Finite Group Databasebeta

← #26371380

Subgroups — #26371380

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#20252241C211yesmaximal, characteristic, complemented
2#20245593C211yesmaximal, characteristic, complemented
3#20245576C211yesmaximal, characteristic, complemented
4#20245532C211yesmaximal, characteristic, complemented
5#20245522C211yesmaximal, characteristic, complemented
6#20245440C211yesmaximal, characteristic, complemented
7#20245440C211yesmaximal, characteristic, complemented
8#20245316C211yesmaximal, characteristic, complemented
9#20245299C211yesmaximal, characteristic
10#20245262C211yesmaximal, characteristic, complemented
11#20245250C211yesmaximal, characteristic, complemented
12C4×#13093967C211yesmaximal, characteristic, complemented
13C4×#13093965C211yesmaximal, characteristic, complemented
14#20245195C211yesmaximal, characteristic, complemented
15C47×#3175C211yesmaximal, characteristic, complemented
16C22×D376C2211yescharacteristic
17#15689597—21no—
18C2×#13093967C2211yescharacteristic
19C2×#13093967C2211yescharacteristic
20C2×#13093965C2211yescharacteristic
21C2×#13093965C2211yescharacteristic
22#15689236—21no—
23#15689236—21no—
24C4×D376C2211yescharacteristic
25C4×D376C2211yescharacteristic
26C4×D376C2211yescharacteristic
27C4×D376C2211yescharacteristic
28#15689161C2211yescharacteristic
29#15689129—21no—
30#15688950C2211yescharacteristic, complemented
31#15688950C2211yescharacteristic, complemented
32#15688948C2211yescharacteristic, complemented
33#15688948C2211yescharacteristic, complemented
34C4⋊(C47⋊C16)C2211yescharacteristic, complemented
35C4⋊(C47⋊C16)C2211yescharacteristic, complemented
36#15688927C2211yescharacteristic, complemented
37#15688927C2211yescharacteristic, complemented
38#15688924C2211yescharacteristic, complemented
39#15688924C2211yescharacteristic, complemented
40#15688923C2211yescharacteristic
41#15688923C2211yescharacteristic
42#15688923C2211yescharacteristic
43#15688923C2211yescharacteristic
44C22⋊(C47⋊C16)C2211yescharacteristic
45C22⋊(C47⋊C16)C2211yescharacteristic
46#15688899C2211yescharacteristic, complemented
47C4×C47⋊C16C2211yescharacteristic, complemented
48C47×#542—21no—
49C47×#500C2211yescharacteristic, complemented
50C47×#495C2211yescharacteristic, complemented
51C47×#489—21no—
52C47×#468—21no—
53C47×#467C2211yescharacteristic
54C47×#466C2211yescharacteristic
55C47×#440—21no—
56C4×Q16×C47C2211yescharacteristic, complemented
57C4×D8×C47C2211yescharacteristic, complemented
58C47×#405C2211yescharacteristic
59C22×D188—21no—
60C2×D376—21no—
61C2×D376—22no—
62C2×D376—22no—
63C2×D376C2311yescharacteristic
64C2×D376C2311yescharacteristic
65C4×D188—21no—
66C4×D188—21no—
67C4×D188—21no—
68C4×D188—21no—
69#13093986—41no—
70#13093986—41no—
71#13093983—21no—
72C22⋊C4×D47—41no—
73C22⋊C4×D47—41no—
74#13093967—22no—
75#13093967—22no—
76#13093965—22no—
77#13093965—22no—
78C2×C47⋊C16C2311yescharacteristic
79C2×C47⋊C16C2311yescharacteristic
80C2×C47⋊C16C2311yescharacteristic
81C2×C47⋊C16C2311yescharacteristic
82#13093958C2311yescharacteristic
83#13093958C2311yescharacteristic
84#13093956—21no—
85#13093946—21no—
86#13093946—21no—
87#13093946—21no—
88#13093946—21no—
89C2×Q16×C47C2311yescharacteristic
90C2×SD16×C47—21no—
91C2×D8×C47C2311yescharacteristic
92C2×M16×C47D411yescharacteristic
93C22×C8×C47C2311yescharacteristic
94C4⋊Q8×C47—21no—
95#126×C47—41no—
96#124×C47—21no—
97#124×C47—41no—
98#123×C47—41no—
99C22⋊Q8×C47—21no—
100C22⋊Q8×C47—41no—
101#121×C47—21no—
102C4×Q8×C47—21no—
103C4×D4×C47—21no—
104#117×C47D411yescharacteristic
105#107×C47—21no—
106#107×C47C2311yescharacteristic
107#107×C47C2311yescharacteristic
108#103×C47—21no—
109#103×C47—21no—
110#102×C47—21no—
111#102×C47—21no—
112#97×C47D411yescharacteristic
113#97×C47D411yescharacteristic
114C4×C8×C47C2311yescharacteristic
115C4×C8×C47C2311yescharacteristic
116C23×D47—41no—
117C2×Q8×C47—21no—
118C2×Q8×C47—41no—
119C2×D4×C47—21no—
120C2×D4×C47—41no—
121C22×C4×C47—41no—
122C22×C4×C47C2×D411yescharacteristic
123C2×D188—24no—
124C2×D188—21no—
125C2×D188—21no—
126C2×D188—42no—
127C2×D188—41no—
128C2×C4×D47—41no—
129C2×C4×D47—41no—
130C2×C4×D47—41no—
131C2×C4×D47—41no—
132Q16×C47—21no—
133Q16×C47—21no—
134SD16×C47—42no—
135D8×C47—21no—
136D8×C47—21no—
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×C47—41no—
147C4⋊C4×C47—41no—
148C4⋊C4×C47—41no—
149C4⋊C4×C47D811yescharacteristic
150C4⋊C4×C47D811yescharacteristic
151C22⋊C4×C47—41no—
152C22⋊C4×C47—41no—
153C22⋊C4×C47—41no—
154C22⋊C4×C47—41no—
155C22⋊C4×C47—41no—
156C22⋊C4×C47D811yescharacteristic
157C22⋊C4×C47D811yescharacteristic
158C42×C47—41no—
159C42×C47C2×D411yescharacteristic
160C42×C47C2×D411yescharacteristic
161C22⋊Dic47—41no—
162(C2×D47)⋊C4—41no—
163(C2×D47)⋊C4—41no—
164(C2×D47)⋊C4—41no—
165(C2×D47)⋊C4—41no—
166C4⋊Dic47—21no—
167C4⋊Dic47—21no—
168C4×Dic47—41no—
169D376—24no—
170D376—21no—
171D376—21no—
172D376#4112yes—
173D376#4112yes—
174C47⋊C16—21no—
175C47⋊C16—21no—
176C47⋊C16—21no—
177C47⋊C16—21no—
178C23×C47—41no—
179C23×C47C2×D811yescharacteristic
180C22×D47—41no—
181C22×D47—41no—
182C22×D47—44no—
183C22×D47—161no—
184C22×D47—161no—
185Q8×C47—41no—
186Q8×C47—41no—
187Q8×C47—161no—
188D4×C47—41no—
189D4×C47—41no—
190D4×C47—161no—
191C2×C4×C47—21no—
192C2×C4×C47—21no—
193C2×C4×C47—41no—
194C2×C4×C47—41no—
195C2×C4×C47—41no—
196C2×C4×C47—161no—
197C2×C4×C47C2×D811yescharacteristic
198C2×C4×C47C2×D811yescharacteristic
199C2×C4×C47C2×D811yescharacteristic
200C2×C4×C47C2×D811yescharacteristic
201C2×C4×C47C2×D811yescharacteristic
202C2×C4×C47C22×D411yescharacteristic
203C2×Dic47—41no—
204C2×Dic47—41no—
205D188—22no—
206D188—22no—
207D188—44no—
208D188—41no—
209D188—41no—
210C4×D47—161no—
211C4×D47—161no—
212C4×D47—161no—
213C4×D47—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—81no—
224C22×C47—81no—
225C22×C47—81no—
226C22×C47C22×D811yescharacteristic
227C2×D47—42no—
228C2×D47—42no—
229C2×D47—81no—
230C2×D47—81no—
231C2×D47—81no—
232C2×D47—81no—
233C2×D47—164no—
234C4×C47—21no—
235C4×C47—21no—
236C4×C47—21no—
237C4×C47—21no—
238C4×C47—21no—
239C4×C47—81no—
240C4×C47—81no—
241C4×C47—81no—
242C4×C47#52511yescharacteristic
243C4×C47#57511yescharacteristic
244Dic47—81no—
245Dic47—81no—
246#3175D4711yescharacteristic, complemented
247#2948—471no—
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—161no—
263C2×C47#310011yescharacteristic
264C2×C47#341511yescharacteristic
265C2×C47#341611yescharacteristic
266D47—82no—
267D47—82no—
268C22×D8—471no—
269#542—21no—
270#518—941no—
271C2×SD32—471no—
272C2×SD32—471no—
273C2×D16—471no—
274C2×D16—471no—
275#500C2×D4711yescharacteristic, complemented
276#495C2×D4711yescharacteristic, complemented
277#489—21no—
278#468—21no—
279#467C2×D4711yescharacteristic
280#466C2×D4711yescharacteristic
281#442—941no—
282#442—941no—
283#440—21no—
284C4×Q16C2×D4711yescharacteristic, complemented
285C4×D8—471no—
286C4×D8—471no—
287C4×D8—471no—
288C4×D8—471no—
289C4×D8C2×D4711yescharacteristic, complemented
290#427—471no—
291#418—941no—
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—941no—
313C2×Q16C22×D4711yescharacteristic
314C2×SD16—21no—
315C2×D8—471no—
316C2×D8—471no—
317C2×D8—942no—
318C2×D8—942no—
319C2×D8—941no—
320C2×D8C22×D4711yescharacteristic
321C2×M16C22⋊D4711yescharacteristic
322C22×C8C22×D4711yescharacteristic
323C4⋊Q8—21no—
324#126—41no—
325#124—21no—
326#124—41no—
327#123—41no—
328C22⋊Q8—21no—
329C22⋊Q8—41no—
330#121—21no—
331C4×Q8—21no—
332C4×D4—21no—
333C4×D4—941no—
334C4×D4—941no—
335C4×D4—941no—
336C4×D4—941no—
337C4×D4—1881no—
338C4×D4—1881no—
339#117—941no—
340#117C22⋊D4711yescharacteristic
341C2×C22⋊C4—1881no—
342C2×C22⋊C4—1881no—
343SD32—942no—
344SD32—942no—
345D16—942no—
346D16—942no—
347C2×C16—471no—
348C2×C16—471no—
349C2×C16—471no—
350C2×C16—471no—
351#107—21no—
352#107—471no—
353#107—471no—
354#107C22×D4711yescharacteristic
355#107C22×D4711yescharacteristic
356#106—941no—
357#103—21no—
358#103—21no—
359#102—21no—
360#102—21no—
361#102—941no—
362#102—941no—
363#102—941no—
364#102—941no—
365#97C22⋊D4711yescharacteristic
366#97C22⋊D4711yescharacteristic
367C4×C8C22×D4711yescharacteristic
368C4×C8C22×D4711yescharacteristic
369C24—1881no—
370C2×Q8—21no—
371C2×Q8—41no—
372C2×D4—21no—
373C2×D4—41no—
374C2×D4—944no—
375C2×D4—941no—
376C2×D4—941no—
377C2×D4—1882no—
378C2×D4—1881no—
379C22×C4—41no—
380C22×C4—1881no—
381C22×C4—1881no—
382C22×C4—1881no—
383C22×C4—1881no—
384C22×C4C2×C22⋊D4711yescharacteristic
385Q16—21no—
386Q16—21no—
387SD16—42no—
388D8—21no—
389D8—21no—
390D8—472no—
391D8—472no—
392D8—944no—
393D8—941no—
394D8—941no—
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—41no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—941no—
408C4⋊C4—941no—
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—41no—
432C23—1884no—
433C23—1881no—
434C23—1881no—
435C23—7521no—
436C23—7521no—
437C23C2×#1062533411yescharacteristic
438Q8—41no—
439Q8—41no—
440Q8—161no—
441D4—41no—
442D4—41no—
443D4—161no—
444D4—942no—
445D4—942no—
446D4—1884no—
447D4—1881no—
448D4—1881no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—161no—
455C2×C4—1881no—
456C2×C4—1881no—
457C2×C4—7521no—
458C2×C4—7521no—
459C2×C4—7521no—
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—
470C8#41×D4711yescharacteristic
471C8#41×D4711yescharacteristic
472C22—21no—
473C22—21no—
474C22—21no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—3761no—
479C22—3761no—
480C22—3761no—
481C22—3761no—
482C22—1882no—
483C22—1882no—
484C22—7524no—
485C22C22×#1062533411yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—81no—
492C4—81no—
493C4—81no—
494C4—3761no—
495C4—3761no—
496C4#1568963011yescharacteristic
497C4#1568992111yescharacteristic
498C2—41no—
499C2—161no—
500C2—3762no—
501C2—3762no—
502C2#2025338411yescharacteristic
503C2#2025652711yescharacteristic
504C2#2025653211yescharacteristic
subgroupG/H
centerC22C22×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC47×#3175C2
socleC22×C47C22×D8
prime radical#20245299C2
hypercenter#3175D47
hypocenterC47#33678
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3175

Complements

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

NH ≅ G/Ntype
1. #20252241C2semidirect
2. #20245593C2semidirect
3. #20245576C2semidirect
4. #20245532C2semidirect
5. #20245522C2semidirect
6. #20245440C2semidirect
7. #20245440C2semidirect
8. #20245316C2semidirect
10. #20245262C2semidirect
11. #20245250C2semidirect
12. C4×#13093967C2semidirect
13. C4×#13093965C2semidirect
14. #20245195C2semidirect
15. C47×#3175C2semidirect
30. #15688950C22semidirect
31. #15688950C22semidirect
32. #15688948C22semidirect
33. #15688948C22semidirect
34. C4⋊(C47⋊C16)C22semidirect
35. C4⋊(C47⋊C16)C22semidirect
36. #15688927C22semidirect
37. #15688927C22semidirect
38. #15688924C22semidirect
39. #15688924C22semidirect
46. #15688899C22semidirect
47. C4×C47⋊C16C22semidirect
49. C47×#500C22semidirect
50. C47×#495C22semidirect
56. C4×Q16×C47C22semidirect
57. C4×D8×C47C22semidirect
246. #3175D47semidirect
275. #500C2×D47semidirect
276. #495C2×D47semidirect
284. C4×Q16C2×D47semidirect
289. C4×D8C2×D47semidirect
311. C47#33678semidirect

Maximal subgroups

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

subgroupindex
#202522412
#202455932
#202455762
#202455322
#202455222
#202454402
#202453162
#202452992
#202452622
#202452502
C4×#130939672
C4×#130939652
#202451952
C47×#31752
#3367847