Finite Group Databasebeta

← #16777827

Subgroups — #16777827

Order 3328.

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

normal subgroups only

This group has 116 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#13129948C211yesmaximal, characteristic
2#13129863C211yesmaximal, characteristic
3#13116707C211yesmaximal, characteristic
4C2×C13×Q32C411yescharacteristic
5Q16×Dic13—21no—
6#11718261—21no—
7#11718249—21no—
8#11718156—21no—
9#11718097C411yescharacteristic
10#11718094C2211yescharacteristic
11C2×C13×Q16—21no—
12Q8×Dic13—41no—
13#88106—41no—
14C13×Q32—21no—
15C13×Q32C812yes—
16C2×C13×C16C2×C411yescharacteristic
17#88075—41no—
18#88058—21no—
19C8×Dic13D411yescharacteristic
20C2×#6090D411yescharacteristic
21#88036—22no—
22#7391—131nomaximal, Sylow
23C2×Q8×C13—41no—
24C13×Q16—22no—
25C13×Q16—41no—
26C2×C8×C13C22⋊C411yescharacteristic
27C4⋊Dic13—41no—
28C4⋊Dic13—81no—
29C4×Dic13—81no—
30C4×Dic13SD1611yescharacteristic
31C2×#1055D811yescharacteristic
32#6092—81no—
33C13×C16C2×C811yescharacteristic
34C13×C16M1611yescharacteristic
35#6090—21no—
36#2176—131no—
37#1398—131no—
38#1369—131no—
39Q8×C13—42no—
40Q8×C13—81no—
41C2×C4×C13—81no—
42C2×C4×C13#10211yescharacteristic
43C2×Dic13—21no—
44C2×Dic13—81no—
45C8×C13C22⋊C811yescharacteristic
46C8×C13#10411yescharacteristic
47#1055—21no—
48C2×Q32#26111yescharacteristic
49C4×Q16—261no—
50M64—261no—
51#367—131no—
52#364—261no—
53#358—261no—
54#346—131no—
55C22×C13#36111yescharacteristic
56C4×C13—82no—
57C4×C13D4⋊C811yescharacteristic
58C4×C13#36011yescharacteristic
59Dic13—41no—
60Dic13—161no—
61C2×Q16—21no—
62C4×Q8—521no—
63Q32—21no—
64Q32#105712yes—
65M32—521no—
66C2×C16—131no—
67C2×C16C2×#26111yescharacteristic
68#107—261no—
69#103—521no—
70C4×C8—131no—
71C32—262no—
72C2×C13—21no—
73C2×C13#133311yescharacteristic
74C2×Q8—41no—
75Q16—22no—
76Q16—41no—
77C2×C8—131no—
78C2×C8C22⋊#26111yescharacteristic
79C4⋊C4—521no—
80C4⋊C4—1041no—
81C42—131no—
82C42—1041no—
83C16—261no—
84C16—1041no—
85C16C2×#105711yescharacteristic
86C16#612211yescharacteristic
87C13#739111yescharacteristic, complemented, Sylow
88Q8—42no—
89Q8—81no—
90C2×C4—81no—
91C2×C4—261no—
92C2×C4—1041no—
93C2×C4#8811511yescharacteristic
94C8—261no—
95C8#8811611yescharacteristic
96C8C22⋊#105711yescharacteristic
97C22#1171827811yescharacteristic
98C4—82no—
99C4—521no—
100C4—2081no—
101C4#1171827511yescharacteristic
102C4D4⋊#105711yescharacteristic
103C2—21no—
104C2#1312979411yescharacteristic
subgroupG/H
centerC2#13129794
commutatorC13×C16C2×C8
FrattiniC2×C16C2×#261
FittingC2×C13×Q32C4
socleC2×C13#1333
prime radicalC22×C13#361
cosocle#11718094C22
hypercenterC2×Q32#261
hypocenterC13#7391
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
87. C13#7391semidirect

Maximal subgroups

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

subgroupindex
#131299482
#131298632
#131167072
#739113