Finite Group Databasebeta

← #20252652

Subgroups — #20252652

Order 6016.

784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#13094069C211yesmaximal, characteristic, complemented
2C2×#13094050C211yesmaximal, characteristic, complemented
3#15689690C211yesmaximal, characteristic, complemented
4#15689265C214yesmaximal, complemented
5#15689255C214yesmaximal, complemented
6#15689128C211yesmaximal, characteristic, complemented
7#15689120C211yesmaximal, characteristic, complemented
8#15689089C211yesmaximal, characteristic, complemented
9C22×D8×C47C211yesmaximal, characteristic, complemented
10#13094069—24no—
11#13094069—24no—
12C2×#10625350C2211yescharacteristic
13C2×#10625350C2211yescharacteristic
14C2×#10625352—21no—
15C2×#10625352C2212yescomplemented
16C22×C22⋊D47—22no—
17C2×D4×D47—21no—
18C2×D4×D47C2212yescomplemented
19#13094050—24no—
20C2×#10625335C2212yescomplemented
21C2×#10625334C2212yescomplemented
22C2×#10625329C2211yescharacteristic, complemented
23#13094020—21no—
24#13094011—21no—
25#13093995C2214yescomplemented
26#13093993—22no—
27#13093983C2211yescharacteristic, complemented
28#13093949C2212yescomplemented
29#13093946C2212yescomplemented
30#13093945C2214yescomplemented
31(C2×D47)⋊C8C2214yescomplemented
32C22×D4×C47C2211yescharacteristic
33C22×D4×C47C2211yescharacteristic, complemented
34C2×D8×C47—24no—
35C2×D8×C47C2214yescomplemented
36C22×C8×C47C2211yescharacteristic, complemented
37C24×C47—21no—
38C24×C47—21no—
39C23×D47—22no—
40C2×D4×C47—21no—
41C2×D4×C47—22no—
42C2×D4×C47—22no—
43C2×D4×C47—22no—
44C2×D4×C47—21no—
45C2×D4×C47D414yescomplemented
46C2×D4×C47C2312yes—
47C2×D4×C47C2312yes—
48C22×C4×C47C2311yescharacteristic
49C2×C22⋊D47—216no—
50C2×C22⋊D47—21no—
51C2×C22⋊D47—22no—
52C2×C22⋊D47—24no—
53C2×C22⋊D47—22no—
54C2×C22⋊D47D412yes—
55C22×Dic47—22no—
56#10625352—28no—
57#10625352—24no—
58#10625352—24no—
59D4×D47—28no—
60D4×D47—24no—
61D4×D47—24no—
62#10625350—22no—
63#10625350—22no—
64#10625350—22no—
65#10625350D414yescomplemented
66C2×D188D411yescharacteristic
67C2×D188C2311yescharacteristic
68C2×C4×D47—21no—
69C2×C4×D47C2312yes—
70C2×Dic94D411yescharacteristic
71C2×Dic94C2311yescharacteristic
72D8×C47—28no—
73C2×C8×C47—22no—
74C2×C8×C47C2312yes—
75C22⋊Dic47—21no—
76C22⋊Dic47—24no—
77#10625335—24no—
78#10625334—24no—
79C4⋊Dic47C2312yes—
80C4×Dic47—21no—
81#10625329—22no—
82C2×C47⋊C8C2312yes—
83C23×C47—22no—
84C23×C47—24no—
85C23×C47—22no—
86C23×C47—42no—
87C23×C47—82no—
88C23×C47—82no—
89C23×C47C2×D411yescharacteristic
90C22×D47—21no—
91C22×D47—28no—
92C22×D47—84no—
93C22×D47C2×D412yes—
94D4×C47—24no—
95D4×C47—22no—
96D4×C47—22no—
97D4×C47—22no—
98D4×C47—42no—
99D4×C47C2×D414yes—
100C2×C4×C47C2×D411yescharacteristic
101C2×C4×C47C2×D412yes—
102C2×C4×C47C2×D412yes—
103C2×C4×C47C2411yescharacteristic
104C22⋊D47—28no—
105C22⋊D47—28no—
106C22⋊D47—24no—
107C22⋊D47—24no—
108C22⋊D47—84no—
109C2×Dic47—28no—
110C2×Dic47—21no—
111C2×Dic47—22no—
112C2×Dic47C2×D412yes—
113D188—22no—
114D188—21no—
115D188C2×D412yes—
116C4×D47—24no—
117C4×D47—22no—
118C4×D47—22no—
119Dic94—22no—
120Dic94—21no—
121Dic94C2×D412yes—
122C8×C47—22no—
123C47⋊C8—22no—
124C22×C47—22no—
125C22×C47—24no—
126C22×C47—44no—
127C22×C47—42no—
128C22×C47—44no—
129C22×C47—84no—
130C22×C47—84no—
131C22×C47#12012yes—
132C22×C47C22×D411yescharacteristic
133C2×D47—22no—
134C2×D47—22no—
135C2×D47—24no—
136C2×D47—42no—
137C2×D47—88no—
138C4×C47#12012yes—
139C4×C47C22×D411yescharacteristic
140C4×C47C22×D411yescharacteristic
141Dic47—22no—
142Dic47—22no—
143Dic47—42no—
144#3008—471nomaximal, Sylow
145C2×C47—22no—
146C2×C47—44no—
147C2×C47—82no—
148C2×C47C2×#12011yescharacteristic
149C2×C47#57612yes—
150D47—42no—
151D47—42no—
152C2×H(5,𝔽2)—471no—
153C2×AGL(1,ℤ/8)—471no—
154C22×D8D4711yescharacteristic, complemented
155#535—471no—
156#449—474no—
157#447—474no—
158#418—471no—
159#416—471no—
160#408—471no—
161C47#300811yescharacteristic, complemented, Sylow
162H(5,𝔽2)—944no—
163H(5,𝔽2)—944no—
164C2×#41—471no—
165C2×#41—472no—
166C2×#41—471no—
167C2×#41—941no—
168C22×D4—472no—
169C22×D4—941no—
170C22×D4—942no—
171C22×D4C2×D4711yescharacteristic
172C22×D4C2×D4711yescharacteristic, complemented
173AGL(1,ℤ/8)—944no—
174C2×SD16—472no—
175C2×D8—24no—
176C2×D8—472no—
177C2×D8C2×D4714yescomplemented
178C2×M16—471no—
179C22×C8C2×D4711yescharacteristic, complemented
180#127—941no—
181#124—941no—
182#121—474no—
183#120—942no—
184#117—471no—
185#103—472no—
186#102—474no—
187#102—472no—
188C22⋊C8—474no—
189C24—21no—
190C24—21no—
191C24—942no—
192#41—474no—
193#41—944no—
194#41—948no—
195#41—944no—
196#41—942no—
197#41—942no—
198#41—942no—
199C2×Q8—471no—
200C2×Q8—471no—
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—21no—
205C2×D4—22no—
206C2×D4—472no—
207C2×D4—471no—
208C2×D4—471no—
209C2×D4—942no—
210C2×D4—944no—
211C2×D4—948no—
212C2×D4—942no—
213C2×D4—9416no—
214C2×D4—941no—
215C2×D4—944no—
216C2×D4—944no—
217C2×D4C22⋊D4714yescomplemented
218C2×D4C22×D4712yes—
219C2×D4C22×D4712yes—
220C22×C4—472no—
221C22×C4—942no—
222C22×C4—941no—
223C22×C4C22×D4711yescharacteristic
224SD16—944no—
225D8—28no—
226D8—944no—
227M16—942no—
228C2×C8—22no—
229C2×C8—472no—
230C2×C8C22×D4712yes—
231C4⋊C4—472no—
232C22⋊C4—944no—
233C22⋊C4—941no—
234C42—941no—
235C23—22no—
236C23—24no—
237C23—22no—
238C23—42no—
239C23—82no—
240C23—82no—
241C23—472no—
242C23—948no—
243C23—941no—
244C23—3764no—
245C23D4×D4711yescharacteristic
246Q8—472no—
247Q8—942no—
248Q8—941no—
249D4—24no—
250D4—22no—
251D4—22no—
252D4—22no—
253D4—42no—
254D4—472no—
255D4—948no—
256D4—948no—
257D4—944no—
258D4—944no—
259D4—942no—
260D4—941no—
261D4—3764no—
262D4C2×C22⋊D4714yes—
263C2×C4—472no—
264C2×C4—948no—
265C2×C4—941no—
266C2×C4—944no—
267C2×C4—942no—
268C2×C4—942no—
269C2×C4—942no—
270C2×C4D4×D4711yescharacteristic
271C2×C4D4×D4712yes—
272C2×C4C2×C22⋊D4712yes—
273C2×C4C23×D4711yescharacteristic
274C8—22no—
275C8—942no—
276C22—22no—
277C22—24no—
278C22—44no—
279C22—42no—
280C22—44no—
281C22—84no—
282C22—84no—
283C22—942no—
284C22—942no—
285C22—944no—
286C22—3768no—
287C22—1882no—
288C22#1309399212yes—
289C22C2×D4×D4711yescharacteristic
290C4—942no—
291C4—942no—
292C4—1882no—
293C4#1309399212yes—
294C4C2×D4×D4711yescharacteristic
295C4C22×C22⋊D4711yescharacteristic
296C2—22no—
297C2—44no—
298C2—82no—
299C2—1882no—
300C2—1882no—
301C2C2×#1309399211yescharacteristic
302C2#1568992412yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC22×D8×C47C2
socleC22×C47C22×D4
hypercenterC22×D8D47
hypocenterC47#3008
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#13094069C2semidirect
2. C2×#13094050C2semidirect
3. #15689690C2semidirect
4. #15689265C2semidirect
5. #15689255C2semidirect
6. #15689128C2semidirect
7. #15689120C2semidirect
8. #15689089C2semidirect
9. C22×D8×C47C2semidirect
15. C2×#10625352C22semidirect
18. C2×D4×D47C22semidirect
20. C2×#10625335C22semidirect
21. C2×#10625334C22semidirect
22. C2×#10625329C22semidirect
25. #13093995C22semidirect
27. #13093983C22semidirect
28. #13093949C22semidirect
29. #13093946C22semidirect
30. #13093945C22semidirect
31. (C2×D47)⋊C8C22semidirect
33. C22×D4×C47C22semidirect
35. C2×D8×C47C22semidirect
36. C22×C8×C47C22semidirect
45. C2×D4×C47D4semidirect
65. #10625350D4semidirect
154. C22×D8D47semidirect
161. C47#3008semidirect
172. C22×D4C2×D47semidirect
177. C2×D8C2×D47semidirect
179. C22×C8C2×D47semidirect
217. C2×D4C22⋊D47semidirect