Finite Group Databasebeta

← #13112985

Subgroups — #13112985

Order 1664.

112 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 23 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#11718722C211yesmaximal, characteristic
2C13×#329C211yesmaximal, characteristic, complemented
3#11718134C211yesmaximal, characteristic, complemented
4#88251C411yescharacteristic
5C13×#124C2211yescharacteristic
6#88196—21no—
7C13×#97—21no—
8#88076—21no—
9#88073C411yescharacteristic
10#88045—21no—
11C2×Q8×C13D411yescharacteristic
12C2×D4×C13C2×C411yescharacteristic
13C2×C22⋊D13—41no—
14#6129—41no—
15D4×D13—41no—
16#6127—21no—
17C2×C8×C13—41no—
18C13×C22⋊C4—41no—
19C42×C13D411yescharacteristic
20#6107—41no—
21#6106—41no—
22#6099—21no—
23#6099—41no—
24#1403—131nomaximal, Sylow
25C23×C13—21no—
26C22×D13—41no—
27Q8×C13—41no—
28D4×C13—41no—
29C2×C4×C13—21no—
30C2×C4×C13—21no—
31C2×C4×C13C22⋊C411yescharacteristic
32C22⋊D13—42no—
33C22⋊D13—41no—
34C2×Dic13—41no—
35D52—21no—
36C4×D13—41no—
37Dic26—21no—
38C8×C13—42no—
39#1055—41no—
40#1055—81no—
41#455—131no—
42#355—131no—
43#329D1311yescharacteristic, complemented
44C22×C13—41no—
45C22×C13—81no—
46C22×C13#9911yescharacteristic
47C2×D13—41no—
48C2×D13—161no—
49C4×C13—21no—
50C4×C13—41no—
51C4×C13—41no—
52Dic13—41no—
53H(5,𝔽2)—131no—
54#137—261no—
55#124C2×D1311yescharacteristic
56#104—261no—
57#101—261no—
58#100—131no—
59#97—21no—
60C2×C13—21no—
61C2×C13—81no—
62C2×C13AΣL(1,𝔽16)11yescharacteristic
63D13—81no—
64#41—261no—
65#41—521no—
66C2×Q8D5211yescharacteristic
67C2×D4—521no—
68C2×D4—521no—
69C2×D4C4×D1311yescharacteristic
70Q16—521no—
71SD16—521no—
72M16—261no—
73M16—521no—
74C2×C8—41no—
75C22⋊C4—41no—
76C42C22⋊D1311yescharacteristic
77C13#140311yescharacteristic, complemented, Sylow
78C23—21no—
79C23—521no—
80Q8—41no—
81Q8—261no—
82D4—41no—
83D4—261no—
84D4—522no—
85D4—521no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—521no—
89C2×C4—521no—
90C2×C4#610311yescharacteristic
91C8—42no—
92C8—521no—
93C8—1041no—
94C22—41no—
95C22—81no—
96C22—521no—
97C22—2081no—
98C22#8804611yescharacteristic
99C4—21no—
100C4—41no—
101C4—41no—
102C4—521no—
103C2—21no—
104C2—81no—
105C2—1041no—
106C2#1171806711yescharacteristic
subgroupG/H
centerC2#11718067
commutatorC2×D4×C13C2×C4
Frattini#124C2×D13
FittingC13×#329C2
socleC2×C13AΣL(1,𝔽16)
prime radical#88251C4
cosocleC13×#124C22
hypercenter#329D13
hypocenterC13#1403
LCSG ▷ C2×D4×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #329

Complements

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

NH ≅ G/Ntype
2. C13×#329C2semidirect
3. #11718134C2semidirect
43. #329D13semidirect
77. C13#1403semidirect

Maximal subgroups

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

subgroupindex
#117187222
C13×#3292
#117181342
#140313