Finite Group Databasebeta

← #13130736

Subgroups — #13130736

Order 1664.

316 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C2×C4⋊C4×D13C211yesmaximal, characteristic
2#11719126C212yesmaximal
3#11718291C214yesmaximal, complemented
4C22×C4×D13C412yes—
5C22×C4×D13C2211yescharacteristic
6C2×#6122C2214yes—
7C2×C13×C4⋊C4C411yescharacteristic
8C2×C4⋊Dic13C411yescharacteristic
9C2×#6101C2212yes—
10C4⋊C4×D13—22no—
11C4⋊C4×D13—22no—
12#88111—22no—
13#88111—22no—
14C23×D13C2×C411yescharacteristic
15C22×C4×C13C2×C412yes—
16C22×C4×C13C2×C411yescharacteristic
17C22×Dic13C2×C412yes—
18C22×Dic13C2311yescharacteristic
19C2×C4×D13—24no—
20C2×C4×D13—22no—
21C2×C4×D13—22no—
22C2×C4×D13—44no—
23C2×C4×D13D412yes—
24C2×C4×D13D412yes—
25#6122—28no—
26C2×#1057—24no—
27C13×C4⋊C4—22no—
28C4⋊Dic13—22no—
29#6101—24no—
30#1821—131nomaximal, Sylow
31C23×C13C22×C411yescharacteristic
32C22×D13—22no—
33C22×D13—22no—
34C22×D13—22no—
35C22×D13C22⋊C411yescharacteristic
36C22×D13C22⋊C411yescharacteristic
37C2×C4×C13—22no—
38C2×C4×C13—22no—
39C2×C4×C13—42no—
40C2×C4×C13C22⋊C412yes—
41C2×Dic13—22no—
42C2×Dic13—42no—
43C2×Dic13C2×D412yes—
44C2×Dic13#4114yes—
45C4×D13—24no—
46C4×D13—24no—
47C4×D13—44no—
48C4×D13—44no—
49#1057—44no—
50C22×C4⋊C4—131no—
51#407—132no—
52#343—134no—
53C22×C13—21no—
54C22×C13—21no—
55C22×C13C2×C22⋊C411yescharacteristic
56C22×C13#11712yes—
57C2×D13—28no—
58C2×D13—21no—
59C2×D13—21no—
60C2×D13—21no—
61C2×D13—21no—
62C2×D13#10012yes—
63C2×D13#10112yes—
64C4×C13—22no—
65C4×C13—42no—
66Dic13—42no—
67Dic13#12314yes—
68C23×C4—131no—
69C23×C4—132no—
70C2×M16—134no—
71C2×C4⋊C4—132no—
72C2×C4⋊C4—131no—
73C2×C4⋊C4—262no—
74C2×C4⋊C4—262no—
75C2×C4⋊C4#26111yescharacteristic
76C22⋊C8—262no—
77C22⋊C8—262no—
78C2×C13—22no—
79C2×C13#38111yescharacteristic
80C2×C13C2×#10011yescharacteristic
81C2×C13C2×#10111yescharacteristic
82D13—22no—
83D13—22no—
84C24—131no—
85C22×C4—131no—
86C22×C4—132no—
87C22×C4—132no—
88C22×C4—132no—
89C22×C4—264no—
90C22×C4—262no—
91C22×C4—262no—
92C22×C4—524no—
93C22×C4C2×#26112yes—
94C22×C4C2×#26111yescharacteristic
95M16—268no—
96C2×C8—264no—
97C4⋊C4—22no—
98C4⋊C4—264no—
99C4⋊C4—262no—
100C13#182111yescharacteristic, complemented, Sylow
101C23—131no—
102C23—131no—
103C23—262no—
104C23—262no—
105C23—262no—
106C23C22×#26111yescharacteristic
107C2×C4—22no—
108C2×C4—22no—
109C2×C4—42no—
110C2×C4—134no—
111C2×C4—132no—
112C2×C4—264no—
113C2×C4—264no—
114C2×C4—262no—
115C2×C4—524no—
116C2×C4—524no—
117C2×C4—522no—
118C2×C4C22⋊#26112yes—
119C8—524no—
120C22—21no—
121C22—21no—
122C22—132no—
123C22—132no—
124C22—268no—
125C22—261no—
126C22—261no—
127C22—261no—
128C22—261no—
129C22#8823712yes—
130C22C2×C22⋊#26111yescharacteristic
131C4—22no—
132C4—42no—
133C4—134no—
134C4—522no—
135C2—22no—
136C2—262no—
137C2—262no—
138C2#1171913511yescharacteristic
139C2D13⋊#10011yescharacteristic
140C2D13⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC2×C13×C4⋊C4C4
socleC22×C13C2×C22⋊C4
prime radicalC23×D13C2×C4
cosocleC22×Dic13C23
hypercenterC2×C4⋊C4#261
hypocenterC13#1821
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #11718291C2semidirect
100. C13#1821semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D132
#117191262
#117182912
#182113