Finite Group Databasebeta

← #20253759

Subgroups — #20253759

Order 6016.

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

normal subgroups only

This group has 484 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
1#15689678C211yesmaximal, characteristic, complemented
2#127×D47C211yesmaximal, characteristic
3#15689486C214yesmaximal, complemented
4#15689471C211yesmaximal, characteristic, complemented
5#15689470C211yesmaximal, characteristic, complemented
6#15689469C211yesmaximal, characteristic, complemented
7#15689126C214yesmaximal, complemented
8C4×#10625324C211yesmaximal, characteristic, complemented
9C47×#486C211yesmaximal, characteristic, complemented
10C2×D4×D47—21no—
11C2×D4×D47—21no—
12C2×D4×D47C2212yes—
13C2×#10625324C2212yes—
14#13094024C2211yescharacteristic, complemented
15#13094021C2211yescharacteristic
16#13094020—21no—
17#13094020—21no—
18#13094020C2212yes—
19#13094015C2212yescomplemented
20#13094004—21no—
21#13094000—21no—
22Q8×Dic47—21no—
23#13093989—21no—
24#13093982C2212yes—
25C42×D47C2211yescharacteristic
26#13093946C2214yescomplemented
27#13093945C2214yescomplemented
28#13093944C2214yescomplemented
29#13093934C2212yescomplemented
30C4×C47⋊C8C2211yescharacteristic, complemented
31C4⋊Q8×C47C2211yescharacteristic, complemented
32#127×C47C2211yescharacteristic
33#102×C47C2214yescomplemented
34C4×C8×C47C2211yescharacteristic, complemented
35C23×D47—22no—
36C2×Q8×C47—21no—
37C2×D4×C47—21no—
38C2×D4×C47—21no—
39C2×D4×C47C2312yes—
40C2×C22⋊D47—22no—
41C2×C22⋊D47—22no—
42C2×C22⋊D47—22no—
43D4×D47—28no—
44D4×D47—44no—
45D4×D47—44no—
46C2×D188—21no—
47C2×D188—21no—
48C2×D188C2312yes—
49C2×C4×D47D411yescharacteristic
50C2×C4×D47D411yescharacteristic
51C2×C4×D47C2311yescharacteristic
52C2×Dic94—21no—
53C2×C8×C47C2312yes—
54C4⋊C4×C47—21no—
55C4⋊C4×C47C2312yes—
56C42×C47C2311yescharacteristic
57(C2×D47)⋊C4—22no—
58C4⋊Dic47—21no—
59C4⋊Dic47—22no—
60C4⋊Dic47C2312yes—
61Dic47⋊C4—22no—
62C4×Dic47—22no—
63C4×Dic47D411yescharacteristic
64C4×Dic47D411yescharacteristic
65C4×Dic47C2311yescharacteristic
66C2×C47⋊C8C2312yes—
67#10625324—24no—
68C23×C47—22no—
69C22×D47—22no—
70C22×D47—44no—
71C22×D47—44no—
72C22×D47—44no—
73C22×D47C2×D411yescharacteristic
74Q8×C47—42no—
75D4×C47—24no—
76D4×C47—42no—
77D4×C47—42no—
78C2×C4×C47—22no—
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2411yescharacteristic
82C22⋊D47—44no—
83C22⋊D47—44no—
84C22⋊D47—44no—
85C2×Dic47—22no—
86C2×Dic47C2×D411yescharacteristic
87C2×Dic47C2×D411yescharacteristic
88C2×Dic47C2×D411yescharacteristic
89D188—24no—
90D188—42no—
91D188—42no—
92C4×D47—22no—
93C4×D47—22no—
94C4×D47#4114yes—
95Dic94—42no—
96C8×C47—22no—
97C47⋊C8—22no—
98C22×C47—42no—
99C22×C47—42no—
100C22×C47—42no—
101C22×C47C22×D411yescharacteristic
102C2×D47—21no—
103C2×D47—21no—
104C2×D47—42no—
105C2×D47—42no—
106C2×D47—42no—
107C2×D47—88no—
108C2×D47#12412yes—
109C4×C47—42no—
110C4×C47AGL(1,ℤ/8)12yes—
111C4×C47AGL(1,ℤ/8)12yes—
112C4×C47C2×#4112yes—
113Dic47—21no—
114Dic47—21no—
115Dic47—42no—
116Dic47#12412yes—
117#3138—471nomaximal, Sylow
118C2×C47—82no—
119C2×C47C2×#12411yescharacteristic
120C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
121C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
122D47—22no—
123D47—82no—
124#533—471no—
125C2×#127—471no—
126#490—474no—
127#486—471no—
128#486—471no—
129#486—471no—
130#486D4711yescharacteristic, complemented
131#418—474no—
132C4×M16—471no—
133C47#313811yescharacteristic, complemented, Sylow
134C22×D4—472no—
135C22×D4—941no—
136C22×D4—941no—
137C2×M16—472no—
138C4⋊Q8—471no—
139C4⋊Q8C2×D4711yescharacteristic, complemented
140#127—472no—
141#127—471no—
142#127—941no—
143#127—941no—
144#127C2×D4711yescharacteristic
145#125—472no—
146C22⋊Q8—941no—
147C22⋊Q8—941no—
148C4×Q8—941no—
149C4×Q8—941no—
150#117—472no—
151C2×C42—471no—
152#102—474no—
153#102—474no—
154#102—474no—
155#102C2×D4714yescomplemented
156#97—472no—
157C4×C8—471no—
158C4×C8C2×D4711yescharacteristic, complemented
159C24—942no—
160C2×Q8—21no—
161C2×Q8—941no—
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—472no—
165C2×D4—948no—
166C2×D4—942no—
167C2×D4—942no—
168C2×D4—942no—
169C2×D4—941no—
170C2×D4—941no—
171C2×D4—1884no—
172C2×D4—1884no—
173C2×D4C22×D4712yes—
174C22×C4—471no—
175C22×C4—471no—
176C22×C4—471no—
177M16—944no—
178C2×C8—472no—
179C2×C8C22×D4712yes—
180C4⋊C4—21no—
181C4⋊C4—472no—
182C4⋊C4—942no—
183C4⋊C4—942no—
184C4⋊C4—941no—
185C4⋊C4C22×D4712yes—
186C22⋊C4—942no—
187C42—471no—
188C42—471no—
189C42—471no—
190C42—942no—
191C42C22×D4711yescharacteristic
192C23—22no—
193C23—471no—
194C23—942no—
195C23—1884no—
196C23—1884no—
197C23—1884no—
198Q8—42no—
199Q8—1882no—
200D4—24no—
201D4—42no—
202D4—42no—
203D4—944no—
204D4—1884no—
205D4—1884no—
206D4—1884no—
207D4—1882no—
208D4—1882no—
209C2×C4—22no—
210C2×C4—471no—
211C2×C4—474no—
212C2×C4—471no—
213C2×C4—471no—
214C2×C4—942no—
215C2×C4—942no—
216C2×C4—942no—
217C2×C4D4×D4711yescharacteristic
218C2×C4D4×D4711yescharacteristic
219C2×C4C23×D4711yescharacteristic
220C8—22no—
221C8—942no—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—472no—
226C22—941no—
227C22—941no—
228C22—3768no—
229C22—1882no—
230C22—1882no—
231C22—1882no—
232C22C2×D4×D4711yescharacteristic
233C4—42no—
234C4—472no—
235C4—941no—
236C4—941no—
237C4—1882no—
238C4#1309404812yes—
239C4#1309405112yes—
240C4#41×D4712yes—
241C2—82no—
242C2—942no—
243C2—3762no—
244C2#124×D4711yescharacteristic
245C2C2×#1309404811yescharacteristic
246C2C2×#1309405111yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#486C2
socleC22×C47C22×D4
hypercenter#486D47
hypocenterC47#3138
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #15689678C2semidirect
3. #15689486C2semidirect
4. #15689471C2semidirect
5. #15689470C2semidirect
6. #15689469C2semidirect
7. #15689126C2semidirect
8. C4×#10625324C2semidirect
9. C47×#486C2semidirect
14. #13094024C22semidirect
19. #13094015C22semidirect
26. #13093946C22semidirect
27. #13093945C22semidirect
28. #13093944C22semidirect
29. #13093934C22semidirect
30. C4×C47⋊C8C22semidirect
31. C4⋊Q8×C47C22semidirect
33. #102×C47C22semidirect
34. C4×C8×C47C22semidirect
130. #486D47semidirect
133. C47#3138semidirect
139. C4⋊Q8C2×D47semidirect
155. #102C2×D47semidirect
158. C4×C8C2×D47semidirect