Finite Group Databasebeta

← #15750330

Subgroups — #15750330

Order 3328.

136 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 43 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#13112787C212yesmaximal
2C13×#1837C211yesmaximal, characteristic
3C13×#423C411yescharacteristic
4C13×#423C2211yescharacteristic
5C2×C4×C8×C13C411yescharacteristic
6C13×#341—22no—
7#11718145—22no—
8C2×C13×M16—21no—
9C2×C13×M16D412yes—
10C22×C8×C13—21no—
11C2×C42×C13C2×C411yescharacteristic
12C13×C4⋊C8—41no—
13C13×C4⋊C8—41no—
14C4×C8×C13—21no—
15C4×C8×C13C812yes—
16#88052—42no—
17#7368—131nomaximal, Sylow
18C22×C4×C13—21no—
19C22×C4×C13C22⋊C411yescharacteristic
20C13×M16—42no—
21C13×M16—42no—
22C2×C8×C13—22no—
23C2×C8×C13—22no—
24C2×C8×C13—41no—
25C2×C8×C13—41no—
26C2×C8×C13—41no—
27C42×C13—21no—
28C42×C13C2×C811yescharacteristic
29C42×C13M1611yescharacteristic
30#6090—82no—
31#1837D1311yescharacteristic
32#1327—132no—
33C23×C13#10111yescharacteristic
34C2×C4×C13—21no—
35C2×C4×C13—21no—
36C2×C4×C13—21no—
37C2×C4×C13—21no—
38C2×C4×C13—42no—
39C2×C4×C13C22⋊C811yescharacteristic
40C2×C4×C13#9911yescharacteristic
41C8×C13—42no—
42C8×C13—42no—
43C8×C13—81no—
44#423Dic1311yescharacteristic
45#423C2×D1311yescharacteristic
46C2×C4×C8Dic1311yescharacteristic
47#349—262no—
48#341—22no—
49C22×C13—21no—
50C22×C13—41no—
51C22×C13#32411yescharacteristic
52C4×C13—22no—
53C4×C13—21no—
54C4×C13—41no—
55C4×C13#35411yescharacteristic
56C4×C13#35511yescharacteristic
57C2×M16—21no—
58C2×M16C22⋊D1312yes—
59C22×C8—21no—
60C2×C42C2×Dic1311yescharacteristic
61M32—522no—
62C4⋊C8—41no—
63C4⋊C8—41no—
64C4×C8—21no—
65C4×C8#105512yes—
66C2×C13—21no—
67C2×C13—41no—
68C2×C13#132411yescharacteristic
69C22×C4—21no—
70C22×C4C22⋊Dic1311yescharacteristic
71M16—42no—
72M16—42no—
73C2×C8—22no—
74C2×C8—22no—
75C2×C8—41no—
76C2×C8—41no—
77C2×C8—41no—
78C42—21no—
79C42C2×#105511yescharacteristic
80C42#609911yescharacteristic
81C16—1042no—
82C13#736811yescharacteristic, complemented, Sylow
83C23#8807611yescharacteristic
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—42no—
89C2×C4C22⋊#105511yescharacteristic
90C2×C4#8807411yescharacteristic
91C8—42no—
92C8—42no—
93C8—81no—
94C22—21no—
95C22—41no—
96C22#1171812011yescharacteristic
97C4—22no—
98C4—21no—
99C4—41no—
100C4#1171813311yescharacteristic
101C4#1171813411yescharacteristic
102C2—21no—
103C2—41no—
104C2#1311278011yescharacteristic
subgroupG/H
centerC4#11718133
commutatorC42×C13C2×C8
Frattini#423C2×D13
FittingC13×#1837C2
socleC2×C13#1324
prime radicalC23×C13#101
cosocleC13×#423C22
hypercenter#1837D13
hypocenterC13#7368
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #423 ◁ #1837

Complements

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

NH ≅ G/Ntype
82. C13#7368semidirect

Maximal subgroups

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

subgroupindex
#131127872
C13×#18372
#736813