Finite Group Databasebeta

← #13130733

Subgroups — #13130733

Order 1664.

300 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C2×#88126C211yesmaximal, characteristic
2#11719135C212yesmaximal
3#11718289C214yesmaximal
4C22×C4×D13C2211yescharacteristic
5C2×C22⋊#261C2214yes—
6C2×C42×C13C411yescharacteristic, complemented
7C2×#6103C2212yes—
8C2×#6101C412yescomplemented
9C2×C4×Dic13C411yescharacteristic, complemented
10#88126—24no—
11(C2×#261)⋊C4—24no—
12C23×D13C2311yescharacteristic
13C22×#261—24no—
14C22×C4×C13C2×C412yes—
15C22×C4×C13C2×C411yescharacteristic
16C22×Dic13C2×C411yescharacteristic
17C22×Dic13C2×C412yes—
18C2×C4×D13—24no—
19C2×C4×D13D414yes—
20C22⋊#261—28no—
21C42×C13—22no—
22#6103—24no—
23#6101—24no—
24C4×Dic13—22no—
25#1820—131nomaximal, Sylow
26C23×C13C22×C411yescharacteristic
27C22×D13—42no—
28C22×D13C2×D412yes—
29C22×D13#4114yes—
30C2×#261—48no—
31C2×#261—44no—
32C2×C4×C13—22no—
33C2×C4×C13—22no—
34C2×C4×C13—42no—
35C2×C4×C13C22⋊C412yes—
36C2×Dic13—22no—
37C2×Dic13—22no—
38C2×Dic13—42no—
39C2×Dic13C22⋊C412yes—
40C4×D13—28no—
41C2×#117—131no—
42#381—132no—
43#342—134no—
44C22×C13—22no—
45C22×C13C2×C22⋊C411yescharacteristic
46C22×C13#11712yes—
47C2×D13—24no—
48C2×D13—44no—
49C2×D13#12314yes—
50#261—84no—
51C4×C13—22no—
52C4×C13—42no—
53Dic13—22no—
54Dic13—42no—
55C23×C4—131no—
56#117—264no—
57C2×C4⋊C4—132no—
58C2×C22⋊C4—132no—
59C2×C22⋊C4—134no—
60C2×C42—131no—
61C2×C42#26111yescharacteristic, complemented
62#95—264no—
63C2×C13—22no—
64C2×C13#38111yescharacteristic
65C2×C13#41012yes—
66D13—24no—
67C24—131no—
68C22×C4—131no—
69C22×C4—134no—
70C22×C4—132no—
71C22×C4—264no—
72C22×C4—264no—
73C22×C4C2×#26112yes—
74C22×C4C2×#26111yescharacteristic
75C4⋊C4—264no—
76C22⋊C4—264no—
77C22⋊C4—268no—
78C42—22no—
79C42—262no—
80C13#182011yescharacteristic, complemented, Sylow
81C23—132no—
82C23—134no—
83C23—522no—
84C23C22×#26111yescharacteristic
85C2×C4—22no—
86C2×C4—22no—
87C2×C4—42no—
88C2×C4—132no—
89C2×C4—268no—
90C2×C4—262no—
91C2×C4—262no—
92C2×C4—522no—
93C2×C4—524no—
94C2×C4—528no—
95C2×C4C22⋊#26112yes—
96C22—22no—
97C22—134no—
98C22—264no—
99C22—524no—
100C22#8823712yes—
101C22C2×C22⋊#26111yescharacteristic
102C4—22no—
103C4—42no—
104C4—262no—
105C4—522no—
106C4—1044no—
107C2—22no—
108C2—264no—
109C2#1171911612yes—
110C2#1171913511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC2×C42×C13C4
socleC22×C13C2×C22⋊C4
prime radical, cosocleC23×D13C23
hypercenterC2×C42#261
hypocenterC13#1820
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
6. C2×C42×C13C4semidirect
8. C2×#6101C4semidirect
9. C2×C4×Dic13C4semidirect
61. C2×C42#261semidirect
80. C13#1820semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#881262
#117191352
#117182892
#182013