Finite Group Databasebeta

← #509×D47 #20256508

Subgroups — #509×D47 #20256508

Order 6016.

400 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#135×D47C211yesmaximal, characteristic, complemented
2C2×D8×D47C211yesmaximal, characteristic, complemented
3#15689561C211yesmaximal, characteristic, complemented
4#15689560C212yesmaximal, complemented
5#15689559C211yesmaximal, characteristic, complemented
6#15689558C211yesmaximal, characteristic, complemented
7#15689557C212yesmaximal, complemented
8SD32×D47C212yesmaximal, complemented
9D16×D47C212yesmaximal, complemented
10M32×D47C211yesmaximal, characteristic, complemented
11C47×#509C211yesmaximal, characteristic, complemented
12#41×D47—21no—
13C2×D4×D47—21no—
14#13094047C2211yescharacteristic, complemented
15#13094046C2211yescharacteristic, complemented
16#13094045—21no—
17#13094044—21no—
18#13094043C2211yescharacteristic, complemented
19Q16×D47C2211yescharacteristic, complemented
20SD16×D47—21no—
21C2×D376C2211yescharacteristic, complemented
22C2×#10625334—21no—
23D8×D47—21no—
24D8×D47—21no—
25D8×D47C2212yes—
26D8×D47C2212yescomplemented
27D8×D47C2211yescharacteristic, complemented
28C2×C8×D47C2211yescharacteristic
29#13093969C2212yescomplemented
30#13093968C2212yescomplemented
31#13093967C2212yescomplemented
32D752C2212yescomplemented
33#13093965C2212yescomplemented
34#13093965C2212yescomplemented
35#13093964C2211yescharacteristic, complemented
36#13093963C2212yescomplemented
37C16×D47C2212yescomplemented
38#135×C47C2211yescharacteristic, complemented
39C2×D8×C47C2211yescharacteristic, complemented
40SD32×C47C2212yescomplemented
41D16×C47C2212yescomplemented
42M32×C47C2211yescharacteristic, complemented
43C23×D47—41no—
44#41×C47—21no—
45C2×D4×C47—21no—
46C2×C22⋊D47—41no—
47#10625354—21no—
48Q8×D47—21no—
49#10625352—21no—
50#10625352—41no—
51D4×D47—22no—
52D4×D47—22no—
53D4×D47—21no—
54D4×D47—41no—
55D4×D47—41no—
56D4×D47—41no—
57#10625350—21no—
58#10625350—41no—
59C2×D188—21no—
60C2×C4×D47—41no—
61C2×C4×D47D411yescharacteristic
62Q16×C47C2311yescharacteristic, complemented
63SD16×C47—21no—
64D8×C47—21no—
65D8×C47C2312yes—
66D8×C47C2311yescharacteristic, complemented
67C2×C8×C47C2311yescharacteristic
68#10625337—21no—
69#10625336—21no—
70#10625335—21no—
71#10625334—22no—
72#10625334—22no—
73#10625334—21no—
74C2×C47⋊C8D411yescharacteristic
75Dic188C2311yescharacteristic, complemented
76D376—21no—
77D376C2312yes—
78D376C2311yescharacteristic, complemented
79#10625325—21no—
80C8×D47D411yescharacteristic
81C8×D47D411yescharacteristic
82C8×D47C2311yescharacteristic
83C8×D47C2311yescharacteristic
84C16×C47C2312yescomplemented
85C47⋊C16C2312yescomplemented
86C23×C47—41no—
87C22×D47—41no—
88C22×D47—41no—
89C22×D47—42no—
90C22×D47—42no—
91C22×D47—84no—
92C22×D47D811yescharacteristic
93Q8×C47—21no—
94D4×C47—22no—
95D4×C47—21no—
96D4×C47—41no—
97D4×C47—41no—
98C2×C4×C47—41no—
99C2×C4×C47C2×D411yescharacteristic
100C22⋊D47—41no—
101C22⋊D47—41no—
102C22⋊D47—41no—
103C22⋊D47—42no—
104C22⋊D47—42no—
105C2×Dic47—41no—
106C2×Dic47D811yescharacteristic
107D188—21no—
108D188—22no—
109D188—41no—
110D188—41no—
111C4×D47—41no—
112C4×D47—41no—
113C4×D47—41no—
114C4×D47D811yescharacteristic
115C4×D47D811yescharacteristic
116C4×D47C2×D411yescharacteristic
117C4×D47C2×D411yescharacteristic
118Dic94—21no—
119Dic94—41no—
120C8×C47C2×D411yescharacteristic
121C8×C47C2411yescharacteristic
122C47⋊C8C2×D411yescharacteristic
123C47⋊C8C2×D411yescharacteristic
124C22×C47—41no—
125C22×C47—42no—
126C22×C47—82no—
127C22×C47C2×D811yescharacteristic
128C2×D47—22no—
129C2×D47—41no—
130C2×D47—42no—
131C2×D47—84no—
132C2×D47—82no—
133C2×D47—82no—
134C2×D47—84no—
135C2×D47C2×D811yescharacteristic
136C2×D47C2×D811yescharacteristic
137C4×C47—41no—
138C4×C47C2×D811yescharacteristic
139C4×C47C22×D411yescharacteristic
140Dic47—41no—
141Dic47C2×D811yescharacteristic
142Dic47C2×D811yescharacteristic
143C2×#509—471nomaximal, Sylow
144C2×C47—21no—
145C2×C47—82no—
146C2×C47—81no—
147C2×C47C22×D811yescharacteristic
148D47—21no—
149D47—81no—
150D47—82no—
151D47#50912yesdirect product factor
152C2×#135—471no—
153C22×D8—471no—
154#509—471no—
155#509—471no—
156#509—472no—
157#509—472no—
158#509—471no—
159#509D4711yescharacteristic, direct product factor
160C2×SD32—472no—
161C2×D16—472no—
162C2×M32—471no—
163C47C2×#50911yescharacteristic, complemented, Sylow
164C2×#41—941no—
165C22×D4—941no—
166#135—471no—
167#135—471no—
168#135—471no—
169#135—941no—
170#135—941no—
171#135C2×D4711yescharacteristic, complemented
172C2×Q16—471no—
173C2×SD16—941no—
174C2×D8—472no—
175C2×D8—472no—
176C2×D8—471no—
177C2×D8—471no—
178C2×D8—941no—
179C2×D8—941no—
180C2×D8—941no—
181C2×D8C2×D4711yescharacteristic, complemented
182C22×C8—471no—
183SD32—472no—
184SD32—472no—
185SD32—472no—
186SD32C2×D4712yescomplemented
187D16—472no—
188D16—472no—
189D16—472no—
190D16C2×D4712yescomplemented
191M32—471no—
192M32—472no—
193M32C2×D4711yescharacteristic, complemented
194C2×C16—472no—
195C24—1881no—
196#41—21no—
197#41—941no—
198#41—941no—
199#41—941no—
200#41—1881no—
201#41—1881no—
202C2×Q8—941no—
203C2×D4—21no—
204C2×D4—942no—
205C2×D4—942no—
206C2×D4—941no—
207C2×D4—941no—
208C2×D4—1881no—
209C2×D4—1881no—
210C2×D4—1881no—
211C2×D4—1881no—
212C22×C4—471no—
213C22×C4—1881no—
214Q16—471no—
215Q16—941no—
216Q16C22×D4711yescharacteristic, complemented
217SD16—21no—
218SD16—941no—
219SD16—941no—
220SD16—941no—
221D8—21no—
222D8—472no—
223D8—471no—
224D8—942no—
225D8—942no—
226D8—941no—
227D8—941no—
228D8C22×D4712yes—
229D8C22×D4711yescharacteristic, complemented
230C2×C8—471no—
231C2×C8—471no—
232C2×C8—471no—
233C2×C8—471no—
234C2×C8—471no—
235C2×C8C22×D4711yescharacteristic
236C16—472no—
237C16C22×D4712yescomplemented
238C23—41no—
239C23—471no—
240C23—3764no—
241C23—1881no—
242C23—1882no—
243C23—1882no—
244C23—1881no—
245Q8—21no—
246Q8—941no—
247Q8—1881no—
248D4—22no—
249D4—21no—
250D4—41no—
251D4—41no—
252D4—942no—
253D4—941no—
254D4—1881no—
255D4—1882no—
256D4—1882no—
257D4—1881no—
258D4—1881no—
259D4—1881no—
260D4—1881no—
261C2×C4—41no—
262C2×C4—471no—
263C2×C4—471no—
264C2×C4—471no—
265C2×C4—471no—
266C2×C4—471no—
267C2×C4—1881no—
268C2×C4—1881no—
269C2×C4—1881no—
270C2×C4—1881no—
271C2×C4D4×D4711yescharacteristic
272C8—471no—
273C8—471no—
274C8D4×D4711yescharacteristic
275C8C23×D4711yescharacteristic
276C22—41no—
277C22—42no—
278C22—82no—
279C22—471no—
280C22—471no—
281C22—942no—
282C22—3762no—
283C22—3764no—
284C22—3762no—
285C22—3764no—
286C22—1881no—
287C22—1882no—
288C22D8×D4711yescharacteristic
289C4—41no—
290C4—471no—
291C4—471no—
292C4—1881no—
293C4D8×D4711yescharacteristic
294C4C2×D4×D4711yescharacteristic
295C2—21no—
296C2—82no—
297C2—81no—
298C2—472no—
299C2—941no—
300C2—3762no—
301C2—3761no—
302C2C2×D8×D4711yescharacteristic
subgroupG/H
centerC2C2×D8×D47
commutatorC8×C47C24
FrattiniC8C23×D47
FittingC47×#509C2
socleC2×C47C22×D8
hypercenter#509D47
hypocenterC47C2×#509
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #135×D47C2semidirect
2. C2×D8×D47C2semidirect
3. #15689561C2semidirect
4. #15689560C2semidirect
5. #15689559C2semidirect
6. #15689558C2semidirect
7. #15689557C2semidirect
8. SD32×D47C2semidirect
9. D16×D47C2semidirect
10. M32×D47C2semidirect
11. C47×#509C2semidirect
14. #13094047C22semidirect
15. #13094046C22semidirect
18. #13094043C22semidirect
19. Q16×D47C22semidirect
21. C2×D376C22semidirect
26. D8×D47C22semidirect
27. D8×D47C22semidirect
29. #13093969C22semidirect
30. #13093968C22semidirect
31. #13093967C22semidirect
32. D752C22semidirect
33. #13093965C22semidirect
34. #13093965C22semidirect
35. #13093964C22semidirect
36. #13093963C22semidirect
37. C16×D47C22semidirect
38. #135×C47C22semidirect
39. C2×D8×C47C22semidirect
40. SD32×C47C22semidirect
41. D16×C47C22semidirect
42. M32×C47C22semidirect
62. Q16×C47C23semidirect
66. D8×C47C23semidirect
75. Dic188C23semidirect
78. D376C23semidirect
84. C16×C47C23semidirect
85. C47⋊C16C23semidirect
151. D47#509direct (N × H)
159. #509D47direct (N × H)
163. C47C2×#509semidirect
171. #135C2×D47semidirect
181. C2×D8C2×D47semidirect
186. SD32C2×D47semidirect
190. D16C2×D47semidirect
193. M32C2×D47semidirect
216. Q16C22×D47semidirect
229. D8C22×D47semidirect
237. C16C22×D47semidirect