Finite Group Databasebeta

← #26373249

Subgroups — #26373249

Order 12032.

602 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20255736C211yesmaximal, characteristic, complemented
2#20245624C211yesmaximal, characteristic, complemented
3#20245583C211yesmaximal, characteristic, complemented
4#20245571C211yesmaximal, characteristic, complemented
5#20245535C211yesmaximal, characteristic, complemented
6#20245489C211yesmaximal, characteristic, complemented
7#20245486C211yesmaximal, characteristic, complemented
8#20245440C211yesmaximal, characteristic, complemented
9#20245311C211yesmaximal, characteristic, complemented
10#20245300C211yesmaximal, characteristic, complemented
11#20245262C211yesmaximal, characteristic, complemented
12#20245214C211yesmaximal, characteristic, complemented
13#20245100C211yesmaximal, characteristic, complemented
14C2×#15688924C211yesmaximal, characteristic, complemented
15C47×#3280C211yesmaximal, characteristic, complemented
16#15689777—21no—
17C2×#13093967C2211yescharacteristic, complemented
18C2×#13093965C2211yescharacteristic
19C2×#13093965C2211yescharacteristic
20C2×#13093964C2211yescharacteristic, complemented
21C22×C47⋊C16C2211yescharacteristic
22#15689528C2211yescharacteristic, complemented
23#15689437—21no—
24#15689437—21no—
25#15689404—21no—
26#15689359C2211yescharacteristic
27#15689359C2211yescharacteristic, complemented
28C4×D376C2211yescharacteristic, complemented
29C2×#13093958C2211yescharacteristic
30C2×#13093958C2211yescharacteristic, complemented
31#15688950C2211yescharacteristic, complemented
32#15688950C2211yescharacteristic, complemented
33#15688950C2211yescharacteristic, complemented
34C4⋊(C47⋊C16)C2211yescharacteristic, complemented
35#15688927C2211yescharacteristic, complemented
36#15688927C2211yescharacteristic, complemented
37#15688927C2211yescharacteristic, complemented
38#15688924C2211yescharacteristic
39#15688924C2211yescharacteristic
40#15688924C2211yescharacteristic
41#15688924C2211yescharacteristic
42#15688924C2211yescharacteristic
43#15688924C2211yescharacteristic
44#15688923C2211yescharacteristic, complemented
45C22⋊(C47⋊C16)C2211yescharacteristic
46C22⋊(C47⋊C16)C2211yescharacteristic, complemented
47#15688899C2211yescharacteristic, complemented
48C2×#135×C47C2211yescharacteristic
49C22×D8×C47C2211yescharacteristic
50C47×#546—21no—
51C47×#495C2211yescharacteristic
52C47×#467C2211yescharacteristic
53C47×#466C2211yescharacteristic
54C47×#463—21no—
55C47×#450—21no—
56C47×#449—21no—
57C4×D8×C47C2211yescharacteristic
58C8×D4×C47C2211yescharacteristic
59C2×#10625352—41no—
60C2×D376C2311yescharacteristic
61#13094024—21no—
62#13094008—41no—
63#13094008—41no—
64#13094004—41no—
65#13093998—21no—
66#13093998—21no—
67C4×D188—21no—
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47—21no—
70#13093967—41no—
71#13093965—22no—
72#13093965—41no—
73#13093964—41no—
74C2×C47⋊C16—41no—
75C2×C47⋊C16C2311yescharacteristic
76C2×C47⋊C16C2311yescharacteristic
77C2×C47⋊C16C2311yescharacteristic
78C2×C47⋊C16C2311yescharacteristic
79#13093958—21no—
80#13093958—21no—
81#13093958—21no—
82#13093958C2311yescharacteristic
83#13093958C2311yescharacteristic
84#13093958C2311yescharacteristic
85#13093946—21no—
86#13093946—21no—
87#13093946—21no—
88C2×#41×C47—21no—
89C22×D4×C47—21no—
90#135×C47—22no—
91#135×C47—41no—
92C2×Q16×C47C2311yescharacteristic
93C2×SD16×C47—21no—
94C2×SD16×C47—21no—
95C2×D8×C47—22no—
96C2×D8×C47—21no—
97C2×D8×C47—41no—
98C2×D8×C47C2311yescharacteristic
99C2×D8×C47C2311yescharacteristic
100C22×C8×C47C2311yescharacteristic
101C22×C8×C47C2311yescharacteristic
102#124×C47—21no—
103#123×C47—41no—
104C22⋊Q8×C47—21no—
105#121×C47—21no—
106#121×C47—41no—
107#120×C47—41no—
108C4×D4×C47—21no—
109C4×D4×C47D411yescharacteristic
110C2×C22⋊C4×C47—41no—
111#107×C47C2311yescharacteristic
112C4⋊C8×C47D411yescharacteristic
113#103×C47—21no—
114#102×C47—21no—
115#102×C47—21no—
116C22⋊C8×C47D411yescharacteristic
117C22⋊C8×C47D411yescharacteristic
118C4×C8×C47C2311yescharacteristic
119C24×C47—41no—
120#41×C47—42no—
121#41×C47—81no—
122C2×Q8×C47—21no—
123C2×D4×C47—21no—
124C2×D4×C47—21no—
125C2×D4×C47—42no—
126C2×D4×C47—41no—
127C2×D4×C47—41no—
128C2×D4×C47—41no—
129C2×D4×C47—81no—
130C2×D4×C47D811yescharacteristic
131C22×C4×C47—41no—
132C22×C4×C47—41no—
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C2×C22⋊D47—41no—
136C2×C22⋊D47—41no—
137C22×Dic47—41no—
138C22×Dic47—41no—
139#10625352—84no—
140C2×D188—21no—
141C2×C4×D47—41no—
142C2×Dic94—41no—
143Q16×C47—21no—
144Q16×C47—21no—
145SD16×C47—42no—
146SD16×C47—81no—
147D8×C47—21no—
148D8×C47—21no—
149D8×C47—21no—
150D8×C47—42no—
151D8×C47#4112yescomplemented
152C2×C8×C47—21no—
153C2×C8×C47—21no—
154C2×C8×C47—21no—
155C2×C8×C47—21no—
156C2×C8×C47C2×D411yescharacteristic
157C2×C8×C47C2×D411yescharacteristic
158C2×C8×C47C2×D411yescharacteristic
159C2×C8×C47C2411yescharacteristic
160C4⋊C4×C47—21no—
161C4⋊C4×C47—41no—
162C4⋊C4×C47D811yescharacteristic
163C22⋊C4×C47—41no—
164C22⋊C4×C47—41no—
165C22⋊C4×C47—41no—
166C22⋊C4×C47—41no—
167C22⋊C4×C47—41no—
168C22⋊C4×C47D811yescharacteristic
169C22⋊C4×C47D811yescharacteristic
170C42×C47C2×D411yescharacteristic
171(C2×D47)⋊C4—41no—
172(C2×D47)⋊C4—41no—
173(C2×D47)⋊C4—41no—
174C4⋊Dic47—21no—
175C4⋊Dic47—21no—
176C4⋊Dic47—21no—
177C4⋊Dic47—41no—
178C4⋊Dic47—41no—
179C4⋊Dic47—41no—
180D376—21no—
181D376—21no—
182C47⋊C16—21no—
183C47⋊C16—21no—
184C47⋊C16—21no—
185C47⋊C16—21no—
186C23×C47—41no—
187C23×C47—41no—
188C23×C47—82no—
189C23×C47—82no—
190C23×C47—161no—
191C23×C47C2×D811yescharacteristic
192C23×C47C2×D811yescharacteristic
193C22×D47—41no—
194Q8×C47—41no—
195Q8×C47—41no—
196D4×C47—22no—
197D4×C47—22no—
198D4×C47—41no—
199D4×C47—41no—
200D4×C47—41no—
201D4×C47—82no—
202D4×C47—82no—
203D4×C47—161no—
204C2×C4×C47—21no—
205C2×C4×C47—21no—
206C2×C4×C47—21no—
207C2×C4×C47—21no—
208C2×C4×C47—41no—
209C2×C4×C47—41no—
210C2×C4×C47—82no—
211C2×C4×C47—161no—
212C2×C4×C47C2×D811yescharacteristic
213C2×C4×C47C2×D811yescharacteristic
214C2×C4×C47C2×D811yescharacteristic
215C2×C4×C47C2×D811yescharacteristic
216C2×C4×C47C22×D411yescharacteristic
217C22⋊D47—82no—
218C22⋊D47—82no—
219C2×Dic47—41no—
220C2×Dic47—41no—
221C2×Dic47—41no—
222C2×Dic47—82no—
223C2×Dic47—82no—
224D188—41no—
225D188—41no—
226C4×D47—82no—
227Dic94—82no—
228C8×C47—21no—
229C8×C47—21no—
230C8×C47—21no—
231C8×C47C2×#4111yescharacteristic
232C8×C47H(5,𝔽2)11yescharacteristic
233#33873—471nomaximal, Sylow
234C22×C47—21no—
235C22×C47—21no—
236C22×C47—21no—
237C22×C47—21no—
238C22×C47—21no—
239C22×C47—42no—
240C22×C47—81no—
241C22×C47—81no—
242C22×C47—81no—
243C22×C47—81no—
244C22×C47—81no—
245C22×C47—164no—
246C22×C47#50912yes—
247C22×C47C22×D811yescharacteristic
248C2×D47—81no—
249C2×D47—81no—
250C2×D47—81no—
251C4×C47—21no—
252C4×C47—21no—
253C4×C47—21no—
254C4×C47—21no—
255C4×C47—81no—
256C4×C47—81no—
257C4×C47#54611yescharacteristic
258C4×C47#57711yescharacteristic
259Dic47—81no—
260Dic47—81no—
261Dic47—81no—
262#3334—471no—
263#3280D4711yescharacteristic, complemented
264#2243—471no—
265#2235—471no—
266#2233—471no—
267#2226—471no—
268#2218—471no—
269#2217—471no—
270#2210—471no—
271#2186—471no—
272#2184—471no—
273#2177—471no—
274#2168—471no—
275#2139—471no—
276C2×#357—471no—
277C2×C47—22no—
278C2×C47—41no—
279C2×C47—82no—
280C2×C47—161no—
281C2×C47#329411yescharacteristic
282C2×C47C2×#50911yescharacteristic
283C2×C47#341611yescharacteristic
284D47—161no—
285C2×#135C2×D4711yescharacteristic
286C22×D8C2×D4711yescharacteristic
287#547—941no—
288#546—21no—
289C2×SD32—471no—
290C2×D16—471no—
291C2×D16—471no—
292C2×M32—471no—
293C22×C16—471no—
294#500—471no—
295#495C2×D4711yescharacteristic
296#480—941no—
297#480—941no—
298#474—941no—
299#467C2×D4711yescharacteristic
300#466—471no—
301#466—471no—
302#466C2×D4711yescharacteristic
303#463—21no—
304#450—21no—
305#449—21no—
306C4×D8—471no—
307C4×D8C2×D4711yescharacteristic
308C8×D4C2×D4711yescharacteristic
309C2×#107—471no—
310C2×#107—471no—
311#367—471no—
312#367—471no—
313#367—471no—
314C4⋊C16—471no—
315#358—471no—
316#358—471no—
317#358—471no—
318#357—471no—
319#357—471no—
320#357—471no—
321#357—471no—
322#357—471no—
323#357—471no—
324#357—471no—
325C22⋊C16—471no—
326C22⋊C16—471no—
327#346—471no—
328C47#3387311yescharacteristic, complemented, Sylow
329C2×#41—21no—
330C2×#41—1881no—
331C22×D4—21no—
332#135—22no—
333#135—41no—
334C2×Q16C22×D4711yescharacteristic
335C2×SD16—21no—
336C2×SD16—21no—
337C2×D8—22no—
338C2×D8—21no—
339C2×D8—41no—
340C2×D8—471no—
341C2×D8C22×D4711yescharacteristic
342C2×D8C22×D4711yescharacteristic
343C22×C8C22×D4711yescharacteristic
344C22×C8C22×D4711yescharacteristic
345C4⋊Q8—941no—
346#124—21no—
347#123—41no—
348#123—1881no—
349#123—1881no—
350C22⋊Q8—21no—
351C22⋊Q8—1881no—
352#121—21no—
353#121—41no—
354#121—941no—
355#121—941no—
356#120—41no—
357C4×D4—21no—
358C4×D4—941no—
359C4×D4C22⋊D4711yescharacteristic
360C2×C4⋊C4—941no—
361C2×C4⋊C4—941no—
362C2×C22⋊C4—41no—
363SD32—1881no—
364D16—942no—
365D16—1881no—
366M32—1881no—
367C2×C16—471no—
368C2×C16—471no—
369C2×C16—471no—
370C2×C16—471no—
371C2×C16—1881no—
372#107—471no—
373#107—471no—
374#107—471no—
375#107—941no—
376#107—941no—
377#107—941no—
378#107C22×D4711yescharacteristic
379C4⋊C8C22⋊D4711yescharacteristic
380#103—21no—
381#102—21no—
382#102—21no—
383#102—941no—
384#102—941no—
385#102—941no—
386C22⋊C8C22⋊D4711yescharacteristic
387C22⋊C8C22⋊D4711yescharacteristic
388C4×C8C22×D4711yescharacteristic
389C24—41no—
390#41—42no—
391#41—81no—
392#41—3764no—
393C2×Q8—21no—
394C2×Q8—1881no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—42no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—81no—
402C2×D4—941no—
403C2×D4—1881no—
404C2×D4—1881no—
405C2×D4#1062533411yescharacteristic
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—1881no—
409C22×C4—1881no—
410C22×C4—1881no—
411C22×C4C2×C22⋊D4711yescharacteristic
412C22×C4C2×C22⋊D4711yescharacteristic
413Q16—21no—
414Q16—21no—
415SD16—42no—
416SD16—81no—
417D8—21no—
418D8—21no—
419D8—21no—
420D8—42no—
421D8—941no—
422D8—941no—
423D8#1062535212yescomplemented
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8C2×C22⋊D4711yescharacteristic
429C2×C8C2×C22⋊D4711yescharacteristic
430C2×C8C2×C22⋊D4711yescharacteristic
431C2×C8C23×D4711yescharacteristic
432C4⋊C4—21no—
433C4⋊C4—41no—
434C4⋊C4—941no—
435C4⋊C4—941no—
436C4⋊C4—941no—
437C4⋊C4—1881no—
438C4⋊C4—1881no—
439C4⋊C4—1881no—
440C4⋊C4#1062533411yescharacteristic
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C22⋊C4—1881no—
447C22⋊C4—1881no—
448C22⋊C4—1881no—
449C22⋊C4#1062533411yescharacteristic
450C22⋊C4#1062533411yescharacteristic
451C42C2×C22⋊D4711yescharacteristic
452C16—941no—
453C16—941no—
454C16—941no—
455C16—941no—
456C23—41no—
457C23—41no—
458C23—82no—
459C23—82no—
460C23—161no—
461C23—1881no—
462C23C2×#1062533411yescharacteristic
463C23C2×#1062533411yescharacteristic
464Q8—41no—
465Q8—41no—
466Q8—3762no—
467D4—22no—
468D4—22no—
469D4—41no—
470D4—41no—
471D4—41no—
472D4—82no—
473D4—82no—
474D4—161no—
475D4—3762no—
476D4—3762no—
477D4—1881no—
478D4—1881no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—82no—
486C2×C4—161no—
487C2×C4—3762no—
488C2×C4—3762no—
489C2×C4—3762no—
490C2×C4—1881no—
491C2×C4—1881no—
492C2×C4—1881no—
493C2×C4C2×#1062533411yescharacteristic
494C2×C4C2×#1062533411yescharacteristic
495C2×C4C2×#1062533411yescharacteristic
496C2×C4C2×#1062533411yescharacteristic
497C2×C4C22×C22⋊D4711yescharacteristic
498C8—21no—
499C8—21no—
500C8—21no—
501C8C2×#1062535211yescharacteristic
502C8#1309406911yescharacteristic
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—42no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—164no—
515C22—3761no—
516C22—3761no—
517C22—3761no—
518C22#1568955812yes—
519C22C22×#1062533411yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—3761no—
527C4—3761no—
528C4—3761no—
529C4#1568976711yescharacteristic
530C4#1568993411yescharacteristic
531C2—22no—
532C2—41no—
533C2—82no—
534C2—161no—
535C2—7521no—
536C2#2025520111yescharacteristic
537C2C2×#1568955811yescharacteristic
538C2#2025653511yescharacteristic
subgroupG/H
centerC22C22×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC47×#3280C2
socleC22×C47C22×D8
hypercenter#3280D47
hypocenterC47#33873
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3280

Complements

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

NH ≅ G/Ntype
1. #20255736C2semidirect
2. #20245624C2semidirect
3. #20245583C2semidirect
4. #20245571C2semidirect
5. #20245535C2semidirect
6. #20245489C2semidirect
7. #20245486C2semidirect
8. #20245440C2semidirect
9. #20245311C2semidirect
10. #20245300C2semidirect
11. #20245262C2semidirect
12. #20245214C2semidirect
13. #20245100C2semidirect
14. C2×#15688924C2semidirect
15. C47×#3280C2semidirect
17. C2×#13093967C22semidirect
20. C2×#13093964C22semidirect
22. #15689528C22semidirect
27. #15689359C22semidirect
28. C4×D376C22semidirect
30. C2×#13093958C22semidirect
31. #15688950C22semidirect
32. #15688950C22semidirect
33. #15688950C22semidirect
34. C4⋊(C47⋊C16)C22semidirect
35. #15688927C22semidirect
36. #15688927C22semidirect
37. #15688927C22semidirect
44. #15688923C22semidirect
46. C22⋊(C47⋊C16)C22semidirect
47. #15688899C22semidirect
151. D8×C47#41semidirect
263. #3280D47semidirect
328. C47#33873semidirect
423. D8#10625352semidirect

Maximal subgroups

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

subgroupindex
#202557362
#202456242
#202455832
#202455712
#202455352
#202454892
#202454862
#202454402
#202453112
#202453002
#202452622
#202452142
#202451002
C2×#156889242
C47×#32802
#3387347