Finite Group Databasebeta

← #26371386

Subgroups — #26371386

Order 12032.

568 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20254027C211yesmaximal, characteristic, complemented
2#20245596C211yesmaximal, characteristic, complemented
3#20245579C211yesmaximal, characteristic, complemented
4#20245535C211yesmaximal, characteristic, complemented
5#20245525C211yesmaximal, characteristic, complemented
6#20245443C211yesmaximal, characteristic, complemented
7#20245443C211yesmaximal, characteristic, complemented
8#20245317C211yesmaximal, characteristic, complemented
9#20245300C211yesmaximal, characteristic
10#20245262C211yesmaximal, characteristic, complemented
11#20245252C211yesmaximal, characteristic, complemented
12C4×#13093968C211yesmaximal, characteristic, complemented
13C4×#13093965C211yesmaximal, characteristic, complemented
14#20245195C211yesmaximal, characteristic, complemented
15C47×#2948C211yesmaximal, characteristic, complemented
16#15689744—21no—
17C2×#13093968C2211yescharacteristic
18C2×#13093968C2211yescharacteristic
19C2×#13093965C2211yescharacteristic
20C2×#13093965C2211yescharacteristic
21#15689528C2211yescharacteristic, complemented
22#15689507C2211yescharacteristic, complemented
23#15689483—21no—
24#15689369—21no—
25#15689364C2211yescharacteristic
26#15689359C2211yescharacteristic
27#15689225—21no—
28C4×Dic188C2211yescharacteristic, complemented
29C4×D376C2211yescharacteristic, complemented
30#15688950C2211yescharacteristic, complemented
31#15688950C2211yescharacteristic, complemented
32#15688948C2211yescharacteristic, complemented
33#15688948C2211yescharacteristic, complemented
34C4⋊(C47⋊C16)C2211yescharacteristic, complemented
35C4⋊(C47⋊C16)C2211yescharacteristic, complemented
36#15688926C2211yescharacteristic, complemented
37#15688926C2211yescharacteristic, complemented
38#15688924C2211yescharacteristic
39#15688924C2211yescharacteristic
40#15688924C2211yescharacteristic
41#15688924C2211yescharacteristic
42#15688923C2211yescharacteristic, complemented
43#15688923C2211yescharacteristic, complemented
44C22⋊(C47⋊C16)C2211yescharacteristic
45C22⋊(C47⋊C16)C2211yescharacteristic
46#15688899C2211yescharacteristic, complemented
47C4×C47⋊C16C2211yescharacteristic, complemented
48C22×D8×C47C2211yescharacteristic
49C47×#518—21no—
50C47×#442—21no—
51C47×#442—21no—
52C4×D8×C47C2211yescharacteristic
53C4×D8×C47C2211yescharacteristic
54C4×D8×C47C2211yescharacteristic
55C4×D8×C47C2211yescharacteristic
56C47×#427C2211yescharacteristic
57C47×#418—21no—
58C47×#405C2211yescharacteristic
59C2×Dic188C2311yescharacteristic
60C2×#10625325—21no—
61C2×D376C2311yescharacteristic
62#13094024—21no—
63#13094019—41no—
64#13094012—21no—
65#13094010—41no—
66#13094006—41no—
67#13094003—21no—
68#13094002—41no—
69#13093998—21no—
70C4×Dic94—21no—
71C4×D188—21no—
72#13093968—22no—
73#13093968—22no—
74#13093965—22no—
75#13093965—22no—
76C2×C47⋊C16C2311yescharacteristic
77C2×C47⋊C16C2311yescharacteristic
78C2×C47⋊C16C2311yescharacteristic
79C2×C47⋊C16C2311yescharacteristic
80#13093958—21no—
81#13093958C2311yescharacteristic
82#13093958C2311yescharacteristic
83#13093949—21no—
84#13093949—21no—
85#13093946—21no—
86#13093946—21no—
87C22×D4×C47—21no—
88C2×D8×C47—22no—
89C2×D8×C47—22no—
90C2×D8×C47—21no—
91C2×D8×C47C2311yescharacteristic
92C2×D8×C47C2311yescharacteristic
93C2×M16×C47D411yescharacteristic
94C22×C8×C47C2311yescharacteristic
95C4×D4×C47—21no—
96C4×D4×C47—21no—
97C4×D4×C47—21no—
98C4×D4×C47—21no—
99C4×D4×C47—41no—
100C4×D4×C47—41no—
101#117×C47—21no—
102#117×C47D411yescharacteristic
103C2×C22⋊C4×C47—41no—
104C2×C22⋊C4×C47—41no—
105#107×C47C2311yescharacteristic
106#107×C47C2311yescharacteristic
107#106×C47—21no—
108#102×C47—21no—
109#102×C47—21no—
110#102×C47—21no—
111#102×C47—21no—
112#97×C47D411yescharacteristic
113#97×C47D411yescharacteristic
114C4×C8×C47C2311yescharacteristic
115C4×C8×C47C2311yescharacteristic
116C24×C47—41no—
117C2×D4×C47—24no—
118C2×D4×C47—21no—
119C2×D4×C47—21no—
120C2×D4×C47—42no—
121C2×D4×C47—41no—
122C22×C4×C47—41no—
123C22×C4×C47—41no—
124C22×C4×C47—41no—
125C22×C4×C47—41no—
126C22×C4×C47C2×D411yescharacteristic
127C2×C22⋊D47—41no—
128C2×D188—21no—
129C2×C4×D47—41no—
130C2×Dic94—21no—
131C2×Dic94—41no—
132D8×C47—24no—
133D8×C47—21no—
134D8×C47—21no—
135D8×C47#4112yes—
136D8×C47#4112yes—
137M16×C47—41no—
138C2×C8×C47—21no—
139C2×C8×C47—21no—
140C2×C8×C47C2×D411yescharacteristic
141C2×C8×C47C2×D411yescharacteristic
142C2×C8×C47C2×D411yescharacteristic
143C2×C8×C47C2411yescharacteristic
144C4⋊C4×C47—21no—
145C4⋊C4×C47—21no—
146C4⋊C4×C47D811yescharacteristic
147C4⋊C4×C47D811yescharacteristic
148C22⋊C4×C47—41no—
149C22⋊C4×C47—41no—
150C22⋊C4×C47—41no—
151C22⋊C4×C47—41no—
152C22⋊C4×C47—41no—
153C22⋊C4×C47D811yescharacteristic
154C22⋊C4×C47D811yescharacteristic
155C42×C47—41no—
156C42×C47C2×D411yescharacteristic
157C42×C47C2×D411yescharacteristic
158C22⋊Dic47—41no—
159(C2×D47)⋊C4—41no—
160(C2×D47)⋊C4—41no—
161(C2×D47)⋊C4—41no—
162(C2×D47)⋊C4—41no—
163C4⋊Dic47—21no—
164C4⋊Dic47—21no—
165C4⋊Dic47—41no—
166Dic47⋊C4—41no—
167Dic47⋊C4—41no—
168C4×Dic47—41no—
169Dic188—21no—
170Dic188—21no—
171D376—21no—
172D376—21no—
173#10625325—42no—
174C47⋊C16—21no—
175C47⋊C16—21no—
176C47⋊C16—21no—
177C47⋊C16—21no—
178C23×C47—44no—
179C23×C47—41no—
180C23×C47—41no—
181C23×C47—161no—
182C23×C47—161no—
183C23×C47C2×D811yescharacteristic
184C22×D47—41no—
185D4×C47—22no—
186D4×C47—22no—
187D4×C47—44no—
188D4×C47—41no—
189D4×C47—41no—
190C2×C4×C47—21no—
191C2×C4×C47—21no—
192C2×C4×C47—41no—
193C2×C4×C47—41no—
194C2×C4×C47—161no—
195C2×C4×C47—161no—
196C2×C4×C47—161no—
197C2×C4×C47—161no—
198C2×C4×C47C2×D811yescharacteristic
199C2×C4×C47C2×D811yescharacteristic
200C2×C4×C47C2×D811yescharacteristic
201C2×C4×C47C2×D811yescharacteristic
202C2×C4×C47C2×D811yescharacteristic
203C2×C4×C47C22×D411yescharacteristic
204C22⋊D47—161no—
205C2×Dic47—41no—
206C2×Dic47—41no—
207C2×Dic47—41no—
208D188—41no—
209D188—41no—
210C4×D47—161no—
211Dic94—41no—
212Dic94—41no—
213Dic94—161no—
214C8×C47—21no—
215C8×C47—21no—
216C8×C47—21no—
217C8×C47C2×#4111yescharacteristic
218C8×C47C2×#4111yescharacteristic
219#33678—471nomaximal, Sylow
220C22×C47—21no—
221C22×C47—21no—
222C22×C47—21no—
223C22×C47—42no—
224C22×C47—42no—
225C22×C47—81no—
226C22×C47—81no—
227C22×C47—81no—
228C22×C47—81no—
229C22×C47—164no—
230C22×C47C22×D811yescharacteristic
231C2×D47—81no—
232C2×D47—81no—
233C2×D47—81no—
234C4×C47—21no—
235C4×C47—21no—
236C4×C47—21no—
237C4×C47—21no—
238C4×C47—21no—
239C4×C47—81no—
240C4×C47—81no—
241C4×C47#52511yescharacteristic
242C4×C47#57511yescharacteristic
243Dic47—81no—
244Dic47—81no—
245Dic47—81no—
246#3175—471no—
247#2948D4711yescharacteristic, complemented
248#2237—471no—
249#2234—471no—
250#2226—471no—
251#2224—471no—
252#2210—471no—
253#2210—471no—
254#2187—471no—
255#2184—471no—
256#2177—471no—
257#2175—471no—
258C4×SD32—471no—
259C4×D16—471no—
260#2164—471no—
261C2×C47—41no—
262C2×C47—82no—
263C2×C47—82no—
264C2×C47#310011yescharacteristic
265C2×C47#341511yescharacteristic
266C2×C47#341611yescharacteristic
267D47—161no—
268C22×D8C2×D4711yescharacteristic
269#542—941no—
270#518—21no—
271C2×SD32—471no—
272C2×SD32—471no—
273C2×D16—471no—
274C2×D16—471no—
275#500—471no—
276#495—471no—
277#489—941no—
278#468—941no—
279#467—471no—
280#466—471no—
281#442—21no—
282#442—21no—
283#440—941no—
284C4×Q16—471no—
285C4×D8—471no—
286C4×D8C2×D4711yescharacteristic
287C4×D8C2×D4711yescharacteristic
288C4×D8C2×D4711yescharacteristic
289C4×D8C2×D4711yescharacteristic
290#427C2×D4711yescharacteristic
291#418—21no—
292#405C2×D4711yescharacteristic
293#367—471no—
294#367—471no—
295#366—471no—
296#366—471no—
297C4⋊C16—471no—
298C4⋊C16—471no—
299#358—471no—
300#358—471no—
301#357—471no—
302#357—471no—
303#357—471no—
304#357—471no—
305#357—471no—
306#357—471no—
307C22⋊C16—471no—
308C22⋊C16—471no—
309#346—471no—
310C4×C16—471no—
311C47#3367811yescharacteristic, complemented, Sylow
312C22×D4—21no—
313C2×Q16—471no—
314C2×SD16—941no—
315C2×D8—22no—
316C2×D8—22no—
317C2×D8—21no—
318C2×D8—471no—
319C2×D8C22×D4711yescharacteristic
320C2×D8C22×D4711yescharacteristic
321C2×M16C22⋊D4711yescharacteristic
322C22×C8C22×D4711yescharacteristic
323C4⋊Q8—941no—
324#126—1881no—
325#124—941no—
326#124—1881no—
327#123—1881no—
328C22⋊Q8—941no—
329C22⋊Q8—1881no—
330#121—941no—
331C4×Q8—941no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—41no—
337C4×D4—41no—
338C4×D4—941no—
339#117—21no—
340#117C22⋊D4711yescharacteristic
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343SD32—942no—
344SD32—942no—
345D16—942no—
346D16—942no—
347C2×C16—471no—
348C2×C16—471no—
349C2×C16—471no—
350C2×C16—471no—
351#107—471no—
352#107—471no—
353#107—941no—
354#107C22×D4711yescharacteristic
355#107C22×D4711yescharacteristic
356#106—21no—
357#103—941no—
358#103—941no—
359#102—21no—
360#102—21no—
361#102—21no—
362#102—21no—
363#102—941no—
364#102—941no—
365#97C22⋊D4711yescharacteristic
366#97C22⋊D4711yescharacteristic
367C4×C8C22×D4711yescharacteristic
368C4×C8C22×D4711yescharacteristic
369C24—41no—
370C2×Q8—941no—
371C2×Q8—1881no—
372C2×D4—24no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—42no—
376C2×D4—41no—
377C2×D4—941no—
378C2×D4—1881no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—1881no—
384C22×C4C2×C22⋊D4711yescharacteristic
385Q16—941no—
386Q16—941no—
387SD16—1882no—
388D8—24no—
389D8—21no—
390D8—21no—
391D8—941no—
392D8—941no—
393D8#1062535012yes—
394D8#1062535012yes—
395M16—41no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8C2×C22⋊D4711yescharacteristic
399C2×C8C2×C22⋊D4711yescharacteristic
400C2×C8C2×C22⋊D4711yescharacteristic
401C2×C8C23×D4711yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—941no—
405C4⋊C4—941no—
406C4⋊C4—1881no—
407C4⋊C4—1881no—
408C4⋊C4—1881no—
409C4⋊C4#1062533411yescharacteristic
410C4⋊C4#1062533411yescharacteristic
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—1881no—
417C22⋊C4—1881no—
418C22⋊C4—1881no—
419C22⋊C4—1881no—
420C22⋊C4—1881no—
421C22⋊C4#1062533411yescharacteristic
422C22⋊C4#1062533411yescharacteristic
423C42—41no—
424C42—1881no—
425C42C2×C22⋊D4711yescharacteristic
426C42C2×C22⋊D4711yescharacteristic
427C16—941no—
428C16—941no—
429C16—941no—
430C16—941no—
431C23—44no—
432C23—41no—
433C23—41no—
434C23—161no—
435C23—161no—
436C23—1881no—
437C23C2×#1062533411yescharacteristic
438Q8—1881no—
439Q8—1881no—
440Q8—7521no—
441D4—22no—
442D4—22no—
443D4—44no—
444D4—41no—
445D4—41no—
446D4—1881no—
447D4—1881no—
448D4—7521no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—161no—
454C2×C4—161no—
455C2×C4—161no—
456C2×C4—161no—
457C2×C4—1881no—
458C2×C4—1881no—
459C2×C4—1881no—
460C2×C4—7521no—
461C2×C4C2×#1062533411yescharacteristic
462C2×C4C2×#1062533411yescharacteristic
463C2×C4C2×#1062533411yescharacteristic
464C2×C4C2×#1062533411yescharacteristic
465C2×C4C2×#1062533411yescharacteristic
466C2×C4C22×C22⋊D4711yescharacteristic
467C8—21no—
468C8—21no—
469C8—21no—
470C8C2×#1062535011yescharacteristic
471C8C2×#1062535011yescharacteristic
472C22—21no—
473C22—21no—
474C22—21no—
475C22—42no—
476C22—42no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—164no—
482C22—3761no—
483C22—3761no—
484C22—3761no—
485C22C22×#1062533411yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—81no—
492C4—81no—
493C4—3761no—
494C4—3761no—
495C4—3761no—
496C4#1568963411yescharacteristic
497C4#1568992111yescharacteristic
498C2—41no—
499C2—82no—
500C2—82no—
501C2—7521no—
502C2#2025338811yescharacteristic
503C2#2025652711yescharacteristic
504C2#2025653511yescharacteristic
subgroupG/H
centerC22C22×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC47×#2948C2
socleC22×C47C22×D8
prime radical#20245300C2
hypercenter#2948D47
hypocenterC47#33678
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2948

Complements

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

NH ≅ G/Ntype
1. #20254027C2semidirect
2. #20245596C2semidirect
3. #20245579C2semidirect
4. #20245535C2semidirect
5. #20245525C2semidirect
6. #20245443C2semidirect
7. #20245443C2semidirect
8. #20245317C2semidirect
10. #20245262C2semidirect
11. #20245252C2semidirect
12. C4×#13093968C2semidirect
13. C4×#13093965C2semidirect
14. #20245195C2semidirect
15. C47×#2948C2semidirect
21. #15689528C22semidirect
22. #15689507C22semidirect
28. C4×Dic188C22semidirect
29. C4×D376C22semidirect
30. #15688950C22semidirect
31. #15688950C22semidirect
32. #15688948C22semidirect
33. #15688948C22semidirect
34. C4⋊(C47⋊C16)C22semidirect
35. C4⋊(C47⋊C16)C22semidirect
36. #15688926C22semidirect
37. #15688926C22semidirect
42. #15688923C22semidirect
43. #15688923C22semidirect
46. #15688899C22semidirect
47. C4×C47⋊C16C22semidirect
247. #2948D47semidirect
311. C47#33678semidirect

Maximal subgroups

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

subgroupindex
#202540272
#202455962
#202455792
#202455352
#202455252
#202454432
#202453172
#202453002
#202452622
#202452522
C4×#130939682
C4×#130939652
#202451952
C47×#29482
#3367847