Finite Group Databasebeta

← #20254230

Subgroups — #20254230

Order 6016.

418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689634C212yesmaximal, complemented
2#15689465C212yesmaximal, complemented
3#15689448C212yesmaximal, complemented
4#15689381C211yesmaximal, characteristic, complemented
5#15689376C211yesmaximal, characteristic, complemented
6#15689369C212yesmaximal, complemented
7#15689287C212yesmaximal, complemented
8#15689270C212yesmaximal, complemented
9C47×#407C211yesmaximal, characteristic, complemented
10C2×#10625350C2212yes—
11C2×Dic188C2211yescharacteristic, complemented
12C2×#10625325C2212yescomplemented
13C2×D376C2211yescharacteristic, complemented
14#13094007—22no—
15#13094003C2212yes—
16#13094003C2212yes—
17#13093998C2212yes—
18#13093998C2212yes—
19#13093993—22no—
20C4×C22⋊D47—22no—
21C4×C22⋊D47—22no—
22#13093983C2212yes—
23#13093958C2212yescomplemented
24#13093956C2211yescharacteristic, complemented
25#13093956C2211yescharacteristic, complemented
26#13093949C2212yescomplemented
27#13093949C2212yescomplemented
28#13093946C2212yescomplemented
29#13093946C2212yescomplemented
30C23×C4×C47C2211yescharacteristic
31C2×M16×C47C2211yescharacteristic
32C2×M16×C47C2211yescharacteristic
33C22⋊C8×C47C2212yes—
34C22⋊C8×C47C2212yes—
35C24×C47D411yescharacteristic
36C22×C4×C47—41no—
37C22×C4×C47—41no—
38C22×C4×C47D411yescharacteristic
39C22×C4×C47D412yes—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C2×C22⋊D47—22no—
43C2×C22⋊D47—22no—
44C2×C22⋊D47—22no—
45#10625350—42no—
46#10625350—42no—
47C2×D188C2312yes—
48C2×C4×D47—22no—
49C2×Dic94C2312yes—
50M16×C47—41no—
51M16×C47—41no—
52C2×C8×C47C2311yescharacteristic
53C2×C8×C47C2312yes—
54C2×C8×C47C2311yescharacteristic
55C22⋊Dic47—22no—
56C22⋊Dic47—22no—
57C22⋊Dic47—22no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—22no—
60C4⋊Dic47C2312yes—
61C4⋊Dic47C2312yes—
62Dic47⋊C4—22no—
63Dic47⋊C4—22no—
64C4×Dic47—22no—
65Dic188—41no—
66D376—41no—
67#10625325—42no—
68C23×C47—41no—
69C23×C47—42no—
70C23×C47C2×D412yes—
71C23×C47C2×D411yescharacteristic
72C22×D47—22no—
73C2×C4×C47—21no—
74C2×C4×C47—21no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—41no—
78C2×C4×C47—42no—
79C2×C4×C47C2×D412yes—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2411yescharacteristic
82C22⋊D47—44no—
83C22⋊D47—44no—
84C22⋊D47—44no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88D188—22no—
89D188—22no—
90C4×D47—44no—
91Dic94—22no—
92Dic94—22no—
93C8×C47—22no—
94C8×C47—21no—
95C8×C47—21no—
96C22×C47—22no—
97C22×C47—21no—
98C22×C47—22no—
99C22×C47—22no—
100C22×C47—22no—
101C22×C47—44no—
102C22×C47C22×D411yescharacteristic
103C2×D47—42no—
104C2×D47—42no—
105C2×D47—42no—
106C4×C47—22no—
107C4×C47—21no—
108C4×C47H(5,𝔽2)11yescharacteristic
109C4×C47H(5,𝔽2)11yescharacteristic
110Dic47—42no—
111Dic47—42no—
112Dic47—42no—
113#3197—471nomaximal, Sylow
114C2×C47—42no—
115C2×C47—41no—
116C2×C47#53411yescharacteristic
117C2×C47#57512yes—
118D47—82no—
119#525—472no—
120#485—472no—
121#482—472no—
122#470—471no—
123#469—471no—
124#468—472no—
125#452—472no—
126#449—472no—
127#407D4711yescharacteristic, complemented
128C47#319711yescharacteristic, complemented, Sylow
129C2×#41—472no—
130C23×C4C2×D4711yescharacteristic
131C2×Q16—471no—
132C2×SD16—472no—
133C2×D8—471no—
134C2×M16C2×D4711yescharacteristic
135C2×M16C2×D4711yescharacteristic
136#123—942no—
137C22⋊Q8—472no—
138C22⋊Q8—472no—
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#106—471no—
148#103—472no—
149#103—472no—
150#102—472no—
151#102—472no—
152C22⋊C8C2×D4712yes—
153C22⋊C8C2×D4712yes—
154C24D18811yescharacteristic
155#41—1882no—
156#41—1882no—
157C2×Q8—472no—
158C2×D4—472no—
159C2×D4—942no—
160C2×D4—942no—
161C2×D4—942no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—942no—
165C22×C4D18811yescharacteristic
166C22×C4D18812yes—
167C22×C4C22×D4712yes—
168C22×C4C22×D4711yescharacteristic
169Q16—1881no—
170SD16—1882no—
171D8—1881no—
172M16—41no—
173M16—41no—
174C2×C8C22×D4711yescharacteristic
175C2×C8C22×D4712yes—
176C2×C8C22×D4711yescharacteristic
177C4⋊C4—472no—
178C4⋊C4—472no—
179C4⋊C4—942no—
180C4⋊C4—942no—
181C22⋊C4—942no—
182C22⋊C4—942no—
183C22⋊C4—942no—
184C22⋊C4—942no—
185C22⋊C4—942no—
186C42—942no—
187C23—41no—
188C23—42no—
189C23—942no—
190C23C2×D18811yescharacteristic
191C23C2×D18812yes—
192Q8—942no—
193Q8—942no—
194D4—942no—
195D4—942no—
196D4—1884no—
197D4—1884no—
198D4—1884no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—942no—
206C2×C4—942no—
207C2×C4—942no—
208C2×C4—1884no—
209C2×C4C2×D18812yes—
210C2×C4C2×D18811yescharacteristic
211C2×C4C23×D4711yescharacteristic
212C8—21no—
213C8—22no—
214C8—21no—
215C22—22no—
216C22—22no—
217C22—22no—
218C22—22no—
219C22—21no—
220C22—44no—
221C22—1882no—
222C22—1882no—
223C22—1882no—
224C22C22×D18811yescharacteristic
225C4—22no—
226C4—21no—
227C4—1882no—
228C4—1882no—
229C4—1882no—
230C4#1309406911yescharacteristic
231C4#1309406911yescharacteristic
232C2—41no—
233C2—42no—
234C2—3762no—
235C2#1568968511yescharacteristic
236C2#1568992312yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#407C2
socleC22×C47C22×D4
hypercenter#407D47
hypocenterC47#3197
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #15689634C2semidirect
2. #15689465C2semidirect
3. #15689448C2semidirect
4. #15689381C2semidirect
5. #15689376C2semidirect
6. #15689369C2semidirect
7. #15689287C2semidirect
8. #15689270C2semidirect
9. C47×#407C2semidirect
11. C2×Dic188C22semidirect
12. C2×#10625325C22semidirect
13. C2×D376C22semidirect
23. #13093958C22semidirect
24. #13093956C22semidirect
25. #13093956C22semidirect
26. #13093949C22semidirect
27. #13093949C22semidirect
28. #13093946C22semidirect
29. #13093946C22semidirect
127. #407D47semidirect
128. C47#3197semidirect