Finite Group Databasebeta

← #15750329

Subgroups — #15750329

Order 3328.

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

normal subgroups only

This group has 136 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#13114973C211yesmaximal, characteristic
2#13112787C211yesmaximal, characteristic
3C13×#1327C211yesmaximal, characteristic
4C13×#423C2211yescharacteristic
5#11718585C411yescharacteristic
6C2×C4×#1055C411yescharacteristic
7C13×#349—21no—
8#11718150—21no—
9#11718150—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#88052—41no—
19C4⋊#1055—41no—
20C4×#1055—21no—
21C4×#1055C812yes—
22#7368—131nomaximal, Sylow
23C22×C4×C13—21no—
24C22×C4×C13C22⋊C411yescharacteristic
25C13×M16—41no—
26C13×M16—41no—
27C2×C8×C13—21no—
28C2×C8×C13—21no—
29C42×C13—21no—
30C42×C13C2×C811yescharacteristic
31C42×C13M1611yescharacteristic
32#6099—42no—
33C2×#1055—22no—
34C2×#1055—41no—
35C2×#1055—41no—
36C2×#1055—41no—
37C13×C16—81no—
38#6090—81no—
39#1837—131no—
40#1327—131no—
41#1327D1311yescharacteristic
42C23×C13#10111yescharacteristic
43C2×C4×C13—21no—
44C2×C4×C13—21no—
45C2×C4×C13—21no—
46C2×C4×C13—21no—
47C2×C4×C13—42no—
48C2×C4×C13C22⋊C811yescharacteristic
49C2×C4×C13#9911yescharacteristic
50C8×C13—41no—
51C8×C13—41no—
52#1055—42no—
53#1055—81no—
54#423—131no—
55#423C2×D1311yescharacteristic
56C2×C4×C8—131no—
57#349—21no—
58#349—261no—
59#341—261no—
60#341—261no—
61C22×C13—21no—
62C22×C13—41no—
63C22×C13#32411yescharacteristic
64C4×C13—22no—
65C4×C13—21no—
66C4×C13—41no—
67C4×C13#35411yescharacteristic
68C4×C13#35511yescharacteristic
69C2×M16—261no—
70C2×M16D5211yescharacteristic
71C2×M16C22⋊D1311yescharacteristic
72C22×C8—261no—
73C2×C42C4×D1311yescharacteristic
74M32—41no—
75M32—521no—
76C4⋊C8—41no—
77C4⋊C8—521no—
78C4×C8—132no—
79C4×C8—261no—
80C2×C13—21no—
81C2×C13—41no—
82C2×C13#132411yescharacteristic
83C22×C4—21no—
84C22×C4#610311yescharacteristic
85M16—41no—
86M16—41no—
87M16—522no—
88C2×C8—21no—
89C2×C8—21no—
90C2×C8—262no—
91C2×C8—521no—
92C2×C8—521no—
93C2×C8—521no—
94C42—21no—
95C42C8×D1311yescharacteristic
96C42#609411yescharacteristic
97C16—81no—
98C16—1041no—
99C13#736811yescharacteristic, complemented, Sylow
100C23#8806411yescharacteristic
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—42no—
106C2×C4#8804611yescharacteristic
107C2×C4#8806011yescharacteristic
108C8—41no—
109C8—41no—
110C8—522no—
111C8—1041no—
112C22—21no—
113C22—41no—
114C22#1171806111yescharacteristic
115C4—22no—
116C4—21no—
117C4—41no—
118C4#1171806511yescharacteristic
119C4#1171806911yescharacteristic
120C2—21no—
121C2—41no—
122C2#1311277911yescharacteristic
subgroupG/H
centerC4#11718065
commutatorC42×C13C2×C8
Frattini#423C2×D13
FittingC13×#1327C2
socleC2×C13#1324
prime radicalC23×C13#101
cosocleC13×#423C22
hypercenter#1327D13
hypocenterC13#7368
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
99. C13#7368semidirect

Maximal subgroups

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

subgroupindex
#131149732
#131127872
C13×#13272
#736813