Finite Group Databasebeta

← #20257179

Subgroups — #20257179

Order 6016.

1540 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×#13094072C211yesmaximal, characteristic, complemented
2C2×#13094070C211yesmaximal, characteristic, complemented
3#15689785C211yesmaximal, characteristic, complemented
4#15689784C211yesmaximal, characteristic, complemented
5#15689780C211yesmaximal, characteristic, complemented
6#15689770C213yesmaximal, complemented
7#15689769C213yesmaximal, complemented
8#15689766C213yesmaximal, complemented
9#15689764C213yesmaximal, complemented
10#15689696C213yesmaximal, complemented
11#15689689C213yesmaximal, complemented
12#15689670C213yesmaximal, complemented
13#124×D47C213yesmaximal, complemented
14C4×#10625354C211yesmaximal, characteristic, complemented
15C47×#548C211yesmaximal, characteristic, complemented
16#13094072—28no—
17#13094070—28no—
18C2×#10625354C2211yescharacteristic
19C2×#10625354C2211yescharacteristic
20C2×#10625354C2213yescomplemented
21C2×#10625350C2213yes—
22C2×#10625350C2213yescomplemented
23C2×#10625350C2213yescomplemented
24C2×Q8×D47C2211yescharacteristic, complemented
25C2×Q8×D47C2213yescomplemented
26C22×D188C2213yes—
27C2×D4×D47C2213yes—
28C2×D4×D47C2213yes—
29#13094023C2213yescomplemented
30#13094020C2213yescomplemented
31#13094013C2213yescomplemented
32#13094012C2213yescomplemented
33#13094011C2213yescomplemented
34#13094010C2213yescomplemented
35#13094010C2216yescomplemented
36#13094010C2211yescharacteristic, complemented
37#13094009C2216yescomplemented
38#13094006C2216yescomplemented
39#13094004C2213yescomplemented
40#13094003C2213yescomplemented
41#13094000C2213yescomplemented
42#13093999C2213yescomplemented
43#13093999C2213yescomplemented
44#13093998C2213yescomplemented
45#13093997C2213yescomplemented
46#13093997C2213yescomplemented
47#13093995C2213yescomplemented
48#13093995C2213yescomplemented
49#13093994C2216yescomplemented
50#13093992C2216yescomplemented
51Q8×Dic47C2211yescharacteristic, complemented
52C4×D188C2213yescomplemented
53C4×D188C2213yescomplemented
54#13093986C2213yescomplemented
55C4×C22⋊D47C2213yescomplemented
56C4×C22⋊D47C2213yescomplemented
57#13093982C2213yescomplemented
58C22⋊C4×D47C2216yescomplemented
59C22⋊C4×D47C2216yescomplemented
60C42×D47C2213yescomplemented
61C2×#41×C47C2211yescharacteristic
62C22×Q8×C47C2211yescharacteristic, complemented
63#124×C47C2213yescomplemented
64C22⋊Q8×C47C2213yescomplemented
65#121×C47C2213yescomplemented
66C4×Q8×C47C2211yescharacteristic, complemented
67C4×D4×C47C2213yescomplemented
68C23×D47C2316yes—
69#41×C47—24no—
70C2×Q8×C47—24no—
71C2×Q8×C47C2313yes—
72C2×Q8×C47C2311yescharacteristic
73C2×D4×C47C2313yes—
74C2×D4×C47C2313yes—
75C22×C4×C47C2313yes—
76C22×C4×C47C2313yes—
77C2×C22⋊D47C2313yes—
78C2×C22⋊D47C2313yes—
79C2×C22⋊D47C2313yes—
80C2×C22⋊D47C2311yescharacteristic
81C2×C22⋊D47C2313yes—
82C2×C22⋊D47C2313yes—
83#10625354—24no—
84#10625354—212no—
85#10625354D418yescomplemented
86Q8×D47—24no—
87Q8×D47—212no—
88D4×D47—212no—
89D4×D47—212no—
90#10625350—212no—
91#10625350—212no—
92#10625350—212no—
93C2×D188—212no—
94C2×D188C2313yes—
95C2×D188C2313yes—
96C2×D188C2313yes—
97C2×D188C2313yes—
98C2×D188C2313yes—
99C2×C4×D47C2316yes—
100C2×C4×D47C2313yes—
101C2×C4×D47C2313yes—
102C2×C4×D47C2313yes—
103C2×C4×D47C2313yes—
104C2×C4×D47C2313yes—
105C2×Dic94C2313yes—
106C2×Dic94C2313yes—
107C2×Dic94C2311yescharacteristic
108C4⋊C4×C47C2313yes—
109C4⋊C4×C47C2313yes—
110C22⋊C4×C47C2311yescharacteristic
111C22⋊C4×C47C2313yes—
112C22⋊C4×C47C2316yes—
113C42×C47C2313yes—
114C22⋊Dic47C2313yes—
115C22⋊Dic47C2316yes—
116C22⋊Dic47C2311yescharacteristic
117(C2×D47)⋊C4C2313yes—
118(C2×D47)⋊C4C2313yes—
119(C2×D47)⋊C4C2316yes—
120(C2×D47)⋊C4C2316yes—
121(C2×D47)⋊C4C2316yes—
122(C2×D47)⋊C4C2311yescharacteristic
123(C2×D47)⋊C4C2311yescharacteristic
124C4⋊Dic47C2313yes—
125C4⋊Dic47C2313yes—
126Dic47⋊C4C2313yes—
127Dic47⋊C4C2313yes—
128C4×Dic47C2311yescharacteristic
129C4×Dic47C2313yes—
130C4×Dic47C2313yes—
131C23×C47C2413yes—
132C23×C47C2411yescharacteristic
133C22×D47—212no—
134C22×D47—46no—
135C22×D47—46no—
136C22×D47C2413yes—
137C22×D47C2411yescharacteristic
138C22×D47C2413yes—
139Q8×C47—26no—
140Q8×C47C2×D414yes—
141D4×C47—26no—
142D4×C47—43no—
143C2×C4×C47—26no—
144C2×C4×C47—26no—
145C2×C4×C47C2413yes—
146C2×C4×C47C2411yescharacteristic
147C2×C4×C47C2411yescharacteristic
148C2×C4×C47C2413yes—
149C2×C4×C47C2413yes—
150C22⋊D47—26no—
151C22⋊D47—26no—
152C22⋊D47—22no—
153C22⋊D47—26no—
154C22⋊D47—43no—
155C22⋊D47—43no—
156C2×Dic47C2411yescharacteristic
157C2×Dic47C2413yes—
158C2×Dic47C2411yescharacteristic
159C2×Dic47C2413yes—
160C2×Dic47C2411yescharacteristic
161D188—26no—
162D188—26no—
163D188—26no—
164D188—43no—
165D188C2×D4112yes—
166C4×D47—212no—
167C4×D47—26no—
168C4×D47—26no—
169C4×D47—43no—
170C4×D47—43no—
171C4×D47C2×D4112yes—
172Dic94—26no—
173Dic94—22no—
174Dic94—26no—
175C22×C47—21no—
176C22×C47—23no—
177C22×C47—21no—
178C22×C47—23no—
179C22×C47—21no—
180C22×C47—23no—
181C22×C47C2511yescharacteristic
182C2×D47—23no—
183C2×D47—23no—
184C2×D47—21no—
185C2×D47—23no—
186C2×D47—21no—
187C2×D47—23no—
188C2×D47—21no—
189C2×D47—23no—
190C2×D47—812no—
191C2×D47C22×D416yes—
192C4×C47—23no—
193C4×C47—21no—
194C4×C47—21no—
195C4×C47—23no—
196C4×C47C22×D416yes—
197Dic47—23no—
198Dic47—21no—
199Dic47—21no—
200Dic47—23no—
201Dic47C22×D412yes—
202#3500—471nomaximal, Sylow
203C2×C47—43no—
204C2×C47—41no—
205C2×C47C23×D411yescharacteristic
206C2×C47#58511yescharacteristic
207C2×C47#58511yescharacteristic
208D47—26no—
209D47—41no—
210D47—43no—
211C2×2−1+4—471no—
212C2×H(5,𝔽2)—471no—
213#548—471no—
214#548—471no—
215#548—471no—
216#548D4711yescharacteristic, complemented
217#546—473no—
218#546—473no—
219#546—473no—
220#546—473no—
221#536—473no—
222#535—473no—
223#532—473no—
224C2×#124—473no—
225C4×#41—471no—
226C47#350011yescharacteristic, complemented, Sylow
2272−1+4—948no—
228H(5,𝔽2)—948no—
229C2×#41—471no—
230C2×#41—473no—
231C2×#41—471no—
232C2×#41—473no—
233C2×#41—473no—
234C2×#41—473no—
235C2×#41C2×D4711yescharacteristic
236C22×Q8—473no—
237C22×Q8—471no—
238C22×Q8C2×D4711yescharacteristic, complemented
239C22×D4—473no—
240C22×D4—473no—
241C22×D4—473no—
242C4⋊Q8—473no—
243#127—473no—
244#124—473no—
245#124—473no—
246#124—473no—
247#124—476no—
248#124—471no—
249#124—473no—
250#124C2×D4713yescomplemented
251#123—476no—
252#123—476no—
253C22⋊Q8—473no—
254C22⋊Q8—473no—
255C22⋊Q8—473no—
256C22⋊Q8C2×D4713yescomplemented
257#121—473no—
258#121—473no—
259#121—473no—
260#121—473no—
261#121—473no—
262#121—473no—
263#121—473no—
264#121C2×D4713yescomplemented
265#120—476no—
266#120—476no—
267C4×Q8—471no—
268C4×Q8C2×D4711yescharacteristic, complemented
269C4×D4—473no—
270C4×D4—473no—
271C4×D4—473no—
272C4×D4—473no—
273C4×D4—473no—
274C4×D4C2×D4713yescomplemented
275#117—473no—
276C2×C22⋊C4—476no—
277C2×C22⋊C4—476no—
278C2×C42—473no—
279C24—476no—
280#41—24no—
281#41—478no—
282#41—9412no—
283#41—9412no—
284#41—9412no—
285#41—9412no—
286#41—944no—
287C2×Q8—24no—
288C2×Q8—473no—
289C2×Q8—473no—
290C2×Q8—471no—
291C2×Q8—9412no—
292C2×Q8—944no—
293C2×Q8C22×D4713yes—
294C2×Q8C22×D4711yescharacteristic
295C2×D4—473no—
296C2×D4—473no—
297C2×D4—473no—
298C2×D4—471no—
299C2×D4—473no—
300C2×D4—473no—
301C2×D4—473no—
302C2×D4—473no—
303C2×D4—473no—
304C2×D4—473no—
305C2×D4—473no—
306C2×D4—9412no—
307C2×D4—9412no—
308C2×D4—9412no—
309C2×D4C22×D4713yes—
310C2×D4C22×D4713yes—
311C22×C4—473no—
312C22×C4—476no—
313C22×C4—473no—
314C22×C4—473no—
315C22×C4—473no—
316C22×C4—473no—
317C22×C4C22×D4713yes—
318C22×C4C22×D4713yes—
319C4⋊C4—473no—
320C4⋊C4—473no—
321C4⋊C4—473no—
322C4⋊C4—473no—
323C4⋊C4C22×D4713yes—
324C4⋊C4C22×D4713yes—
325C22⋊C4—473no—
326C22⋊C4—476no—
327C22⋊C4—471no—
328C22⋊C4—473no—
329C22⋊C4—473no—
330C22⋊C4—476no—
331C22⋊C4—476no—
332C22⋊C4—476no—
333C22⋊C4—471no—
334C22⋊C4—471no—
335C22⋊C4C22×D4713yes—
336C22⋊C4C22×D4716yes—
337C22⋊C4C22×D4711yescharacteristic
338C42—471no—
339C42—473no—
340C42—473no—
341C42C22×D4713yes—
342C23—473no—
343C23—473no—
344C23—471no—
345C23—9412no—
346C23—1886no—
347C23—1886no—
348C23C23×D4713yes—
349C23C23×D4711yescharacteristic
350Q8—26no—
351Q8—946no—
352Q8—942no—
353Q8—946no—
354Q8D4×D4714yes—
355D4—26no—
356D4—43no—
357D4—4712no—
358D4—946no—
359D4—946no—
360D4—946no—
361D4—942no—
362D4—946no—
363D4—946no—
364D4—946no—
365D4—1883no—
366D4—1883no—
367D4—1883no—
368C2×C4—26no—
369C2×C4—26no—
370C2×C4—471no—
371C2×C4—4712no—
372C2×C4—471no—
373C2×C4—473no—
374C2×C4—473no—
375C2×C4—471no—
376C2×C4—9412no—
377C2×C4—946no—
378C2×C4—946no—
379C2×C4—1883no—
380C2×C4—1883no—
381C2×C4C23×D4711yescharacteristic
382C2×C4C23×D4713yes—
383C2×C4C23×D4713yes—
384C2×C4C23×D4711yescharacteristic
385C2×C4C23×D4713yes—
386C22—21no—
387C22—23no—
388C22—21no—
389C22—23no—
390C22—21no—
391C22—23no—
392C22—476no—
393C22—943no—
394C22—943no—
395C22—941no—
396C22—943no—
397C22—941no—
398C22—943no—
399C22—941no—
400C22—943no—
401C22—37612no—
402C22C24×D4711yescharacteristic
403C4—21no—
404C4—23no—
405C4—23no—
406C4—21no—
407C4—472no—
408C4—941no—
409C4—943no—
410C4—941no—
411C4—943no—
412C4C2×D4×D4716yes—
413C2—43no—
414C2—41no—
415C2—946no—
416C2—1883no—
417C2—1881no—
418C2C22×D4×D4711yescharacteristic
419C2#1568995911yescharacteristic
420C2#1568996011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#548C2
hypercenter#548D47
hypocenterC47#3500
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#13094072C2semidirect
2. C2×#13094070C2semidirect
3. #15689785C2semidirect
4. #15689784C2semidirect
5. #15689780C2semidirect
6. #15689770C2semidirect
7. #15689769C2semidirect
8. #15689766C2semidirect
9. #15689764C2semidirect
10. #15689696C2semidirect
11. #15689689C2semidirect
12. #15689670C2semidirect
13. #124×D47C2semidirect
14. C4×#10625354C2semidirect
15. C47×#548C2semidirect
20. C2×#10625354C22semidirect
22. C2×#10625350C22semidirect
23. C2×#10625350C22semidirect
24. C2×Q8×D47C22semidirect
25. C2×Q8×D47C22semidirect
29. #13094023C22semidirect
30. #13094020C22semidirect
31. #13094013C22semidirect
32. #13094012C22semidirect
33. #13094011C22semidirect
34. #13094010C22semidirect
35. #13094010C22semidirect
36. #13094010C22semidirect
37. #13094009C22semidirect
38. #13094006C22semidirect
39. #13094004C22semidirect
40. #13094003C22semidirect
41. #13094000C22semidirect
42. #13093999C22semidirect
43. #13093999C22semidirect
44. #13093998C22semidirect
45. #13093997C22semidirect
46. #13093997C22semidirect
47. #13093995C22semidirect
48. #13093995C22semidirect
49. #13093994C22semidirect
50. #13093992C22semidirect
51. Q8×Dic47C22semidirect
52. C4×D188C22semidirect
53. C4×D188C22semidirect
54. #13093986C22semidirect
55. C4×C22⋊D47C22semidirect
56. C4×C22⋊D47C22semidirect
57. #13093982C22semidirect
58. C22⋊C4×D47C22semidirect
59. C22⋊C4×D47C22semidirect
60. C42×D47C22semidirect
62. C22×Q8×C47C22semidirect
63. #124×C47C22semidirect
64. C22⋊Q8×C47C22semidirect
65. #121×C47C22semidirect
66. C4×Q8×C47C22semidirect
67. C4×D4×C47C22semidirect
85. #10625354D4semidirect
216. #548D47semidirect
226. C47#3500semidirect
238. C22×Q8C2×D47semidirect
250. #124C2×D47semidirect
256. C22⋊Q8C2×D47semidirect
264. #121C2×D47semidirect
268. C4×Q8C2×D47semidirect
274. C4×D4C2×D47semidirect