Finite Group Databasebeta

← C22×#13093947 #20251877

Subgroups — C22×#13093947 #20251877

Order 6016.

816 conjugacy classes of subgroups; only the 349 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 349 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
1C23×Dic94C211yesmaximal, characteristic
2C23×C47⋊C8C211yesmaximal, characteristic
3C2×#13093947C2112yesmaximal, direct product factor
4C22×C4⋊C4×C47C211yesmaximal, characteristic
5C22×Dic94—23no—
6C22×Dic94—24no—
7C22×Dic94C418yescomplemented
8C22×Dic94C2216yes—
9C23×Dic47—21no—
10C22×C47⋊C8—24no—
11C22×C47⋊C8C2216yes—
12#13093947C22116yesdirect product factor
13C23×C4×C47—21no—
14C23×C4×C47C2211yescharacteristic
15C2×C4⋊C4×C47—23no—
16C2×C4⋊C4×C47C2216yes—
17C24×C47D411yescharacteristic
18C22×C4×C47—26no—
19C22×C4×C47—44no—
20C22×C4×C47C2×C414yes—
21C22×C4×C47D413yes—
22C22×C4×C47D414yes—
23C22×C4×C47C2313yes—
24C22×Dic47—28no—
25C22×Dic47—26no—
26C2×Dic94—224no—
27C2×Dic94—26no—
28C2×Dic94—212no—
29C2×Dic94C2×C4124yescomplemented
30C2×Dic94C2314yes—
31C4⋊C4×C47—26no—
32C4⋊C4×C47C2314yes—
33C2×C47⋊C8—212no—
34C2×C47⋊C8C2314yes—
35C23×C47C22⋊C414yes—
36C23×C47SD1614yes—
37C23×C47Q1614yes—
38C23×C47C2×D413yes—
39C2×C4×C47—24no—
40C2×C4×C47—412no—
41C2×C4×C47C22⋊C4112yes—
42C2×C4×C47C22×C416yes—
43C2×C4×C47C2×D416yes—
44C2×C4×C47C2×D413yes—
45C2×C4×C47C2411yescharacteristic
46C2×Dic47—224no—
47C2×Dic47—24no—
48Dic94—224no—
49Dic94—24no—
50Dic94C22×C418yescomplemented
51C47⋊C8—24no—
52C22×C47#103116yescomplemented
53C22×C47C2×C22⋊C416yes—
54C22×C47C2×SD1616yes—
55C22×C47C2×Q1616yes—
56C22×C47C22×D411yescharacteristic
57C4×C47—44no—
58C4×C47C2×C22⋊C416yes—
59C4×C47C23×C411yescharacteristic
60C4×C47C22×D411yescharacteristic
61Dic47—28no—
62C22×#103—471nomaximal, Sylow
63C2×C47C2×#103112yescomplemented
64C2×C47C22×C22⋊C411yescharacteristic
65C2×C47C22×SD1611yescharacteristic
66C2×C47C22×Q1611yescharacteristic
67C23×Q8—471no—
68C23×C8—471no—
69C22×C4⋊C4D4711yescharacteristic
70C2×#103—4712no—
71C47C22×#10311yescharacteristic, complemented, Sylow
72C22×Q8—478no—
73C22×Q8—476no—
74C22×Q8—944no—
75C22×Q8—943no—
76C23×C4—21no—
77C23×C4—941no—
78C23×C4C2×D4711yescharacteristic
79C22×C8—476no—
80C22×C8—944no—
81C2×C4⋊C4—23no—
82C2×C4⋊C4C2×D4716yes—
83#103—4716no—
84C24C22⋊D4711yescharacteristic
85C2×Q8—4724no—
86C2×Q8—474no—
87C2×Q8—9424no—
88C2×Q8—9412no—
89C2×Q8—946no—
90C22×C4—26no—
91C22×C4—44no—
92C22×C4—948no—
93C22×C4—946no—
94C22×C4C4×D4714yes—
95C22×C4D18814yes—
96C22×C4C22⋊D4713yes—
97C22×C4C22×D4713yes—
98C2×C8—474no—
99C2×C8—9412no—
100C4⋊C4—26no—
101C4⋊C4C22×D4714yes—
102C23(C2×D47)⋊C414yes—
103C23#1062533514yes—
104C23#1062533714yes—
105C23C2×C22⋊D4713yes—
106Q8—478no—
107Q8—9424no—
108Q8—944no—
109C2×C4—24no—
110C2×C4—412no—
111C2×C4—9424no—
112C2×C4—944no—
113C2×C4(C2×D47)⋊C4112yes—
114C2×C4C2×C4×D4716yes—
115C2×C4C2×D18816yes—
116C2×C4C2×C22⋊D4713yes—
117C2×C4C23×D4711yescharacteristic
118C8—944no—
119C22#13093947116yesdirect product factor
120C22C2×(C2×D47)⋊C416yes—
121C22C2×#1062533516yes—
122C22C2×#1062533716yes—
123C22C22×C22⋊D4711yescharacteristic
124C4—44no—
125C4—948no—
126C4C2×(C2×D47)⋊C416yes—
127C4C22×C4×D4711yescharacteristic
128C4C22×D18811yescharacteristic
129C2C2×#13093947112yesdirect product factor
130C2C22×(C2×D47)⋊C411yescharacteristic
131C2C22×#1062533511yescharacteristic
132C2C22×#1062533711yescharacteristic
subgroupG/H
centerC24C22⋊D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC22×C4⋊C4×C47C2
socleC24×C47D4
hypercenterC22×C4⋊C4D47
hypocenterC47C22×#103
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#13093947C2direct (N × H)
7. C22×Dic94C4semidirect
12. #13093947C22direct (N × H)
29. C2×Dic94C2×C4semidirect
50. Dic94C22×C4semidirect
52. C22×C47#103semidirect
63. C2×C47C2×#103semidirect
71. C47C22×#103semidirect
119. C22#13093947direct (N × H)
129. C2C2×#13093947direct (N × H)