Finite Group Databasebeta

← #35375549

Subgroups — #35375549

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#24917535C211yesmaximal, characteristic
2#24916481C211yesmaximal, characteristic
3#24916410C211yesmaximal, characteristic, complemented
4#24906367C211yesmaximal, characteristic, complemented
5#24906355C211yesmaximal, characteristic, complemented
6#24906343C211yesmaximal, characteristic, complemented
7#24906336C211yesmaximal, characteristic, complemented
8#24906315C211yesmaximal, characteristic, complemented
9#24906308C211yesmaximal, characteristic, complemented
10#24906283C211yesmaximal, characteristic, complemented
11C8×Dic332C211yesmaximal, characteristic, complemented
12#24906248C211yesmaximal, characteristic, complemented
13#24905937C211yesmaximal, characteristic, complemented
14#24905851C211yesmaximal, characteristic
15C83×#1453C211yesmaximal, characteristic, complemented
16#19128258C2211yescharacteristic
17C4×#13050590C2211yescharacteristic
18#19128043C411yescharacteristic
19#19128043C411yescharacteristic
20#19127987C411yescharacteristic
21#19127982C411yescharacteristic
22#19127912C411yescharacteristic
23#19127907C411yescharacteristic
24#19127865C411yescharacteristic
25#19127865C411yescharacteristic
26#19127831C2211yescharacteristic
27#19127831C2211yescharacteristic
28#19127829—21no—
29#19127829—21no—
30C8×Dic166C2211yescharacteristic
31C8×Dic166C2211yescharacteristic
32C8×Dic166C2211yescharacteristic
33C8×Dic166C2211yescharacteristic
34C4×Dic332C2211yescharacteristic
35C4×Dic332C2211yescharacteristic
36C4×#13050579C2211yescharacteristic
37C4×#13050579C2211yescharacteristic
38#19127780C2211yescharacteristic
39#19127780C2211yescharacteristic
40#19127777—21no—
41#19127777—21no—
42#19127758C2211yescharacteristic
43#19127756—21no—
44#19127729—21no—
45C2×C4⋊(C83⋊C8)C2211yescharacteristic
46#19127659—21no—
47#19127653—21no—
48#19127454C2211yescharacteristic
49#19127454C2211yescharacteristic
50#19127452C2211yescharacteristic
51#19127452C2211yescharacteristic
52#19127433C2211yescharacteristic
53#19127433C2211yescharacteristic
54#19127433C2211yescharacteristic
55#19127433C2211yescharacteristic
56#19127433C2211yescharacteristic
57#19127433C2211yescharacteristic
58#19127430C2211yescharacteristic
59#19127430C2211yescharacteristic
60#431×C83C2211yescharacteristic
61#431×C83C2211yescharacteristic
62C4×M16×C83C2211yescharacteristic
63#322×C83C2211yescharacteristic
64#322×C83C2211yescharacteristic
65#322×C83C2211yescharacteristic
66C82×C83C2211yescharacteristic
67C2×#13050590C2×C411yescharacteristic
68C2×Dic332C2×C411yescharacteristic
69C2×Dic332C2×C411yescharacteristic
70C2×#13050579C2×C411yescharacteristic
71C2×#13050579C2×C411yescharacteristic
72C2×#13050573—21no—
73C2×#13050573—21no—
74C22×C83⋊C8—21no—
75#14581792C2×C411yescharacteristic
76#14581792C2×C411yescharacteristic
77#14581784—21no—
78#14581771—21no—
79#14581771C2×C411yescharacteristic
80#14581771C2×C411yescharacteristic
81C4×Dic166—21no—
82C4×Dic166C2×C411yescharacteristic
83C4×Dic166C2311yescharacteristic
84C4×Dic166C2311yescharacteristic
85C4×Dic166C2311yescharacteristic
86C4×D332C2×C411yescharacteristic
87C4×D332C2311yescharacteristic
88C4×C22⋊D83—21no—
89C4×C22⋊D83—21no—
90#14581751—21no—
91#14581751C2×C411yescharacteristic
92#14581749—21no—
93C42×D83—21no—
94#14581726C2×C411yescharacteristic
95#14581726C2×C411yescharacteristic
96#14581724C2×C411yescharacteristic
97#14581724C2×C411yescharacteristic
98C4⋊(C83⋊C8)—21no—
99C4⋊(C83⋊C8)C2311yescharacteristic
100C4⋊(C83⋊C8)C2311yescharacteristic
101C4⋊(C83⋊C8)C2311yescharacteristic
102C4⋊(C83⋊C8)C2311yescharacteristic
103Dic83⋊C8—21no—
104Dic83⋊C8—21no—
105Dic83⋊C8—21no—
106Dic83⋊C8—21no—
107Dic83⋊C8—21no—
108Dic83⋊C8—21no—
109#14581717C2×C411yescharacteristic
110#14581717C2×C411yescharacteristic
111#14581717C2×C411yescharacteristic
112#14581717C2×C411yescharacteristic
113#14581717C2×C411yescharacteristic
114#14581717C2×C411yescharacteristic
115#14581714C2×C411yescharacteristic
116#14581714C2×C411yescharacteristic
117C22⋊(C83⋊C8)—21no—
118(C2×D83)⋊C8—21no—
119(C2×D83)⋊C8—21no—
120#14581703—21no—
121#14581702—21no—
122#14581702—21no—
123C8×Dic83—21no—
124C8×Dic83—21no—
125C8×Dic83—21no—
126C8×Dic83—21no—
127C2×M16×C83D411yescharacteristic
128C2×M16×C83D411yescharacteristic
129C2×C42×C83C2311yescharacteristic
130C4⋊C8×C83—21no—
131C4⋊C8×C83C2×C411yescharacteristic
132C4⋊C8×C83C2×C411yescharacteristic
133C22⋊C8×C83—21no—
134C22⋊C8×C83C2×C411yescharacteristic
135C22⋊C8×C83C2×C411yescharacteristic
136#97×C83D411yescharacteristic
137#97×C83D411yescharacteristic
138C4×C8×C83C2311yescharacteristic
139C4×C8×C83C2311yescharacteristic
140C4×C8×C83C2311yescharacteristic
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#13050590—22no—
145#13050590—41no—
146C2×Dic166—21no—
147C2×Dic166C22×C411yescharacteristic
148C2×Dic166C22×C411yescharacteristic
149C2×Dic166C22×C411yescharacteristic
150C2×D332C22×C411yescharacteristic
151C2×C22⋊D83—21no—
152C2×C4×D83—21no—
153C2×C4×D83—21no—
154C2×C4×D83—21no—
155Dic332—22no—
156Dic332—22no—
157#13050579—41no—
158#13050579—41no—
159#13050573—42no—
160#13050573—42no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8—21no—
163C2×C83⋊C8—21no—
164C2×C83⋊C8—21no—
165C2×C83⋊C8—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—
179C22⋊Dic83—21no—
180C22⋊Dic83—21no—
181C22⋊Dic83—21no—
182(C2×D83)⋊C4—21no—
183(C2×D83)⋊C4—21no—
184C4×Dic83—21no—
185C4×Dic83—21no—
186C4×Dic83—21no—
187C4×Dic83—21no—
188C4×Dic83—21no—
189C22×C4×C83C22×C411yescharacteristic
190C22×C4×C83C2×D411yescharacteristic
191C22×C4×C83#4111yescharacteristic
192M16×C83—22no—
193M16×C83—41no—
194C2×C8×C83—21no—
195C2×C8×C83—21no—
196C2×C8×C83C22×C411yescharacteristic
197C2×C8×C83C22×C411yescharacteristic
198C2×C8×C83C22×C411yescharacteristic
199C2×C8×C83C22×C411yescharacteristic
200C2×C8×C83C2×D411yescharacteristic
201C2×C8×C83C2×D411yescharacteristic
202C2×C8×C83C2×D411yescharacteristic
203C2×C8×C83C2×D411yescharacteristic
204C42×C83C22×C411yescharacteristic
205C42×C83C2×D411yescharacteristic
206C42×C83#4111yescharacteristic
207C42×C83C2411yescharacteristic
208C23×C83C4×D411yescharacteristic
209C22×D83—21no—
210C2×C4×C83—21no—
211C2×C4×C83—21no—
212C2×C4×C83—21no—
213C2×C4×C83—21no—
214C2×C4×C83—41no—
215C2×C4×C83C4×D411yescharacteristic
216C2×C4×C83C4×D411yescharacteristic
217C2×C4×C83C4×D411yescharacteristic
218C2×C4×C83C23×C411yescharacteristic
219C2×C4×C83C22×D411yescharacteristic
220C2×C4×C83C2×#4111yescharacteristic
221C22⋊D83—42no—
222C2×Dic83—21no—
223C2×Dic83—21no—
224C2×Dic83—21no—
225C2×Dic83—21no—
226C2×Dic83—21no—
227C2×Dic83—21no—
228C2×Dic83—21no—
229D332—21no—
230D332—21no—
231C4×D83—42no—
232C4×D83—41no—
233C4×D83—41no—
234C4×D83—81no—
235Dic166—21no—
236Dic166—21no—
237Dic166—21no—
238Dic166—21no—
239Dic166—21no—
240Dic166—81no—
241Dic166#13112yes—
242C8×C83—21no—
243C8×C83—21no—
244C8×C83—21no—
245C8×C83—21no—
246C8×C83—21no—
247C8×C83—21no—
248C8×C83—21no—
249C8×C83—41no—
250C8×C83—41no—
251C8×C83#13712yes—
252C83⋊C8—41no—
253C83⋊C8—41no—
254C83⋊C8—41no—
255C83⋊C8—41no—
256C22×C83—21no—
257C22×C83—21no—
258C22×C83—21no—
259C22×C83C2×C4×D411yescharacteristic
260C2×D83—41no—
261C2×D83—41no—
262C2×D83—41no—
263C4×C83—21no—
264C4×C83—21no—
265C4×C83—21no—
266C4×C83—21no—
267C4×C83C2×#13111yescharacteristic
268C4×C83#56811yescharacteristic
269C4×C83C2×#13711yescharacteristic
270C4×C83#57511yescharacteristic
271Dic83—22no—
272Dic83—41no—
273Dic83—41no—
274Dic83—41no—
275Dic83—41no—
276Dic83—41no—
277Dic83—41no—
278#18013—831nomaximal, Sylow
279C2×C83—41no—
280C2×C83#293311yescharacteristic
281C2×C83C4×#13711yescharacteristic
282C2×C83#295711yescharacteristic
283D83—81no—
284#3107—831no—
285#2971—831no—
286#2962—831no—
287#1592—831no—
288#1590—831no—
289#1588—831no—
290#1587—831no—
291#1584—831no—
292#1583—831no—
293#1579—831no—
294C8×Q16—831no—
295#1573—831no—
296#1497—831no—
297#1477—831no—
298#1453D8311yescharacteristic, complemented
299C83#1801311yescharacteristic, complemented, Sylow
300#533—831no—
301C4×#41—831no—
302#485—831no—
303#485—831no—
304#475—831no—
305#474—831no—
306#462—831no—
307#461—831no—
308#452—831no—
309#452—831no—
310#446—831no—
311#446—831no—
312#446—1661no—
313#446—1661no—
314C8×Q8—831no—
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—831no—
324#436—1661no—
325#436—1661no—
326#432—831no—
327#432—1661no—
328#431C2×D8311yescharacteristic
329#431C2×D8311yescharacteristic
330#424—1661no—
331C2×C4⋊C8—831no—
332#405—1661no—
333C4×M16—1661no—
334C4×M16C2×D8311yescharacteristic
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⋊C8—831no—
344Q8⋊C8—831no—
345D4⋊C8—831no—
346D4⋊C8—831no—
347#322C2×D8311yescharacteristic
348#322C2×D8311yescharacteristic
349#322C2×D8311yescharacteristic
350C82C2×D8311yescharacteristic
351C2×#41—831no—
352C2×Q16—831no—
353C2×Q16—831no—
354C2×SD16—831no—
355C2×SD16—831no—
356C2×M16—1661no—
357C2×M16—1661no—
358C2×M16D33211yescharacteristic
359C2×M16D33211yescharacteristic
360C22×C8—1661no—
361C4⋊Q8—831no—
362C4⋊Q8—831no—
363#125—1661no—
364C22⋊Q8—831no—
365C22⋊Q8—831no—
366C22⋊Q8—1661no—
367C4×Q8—831no—
368C4×Q8—831no—
369C4×Q8—831no—
370C4×Q8—831no—
371C4×Q8—1661no—
372C4×D4—831no—
373C4×D4—831no—
374C4×D4—1661no—
375C4×D4—1661no—
376#117—831no—
377#117—1661no—
378#117—1661no—
379C2×C42—1661no—
380C2×C42C22×D8311yescharacteristic
381#107—831no—
382#107—831no—
383#106—831no—
384#106—831no—
385C4⋊C8—21no—
386C4⋊C8—831no—
387C4⋊C8—831no—
388C4⋊C8—831no—
389C4⋊C8—831no—
390C4⋊C8—1661no—
391C4⋊C8—1661no—
392C4⋊C8—1661no—
393C4⋊C8—1661no—
394C4⋊C8—1661no—
395C4⋊C8—1661no—
396C4⋊C8—1661no—
397C4⋊C8C4×D8311yescharacteristic
398C4⋊C8C4×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—1661no—
409C22⋊C8—1661no—
410C22⋊C8—1661no—
411C22⋊C8C4×D8311yescharacteristic
412C22⋊C8C4×D8311yescharacteristic
413#97—1661no—
414#97—1661no—
415#97—1661no—
416#97D33211yescharacteristic
417#97D33211yescharacteristic
418C4×C8—1661no—
419C4×C8—1661no—
420C4×C8—1661no—
421C4×C8—1661no—
422C4×C8C22×D8311yescharacteristic
423C4×C8C22×D8311yescharacteristic
424C4×C8C22×D8311yescharacteristic
425C4×C8C22×D8311yescharacteristic
426C4×C8C22×D8311yescharacteristic
427C4×C8C22×D8311yescharacteristic
428#41—3321no—
429#41—1662no—
430C2×Q8—831no—
431C2×Q8—831no—
432C2×Q8—831no—
433C2×Q8—1661no—
434C2×D4—831no—
435C2×D4—1661no—
436C22×C4—1661no—
437C22×C4—1661no—
438C22×C4—1661no—
439C22×C4C2×C4×D8311yescharacteristic
440C22×C4C2×D33211yescharacteristic
441C22×C4#1305059011yescharacteristic
442Q16—1662no—
443Q16—1662no—
444SD16—3321no—
445SD16—3321no—
446M16—22no—
447M16—41no—
448M16—3322no—
449M16—3322no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—3322no—
453C2×C8—1661no—
454C2×C8—1661no—
455C2×C8—1661no—
456C2×C8—1661no—
457C2×C8C2×C4×D8311yescharacteristic
458C2×C8C2×C4×D8311yescharacteristic
459C2×C8C2×C4×D8311yescharacteristic
460C2×C8C2×C4×D8311yescharacteristic
461C2×C8C2×D33211yescharacteristic
462C2×C8C2×D33211yescharacteristic
463C2×C8C2×D33211yescharacteristic
464C2×C8C2×D33211yescharacteristic
465C4⋊C4—831no—
466C4⋊C4—831no—
467C4⋊C4—831no—
468C4⋊C4—831no—
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—
483C42—1661no—
484C42—1661no—
485C42—1661no—
486C42—1661no—
487C42—1661no—
488C42C2×C4×D8311yescharacteristic
489C42C2×D33211yescharacteristic
490C42#1305059011yescharacteristic
491C42C23×D8311yescharacteristic
492C23—1661no—
493C23C4×D33211yescharacteristic
494Q8—832no—
495Q8—6641no—
496Q8—1661no—
497Q8—1661no—
498Q8—1661no—
499Q8—1661no—
500Q8—1661no—
501D4—3322no—
502D4—1661no—
503D4—1661no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—3322no—
510C2×C4—3321no—
511C2×C4—3321no—
512C2×C4—6641no—
513C2×C4—1661no—
514C2×C4—1661no—
515C2×C4—1661no—
516C2×C4—1661no—
517C2×C4—1661no—
518C2×C4—1661no—
519C2×C4—1661no—
520C2×C4C4×D33211yescharacteristic
521C2×C4C4×D33211yescharacteristic
522C2×C4C4×D33211yescharacteristic
523C2×C4C22×C4×D8311yescharacteristic
524C2×C4C22×D33211yescharacteristic
525C2×C4C2×#1305059011yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—3321no—
536C8—3321no—
537C8—3321no—
538C8—3321no—
539C8#1458182512yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—3321no—
544C22—3321no—
545C22—3321no—
546C22C2×C4×D33211yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—3321no—
552C4—3321no—
553C4—3321no—
554C4—3321no—
555C4—3321no—
556C4—3321no—
557C4—1662no—
558C4#131×D8311yescharacteristic
559C4#1912846611yescharacteristic
560C4C2×#1458182511yescharacteristic
561C4#1912850111yescharacteristic
562C2—41no—
563C2—6641no—
564C2#2491619111yescharacteristic
565C2C4×#1458182511yescharacteristic
566C2#2491638111yescharacteristic
subgroupG/H
centerC2×C4C22×D332
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1453C2
socleC22×C83C2×C4×D4
prime radicalC2×#13050590C2×C4
cosocleC42×C83C24
hypercenter#1453D83
hypocenterC83#18013
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1453

Complements

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

NH ≅ G/Ntype
3. #24916410C2semidirect
4. #24906367C2semidirect
5. #24906355C2semidirect
6. #24906343C2semidirect
7. #24906336C2semidirect
8. #24906315C2semidirect
9. #24906308C2semidirect
10. #24906283C2semidirect
11. C8×Dic332C2semidirect
12. #24906248C2semidirect
13. #24905937C2semidirect
15. C83×#1453C2semidirect
298. #1453D83semidirect
299. C83#18013semidirect

Maximal subgroups

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

subgroupindex
#249175352
#249164812
#249164102
#249063672
#249063552
#249063432
#249063362
#249063152
#249063082
#249062832
C8×Dic3322
#249062482
#249059372
#249058512
C83×#14532
#1801383