Finite Group Databasebeta

← #15750323

Subgroups — #15750323

Order 3328.

120 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 45 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#13116596C211yesmaximal, characteristic
2#13112976C211yesmaximal, characteristic
3C13×#1400C211yesmaximal, characteristic
4C2×C13×M32C2211yescharacteristic
5#11718762C411yescharacteristic
6C22×#6090C411yescharacteristic
7C13×M64—21no—
8#11718093—21no—
9#11718093—21no—
10#11718091—21no—
11C22×C8×C13C2×C411yescharacteristic
12#88180C811yescharacteristic
13C2×#6099C811yescharacteristic
14C13×M32—41no—
15C2×C13×C16D411yescharacteristic
16C2×C13×C16D411yescharacteristic
17#88055—21no—
18C8×Dic13—21no—
19C2×#6090—21no—
20C2×#6090—41no—
21C13×C32—41no—
22#88034—41no—
23#7365—131nomaximal, Sylow
24C22×C4×C13C2×C811yescharacteristic
25C2×C8×C13—21no—
26C2×C8×C13—21no—
27C2×C8×C13C22⋊C411yescharacteristic
28C2×C8×C13M1611yescharacteristic
29C22⋊Dic13C1612yes—
30C4⋊Dic13—21no—
31C4×Dic13—21no—
32#6099—41no—
33C2×#1055—21no—
34C13×C16—21no—
35C13×C16—21no—
36#6090—41no—
37#2151—131no—
38#1400—131no—
39#1400D1311yescharacteristic
40C23×C13C2×C1611yescharacteristic
41C2×C4×C13—21no—
42C2×C4×C13—21no—
43C2×C4×C13C22⋊C811yescharacteristic
44C2×C4×C13M3211yescharacteristic
45C2×Dic13—22no—
46C8×C13—21no—
47C8×C13#9911yescharacteristic
48C8×C13#10111yescharacteristic
49#1055—41no—
50C2×M32C2×D1311yescharacteristic
51C22×C16—131no—
52#405—131no—
53M64—21no—
54M64—261no—
55C4⋊C16—261no—
56C4⋊C16—261no—
57C22×C13—21no—
58C22×C13—41no—
59C22×C13C22⋊C1611yescharacteristic
60C4×C13—21no—
61C4×C13#32411yescharacteristic
62C4×C13#34911yescharacteristic
63Dic13—42no—
64C2×M16—131no—
65C22×C8C4×D1311yescharacteristic
66#117—131no—
67M32—41no—
68C2×C16—261no—
69C2×C16—521no—
70C2×C16D5211yescharacteristic
71C2×C16C22⋊D1311yescharacteristic
72#97—261no—
73C4×C8—261no—
74C32—41no—
75C32—521no—
76C2×C13—21no—
77C2×C13—41no—
78C2×C13#132211yescharacteristic
79C22×C4C8×D1311yescharacteristic
80M16—521no—
81C2×C8—21no—
82C2×C8—21no—
83C2×C8—261no—
84C2×C8#609411yescharacteristic
85C2×C8#610311yescharacteristic
86C4⋊C4—261no—
87C22⋊C4—132no—
88C42—261no—
89C16—21no—
90C16—21no—
91C16—521no—
92C13#736511yescharacteristic, complemented, Sylow
93C23C16×D1311yescharacteristic
94C2×C4—21no—
95C2×C4—21no—
96C2×C4—262no—
97C2×C4#8803811yescharacteristic
98C2×C4#8806011yescharacteristic
99C8—21no—
100C8—521no—
101C8#8804611yescharacteristic
102C8#8806411yescharacteristic
103C22—21no—
104C22—41no—
105C22#1171809911yescharacteristic
106C4—21no—
107C4—522no—
108C4#1171806111yescharacteristic
109C4#1171810611yescharacteristic
110C2—21no—
111C2—41no—
112C2#1311277511yescharacteristic
subgroupG/H
centerC8#88046
commutator, prime radicalC23×C13C2×C16
FrattiniC2×M32C2×D13
FittingC13×#1400C2
socleC2×C13#1322
cosocleC2×C13×M32C22
hypercenter#1400D13
hypocenterC13#7365
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C2×C8 ◁ C2×M32 ◁ #1400

Complements

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

NH ≅ G/Ntype
92. C13#7365semidirect

Maximal subgroups

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

subgroupindex
#131165962
#131129762
C13×#14002
#736513