
53#19127433C2211yescharacteristic
54#19127433C2211yescharacteristic
55#19127433C2211yescharacteristic
56#19127423C2211yescharacteristic
57#19127423C2211yescharacteristic
58#19127422C2211yescharacteristic
59C8×C83⋊C8C2211yescharacteristic
60#529×C83C2211yescharacteristic
61#431×C83C2211yescharacteristic
62#423×C83C2211yescharacteristic
63Q8⋊C8×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65D4⋊C8×C83C2211yescharacteristic
66D4⋊C8×C83C2211yescharacteristic
67C22×Dic166C2×C411yescharacteristic
68C2×#13050580C2×C411yescharacteristic
69C2×#13050580C2×C411yescharacteristic
70C2×#13050578C2×C411yescharacteristic
71C2×#13050578C2×C411yescharacteristic
72C2×#13050574—21no—
73C2×#13050574D411yescharacteristic
74C2×#13050574D411yescharacteristic
75C22×C83⋊C8—21no—
76C4×Dic166—21no—
77C4×Dic166—21no—
78C4×Dic166C2×C411yescharacteristic
79C4×Dic166C2×C411yescharacteristic
80C4×Dic166C2311yescharacteristic
81C4×Dic166C2311yescharacteristic
82C2×C4⋊Dic83C2×C411yescharacteristic
83C2×Dic83⋊C4—21no—
84C2×C4×Dic83—21no—
85#14581725C2×C411yescharacteristic
86#14581725C2×C411yescharacteristic
87#14581723C2×C411yescharacteristic
88#14581723C2×C411yescharacteristic
89C4⋊(C83⋊C8)—21no—
90C4⋊(C83⋊C8)—21no—
91C4⋊(C83⋊C8)C2×C411yescharacteristic
92C4⋊(C83⋊C8)C2×C411yescharacteristic
93C4⋊(C83⋊C8)C2311yescharacteristic
94C4⋊(C83⋊C8)C2311yescharacteristic
95Dic83⋊C8—21no—
96Dic83⋊C8—21no—
97Dic83⋊C8—21no—
98Dic83⋊C8—21no—
99#14581716C2×C411yescharacteristic
100#14581716C2×C411yescharacteristic
101#14581715C2×C411yescharacteristic
102#14581715C2×C411yescharacteristic
103#14581715C2×C411yescharacteristic
104#14581715C2×C411yescharacteristic
105#14581713C2×C411yescharacteristic
106#14581713C2×C411yescharacteristic
107C22⋊(C83⋊C8)—21no—
108C22⋊(C83⋊C8)—21no—
109C22⋊(C83⋊C8)—21no—
110C22⋊(C83⋊C8)C2×C411yescharacteristic
111C22⋊(C83⋊C8)C2×C411yescharacteristic
112#14581703—21no—
113#14581703D411yescharacteristic
114#14581703D411yescharacteristic
115#14581702—21no—
116#14581702—21no—
117C4×C83⋊C8—21no—
118C4×C83⋊C8—21no—
119C4×C83⋊C8C2311yescharacteristic
120C4×C83⋊C8C2311yescharacteristic
121C4×C83⋊C8C2311yescharacteristic
122C4×C83⋊C8C2311yescharacteristic
123C8×Dic83—21no—
124C8×Dic83—21no—
125C2×M16×C83—21no—
126#126×C83—21no—
127#125×C83C2×C411yescharacteristic
128#124×C83C2×C411yescharacteristic
129#123×C83—21no—
130C22⋊Q8×C83C2×C411yescharacteristic
131#121×C83C2×C411yescharacteristic
132C4×Q8×C83C2311yescharacteristic
133C4×D4×C83—21no—
134C4×D4×C83C2311yescharacteristic
135#117×C83—21no—
136C2×C42×C83C2311yescharacteristic
137C4⋊C8×C83—21no—
138C4⋊C8×C83—21no—
139C4⋊C8×C83C2311yescharacteristic
140C4⋊C8×C83C2311yescharacteristic
141C22⋊C8×C83—21no—
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C2×Dic166—22no—
145C2×Dic166—21no—
146C2×Dic166—41no—
147C2×Dic166C22×C411yescharacteristic
148C2×Dic166C22×C411yescharacteristic
149C22×Dic83—21no—
150C22×Dic83—21no—
151#13050580—22no—
152#13050580—41no—
153#13050578—22no—
154#13050578—41no—
155#13050574—22no—
156#13050574—41no—
157#13050574—42no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8—42no—
161C2×C83⋊C8C22×C411yescharacteristic
162C2×C83⋊C8C22×C411yescharacteristic
163C2×C83⋊C8C22×C411yescharacteristic
164C2×C83⋊C8C22×C411yescharacteristic
165C2×C83⋊C8C2×D411yescharacteristic
166C2×C83⋊C8C2×D411yescharacteristic
167C2×C83⋊C8C2×D411yescharacteristic
168C2×C83⋊C8C2×D411yescharacteristic
169C4⋊Dic83—21no—
170C4⋊Dic83C22×C411yescharacteristic
171C4⋊Dic83C22×C411yescharacteristic
172Dic83⋊C4—21no—
173Dic83⋊C4—21no—
174Dic83⋊C4—21no—
175Dic83⋊C4—21no—
176C4×Dic83—21no—
177C4×Dic83—21no—
178C4×Dic83—21no—
179C4×Dic83—21no—
180C2×Q8×C83C22×C411yescharacteristic
181C2×D4×C83—21no—
182C2×D4×C83C22×C411yescharacteristic
183C22×C4×C83—21no—
184C22×C4×C83C22×C411yescharacteristic
185C22×C4×C83C2×D411yescharacteristic
186C22×C4×C83#4111yescharacteristic
187M16×C83—42no—
188C2×C8×C83—21no—
189C2×C8×C83—21no—
190C2×C8×C83—21no—
191C2×C8×C83—21no—
192C4⋊C4×C83—21no—
193C4⋊C4×C83—21no—
194C4⋊C4×C83—21no—
195C4⋊C4×C83—21no—
196C4⋊C4×C83C22×C411yescharacteristic
197C4⋊C4×C83C22×C411yescharacteristic
198C22⋊C4×C83—21no—
199C22⋊C4×C83—21no—
200C22⋊C4×C83—21no—
201C22⋊C4×C83—21no—
202C22⋊C4×C83—21no—
203C42×C83—21no—
204C42×C83C22×C411yescharacteristic
205C42×C83C2×D411yescharacteristic
206C42×C83#4111yescharacteristic
207C42×C83C2411yescharacteristic
208C23×C83—21no—
209C23×C83C4×D411yescharacteristic
210Q8×C83—21no—
211Q8×C83—21no—
212D4×C83—21no—
213D4×C83—21no—
214D4×C83—81no—
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×C83—41no—
224C2×C4×C83—41no—
225C2×C4×C83C4×D411yescharacteristic
226C2×C4×C83C4×D411yescharacteristic
227C2×C4×C83C4×D411yescharacteristic
228C2×C4×C83C23×C411yescharacteristic
229C2×C4×C83C22×D411yescharacteristic
230C2×C4×C83C2×#4111yescharacteristic
231C2×Dic83—21no—
232C2×Dic83—21no—
233C2×Dic83—21no—
234C2×Dic83—21no—
235C2×Dic83—42no—
236C2×Dic83—81no—
237Dic166—21no—
238Dic166—21no—
239Dic166—21no—
240Dic166—42no—
241Dic166#13112yes—
242C8×C83—41no—
243C8×C83—41no—
244C8×C83—41no—
245C8×C83—41no—
246C83⋊C8—21no—
247C83⋊C8—21no—
248C83⋊C8—21no—
249C83⋊C8—21no—
250C83⋊C8—21no—
251C83⋊C8—21no—
252C83⋊C8—21no—
253C83⋊C8—41no—
254C83⋊C8—41no—
255C83⋊C8#13712yes—
256C22×C83—21no—
257C22×C83—21no—
258C22×C83—21no—
259C22×C83—41no—
260C22×C83—41no—
261C22×C83—41no—
262C22×C83C2×C4×D411yescharacteristic
263C4×C83—21no—
264C4×C83—21no—
265C4×C83—21no—
266C4×C83—21no—
267C4×C83—41no—
268C4×C83—41no—
269C4×C83—41no—
270C4×C83C2×#13111yescharacteristic
271C4×C83#56811yescharacteristic
272C4×C83C2×#13711yescharacteristic
273C4×C83#57511yescharacteristic
274Dic83—22no—
275Dic83—41no—
276Dic83—41no—
277Dic83—41no—
278#18012—831nomaximal, Sylow
279C2×C83—41no—
280C2×C83—81no—
281C2×C83#293311yescharacteristic
282C2×C83C4×#13711yescharacteristic
283C2×C83#295711yescharacteristic
284#3108—831no—
285#2969—831no—
286Q8×M16—831no—
287#1593—831no—
288#1590—831no—
289#1587—831no—
290#1585—831no—
291#1584—831no—
292#1583—831no—
293SD16⋊C8—831no—
294C8×Q16—831no—
295#1574—831no—
296#1495D8311yescharacteristic
297#1479—831no—
298#1453—831no—
299C83#1801211yescharacteristic, complemented, Sylow
300#529C2×D8311yescharacteristic
301C2×C4×Q8—831no—
302#483—831no—
303#480—831no—
304#479—831no—
305#479—831no—
306#464—831no—
307#464—831no—
308#451—831no—
309#448—831no—
310#446—831no—
311#446—831no—
312#446—831no—
313#446—1661no—
314#446—1661no—
315C8×Q8—831no—
316C8×Q8—831no—
317C8×Q8—831no—
318C4×Q16—831no—
319C4×Q16—831no—
320C4×SD16—831no—
321C4×SD16—831no—
322#436—831no—
323#436—1661no—
324#435—1661no—
325C8×D4—831no—
326#433—1661no—
327#431—831no—
328#431—831no—
329#431C2×D8311yescharacteristic
330#423—1661no—
331#423C2×D8311yescharacteristic
332#405—1661no—
333C4×M16—831no—
334C4×M16—1661no—
335#335—831no—
336#335—831no—
337#334—831no—
338#334—831no—
339Q8⋊C8—831no—
340Q8⋊C8—831no—
341Q8⋊C8—831no—
342Q8⋊C8—831no—
343Q8⋊C8C2×D8311yescharacteristic
344Q8⋊C8C2×D8311yescharacteristic
345D4⋊C8C2×D8311yescharacteristic
346D4⋊C8C2×D8311yescharacteristic
347#322—831no—
348#322—831no—
349#322—831no—
350C82—831no—
351C22×Q8—831no—
352C2×Q16—831no—
353C2×Q16—831no—
354C2×SD16—831no—
355C2×SD16—831no—
356C2×M16—21no—
357C2×M16—831no—
358C2×M16—831no—
359C2×M16—1661no—
360C22×C8—1661no—
361#126—21no—
362#125C4×D8311yescharacteristic
363#124C4×D8311yescharacteristic
364#123—21no—
365C22⋊Q8C4×D8311yescharacteristic
366#121C4×D8311yescharacteristic
367C4×Q8—831no—
368C4×Q8—831no—
369C4×Q8—831no—
370C4×Q8—831no—
371C4×Q8—1661no—
372C4×Q8—1661no—
373C4×Q8C22×D8311yescharacteristic
374C4×D4—21no—
375C4×D4C22×D8311yescharacteristic
376#117—21no—
377C2×C4⋊C4—831no—
378C2×C4⋊C4—1661no—
379C2×C42—1661no—
380C2×C42C22×D8311yescharacteristic
381#107—831no—
382#107—831no—
383#106—831no—
384#106—831no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—831no—
388C4⋊C8—831no—
389C4⋊C8—831no—
390C4⋊C8—831no—
391C4⋊C8—1661no—
392C4⋊C8—1661no—
393C4⋊C8—1661no—
394C4⋊C8—1661no—
395C4⋊C8—1661no—
396C4⋊C8—1661no—
397C4⋊C8C22×D8311yescharacteristic
398C4⋊C8C22×D8311yescharacteristic
399#103—831no—
400#103—831no—
401#103—831no—
402#103—831no—
403#103—831no—
404#103—831no—
405#102—831no—
406#102—831no—
407C22⋊C8—21no—
408C22⋊C8—831no—
409C22⋊C8—831no—
410C22⋊C8—1661no—
411C22⋊C8—1661no—
412C22⋊C8—1661no—
413#97—831no—
414#97—831no—
415#97—1661no—
416#97—1661no—
417#97—1661no—
418C4×C8—831no—
419C4×C8—831no—
420C4×C8—831no—
421C4×C8—831no—
422C4×C8—1661no—
423C4×C8—1661no—
424C4×C8—1661no—
425C4×C8—1661no—
426C4×C8C22×D8311yescharacteristic
427C4×C8C22×D8311yescharacteristic
428C2×Q8—3321no—
429C2×Q8—831no—
430C2×Q8—831no—
431C2×Q8—1662no—
432C2×Q8—1661no—
433C2×Q8C2×C4×D8311yescharacteristic
434C2×D4—21no—
435C2×D4C2×C4×D8311yescharacteristic
436C22×C4—21no—
437C22×C4—1661no—
438C22×C4—1661no—
439C22×C4C2×C4×D8311yescharacteristic
440C22×C4D4×D8311yescharacteristic
441C22×C4#1305058911yescharacteristic
442Q16—3321no—
443Q16—1662no—
444SD16—3321no—
445SD16—1662no—
446M16—42no—
447M16—3322no—
448M16—3321no—
449M16—1662no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—3322no—
455C2×C8—831no—
456C2×C8—831no—
457C2×C8—831no—
458C2×C8—831no—
459C2×C8—831no—
460C2×C8—831no—
461C2×C8—831no—
462C2×C8—831no—
463C2×C8—1661no—
464C2×C8—1661no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—831no—
470C4⋊C4—831no—
471C4⋊C4—1661no—
472C4⋊C4—1661no—
473C4⋊C4—1661no—
474C4⋊C4—1661no—
475C4⋊C4—1661no—
476C4⋊C4C2×C4×D8311yescharacteristic
477C4⋊C4C2×C4×D8311yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C42—21no—
484C42—1661no—
485C42—1661no—
486C42—1661no—
487C42—1661no—
488C42C2×C4×D8311yescharacteristic
489C42D4×D8311yescharacteristic
490C42#1305058911yescharacteristic
491C42C23×D8311yescharacteristic
492C23—21no—
493C23(C22⋊D83)⋊C411yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—3322no—
497Q8—832no—
498Q8—1661no—
499Q8—1661no—
500Q8—1661no—
501D4—21no—
502D4—21no—
503D4—81no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—3322no—
515C2×C4—6641no—
516C2×C4—1661no—
517C2×C4—1661no—
518C2×C4—1661no—
519C2×C4—1661no—
520C2×C4(C22⋊D83)⋊C411yescharacteristic
521C2×C4(C22⋊D83)⋊C411yescharacteristic
522C2×C4(C22⋊D83)⋊C411yescharacteristic
523C2×C4C22×C4×D8311yescharacteristic
524C2×C4C2×D4×D8311yescharacteristic
525C2×C4C2×#1305058911yescharacteristic
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—3321no—
531C8—3321no—
532C8—832no—
533C8—1661no—
534C8—1661no—
535C8—1661no—
536C8—1661no—
537C8—1661no—
538C8—1661no—
539C8—1661no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×(C22⋊D83)⋊C411yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—3321no—
555C4—3321no—
556C4—3321no—
557C4—1662no—
558C4#131×D8311yescharacteristic
559C4#1912846611yescharacteristic
560C4#137×D8311yescharacteristic
561C4#1912849711yescharacteristic
562C2—41no—
563C2—81no—
564C2#2491619311yescharacteristic
565C2#2491628711yescharacteristic
566C2#2491637611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1495C2
socleC22×C83C2×C4×D4
prime radical#121×C83C2×C4
cosocleC42×C83C24
hypercenter#1495D83
hypocenterC83#18012
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1495

Complements

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

NH ≅ G/Ntype
3. #24916414C2semidirect
4. #24906369C2semidirect
5. #24906356C2semidirect
6. #24906337C2semidirect
7. #24906317C2semidirect
8. #24906310C2semidirect
9. #24906309C2semidirect
10. #24906272C2semidirect
11. #24906267C2semidirect
12. #24906254C2semidirect
13. #24905859C2semidirect
14. #24905758C2semidirect
299. C83#18012semidirect

Maximal subgroups

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

subgroupindex
#249175392
#249164682
#249164142
#249063692
#249063562
#249063372
#249063172
#249063102
#249063092
#249062722
#249062672
#249062542
#249058592
#249057582
C83×#14952
#1801283