Finite Group Databasebeta

← #20252625

Subgroups — #20252625

Order 6016.

738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C23×Dic94C211yesmaximal, characteristic, complemented
2C2×#13094057C212yesmaximal, complemented
3#15689634C211yesmaximal, characteristic
4#15689281C214yesmaximal, complemented
5#15689264C214yesmaximal, complemented
6#15689133C212yesmaximal, complemented
7C47×#407C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C22×Dic94—22no—
10C22×Dic94—21no—
11C22×Dic94—28no—
12C22×Dic94C2214yes—
13C22×Dic94C2212yes—
14C23×Dic47—21no—
15#13094057—28no—
16C2×Dic188C2214yescomplemented
17C2×#10625325C2214yescomplemented
18#13094007—21no—
19#13094003C2212yes—
20#13093998C2212yes—
21#13093993—21no—
22C4×C22⋊D47—22no—
23#13093983C2211yescharacteristic
24#13093949C2218yescomplemented
25C23×C4×C47C2211yescharacteristic
26C2×M16×C47C2212yes—
27C22⋊C8×C47C2214yes—
28C24×C47D411yescharacteristic
29C22×C4×C47—24no—
30C22×C4×C47D412yes—
31C22×C4×C47D411yescharacteristic
32C22×C4×C47C2312yes—
33C22×C4×C47C2311yescharacteristic
34C2×C22⋊D47—22no—
35C2×C22⋊D47—21no—
36C22×Dic47—28no—
37C22×Dic47—24no—
38C22×Dic47—22no—
39#10625350—24no—
40C2×D188C2311yescharacteristic
41C2×C4×D47—21no—
42C2×Dic94—28no—
43C2×Dic94—216no—
44C2×Dic94—24no—
45C2×Dic94—22no—
46C2×Dic94—24no—
47C2×Dic94—216no—
48C2×Dic94D418yescomplemented
49C2×Dic94C2311yescharacteristic
50C2×Dic94C2314yes—
51M16×C47—24no—
52C2×C8×C47C2314yes—
53C22⋊Dic47—21no—
54C22⋊Dic47—22no—
55(C2×D47)⋊C4—22no—
56C4⋊Dic47C2312yes—
57Dic47⋊C4—22no—
58C4×Dic47—21no—
59Dic188—28no—
60#10625325—28no—
61C23×C47—22no—
62C23×C47—24no—
63C23×C47C2×D411yescharacteristic
64C23×C47C2×D412yes—
65C22×D47—21no—
66C2×C4×C47—22no—
67C2×C4×C47—24no—
68C2×C4×C47—24no—
69C2×C4×C47C2×D412yes—
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D414yes—
72C2×C4×C47C2411yescharacteristic
73C22⋊D47—42no—
74C22⋊D47—44no—
75C2×Dic47—216no—
76C2×Dic47—28no—
77C2×Dic47—24no—
78C2×Dic47—22no—
79C2×Dic47—21no—
80D188—22no—
81C4×D47—42no—
82Dic94—216no—
83Dic94—28no—
84Dic94—24no—
85Dic94—22no—
86Dic94C2×D418yes—
87C8×C47—24no—
88C22×C47—28no—
89C22×C47—22no—
90C22×C47—22no—
91C22×C47—22no—
92C22×C47#12012yes—
93C22×C47#13714yescomplemented
94C22×C47C22×D411yescharacteristic
95C2×D47—41no—
96C2×D47—42no—
97C4×C47—22no—
98C4×C47#12012yes—
99C4×C47C22×D412yes—
100Dic47—28no—
101Dic47—41no—
102Dic47—42no—
103#3004—471nomaximal, Sylow
104C2×C47—22no—
105C2×C47—24no—
106C2×C47C2×#12011yescharacteristic
107C2×C47C2×#13712yes—
108D47—81no—
109C23×Q8—471no—
110C2×#137—472no—
111#525—471no—
112#451—474no—
113#448—474no—
114#419—472no—
115#407D4711yescharacteristic, complemented
116C47#300411yescharacteristic, complemented, Sylow
117C2×#41—471no—
118C22×Q8—472no—
119C22×Q8—474no—
120C22×Q8—948no—
121C22×Q8—942no—
122C22×Q8—941no—
123C23×C4—941no—
124C23×C4C2×D4711yescharacteristic
125#137—948no—
126C2×Q16—474no—
127C2×SD16—474no—
128C2×M16C2×D4712yes—
129#123—941no—
130C22⋊Q8—472no—
131#121—472no—
132#120—941no—
133C4×D4—942no—
134#117—471no—
135#103—478no—
136C22⋊C8C2×D4714yes—
137C24D18811yescharacteristic
138#41—944no—
139C2×Q8—478no—
140C2×Q8—474no—
141C2×Q8—471no—
142C2×Q8—9416no—
143C2×Q8—948no—
144C2×Q8—9416no—
145C2×Q8—944no—
146C2×Q8—942no—
147C2×Q8—944no—
148C2×D4—471no—
149C2×D4—942no—
150C2×D4—941no—
151C22×C4—24no—
152C22×C4—948no—
153C22×C4—944no—
154C22×C4—942no—
155C22×C4—941no—
156C22×C4D18812yes—
157C22×C4D18811yescharacteristic
158C22×C4C22×D4712yes—
159C22×C4C22×D4711yescharacteristic
160Q16—948no—
161SD16—948no—
162M16—24no—
163C2×C8C22×D4714yes—
164C4⋊C4—472no—
165C4⋊C4—942no—
166C22⋊C4—941no—
167C22⋊C4—942no—
168C22⋊C4—942no—
169C42—941no—
170C23—22no—
171C23—24no—
172C23—941no—
173C23C2×D18811yescharacteristic
174C23C2×D18812yes—
175Q8—478no—
176Q8—9416no—
177Q8—948no—
178Q8—944no—
179Q8—942no—
180D4—942no—
181D4—1882no—
182D4—1884no—
183C2×C4—22no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—9416no—
187C2×C4—948no—
188C2×C4—944no—
189C2×C4—942no—
190C2×C4—941no—
191C2×C4—1882no—
192C2×C4C2×D18812yes—
193C2×C4C2×D18811yescharacteristic
194C2×C4D4×D4714yes—
195C2×C4C23×D4711yescharacteristic
196C8—24no—
197C22—28no—
198C22—22no—
199C22—22no—
200C22—22no—
201C22—1881no—
202C22—1882no—
203C22#1309399412yes—
204C22#1309405714yescomplemented
205C22C22×D18811yescharacteristic
206C4—22no—
207C4—948no—
208C4—1881no—
209C4—1882no—
210C4#1309399412yes—
211C4C2×D4×D4712yes—
212C2—22no—
213C2—24no—
214C2—3761no—
215C2C2×#1309399411yescharacteristic
216C2C2×#1309405712yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#407C2
socleC22×C47C22×D4
hypercenter#407D47
hypocenterC47#3004
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. C23×Dic94C2semidirect
2. C2×#13094057C2semidirect
4. #15689281C2semidirect
5. #15689264C2semidirect
6. #15689133C2semidirect
7. C47×#407C2semidirect
16. C2×Dic188C22semidirect
17. C2×#10625325C22semidirect
24. #13093949C22semidirect
48. C2×Dic94D4semidirect
93. C22×C47#137semidirect
115. #407D47semidirect
116. C47#3004semidirect
204. C22#13094057semidirect