Finite Group Databasebeta

← #16777938

Subgroups — #16777938

Order 3328.

144 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 32 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#13129783C211yesmaximal, characteristic
2#13129744C211yesmaximal, characteristic
3#13116412C211yesmaximal, characteristic
4#11719129—21no—
5#11718786C411yescharacteristic
6#11718779C2211yescharacteristic
7#11718284—21no—
8C13×H(3,ℤ/4)C411yescharacteristic
9#11718125—21no—
10#11718124—21no—
11C2×#6122—22no—
12C2×C13×M16C2×C411yescharacteristic
13C13×#117—21no—
14C2×C4×Dic13D411yescharacteristic
15C2×#6099—21no—
16C2×#6099D411yescharacteristic
17#88112—41no—
18C4⋊#1057—41no—
19#88106—41no—
20#88059—41no—
21#88054—41no—
22#7440—131nomaximal, Sylow
23C22×C4×C13C22⋊C411yescharacteristic
24C22×Dic13—21no—
25#6122—82no—
26C2×#1057—42no—
27C13×M16—41no—
28C2×C8×C13—21no—
29C13×C4⋊C4—41no—
30C13×C22⋊C4—41no—
31C42×C13—41no—
32C4×Dic13—21no—
33C4×Dic13SD1611yescharacteristic
34C4×Dic13Q1611yescharacteristic
35#6099—41no—
36#6099—41no—
37#6099—41no—
38C2×#1055—21no—
39C2×#1055—41no—
40#6092—81no—
41#2102—131no—
42#1327—131no—
43#1309—131no—
44C23×C13#10411yescharacteristic
45C2×C4×C13—21no—
46C2×C4×C13—21no—
47C2×C4×C13—81no—
48C2×C4×C13#9911yescharacteristic
49C2×C4×C13#10311yescharacteristic
50C2×Dic13—21no—
51C2×Dic13—21no—
52C2×Dic13—41no—
53C2×Dic13—41no—
54#1057—82no—
55C8×C13—41no—
56#1055—41no—
57#1055—81no—
58#430—131no—
59#423—131no—
60#423—261no—
61#349—261no—
62#344—261no—
63#339—261no—
64H(3,ℤ/4)#26111yescharacteristic
65C22×C13—21no—
66C22×C13—41no—
67C22×C13#32811yescharacteristic
68C4×C13—21no—
69C4×C13—161no—
70C4×C13#35211yescharacteristic
71C4×C13#35511yescharacteristic
72Dic13—21no—
73Dic13—21no—
74Dic13—41no—
75C2×M16—131no—
76C2×M16—261no—
77C2×M16—262no—
78C2×M16C2×#26111yescharacteristic
79#117—21no—
80C2×C42—131no—
81M32—521no—
82#108—521no—
83C4⋊C8—521no—
84C4⋊C8—521no—
85C4⋊C8—521no—
86C2×C13—21no—
87C2×C13—41no—
88C2×C13#135311yescharacteristic
89C22×C4—261no—
90C22×C4C22⋊#26111yescharacteristic
91M16—41no—
92M16—521no—
93M16—521no—
94M16—521no—
95M16—1042no—
96C2×C8—21no—
97C2×C8—261no—
98C2×C8—521no—
99C2×C8—522no—
100C4⋊C4—41no—
101C22⋊C4—41no—
102C42—41no—
103C42—131no—
104C42—131no—
105C42—261no—
106C16—1041no—
107C13#744011yescharacteristic, complemented, Sylow
108C23#8811611yescharacteristic
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—81no—
112C2×C4—261no—
113C2×C4—261no—
114C2×C4—521no—
115C2×C4—521no—
116C2×C4#8810711yescharacteristic
117C2×C4#8811711yescharacteristic
118C8—41no—
119C8—521no—
120C8—1042no—
121C8—1041no—
122C22—21no—
123C22—41no—
124C22#1171824111yescharacteristic
125C4—21no—
126C4—161no—
127C4—261no—
128C4—261no—
129C4—521no—
130C4#1171822811yescharacteristic
131C4#1171823711yescharacteristic
132C2—21no—
133C2—41no—
134C2#1312983411yescharacteristic
subgroupG/H
centerC2#13129834
commutatorC2×C13×M16C2×C4
FrattiniC2×M16C2×#261
FittingC13×H(3,ℤ/4)C4
socleC2×C13#1353
prime radicalC23×C13#104
cosocle#11718779C22
hypercenterH(3,ℤ/4)#261
hypocenterC13#7440
LCSG ▷ C2×C13×M16 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
107. C13#7440semidirect

Maximal subgroups

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

subgroupindex
#131297832
#131297442
#131164122
#744013