Finite Group Databasebeta

← #16777766

Subgroups — #16777766

Order 3328.

126 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 46 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#13129951C212yesmaximal
2#13116592C211yesmaximal, characteristic
3C2×C4×C8×C13C411yescharacteristic
4C2×#88052C411yescharacteristic
5C2×#88052C2211yescharacteristic
6#11718249—22no—
7C4⋊#6090—22no—
8C22×C8×C13C811yescharacteristic
9C22×C8×C13C2×C411yescharacteristic
10C2×C42×C13C811yescharacteristic
11C4×C8×C13—21no—
12C4×C8×C13—21no—
13#88052—41no—
14#88052—41no—
15C2×#6090—21no—
16C2×#6090D412yes—
17#88036—42no—
18#7364—131nomaximal, Sylow
19C22×C4×C13—21no—
20C22×C4×C13C2×C811yescharacteristic
21C2×C8×C13—21no—
22C2×C8×C13—21no—
23C2×C8×C13—21no—
24C2×C8×C13—41no—
25C2×C8×C13C22⋊C411yescharacteristic
26C2×C8×C13M1611yescharacteristic
27C42×C13—21no—
28C42×C13C1611yescharacteristic
29C42×C13C1611yescharacteristic
30#6090—22no—
31#6090—41no—
32#2150—131no—
33#1400—132no—
34C23×C13M3211yescharacteristic
35C2×C4×C13—21no—
36C2×C4×C13—21no—
37C2×C4×C13—21no—
38C2×C4×C13—21no—
39C2×C4×C13—42no—
40C2×C4×C13C22⋊C811yescharacteristic
41C2×C4×C13C2×C1611yescharacteristic
42C8×C13—21no—
43C8×C13—41no—
44C8×C13#9911yescharacteristic
45C8×C13#10111yescharacteristic
46C2×M32—131no—
47C2×M32—131no—
48C2×C4×C8#26111yescharacteristic
49M64—262no—
50C4⋊C16—262no—
51C22×C13—21no—
52C22×C13—41no—
53C22×C13C22⋊C1611yescharacteristic
54C4×C13—22no—
55C4×C13—21no—
56C4×C13—41no—
57C4×C13#32411yescharacteristic
58C4×C13#34911yescharacteristic
59C22×C8#105711yescharacteristic
60C22×C8C2×#26111yescharacteristic
61C2×C42#105711yescharacteristic
62M32—521no—
63M32—521no—
64C2×C16—132no—
65C2×C16—261no—
66C4×C8—21no—
67C4×C8—21no—
68C32—522no—
69C2×C13—21no—
70C2×C13—41no—
71C2×C13#132211yescharacteristic
72C22×C4—21no—
73C22×C4C2×#105711yescharacteristic
74C2×C8—21no—
75C2×C8—21no—
76C2×C8—21no—
77C2×C8—41no—
78C2×C8#612211yescharacteristic
79C2×C8C22⋊#26111yescharacteristic
80C42—21no—
81C42#609211yescharacteristic
82C42#609211yescharacteristic
83C16—262no—
84C16—521no—
85C13#736411yescharacteristic, complemented, Sylow
86C23#8810611yescharacteristic
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—42no—
92C2×C4C2×#609211yescharacteristic
93C2×C4C22⋊#105711yescharacteristic
94C8—21no—
95C8—41no—
96C8#8810711yescharacteristic
97C8#8811311yescharacteristic
98C22—21no—
99C22—41no—
100C22C22⋊#609211yescharacteristic
101C4—22no—
102C4—21no—
103C4—41no—
104C4#1171828411yescharacteristic
105C4#1171828511yescharacteristic
106C2—21no—
107C2—41no—
108C2#1312977211yescharacteristic
subgroupG/H
centerC8#88107
commutatorC2×C4×C13C2×C16
FrattiniC22×C8C2×#261
FittingC2×C4×C8×C13C4
socleC2×C13#1322
prime radicalC23×C13M32
cosocleC2×#88052C22
hypercenterC2×C4×C8#261
hypocenterC13#7364
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C2×C8 ◁ C22×C8 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
85. C13#7364semidirect

Maximal subgroups

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

subgroupindex
#131299512
#131165922
#736413