Finite Group Databasebeta

← #15750014

Subgroups — #15750014

Order 3328.

148 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 63 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#13116652C212yesmaximal
2C13×#2151C211yesmaximal, characteristic
3C2×C13×M32C411yescharacteristic
4C22×C13×C16C411yescharacteristic
5C13×#405C2211yescharacteristic
6C13×C4⋊C16—22no—
7#11718145—22no—
8#11718058C414yes—
9#11718055—22no—
10C2×C13×M16D411yescharacteristic
11C22×C8×C13C2×C411yescharacteristic
12C13×#117Q811yescharacteristic
13C13×M32—41no—
14C2×C13×C16—21no—
15C2×C13×C16—21no—
16C2×C13×C16—41no—
17C13×#97C2×C412yes—
18C4×C8×C13D412yes—
19#88052—24no—
20#7239—131nomaximal, Sylow
21C22×C4×C13C4⋊C411yescharacteristic
22C13×M16—41no—
23C2×C8×C13—21no—
24C2×C8×C13—21no—
25C2×C8×C13C4211yescharacteristic
26C2×C8×C13C22⋊C412yes—
27C2×C8×C13C22⋊C411yescharacteristic
28C13×C4⋊C4—21no—
29C13×C22⋊C4—21no—
30C42×C13C4⋊C412yes—
31C13×C16—41no—
32C13×C16—41no—
33#6090—44no—
34#2166—132no—
35#2151D1311yescharacteristic
36C23×C13#10811yescharacteristic
37C2×C4×C13—21no—
38C2×C4×C13—21no—
39C2×C4×C13—22no—
40C2×C4×C13#9511yescharacteristic
41C2×C4×C13#10811yescharacteristic
42C8×C13—22no—
43C8×C13—21no—
44C8×C13#10011yescharacteristic
45C8×C13#10111yescharacteristic
46C2×M32Dic1311yescharacteristic
47C22×C16Dic1311yescharacteristic
48#405C2×D1311yescharacteristic
49#364—262no—
50C4⋊C16—22no—
51#349—262no—
52#347—134no—
53C22×C13—21no—
54C22×C13—41no—
55C22×C13#34111yescharacteristic
56C4×C13—21no—
57C4×C13—42no—
58C4×C13H(3,ℤ/4)11yescharacteristic
59C4×C13#34311yescharacteristic
60C2×M16D5211yescharacteristic
61C22×C8C2×Dic1311yescharacteristic
62#117Dic2611yescharacteristic
63M32—41no—
64M32—264no—
65C2×C16—21no—
66C2×C16—21no—
67C2×C16—41no—
68#97C4×D1312yes—
69C4×C8C22⋊D1312yes—
70C2×C13—21no—
71C2×C13—41no—
72C2×C13#129011yescharacteristic
73C22×C4C4⋊Dic1311yescharacteristic
74M16—41no—
75C2×C8—21no—
76C2×C8—21no—
77C2×C8C4×Dic1311yescharacteristic
78C2×C8#610312yes—
79C2×C8C22⋊Dic1311yescharacteristic
80C4⋊C4—21no—
81C22⋊C4—21no—
82C42#610112yes—
83C16—41no—
84C16—41no—
85C16—524no—
86C13#723911yescharacteristic, complemented, Sylow
87C23#8805911yescharacteristic
88C2×C4—21no—
89C2×C4—21no—
90C2×C4—22no—
91C2×C4#8805911yescharacteristic
92C2×C4#8807111yescharacteristic
93C8—22no—
94C8—21no—
95C8#8807311yescharacteristic
96C8#8807611yescharacteristic
97C22—21no—
98C22—41no—
99C22#1171814411yescharacteristic
100C4—21no—
101C4—42no—
102C4#1171812211yescharacteristic
103C4#1171814911yescharacteristic
104C2—21no—
105C2—41no—
106C2#1311270611yescharacteristic
subgroupG/H
centerC4#11718149
commutatorC2×C8×C13C42
Frattini#405C2×D13
FittingC13×#2151C2
socleC2×C13#1290
prime radicalC23×C13#108
cosocleC13×#405C22
hypercenter#2151D13
hypocenterC13#7239
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C8 ◁ #2151

Complements

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

NH ≅ G/Ntype
86. C13#7239semidirect

Maximal subgroups

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

subgroupindex
#131166522
C13×#21512
#723913