Finite Group Databasebeta

← #15750393

Subgroups — #15750393

Order 3328.

116 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 47 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#13112972C211yesmaximal, characteristic
2#13112904C211yesmaximal, characteristic
3C13×#2176C211yesmaximal, characteristic
4C2×C13×Q32C411yescharacteristic
5C4×C13×Q16—21no—
6C13×#367C411yescharacteristic
7C13×#358—21no—
8C13×#346C2211yescharacteristic
9#11718091—21no—
10#11718055—21no—
11C2×C13×Q16—21no—
12C4×Q8×C13—41no—
13C13×Q32—21no—
14C13×Q32C812yes—
15C2×C13×C16C2×C411yescharacteristic
16C2×C13×C16D411yescharacteristic
17C13×#107—21no—
18C13×#103—41no—
19C4×C8×C13D411yescharacteristic
20#88052—41no—
21#88034—22no—
22#7391—131nomaximal, Sylow
23C2×Q8×C13—41no—
24C13×Q16—22no—
25C13×Q16—41no—
26C2×C8×C13C22⋊C411yescharacteristic
27C2×C8×C13D811yescharacteristic
28C13×C4⋊C4—41no—
29C13×C4⋊C4—81no—
30C42×C13—81no—
31C42×C13SD1611yescharacteristic
32C13×C16—21no—
33C13×C16C2×C811yescharacteristic
34C13×C16M1611yescharacteristic
35#6090—81no—
36#2176D1311yescharacteristic
37#1398—131no—
38#1369—131no—
39Q8×C13—42no—
40Q8×C13—81no—
41C2×C4×C13—21no—
42C2×C4×C13—81no—
43C2×C4×C13—81no—
44C2×C4×C13#10211yescharacteristic
45C8×C13—21no—
46C8×C13C22⋊C811yescharacteristic
47C8×C13#10411yescharacteristic
48C2×Q32Dic1311yescharacteristic
49C4×Q16—21no—
50M64—261no—
51#367Dic1311yescharacteristic
52#364—261no—
53#358—21no—
54#346C2×D1311yescharacteristic
55C22×C13#36111yescharacteristic
56C4×C13—41no—
57C4×C13—82no—
58C4×C13—161no—
59C4×C13D4⋊C811yescharacteristic
60C4×C13#36011yescharacteristic
61C2×Q16—21no—
62C4×Q8—41no—
63Q32—21no—
64Q32#105512yes—
65M32—521no—
66C2×C16C2×Dic1311yescharacteristic
67C2×C16C22⋊D1311yescharacteristic
68#107—21no—
69#103—41no—
70C4×C8C22⋊D1311yescharacteristic
71C32—262no—
72C2×C13—21no—
73C2×C13#133311yescharacteristic
74C2×Q8—41no—
75Q16—22no—
76Q16—41no—
77C2×C8#610411yescharacteristic
78C2×C8C22⋊Dic1311yescharacteristic
79C4⋊C4—41no—
80C4⋊C4—81no—
81C42—81no—
82C42#610511yescharacteristic
83C16—21no—
84C16—1041no—
85C16C2×#105511yescharacteristic
86C16#609911yescharacteristic
87C13#739111yescharacteristic, complemented, Sylow
88Q8—42no—
89Q8—81no—
90C2×C4—21no—
91C2×C4—81no—
92C2×C4—81no—
93C2×C4#8807211yescharacteristic
94C8—21no—
95C8C22⋊#105511yescharacteristic
96C8#8807711yescharacteristic
97C22#1171815511yescharacteristic
98C4—41no—
99C4—82no—
100C4—161no—
101C4D4⋊#105511yescharacteristic
102C4#1171815811yescharacteristic
103C2—21no—
104C2#1311280311yescharacteristic
subgroupG/H
centerC2#13112803
commutatorC13×C16C2×C8
Frattini#346C2×D13
FittingC13×#2176C2
socleC2×C13#1333
prime radicalC22×C13#361
cosocleC13×#346C22
hypercenter#2176D13
hypocenterC13#7391
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #346 ◁ #2176

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
#131129722
#131129042
C13×#21762
#739113