Finite Group Databasebeta

← #15750319

Subgroups — #15750319

Order 3328.

124 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 49 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#13116594C211yesmaximal, characteristic
2C22⋊#88034C211yesmaximal, characteristic
3C13×C22⋊C32C211yesmaximal, characteristic
4C22×C13×C16C2211yescharacteristic
5#11718762C411yescharacteristic
6C2×#88052C411yescharacteristic
7C2×C13×C32—21no—
8#11718093—21no—
9#11718093—21no—
10C2×#88034—21no—
11C22×C8×C13C2×C411yescharacteristic
12#88180C811yescharacteristic
13C2×#6099C811yescharacteristic
14C2×C13×C16—41no—
15C2×C13×C16D411yescharacteristic
16C2×C13×C16D411yescharacteristic
17#88055—21no—
18C8×Dic13—21no—
19#88052—41no—
20C2×#6090—21no—
21C13×C32—41no—
22#88034—41no—
23#7363—131nomaximal, Sylow
24C22×C4×C13C2×C811yescharacteristic
25C2×C8×C13—21no—
26C2×C8×C13—21no—
27C2×C8×C13C22⋊C411yescharacteristic
28C2×C8×C13M1611yescharacteristic
29C22⋊Dic13—21no—
30C4⋊Dic13C1611yescharacteristic
31C4⋊Dic13C1611yescharacteristic
32C4×Dic13—21no—
33#6099—41no—
34C2×#1055—21no—
35C13×C16—21no—
36C13×C16—21no—
37#6090—41no—
38#2151—131no—
39C22⋊C32—131no—
40C22⋊C32D1311yescharacteristic
41C23×C13M3211yescharacteristic
42C2×C4×C13—21no—
43C2×C4×C13—21no—
44C2×C4×C13C22⋊C811yescharacteristic
45C2×C4×C13C2×C1611yescharacteristic
46C2×Dic13—21no—
47C2×Dic13—21no—
48C8×C13—21no—
49C8×C13#9911yescharacteristic
50C8×C13#10111yescharacteristic
51#1055—41no—
52C2×M32—131no—
53C22×C16C2×D1311yescharacteristic
54#405—131no—
55C2×C32—21no—
56C2×C32—261no—
57C4⋊C16—261no—
58C4⋊C16—261no—
59C22×C13—21no—
60C22×C13—21no—
61C22×C13—21no—
62C22×C13C22⋊C1611yescharacteristic
63C4×C13—21no—
64C4×C13#32411yescharacteristic
65C4×C13#34911yescharacteristic
66Dic13—41no—
67Dic13—41no—
68C2×M16—131no—
69C22×C8C4×D1311yescharacteristic
70#117—131no—
71M32—521no—
72C2×C16—41no—
73C2×C16—261no—
74C2×C16D5211yescharacteristic
75C2×C16C22⋊D1311yescharacteristic
76#97—261no—
77C4×C8—261no—
78C32—41no—
79C32—521no—
80C2×C13—41no—
81C2×C13#132211yescharacteristic
82C2×C13#140111yescharacteristic
83C2×C13#140111yescharacteristic
84C22×C4C8×D1311yescharacteristic
85M16—521no—
86C2×C8—21no—
87C2×C8—21no—
88C2×C8—261no—
89C2×C8#609411yescharacteristic
90C2×C8#610311yescharacteristic
91C4⋊C4—131no—
92C4⋊C4—131no—
93C22⋊C4—261no—
94C42—261no—
95C16—21no—
96C16—21no—
97C16—521no—
98C13#736311yescharacteristic, complemented, Sylow
99C23#8803811yescharacteristic
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—261no—
103C2×C4—261no—
104C2×C4C16×D1311yescharacteristic
105C2×C4#8806011yescharacteristic
106C8—21no—
107C8—521no—
108C8#8804611yescharacteristic
109C8#8806411yescharacteristic
110C22—21no—
111C22—21no—
112C22—21no—
113C22#1171809911yescharacteristic
114C4—21no—
115C4—521no—
116C4—521no—
117C4#1171806111yescharacteristic
118C4#1171810611yescharacteristic
119C2—41no—
120C2#1311277511yescharacteristic
121C2#1311297711yescharacteristic
122C2#1311297911yescharacteristic
subgroupG/H
centerC2×C8#6103
commutatorC2×C4×C13C2×C16
FrattiniC22×C16C2×D13
FittingC13×C22⋊C32C2
socleC22×C13C22⋊C16
prime radicalC23×C13M32
cosocleC22×C13×C16C22
hypercenterC22⋊C32D13
hypocenterC13#7363
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C22×C16 ◁ C22⋊C32

Complements

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

NH ≅ G/Ntype
98. C13#7363semidirect

Maximal subgroups

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

subgroupindex
#131165942
C22⋊#880342
C13×C22⋊C322
#736313