Finite Group Databasebeta

← #20252237

Subgroups — #20252237

Order 6016.

528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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×D8×D47C211yesmaximal, characteristic
2#15689595C212yesmaximal, complemented
3#15689236C211yesmaximal, characteristic, complemented
4#15689235C211yesmaximal, characteristic, complemented
5#15689234C211yesmaximal, characteristic, complemented
6C4×#10625334C212yesmaximal, complemented
7#15689203C212yesmaximal, complemented
8#15689158C211yesmaximal, characteristic, complemented
9#15689126C212yesmaximal, complemented
10#15689080C211yesmaximal, characteristic, complemented
11C47×#442C211yesmaximal, characteristic, complemented
12C2×D4×D47C2212yes—
13C2×D376C2211yescharacteristic
14C2×#10625334C2212yes—
15D8×D47C418yescomplemented
16C2×#10625324C2211yescharacteristic
17C2×C8×D47C2211yescharacteristic
18C4×D188C2212yescomplemented
19D4×Dic47C2212yescomplemented
20#13093986C2212yescomplemented
21C4×C22⋊D47—22no—
22(C22⋊D47)⋊C4—22no—
23#13093982C2212yes—
24#13093981C2211yescharacteristic
25C2×(C2×D47)⋊C4—22no—
26C22⋊C4×D47—22no—
27#13093957C2212yescomplemented
28#13093956C2211yescharacteristic, complemented
29#13093946C2212yescomplemented
30#13093945C2212yescomplemented
31#13093944C2212yescomplemented
32#13093934C2211yescharacteristic, complemented
33C4×C47⋊C8C2211yescharacteristic, complemented
34C8×Dic47C2211yescharacteristic, complemented
35C2×D8×C47C2211yescharacteristic
36C4×D4×C47C2212yescomplemented
37#106×C47C2211yescharacteristic, complemented
38#102×C47C2212yescomplemented
39#97×C47C2211yescharacteristic, complemented
40C23×D47—22no—
41C2×D4×C47C2312yes—
42C22×C4×C47—22no—
43C2×C22⋊D47—22no—
44C22×Dic47—22no—
45D4×D47—24no—
46D4×D47C2×C418yescomplemented
47C2×D188C2312yes—
48C2×C4×D47—22no—
49C2×C4×D47—22no—
50C2×C4×D47C2311yescharacteristic
51D8×C47C2×C414yescomplemented
52C2×C8×C47C2311yescharacteristic
53C2×C8×C47C2311yescharacteristic
54C4⋊C4×C47C2312yes—
55C22⋊C4×C47—22no—
56C42×C47C2311yescharacteristic
57C22⋊Dic47—22no—
58#10625334C2×C418yescomplemented
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—22no—
62(C2×D47)⋊C4D412yes—
63C4⋊Dic47C2312yes—
64Dic47⋊C4D412yes—
65C4×Dic47—22no—
66C4×Dic47C2311yescharacteristic
67C2×C47⋊C8C2311yescharacteristic
68C2×C47⋊C8C2311yescharacteristic
69D376C2×C414yescomplemented
70#10625324—22no—
71C8×D47C2×C414yescomplemented
72C23×C47—22no—
73C22×D47—22no—
74C22×D47—28no—
75C22×D47—82no—
76C22×D47—82no—
77C22×D47C2×D411yescharacteristic
78D4×C47—22no—
79D4×C47C22×C414yes—
80C2×C4×C47—22no—
81C2×C4×C47—82no—
82C2×C4×C47C2×D412yes—
83C2×C4×C47C2411yescharacteristic
84C22⋊D47—28no—
85C2×Dic47—22no—
86C2×Dic47—82no—
87C2×Dic47C2×D412yes—
88C2×Dic47C2×D411yescharacteristic
89D188—22no—
90D188C22×C414yes—
91C4×D47—82no—
92C4×D47—82no—
93C4×D47C22×C412yes—
94C4×D47#4112yes—
95C8×C47—21no—
96C8×C47C22×C412yes—
97C47⋊C8—21no—
98C47⋊C8C22×C412yes—
99C22×C47—24no—
100C22×C47—42no—
101C22×C47—42no—
102C22×C47C22×D411yescharacteristic
103C2×D47—22no—
104C2×D47—24no—
105C2×D47—42no—
106C2×D47—42no—
107C2×D47—88no—
108C2×D47C4×D412yes—
109C4×C47—22no—
110C4×C47—42no—
111C4×C47C23×C411yescharacteristic
112C4×C47C2×#4111yescharacteristic
113Dic47—22no—
114Dic47—42no—
115Dic47C4×D412yes—
116#2948—471nomaximal, Sylow
117C2×C47—44no—
118C2×C47C2×C4×D411yescharacteristic
119C2×C47#57612yes—
120D47—22no—
121D47—44no—
122C22×D8—471no—
123#518—472no—
124#442—471no—
125#442—471no—
126#442—471no—
127#442D4711yescharacteristic, complemented
128C4×D8—472no—
129C4×D8—472no—
130#427—471no—
131#418—472no—
132#405—471no—
133C47#294811yescharacteristic, complemented, Sylow
134C22×D4—472no—
135C2×D8—472no—
136C2×D8—478no—
137C2×D8—471no—
138C2×D8C2×D4711yescharacteristic
139C2×M16—471no—
140C22×C8—471no—
141C4×D4—472no—
142C4×D4—472no—
143C4×D4—472no—
144C4×D4—942no—
145C4×D4—942no—
146C4×D4C2×D4712yescomplemented
147#117—471no—
148#117—472no—
149C2×C22⋊C4—942no—
150C2×C22⋊C4—942no—
151#107—472no—
152#106—471no—
153#106C2×D4711yescharacteristic, complemented
154#102—472no—
155#102—472no—
156#102—472no—
157#102C2×D4712yescomplemented
158#97—471no—
159#97C2×D4711yescharacteristic, complemented
160C4×C8—471no—
161C4×C8—471no—
162C24—942no—
163C2×D4—478no—
164C2×D4—472no—
165C2×D4—944no—
166C2×D4—942no—
167C2×D4C22×D4712yes—
168C22×C4—22no—
169C22×C4—471no—
170C22×C4—942no—
171C22×C4—942no—
172C22×C4—942no—
173D8—478no—
174D8—474no—
175D8C4×D4714yescomplemented
176M16—942no—
177C2×C8—471no—
178C2×C8—474no—
179C2×C8—471no—
180C2×C8C22×D4711yescharacteristic
181C2×C8C22×D4711yescharacteristic
182C4⋊C4—472no—
183C4⋊C4—472no—
184C4⋊C4C22×D4712yes—
185C22⋊C4—22no—
186C22⋊C4—472no—
187C22⋊C4—942no—
188C22⋊C4—942no—
189C22⋊C4—942no—
190C22⋊C4—942no—
191C42—471no—
192C42—942no—
193C42C22×D4711yescharacteristic
194C23—22no—
195C23—471no—
196C23—948no—
197C23—942no—
198C23—3762no—
199C23—3762no—
200D4—22no—
201D4—474no—
202D4—948no—
203D4—942no—
204D4C2×C4×D4714yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—471no—
208C2×C4—472no—
209C2×C4—472no—
210C2×C4—472no—
211C2×C4—942no—
212C2×C4—3762no—
213C2×C4—3762no—
214C2×C4—3762no—
215C2×C4D4×D4712yes—
216C2×C4C23×D4711yescharacteristic
217C8—21no—
218C8—472no—
219C8—941no—
220C8C2×C4×D4712yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—472no—
225C22—942no—
226C22—944no—
227C22—3768no—
228C22—1882no—
229C22—1882no—
230C22C2×D4×D4711yescharacteristic
231C4—22no—
232C4—42no—
233C4—472no—
234C4—942no—
235C4—1882no—
236C4C22×C4×D4711yescharacteristic
237C4#41×D4711yescharacteristic
238C2—44no—
239C2—942no—
240C2—1884no—
241C2C4×D4×D4711yescharacteristic
242C2#1568992712yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC47×#442C2
socleC22×C47C22×D4
hypercenter#442D47
hypocenterC47#2948
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #15689595C2semidirect
3. #15689236C2semidirect
4. #15689235C2semidirect
5. #15689234C2semidirect
6. C4×#10625334C2semidirect
7. #15689203C2semidirect
8. #15689158C2semidirect
9. #15689126C2semidirect
10. #15689080C2semidirect
11. C47×#442C2semidirect
15. D8×D47C4semidirect
18. C4×D188C22semidirect
19. D4×Dic47C22semidirect
20. #13093986C22semidirect
27. #13093957C22semidirect
28. #13093956C22semidirect
29. #13093946C22semidirect
30. #13093945C22semidirect
31. #13093944C22semidirect
32. #13093934C22semidirect
33. C4×C47⋊C8C22semidirect
34. C8×Dic47C22semidirect
36. C4×D4×C47C22semidirect
37. #106×C47C22semidirect
38. #102×C47C22semidirect
39. #97×C47C22semidirect
46. D4×D47C2×C4semidirect
51. D8×C47C2×C4semidirect
58. #10625334C2×C4semidirect
69. D376C2×C4semidirect
71. C8×D47C2×C4semidirect
127. #442D47semidirect
133. C47#2948semidirect
146. C4×D4C2×D47semidirect
153. #106C2×D47semidirect
157. #102C2×D47semidirect
159. #97C2×D47semidirect
175. D8C4×D47semidirect