Finite Group Databasebeta

← #20254175

Subgroups — #20254175

Order 6016.

424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 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#15689633C212yesmaximal, complemented
2#15689466C212yesmaximal, complemented
3#15689445C212yesmaximal, complemented
4#15689364C211yesmaximal, characteristic, complemented
5#15689350C212yesmaximal, complemented
6#15689286C212yesmaximal, complemented
7#15689265C212yesmaximal, complemented
8C2×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
9C47×#466C211yesmaximal, characteristic, complemented
10C2×#10625352C2212yes—
11C22×C4×D47C2211yescharacteristic
12C2×Dic188C2211yescharacteristic, complemented
13C2×#10625335C2212yescomplemented
14C22×C47⋊C8C2211yescharacteristic
15#13094006—22no—
16#13094004C2212yes—
17#13094003C2212yes—
18#13093995C2212yes—
19#13093992—22no—
20D4×Dic47—22no—
21(C22⋊D47)⋊C4—22no—
22#13093982C2212yes—
23#13093958C2211yescharacteristic, complemented
24#13093955C2212yescomplemented
25#13093949C2212yescomplemented
26#13093947C2212yescomplemented
27#13093945C2212yescomplemented
28(C2×D47)⋊C8C2212yes—
29(C2×D47)⋊C8C2212yes—
30C2×D8×C47C2211yescharacteristic, complemented
31C22×C8×C47C2211yescharacteristic
32#121×C47C2212yes—
33#107×C47C2211yescharacteristic, complemented
34#102×C47C2212yescomplemented
35C23×D47D411yescharacteristic
36C2×D4×C47—22no—
37C2×D4×C47C2312yes—
38C22×C4×C47C2311yescharacteristic
39C2×C22⋊D47—22no—
40C2×C22⋊D47—22no—
41C22×Dic47—22no—
42C22×Dic47D411yescharacteristic
43#10625352—42no—
44#10625352—42no—
45C2×C4×D47—41no—
46C2×C4×D47—41no—
47C2×C4×D47D412yes—
48C2×C4×D47C2312yes—
49C2×Dic94C2312yes—
50D8×C47—41no—
51C2×C8×C47—41no—
52C2×C8×C47C2311yescharacteristic
53C2×C8×C47C2311yescharacteristic
54C4⋊C4×C47C2312yes—
55C22⋊C4×C47—22no—
56C22⋊Dic47—22no—
57C22⋊Dic47—22no—
58#10625335—42no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—22no—
61C4⋊Dic47—22no—
62C4⋊Dic47C2312yes—
63Dic47⋊C4—22no—
64C4×Dic47—22no—
65C2×C47⋊C8—41no—
66C2×C47⋊C8C2312yes—
67Dic188—41no—
68C23×C47—22no—
69C23×C47C2×D411yescharacteristic
70C22×D47—22no—
71C22×D47—41no—
72C22×D47—41no—
73C22×D47C2×D412yes—
74D4×C47—22no—
75D4×C47—22no—
76D4×C47—44no—
77C2×C4×C47—21no—
78C2×C4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2411yescharacteristic
82C22⋊D47—44no—
83C22⋊D47—44no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—41no—
87C2×Dic47—44no—
88C2×Dic47C2×D412yes—
89C4×D47—22no—
90C4×D47—22no—
91C4×D47—42no—
92Dic94—22no—
93Dic94—22no—
94C8×C47—21no—
95C8×C47—21no—
96C47⋊C8—22no—
97C22×C47—21no—
98C22×C47—21no—
99C22×C47—42no—
100C22×C47—42no—
101C22×C47—42no—
102C22×C47#13512yes—
103C22×C47C22×D411yescharacteristic
104C2×D47—22no—
105C2×D47—22no—
106C2×D47—22no—
107C2×D47—44no—
108C4×C47—21no—
109C4×C47—42no—
110C4×C47H(5,𝔽2)11yescharacteristic
111C4×C47H(5,𝔽2)11yescharacteristic
112Dic47—22no—
113Dic47—42no—
114Dic47—42no—
115#3191—471nomaximal, Sylow
116C2×C47—22no—
117C2×C47—82no—
118C2×C47#53411yescharacteristic
119C2×C47C2×#13511yescharacteristic
120C2×C47#57511yescharacteristic
121D47—42no—
122#525—472no—
123#485—472no—
124#482—472no—
125#467—471no—
126#466D4711yescharacteristic, complemented
127#465—472no—
128#452—472no—
129#449—472no—
130C2×C22⋊C8—471no—
131C47#319111yescharacteristic, complemented, Sylow
132C2×#41—472no—
133C23×C4—471no—
134C2×Q16—471no—
135C2×SD16—472no—
136C2×D8C2×D4711yescharacteristic, complemented
137C22×C8—471no—
138C22×C8C2×D4711yescharacteristic
139#123—942no—
140C22⋊Q8—472no—
141C22⋊Q8—472no—
142#121—472no—
143#121C2×D4712yes—
144#120—942no—
145C4×D4—942no—
146C4×D4—942no—
147#117—472no—
148#107—471no—
149#107C2×D4711yescharacteristic, complemented
150#106—472no—
151#103—472no—
152#103—472no—
153#102—472no—
154#102C2×D4712yescomplemented
155C22⋊C8—472no—
156C22⋊C8—472no—
157C24—471no—
158#41—1882no—
159#41—1882no—
160C2×Q8—472no—
161C2×D4—22no—
162C2×D4—942no—
163C2×D4—942no—
164C2×D4C22×D4712yes—
165C22×C4—471no—
166C22×C4—472no—
167C22×C4—472no—
168C22×C4—942no—
169C22×C4—1881no—
170C22×C4—1881no—
171C22×C4C22×D4711yescharacteristic
172Q16—1881no—
173SD16—1882no—
174D8—41no—
175C2×C8—41no—
176C2×C8—472no—
177C2×C8—1881no—
178C2×C8C22×D4711yescharacteristic
179C2×C8C22×D4711yescharacteristic
180C4⋊C4—472no—
181C4⋊C4—942no—
182C4⋊C4—942no—
183C4⋊C4C22×D4712yes—
184C22⋊C4—22no—
185C22⋊C4—942no—
186C22⋊C4—942no—
187C22⋊C4—942no—
188C22⋊C4—942no—
189C42—942no—
190C23—22no—
191C23—472no—
192C23—942no—
193C23—1881no—
194C23—1881no—
195C23D4×D4711yescharacteristic
196Q8—942no—
197Q8—942no—
198D4—22no—
199D4—22no—
200D4—44no—
201D4—1884no—
202D4—1884no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—472no—
207C2×C4—942no—
208C2×C4—942no—
209C2×C4—942no—
210C2×C4—942no—
211C2×C4—1882no—
212C2×C4—1881no—
213C2×C4—1884no—
214C2×C4D4×D4711yescharacteristic
215C2×C4C23×D4711yescharacteristic
216C8—21no—
217C8—21no—
218C8—942no—
219C22—21no—
220C22—21no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22—942no—
225C22—942no—
226C22—942no—
227C22—1884no—
228C22#1309404312yes—
229C22C2×D4×D4711yescharacteristic
230C4—21no—
231C4—42no—
232C4—942no—
233C4—1882no—
234C4—1882no—
235C4#1309406911yescharacteristic
236C4#1309407011yescharacteristic
237C2—22no—
238C2—82no—
239C2—1882no—
240C2#1568968111yescharacteristic
241C2C2×#1309404311yescharacteristic
242C2#1568992011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#466C2
socleC22×C47C22×D4
hypercenter#466D47
hypocenterC47#3191
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #15689633C2semidirect
2. #15689466C2semidirect
3. #15689445C2semidirect
4. #15689364C2semidirect
5. #15689350C2semidirect
6. #15689286C2semidirect
7. #15689265C2semidirect
8. C2×(C2×D47)⋊C8C2semidirect
9. C47×#466C2semidirect
12. C2×Dic188C22semidirect
13. C2×#10625335C22semidirect
23. #13093958C22semidirect
24. #13093955C22semidirect
25. #13093949C22semidirect
26. #13093947C22semidirect
27. #13093945C22semidirect
30. C2×D8×C47C22semidirect
33. #107×C47C22semidirect
34. #102×C47C22semidirect
126. #466D47semidirect
131. C47#3191semidirect
136. C2×D8C2×D47semidirect
149. #107C2×D47semidirect
154. #102C2×D47semidirect