Finite Group Databasebeta

← #15750542

Subgroups — #15750542

Order 3328.

136 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 37 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#13116411C211yesmaximal, characteristic
2#13112787C211yesmaximal, characteristic
3C13×#1307C211yesmaximal, characteristic
4C13×#432—21no—
5C13×#423C2211yescharacteristic
6#11718786C411yescharacteristic
7#11718151—21no—
8#11718149C411yescharacteristic
9#11718145—21no—
10#11718115—21no—
11C2×C13×M16C2×C411yescharacteristic
12C2×C13×M16D411yescharacteristic
13C2×C42×C13D411yescharacteristic
14#88180—21no—
15C2×#6099—21no—
16C13×C4⋊C8—41no—
17C13×C4⋊C8—41no—
18C13×C22⋊C8—22no—
19C13×#97—41no—
20#88059—41no—
21#88052—41no—
22#7441—131nomaximal, Sylow
23C22×C4×C13—21no—
24C22×C4×C13C22⋊C411yescharacteristic
25C13×M16—41no—
26C13×M16—41no—
27C2×C8×C13—21no—
28C2×C8×C13—21no—
29C2×C8×C13—42no—
30C42×C13—21no—
31C42×C13SD1611yescharacteristic
32C42×C13Q1611yescharacteristic
33C22⋊Dic13—41no—
34C4⋊Dic13—41no—
35C4×Dic13—41no—
36#6099—41no—
37#6099—41no—
38C2×#1055—41no—
39#6090—81no—
40#2102—131no—
41#1327—131no—
42#1307D1311yescharacteristic
43C23×C13#10411yescharacteristic
44C2×C4×C13—21no—
45C2×C4×C13—21no—
46C2×C4×C13—21no—
47C2×C4×C13—21no—
48C2×C4×C13—81no—
49C2×C4×C13#9911yescharacteristic
50C2×C4×C13#10311yescharacteristic
51C2×Dic13—81no—
52C8×C13—41no—
53C8×C13—41no—
54C8×C13—82no—
55#1055—81no—
56#432—21no—
57#430—131no—
58#423C2×D1311yescharacteristic
59#349—261no—
60#344—261no—
61#339—261no—
62H(3,ℤ/4)—131no—
63C22×C13—21no—
64C22×C13—41no—
65C22×C13#32811yescharacteristic
66C4×C13—21no—
67C4×C13—41no—
68C4×C13—41no—
69C4×C13#35211yescharacteristic
70C4×C13#35511yescharacteristic
71Dic13—161no—
72C2×M16—261no—
73C2×M16C4×D1311yescharacteristic
74C2×M16D5211yescharacteristic
75#117—261no—
76C2×C42C22⋊D1311yescharacteristic
77M32—521no—
78#108—521no—
79C4⋊C8—41no—
80C4⋊C8—41no—
81C22⋊C8—22no—
82#97—41no—
83C2×C13—21no—
84C2×C13—41no—
85C2×C13#135311yescharacteristic
86C22×C4—21no—
87C22×C4#610311yescharacteristic
88M16—41no—
89M16—41no—
90M16—521no—
91M16—521no—
92C2×C8—21no—
93C2×C8—21no—
94C2×C8—42no—
95C2×C8—521no—
96C4⋊C4—521no—
97C22⋊C4—521no—
98C42—21no—
99C42—521no—
100C42#610511yescharacteristic
101C42#610711yescharacteristic
102C16—1041no—
103C13#744111yescharacteristic, complemented, Sylow
104C23#8804511yescharacteristic
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—21no—
108C2×C4—21no—
109C2×C4—81no—
110C2×C4—1041no—
111C2×C4#8804611yescharacteristic
112C2×C4#8805011yescharacteristic
113C8—41no—
114C8—41no—
115C8—82no—
116C8—1041no—
117C22—21no—
118C22—41no—
119C22#1171804411yescharacteristic
120C4—21no—
121C4—41no—
122C4—41no—
123C4—2081no—
124C4#1171806811yescharacteristic
125C4#1171806911yescharacteristic
126C2—21no—
127C2—41no—
128C2#1311286211yescharacteristic
subgroupG/H
centerC2#13112862
commutatorC2×C13×M16C2×C4
Frattini#423C2×D13
FittingC13×#1307C2
socleC2×C13#1353
prime radicalC23×C13#104
cosocleC13×#423C22
hypercenter#1307D13
hypocenterC13#7441
LCSG ▷ C2×C13×M16 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #423 ◁ #1307

Complements

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

NH ≅ G/Ntype
103. C13#7441semidirect

Maximal subgroups

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

subgroupindex
#131164112
#131127872
C13×#13072
#744113