Finite Group Databasebeta

← #20254185

Subgroups — #20254185

Order 6016.

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

normal subgroups only

This group has 514 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×#13093998C211yesmaximal, characteristic, complemented
2#15689441C212yesmaximal, complemented
3#15689439C212yesmaximal, complemented
4#15689374C214yesmaximal, complemented
5#15689257C212yesmaximal, complemented
6#15689256C212yesmaximal, complemented
7#15689087C211yesmaximal, characteristic, complemented
8C2×#121×C47C211yesmaximal, characteristic, complemented
9C22×D188C2211yescharacteristic, complemented
10C22×C22⋊D47—21no—
11C2×#10625334C2214yescomplemented
12C2×#10625329C2212yescomplemented
13#13093998—21no—
14#13093998—21no—
15#13093998C2212yes—
16#13093998C2212yescomplemented
17C2×C4⋊Dic47C2211yescharacteristic, complemented
18C2×(C2×D47)⋊C4—21no—
19#13093955C2214yescomplemented
20#13093945C2214yescomplemented
21#13093944C2214yescomplemented
22C22⋊(C47⋊C8)C2212yescomplemented
23C22⋊(C47⋊C8)C2212yescomplemented
24C22×D4×C47—21no—
25C22×D4×C47C2211yescharacteristic, complemented
26C23×C4×C47C2211yescharacteristic
27#121×C47—21no—
28#121×C47—21no—
29#121×C47C2212yes—
30#121×C47C2212yescomplemented
31C2×C4⋊C4×C47C2211yescharacteristic, complemented
32C2×C22⋊C4×C47—21no—
33C24×C47—21no—
34C24×C47D411yescharacteristic
35C23×D47—21no—
36C2×D4×C47—22no—
37C2×D4×C47—22no—
38C2×D4×C47—21no—
39C2×D4×C47—42no—
40C2×D4×C47—44no—
41C2×D4×C47C2312yes—
42C22×C4×C47—21no—
43C22×C4×C47—42no—
44C22×C4×C47D411yescharacteristic
45C22×C4×C47D411yescharacteristic
46C22×C4×C47D411yescharacteristic
47C22×C4×C47C2311yescharacteristic
48C22×C4×C47C2311yescharacteristic
49C22×C4×C47C2311yescharacteristic
50C2×C22⋊D47—22no—
51C2×C22⋊D47—22no—
52C2×C22⋊D47—44no—
53C22×Dic47—21no—
54C2×D188—21no—
55C2×D188—42no—
56C2×D188C2312yes—
57C4⋊C4×C47—21no—
58C4⋊C4×C47C2312yes—
59C22⋊C4×C47—22no—
60C22⋊C4×C47—22no—
61#10625334—44no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—22no—
64C4⋊Dic47—21no—
65C4⋊Dic47C2312yes—
66#10625329—42no—
67C2×C47⋊C8C2314yes—
68C23×C47—22no—
69C23×C47—22no—
70C23×C47—22no—
71C23×C47—41no—
72C23×C47—42no—
73C23×C47—42no—
74C23×C47—42no—
75C23×C47C2×D411yescharacteristic
76C23×C47C2×D411yescharacteristic
77C23×C47C2×D411yescharacteristic
78C22×D47—22no—
79C22×D47—42no—
80C22×D47—42no—
81C22×D47—42no—
82D4×C47—24no—
83D4×C47—42no—
84D4×C47—44no—
85D4×C47—44no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—41no—
91C2×C4×C47—41no—
92C2×C4×C47—41no—
93C2×C4×C47—42no—
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47C2×D411yescharacteristic
97C2×C4×C47C2411yescharacteristic
98C22⋊D47—44no—
99C22⋊D47—44no—
100C2×Dic47—22no—
101C2×Dic47—42no—
102D188—24no—
103D188—42no—
104C47⋊C8—24no—
105C22×C47—21no—
106C22×C47—21no—
107C22×C47—21no—
108C22×C47—21no—
109C22×C47—21no—
110C22×C47—21no—
111C22×C47—21no—
112C22×C47—44no—
113C22×C47—42no—
114C22×C47—42no—
115C22×C47—42no—
116C22×C47—84no—
117C22×C47AGL(1,ℤ/8)12yes—
118C22×C47AGL(1,ℤ/8)12yes—
119C22×C47C22×D411yescharacteristic
120C2×D47—42no—
121C2×D47—42no—
122C2×D47—42no—
123C2×D47—84no—
124C4×C47—21no—
125C4×C47—21no—
126C4×C47—21no—
127C4×C47—42no—
128C4×C47H(5,𝔽2)12yes—
129Dic47—42no—
130#3192—471nomaximal, Sylow
131C2×C47—22no—
132C2×C47—22no—
133C2×C47—41no—
134C2×C47—82no—
135C2×C47#53411yescharacteristic
136C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
138D47—82no—
139C2×#121—471no—
140C2×#121D4711yescharacteristic, complemented
141#481—472no—
142#481—472no—
143#469—474no—
144#447—472no—
145#447—472no—
146#407—471no—
147C47#319211yescharacteristic, complemented, Sylow
148C22×D4—21no—
149C22×D4—471no—
150C22×D4—941no—
151C22×D4C2×D4711yescharacteristic, complemented
152C23×C4C2×D4711yescharacteristic
153C2×D8—474no—
154C2×M16—472no—
155#121—21no—
156#121—21no—
157#121—472no—
158#121—472no—
159#121—941no—
160#121—941no—
161#121C2×D4712yes—
162#121C2×D4712yescomplemented
163C2×C4⋊C4—471no—
164C2×C4⋊C4C2×D4711yescharacteristic, complemented
165C2×C22⋊C4—21no—
166C2×C22⋊C4—941no—
167#106—474no—
168#102—474no—
169#102—474no—
170C22⋊C8—472no—
171C22⋊C8—472no—
172C24—21no—
173C24—941no—
174C24C22⋊D4711yescharacteristic
175C2×D4—22no—
176C2×D4—22no—
177C2×D4—21no—
178C2×D4—42no—
179C2×D4—44no—
180C2×D4—472no—
181C2×D4—942no—
182C2×D4—942no—
183C2×D4—941no—
184C2×D4—1882no—
185C2×D4—1884no—
186C2×D4C22×D4712yes—
187C22×C4—21no—
188C22×C4—42no—
189C22×C4—941no—
190C22×C4C22⋊D4711yescharacteristic
191C22×C4C22⋊D4711yescharacteristic
192C22×C4C22⋊D4711yescharacteristic
193C22×C4C22×D4711yescharacteristic
194C22×C4C22×D4711yescharacteristic
195C22×C4C22×D4711yescharacteristic
196D8—1884no—
197M16—1882no—
198C2×C8—474no—
199C4⋊C4—21no—
200C4⋊C4—472no—
201C4⋊C4—941no—
202C4⋊C4C22×D4712yes—
203C22⋊C4—22no—
204C22⋊C4—22no—
205C22⋊C4—942no—
206C22⋊C4—942no—
207C23—22no—
208C23—22no—
209C23—22no—
210C23—41no—
211C23—42no—
212C23—42no—
213C23—42no—
214C23—942no—
215C23—1882no—
216C23—1882no—
217C23—1882no—
218C23C2×C22⋊D4711yescharacteristic
219C23C2×C22⋊D4711yescharacteristic
220C23C2×C22⋊D4711yescharacteristic
221D4—24no—
222D4—42no—
223D4—44no—
224D4—44no—
225D4—944no—
226D4—1882no—
227D4—1884no—
228D4—1884no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—942no—
238C2×C4—1882no—
239C2×C4C2×C22⋊D4711yescharacteristic
240C2×C4C2×C22⋊D4711yescharacteristic
241C2×C4C2×C22⋊D4711yescharacteristic
242C2×C4C23×D4711yescharacteristic
243C8—944no—
244C22—21no—
245C22—21no—
246C22—21no—
247C22—21no—
248C22—21no—
249C22—21no—
250C22—21no—
251C22—44no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—84no—
256C22—3764no—
257C22—1882no—
258C22—1882no—
259C22—1882no—
260C22#1309404912yes—
261C22#1309405012yes—
262C22C22×C22⋊D4711yescharacteristic
263C4—21no—
264C4—21no—
265C4—21no—
266C4—42no—
267C4—1882no—
268C4#1309406912yes—
269C2—22no—
270C2—22no—
271C2—41no—
272C2—82no—
273C2—3762no—
274C2#1568968211yescharacteristic
275C2C2×#1309404911yescharacteristic
276C2C2×#1309405011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#121×C47C2
socleC22×C47C22×D4
hypercenterC2×#121D47
hypocenterC47#3192
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#13093998C2semidirect
2. #15689441C2semidirect
3. #15689439C2semidirect
4. #15689374C2semidirect
5. #15689257C2semidirect
6. #15689256C2semidirect
7. #15689087C2semidirect
8. C2×#121×C47C2semidirect
9. C22×D188C22semidirect
11. C2×#10625334C22semidirect
12. C2×#10625329C22semidirect
16. #13093998C22semidirect
17. C2×C4⋊Dic47C22semidirect
19. #13093955C22semidirect
20. #13093945C22semidirect
21. #13093944C22semidirect
22. C22⋊(C47⋊C8)C22semidirect
23. C22⋊(C47⋊C8)C22semidirect
25. C22×D4×C47C22semidirect
30. #121×C47C22semidirect
31. C2×C4⋊C4×C47C22semidirect
140. C2×#121D47semidirect
147. C47#3192semidirect
151. C22×D4C2×D47semidirect
162. #121C2×D47semidirect
164. C2×C4⋊C4C2×D47semidirect