Finite Group Databasebeta

← #20254231

Subgroups — #20254231

Order 6016.

418 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 109 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#15689636C212yesmaximal, complemented
2#15689462C212yesmaximal, complemented
3#15689449C212yesmaximal, complemented
4#15689376C211yesmaximal, characteristic, complemented
5#15689371C212yesmaximal, complemented
6#15689284C212yesmaximal, complemented
7#15689271C212yesmaximal, complemented
8#15689086C211yesmaximal, characteristic, complemented
9C47×#470C211yesmaximal, characteristic, complemented
10C2×#10625354C2212yes—
11C22×C4×D47C2211yescharacteristic
12C2×#10625336C2212yescomplemented
13C2×D376C2211yescharacteristic, complemented
14C2×#10625329C2211yescharacteristic
15#13094009—22no—
16#13094000C2212yes—
17#13093999C2212yes—
18#13093998C2212yes—
19#13093994—22no—
20#13093986—22no—
21(C22⋊D47)⋊C4—22no—
22#13093982C2212yes—
23#13093957C2212yescomplemented
24#13093956C2211yescharacteristic, complemented
25#13093948C2212yescomplemented
26#13093946C2212yescomplemented
27#13093944C2212yescomplemented
28(C2×D47)⋊C8C2212yes—
29(C2×D47)⋊C8C2212yes—
30C2×Q16×C47C2211yescharacteristic, complemented
31C2×M16×C47C2211yescharacteristic
32C22⋊Q8×C47C2212yes—
33#106×C47C2211yescharacteristic, complemented
34#103×C47C2212yescomplemented
35C23×D47D411yescharacteristic
36C2×Q8×C47C2312yes—
37C22×C4×C47C2311yescharacteristic
38C2×C22⋊D47—22no—
39C22×Dic47D411yescharacteristic
40#10625354—42no—
41#10625354—42no—
42C2×D188—22no—
43C2×D188—22no—
44C2×D188C2312yes—
45C2×C4×D47—22no—
46C2×C4×D47—41no—
47C2×C4×D47—41no—
48C2×C4×D47D412yes—
49C2×C4×D47C2312yes—
50Q16×C47—41no—
51M16×C47—41no—
52C2×C8×C47C2311yescharacteristic
53C2×C8×C47C2311yescharacteristic
54C4⋊C4×C47—22no—
55C4⋊C4×C47C2312yes—
56C22⋊C4×C47—22no—
57#10625336—42no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—22no—
62C4⋊Dic47C2312yes—
63Dic47⋊C4—22no—
64C4×Dic47—22no—
65#10625329—41no—
66C2×C47⋊C8C2312yes—
67D376—41no—
68C23×C47C2×D411yescharacteristic
69C22×D47—22no—
70C22×D47—41no—
71C22×D47—42no—
72C22×D47C2×D412yes—
73Q8×C47—22no—
74Q8×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2411yescharacteristic
81C22⋊D47—44no—
82C2×Dic47—22no—
83C2×Dic47—41no—
84C2×Dic47C2×D412yes—
85D188—22no—
86D188—22no—
87D188—44no—
88D188—44no—
89C4×D47—22no—
90C4×D47—22no—
91C4×D47—42no—
92C4×D47—44no—
93C8×C47—21no—
94C8×C47—21no—
95C47⋊C8—22no—
96C22×C47—21no—
97C22×C47—22no—
98C22×C47C22×D411yescharacteristic
99C2×D47—22no—
100C2×D47—22no—
101C2×D47—22no—
102C2×D47—44no—
103C2×D47—42no—
104C2×D47—42no—
105C2×D47—42no—
106C4×C47—21no—
107C4×C47—42no—
108C4×C47—42no—
109C4×C47H(5,𝔽2)11yescharacteristic
110C4×C47H(5,𝔽2)11yescharacteristic
111Dic47—22no—
112Dic47—42no—
113#3197—471nomaximal, Sylow
114C2×C47—41no—
115C2×C47#53411yescharacteristic
116C2×C47#57512yes—
117D47—42no—
118D47—82no—
119#525—472no—
120#485—472no—
121#482—472no—
122#470D4711yescharacteristic, complemented
123#469—471no—
124#468—472no—
125#452—472no—
126#449—472no—
127#407—471no—
128C47#319711yescharacteristic, complemented, Sylow
129C2×#41—472no—
130C23×C4—471no—
131C2×Q16C2×D4711yescharacteristic, complemented
132C2×SD16—472no—
133C2×D8—471no—
134C2×M16—471no—
135C2×M16C2×D4711yescharacteristic
136#123—942no—
137C22⋊Q8—472no—
138C22⋊Q8C2×D4712yes—
139#121—472no—
140#121—472no—
141#120—942no—
142C4×D4—942no—
143C4×D4—942no—
144#117—472no—
145#107—472no—
146#106—471no—
147#106C2×D4711yescharacteristic, complemented
148#103—472no—
149#103C2×D4712yescomplemented
150#102—472no—
151#102—472no—
152C22⋊C8—472no—
153C22⋊C8—472no—
154C24—471no—
155#41—1882no—
156#41—1882no—
157C2×Q8C22×D4712yes—
158C2×D4—472no—
159C2×D4—942no—
160C2×D4—942no—
161C2×D4—942no—
162C22×C4—471no—
163C22×C4—472no—
164C22×C4—472no—
165C22×C4—942no—
166C22×C4—1881no—
167C22×C4—1881no—
168C22×C4C22×D4711yescharacteristic
169Q16—41no—
170SD16—1882no—
171D8—1881no—
172M16—41no—
173M16—1881no—
174C2×C8—472no—
175C2×C8C22×D4711yescharacteristic
176C2×C8C22×D4711yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—472no—
179C4⋊C4—942no—
180C4⋊C4C22×D4712yes—
181C22⋊C4—22no—
182C22⋊C4—942no—
183C22⋊C4—942no—
184C22⋊C4—942no—
185C22⋊C4—942no—
186C42—942no—
187C23—472no—
188C23—942no—
189C23—1881no—
190C23—1882no—
191C23D4×D4711yescharacteristic
192Q8—22no—
193Q8—22no—
194D4—942no—
195D4—942no—
196D4—1884no—
197D4—1884no—
198D4—1884no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—472no—
204C2×C4—942no—
205C2×C4—942no—
206C2×C4—942no—
207C2×C4—1882no—
208C2×C4—1884no—
209C2×C4—1881no—
210C2×C4D4×D4711yescharacteristic
211C2×C4C23×D4711yescharacteristic
212C8—21no—
213C8—21no—
214C8—942no—
215C22—22no—
216C22—21no—
217C22—942no—
218C22—942no—
219C22—942no—
220C22—1884no—
221C22—1882no—
222C22—1882no—
223C22—1882no—
224C22C2×D4×D4711yescharacteristic
225C4—21no—
226C4—42no—
227C4—42no—
228C4—942no—
229C4—1882no—
230C4#1309406911yescharacteristic
231C4#1309407011yescharacteristic
232C2—41no—
233C2—3762no—
234C2—1882no—
235C2#1568968111yescharacteristic
236C2#1568992212yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#470C2
socleC22×C47C22×D4
hypercenter#470D47
hypocenterC47#3197
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #15689636C2semidirect
2. #15689462C2semidirect
3. #15689449C2semidirect
4. #15689376C2semidirect
5. #15689371C2semidirect
6. #15689284C2semidirect
7. #15689271C2semidirect
8. #15689086C2semidirect
9. C47×#470C2semidirect
12. C2×#10625336C22semidirect
13. C2×D376C22semidirect
23. #13093957C22semidirect
24. #13093956C22semidirect
25. #13093948C22semidirect
26. #13093946C22semidirect
27. #13093944C22semidirect
30. C2×Q16×C47C22semidirect
33. #106×C47C22semidirect
34. #103×C47C22semidirect
122. #470D47semidirect
128. C47#3197semidirect
131. C2×Q16C2×D47semidirect
147. #106C2×D47semidirect
149. #103C2×D47semidirect