Finite Group Databasebeta

← D8×#1057 #13130415

Subgroups — D8×#1057 #13130415

Order 1664.

196 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 74 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
1D4×#1057C212yesmaximal, complemented
2D8×Dic13C211yesmaximal, characteristic
3D4⋊#1057C212yesmaximal, complemented
4#11718254C211yesmaximal, characteristic, complemented
5C8×#1057C211yesmaximal, characteristic, complemented
6C22×#1057—22no—
7C2×C13×D8C411yescharacteristic
8D4×Dic13C2212yes—
9C22⋊#1057—22no—
10C4⋊#1057C2212yes—
11C4×#1057C2211yescharacteristic
12C4×#1057C2211yescharacteristic
13#88072C412yes—
14#88058C411yescharacteristic
15C8×Dic13C2211yescharacteristic
16C2×D4×C13C2×C412yes—
17C22×Dic13—22no—
18C2×#1057—21no—
19C2×#1057—22no—
20C2×#1057—44no—
21C2×#1057D411yescharacteristic
22C2×#1057D411yescharacteristic
23C13×D8C814yescomplemented
24C2×C8×C13C2×C411yescharacteristic
25C22⋊Dic13—22no—
26C4⋊Dic13C2×C412yes—
27C4×Dic13C2311yescharacteristic
28C2×#1055C2×C411yescharacteristic
29C8×D8—131nomaximal, Sylow
30C23×C13—22no—
31D4×C13—22no—
32D4×C13C2×C814yescomplemented
33C2×C4×C13C22×C411yescharacteristic
34C2×Dic13—22no—
35C2×Dic13—42no—
36C2×Dic13—42no—
37C2×Dic13C2×D411yescharacteristic
38C2×Dic13#4111yescharacteristic
39#1057—22no—
40#1057—21no—
41#1057—42no—
42#1057D812yesdirect product factor
43C8×C13C2×C812yescomplemented
44#1055—21no—
45C4×D8—131no—
46C8×D4—132no—
47#335—131no—
48D4⋊C8—132no—
49C82—131no—
50C22×C13—24no—
51C22×C13—42no—
52C22×C13—42no—
53C22×C13C4×D411yescharacteristic
54C4×C13C22×C811yescharacteristic
55C4×C13#13111yescharacteristic
56Dic13—21no—
57Dic13—42no—
58Dic13C2×D811yescharacteristic
59Dic13#13511yescharacteristic
60C2×D8#26111yescharacteristic
61C22×C8—262no—
62C4×D4—132no—
63#107—131no—
64C4⋊C8—132no—
65#102—132no—
66C22⋊C8—262no—
67C4×C8—131no—
68C4×C8—131no—
69C4×C8—131no—
70C2×C13—44no—
71C2×C13C8×D411yescharacteristic
72C2×C13C4×D811yescharacteristic
73C2×C13#44311yescharacteristic
74C2×D4C2×#26112yes—
75C22×C4—262no—
76D8#105714yesdirect product factor
77C2×C8—131no—
78C2×C8—131no—
79C2×C8—131no—
80C2×C8—261no—
81C2×C8—262no—
82C2×C8—524no—
83C2×C8C2×#26111yescharacteristic
84C4⋊C4—132no—
85C22⋊C4—262no—
86C42—131no—
87C13C8×D811yescharacteristic, complemented, Sylow
88C23—22no—
89D4—22no—
90D4C2×#105714yescomplemented
91C2×C4—131no—
92C2×C4—131no—
93C2×C4—262no—
94C2×C4—522no—
95C2×C4—522no—
96C2×C4C22×#26111yescharacteristic
97C8—132no—
98C8—261no—
99C8—262no—
100C8—261no—
101C8—522no—
102C8C2×#105712yescomplemented
103C22—24no—
104C22—42no—
105C22—42no—
106C22D4×#26111yescharacteristic
107C4—131no—
108C4—131no—
109C4—261no—
110C4—522no—
111C4#8823811yescharacteristic
112C4C22×#105711yescharacteristic
113C2—44no—
114C2D8×#26111yescharacteristic
115C2#1171910311yescharacteristic
116C2D4×#105711yescharacteristic
subgroupG/H
centerC22D4×#261
commutatorC4×C13C22×C8
FrattiniC2×C4C22×#261
Fitting, prime radicalC2×C13×D8C4
socleC22×C13C4×D4
cosocleC4×Dic13C23
hypercenterC2×D8#261
hypocenterC13C8×D8
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. D4×#1057C2semidirect
3. D4⋊#1057C2semidirect
4. #11718254C2semidirect
5. C8×#1057C2semidirect
23. C13×D8C8semidirect
32. D4×C13C2×C8semidirect
42. #1057D8direct (N × H)
43. C8×C13C2×C8semidirect
76. D8#1057direct (N × H)
87. C13C8×D8semidirect
90. D4C2×#1057semidirect
102. C8C2×#1057semidirect

Maximal subgroups

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

subgroupindex
D4×#10572
D8×Dic132
D4⋊#10572
#117182542
C8×#10572
C8×D813