Finite Group Databasebeta

← #20249100

Subgroups — #20249100

Order 6016.

1134 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C2×#13094007C211yesmaximal, characteristic, complemented
2C2×#13093993C212yesmaximal, complemented
3#15689037C214yesmaximal, complemented
4#15689031C214yesmaximal, complemented
5#15688986C211yesmaximal, characteristic, complemented
6#15688979C212yesmaximal, complemented
7C23×D4×C47C211yesmaximal, characteristic, complemented
8C22×C22⋊D47C2211yescharacteristic
9C22×C22⋊D47C2214yescomplemented
10#13094007—24no—
11#13093993—28no—
12C2×Dic47⋊C4C2212yescomplemented
13C2×C22⋊Dic47C2211yescharacteristic
14C2×C22⋊Dic47C2212yes—
15C2×C22⋊Dic47C2214yescomplemented
16C2×C22⋊Dic47C2218yescomplemented
17C2×(C2×D47)⋊C4C2212yescomplemented
18C47⋊#95C2214yescomplemented
19C25×C47C2212yes—
20C22×D4×C47—28no—
21C22×D4×C47—24no—
22C22×D4×C47C2214yes—
23C23×C4×C47C2211yescharacteristic
24C24×C47—24no—
25C24×C47—24no—
26C24×C47—48no—
27C24×C47D418yescomplemented
28C24×C47C2314yes—
29C24×C47C2311yescharacteristic
30C23×D47C2311yescharacteristic
31C2×D4×C47—232no—
32C2×D4×C47—216no—
33C2×D4×C47—28no—
34C22×C4×C47—24no—
35C22×C4×C47D414yescomplemented
36C22×C4×C47C2312yes—
37C2×C22⋊D47—24no—
38C2×C22⋊D47—28no—
39C2×C22⋊D47—22no—
40C2×C22⋊D47—48no—
41C22×Dic47C2314yes—
42C22×Dic47C2312yes—
43C22×Dic47C2311yescharacteristic
44C22⋊Dic47—24no—
45C22⋊Dic47—22no—
46C22⋊Dic47—28no—
47C22⋊Dic47—48no—
48(C2×D47)⋊C4—24no—
49Dic47⋊C4—24no—
50C23×C47—24no—
51C23×C47—216no—
52C23×C47—24no—
53C23×C47—24no—
54C23×C47—28no—
55C23×C47—28no—
56C23×C47—416no—
57C23×C47—416no—
58C23×C47—416no—
59C23×C47C2×D418yes—
60C23×C47C2×D414yes—
61C23×C47C2×D412yes—
62C23×C47C2411yescharacteristic
63C22×D47—21no—
64C22×D47—22no—
65C22×D47—24no—
66D4×C47—232no—
67C2×C4×C47—28no—
68C2×C4×C47—24no—
69C2×C4×C47C2×D414yes—
70C22⋊D47—416no—
71C22⋊D47—44no—
72C2×Dic47—21no—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—24no—
76C2×Dic47—24no—
77C2×Dic47—28no—
78C22×C47—28no—
79C22×C47—24no—
80C22×C47—28no—
81C22×C47—28no—
82C22×C47—28no—
83C22×C47—432no—
84C22×C47—48no—
85C22×C47—48no—
86C22×C47#12014yes—
87C22×C47C22×D412yes—
88C22×C47C22×D411yescharacteristic
89C22×C47H(5,𝔽2)14yes—
90C2×D47—41no—
91C2×D47—44no—
92C2×D47—42no—
93C4×C47—24no—
94Dic47—41no—
95Dic47—44no—
96Dic47—42no—
97#2613—471nomaximal, Sylow
98C2×C47—24no—
99C2×C47—48no—
100C2×C47C2×#12011yescharacteristic
101C2×C47#53414yes—
102C2×C47#53512yes—
103D47—81no—
104C23×D4D4711yescharacteristic, complemented
105C2×#123—471no—
106C2×#120—472no—
107#394—474no—
108#392—474no—
109#381—471no—
110#379—472no—
111C47#261311yescharacteristic, complemented, Sylow
112C25C2×D4712yes—
113C22×D4—28no—
114C22×D4—24no—
115C22×D4—471no—
116C22×D4—474no—
117C22×D4C2×D4714yes—
118C23×C4C2×D4711yescharacteristic
119#123—944no—
120#120—948no—
121C2×C4⋊C4—472no—
122C2×C22⋊C4—472no—
123C2×C22⋊C4—474no—
124C2×C22⋊C4—471no—
125C2×C22⋊C4—472no—
126C2×C22⋊C4—478no—
127#95—474no—
128C24—24no—
129C24—24no—
130C24—48no—
131C24—471no—
132C24C22⋊D4718yescomplemented
133C24C22×D4714yes—
134C24C22×D4711yescharacteristic
135C2×D4—232no—
136C2×D4—216no—
137C2×D4—28no—
138C2×D4—948no—
139C2×D4—944no—
140C2×D4—942no—
141C2×D4—1888no—
142C22×C4—24no—
143C22×C4—474no—
144C22×C4—472no—
145C22×C4—471no—
146C22×C4C22⋊D4714yescomplemented
147C22×C4C22×D4712yes—
148C4⋊C4—944no—
149C22⋊C4—948no—
150C22⋊C4—944no—
151C22⋊C4—942no—
152C22⋊C4—944no—
153C22⋊C4—1888no—
154C23—24no—
155C23—216no—
156C23—24no—
157C23—24no—
158C23—28no—
159C23—28no—
160C23—416no—
161C23—416no—
162C23—416no—
163C23—941no—
164C23—942no—
165C23—944no—
166C23C2×C22⋊D4718yes—
167C23C2×C22⋊D4714yes—
168C23C2×C22⋊D4712yes—
169C23C23×D4711yescharacteristic
170D4—232no—
171D4—18816no—
172D4—1884no—
173C2×C4—28no—
174C2×C4—24no—
175C2×C4—942no—
176C2×C4—942no—
177C2×C4—944no—
178C2×C4—941no—
179C2×C4—944no—
180C2×C4—948no—
181C2×C4C2×C22⋊D4714yes—
182C22—28no—
183C22—24no—
184C22—28no—
185C22—28no—
186C22—28no—
187C22—432no—
188C22—48no—
189C22—48no—
190C22—1881no—
191C22—1884no—
192C22—1882no—
193C22#1309399314yes—
194C22C22×C22⋊D4712yes—
195C22C22×C22⋊D4711yescharacteristic
196C22#1309406914yes—
197C4—24no—
198C4—1881no—
199C4—1884no—
200C4—1882no—
201C2—24no—
202C2—48no—
203C2—3761no—
204C2C2×#1309399311yescharacteristic
205C2#1568968214yes—
206C2#1568969012yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC23×D4×C47C2
hypercenterC23×D4D47
hypocenterC47#2613
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C2×#13094007C2semidirect
2. C2×#13093993C2semidirect
3. #15689037C2semidirect
4. #15689031C2semidirect
5. #15688986C2semidirect
6. #15688979C2semidirect
7. C23×D4×C47C2semidirect
9. C22×C22⋊D47C22semidirect
12. C2×Dic47⋊C4C22semidirect
15. C2×C22⋊Dic47C22semidirect
16. C2×C22⋊Dic47C22semidirect
17. C2×(C2×D47)⋊C4C22semidirect
18. C47⋊#95C22semidirect
27. C24×C47D4semidirect
35. C22×C4×C47D4semidirect
104. C23×D4D47semidirect
111. C47#2613semidirect
132. C24C22⋊D47semidirect
146. C22×C4C22⋊D47semidirect