Finite Group Databasebeta

← #35374441

Subgroups — #35374441

Order 21248.

624 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917532C211yesmaximal, characteristic
2C8×#13050591C211yesmaximal, characteristic
3#24916394C211yesmaximal, characteristic, complemented
4#24906313C211yesmaximal, characteristic, complemented
5#24906301C211yesmaximal, characteristic, complemented
6#24906297C211yesmaximal, characteristic, complemented
7#24906282C211yesmaximal, characteristic, complemented
8#24906279C211yesmaximal, characteristic, complemented
9#24906278C211yesmaximal, characteristic, complemented
10#24906274C211yesmaximal, characteristic, complemented
11#24906253C211yesmaximal, characteristic, complemented
12#24905901C211yesmaximal, characteristic
13#24905882C211yesmaximal, characteristic, complemented
14#24905749C211yesmaximal, characteristic, complemented
15C83×#1584C211yesmaximal, characteristic, complemented
16#19128255C2211yescharacteristic
17C4×#13050591C2211yescharacteristic
18#19128044C411yescharacteristic
19#19128040C411yescharacteristic
20#19127984C411yescharacteristic
21#19127980C411yescharacteristic
22#19127909C411yescharacteristic
23#19127905C411yescharacteristic
24#19127866C411yescharacteristic
25#19127862C411yescharacteristic
26#19127831C2211yescharacteristic
27#19127829—21no—
28Q8×C83⋊C8C2211yescharacteristic
29Q8×C83⋊C8C2211yescharacteristic
30#19127825—21no—
31#19127825C2211yescharacteristic
32C4×#13050580C2211yescharacteristic
33C4×#13050579C2211yescharacteristic
34C4×#13050577C2211yescharacteristic
35C8×D332—21no—
36C8×D332C2211yescharacteristic
37#19127766—21no—
38#19127766C2211yescharacteristic
39#19127753—21no—
40#19127753C2211yescharacteristic
41#19127752C2211yescharacteristic
42#19127726—21no—
43#19127723C2211yescharacteristic
44#19127658—21no—
45C4×#13050573C2211yescharacteristic
46C4×C8×D83—21no—
47C4×C8×D83C2211yescharacteristic
48#19127453C2211yescharacteristic
49#19127452C2211yescharacteristic
50#19127451C2211yescharacteristic
51#19127433C2211yescharacteristic
52Q8⋊(C83⋊C8)C2211yescharacteristic
53Q8⋊(C83⋊C8)C2211yescharacteristic
54#19127431C2211yescharacteristic
55#19127430C2211yescharacteristic
56#19127428C2211yescharacteristic
57#19127423C2211yescharacteristic
58#19127422C2211yescharacteristic
59#19127422C2211yescharacteristic
60#446×C83C2211yescharacteristic
61C8×Q8×C83C2211yescharacteristic
62C4×Q16×C83C2211yescharacteristic
63#335×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65Q8⋊C8×C83C2211yescharacteristic
66#322×C83C2211yescharacteristic
67C2×#13050591C2×C411yescharacteristic
68C2×#13050580C2×C411yescharacteristic
69C2×#13050579C2×C411yescharacteristic
70C2×#13050577C2×C411yescharacteristic
71C2×#13050573—21no—
72C2×#13050573—21no—
73C2×C8×D83—21no—
74C2×C8×D83—21no—
75C2×C8×D83D411yescharacteristic
76C2×C8×D83D411yescharacteristic
77#14581791C2×C411yescharacteristic
78#14581790C2×C411yescharacteristic
79#14581782—21no—
80#14581772C2×C411yescharacteristic
81#14581770—21no—
82#14581768C2×C411yescharacteristic
83Q8×Dic83C2×C411yescharacteristic
84C4×Dic166—21no—
85C4×Dic166C2311yescharacteristic
86C4×D332—21no—
87C4×D332C2311yescharacteristic
88#14581754—21no—
89#14581754C2×C411yescharacteristic
90#14581750—21no—
91#14581750C2×C411yescharacteristic
92#14581749—21no—
93C42×D83—21no—
94C42×D83C2311yescharacteristic
95#14581725C2×C411yescharacteristic
96#14581724C2×C411yescharacteristic
97#14581723C2×C411yescharacteristic
98C4⋊(C83⋊C8)—21no—
99C4⋊(C83⋊C8)—21no—
100C4⋊(C83⋊C8)C2311yescharacteristic
101C4⋊(C83⋊C8)C2311yescharacteristic
102Dic83⋊C8—21no—
103Dic83⋊C8—21no—
104Dic83⋊C8—21no—
105Dic83⋊C8C2×C411yescharacteristic
106Dic83⋊C8C2×C411yescharacteristic
107#14581717C2×C411yescharacteristic
108#14581716C2×C411yescharacteristic
109#14581716C2×C411yescharacteristic
110#14581715C2×C411yescharacteristic
111#14581714C2×C411yescharacteristic
112#14581712C2×C411yescharacteristic
113(C2×D83)⋊C8—21no—
114(C2×D83)⋊C8—21no—
115(C2×D83)⋊C8—21no—
116(C2×D83)⋊C8C2×C411yescharacteristic
117(C2×D83)⋊C8C2×C411yescharacteristic
118#14581702—21no—
119#14581702—21no—
120C4×C83⋊C8—21no—
121C4×C83⋊C8—21no—
122C4×C83⋊C8C2311yescharacteristic
123C4×C83⋊C8C2311yescharacteristic
124C4×C83⋊C8C2311yescharacteristic
125C8×Dic83—21no—
126C8×Dic83—21no—
127C8×Dic83D411yescharacteristic
128C8×Dic83D411yescharacteristic
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
144#13050591—22no—
145#13050591—22no—
146C2×Dic166—21no—
147C2×Dic166C22×C411yescharacteristic
148C2×D332—21no—
149C2×D332C22×C411yescharacteristic
150C2×C4×D83—21no—
151C2×C4×D83—21no—
152C2×C4×D83—21no—
153C2×C4×D83C22×C411yescharacteristic
154C2×C4×D83C2×D411yescharacteristic
155C2×C4×D83#4111yescharacteristic
156#13050580—22no—
157#13050579—22no—
158#13050577—22no—
159#13050573—42no—
160#13050573—42no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8—21no—
163C2×C83⋊C8—21no—
164C2×C83⋊C8C22×C411yescharacteristic
165C2×C83⋊C8C22×C411yescharacteristic
166C2×C83⋊C8C2×D411yescharacteristic
167C2×C83⋊C8C2×D411yescharacteristic
168C8×D83—22no—
169C8×D83—41no—
170C8×D83—42no—
171C8×D83—42no—
172C4⋊Dic83—21no—
173C4⋊Dic83—21no—
174C4⋊Dic83C22×C411yescharacteristic
175C4⋊Dic83C22×C411yescharacteristic
176Dic83⋊C4—21no—
177Dic83⋊C4—21no—
178Dic83⋊C4—21no—
179Dic83⋊C4—21no—
180Dic83⋊C4—21no—
181(C2×D83)⋊C4—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×Dic83C22×C411yescharacteristic
190C4×Dic83C2×D411yescharacteristic
191C4×Dic83#4111yescharacteristic
192C2×Q8×C83C22×C411yescharacteristic
193C2×Q8×C83C22×C411yescharacteristic
194Q16×C83—22no—
195C2×C8×C83—21no—
196C2×C8×C83—21no—
197C2×C8×C83—21no—
198C2×C8×C83C22×C411yescharacteristic
199C2×C8×C83C22×C411yescharacteristic
200C2×C8×C83C2×D411yescharacteristic
201C2×C8×C83C2×D411yescharacteristic
202C4⋊C4×C83—21no—
203C4⋊C4×C83—21no—
204C4⋊C4×C83C22×C411yescharacteristic
205C4⋊C4×C83C22×C411yescharacteristic
206C42×C83—21no—
207C42×C83—21no—
208C42×C83C2411yescharacteristic
209C22×D83—21no—
210C22×D83C4×D411yescharacteristic
211Q8×C83—21no—
212Q8×C83—21no—
213Q8×C83—21no—
214Q8×C83#13112yes—
215C2×C4×C83—21no—
216C2×C4×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83C23×C411yescharacteristic
220C2×C4×C83C22×D411yescharacteristic
221C2×C4×C83C2×#4111yescharacteristic
222C2×Dic83—21no—
223C2×Dic83—21no—
224C2×Dic83—21no—
225C2×Dic83C4×D411yescharacteristic
226C2×Dic83C4×D411yescharacteristic
227C2×Dic83C4×D411yescharacteristic
228D332—24no—
229D332—21no—
230D332#13112yes—
231C4×D83—24no—
232C4×D83—21no—
233C4×D83—21no—
234C4×D83—21no—
235C4×D83—21no—
236C4×D83—22no—
237C4×D83—41no—
238C4×D83—41no—
239C4×D83—42no—
240Dic166—21no—
241Dic166—21no—
242Dic166—42no—
243C8×C83—21no—
244C8×C83—21no—
245C8×C83—21no—
246C8×C83—41no—
247C8×C83—41no—
248C8×C83—41no—
249C8×C83#13712yes—
250C83⋊C8—21no—
251C83⋊C8—21no—
252C83⋊C8—21no—
253C83⋊C8—21no—
254C83⋊C8—41no—
255C83⋊C8—41no—
256C83⋊C8—41no—
257C22×C83C2×C4×D411yescharacteristic
258C2×D83—21no—
259C2×D83—22no—
260C2×D83—21no—
261C2×D83—21no—
262C2×D83—41no—
263C2×D83—41no—
264C4×C83—22no—
265C4×C83—21no—
266C4×C83—41no—
267C4×C83—41no—
268C4×C83—41no—
269C4×C83C2×#13111yescharacteristic
270C4×C83C2×#13111yescharacteristic
271C4×C83C2×#13711yescharacteristic
272C4×C83#57511yescharacteristic
273Dic83—21no—
274Dic83—21no—
275Dic83—41no—
276Dic83—41no—
277Dic83—41no—
278Dic83#44412yes—
279#17916—831nomaximal, Sylow
280C2×C83#292911yescharacteristic
281C2×C83C4×#13711yescharacteristic
282C2×C83C2×#44411yescharacteristic
283D83—41no—
284D83—42no—
285#3107—831no—
286C8×#41—831no—
287#2960—831no—
288#1584—831no—
289#1584D8311yescharacteristic, complemented
290#1582—831no—
291#1582—831no—
292#1579—831no—
293#1579—831no—
294SD16⋊C8—831no—
295SD16⋊C8—831no—
296#1574—831no—
297#1489—831no—
298#1485—831no—
299#1451—831no—
300C83#1791611yescharacteristic, complemented, Sylow
301#533—831no—
302C4×#41—831no—
303#485—831no—
304#485—831no—
305#475—831no—
306#474—831no—
307#462—831no—
308#461—831no—
309#452—831no—
310#452—831no—
311#446—831no—
312#446—1661no—
313#446C2×D8311yescharacteristic
314C8×Q8—831no—
315C8×Q8—831no—
316C8×Q8—831no—
317C8×Q8—1661no—
318C8×Q8C2×D8311yescharacteristic
319C4×Q16—831no—
320C4×Q16C2×D8311yescharacteristic
321C4×SD16—831no—
322C4×SD16—831no—
323C8×D4—831no—
324C8×D4—831no—
325C8×D4—1661no—
326C8×D4—1661no—
327#431—831no—
328#431—831no—
329#431—1661no—
330#424—1661no—
331#423—831no—
332#405—1661no—
333C4×M16—831no—
334C2×C4×C8—831no—
335C2×C4×C8—1661no—
336#335—831no—
337#335C2×D8311yescharacteristic
338#334—831no—
339#334—831no—
340Q8⋊C8—831no—
341Q8⋊C8—831no—
342Q8⋊C8—831no—
343Q8⋊C8—831no—
344Q8⋊C8C2×D8311yescharacteristic
345Q8⋊C8C2×D8311yescharacteristic
346D4⋊C8—831no—
347D4⋊C8—831no—
348#322—831no—
349#322—831no—
350#322—831no—
351#322C2×D8311yescharacteristic
352C2×#41—831no—
353C2×Q16—831no—
354C2×Q16C4×D8311yescharacteristic
355C2×SD16—831no—
356C2×SD16—831no—
357C2×M16—1661no—
358C2×M16—1661no—
359C22×C8—831no—
360C22×C8—831no—
361C22×C8—1661no—
362C22×C8—1661no—
363C4⋊Q8—831no—
364C4⋊Q8—831no—
365#125—1661no—
366C22⋊Q8—831no—
367C22⋊Q8—831no—
368C22⋊Q8—1661no—
369C4×Q8—831no—
370C4×Q8—831no—
371C4×Q8—1661no—
372C4×Q8C22×D8311yescharacteristic
373C4×Q8C22×D8311yescharacteristic
374C4×D4—831no—
375C4×D4—831no—
376C4×D4—1661no—
377C4×D4—1661no—
378#117—831no—
379#117—1661no—
380#117—1661no—
381C2×C42—831no—
382C2×C42—1661no—
383#107—831no—
384#107C4×D8311yescharacteristic
385#106—831no—
386#106—831no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—831no—
390C4⋊C8—831no—
391C4⋊C8—831no—
392C4⋊C8—831no—
393C4⋊C8—1661no—
394C4⋊C8—1661no—
395C4⋊C8—1661no—
396C4⋊C8—1661no—
397C4⋊C8—1661no—
398C4⋊C8C22×D8311yescharacteristic
399C4⋊C8C22×D8311yescharacteristic
400#103—831no—
401#103—831no—
402#103—831no—
403#103—831no—
404#103C4×D8311yescharacteristic
405#103C4×D8311yescharacteristic
406#102—831no—
407#102—831no—
408C22⋊C8—831no—
409C22⋊C8—831no—
410C22⋊C8—1661no—
411C22⋊C8—1661no—
412C22⋊C8—1661no—
413#97—21no—
414#97—1661no—
415#97—1661no—
416C4×C8—21no—
417C4×C8—831no—
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
428C4×C8C22×D8311yescharacteristic
429#41—1662no—
430#41—1662no—
431C2×Q8—831no—
432C2×Q8—1661no—
433C2×Q8C2×C4×D8311yescharacteristic
434C2×Q8C2×C4×D8311yescharacteristic
435C2×D4—831no—
436C2×D4—1661no—
437C22×C4—831no—
438C22×C4—831no—
439C22×C4—831no—
440C22×C4—1661no—
441C22×C4—1661no—
442C22×C4—1661no—
443Q16—22no—
444Q16—1662no—
445SD16—1662no—
446SD16—1662no—
447M16—3322no—
448M16—3322no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—3321no—
453C2×C8—3322no—
454C2×C8—3322no—
455C2×C8—831no—
456C2×C8—831no—
457C2×C8—831no—
458C2×C8—831no—
459C2×C8—1661no—
460C2×C8—1661no—
461C2×C8—1661no—
462C2×C8—1662no—
463C2×C8C2×C4×D8311yescharacteristic
464C2×C8C2×C4×D8311yescharacteristic
465C2×C8D4×D8311yescharacteristic
466C2×C8D4×D8311yescharacteristic
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⋊C4—1661no—
477C4⋊C4—1661no—
478C4⋊C4C2×C4×D8311yescharacteristic
479C4⋊C4C2×C4×D8311yescharacteristic
480C22⋊C4—1661no—
481C22⋊C4—1661no—
482C22⋊C4—1661no—
483C22⋊C4—1661no—
484C22⋊C4—1661no—
485C42—21no—
486C42—21no—
487C42—831no—
488C42—831no—
489C42—831no—
490C42—1661no—
491C42—1661no—
492C42—1661no—
493C42C23×D8311yescharacteristic
494C23—831no—
495C23—1661no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—3322no—
500Q8—1661no—
501Q8—1661no—
502Q8#1458180012yes—
503D4—832no—
504D4—1664no—
505D4—1661no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—3322no—
511C2×C4—3321no—
512C2×C4—3321no—
513C2×C4—831no—
514C2×C4—831no—
515C2×C4—831no—
516C2×C4—1662no—
517C2×C4—1664no—
518C2×C4—1661no—
519C2×C4—1661no—
520C2×C4—1661no—
521C2×C4—1661no—
522C2×C4—1661no—
523C2×C4—1661no—
524C2×C4—1661no—
525C2×C4C22×C4×D8311yescharacteristic
526C2×C4C2×D4×D8311yescharacteristic
527C2×C4#41×D8311yescharacteristic
528C8—21no—
529C8—21no—
530C8—21no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—3321no—
535C8—3321no—
536C8—3321no—
537C8—1661no—
538C8—1661no—
539C8—1661no—
540C8—1661no—
541C8#1458182412yes—
542C22—3321no—
543C22—3321no—
544C22—1661no—
545C22—1661no—
546C22—1662no—
547C22—1661no—
548C22C4×D4×D8311yescharacteristic
549C4—21no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—3321no—
555C4—3321no—
556C4—3321no—
557C4—832no—
558C4—1661no—
559C4—1661no—
560C4#131×D8311yescharacteristic
561C4C2×#1458180011yescharacteristic
562C4C2×#1458182411yescharacteristic
563C4#1912849811yescharacteristic
564C2—3322no—
565C2—3321no—
566C2#2491615411yescharacteristic
567C2C4×#1458182411yescharacteristic
568C2#444×D8311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1584C2
socleC22×C83C2×C4×D4
prime radicalC2×#13050591C2×C4
cosocleC42×C83C24
hypercenter#1584D83
hypocenterC83#17916
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
3. #24916394C2semidirect
4. #24906313C2semidirect
5. #24906301C2semidirect
6. #24906297C2semidirect
7. #24906282C2semidirect
8. #24906279C2semidirect
9. #24906278C2semidirect
10. #24906274C2semidirect
11. #24906253C2semidirect
13. #24905882C2semidirect
14. #24905749C2semidirect
15. C83×#1584C2semidirect
289. #1584D83semidirect
300. C83#17916semidirect

Maximal subgroups

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

subgroupindex
#249175322
C8×#130505912
#249163942
#249063132
#249063012
#249062972
#249062822
#249062792
#249062782
#249062742
#249062532
#249059012
#249058822
#249057492
C83×#15842
#1791683