Finite Group Databasebeta

← #26373243

Subgroups — #26373243

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#20255075C211yesmaximal, characteristic, complemented
2#20245627C211yesmaximal, characteristic, complemented
3#20245585C211yesmaximal, characteristic, complemented
4#20245573C211yesmaximal, characteristic, complemented
5#20245532C211yesmaximal, characteristic, complemented
6#20245489C211yesmaximal, characteristic, complemented
7#20245482C211yesmaximal, characteristic, complemented
8#20245443C211yesmaximal, characteristic, complemented
9#20245309C211yesmaximal, characteristic, complemented
10#20245299C211yesmaximal, characteristic, complemented
11#20245262C211yesmaximal, characteristic, complemented
12#20245214C211yesmaximal, characteristic, complemented
13#20245098C211yesmaximal, characteristic, complemented
14C2×#15688923C211yesmaximal, characteristic, complemented
15C47×#3334C211yesmaximal, characteristic, complemented
16C2×#13094046C2211yescharacteristic
17C22×D376C2211yescharacteristic
18#15689769—21no—
19C2×#13093968C2211yescharacteristic, complemented
20C2×#13093965C2211yescharacteristic
21C2×#13093965C2211yescharacteristic
22C2×#13093964C2211yescharacteristic, complemented
23C22×C47⋊C16C2211yescharacteristic
24#15689507C2211yescharacteristic
25#15689364C2211yescharacteristic
26#15689359C2211yescharacteristic
27#15689339—21no—
28#15689276—21no—
29#15689270—21no—
30C4×D376C2211yescharacteristic
31#15688950C2211yescharacteristic, complemented
32#15688950C2211yescharacteristic, complemented
33#15688950C2211yescharacteristic, complemented
34C4⋊(C47⋊C16)C2211yescharacteristic, complemented
35#15688926C2211yescharacteristic, complemented
36#15688926C2211yescharacteristic, complemented
37#15688926C2211yescharacteristic, complemented
38#15688924C2211yescharacteristic, complemented
39#15688923C2211yescharacteristic
40#15688923C2211yescharacteristic
41#15688923C2211yescharacteristic
42#15688923C2211yescharacteristic
43#15688923C2211yescharacteristic
44#15688923C2211yescharacteristic
45C22⋊(C47⋊C16)C2211yescharacteristic
46C22⋊(C47⋊C16)C2211yescharacteristic, complemented
47#15688899C2211yescharacteristic, complemented
48C47×#547—21no—
49C47×#500C2211yescharacteristic, complemented
50C47×#480—21no—
51C47×#480—21no—
52C47×#474—21no—
53C47×#466C2211yescharacteristic
54C47×#466C2211yescharacteristic, complemented
55C4×D8×C47C2211yescharacteristic, complemented
56C8×D4×C47C2211yescharacteristic
57C2×#107×C47C2211yescharacteristic
58C2×#107×C47C2211yescharacteristic, complemented
59C2×#10625350—21no—
60C22×D188—21no—
61#13094046—22no—
62#13094046—41no—
63C2×Dic188C2311yescharacteristic
64C2×#10625325—21no—
65C2×#10625325—21no—
66C2×D376—22no—
67C2×D376—21no—
68C2×D376—41no—
69C2×D376C2311yescharacteristic
70C2×D376C2311yescharacteristic
71#13094012—21no—
72#13094009—41no—
73#13094003—21no—
74#13093998—21no—
75#13093997—41no—
76#13093992—41no—
77C4×D188—21no—
78C22⋊C4×D47—41no—
79#13093968—41no—
80#13093965—22no—
81#13093965—41no—
82#13093964—41no—
83C2×C47⋊C16—41no—
84C2×C47⋊C16C2311yescharacteristic
85C2×C47⋊C16C2311yescharacteristic
86C2×C47⋊C16C2311yescharacteristic
87C2×C47⋊C16C2311yescharacteristic
88#13093958C2311yescharacteristic
89#13093949—21no—
90#13093946—21no—
91#13093946—21no—
92C2×#41×C47—41no—
93C2×D8×C47C2311yescharacteristic
94C22×C8×C47C2311yescharacteristic
95C22×C8×C47C2311yescharacteristic
96C4⋊Q8×C47—21no—
97#123×C47—41no—
98#123×C47—41no—
99C22⋊Q8×C47—41no—
100#121×C47—21no—
101#121×C47—21no—
102C4×D4×C47—21no—
103C4×D4×C47D411yescharacteristic
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106#107×C47—21no—
107#107×C47—21no—
108#107×C47—21no—
109#107×C47C2311yescharacteristic
110#107×C47C2311yescharacteristic
111#107×C47C2311yescharacteristic
112C4⋊C8×C47D411yescharacteristic
113#102×C47—21no—
114#102×C47—21no—
115#102×C47—21no—
116C22⋊C8×C47D411yescharacteristic
117C22⋊C8×C47D411yescharacteristic
118C4×C8×C47C2311yescharacteristic
119C23×D47—41no—
120#41×C47—84no—
121C2×Q8×C47—41no—
122C2×D4×C47—21no—
123C2×D4×C47—41no—
124C2×D4×C47—41no—
125C2×D4×C47D811yescharacteristic
126C22×C4×C47—41no—
127C22×C4×C47—41no—
128C22×C4×C47—41no—
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C2×C22⋊D47—41no—
132C2×C22⋊D47—41no—
133#10625350—42no—
134#10625350—81no—
135C2×D188—21no—
136C2×D188—21no—
137C2×D188—42no—
138C2×D188—41no—
139C2×D188—81no—
140C2×C4×D47—41no—
141C2×C4×D47—41no—
142C2×Dic94—21no—
143D8×C47—21no—
144D8×C47—21no—
145C2×C8×C47—21no—
146C2×C8×C47—21no—
147C2×C8×C47—21no—
148C2×C8×C47—21no—
149C2×C8×C47C2×D411yescharacteristic
150C2×C8×C47C2×D411yescharacteristic
151C2×C8×C47C2×D411yescharacteristic
152C2×C8×C47C2411yescharacteristic
153C4⋊C4×C47—21no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—21no—
156C4⋊C4×C47—41no—
157C4⋊C4×C47—41no—
158C4⋊C4×C47—41no—
159C4⋊C4×C47D811yescharacteristic
160C22⋊C4×C47—41no—
161C22⋊C4×C47—41no—
162C22⋊C4×C47—41no—
163C22⋊C4×C47D811yescharacteristic
164C22⋊C4×C47D811yescharacteristic
165C42×C47C2×D411yescharacteristic
166C22⋊Dic47—41no—
167(C2×D47)⋊C4—41no—
168(C2×D47)⋊C4—41no—
169(C2×D47)⋊C4—41no—
170(C2×D47)⋊C4—41no—
171C4⋊Dic47—21no—
172Dic47⋊C4—41no—
173Dic188—21no—
174Dic188—21no—
175D376—21no—
176D376—21no—
177D376—21no—
178D376—42no—
179D376#4112yescomplemented
180#10625325—42no—
181#10625325—81no—
182C47⋊C16—21no—
183C47⋊C16—21no—
184C47⋊C16—21no—
185C47⋊C16—21no—
186C23×C47—41no—
187C23×C47C2×D811yescharacteristic
188C23×C47C2×D811yescharacteristic
189C22×D47—41no—
190C22×D47—41no—
191C22×D47—82no—
192C22×D47—82no—
193C22×D47—161no—
194Q8×C47—82no—
195D4×C47—22no—
196D4×C47—41no—
197D4×C47—41no—
198D4×C47—82no—
199D4×C47—82no—
200C2×C4×C47—21no—
201C2×C4×C47—21no—
202C2×C4×C47—21no—
203C2×C4×C47—21no—
204C2×C4×C47—41no—
205C2×C4×C47—41no—
206C2×C4×C47—41no—
207C2×C4×C47—82no—
208C2×C4×C47—82no—
209C2×C4×C47—82no—
210C2×C4×C47C2×D811yescharacteristic
211C2×C4×C47C2×D811yescharacteristic
212C2×C4×C47C2×D811yescharacteristic
213C2×C4×C47C2×D811yescharacteristic
214C2×C4×C47C22×D411yescharacteristic
215C22⋊D47—82no—
216C22⋊D47—161no—
217C2×Dic47—41no—
218C2×Dic47—41no—
219D188—22no—
220D188—41no—
221D188—41no—
222D188—41no—
223D188—82no—
224C4×D47—82no—
225C4×D47—161no—
226Dic94—41no—
227Dic94—41no—
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—81no—
240C22×C47—81no—
241C22×C47—81no—
242C22×C47#50912yes—
243C22×C47C22×D811yescharacteristic
244C2×D47—42no—
245C2×D47—81no—
246C2×D47—81no—
247C2×D47—81no—
248C2×D47—81no—
249C2×D47—81no—
250C2×D47—164no—
251C4×C47—21no—
252C4×C47—21no—
253C4×C47—21no—
254C4×C47—21no—
255C4×C47—81no—
256C4×C47—81no—
257C4×C47—81no—
258C4×C47#54611yescharacteristic
259C4×C47#57711yescharacteristic
260Dic47—81no—
261Dic47—81no—
262#3334D4711yescharacteristic, complemented
263#3280—471no—
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—161no—
280C2×C47#329411yescharacteristic
281C2×C47C2×#50911yescharacteristic
282C2×C47#341611yescharacteristic
283D47—82no—
284D47—161no—
285C2×#135—471no—
286C22×D8—471no—
287#547—21no—
288#546—941no—
289C2×SD32—471no—
290C2×D16—471no—
291C2×D16—471no—
292C2×M32—471no—
293C22×C16—471no—
294#500C2×D4711yescharacteristic, complemented
295#495—471no—
296#480—21no—
297#480—21no—
298#474—21no—
299#467—471no—
300#466—471no—
301#466C2×D4711yescharacteristic
302#466C2×D4711yescharacteristic, complemented
303#463—941no—
304#450—941no—
305#449—941no—
306C4×D8—471no—
307C4×D8C2×D4711yescharacteristic, complemented
308C8×D4C2×D4711yescharacteristic
309C2×#107C2×D4711yescharacteristic
310C2×#107C2×D4711yescharacteristic, complemented
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—41no—
330C2×#41—941no—
331C22×D4—941no—
332#135—942no—
333#135—1881no—
334C2×Q16—471no—
335C2×SD16—941no—
336C2×SD16—941no—
337C2×D8—471no—
338C2×D8—471no—
339C2×D8—942no—
340C2×D8—941no—
341C2×D8—1881no—
342C2×D8C22×D4711yescharacteristic
343C22×C8C22×D4711yescharacteristic
344C22×C8C22×D4711yescharacteristic
345C4⋊Q8—21no—
346#124—941no—
347#123—41no—
348#123—41no—
349#123—1881no—
350C22⋊Q8—41no—
351C22⋊Q8—941no—
352#121—21no—
353#121—21no—
354#121—941no—
355#121—1881no—
356#120—1881no—
357C4×D4—21no—
358C4×D4—941no—
359C4×D4C22⋊D4711yescharacteristic
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C22⋊C4—1881no—
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—21no—
373#107—21no—
374#107—21no—
375#107—471no—
376#107C22×D4711yescharacteristic
377#107C22×D4711yescharacteristic
378#107C22×D4711yescharacteristic
379C4⋊C8C22⋊D4711yescharacteristic
380#103—941no—
381#102—21no—
382#102—21no—
383#102—21no—
384#102—941no—
385#102—941no—
386C22⋊C8C22⋊D4711yescharacteristic
387C22⋊C8C22⋊D4711yescharacteristic
388C4×C8C22×D4711yescharacteristic
389C24—1881no—
390#41—84no—
391#41—3761no—
392#41—1882no—
393C2×Q8—41no—
394C2×Q8—941no—
395C2×D4—21no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—941no—
399C2×D4—941no—
400C2×D4—3761no—
401C2×D4—1882no—
402C2×D4—1881no—
403C2×D4—1881no—
404C2×D4—1881no—
405C2×D4#1062533411yescharacteristic
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—1881no—
410C22×C4—1881no—
411C22×C4C2×C22⋊D4711yescharacteristic
412C22×C4C2×C22⋊D4711yescharacteristic
413Q16—941no—
414Q16—941no—
415SD16—3761no—
416SD16—1882no—
417D8—21no—
418D8—21no—
419D8—472no—
420D8—941no—
421D8—941no—
422D8—941no—
423D8—1882no—
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—21no—
434C4⋊C4—21no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—41no—
438C4⋊C4—941no—
439C4⋊C4—1881no—
440C4⋊C4#1062533411yescharacteristic
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—1881no—
445C22⋊C4—1881no—
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—3762no—
458C23—3762no—
459C23—1881no—
460C23—1881no—
461C23—7521no—
462C23C2×#1062533411yescharacteristic
463C23C2×#1062533411yescharacteristic
464Q8—82no—
465Q8—1881no—
466Q8—1881no—
467D4—22no—
468D4—41no—
469D4—41no—
470D4—82no—
471D4—82no—
472D4—942no—
473D4—3762no—
474D4—3762no—
475D4—1881no—
476D4—1881no—
477D4—1881no—
478D4—7521no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—82no—
487C2×C4—82no—
488C2×C4—82no—
489C2×C4—3762no—
490C2×C4—1881no—
491C2×C4—1881no—
492C2×C4—7521no—
493C2×C4C2×#1062533411yescharacteristic
494C2×C4C2×#1062533411yescharacteristic
495C2×C4C2×#1062533411yescharacteristic
496C2×C4C2×#1062533411yescharacteristic
497C2×C4C22×C22⋊D4711yescharacteristic
498C8—21no—
499C8—21no—
500C8—21no—
501C8#41×D4711yescharacteristic
502C8#1309407011yescharacteristic
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—3761no—
512C22—3761no—
513C22—3761no—
514C22—3761no—
515C22—3761no—
516C22—1882no—
517C22—7524no—
518C22#1568955912yes—
519C22C22×#1062533411yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—81no—
527C4—3761no—
528C4—3761no—
529C4#1568976111yescharacteristic
530C4#1568993111yescharacteristic
531C2—22no—
532C2—41no—
533C2—161no—
534C2—3762no—
535C2—7521no—
536C2#2025519511yescharacteristic
537C2C2×#1568955911yescharacteristic
538C2#2025653211yescharacteristic
subgroupG/H
centerC22C22×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC47×#3334C2
socleC22×C47C22×D8
hypercenter#3334D47
hypocenterC47#33873
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. #20255075C2semidirect
2. #20245627C2semidirect
3. #20245585C2semidirect
4. #20245573C2semidirect
5. #20245532C2semidirect
6. #20245489C2semidirect
7. #20245482C2semidirect
8. #20245443C2semidirect
9. #20245309C2semidirect
10. #20245299C2semidirect
11. #20245262C2semidirect
12. #20245214C2semidirect
13. #20245098C2semidirect
14. C2×#15688923C2semidirect
15. C47×#3334C2semidirect
19. C2×#13093968C22semidirect
22. C2×#13093964C22semidirect
31. #15688950C22semidirect
32. #15688950C22semidirect
33. #15688950C22semidirect
34. C4⋊(C47⋊C16)C22semidirect
35. #15688926C22semidirect
36. #15688926C22semidirect
37. #15688926C22semidirect
38. #15688924C22semidirect
46. C22⋊(C47⋊C16)C22semidirect
47. #15688899C22semidirect
49. C47×#500C22semidirect
54. C47×#466C22semidirect
55. C4×D8×C47C22semidirect
58. C2×#107×C47C22semidirect
179. D376#41semidirect
262. #3334D47semidirect
294. #500C2×D47semidirect
302. #466C2×D47semidirect
307. C4×D8C2×D47semidirect
310. C2×#107C2×D47semidirect
328. C47#33873semidirect

Maximal subgroups

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

subgroupindex
#202550752
#202456272
#202455852
#202455732
#202455322
#202454892
#202454822
#202454432
#202453092
#202452992
#202452622
#202452142
#202450982
C2×#156889232
C47×#33342
#3387347