Finite Group Databasebeta

← #15750398

Subgroups — #15750398

Order 3328.

110 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 53 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#13116744C211yesmaximal, characteristic
2#13112970C211yesmaximal, characteristic
3C13×C4⋊C32C211yesmaximal, characteristic
4C8×Dic26C411yescharacteristic
5C2×C13×C32—21no—
6C4×C13×C16C2211yescharacteristic
7#11718094—21no—
8#11718093—21no—
9C2×#88034—21no—
10C4⋊#6090C411yescharacteristic
11C4×Dic26C811yescharacteristic
12C2×C13×C16D411yescharacteristic
13C2×C13×C16D411yescharacteristic
14C4×C8×C13C2×C411yescharacteristic
15#88054—21no—
16C8×Dic13—21no—
17C2×#6090—21no—
18C4⋊#1055C811yescharacteristic
19C13×C32—41no—
20#88034—22no—
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—21no—
31C13×C16SD1611yescharacteristic
32C13×C16Q1611yescharacteristic
33#6090—41no—
34#2183—131no—
35C4⋊C32D1311yescharacteristic
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—21no—
49C2×C32—261no—
50C4⋊C16—131no—
51C4⋊C16—261no—
52#346—261no—
53C4×C16C2×D1311yescharacteristic
54C22×C13C22⋊C1611yescharacteristic
55C4×C13—21no—
56C4×C13—21no—
57C4×C13Q8⋊C811yescharacteristic
58C4×C13#35011yescharacteristic
59Dic13—41no—
60Dic13—41no—
61C4×Q8—131no—
62C2×C16—261no—
63C2×C16D5211yescharacteristic
64C2×C16C22⋊D1311yescharacteristic
65C4⋊C8—131no—
66C4⋊C8—261no—
67C4×C8—261no—
68C4×C8C4×D1311yescharacteristic
69C32—41no—
70C32—262no—
71C2×C13Q8⋊C1611yescharacteristic
72C2×C13#140011yescharacteristic
73C2×C13#140111yescharacteristic
74C2×Q8—131no—
75C2×C8—261no—
76C2×C8#609411yescharacteristic
77C2×C8#610311yescharacteristic
78C4⋊C4—131no—
79C4⋊C4—261no—
80C42—261no—
81C42C8×D1311yescharacteristic
82C16—21no—
83C16—521no—
84C16#610511yescharacteristic
85C16#610711yescharacteristic
86C13#739311yescharacteristic, complemented, Sylow
87Q8—521no—
88C2×C4—261no—
89C2×C4—261no—
90C2×C4C16×D1311yescharacteristic
91C2×C4#8803811yescharacteristic
92C2×C4#8806011yescharacteristic
93C8—21no—
94C8—521no—
95C8#8805011yescharacteristic
96C8#8806511yescharacteristic
97C22#1171809911yescharacteristic
98C4—21no—
99C4—21no—
100C4—521no—
101C4—521no—
102C4#1171807611yescharacteristic
103C4#1171810711yescharacteristic
104C2#1311281411yescharacteristic
105C2#1311297511yescharacteristic
106C2#1311297711yescharacteristic
subgroupG/H
centerC2×C8#6103
commutatorC2×C4×C13C2×C16
FrattiniC4×C16C2×D13
FittingC13×C4⋊C32C2
socle, prime radicalC22×C13C22⋊C16
cosocleC4×C13×C16C22
hypercenterC4⋊C32D13
hypocenterC13#7393
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C4×C16 ◁ C4⋊C32

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
#131167442
#131129702
C13×C4⋊C322
#739313