Finite Group Databasebeta

← D13⋊#1425 #16791426

Subgroups — D13⋊#1425 #16791426

Order 3328.

182 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 78 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
1D13⋊#368C212yesmaximal
2#13130000C212yesmaximal, complemented
3#13129999C212yesmaximal, complemented
4C2×D13×C32C211yesmaximal, characteristic
5D13⋊#108—22no—
6C2×C16×D13C2211yescharacteristic
7#11718224—22no—
8#11718223C2214yes—
9C2×C13×C32C411yescharacteristic
10C2×#88034C411yescharacteristic
11D13×C32C411yescharacteristic
12D13×C32C411yescharacteristic
13D13×C32C2211yescharacteristic
14D13×C32C2211yescharacteristic
15D13⋊M16—42no—
16C2×C8×D13D411yescharacteristic
17#88104—24no—
18#88103—42no—
19C2×C13×C16C2×C411yescharacteristic
20C2×#6090Q811yescharacteristic
21C16×D13C2×C411yescharacteristic
22C16×D13D411yescharacteristic
23C16×D13Q811yescharacteristic
24C16×D13C2311yescharacteristic
25C13×C32C2×C411yescharacteristic
26C13×C32C2×C411yescharacteristic
27#88034C2×C411yescharacteristic
28#88034C2×C411yescharacteristic
29C2×#1425—131nomaximal, Sylow
30C2×C4×D13D811yescharacteristic
31#6122—82no—
32#6118—44no—
33D13⋊C8—82no—
34C2×C8×C13C4⋊C411yescharacteristic
35C2×#1055Q1611yescharacteristic
36C8×D13C4⋊C411yescharacteristic
37C8×D13D811yescharacteristic
38C8×D13Q1611yescharacteristic
39C8×D13C2×D411yescharacteristic
40C13×C16C4⋊C411yescharacteristic
41C13×C16C22×C411yescharacteristic
42#6090C4⋊C411yescharacteristic
43#6090C2×Q811yescharacteristic
44C22×C32—131no—
45C2×#368—132no—
46#1425—132no—
47#1425—132no—
48C22×D13Q3211yescharacteristic
49C2×C4×C13#10711yescharacteristic
50C2×Dic13D1611yescharacteristic
51C4×D13#10711yescharacteristic
52C4×D13D1611yescharacteristic
53C4×D13Q3211yescharacteristic
54C4×D13C2×D811yescharacteristic
55#1057—84no—
56C8×C13#10711yescharacteristic
57C8×C13C2×C4⋊C411yescharacteristic
58#1055#10711yescharacteristic
59#1055C2×Q1611yescharacteristic
60C22×C16—131no—
61C2×#108—262no—
62C2×C32—131no—
63C2×C32—131no—
64C2×C32—131no—
65C2×C32—131no—
66C2×C32—131no—
67C2×C32#26111yescharacteristic
68#368—134no—
69#368—262no—
70C22×C13#36611yescharacteristic
71C2×D13—22no—
72C2×D13#36611yescharacteristic
73C2×D13C2×Q3211yescharacteristic
74C4×C13#36611yescharacteristic
75C4×C13C2×#10711yescharacteristic
76Dic13#36611yescharacteristic
77Dic13C2×D1611yescharacteristic
78C2×M16—522no—
79C22×C8—131no—
80C2×C16—131no—
81C2×C16—131no—
82C2×C16—131no—
83C2×C16—131no—
84C2×C16—131no—
85C2×C16C2×#26111yescharacteristic
86#108—264no—
87#108—522no—
88C32—131no—
89C32—131no—
90C32C2×#26111yescharacteristic
91C32C2×#26111yescharacteristic
92C2×C13—21no—
93C2×C13C2×#36611yescharacteristic
94D13—21no—
95D13#142512yescomplemented
96C22×C4—131no—
97M16—524no—
98M16—1042no—
99C2×C8—131no—
100C2×C8—131no—
101C2×C8—131no—
102C2×C8—131no—
103C2×C8—131no—
104C2×C8—1042no—
105C2×C8C4⋊#26111yescharacteristic
106C16—131no—
107C16—131no—
108C16C4⋊#26111yescharacteristic
109C16C22×#26111yescharacteristic
110C13C2×#142511yescharacteristic, complemented, Sylow
111C23—131no—
112C2×C4—131no—
113C2×C4—131no—
114C2×C4—131no—
115C2×C4—131no—
116C2×C4—131no—
117C2×C4#8810211yescharacteristic
118C8—131no—
119C8—131no—
120C8—1044no—
121C8#8810211yescharacteristic
122C8C2×C4⋊#26111yescharacteristic
123C22—131no—
124C22—131no—
125C22—262no—
126C22#1171822111yescharacteristic
127C4—131no—
128C4—131no—
129C4#1171822111yescharacteristic
130C4C2×#8810211yescharacteristic
131C2—21no—
132C2—132no—
133C2—261no—
134C2C2×#1171822111yescharacteristic
subgroupG/H
centerC4#11718221
commutatorC13×C16C22×C4
FrattiniC16C22×#261
FittingC2×C13×C32C4
socleC2×C13C2×#366
prime radicalC22×D13Q32
cosocleC16×D13C23
hypercenterC2×C32#261
hypocenterC13C2×#1425
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32

Complements

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

NH ≅ G/Ntype
2. #13130000C2semidirect
3. #13129999C2semidirect
95. D13#1425semidirect
110. C13C2×#1425semidirect

Maximal subgroups

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

subgroupindex
D13⋊#3682
#131300002
#131299992
C2×D13×C322
C2×#142513