Finite Group Databasebeta

← #15750366

Subgroups — #15750366

Order 3328.

118 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 55 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#13113034C211yesmaximal, characteristic, complemented
2#13112970C211yesmaximal, characteristic, complemented
3C13×#2170C211yesmaximal, characteristic
4C13×#504—21no—
5C13×#443C411yescharacteristic
6C13×#364C411yescharacteristic
7C13×#350—21no—
8C4×C13×C16C2211yescharacteristic
9#11718091—21no—
10C2×#88034—21no—
11C13×#135C811yescharacteristic
12C13×#131—21no—
13C13×M32—21no—
14C13×M32—41no—
15C2×C13×C16—41no—
16C2×C13×C16D411yescharacteristic
17C2×C13×C16D411yescharacteristic
18C13×#108C811yescharacteristic
19C13×#104—21no—
20C4×C8×C13C2×C411yescharacteristic
21#88034—22no—
22#88034—41no—
23#7382—131nomaximal, Sylow
24C13×#41—21no—
25C13×Q16C1611yescharacteristic
26C13×SD16—21no—
27C13×D8C1611yescharacteristic
28C13×M16—21no—
29C13×M16—41no—
30C2×C8×C13—41no—
31C2×C8×C13C22⋊C411yescharacteristic
32C2×C8×C13C2×C811yescharacteristic
33C42×C13M1611yescharacteristic
34C13×C16—21no—
35C13×C16—41no—
36C13×C16D811yescharacteristic
37C13×C16SD1611yescharacteristic
38#2170D1311yescharacteristic
39#1422—131no—
40#1397—131no—
41Q8×C13—21no—
42D4×C13—21no—
43D4×C13—41no—
44C2×C4×C13—21no—
45C2×C4×C13—41no—
46C2×C4×C13C22⋊C811yescharacteristic
47C8×C13—41no—
48C8×C13#10211yescharacteristic
49C8×C13#10411yescharacteristic
50C8×C13C2×C1611yescharacteristic
51C8×C13M3211yescharacteristic
52#504—21no—
53#443Dic1311yescharacteristic
54M64—261no—
55C2×C32—261no—
56#364Dic1311yescharacteristic
57#350—21no—
58C4×C16C2×D1311yescharacteristic
59C22×C13—41no—
60C22×C13#35011yescharacteristic
61C4×C13—41no—
62C4×C13—41no—
63C4×C13D4⋊C811yescharacteristic
64C4×C13C22⋊C1611yescharacteristic
65#135#105511yescharacteristic
66#131—21no—
67M32—21no—
68M32—41no—
69C2×C16—41no—
70C2×C16C22⋊D1311yescharacteristic
71C2×C16C22⋊D1311yescharacteristic
72#108#105511yescharacteristic
73#104—21no—
74C4×C8C2×Dic1311yescharacteristic
75C32—262no—
76C32—521no—
77C2×C13—21no—
78C2×C13—81no—
79C2×C13D4⋊C1611yescharacteristic
80#41—21no—
81Q16#609011yescharacteristic
82SD16—21no—
83D8#609011yescharacteristic
84M16—21no—
85M16—41no—
86C2×C8—41no—
87C2×C8C2×#105511yescharacteristic
88C2×C8C22⋊Dic1311yescharacteristic
89C42#609911yescharacteristic
90C16—21no—
91C16—41no—
92C16#610411yescharacteristic
93C16#610511yescharacteristic
94C13#738211yescharacteristic, complemented, Sylow
95Q8—21no—
96D4—21no—
97D4—41no—
98C2×C4—21no—
99C2×C4—41no—
100C2×C4C22⋊#105511yescharacteristic
101C8—41no—
102C8C2×#609011yescharacteristic
103C8#8805211yescharacteristic
104C8#8807211yescharacteristic
105C8#8807711yescharacteristic
106C22—41no—
107C22#1171815311yescharacteristic
108C4—41no—
109C4—41no—
110C4D4⋊#105511yescharacteristic
111C4C22⋊#609011yescharacteristic
112C2—21no—
113C2—81no—
114C2D4⋊#609011yescharacteristic
subgroupG/H
centerC8#88072
commutatorC8×C13C2×C16
FrattiniC4×C16C2×D13
FittingC13×#2170C2
socleC2×C13D4⋊C16
prime radicalC13×#135C8
cosocleC4×C13×C16C22
hypercenter#2170D13
hypocenterC13#7382
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C2×C16 ◁ C4×C16 ◁ #2170

Complements

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

NH ≅ G/Ntype
1. #13113034C2semidirect
2. #13112970C2semidirect
94. C13#7382semidirect

Maximal subgroups

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

subgroupindex
#131130342
#131129702
C13×#21702
#738213