Finite Group Databasebeta

← #16777956

Subgroups — #16777956

Order 3328.

102 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 40 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#13129994C211yesmaximal, characteristic
2#13129870C211yesmaximal, characteristic
3#13117113C211yesmaximal, characteristic
4#11718539—21no—
5#11718254—21no—
6C2×#88036—21no—
7C13×#366C411yescharacteristic
8#11718096C411yescharacteristic
9C16×Dic13C2211yescharacteristic
10#11718082—21no—
11#88144—41no—
12C4⋊#1057—41no—
13C2×C13×C16C2×C411yescharacteristic
14C13×#107—21no—
15#88058—21no—
16C8×Dic13D411yescharacteristic
17C2×#6090D411yescharacteristic
18#88048—41no—
19#88036—41no—
20#7452—131nomaximal, Sylow
21C2×#1057—81no—
22C2×C8×C13C22⋊C411yescharacteristic
23C13×C4⋊C4—41no—
24C4⋊Dic13—41no—
25C4⋊Dic13—81no—
26#6101—81no—
27C4×Dic13D811yescharacteristic
28C2×#1055SD1611yescharacteristic
29C13×C16—21no—
30#6090SD1611yescharacteristic
31#6090Q1611yescharacteristic
32#2253—131no—
33C4⋊C32—131no—
34#1372—131no—
35C2×C4×C13—81no—
36C2×C4×C13#10211yescharacteristic
37C2×Dic13—81no—
38C2×Dic13D1611yescharacteristic
39C2×Dic13SD3211yescharacteristic
40#1057—161no—
41C8×C13#10111yescharacteristic
42C8×C13#10311yescharacteristic
43#1055—21no—
44#499—261no—
45C2×C32—261no—
46#367—261no—
47#366—131no—
48#366#26111yescharacteristic
49C4×C16—131no—
50#335—261no—
51C22×C13#35711yescharacteristic
52C4×C13—161no—
53C4×C13#33211yescharacteristic
54C4×C13#36211yescharacteristic
55Dic13—21no—
56Dic13—21no—
57Dic13—161no—
58#125—521no—
59C2×C16—131no—
60C2×C16C2×#26111yescharacteristic
61#107—21no—
62#107—261no—
63#106—521no—
64C4⋊C8—521no—
65C4×C8—131no—
66C32—521no—
67C2×C13#136411yescharacteristic
68C2×C13#141711yescharacteristic
69C2×C13#141811yescharacteristic
70C2×C8—131no—
71C2×C8—1041no—
72C2×C8C22⋊#26111yescharacteristic
73C4⋊C4—41no—
74C4⋊C4—521no—
75C4⋊C4—1041no—
76C4⋊C4—1041no—
77C42—131no—
78C16—21no—
79C16—131no—
80C16—131no—
81C13#745211yescharacteristic, complemented, Sylow
82C2×C4—81no—
83C2×C4—131no—
84C2×C4—131no—
85C2×C4—1041no—
86C2×C4#8811511yescharacteristic
87C8—261no—
88C8—2081no—
89C8#8811311yescharacteristic
90C8#8811711yescharacteristic
91C22#1171827611yescharacteristic
92C4—161no—
93C4—261no—
94C4—261no—
95C4—2081no—
96C4#1171824511yescharacteristic
97C4#1171828211yescharacteristic
98C2#1312985411yescharacteristic
99C2#1312998711yescharacteristic
100C2#1312999011yescharacteristic
subgroupG/H
centerC22#11718276
commutatorC2×C13×C16C2×C4
FrattiniC2×C16C2×#261
FittingC13×#366C4
socle, prime radicalC22×C13#357
cosocleC16×Dic13C22
hypercenter#366#261
hypocenterC13#7452
LCSG ▷ C2×C13×C16 ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #366

Complements

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

NH ≅ G/Ntype
81. C13#7452semidirect

Maximal subgroups

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

subgroupindex
#131299942
#131298702
#131171132
#745213