Finite Group Databasebeta

← #16777833

Subgroups — #16777833

Order 3328.

110 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 48 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
1C4⋊#88036C211yesmaximal, characteristic
2#13129943C211yesmaximal, characteristic
3#13116741C211yesmaximal, characteristic
4C8×Dic26C411yescharacteristic
5C2×#88036—21no—
6C2×#88036—21no—
7C13×C4⋊C16C411yescharacteristic
8#11718094—21no—
9#11718093—21no—
10C4×#6090C2211yescharacteristic
11C4×Dic26C811yescharacteristic
12C2×C13×C16—21no—
13C4×C8×C13C2×C411yescharacteristic
14#88054—21no—
15C8×Dic13—21no—
16C2×#6090D411yescharacteristic
17C2×#6090D411yescharacteristic
18C4⋊#1055C811yescharacteristic
19#88036—22no—
20#88036—41no—
21#7393—131nomaximal, Sylow
22C2×Dic26C1611yescharacteristic
23C2×C8×C13C22⋊C411yescharacteristic
24C2×C8×C13M1611yescharacteristic
25C42×C13C2×C811yescharacteristic
26C4⋊Dic13C1611yescharacteristic
27#6101—21no—
28C4×Dic13—21no—
29C2×#1055—21no—
30C13×C16—41no—
31#6090—21no—
32#6090SD1611yescharacteristic
33#6090Q1611yescharacteristic
34#2183—131no—
35C4⋊C32—131no—
36#1397—131no—
37C2×C4×C13C22⋊C811yescharacteristic
38C2×C4×C13C2×C1611yescharacteristic
39C2×C4×C13M3211yescharacteristic
40C2×Dic13—21no—
41C2×Dic13—21no—
42Dic26—41no—
43C8×C13—21no—
44C8×C13#10311yescharacteristic
45C8×C13#10411yescharacteristic
46#1055—41no—
47C8×Q8—131no—
48C2×C32—261no—
49C2×C32—261no—
50C4⋊C16—261no—
51C4⋊C16#26111yescharacteristic
52#346—261no—
53C4×C16—131no—
54C22×C13C22⋊C1611yescharacteristic
55C4×C13—21no—
56C4×C13—21no—
57C4×C13Q8⋊C811yescharacteristic
58C4×C13#35011yescharacteristic
59Dic13—41no—
60Dic13—41no—
61C4×Q8—131no—
62C2×C16—21no—
63C2×C16—131no—
64C2×C16—131no—
65C4⋊C8—131no—
66C4⋊C8—261no—
67C4×C8—261no—
68C4×C8C2×#26111yescharacteristic
69C32—262no—
70C32—521no—
71C2×C13Q8⋊C1611yescharacteristic
72C2×C13#140011yescharacteristic
73C2×C13#140111yescharacteristic
74C2×Q8—131no—
75C2×C8—261no—
76C2×C8#611811yescharacteristic
77C2×C8C22⋊#26111yescharacteristic
78C4⋊C4—131no—
79C4⋊C4—261no—
80C42—261no—
81C42D13⋊C811yescharacteristic
82C16—41no—
83C16—131no—
84C16—131no—
85C16—261no—
86C13#739311yescharacteristic, complemented, Sylow
87Q8—521no—
88C2×C4—261no—
89C2×C4—261no—
90C2×C4D13⋊C1611yescharacteristic
91C2×C4#8809811yescharacteristic
92C2×C4#8811111yescharacteristic
93C8—21no—
94C8—521no—
95C8#8811611yescharacteristic
96C8#8811711yescharacteristic
97C22#1171825911yescharacteristic
98C4—21no—
99C4—21no—
100C4—521no—
101C4—521no—
102C4#1171824411yescharacteristic
103C4#1171827011yescharacteristic
104C2#1312980311yescharacteristic
105C2#1312995211yescharacteristic
106C2#1312995411yescharacteristic
subgroupG/H
centerC2×C8C22⋊#261
commutatorC2×C4×C13C2×C16
FrattiniC4×C8C2×#261
FittingC13×C4⋊C16C4
socle, prime radicalC22×C13C22⋊C16
cosocleC4×#6090C22
hypercenterC4⋊C16#261
hypocenterC13#7393
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C4⋊C16

Complements

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

NH ≅ G/Ntype
86. C13#7393semidirect

Maximal subgroups

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

subgroupindex
C4⋊#880362
#131299432
#131167412
#739313