Finite Group Databasebeta

← #15750340

Subgroups — #15750340

Order 3328.

152 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 39 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#13115007C211yesmaximal, characteristic
2#13112787C211yesmaximal, characteristic
3C13×#1327C211yesmaximal, characteristic
4C13×#423C2211yescharacteristic
5C2×#88062—21no—
6C2×#88062—21no—
7#11718585C411yescharacteristic
8C2×C4×#1055C411yescharacteristic
9C13×#349—21no—
10#11718145—21no—
11C2×C13×M16D411yescharacteristic
12C2×C13×M16D411yescharacteristic
13C2×C42×C13C2×C411yescharacteristic
14C2×#6099—21no—
15C22×#1055—21no—
16C13×M32—41no—
17C13×C4⋊C8—41no—
18#88062—42no—
19#88062—42no—
20#88052—41no—
21C4⋊#1055—41no—
22C4×#1055—21no—
23C4×#1055C812yes—
24#7373—131nomaximal, Sylow
25C22×C4×C13—21no—
26C22×C4×C13C22⋊C411yescharacteristic
27C13×M16—41no—
28C13×M16—41no—
29C2×C8×C13—21no—
30C2×C8×C13—21no—
31C42×C13—21no—
32C42×C13C2×C811yescharacteristic
33C42×C13M1611yescharacteristic
34#6099—41no—
35#6099—41no—
36C2×#1055—22no—
37C2×#1055—22no—
38C2×#1055—22no—
39C2×#1055—41no—
40C13×C16—81no—
41#6090—81no—
42#1848—131no—
43#1327—131no—
44#1327D1311yescharacteristic
45C23×C13#10111yescharacteristic
46C2×C4×C13—21no—
47C2×C4×C13—21no—
48C2×C4×C13—21no—
49C2×C4×C13—21no—
50C2×C4×C13—42no—
51C2×C4×C13C22⋊C811yescharacteristic
52C2×C4×C13#9911yescharacteristic
53C8×C13—41no—
54C8×C13—41no—
55#1055—24no—
56#1055—81no—
57C2×#108—261no—
58C2×#108—261no—
59#423—131no—
60#423C2×D1311yescharacteristic
61C2×C4×C8—131no—
62#349—21no—
63#349—261no—
64C22×C13—21no—
65C22×C13—41no—
66C22×C13#32411yescharacteristic
67C4×C13—22no—
68C4×C13—21no—
69C4×C13—41no—
70C4×C13#35311yescharacteristic
71C4×C13#35611yescharacteristic
72C2×M16—261no—
73C2×M16D5211yescharacteristic
74C2×M16C22⋊D1311yescharacteristic
75C22×C8—261no—
76C2×C42C4×D1311yescharacteristic
77M32—41no—
78M32—521no—
79#108—522no—
80#108—522no—
81C4⋊C8—41no—
82C4⋊C8—521no—
83C4×C8—132no—
84C4×C8—261no—
85C2×C13—21no—
86C2×C13—41no—
87C2×C13#132511yescharacteristic
88C22×C4—21no—
89C22×C4#610311yescharacteristic
90M16—41no—
91M16—41no—
92M16—521no—
93M16—521no—
94C2×C8—21no—
95C2×C8—21no—
96C2×C8—262no—
97C2×C8—262no—
98C2×C8—262no—
99C2×C8—521no—
100C42—21no—
101C42C8×D1311yescharacteristic
102C42#609411yescharacteristic
103C16—81no—
104C16—1041no—
105C13#737311yescharacteristic, complemented, Sylow
106C23#8806411yescharacteristic
107C2×C4—21no—
108C2×C4—21no—
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—42no—
112C2×C4#8804611yescharacteristic
113C2×C4#8806011yescharacteristic
114C8—41no—
115C8—41no—
116C8—264no—
117C8—1041no—
118C22—21no—
119C22—41no—
120C22#1171806111yescharacteristic
121C4—22no—
122C4—21no—
123C4—41no—
124C4#1171806611yescharacteristic
125C4#1171807011yescharacteristic
126C2—21no—
127C2—41no—
128C2#1311278111yescharacteristic
subgroupG/H
centerC4#11718066
commutatorC42×C13C2×C8
Frattini#423C2×D13
FittingC13×#1327C2
socleC2×C13#1325
prime radicalC23×C13#101
cosocleC13×#423C22
hypercenter#1327D13
hypocenterC13#7373
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #423 ◁ #1327

Complements

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

NH ≅ G/Ntype
105. C13#7373semidirect

Maximal subgroups

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

subgroupindex
#131150072
#131127872
C13×#13272
#737313