Finite Group Databasebeta

← C22×#13093959 #20251990

Subgroups — C22×#13093959 #20251990

Order 6016.

480 conjugacy classes of subgroups; only the 269 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 269 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
1C22×#10625329C211yesmaximal, characteristic
2C23×C47⋊C8C211yesmaximal, characteristic
3C2×#13093959C2112yesmaximal, direct product factor
4C22×M16×C47C211yesmaximal, characteristic
5C2×#10625329—23no—
6C2×#10625329C2216yes—
7C22×C47⋊C8—21no—
8C22×C47⋊C8C416yes—
9C22×C47⋊C8C412yes—
10C22×C47⋊C8C2216yes—
11#13093959C22116yesdirect product factor
12C23×C4×C47C2211yescharacteristic
13C2×M16×C47—23no—
14C2×M16×C47C2216yes—
15C22×C8×C47—21no—
16C24×C47Q811yescharacteristic
17C22×C4×C47C2×C413yes—
18C22×C4×C47C2×C411yescharacteristic
19C22×C4×C47D413yes—
20C22×C4×C47D411yescharacteristic
21C22×C4×C47Q813yes—
22C22×C4×C47C2313yes—
23M16×C47—26no—
24M16×C47C2314yes—
25C2×C8×C47—26no—
26#10625329—26no—
27#10625329C2314yes—
28C2×C47⋊C8—26no—
29C2×C47⋊C8C2×C4112yes—
30C2×C47⋊C8C2×C4112yes—
31C2×C47⋊C8C2314yes—
32C23×C47—24no—
33C23×C47C4⋊C413yes—
34C23×C47C4⋊C411yescharacteristic
35C23×C47C2×Q813yes—
36C2×C4×C47C4⋊C416yes—
37C2×C4×C47C4⋊C413yes—
38C2×C4×C47C4⋊C413yes—
39C2×C4×C47C22×C413yes—
40C2×C4×C47C22×C413yes—
41C2×C4×C47C2×D413yes—
42C2×C4×C47C2×D413yes—
43C2×C4×C47C2×Q813yes—
44C2×C4×C47C2411yescharacteristic
45C8×C47—24no—
46C47⋊C8—24no—
47C47⋊C8C22×C418yes—
48C22×C47—26no—
49C22×C47—26no—
50C22×C47#10814yescomplemented
51C22×C47C2×C4⋊C413yes—
52C22×C47C2×C4⋊C413yes—
53C22×C47C22×Q811yescharacteristic
54C4×C47C2×C4⋊C413yes—
55C4×C47C2×C4⋊C413yes—
56C4×C47C23×C411yescharacteristic
57C4×C47C22×D411yescharacteristic
58C22×#108—471nomaximal, Sylow
59C2×C47—23no—
60C2×C47—21no—
61C2×C47C2×#10816yescomplemented
62C2×C47C22×C4⋊C411yescharacteristic
63C22×M16—471no—
64C22×M16D4711yescharacteristic
65C23×C8—471no—
66C2×#108—4712no—
67C47C22×#10811yescharacteristic, complemented, Sylow
68C23×C4C2×D4711yescharacteristic
69C2×M16—23no—
70C2×M16—476no—
71C2×M16—943no—
72C2×M16C2×D4716yes—
73C22×C8—21no—
74C22×C8—472no—
75C22×C8—476no—
76C22×C8—476no—
77C22×C8—941no—
78#108—4716no—
79C24Dic9411yescharacteristic
80C22×C4Dic9413yes—
81C22×C4C4×D4711yescharacteristic
82C22×C4C4×D4713yes—
83C22×C4C22⋊D4713yes—
84C22×C4C22⋊D4711yescharacteristic
85C22×C4C22×D4713yes—
86M16—26no—
87M16—474no—
88M16—946no—
89M16C22×D4714yes—
90C2×C8—26no—
91C2×C8—4712no—
92C2×C8—4712no—
93C2×C8—474no—
94C2×C8—946no—
95C23—24no—
96C23Dic47⋊C413yes—
97C23Dic47⋊C411yescharacteristic
98C23C2×Dic9413yes—
99C2×C4Dic47⋊C416yes—
100C2×C4Dic47⋊C413yes—
101C2×C4Dic47⋊C413yes—
102C2×C4C2×Dic9413yes—
103C2×C4C2×C4×D4713yes—
104C2×C4C2×C4×D4713yes—
105C2×C4C2×C22⋊D4713yes—
106C2×C4C2×C22⋊D4713yes—
107C2×C4C23×D4711yescharacteristic
108C8—24no—
109C8—478no—
110C8—944no—
111C22—26no—
112C22—26no—
113C22#1309395914yesdirect product factor
114C22C2×Dic47⋊C413yes—
115C22C2×Dic47⋊C413yes—
116C22C22×Dic9411yescharacteristic
117C4C2×Dic47⋊C413yes—
118C4C2×Dic47⋊C413yes—
119C4C22×C4×D4711yescharacteristic
120C4C22×C22⋊D4711yescharacteristic
121C2—23no—
122C2—21no—
123C2C2×#1309395916yesdirect product factor
124C2C22×Dic47⋊C411yescharacteristic
subgroupG/H
centerC22×C4C22⋊D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC22×M16×C47C2
socleC23×C47C4⋊C4
hypercenterC22×M16D47
hypocenterC47C22×#108
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
3. C2×#13093959C2direct (N × H)
11. #13093959C22direct (N × H)
50. C22×C47#108semidirect
61. C2×C47C2×#108semidirect
67. C47C22×#108semidirect
113. C22#13093959direct (N × H)
123. C2C2×#13093959direct (N × H)