Finite Group Databasebeta

← #15750341

Subgroups — #15750341

Order 3328.

152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 43 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#13112787C212yesmaximal
2C13×#1848C211yesmaximal, characteristic
3C2×C13×#108—22no—
4C13×#423C411yescharacteristic
5C13×#423C2211yescharacteristic
6C2×C4×C8×C13C411yescharacteristic
7#11718145—22no—
8C2×C13×M16—21no—
9C2×C13×M16D412yes—
10C22×C8×C13—21no—
11C2×C42×C13C2×C411yescharacteristic
12C13×#108—44no—
13C13×C4⋊C8—41no—
14C13×C4⋊C8—41no—
15C4×C8×C13—21no—
16C4×C8×C13C812yes—
17#88052—42no—
18#7373—131nomaximal, Sylow
19C22×C4×C13—21no—
20C22×C4×C13C22⋊C411yescharacteristic
21C13×M16—42no—
22C13×M16—42no—
23C2×C8×C13—22no—
24C2×C8×C13—22no—
25C2×C8×C13—22no—
26C2×C8×C13—22no—
27C2×C8×C13—41no—
28C42×C13—21no—
29C42×C13C2×C811yescharacteristic
30C42×C13M1611yescharacteristic
31#6090—82no—
32#1848D1311yescharacteristic
33#1327—132no—
34C23×C13#10111yescharacteristic
35C2×C4×C13—21no—
36C2×C4×C13—21no—
37C2×C4×C13—21no—
38C2×C4×C13—21no—
39C2×C4×C13—42no—
40C2×C4×C13C22⋊C811yescharacteristic
41C2×C4×C13#9911yescharacteristic
42C8×C13—24no—
43C8×C13—42no—
44C8×C13—81no—
45C2×#108—22no—
46#423Dic1311yescharacteristic
47#423C2×D1311yescharacteristic
48C2×C4×C8Dic1311yescharacteristic
49#349—262no—
50C22×C13—21no—
51C22×C13—41no—
52C22×C13#32411yescharacteristic
53C4×C13—22no—
54C4×C13—21no—
55C4×C13—41no—
56C4×C13#35311yescharacteristic
57C4×C13#35611yescharacteristic
58C2×M16—21no—
59C2×M16C22⋊D1312yes—
60C22×C8—21no—
61C2×C42C2×Dic1311yescharacteristic
62M32—522no—
63#108—44no—
64C4⋊C8—41no—
65C4⋊C8—41no—
66C4×C8—21no—
67C4×C8#105512yes—
68C2×C13—21no—
69C2×C13—41no—
70C2×C13#132511yescharacteristic
71C22×C4—21no—
72C22×C4C22⋊Dic1311yescharacteristic
73M16—42no—
74M16—42no—
75C2×C8—22no—
76C2×C8—22no—
77C2×C8—22no—
78C2×C8—22no—
79C2×C8—41no—
80C42—21no—
81C42C2×#105511yescharacteristic
82C42#609911yescharacteristic
83C16—1042no—
84C13#737311yescharacteristic, complemented, Sylow
85C23#8807611yescharacteristic
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—21no—
90C2×C4—42no—
91C2×C4C22⋊#105511yescharacteristic
92C2×C4#8807411yescharacteristic
93C8—24no—
94C8—42no—
95C8—81no—
96C22—21no—
97C22—41no—
98C22#1171812011yescharacteristic
99C4—22no—
100C4—21no—
101C4—41no—
102C4#1171813711yescharacteristic
103C4#1171814011yescharacteristic
104C2—21no—
105C2—41no—
106C2#1311278211yescharacteristic
subgroupG/H
centerC4#11718137
commutatorC42×C13C2×C8
Frattini#423C2×D13
FittingC13×#1848C2
socleC2×C13#1325
prime radicalC23×C13#101
cosocleC13×#423C22
hypercenter#1848D13
hypocenterC13#7373
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #423 ◁ #1848

Complements

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

NH ≅ G/Ntype
84. C13#7373semidirect

Maximal subgroups

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

subgroupindex
#131127872
C13×#18482
#737313