Finite Group Databasebeta

← #20241793

Subgroups — #20241793

Order 6016.

212 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 65 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#15689655C211yesmaximal, characteristic
2#15689175C211yesmaximal, characteristic, complemented
3#15689174C211yesmaximal, characteristic, complemented
4#15688855C211yesmaximal, characteristic, complemented
5#15688853C211yesmaximal, characteristic, complemented
6D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
7C47×D4⋊C8C211yesmaximal, characteristic, complemented
8#13094017—21no—
9#13094015C411yescharacteristic
10#13094011C411yescharacteristic
11#13094006—21no—
12#13094004C411yescharacteristic
13#13093995C411yescharacteristic
14C4×Dic94C2211yescharacteristic
15C4×C22⋊D47—21no—
16#13093983—21no—
17C42×D47C2211yescharacteristic
18C4⋊(C47⋊C8)C2211yescharacteristic
19Dic47⋊C8—21no—
20(C2×D47)⋊C8—21no—
21(C2×D47)⋊C8—21no—
22C4×C47⋊C8C2211yescharacteristic
23C8×Dic47—21no—
24C4×D4×C47C2211yescharacteristic
25C4⋊C8×C47C2211yescharacteristic
26C4×C8×C47C2211yescharacteristic
27C2×D4×C47C2×C411yescharacteristic
28C22×C4×C47—21no—
29C2×C22⋊D47—21no—
30C2×C4×D47C2×C411yescharacteristic
31C2×C4×D47D411yescharacteristic
32C2×C4×D47D411yescharacteristic
33C2×Dic94C2×C411yescharacteristic
34C2×C8×C47—21no—
35C2×C8×C47—21no—
36C4⋊C4×C47C2×C411yescharacteristic
37C22⋊C4×C47—21no—
38C42×C47C2311yescharacteristic
39C22⋊Dic47—21no—
40C22⋊Dic47—21no—
41C22⋊Dic47—21no—
42(C2×D47)⋊C4—21no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45C4⋊Dic47C2×C411yescharacteristic
46Dic47⋊C4—21no—
47Dic47⋊C4—21no—
48C4×Dic47—21no—
49C4×Dic47C2×C411yescharacteristic
50C4×Dic47D411yescharacteristic
51C4×Dic47D411yescharacteristic
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C23×C47—21no—
55C22×D47C22⋊C411yescharacteristic
56D4×C47—21no—
57D4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—41no—
60C2×C4×C47—41no—
61C2×C4×C47C22×C411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C22⋊D47—42no—
65C2×Dic47—21no—
66C2×Dic47—21no—
67C2×Dic47C22⋊C411yescharacteristic
68C2×Dic47C22⋊C411yescharacteristic
69C2×Dic47C22⋊C411yescharacteristic
70C4×D47—21no—
71C4×D47—21no—
72C4×D47—21no—
73C4×D47—21no—
74C4×D47—41no—
75Dic94—21no—
76Dic94—21no—
77C8×C47—41no—
78C8×C47—41no—
79C47⋊C8—41no—
80C47⋊C8—41no—
81C22×C47—41no—
82C22×C47—41no—
83C22×C47—41no—
84C22×C47C2×C22⋊C411yescharacteristic
85C2×D47—21no—
86C2×D47—21no—
87C2×D47—21no—
88C4×C47—21no—
89C4×C47—41no—
90C4×C47#13111yescharacteristic
91C4×C47#13111yescharacteristic
92C4×C47#13511yescharacteristic
93C4×C47#13511yescharacteristic
94Dic47—21no—
95Dic47—21no—
96Dic47—21no—
97Dic47—41no—
98Dic47—41no—
99#1482—471nomaximal, Sylow
100C2×C47—81no—
101C2×C47#40811yescharacteristic
102C2×C47#41611yescharacteristic
103C2×C47#42111yescharacteristic
104D47—41no—
105#529—471no—
106#431—471no—
107#431—471no—
108Q8⋊C8—471no—
109Q8⋊C8—471no—
110D4⋊C8—471no—
111D4⋊C8D4711yescharacteristic, complemented
112C47#148211yescharacteristic, complemented, Sylow
113#126—941no—
114#125—471no—
115#124—471no—
116#123—941no—
117C22⋊Q8—471no—
118#121—471no—
119C4×Q8—471no—
120C4×D4—941no—
121C4×D4C2×D4711yescharacteristic
122#117—941no—
123C2×C42—471no—
124C4⋊C8—471no—
125C4⋊C8—941no—
126C4⋊C8C2×D4711yescharacteristic
127C22⋊C8—941no—
128C22⋊C8—941no—
129C4×C8—471no—
130C4×C8—941no—
131C4×C8C2×D4711yescharacteristic
132C2×Q8—471no—
133C2×D4—941no—
134C2×D4C4×D4711yescharacteristic
135C22×C4—21no—
136C22×C4—471no—
137C22×C4—471no—
138C22×C4—471no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—941no—
142C2×C8—941no—
143C4⋊C4—471no—
144C4⋊C4—941no—
145C4⋊C4—941no—
146C4⋊C4—941no—
147C4⋊C4—941no—
148C4⋊C4C4×D4711yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—941no—
151C22⋊C4—941no—
152C22⋊C4—941no—
153C22⋊C4—941no—
154C42—471no—
155C42—471no—
156C42—471no—
157C42—941no—
158C42C22×D4711yescharacteristic
159C23—21no—
160C23—471no—
161Q8—941no—
162Q8—941no—
163D4—21no—
164D4—21no—
165D4—1882no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—471no—
170C2×C4—471no—
171C2×C4—471no—
172C2×C4—941no—
173C2×C4—941no—
174C2×C4—941no—
175C2×C4—941no—
176C2×C4—941no—
177C2×C4—941no—
178C2×C4—1881no—
179C2×C4C2×C4×D4711yescharacteristic
180C2×C4D4×D4711yescharacteristic
181C2×C4D4×D4711yescharacteristic
182C8—41no—
183C8—41no—
184C8—1881no—
185C8—1881no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—941no—
190C22—941no—
191C22—941no—
192C22C22⋊C4×D4711yescharacteristic
193C4—21no—
194C4—41no—
195C4—941no—
196C4—941no—
197C4—941no—
198C4—1881no—
199C4—1881no—
200C4#1309403011yescharacteristic
201C4#1309403211yescharacteristic
202C4#1309404311yescharacteristic
203C4#1309404511yescharacteristic
204C2—81no—
205C2—1881no—
206C2#1568908811yescharacteristic
207C2#1568911611yescharacteristic
208C2#1568913811yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×D4⋊C8C2
socleC22×C47C2×C22⋊C4
hypercenterD4⋊C8D47
hypocenterC47#1482
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #15689175C2semidirect
3. #15689174C2semidirect
4. #15688855C2semidirect
5. #15688853C2semidirect
6. D4⋊(C47⋊C8)C2semidirect
7. C47×D4⋊C8C2semidirect
111. D4⋊C8D47semidirect
112. C47#1482semidirect