Finite Group Databasebeta

← #20252995

Subgroups — #20252995

Order 6016.

500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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×#13094043C211yesmaximal, characteristic, complemented
2C2×M16×D47C211yesmaximal, characteristic, complemented
3#15689633C212yesmaximal, complemented
4#15689382C211yesmaximal, characteristic, complemented
5#15689381C211yesmaximal, characteristic, complemented
6#15689373C211yesmaximal, characteristic, complemented
7#15689368C212yesmaximal, complemented
8#15689367C212yesmaximal, complemented
9#15689158C211yesmaximal, characteristic, complemented
10#15689116C212yesmaximal, complemented
11C47×#469C211yesmaximal, characteristic, complemented
12C2×#10625352C2212yes—
13C22×C4×D47C2211yescharacteristic
14#13094043—24no—
15C2×Dic188C2211yescharacteristic, complemented
16C2×#10625335C2212yescomplemented
17C2×#10625329C2211yescharacteristic
18C2×#10625324C2211yescharacteristic
19C2×#10625324C2211yescharacteristic
20M16×D47—24no—
21C2×C8×D47C2211yescharacteristic
22C2×C8×D47C2211yescharacteristic
23#13094006—22no—
24#13094004C2212yes—
25#13094003C2212yes—
26#13093995C2212yes—
27#13093992—22no—
28D4×Dic47—22no—
29(C22⋊D47)⋊C4—22no—
30#13093982C2212yes—
31#13093957C2212yescomplemented
32#13093956C2211yescharacteristic, complemented
33#13093949C2212yescomplemented
34#13093947C2212yescomplemented
35#13093945C2212yescomplemented
36C2×D8×C47C2211yescharacteristic, complemented
37C2×M16×C47C2211yescharacteristic
38#121×C47C2212yes—
39#106×C47C2211yescharacteristic, complemented
40#102×C47C2212yescomplemented
41C23×D47D411yescharacteristic
42C2×D4×C47—22no—
43C2×D4×C47C2312yes—
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—22no—
46C2×C22⋊D47—22no—
47C22×Dic47—22no—
48C22×Dic47D411yescharacteristic
49#10625352—24no—
50#10625352—24no—
51C2×C4×D47—22no—
52C2×C4×D47—22no—
53C2×C4×D47D411yescharacteristic
54C2×C4×D47D411yescharacteristic
55C2×C4×D47C2311yescharacteristic
56C2×C4×D47C2311yescharacteristic
57C2×Dic94C2312yes—
58D8×C47—22no—
59M16×C47—22no—
60C2×C8×C47C2311yescharacteristic
61C2×C8×C47C2311yescharacteristic
62C4⋊C4×C47C2312yes—
63C22⋊C4×C47—22no—
64C22⋊Dic47—22no—
65C22⋊Dic47—22no—
66#10625335—24no—
67(C2×D47)⋊C4—22no—
68(C2×D47)⋊C4—22no—
69C4⋊Dic47—22no—
70C4⋊Dic47C2312yes—
71Dic47⋊C4—22no—
72C4×Dic47—22no—
73#10625329—22no—
74C2×C47⋊C8C2311yescharacteristic
75C2×C47⋊C8C2311yescharacteristic
76Dic188—22no—
77#10625324—22no—
78#10625324—22no—
79C8×D47—22no—
80C8×D47D414yescomplemented
81C23×C47—22no—
82C23×C47C2×D411yescharacteristic
83C22×D47—22no—
84C22×D47—42no—
85C22×D47C2×D411yescharacteristic
86C22×D47C2×D411yescharacteristic
87D4×C47—22no—
88D4×C47—22no—
89D4×C47—44no—
90C2×C4×C47—21no—
91C2×C4×C47—21no—
92C2×C4×C47—22no—
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47C2411yescharacteristic
95C22⋊D47—44no—
96C22⋊D47—44no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—44no—
101C2×Dic47C2×D411yescharacteristic
102C2×Dic47C2×D411yescharacteristic
103C4×D47—22no—
104C4×D47—21no—
105C4×D47—21no—
106C4×D47—22no—
107C4×D47C2×D412yes—
108C4×D47#4112yes—
109Dic94—22no—
110Dic94—22no—
111C8×C47—21no—
112C8×C47C2×D412yes—
113C47⋊C8—21no—
114C47⋊C8C2×D412yes—
115C22×C47—21no—
116C22×C47—22no—
117C22×C47—42no—
118C22×C47—42no—
119C22×C47—42no—
120C22×C47C22×D411yescharacteristic
121C2×D47—22no—
122C2×D47—21no—
123C2×D47—22no—
124C2×D47—44no—
125C2×D47#12112yes—
126C4×C47—21no—
127C4×C47—42no—
128C4×C47C22×D411yescharacteristic
129C4×C47C2×#4111yescharacteristic
130Dic47—21no—
131Dic47—42no—
132Dic47—42no—
133Dic47#12112yes—
134#3054—471nomaximal, Sylow
135C2×C47—41no—
136C2×C47—82no—
137C2×C47C2×#12111yescharacteristic
138C2×C47#57512yes—
139D47—22no—
140D47—41no—
141C2×#135—471no—
142C22×M16—471no—
143#525—472no—
144#470—471no—
145#470—471no—
146#469—471no—
147#469D4711yescharacteristic, complemented
148#468—472no—
149#468—472no—
150#427—471no—
151#416—472no—
152C47#305411yescharacteristic, complemented, Sylow
153C2×#41—472no—
154C23×C4—471no—
155#135—944no—
156C2×Q16—471no—
157C2×SD16—472no—
158C2×D8C2×D4711yescharacteristic, complemented
159C2×M16—471no—
160C2×M16—471no—
161C2×M16—471no—
162C2×M16—944no—
163C2×M16C2×D4711yescharacteristic
164C22×C8—471no—
165C22×C8—471no—
166#123—942no—
167C22⋊Q8—472no—
168C22⋊Q8—472no—
169#121—472no—
170#121C2×D4712yes—
171#120—942no—
172C4×D4—942no—
173C4×D4—942no—
174#117—472no—
175#107—472no—
176#106—471no—
177#106C2×D4711yescharacteristic, complemented
178#103—472no—
179#103—472no—
180#102—472no—
181#102C2×D4712yescomplemented
182C24—471no—
183#41—944no—
184#41—944no—
185C2×Q8—472no—
186C2×D4—22no—
187C2×D4—942no—
188C2×D4—942no—
189C2×D4C22×D4712yes—
190C22×C4—471no—
191C22×C4—471no—
192C22×C4—471no—
193C22×C4—471no—
194C22×C4—471no—
195C22×C4—942no—
196C22×C4—942no—
197C22×C4—942no—
198C22×C4C22×D4711yescharacteristic
199Q16—942no—
200SD16—944no—
201D8—22no—
202M16—22no—
203M16—942no—
204M16—942no—
205M16—942no—
206C2×C8—471no—
207C2×C8—474no—
208C2×C8—471no—
209C2×C8—942no—
210C2×C8C22×D4711yescharacteristic
211C2×C8C22×D4711yescharacteristic
212C4⋊C4—472no—
213C4⋊C4—942no—
214C4⋊C4—942no—
215C4⋊C4C22×D4712yes—
216C22⋊C4—22no—
217C22⋊C4—942no—
218C22⋊C4—942no—
219C22⋊C4—942no—
220C22⋊C4—942no—
221C42—942no—
222C23—22no—
223C23—471no—
224C23—471no—
225C23—942no—
226C23—1882no—
227C23D4×D4711yescharacteristic
228Q8—942no—
229Q8—942no—
230D4—22no—
231D4—22no—
232D4—44no—
233D4—1884no—
234D4—1884no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—471no—
239C2×C4—472no—
240C2×C4—472no—
241C2×C4—471no—
242C2×C4—942no—
243C2×C4—942no—
244C2×C4—942no—
245C2×C4—941no—
246C2×C4—941no—
247C2×C4—942no—
248C2×C4—942no—
249C2×C4—1884no—
250C2×C4D4×D4711yescharacteristic
251C2×C4C23×D4711yescharacteristic
252C8—21no—
253C8—472no—
254C8—941no—
255C8D4×D4712yes—
256C22—21no—
257C22—22no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—472no—
262C22—942no—
263C22—941no—
264C22—942no—
265C22—1884no—
266C22C2×D4×D4711yescharacteristic
267C4—21no—
268C4—42no—
269C4—472no—
270C4—941no—
271C4—1882no—
272C4—1882no—
273C4C2×D4×D4711yescharacteristic
274C4#41×D4711yescharacteristic
275C2—41no—
276C2—82no—
277C2—942no—
278C2—1881no—
279C2#121×D4711yescharacteristic
280C2#1568991912yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#469C2
socleC22×C47C22×D4
hypercenter#469D47
hypocenterC47#3054
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×#13094043C2semidirect
2. C2×M16×D47C2semidirect
3. #15689633C2semidirect
4. #15689382C2semidirect
5. #15689381C2semidirect
6. #15689373C2semidirect
7. #15689368C2semidirect
8. #15689367C2semidirect
9. #15689158C2semidirect
10. #15689116C2semidirect
11. C47×#469C2semidirect
15. C2×Dic188C22semidirect
16. C2×#10625335C22semidirect
31. #13093957C22semidirect
32. #13093956C22semidirect
33. #13093949C22semidirect
34. #13093947C22semidirect
35. #13093945C22semidirect
36. C2×D8×C47C22semidirect
39. #106×C47C22semidirect
40. #102×C47C22semidirect
80. C8×D47D4semidirect
147. #469D47semidirect
152. C47#3054semidirect
158. C2×D8C2×D47semidirect
177. #106C2×D47semidirect
181. #102C2×D47semidirect