Finite Group Databasebeta

← #20253321

Subgroups — #20253321

Order 6016.

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

normal subgroups only

This group has 414 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#15689634C211yesmaximal, characteristic
2C2×#13093983C211yesmaximal, characteristic, complemented
3#15689465C214yesmaximal, complemented
4#15689448C214yesmaximal, complemented
5#15689165C212yesmaximal, complemented
6#15689125C212yesmaximal, complemented
7C47×#407C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094007—21no—
10#13094003C2212yes—
11#13093998C2212yes—
12#13093993—21no—
13C4×C22⋊D47—22no—
14#13093983—22no—
15#13093983C2214yes—
16#13093983C2211yescharacteristic
17C2×C4⋊Dic47C2212yes—
18C2×C22⋊Dic47—21no—
19C2×C4×Dic47—21no—
20#13093958C2214yescomplemented
21#13093956C2214yescomplemented
22#13093949C2214yescomplemented
23#13093946C2214yescomplemented
24C23×C4×C47C2211yescharacteristic
25C2×M16×C47C2212yes—
26C22⋊C8×C47C2214yes—
27C24×C47D411yescharacteristic
28C22×C4×C47—24no—
29C22×C4×C47D411yescharacteristic
30C22×C4×C47D412yes—
31C22×C4×C47C2312yes—
32C22×C4×C47C2311yescharacteristic
33C2×C22⋊D47—22no—
34C2×C22⋊D47—21no—
35C22×Dic47—22no—
36#10625350—24no—
37C2×D188C2311yescharacteristic
38C2×C4×D47—21no—
39C2×Dic94C2311yescharacteristic
40M16×C47—24no—
41C2×C8×C47C2314yes—
42C22⋊Dic47—24no—
43C22⋊Dic47—21no—
44C22⋊Dic47—22no—
45(C2×D47)⋊C4—22no—
46C4⋊Dic47—22no—
47C4⋊Dic47C2314yes—
48C4⋊Dic47C2312yes—
49Dic47⋊C4—22no—
50C4×Dic47—24no—
51C4×Dic47—21no—
52C23×C47—22no—
53C23×C47—42no—
54C23×C47C2×D412yes—
55C23×C47C2×D411yescharacteristic
56C22×D47—21no—
57C2×C4×C47—22no—
58C2×C4×C47—24no—
59C2×C4×C47—24no—
60C2×C4×C47C2×D412yes—
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47#4114yes—
63C2×C4×C47C2411yescharacteristic
64C22⋊D47—44no—
65C22⋊D47—42no—
66C2×Dic47—24no—
67C2×Dic47—22no—
68C2×Dic47—21no—
69C2×Dic47—44no—
70D188—22no—
71C4×D47—42no—
72Dic94—22no—
73C8×C47—24no—
74C22×C47—22no—
75C22×C47—22no—
76C22×C47—22no—
77C22×C47—22no—
78C22×C47—44no—
79C22×C47#12312yes—
80C22×C47C22×D411yescharacteristic
81C2×D47—41no—
82C2×D47—42no—
83C4×C47—22no—
84C4×C47#12312yes—
85C4×C47C2×#4112yes—
86Dic47—41no—
87Dic47—44no—
88Dic47—42no—
89#3093—471nomaximal, Sylow
90C2×C47—22no—
91C2×C47—42no—
92C2×C47C2×#12311yescharacteristic
93C2×C47#57512yes—
94D47—81no—
95#525—471no—
96C2×#117—471no—
97#485—474no—
98#482—474no—
99#428—472no—
100#417—472no—
101#407D4711yescharacteristic, complemented
102C47#309311yescharacteristic, complemented, Sylow
103C2×#41—471no—
104C23×C4C2×D4711yescharacteristic
105C2×M16C2×D4712yes—
106#123—941no—
107C22⋊Q8—472no—
108#121—472no—
109#120—941no—
110C4×D4—942no—
111#117—474no—
112#117—471no—
113#117—942no—
114C2×C4⋊C4—472no—
115C2×C22⋊C4—941no—
116C2×C42—941no—
117#107—474no—
118#106—474no—
119#103—474no—
120#102—474no—
121C22⋊C8C2×D4714yes—
122C24D18811yescharacteristic
123#41—944no—
124C2×Q8—471no—
125C2×D4—471no—
126C2×D4—942no—
127C2×D4—941no—
128C22×C4—24no—
129C22×C4—942no—
130C22×C4—941no—
131C22×C4D18811yescharacteristic
132C22×C4D18812yes—
133C22×C4C22×D4712yes—
134C22×C4C22×D4711yescharacteristic
135M16—24no—
136C2×C8C22×D4714yes—
137C4⋊C4—474no—
138C4⋊C4—472no—
139C4⋊C4—942no—
140C4⋊C4—942no—
141C22⋊C4—944no—
142C22⋊C4—941no—
143C22⋊C4—942no—
144C22⋊C4—942no—
145C42—944no—
146C42—941no—
147C23—22no—
148C23—42no—
149C23—941no—
150C23C2×D18812yes—
151C23C2×D18811yescharacteristic
152Q8—942no—
153D4—942no—
154D4—1884no—
155D4—1882no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—944no—
160C2×C4—942no—
161C2×C4—941no—
162C2×C4—1884no—
163C2×C4—1882no—
164C2×C4C2×D18812yes—
165C2×C4C2×D18811yescharacteristic
166C2×C4#1062535214yes—
167C2×C4C23×D4711yescharacteristic
168C8—24no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—1881no—
175C22—1882no—
176C22#1309400812yes—
177C22C22×D18811yescharacteristic
178C4—22no—
179C4—1881no—
180C4—1884no—
181C4—1882no—
182C4#1309400812yes—
183C4C2×#1062535212yes—
184C2—22no—
185C2—42no—
186C2—3761no—
187C2C2×#1309400811yescharacteristic
188C2#1568992312yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#407C2
socleC22×C47C22×D4
hypercenter#407D47
hypocenterC47#3093
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#13093983C2semidirect
3. #15689465C2semidirect
4. #15689448C2semidirect
5. #15689165C2semidirect
6. #15689125C2semidirect
7. C47×#407C2semidirect
20. #13093958C22semidirect
21. #13093956C22semidirect
22. #13093949C22semidirect
23. #13093946C22semidirect
101. #407D47semidirect
102. C47#3093semidirect