Finite Group Databasebeta

← #20257041

Subgroups — #20257041

Order 6016.

1536 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094071C211yesmaximal, characteristic, complemented
2C2×#41×D47C211yesmaximal, characteristic, complemented
3#15689793C213yesmaximal, complemented
4#15689792C211yesmaximal, characteristic, complemented
5#15689791C213yesmaximal, complemented
6#15689785C211yesmaximal, characteristic, complemented
7#15689782C213yesmaximal, complemented
8#15689780C211yesmaximal, characteristic, complemented
9#15689779C213yesmaximal, complemented
10#15689689C213yesmaximal, complemented
11#15689686C213yesmaximal, complemented
12#15689633C213yesmaximal, complemented
13#15689632C213yesmaximal, complemented
14#15689599C211yesmaximal, characteristic, complemented
15C47×#550C211yesmaximal, characteristic, complemented
16#13094071—28no—
17C2×#10625354C2211yescharacteristic
18C2×#10625350C2213yes—
19C2×#10625350C2213yes—
20C2×#10625352C2213yes—
21C2×#10625352C2213yes—
22C2×#10625352C2213yescomplemented
23#41×D47—28no—
24C22×Dic94C2213yescomplemented
25C2×Q8×D47C2211yescharacteristic
26C2×Q8×D47C2211yescharacteristic, complemented
27C2×D4×D47C2213yes—
28C22×C4×D47C2213yes—
29#13094020C2213yescomplemented
30#13094020C2216yescomplemented
31#13094012C2213yescomplemented
32#13094011C2213yescomplemented
33#13094010C2216yescomplemented
34#13094009C2211yescharacteristic
35#13094006C2213yes—
36#13094004C2213yescomplemented
37#13094003C2213yescomplemented
38#13094002C2213yescomplemented
39#13094001C2213yescomplemented
40#13093999C2213yescomplemented
41#13093998C2213yescomplemented
42#13093997C2213yescomplemented
43#13093996C2216yescomplemented
44#13093996C2216yescomplemented
45#13093996C2213yescomplemented
46#13093995C2213yescomplemented
47#13093995C2213yescomplemented
48#13093994C2213yes—
49#13093992C2213yes—
50#13093992C2216yes—
51Q8×Dic47C2211yescharacteristic, complemented
52C4×Dic94C2213yescomplemented
53#13093989C2213yescomplemented
54C4×D188C2213yescomplemented
55D4×Dic47C2216yescomplemented
56C4×C22⋊D47C2213yescomplemented
57C4×C22⋊D47C2213yescomplemented
58(C22⋊D47)⋊C4C2216yescomplemented
59#13093982C2213yes—
60#13093981C2213yes—
61C2×#41×C47C2211yescharacteristic
62C2×#41×C47C2211yescharacteristic, complemented
63#127×C47C2213yescomplemented
64#121×C47C2213yescomplemented
65#121×C47C2213yescomplemented
66C4×Q8×C47C2211yescharacteristic, complemented
67C4×D4×C47C2213yescomplemented
68C23×D47C2313yes—
69#41×C47—24no—
70#41×C47—24no—
71C2×Q8×C47C2311yescharacteristic
72C2×D4×C47C2313yes—
73C2×D4×C47C2313yes—
74C2×D4×C47C2313yes—
75C2×D4×C47C2316yes—
76C22×C4×C47C2313yes—
77C22×C4×C47C2313yes—
78C2×C22⋊D47C2313yes—
79C2×C22⋊D47C2316yes—
80C2×C22⋊D47C2313yes—
81C2×C22⋊D47C2316yes—
82C2×C22⋊D47C2313yes—
83C2×C22⋊D47C2313yes—
84C22×Dic47C2316yes—
85C22×Dic47C2313yes—
86#10625354—24no—
87Q8×D47—24no—
88Q8×D47D418yescomplemented
89#10625352—212no—
90#10625352—212no—
91#10625352—212no—
92D4×D47—212no—
93#10625350—212no—
94#10625350—212no—
95C2×D188C2311yescharacteristic
96C2×D188C2313yes—
97C2×D188C2313yes—
98C2×C4×D47—212no—
99C2×C4×D47C2313yes—
100C2×C4×D47C2313yes—
101C2×C4×D47C2313yes—
102C2×C4×D47C2311yescharacteristic
103C2×C4×D47C2313yes—
104C2×Dic94—212no—
105C2×Dic94C2313yes—
106C2×Dic94C2313yes—
107C2×Dic94C2313yes—
108C4⋊C4×C47C2311yescharacteristic
109C4⋊C4×C47C2313yes—
110C22⋊C4×C47C2313yes—
111C22⋊C4×C47C2313yes—
112C42×C47C2313yes—
113C22⋊Dic47C2313yes—
114C22⋊Dic47C2313yes—
115C22⋊Dic47C2316yes—
116(C2×D47)⋊C4C2311yescharacteristic
117(C2×D47)⋊C4C2313yes—
118(C2×D47)⋊C4C2316yes—
119(C2×D47)⋊C4C2311yescharacteristic
120(C2×D47)⋊C4C2313yes—
121(C2×D47)⋊C4C2311yescharacteristic
122(C2×D47)⋊C4C2313yes—
123C4⋊Dic47C2313yes—
124C4⋊Dic47C2313yes—
125Dic47⋊C4C2313yes—
126Dic47⋊C4C2313yes—
127Dic47⋊C4C2313yes—
128Dic47⋊C4C2311yescharacteristic
129C4×Dic47C2313yes—
130C4×Dic47C2316yes—
131C23×C47C2413yes—
132C23×C47C2413yes—
133C22×D47—26no—
134C22×D47—43no—
135C22×D47—43no—
136C22×D47C2413yes—
137C22×D47C2411yescharacteristic
138C22×D47C2411yescharacteristic
139Q8×C47C2×D414yes—
140D4×C47—26no—
141D4×C47—26no—
142D4×C47—46no—
143D4×C47—43no—
144C2×C4×C47—26no—
145C2×C4×C47—26no—
146C2×C4×C47C2413yes—
147C2×C4×C47C2411yescharacteristic
148C2×C4×C47C2411yescharacteristic
149C2×C4×C47C2411yescharacteristic
150C2×C4×C47C2413yes—
151C22⋊D47—26no—
152C22⋊D47—212no—
153C22⋊D47—26no—
154C22⋊D47—43no—
155C22⋊D47—43no—
156C22⋊D47—46no—
157C2×Dic47—212no—
158C2×Dic47—26no—
159C2×Dic47C2411yescharacteristic
160C2×Dic47C2413yes—
161C2×Dic47C2411yescharacteristic
162C2×Dic47C2413yes—
163C2×Dic47C2413yes—
164D188—22no—
165D188—26no—
166D188—43no—
167C4×D47—22no—
168C4×D47—26no—
169C4×D47—26no—
170C4×D47—26no—
171C4×D47C2×D4112yes—
172Dic94—26no—
173Dic94—26no—
174Dic94C2×D4112yes—
175C22×C47—23no—
176C22×C47—23no—
177C22×C47—23no—
178C22×C47—23no—
179C22×C47—23no—
180C22×C47—23no—
181C22×C47C2511yescharacteristic
182C2×D47—21no—
183C2×D47—21no—
184C2×D47—21no—
185C2×D47—23no—
186C2×D47—21no—
187C2×D47—23no—
188C2×D47—21no—
189C2×D47—23no—
190C2×D47—412no—
191C2×D47C22×D412yes—
192C4×C47—21no—
193C4×C47—21no—
194C4×C47—23no—
195C4×C47—21no—
196C4×C47C22×D416yes—
197Dic47—23no—
198Dic47—21no—
199Dic47—21no—
200Dic47—23no—
201Dic47C22×D416yes—
202#3487—471nomaximal, Sylow
203C2×C47—43no—
204C2×C47—43no—
205C2×C47C23×D411yescharacteristic
206C2×C47#58511yescharacteristic
207C2×C47#58511yescharacteristic
208D47—22no—
209D47—41no—
210D47—43no—
211C2×2−1+4—471no—
212C22×#41—471no—
213#550—471no—
214#550—473no—
215#550—473no—
216#550D4711yescharacteristic, complemented
217#548—471no—
218#548—473no—
219#548—471no—
220#548—473no—
221#535—473no—
222#535—473no—
223#525—473no—
224#525—473no—
225#519—471no—
226C47#348711yescharacteristic, complemented, Sylow
2272−1+4—948no—
228C2×#41—471no—
229C2×#41—473no—
230C2×#41—473no—
231C2×#41—473no—
232C2×#41—473no—
233C2×#41—473no—
234C2×#41—948no—
235C2×#41C2×D4711yescharacteristic
236C2×#41C2×D4711yescharacteristic, complemented
237C22×Q8—471no—
238C22×Q8—471no—
239C22×Q8—473no—
240C22×D4—473no—
241C23×C4—473no—
242#127—476no—
243#127—473no—
244#127C2×D4713yescomplemented
245#124—473no—
246#124—476no—
247#124—473no—
248#123—471no—
249#123—473no—
250C22⋊Q8—473no—
251C22⋊Q8—473no—
252C22⋊Q8—473no—
253C22⋊Q8—473no—
254#121—473no—
255#121—473no—
256#121—473no—
257#121—476no—
258#121—476no—
259#121—473no—
260#121—473no—
261#121—473no—
262#121C2×D4713yescomplemented
263#121C2×D4713yescomplemented
264#120—476no—
265#120—473no—
266#120—473no—
267C4×Q8—471no—
268C4×Q8—473no—
269C4×Q8—473no—
270C4×Q8C2×D4711yescharacteristic, complemented
271C4×D4—476no—
272C4×D4—473no—
273C4×D4—473no—
274C4×D4—476no—
275C4×D4—473no—
276C4×D4C2×D4713yescomplemented
277#117—473no—
278#117—473no—
279C24—473no—
280#41—24no—
281#41—24no—
282#41—9412no—
283#41—9412no—
284#41—9412no—
285#41—9412no—
286#41—9412no—
287#41—944no—
288C2×Q8—478no—
289C2×Q8—473no—
290C2×Q8—473no—
291C2×Q8—473no—
292C2×Q8—9412no—
293C2×Q8—944no—
294C2×Q8C22×D4711yescharacteristic
295C2×D4—473no—
296C2×D4—476no—
297C2×D4—473no—
298C2×D4—476no—
299C2×D4—473no—
300C2×D4—473no—
301C2×D4—471no—
302C2×D4—473no—
303C2×D4—473no—
304C2×D4—9412no—
305C2×D4C22×D4713yes—
306C2×D4C22×D4713yes—
307C2×D4C22×D4716yes—
308C2×D4C22×D4713yes—
309C22×C4—473no—
310C22×C4—476no—
311C22×C4—473no—
312C22×C4—473no—
313C22×C4—473no—
314C22×C4—473no—
315C22×C4—471no—
316C22×C4—9412no—
317C22×C4C22×D4713yes—
318C22×C4C22×D4713yes—
319C4⋊C4—473no—
320C4⋊C4—473no—
321C4⋊C4—473no—
322C4⋊C4—471no—
323C4⋊C4—473no—
324C4⋊C4—473no—
325C4⋊C4C22×D4713yes—
326C4⋊C4C22×D4711yescharacteristic
327C22⋊C4—473no—
328C22⋊C4—473no—
329C22⋊C4—476no—
330C22⋊C4—473no—
331C22⋊C4—471no—
332C22⋊C4—471no—
333C22⋊C4—471no—
334C22⋊C4—473no—
335C22⋊C4—476no—
336C22⋊C4—473no—
337C22⋊C4C22×D4713yes—
338C22⋊C4C22×D4713yes—
339C42—476no—
340C42—473no—
341C42C22×D4713yes—
342C23—471no—
343C23—473no—
344C23—471no—
345C23—946no—
346C23—1883no—
347C23—1883no—
348C23C23×D4713yes—
349C23C23×D4713yes—
350Q8—4712no—
351Q8—946no—
352Q8—946no—
353Q8D4×D4714yes—
354D4—26no—
355D4—26no—
356D4—46no—
357D4—43no—
358D4—942no—
359D4—9412no—
360D4—946no—
361D4—946no—
362D4—946no—
363D4—1883no—
364D4—1883no—
365D4—1886no—
366D4—1883no—
367C2×C4—26no—
368C2×C4—26no—
369C2×C4—473no—
370C2×C4—4712no—
371C2×C4—471no—
372C2×C4—473no—
373C2×C4—473no—
374C2×C4—471no—
375C2×C4—946no—
376C2×C4—942no—
377C2×C4—946no—
378C2×C4—9412no—
379C2×C4—946no—
380C2×C4—946no—
381C2×C4C23×D4713yes—
382C2×C4C23×D4711yescharacteristic
383C2×C4C23×D4711yescharacteristic
384C2×C4C23×D4711yescharacteristic
385C2×C4C23×D4713yes—
386C22—23no—
387C22—23no—
388C22—23no—
389C22—23no—
390C22—23no—
391C22—23no—
392C22—472no—
393C22—941no—
394C22—941no—
395C22—941no—
396C22—943no—
397C22—941no—
398C22—943no—
399C22—941no—
400C22—943no—
401C22—18812no—
402C22C24×D4711yescharacteristic
403C4—21no—
404C4—21no—
405C4—23no—
406C4—21no—
407C4—476no—
408C4—941no—
409C4—943no—
410C4—941no—
411C4—943no—
412C4C2×D4×D4716yes—
413C2—43no—
414C2—43no—
415C2—942no—
416C2—1883no—
417C2—1881no—
418C2C22×D4×D4711yescharacteristic
419C2#1568995811yescharacteristic
420C2#1568995911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#550C2
hypercenter#550D47
hypocenterC47#3487
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#13094071C2semidirect
2. C2×#41×D47C2semidirect
3. #15689793C2semidirect
4. #15689792C2semidirect
5. #15689791C2semidirect
6. #15689785C2semidirect
7. #15689782C2semidirect
8. #15689780C2semidirect
9. #15689779C2semidirect
10. #15689689C2semidirect
11. #15689686C2semidirect
12. #15689633C2semidirect
13. #15689632C2semidirect
14. #15689599C2semidirect
15. C47×#550C2semidirect
22. C2×#10625352C22semidirect
24. C22×Dic94C22semidirect
26. C2×Q8×D47C22semidirect
29. #13094020C22semidirect
30. #13094020C22semidirect
31. #13094012C22semidirect
32. #13094011C22semidirect
33. #13094010C22semidirect
36. #13094004C22semidirect
37. #13094003C22semidirect
38. #13094002C22semidirect
39. #13094001C22semidirect
40. #13093999C22semidirect
41. #13093998C22semidirect
42. #13093997C22semidirect
43. #13093996C22semidirect
44. #13093996C22semidirect
45. #13093996C22semidirect
46. #13093995C22semidirect
47. #13093995C22semidirect
51. Q8×Dic47C22semidirect
52. C4×Dic94C22semidirect
53. #13093989C22semidirect
54. C4×D188C22semidirect
55. D4×Dic47C22semidirect
56. C4×C22⋊D47C22semidirect
57. C4×C22⋊D47C22semidirect
58. (C22⋊D47)⋊C4C22semidirect
62. C2×#41×C47C22semidirect
63. #127×C47C22semidirect
64. #121×C47C22semidirect
65. #121×C47C22semidirect
66. C4×Q8×C47C22semidirect
67. C4×D4×C47C22semidirect
88. Q8×D47D4semidirect
216. #550D47semidirect
226. C47#3487semidirect
236. C2×#41C2×D47semidirect
244. #127C2×D47semidirect
262. #121C2×D47semidirect
263. #121C2×D47semidirect
270. C4×Q8C2×D47semidirect
276. C4×D4C2×D47semidirect