Finite Group Databasebeta

← #15750576

Subgroups — #15750576

Order 3328.

102 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 51 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⋊#88034C211yesmaximal, characteristic
2#13112910C211yesmaximal, characteristic
3C13×#2253C211yesmaximal, characteristic
4C13×#499—21no—
5C13×#367—21no—
6C13×#366C411yescharacteristic
7C13×#366C411yescharacteristic
8C4×C13×C16C2211yescharacteristic
9C2×#88034—21no—
10#11718050—21no—
11C13×#125—41no—
12C2×C13×C16C2×C411yescharacteristic
13C2×C13×C16D411yescharacteristic
14C13×#107—21no—
15C13×#107—21no—
16C13×#106—41no—
17C4×C8×C13D411yescharacteristic
18C4⋊#1055—41no—
19#88034—41no—
20#7452—131nomaximal, Sylow
21C2×C8×C13C22⋊C411yescharacteristic
22C2×C8×C13SD1611yescharacteristic
23C13×C4⋊C4—41no—
24C13×C4⋊C4—41no—
25C13×C4⋊C4—81no—
26C13×C4⋊C4—81no—
27C42×C13D811yescharacteristic
28C2×#1055—81no—
29C13×C16—21no—
30C13×C16SD1611yescharacteristic
31C13×C16Q1611yescharacteristic
32#2253D1311yescharacteristic
33C4⋊C32—131no—
34#1372—131no—
35C2×C4×C13—81no—
36C2×C4×C13—81no—
37C2×C4×C13#10211yescharacteristic
38C2×C4×C13D1611yescharacteristic
39C2×C4×C13SD3211yescharacteristic
40C8×C13—21no—
41C8×C13#10111yescharacteristic
42C8×C13#10311yescharacteristic
43#1055—161no—
44#499—21no—
45C2×C32—261no—
46#367—21no—
47#366Dic1311yescharacteristic
48#366Dic1311yescharacteristic
49C4×C16C2×D1311yescharacteristic
50#335—261no—
51C22×C13#35711yescharacteristic
52C4×C13—21no—
53C4×C13—21no—
54C4×C13—161no—
55C4×C13—161no—
56C4×C13#33211yescharacteristic
57C4×C13#36211yescharacteristic
58#125—41no—
59C2×C16C2×Dic1311yescharacteristic
60C2×C16C22⋊D1311yescharacteristic
61#107—21no—
62#107—21no—
63#106—41no—
64C4⋊C8—521no—
65C4×C8C22⋊D1311yescharacteristic
66C32—521no—
67C2×C13#136411yescharacteristic
68C2×C13#141711yescharacteristic
69C2×C13#141811yescharacteristic
70C2×C8—1041no—
71C2×C8#610511yescharacteristic
72C2×C8C22⋊Dic1311yescharacteristic
73C4⋊C4—41no—
74C4⋊C4—41no—
75C4⋊C4—81no—
76C4⋊C4—81no—
77C42#610411yescharacteristic
78C16—21no—
79C16#610611yescharacteristic
80C16#610711yescharacteristic
81C13#745211yescharacteristic, complemented, Sylow
82C2×C4—81no—
83C2×C4—81no—
84C2×C4#8806611yescharacteristic
85C2×C4#8806711yescharacteristic
86C2×C4#8807211yescharacteristic
87C8—21no—
88C8—2081no—
89C8#8807511yescharacteristic
90C8#8807611yescharacteristic
91C22#1171815411yescharacteristic
92C4—21no—
93C4—21no—
94C4—161no—
95C4—161no—
96C4#1171813911yescharacteristic
97C4#1171815711yescharacteristic
98C2#1311289111yescharacteristic
99C2#1311302011yescharacteristic
100C2#1311302311yescharacteristic
subgroupG/H
centerC22#11718154
commutatorC2×C13×C16C2×C4
FrattiniC4×C16C2×D13
FittingC13×#2253C2
socle, prime radicalC22×C13#357
cosocleC4×C13×C16C22
hypercenter#2253D13
hypocenterC13#7452
LCSG ▷ C2×C13×C16 ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×C16 ◁ #2253

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
C4⋊#880342
#131129102
C13×#22532
#745213