Finite Group Databasebeta

← #20254431

Subgroups — #20254431

Order 6016.

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

normal subgroups only

This group has 420 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#15689727C211yesmaximal, characteristic, complemented
2#15689686C211yesmaximal, characteristic, complemented
3#15689510C211yesmaximal, characteristic, complemented
4#15689487C211yesmaximal, characteristic, complemented
5#15689478C211yesmaximal, characteristic, complemented
6#15689336C212yesmaximal, complemented
7#15689316C212yesmaximal, complemented
8#15689265C212yesmaximal, complemented
9#15689255C212yesmaximal, complemented
10#15689182C211yesmaximal, characteristic, complemented
11C47×#493C211yesmaximal, characteristic, complemented
12C2×#10625352C2211yescharacteristic
13C2×D4×D47C2211yescharacteristic
14C2×#10625335C2212yescomplemented
15C2×#10625334C2212yes—
16#13094020C2211yescharacteristic
17#13094016C2211yescharacteristic, complemented
18#13094012C2211yescharacteristic
19#13094011C2211yescharacteristic
20#13094005—22no—
21#13093996—22no—
22#13093996—22no—
23#13093995C2212yes—
24#13093992—22no—
25D4×Dic47C2212yescomplemented
26#13093981C2211yescharacteristic
27Dic47⋊C8C2212yescomplemented
28#13093949C2212yescomplemented
29#13093946C2212yes—
30#13093945C2212yes—
31#13093945C2212yescomplemented
32(C2×D47)⋊C8C2212yes—
33#13093935C2211yescharacteristic, complemented
34C2×D8×C47C2212yes—
35C2×D8×C47C2212yescomplemented
36#127×C47C2211yescharacteristic
37#127×C47C2211yescharacteristic, complemented
38C4×C8×C47C2211yescharacteristic, complemented
39C23×D47—21no—
40C2×D4×C47—22no—
41C2×D4×C47—22no—
42C2×D4×C47C2311yescharacteristic
43C2×D4×C47C2311yescharacteristic
44C2×D4×C47C2312yes—
45C2×C22⋊D47—21no—
46C2×C22⋊D47—22no—
47C2×C22⋊D47—21no—
48C2×C22⋊D47—22no—
49C22×Dic47—21no—
50C22×Dic47—22no—
51#10625352—42no—
52D4×D47—42no—
53C2×D188C2311yescharacteristic
54C2×C4×D47C2311yescharacteristic
55C2×Dic94C2311yescharacteristic
56D8×C47—42no—
57D8×C47—42no—
58C2×C8×C47C2312yes—
59C42×C47C2311yescharacteristic
60C22⋊Dic47—22no—
61C22⋊Dic47—22no—
62C22⋊Dic47—22no—
63#10625335—42no—
64#10625334—42no—
65(C2×D47)⋊C4—22no—
66(C2×D47)⋊C4D412yes—
67C4⋊Dic47C2312yes—
68Dic47⋊C4—22no—
69Dic47⋊C4D412yes—
70C4×Dic47C2311yescharacteristic
71C2×C47⋊C8C2312yes—
72C23×C47—22no—
73C23×C47—21no—
74C23×C47—21no—
75C22×D47—21no—
76C22×D47—42no—
77C22×D47—82no—
78C22×D47C2×D411yescharacteristic
79D4×C47—22no—
80D4×C47—22no—
81D4×C47—22no—
82D4×C47—22no—
83D4×C47—82no—
84D4×C47—82no—
85C2×C4×C47C2×D412yes—
86C2×C4×C47C2411yescharacteristic
87C22⋊D47—42no—
88C22⋊D47—42no—
89C22⋊D47—82no—
90C22⋊D47—82no—
91C2×Dic47—22no—
92C2×Dic47—21no—
93C2×Dic47—42no—
94C2×Dic47—82no—
95C2×Dic47C2×D412yes—
96C2×Dic47C2×D411yescharacteristic
97D188—22no—
98C4×D47—22no—
99Dic94—22no—
100C8×C47—22no—
101C47⋊C8—22no—
102C22×C47—41no—
103C22×C47—41no—
104C22×C47—42no—
105C22×C47—42no—
106C22×C47—42no—
107C22×C47—42no—
108C22×C47—42no—
109C22×C47C22×D411yescharacteristic
110C2×D47—21no—
111C2×D47—22no—
112C2×D47—41no—
113C2×D47—42no—
114C2×D47—84no—
115C4×C47—22no—
116C4×C47H(5,𝔽2)12yes—
117Dic47—21no—
118Dic47—22no—
119Dic47—41no—
120Dic47—42no—
121#3220—471nomaximal, Sylow
122C2×C47—81no—
123C2×C47—81no—
124C2×C47—82no—
125C2×C47#53511yescharacteristic
126C2×C47#57612yes—
127D47—41no—
128D47—81no—
129#540—471no—
130#535—471no—
131#496—471no—
132#493D4711yescharacteristic, complemented
133#490—471no—
134#488—471no—
135#463—472no—
136#459—472no—
137#449—472no—
138#447—472no—
139#433—471no—
140C47#322011yescharacteristic, complemented, Sylow
141C2×#41—471no—
142C22×D4—471no—
143C2×SD16—472no—
144C2×D8—472no—
145C2×D8C2×D4712yes—
146C2×D8C2×D4712yescomplemented
147#127—471no—
148#127C2×D4711yescharacteristic
149#127C2×D4711yescharacteristic, complemented
150#125—471no—
151#124—471no—
152#124—471no—
153#123—942no—
154#121—472no—
155#121—942no—
156#121—942no—
157#120—942no—
158C4×D4—472no—
159#117—471no—
160C4⋊C8—472no—
161#103—472no—
162#102—472no—
163#102—472no—
164#102—472no—
165C22⋊C8—472no—
166#97—471no—
167C4×C8C2×D4711yescharacteristic, complemented
168C24—941no—
169#41—1882no—
170C2×Q8—471no—
171C2×D4—22no—
172C2×D4—22no—
173C2×D4—471no—
174C2×D4—942no—
175C2×D4—941no—
176C2×D4—942no—
177C2×D4—941no—
178C2×D4—1882no—
179C2×D4C22×D4711yescharacteristic
180C2×D4C22×D4711yescharacteristic
181C2×D4C22×D4712yes—
182C22×C4—471no—
183C22×C4—942no—
184C22×C4—941no—
185SD16—1882no—
186D8—42no—
187D8—42no—
188D8—1882no—
189C2×C8—472no—
190C2×C8C22×D4712yes—
191C4⋊C4—472no—
192C4⋊C4—472no—
193C4⋊C4—942no—
194C22⋊C4—472no—
195C22⋊C4—942no—
196C22⋊C4—942no—
197C22⋊C4—942no—
198C22⋊C4—942no—
199C42—471no—
200C42C22×D4711yescharacteristic
201C23—22no—
202C23—21no—
203C23—21no—
204C23—471no—
205C23—941no—
206C23—3762no—
207C23—1882no—
208Q8—942no—
209D4—22no—
210D4—22no—
211D4—22no—
212D4—22no—
213D4—82no—
214D4—82no—
215D4—942no—
216D4—3762no—
217D4—3762no—
218D4—1882no—
219D4—1882no—
220C2×C4—472no—
221C2×C4—471no—
222C2×C4—942no—
223C2×C4—941no—
224C2×C4—942no—
225C2×C4—3762no—
226C2×C4—1882no—
227C2×C4D4×D4712yes—
228C2×C4C23×D4711yescharacteristic
229C8—22no—
230C8—942no—
231C22—42no—
232C22—42no—
233C22—42no—
234C22—42no—
235C22—41no—
236C22—41no—
237C22—42no—
238C22—942no—
239C22—941no—
240C22—3764no—
241C22—1882no—
242C22—1881no—
243C22C2×D4×D4711yescharacteristic
244C4—22no—
245C4—942no—
246C4—941no—
247C4—1882no—
248C4—1881no—
249C4#1309406912yes—
250C2—81no—
251C2—82no—
252C2—81no—
253C2—3761no—
254C2—1881no—
255C2#1568968611yescharacteristic
256C2#1568992412yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#493C2
socleC22×C47C22×D4
hypercenter#493D47
hypocenterC47#3220
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #15689727C2semidirect
2. #15689686C2semidirect
3. #15689510C2semidirect
4. #15689487C2semidirect
5. #15689478C2semidirect
6. #15689336C2semidirect
7. #15689316C2semidirect
8. #15689265C2semidirect
9. #15689255C2semidirect
10. #15689182C2semidirect
11. C47×#493C2semidirect
14. C2×#10625335C22semidirect
17. #13094016C22semidirect
25. D4×Dic47C22semidirect
27. Dic47⋊C8C22semidirect
28. #13093949C22semidirect
31. #13093945C22semidirect
33. #13093935C22semidirect
35. C2×D8×C47C22semidirect
37. #127×C47C22semidirect
38. C4×C8×C47C22semidirect
132. #493D47semidirect
140. C47#3220semidirect
146. C2×D8C2×D47semidirect
149. #127C2×D47semidirect
167. C4×C8C2×D47semidirect