Finite Group Databasebeta

← #20254987

Subgroups — #20254987

Order 6016.

546 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 125 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×#13094051C212yesmaximal, complemented
2#15689776C211yesmaximal, characteristic, complemented
3#15689758C211yesmaximal, characteristic, complemented
4#15689366C212yesmaximal, complemented
5#15689325C211yesmaximal, characteristic, complemented
6#15689315C211yesmaximal, characteristic, complemented
7#15689272C212yesmaximal, complemented
8#15689267C212yesmaximal, complemented
9C4×D376C211yesmaximal, characteristic, complemented
10#15689202C211yesmaximal, characteristic, complemented
11C47×#492C211yesmaximal, characteristic, complemented
12C2×#10625354C2212yescomplemented
13C2×D4×D47—21no—
14C2×D4×D47C2212yes—
15#13094051—28no—
16C2×#10625336C2212yes—
17C2×D376C2211yescharacteristic
18C2×#10625334C2212yescomplemented
19C2×#10625324C2212yescomplemented
20#13094009—22no—
21#13094000C2212yescomplemented
22#13093999—21no—
23#13093995—21no—
24#13093995C2212yes—
25#13093992—22no—
26C4×D188C2211yescharacteristic
27C4×D188C2211yescharacteristic
28C4×D188C2211yescharacteristic, complemented
29C4⋊C4×D47—21no—
30#13093958C2211yescharacteristic, complemented
31C4⋊(C47⋊C8)C2211yescharacteristic, complemented
32#13093948C2212yescomplemented
33#13093946C2211yescharacteristic
34#13093946C2211yescharacteristic, complemented
35#13093945C2212yescomplemented
36(C2×D47)⋊C8C2212yescomplemented
37C2×SD16×C47C2212yescomplemented
38C2×SD16×C47C2212yescomplemented
39C4⋊Q8×C47C2211yescharacteristic, complemented
40#127×C47C2211yescharacteristic
41C4×C8×C47C2211yescharacteristic, complemented
42C23×D47—22no—
43C2×Q8×C47C2312yes—
44C2×D4×C47—21no—
45C2×D4×C47—21no—
46C2×D4×C47C2312yes—
47C2×C22⋊D47—22no—
48C2×C22⋊D47—22no—
49#10625354—24no—
50#10625354—42no—
51D4×D47—24no—
52D4×D47—42no—
53D4×D47—44no—
54C2×D188—22no—
55C2×D188D411yescharacteristic
56C2×D188C2311yescharacteristic
57C2×D188C2311yescharacteristic
58C2×C4×D47—21no—
59C2×C4×D47—21no—
60C2×C4×D47—22no—
61C2×C4×D47C2312yes—
62SD16×C47—24no—
63SD16×C47—42no—
64C2×C8×C47C2311yescharacteristic
65C2×C8×C47C2311yescharacteristic
66C4⋊C4×C47—21no—
67C4⋊C4×C47—21no—
68C42×C47C2311yescharacteristic
69C22⋊Dic47—22no—
70#10625336—24no—
71#10625334—24no—
72(C2×D47)⋊C4—22no—
73(C2×D47)⋊C4—21no—
74(C2×D47)⋊C4—21no—
75(C2×D47)⋊C4D412yes—
76C4⋊Dic47D411yescharacteristic
77C4⋊Dic47C2311yescharacteristic
78C4⋊Dic47C2311yescharacteristic
79Dic47⋊C4—22no—
80C2×C47⋊C8C2312yes—
81D376D414yescomplemented
82#10625324—24no—
83C23×C47—22no—
84C22×D47—21no—
85C22×D47—21no—
86C22×D47—44no—
87C22×D47—44no—
88C22×D47—82no—
89C22×D47C2×D412yes—
90Q8×C47—22no—
91Q8×C47—22no—
92D4×C47—22no—
93D4×C47—22no—
94D4×C47—42no—
95D4×C47—81no—
96C2×C4×C47—22no—
97C2×C4×C47C2×D411yescharacteristic
98C2×C4×C47C2×D411yescharacteristic
99C2×C4×C47C2411yescharacteristic
100C22⋊D47—44no—
101C22⋊D47—44no—
102C2×Dic47—21no—
103C2×Dic47—21no—
104C2×Dic47C2×D412yes—
105D188—22no—
106D188—21no—
107D188—21no—
108D188—44no—
109D188C2×D412yes—
110D188C2×D412yescomplemented
111C4×D47—22no—
112C4×D47—22no—
113C4×D47—44no—
114C4×D47—42no—
115C4×D47—42no—
116C8×C47—21no—
117C8×C47C2×D412yescomplemented
118C47⋊C8—22no—
119C22×C47—42no—
120C22×C47—42no—
121C22×C47—42no—
122C22×C47C22×D411yescharacteristic
123C2×D47—22no—
124C2×D47—22no—
125C2×D47—22no—
126C2×D47—22no—
127C2×D47—22no—
128C2×D47—41no—
129C2×D47—41no—
130C2×D47—41no—
131C2×D47—41no—
132C2×D47—88no—
133C4×C47—21no—
134C4×C47—42no—
135C4×C47AGL(1,ℤ/8)12yescomplemented
136C4×C47C22×D411yescharacteristic
137C4×C47H(5,𝔽2)11yescharacteristic
138Dic47—22no—
139Dic47—41no—
140Dic47—41no—
141#3272—471nomaximal, Sylow
142C2×C47—82no—
143C2×C47D4211yescharacteristic
144C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
145C2×C47#57711yescharacteristic
146D47—42no—
147D47—42no—
148D47—42no—
149C2×AGL(1,ℤ/8)—472no—
150#547—471no—
151D42—471no—
152#492D4711yescharacteristic, complemented
153#468—472no—
154#461—471no—
155#459—471no—
156#450—472no—
157#449—472no—
158C4×D8—471no—
159#436—471no—
160C47#327211yescharacteristic, complemented, Sylow
161C2×#41—472no—
162C22×D4—472no—
163C22×D4—941no—
164AGL(1,ℤ/8)—948no—
165C2×SD16—472no—
166C2×SD16C2×D4712yescomplemented
167C2×SD16C2×D4712yescomplemented
168C2×D8—472no—
169C2×D8—471no—
170C2×M16—472no—
171C4⋊Q8C2×D4711yescharacteristic, complemented
172#127C2×D4711yescharacteristic
173#123—942no—
174C22⋊Q8—472no—
175#121—472no—
176#121—941no—
177#121—941no—
178#120—942no—
179C4×D4—471no—
180C4×D4—471no—
181C4×D4—471no—
182C2×C4⋊C4—941no—
183#107—471no—
184C4⋊C8—471no—
185#103—472no—
186#102—472no—
187#102—471no—
188#102—471no—
189C22⋊C8—472no—
190C4×C8C2×D4711yescharacteristic, complemented
191C24—942no—
192#41—944no—
193#41—1882no—
194C2×Q8C22×D4712yes—
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—471no—
198C2×D4—471no—
199C2×D4—471no—
200C2×D4—942no—
201C2×D4—942no—
202C2×D4—944no—
203C2×D4—942no—
204C2×D4—1882no—
205C2×D4—1884no—
206C2×D4C22×D4712yes—
207C22×C4—472no—
208C22×C4—942no—
209C22×C4—941no—
210C22×C4—941no—
211SD16—24no—
212SD16—42no—
213SD16—944no—
214D8—474no—
215D8—944no—
216M16—944no—
217C2×C8—472no—
218C2×C8C22×D4711yescharacteristic
219C2×C8C22×D4711yescharacteristic
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—471no—
223C4⋊C4—471no—
224C4⋊C4—471no—
225C4⋊C4—942no—
226C22⋊C4—472no—
227C22⋊C4—942no—
228C22⋊C4—942no—
229C22⋊C4—941no—
230C22⋊C4—941no—
231C42C22×D4711yescharacteristic
232C23—22no—
233C23—472no—
234C23—941no—
235C23—941no—
236C23—3762no—
237C23—1884no—
238C23—1884no—
239Q8—22no—
240Q8—22no—
241D4—22no—
242D4—22no—
243D4—42no—
244D4—81no—
245D4—472no—
246D4—472no—
247D4—942no—
248D4—941no—
249D4—941no—
250D4—1884no—
251D4—1884no—
252D4—1884no—
253C2×C4—22no—
254C2×C4—472no—
255C2×C4—942no—
256C2×C4—942no—
257C2×C4—941no—
258C2×C4—941no—
259C2×C4—1884no—
260C2×C4—1882no—
261C2×C4—1882no—
262C2×C4D4×D4711yescharacteristic
263C2×C4D4×D4711yescharacteristic
264C2×C4C23×D4711yescharacteristic
265C8—21no—
266C8—942no—
267C8D4×D4712yescomplemented
268C22—42no—
269C22—42no—
270C22—42no—
271C22—942no—
272C22—942no—
273C22—942no—
274C22—942no—
275C22—942no—
276C22—3768no—
277C22—1881no—
278C22—1881no—
279C22—1881no—
280C22—1881no—
281C22C2×D4×D4711yescharacteristic
282C4—21no—
283C4—42no—
284C4—942no—
285C4—1881no—
286C4—1881no—
287C4#1309405112yescomplemented
288C4C2×D4×D4711yescharacteristic
289C4#1309406911yescharacteristic
290C2—82no—
291C2—1882no—
292C2—1882no—
293C2—1882no—
294C2#1568975811yescharacteristic
295C2C2×#1309405111yescharacteristic
296C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#492C2
socleC22×C47C22×D4
hypercenter#492D47
hypocenterC47#3272
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. C2×#13094051C2semidirect
2. #15689776C2semidirect
3. #15689758C2semidirect
4. #15689366C2semidirect
5. #15689325C2semidirect
6. #15689315C2semidirect
7. #15689272C2semidirect
8. #15689267C2semidirect
9. C4×D376C2semidirect
10. #15689202C2semidirect
11. C47×#492C2semidirect
12. C2×#10625354C22semidirect
18. C2×#10625334C22semidirect
19. C2×#10625324C22semidirect
21. #13094000C22semidirect
28. C4×D188C22semidirect
30. #13093958C22semidirect
31. C4⋊(C47⋊C8)C22semidirect
32. #13093948C22semidirect
34. #13093946C22semidirect
35. #13093945C22semidirect
36. (C2×D47)⋊C8C22semidirect
37. C2×SD16×C47C22semidirect
38. C2×SD16×C47C22semidirect
39. C4⋊Q8×C47C22semidirect
41. C4×C8×C47C22semidirect
81. D376D4semidirect
110. D188C2×D4semidirect
117. C8×C47C2×D4semidirect
135. C4×C47AGL(1,ℤ/8)semidirect
152. #492D47semidirect
160. C47#3272semidirect
166. C2×SD16C2×D47semidirect
167. C2×SD16C2×D47semidirect
171. C4⋊Q8C2×D47semidirect
190. C4×C8C2×D47semidirect
267. C8D4×D47semidirect
287. C4#13094051semidirect