Finite Group Databasebeta

← #20241850

Subgroups — #20241850

Order 6016.

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

normal subgroups only

This group has 216 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#15689174C211yesmaximal, characteristic, complemented
3#15689145C211yesmaximal, characteristic, complemented
4#15688855C211yesmaximal, characteristic, complemented
5#15688853C211yesmaximal, characteristic, complemented
6D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
7C47×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10625324—21no—
9#13094017—21no—
10#13094015C411yescharacteristic
11#13094011C411yescharacteristic
12#13094006—21no—
13#13094004C411yescharacteristic
14#13093995C411yescharacteristic
15C4×Dic94C2211yescharacteristic
16C4×C22⋊D47—21no—
17#13093983—21no—
18C42×D47C2211yescharacteristic
19C4⋊(C47⋊C8)C2211yescharacteristic
20Dic47⋊C8—21no—
21Dic47⋊C8—21no—
22(C2×D47)⋊C8—21no—
23C4×C47⋊C8C2211yescharacteristic
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—
54#10625324—42no—
55C23×C47—21no—
56C22×D47C22⋊C411yescharacteristic
57D4×C47—21no—
58D4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47C22×C411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C22⋊D47—42no—
66C2×Dic47—21no—
67C2×Dic47—21no—
68C2×Dic47C22⋊C411yescharacteristic
69C2×Dic47C22⋊C411yescharacteristic
70C2×Dic47C22⋊C411yescharacteristic
71C4×D47—21no—
72C4×D47—21no—
73C4×D47—21no—
74C4×D47—21no—
75C4×D47—41no—
76Dic94—21no—
77Dic94—21no—
78C8×C47—41no—
79C8×C47—41no—
80C47⋊C8—41no—
81C47⋊C8—41no—
82C22×C47—41no—
83C22×C47—41no—
84C22×C47—41no—
85C22×C47C2×C22⋊C411yescharacteristic
86C2×D47—21no—
87C2×D47—21no—
88C2×D47—21no—
89C4×C47—21no—
90C4×C47—41no—
91C4×C47#13111yescharacteristic
92C4×C47#13111yescharacteristic
93C4×C47AGL(1,ℤ/8)11yescharacteristic
94C4×C47#13711yescharacteristic
95Dic47—21no—
96Dic47—21no—
97Dic47—21no—
98Dic47—41no—
99Dic47—41no—
100#1495—471nomaximal, Sylow
101C2×C47—81no—
102C2×C47#40811yescharacteristic
103C2×C47#41711yescharacteristic
104C2×C47#42111yescharacteristic
105D47—41no—
106#529—471no—
107#431—471no—
108#423—471no—
109Q8⋊C8—471no—
110Q8⋊C8—471no—
111D4⋊C8—471no—
112D4⋊C8D4711yescharacteristic, complemented
113C47#149511yescharacteristic, complemented, Sylow
114C2×M16—941no—
115#126—941no—
116#125—471no—
117#124—471no—
118#123—941no—
119C22⋊Q8—471no—
120#121—471no—
121C4×Q8—471no—
122C4×D4—941no—
123C4×D4C2×D4711yescharacteristic
124#117—941no—
125C2×C42—471no—
126C4⋊C8—471no—
127C4⋊C8—941no—
128C4⋊C8—941no—
129C4⋊C8C2×D4711yescharacteristic
130C22⋊C8—941no—
131C4×C8—471no—
132C4×C8C2×D4711yescharacteristic
133C2×Q8—471no—
134C2×D4—941no—
135C2×D4C4×D4711yescharacteristic
136C22×C4—21no—
137C22×C4—471no—
138C22×C4—471no—
139C22×C4—471no—
140M16—1882no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—941no—
144C2×C8—941no—
145C4⋊C4—471no—
146C4⋊C4—941no—
147C4⋊C4—941no—
148C4⋊C4—941no—
149C4⋊C4—941no—
150C4⋊C4C4×D4711yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—941no—
153C22⋊C4—941no—
154C22⋊C4—941no—
155C22⋊C4—941no—
156C42—471no—
157C42—471no—
158C42—471no—
159C42—941no—
160C42C22×D4711yescharacteristic
161C23—21no—
162C23—471no—
163Q8—941no—
164Q8—941no—
165D4—21no—
166D4—21no—
167D4—1882no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—471no—
172C2×C4—471no—
173C2×C4—471no—
174C2×C4—941no—
175C2×C4—941no—
176C2×C4—941no—
177C2×C4—941no—
178C2×C4—941no—
179C2×C4—941no—
180C2×C4—1881no—
181C2×C4C2×C4×D4711yescharacteristic
182C2×C4D4×D4711yescharacteristic
183C2×C4D4×D4711yescharacteristic
184C8—41no—
185C8—41no—
186C8—1881no—
187C8—1881no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—941no—
192C22—941no—
193C22—941no—
194C22C22⋊C4×D4711yescharacteristic
195C4—21no—
196C4—41no—
197C4—941no—
198C4—941no—
199C4—941no—
200C4—1881no—
201C4—1881no—
202C4#1309403011yescharacteristic
203C4#1309403211yescharacteristic
204C4#1309404811yescharacteristic
205C4#1309405311yescharacteristic
206C2—81no—
207C2—1881no—
208C2#1568908811yescharacteristic
209C2#1568912111yescharacteristic
210C2#1568913811yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×D4⋊C8C2
socleC22×C47C2×C22⋊C4
hypercenterD4⋊C8D47
hypocenterC47#1495
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. #15689174C2semidirect
3. #15689145C2semidirect
4. #15688855C2semidirect
5. #15688853C2semidirect
6. D4⋊(C47⋊C8)C2semidirect
7. C47×D4⋊C8C2semidirect
112. D4⋊C8D47semidirect
113. C47#1495semidirect