Finite Group Databasebeta

← #20241824

Subgroups — #20241824

Order 6016.

266 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C4×#10625352C211yesmaximal, characteristic
2#15689145C211yesmaximal, characteristic, complemented
3C4×#10625324C211yesmaximal, characteristic, complemented
4#15688855C211yesmaximal, characteristic, complemented
5#15688853C211yesmaximal, characteristic, complemented
6D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
7C47×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10625352C411yescharacteristic
9C2×#10625324—21no—
10C2×#10625324—21no—
11C4×Dic94C2211yescharacteristic
12#13093989C411yescharacteristic
13D4×Dic47C411yescharacteristic
14C4×C22⋊D47—21no—
15(C22⋊D47)⋊C4—21no—
16#13093982C411yescharacteristic
17#13093980—21no—
18C2×C4×Dic47—21no—
19C42×D47C2211yescharacteristic
20C4⋊(C47⋊C8)C2211yescharacteristic
21Dic47⋊C8—21no—
22#13093934—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—
30C22×Dic47—21no—
31C22×Dic47—21no—
32#10625352—22no—
33#10625352—22no—
34C2×C4×D47C2×C411yescharacteristic
35C2×C4×D47D411yescharacteristic
36C2×C4×D47D411yescharacteristic
37C2×Dic94C2×C411yescharacteristic
38C2×C8×C47—21no—
39C2×C8×C47—21no—
40C4⋊C4×C47C2×C411yescharacteristic
41C22⋊C4×C47—21no—
42C42×C47C2311yescharacteristic
43C22⋊Dic47—21no—
44(C2×D47)⋊C4—21no—
45C4⋊Dic47C2×C411yescharacteristic
46Dic47⋊C4—21no—
47Dic47⋊C4—21no—
48C4×Dic47—21no—
49C4×Dic47—21no—
50C4×Dic47—21no—
51C4×Dic47C2×C411yescharacteristic
52C4×Dic47D411yescharacteristic
53C4×Dic47D411yescharacteristic
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56#10625324—24no—
57#10625324—42no—
58C23×C47—21no—
59C22×D47C22⋊C411yescharacteristic
60D4×C47—21no—
61D4×C47M1612yescomplemented
62C2×C4×C47—21no—
63C2×C4×C47—41no—
64C2×C4×C47—41no—
65C2×C4×C47C22×C411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C22⋊D47—24no—
69C2×Dic47—24no—
70C2×Dic47—21no—
71C2×Dic47—21no—
72C2×Dic47—42no—
73C2×Dic47C22⋊C411yescharacteristic
74C2×Dic47C22⋊C411yescharacteristic
75C2×Dic47C22⋊C411yescharacteristic
76C4×D47—21no—
77C4×D47—21no—
78C4×D47—21no—
79C4×D47—21no—
80C4×D47—22no—
81Dic94—21no—
82Dic94M1612yescomplemented
83C8×C47—22no—
84C8×C47—41no—
85C47⋊C8—22no—
86C47⋊C8—41no—
87C22×C47—22no—
88C22×C47—41no—
89C22×C47—41no—
90C22×C47C2×C22⋊C411yescharacteristic
91C2×D47—21no—
92C2×D47—21no—
93C2×D47—21no—
94C4×C47—21no—
95C4×C47—41no—
96C4×C47C2×M1611yescharacteristic
97C4×C47C2×M1611yescharacteristic
98C4×C47AGL(1,ℤ/8)11yescharacteristic
99C4×C47#13711yescharacteristic
100Dic47—22no—
101Dic47—21no—
102Dic47—21no—
103Dic47—41no—
104Dic47#10412yes—
105#1489—471nomaximal, Sylow
106C2×C47—42no—
107C2×C47#40711yescharacteristic
108C2×C47#41711yescharacteristic
109C2×C47C2×#10411yescharacteristic
110D47—41no—
111C4×#41—471no—
112#423—471no—
113C4×M16—471no—
114Q8⋊C8—471no—
115Q8⋊C8—471no—
116D4⋊C8—471no—
117D4⋊C8D4711yescharacteristic, complemented
118C47#148911yescharacteristic, complemented, Sylow
119C2×#41—471no—
120C2×M16—941no—
121C2×M16—941no—
122C4×Q8—471no—
123C4×Q8—471no—
124C4×D4—471no—
125C4×D4—941no—
126C4×D4—941no—
127C4×D4C2×D4711yescharacteristic
128#117—471no—
129#117—941no—
130C2×C42—471no—
131C2×C42—941no—
132C4⋊C8—471no—
133C4⋊C8—941no—
134C4⋊C8C2×D4711yescharacteristic
135#97—941no—
136C4×C8—471no—
137C4×C8C2×D4711yescharacteristic
138#41—942no—
139#41—942no—
140C2×Q8—471no—
141C2×D4—941no—
142C2×D4C4×D4711yescharacteristic
143C22×C4—21no—
144C22×C4—471no—
145C22×C4—471no—
146C22×C4—471no—
147C22×C4—941no—
148C22×C4—941no—
149M16—944no—
150M16—1882no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—941no—
154C2×C8—941no—
155C4⋊C4—471no—
156C4⋊C4—941no—
157C4⋊C4—941no—
158C4⋊C4C4×D4711yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—941no—
161C22⋊C4—941no—
162C42—471no—
163C42—471no—
164C42—471no—
165C42—941no—
166C42—941no—
167C42—941no—
168C42C22×D4711yescharacteristic
169C23—21no—
170C23—471no—
171Q8—472no—
172Q8—941no—
173D4—21no—
174D4—944no—
175D4#1062532412yescomplemented
176C2×C4—21no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—471no—
180C2×C4—471no—
181C2×C4—471no—
182C2×C4—942no—
183C2×C4—944no—
184C2×C4—941no—
185C2×C4—941no—
186C2×C4—941no—
187C2×C4—941no—
188C2×C4—941no—
189C2×C4—941no—
190C2×C4—1882no—
191C2×C4C2×C4×D4711yescharacteristic
192C2×C4D4×D4711yescharacteristic
193C2×C4D4×D4711yescharacteristic
194C8—22no—
195C8—41no—
196C8—942no—
197C8—1881no—
198C22—22no—
199C22—41no—
200C22—41no—
201C22—941no—
202C22—941no—
203C22—941no—
204C22C22⋊C4×D4711yescharacteristic
205C4—21no—
206C4—41no—
207C4—472no—
208C4—941no—
209C4—942no—
210C4—941no—
211C4—1881no—
212C4M16×D4711yescharacteristic
213C4C2×#1062532411yescharacteristic
214C4#1309404811yescharacteristic
215C4#1309405311yescharacteristic
216C2—42no—
217C2—1881no—
218C2#1568908511yescharacteristic
219C2#1568912111yescharacteristic
220C2#104×D4711yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×D4⋊C8C2
socleC22×C47C2×C22⋊C4
hypercenterD4⋊C8D47
hypocenterC47#1489
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. #15689145C2semidirect
3. C4×#10625324C2semidirect
4. #15688855C2semidirect
5. #15688853C2semidirect
6. D4⋊(C47⋊C8)C2semidirect
7. C47×D4⋊C8C2semidirect
61. D4×C47M16semidirect
82. Dic94M16semidirect
117. D4⋊C8D47semidirect
118. C47#1489semidirect
175. D4#10625324semidirect