Finite Group Databasebeta

← #20241742

Subgroups — #20241742

Order 6016.

204 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 63 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×#13094014C211yesmaximal, characteristic
2#15689177C211yesmaximal, characteristic
3#15689173C211yesmaximal, characteristic
4#15688849C211yesmaximal, characteristic
5#15688848C211yesmaximal, characteristic
6#15688848C211yesmaximal, characteristic
7C47×#324C211yesmaximal, characteristic
8#13094014—21no—
9#13094014—21no—
10#13094014—21no—
11#13094014—21no—
12C2×C4⋊Dic47C411yescharacteristic
13C2×Dic47⋊C4C411yescharacteristic
14C2×Dic47⋊C4C411yescharacteristic
15C2×Dic47⋊C4C411yescharacteristic
16C2×Dic47⋊C4C2211yescharacteristic
17C2×C4×Dic47C2211yescharacteristic
18Dic47⋊C8—21no—
19Dic47⋊C8—21no—
20C22⋊(C47⋊C8)C2211yescharacteristic
21C22⋊(C47⋊C8)C2211yescharacteristic
22#13093934—21no—
23C8×Dic47—21no—
24C2×C4⋊C4×C47C2211yescharacteristic
25C22⋊C8×C47C2211yescharacteristic
26C22⋊C8×C47C2211yescharacteristic
27C22×C4×C47C2×C411yescharacteristic
28C22×C4×C47C2×C411yescharacteristic
29C22×C4×C47C2311yescharacteristic
30C22×Dic47C2×C411yescharacteristic
31C22×Dic47C2×C411yescharacteristic
32C22×Dic47C2×C411yescharacteristic
33C22×Dic47C2×C411yescharacteristic
34C2×C8×C47—21no—
35C2×C8×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊Dic47—21no—
39C4⋊Dic47—21no—
40Dic47⋊C4—21no—
41Dic47⋊C4—21no—
42Dic47⋊C4—21no—
43Dic47⋊C4—21no—
44Dic47⋊C4—21no—
45Dic47⋊C4—21no—
46Dic47⋊C4—21no—
47Dic47⋊C4—21no—
48C4×Dic47D411yescharacteristic
49C4×Dic47D411yescharacteristic
50C4×Dic47D411yescharacteristic
51C4×Dic47D411yescharacteristic
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C23×C47C22×C411yescharacteristic
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—41no—
60C2×C4×C47—41no—
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×Dic47—21no—
64C2×Dic47—21no—
65C2×Dic47—22no—
66C2×Dic47—21no—
67C2×Dic47—21no—
68C2×Dic47—21no—
69C2×Dic47—21no—
70C2×Dic47—41no—
71C2×Dic47C22⋊C411yescharacteristic
72C2×Dic47C22⋊C411yescharacteristic
73C2×Dic47C22⋊C411yescharacteristic
74C2×Dic47C22⋊C411yescharacteristic
75C8×C47—41no—
76C8×C47—41no—
77C47⋊C8—41no—
78C47⋊C8—41no—
79C22×C47—21no—
80C22×C47—21no—
81C22×C47C2×C22⋊C411yescharacteristic
82C22×C47#13111yescharacteristic
83C22×C47#13111yescharacteristic
84C4×C47—21no—
85C4×C47—21no—
86C4×C47—41no—
87C4×C47—41no—
88Dic47—21no—
89Dic47—21no—
90Dic47—21no—
91Dic47—41no—
92Dic47—41no—
93Dic47#10112yes—
94#1470—471nomaximal, Sylow
95C2×C47—21no—
96C2×C47—21no—
97C2×C47#40811yescharacteristic
98C2×C47#41011yescharacteristic
99C2×C47C2×#10111yescharacteristic
100C2×#125—471no—
101#432—471no—
102#431—471no—
103#324—471no—
104#324—471no—
105#324—471no—
106#324D4711yescharacteristic
107C47#147011yescharacteristic, complemented, Sylow
108#125—941no—
109#125—941no—
110#125—941no—
111#125—941no—
112C2×C4⋊C4—471no—
113C2×C4⋊C4—471no—
114C2×C4⋊C4—471no—
115C2×C4⋊C4—471no—
116C2×C4⋊C4—471no—
117C2×C4⋊C4C2×D4711yescharacteristic
118C2×C42—471no—
119C4⋊C8—941no—
120C4⋊C8—941no—
121C22⋊C8—471no—
122C22⋊C8—471no—
123C22⋊C8C2×D4711yescharacteristic
124C22⋊C8C2×D4711yescharacteristic
125#97—941no—
126C4×C8—941no—
127C22×C4—471no—
128C22×C4—471no—
129C22×C4—471no—
130C22×C4—471no—
131C22×C4C4×D4711yescharacteristic
132C22×C4C4×D4711yescharacteristic
133C22×C4C22×D4711yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—941no—
137C2×C8—941no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—941no—
141C4⋊C4—941no—
142C4⋊C4—941no—
143C4⋊C4—941no—
144C4⋊C4—941no—
145C4⋊C4—941no—
146C4⋊C4—941no—
147C4⋊C4—941no—
148C4⋊C4—941no—
149C4⋊C4—941no—
150C42—471no—
151C42—471no—
152C42—471no—
153C42—471no—
154C23C2×C4×D4711yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—471no—
162C2×C4—471no—
163C2×C4—471no—
164C2×C4—471no—
165C2×C4—942no—
166C2×C4—941no—
167C2×C4—941no—
168C2×C4—941no—
169C2×C4—941no—
170C2×C4—941no—
171C2×C4—941no—
172C2×C4—1881no—
173C2×C4D4×D4711yescharacteristic
174C2×C4D4×D4711yescharacteristic
175C8—41no—
176C8—41no—
177C8—1881no—
178C8—1881no—
179C22—21no—
180C22—21no—
181C22C22⋊C4×D4711yescharacteristic
182C22#1309403011yescharacteristic
183C22#1309403211yescharacteristic
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—472no—
189C4—941no—
190C4—941no—
191C4—941no—
192C4—1881no—
193C4—1881no—
194C2—21no—
195C2—21no—
196C2#1568908811yescharacteristic
197C2#1568909511yescharacteristic
198C2#101×D4711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#324C2
socleC22×C47C2×C22⋊C4
hypercenter#324D47
hypocenterC47#1470
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
107. C47#1470semidirect