Finite Group Databasebeta

← #20252655

Subgroups — #20252655

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×#13094070C211yesmaximal, characteristic, complemented
2C22×#10625334C211yesmaximal, characteristic, complemented
3#15689690C211yesmaximal, characteristic, complemented
4#15689267C214yesmaximal, complemented
5#15689255C214yesmaximal, complemented
6#15689129C211yesmaximal, characteristic, complemented
7#15689119C211yesmaximal, characteristic, complemented
8#15689091C211yesmaximal, characteristic, complemented
9C2×AGL(1,ℤ/8)×C47C211yesmaximal, characteristic, complemented
10#13094070—24no—
11#13094070—24no—
12C2×#10625354C2212yescomplemented
13C2×#10625350—21no—
14C2×#10625350C2211yescharacteristic
15C22×D188—21no—
16C22×D188C2211yescharacteristic
17C2×D4×D47—22no—
18C2×D4×D47C2212yescomplemented
19C2×#10625334—24no—
20C2×#10625334C2214yescomplemented
21C22×C47⋊C8C2211yescharacteristic, complemented
22#13094020—21no—
23#13094011—21no—
24#13093995C2214yescomplemented
25#13093993—22no—
26#13093983C2211yescharacteristic, complemented
27#13093948C2212yescomplemented
28#13093946C2214yescomplemented
29#13093945C2212yescomplemented
30(C2×D47)⋊C8C2214yescomplemented
31C2×#41×C47C2211yescharacteristic
32C22×D4×C47C2211yescharacteristic, complemented
33AGL(1,ℤ/8)×C47—24no—
34C2×SD16×C47C2212yescomplemented
35C2×D8×C47C2212yescomplemented
36C2×M16×C47C2211yescharacteristic, complemented
37C24×C47—21no—
38C23×D47—21no—
39C23×D47—22no—
40#41×C47—22no—
41#41×C47D414yescomplemented
42C2×Q8×C47C2311yescharacteristic
43C2×D4×C47—21no—
44C2×D4×C47—22no—
45C2×D4×C47—22no—
46C2×D4×C47—21no—
47C2×D4×C47C2312yes—
48C2×D4×C47C2311yescharacteristic
49C22×C4×C47—21no—
50C22×C4×C47C2311yescharacteristic
51C2×C22⋊D47—24no—
52C2×C22⋊D47—22no—
53C2×C22⋊D47D412yes—
54#10625354—24no—
55#10625354—24no—
56D4×D47—216no—
57D4×D47—24no—
58D4×D47—24no—
59#10625350—28no—
60#10625350—22no—
61#10625350—22no—
62C2×D188—28no—
63C2×D188—22no—
64C2×D188—21no—
65C2×D188—22no—
66C2×D188D411yescharacteristic
67C2×D188D414yescomplemented
68C2×D188C2312yes—
69C2×C4×D47—22no—
70C2×C4×D47C2312yes—
71C2×Dic94D411yescharacteristic
72SD16×C47—24no—
73D8×C47—24no—
74M16×C47—22no—
75C2×C8×C47C2312yes—
76C22⋊Dic47—21no—
77C22⋊Dic47—24no—
78#10625334—28no—
79C4⋊Dic47C2312yes—
80C4×Dic47—21no—
81C2×C47⋊C8—22no—
82C2×C47⋊C8C2312yes—
83C23×C47—21no—
84C23×C47—22no—
85C23×C47—42no—
86C23×C47—82no—
87C23×C47C2×D411yescharacteristic
88C22×D47—22no—
89C22×D47—28no—
90C22×D47—24no—
91C22×D47—84no—
92C22×D47—82no—
93C22×D47C2×D412yes—
94Q8×C47—21no—
95Q8×C47C2×D412yes—
96D4×C47—24no—
97D4×C47—21no—
98D4×C47—22no—
99D4×C47—22no—
100D4×C47—42no—
101D4×C47C2×D412yes—
102C2×C4×C47—21no—
103C2×C4×C47—24no—
104C2×C4×C47C2×D411yescharacteristic
105C2×C4×C47C2×D412yes—
106C2×C4×C47C2×D412yes—
107C2×C4×C47C2411yescharacteristic
108C22⋊D47—28no—
109C22⋊D47—24no—
110C22⋊D47—84no—
111C2×Dic47—22no—
112C2×Dic47C2×D412yes—
113D188—28no—
114D188—22no—
115D188—24no—
116D188—22no—
117D188C2×D414yes—
118C4×D47—28no—
119C4×D47—22no—
120C4×D47—22no—
121Dic94—22no—
122C8×C47—22no—
123C47⋊C8—22no—
124C22×C47—22no—
125C22×C47—22no—
126C22×C47—42no—
127C22×C47—42no—
128C22×C47—44no—
129C22×C47—84no—
130C22×C47#12012yes—
131C22×C47C22×D411yescharacteristic
132C2×D47—22no—
133C2×D47—24no—
134C2×D47—24no—
135C2×D47—44no—
136C2×D47—84no—
137C2×D47—88no—
138C4×C47—22no—
139C4×C47#12012yes—
140C4×C47C22×D411yescharacteristic
141C4×C47C22×D411yescharacteristic
142Dic47—22no—
143Dic47—42no—
144#3008—471nomaximal, Sylow
145C2×C47—22no—
146C2×C47—42no—
147C2×C47—82no—
148C2×C47C2×#12011yescharacteristic
149C2×C47#57612yes—
150D47—42no—
151D47—44no—
152C2×H(5,𝔽2)—471no—
153C2×AGL(1,ℤ/8)D4711yescharacteristic, complemented
154C22×D8—471no—
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—941no—
167C2×#41C2×D4711yescharacteristic
168C22×D4—472no—
169C22×D4—471no—
170C22×D4—941no—
171C22×D4—942no—
172C22×D4C2×D4711yescharacteristic, complemented
173AGL(1,ℤ/8)—24no—
174C2×SD16C2×D4712yescomplemented
175C2×D8—474no—
176C2×D8—944no—
177C2×D8C2×D4712yescomplemented
178C2×M16C2×D4711yescharacteristic, complemented
179C22×C8—471no—
180#127—941no—
181#124—941no—
182#121—474no—
183#120—942no—
184#117—471no—
185#103—472no—
186#102—472no—
187#102—474no—
188C22⋊C8—474no—
189C24—21no—
190C24—942no—
191C24—941no—
192#41—22no—
193#41—948no—
194#41—944no—
195#41—944no—
196#41—942no—
197#41—942no—
198#41C22⋊D4714yescomplemented
199C2×Q8—471no—
200C2×Q8C22×D4711yescharacteristic
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—22no—
205C2×D4—472no—
206C2×D4—474no—
207C2×D4—471no—
208C2×D4—472no—
209C2×D4—942no—
210C2×D4—948no—
211C2×D4—942no—
212C2×D4—944no—
213C2×D4—9416no—
214C2×D4—944no—
215C2×D4—944no—
216C2×D4—941no—
217C2×D4—942no—
218C2×D4C22×D4712yes—
219C2×D4C22×D4711yescharacteristic
220C22×C4—21no—
221C22×C4—472no—
222C22×C4—942no—
223C22×C4C22×D4711yescharacteristic
224SD16—24no—
225D8—24no—
226D8—948no—
227M16—22no—
228C2×C8—472no—
229C2×C8—942no—
230C2×C8C22×D4712yes—
231C4⋊C4—472no—
232C22⋊C4—944no—
233C22⋊C4—941no—
234C42—941no—
235C23—21no—
236C23—22no—
237C23—42no—
238C23—82no—
239C23—472no—
240C23—948no—
241C23—944no—
242C23—942no—
243C23—3762no—
244C23—3764no—
245C23D4×D4711yescharacteristic
246Q8—21no—
247Q8—942no—
248Q8C2×C22⋊D4712yes—
249D4—24no—
250D4—21no—
251D4—22no—
252D4—22no—
253D4—42no—
254D4—474no—
255D4—948no—
256D4—948no—
257D4—944no—
258D4—944no—
259D4—942no—
260D4—942no—
261D4—3764no—
262D4C2×C22⋊D4712yes—
263C2×C4—21no—
264C2×C4—24no—
265C2×C4—472no—
266C2×C4—948no—
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—22no—
278C22—42no—
279C22—42no—
280C22—44no—
281C22—84no—
282C22—944no—
283C22—942no—
284C22—944no—
285C22—3764no—
286C22—3768no—
287C22—1884no—
288C22#1309399212yes—
289C22C2×D4×D4711yescharacteristic
290C4—22no—
291C4—942no—
292C4—1882no—
293C4#1309399212yes—
294C4C2×D4×D4711yescharacteristic
295C4C22×C22⋊D4711yescharacteristic
296C2—22no—
297C2—42no—
298C2—82no—
299C2—1882no—
300C2—1884no—
301C2C2×#1309399211yescharacteristic
302C2#1568992712yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×AGL(1,ℤ/8)×C47C2
socleC22×C47C22×D4
hypercenterC2×AGL(1,ℤ/8)D47
hypocenterC47#3008
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#13094070C2semidirect
2. C22×#10625334C2semidirect
3. #15689690C2semidirect
4. #15689267C2semidirect
5. #15689255C2semidirect
6. #15689129C2semidirect
7. #15689119C2semidirect
8. #15689091C2semidirect
9. C2×AGL(1,ℤ/8)×C47C2semidirect
12. C2×#10625354C22semidirect
18. C2×D4×D47C22semidirect
20. C2×#10625334C22semidirect
21. C22×C47⋊C8C22semidirect
24. #13093995C22semidirect
26. #13093983C22semidirect
27. #13093948C22semidirect
28. #13093946C22semidirect
29. #13093945C22semidirect
30. (C2×D47)⋊C8C22semidirect
32. C22×D4×C47C22semidirect
34. C2×SD16×C47C22semidirect
35. C2×D8×C47C22semidirect
36. C2×M16×C47C22semidirect
41. #41×C47D4semidirect
67. C2×D188D4semidirect
153. C2×AGL(1,ℤ/8)D47semidirect
161. C47#3008semidirect
172. C22×D4C2×D47semidirect
174. C2×SD16C2×D47semidirect
177. C2×D8C2×D47semidirect
178. C2×M16C2×D47semidirect
198. #41C22⋊D47semidirect