Finite Group Databasebeta

← #20253487

Subgroups — #20253487

Order 6016.

444 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 133 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#15689680C211yesmaximal, characteristic, complemented
2#15689458C212yesmaximal, complemented
3#15689403C212yesmaximal, complemented
4#15689328C212yesmaximal, complemented
5#15689274C212yesmaximal
6#15689223C214yesmaximal, complemented
7#15689180C211yesmaximal, characteristic, complemented
8C2×C4×D4×C47C211yesmaximal, characteristic
9C2×#10625335C2214yes—
10#13094024C2211yescharacteristic, complemented
11#13094024C2211yescharacteristic, complemented
12#13094016—21no—
13#13094003—21no—
14#13094003C2212yes—
15C4×Dic94—21no—
16C4×Dic94C2212yescomplemented
17#13093983—21no—
18#13093957C2214yescomplemented
19C4⋊(C47⋊C8)C2212yescomplemented
20#13093947C2214yescomplemented
21#13093945C2214yes—
22C22⋊(C47⋊C8)C2212yes—
23#13093935C2212yescomplemented
24C22×D4×C47C2211yescharacteristic
25C23×C4×C47—21no—
26C4×D4×C47—21no—
27C4×D4×C47—21no—
28C4×D4×C47C2212yes—
29C4×D4×C47C2212yes—
30C2×C4⋊C4×C47C2211yescharacteristic
31C2×C22⋊C4×C47—21no—
32C2×C42×C47C2211yescharacteristic
33C24×C47—21no—
34C2×D4×C47—24no—
35C2×D4×C47—21no—
36C2×D4×C47C2312yes—
37C22×C4×C47—21no—
38C22×C4×C47—22no—
39C22×C4×C47—22no—
40C22×C4×C47—44no—
41C22×C4×C47D411yescharacteristic
42C22×C4×C47D411yescharacteristic
43C22×C4×C47C2311yescharacteristic
44C2×Dic94—21no—
45C2×Dic94C2312yes—
46C4⋊C4×C47—21no—
47C4⋊C4×C47C2312yes—
48C22⋊C4×C47—22no—
49C22⋊C4×C47—22no—
50C42×C47D411yescharacteristic
51C42×C47D411yescharacteristic
52C42×C47C2311yescharacteristic
53C42×C47C2311yescharacteristic
54C22⋊Dic47—22no—
55#10625335—28no—
56C4⋊Dic47—21no—
57C4⋊Dic47—21no—
58C4⋊Dic47—21no—
59C4⋊Dic47C2312yes—
60Dic47⋊C4—22no—
61Dic47⋊C4—22no—
62C4×Dic47—22no—
63C2×C47⋊C8C2314yes—
64C23×C47—24no—
65C23×C47—22no—
66C23×C47—42no—
67C23×C47—42no—
68C23×C47C2×D411yescharacteristic
69D4×C47—24no—
70D4×C47—22no—
71D4×C47#4114yes—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—44no—
77C2×C4×C47—42no—
78C2×C4×C47—44no—
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2411yescharacteristic
85C2×Dic47—22no—
86C2×Dic47—22no—
87Dic94—24no—
88Dic94—42no—
89C47⋊C8—24no—
90C22×C47—21no—
91C22×C47—21no—
92C22×C47—24no—
93C22×C47—48no—
94C22×C47—42no—
95C22×C47—42no—
96C22×C47#13712yes—
97C22×C47C22×D411yescharacteristic
98C4×C47—21no—
99C4×C47—21no—
100C4×C47—21no—
101C4×C47—21no—
102C4×C47—42no—
103C4×C47AGL(1,ℤ/8)12yes—
104C4×C47C2×#4112yes—
105Dic47—42no—
106Dic47—42no—
107#3110—471nomaximal, Sylow
108C2×C47—22no—
109C2×C47—44no—
110C2×C47#52511yescharacteristic
111C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
112C2×C47C2×#13711yescharacteristic
113#533—471no—
114C2×C4×D4D4711yescharacteristic
115#484—472no—
116#474—472no—
117#461—472no—
118#450—472no—
119#440—474no—
120#432—471no—
121C47#311011yescharacteristic, complemented, Sylow
122C22×D4C2×D4711yescharacteristic
123C23×C4—21no—
124C2×SD16—474no—
125C4⋊Q8—471no—
126C4⋊Q8—471no—
127#125—941no—
128C22⋊Q8—472no—
129C22⋊Q8—941no—
130C4×Q8—472no—
131C4×Q8—941no—
132C4×D4—21no—
133C4×D4—21no—
134C4×D4C2×D4712yes—
135C4×D4C2×D4712yes—
136#117—941no—
137C2×C4⋊C4C2×D4711yescharacteristic
138C2×C22⋊C4—21no—
139C2×C42C2×D4711yescharacteristic
140#107—474no—
141C4⋊C8—472no—
142#103—474no—
143#102—474no—
144C22⋊C8—472no—
145#97—472no—
146C24—21no—
147C2×Q8—472no—
148C2×Q8—941no—
149C2×D4—24no—
150C2×D4—21no—
151C2×D4C22×D4712yes—
152C22×C4—21no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—44no—
156C22×C4C22⋊D4711yescharacteristic
157C22×C4C22⋊D4711yescharacteristic
158C22×C4C22×D4711yescharacteristic
159SD16—948no—
160C2×C8—474no—
161C4⋊C4—21no—
162C4⋊C4—472no—
163C4⋊C4—942no—
164C4⋊C4—942no—
165C4⋊C4—941no—
166C4⋊C4—941no—
167C4⋊C4—941no—
168C4⋊C4C22×D4712yes—
169C22⋊C4—22no—
170C22⋊C4—22no—
171C22⋊C4—942no—
172C42—942no—
173C42C22⋊D4711yescharacteristic
174C42C22⋊D4711yescharacteristic
175C42C22×D4711yescharacteristic
176C42C22×D4711yescharacteristic
177C23—24no—
178C23—22no—
179C23—42no—
180C23—42no—
181C23C2×C22⋊D4711yescharacteristic
182Q8—944no—
183Q8—1882no—
184D4—24no—
185D4—22no—
186D4#1062535014yes—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—44no—
192C2×C4—42no—
193C2×C4—44no—
194C2×C4—942no—
195C2×C4—942no—
196C2×C4C2×C22⋊D4711yescharacteristic
197C2×C4C2×C22⋊D4711yescharacteristic
198C2×C4C2×C22⋊D4711yescharacteristic
199C2×C4C2×C22⋊D4711yescharacteristic
200C2×C4C2×C22⋊D4711yescharacteristic
201C2×C4C23×D4711yescharacteristic
202C8—944no—
203C22—21no—
204C22—21no—
205C22—24no—
206C22—48no—
207C22—42no—
208C22—42no—
209C22#1309405412yes—
210C22C22×C22⋊D4711yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—21no—
215C4—42no—
216C4—1882no—
217C4—1882no—
218C4#1309405012yes—
219C4C2×#1062535012yes—
220C2—22no—
221C2—44no—
222C2#1568963411yescharacteristic
223C2C2×#1309405011yescharacteristic
224C2C2×#1309405411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×C4×D4×C47C2
socleC22×C47C22×D4
hypercenterC2×C4×D4D47
hypocenterC47#3110
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #15689680C2semidirect
2. #15689458C2semidirect
3. #15689403C2semidirect
4. #15689328C2semidirect
6. #15689223C2semidirect
7. #15689180C2semidirect
10. #13094024C22semidirect
11. #13094024C22semidirect
16. C4×Dic94C22semidirect
18. #13093957C22semidirect
19. C4⋊(C47⋊C8)C22semidirect
20. #13093947C22semidirect
23. #13093935C22semidirect
121. C47#3110semidirect