Finite Group Databasebeta

← #13131701

Subgroups — #13131701

Order 1664.

452 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 164 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×#88147C211yesmaximal, characteristic
2#11719127C214yesmaximal, complemented
3#11719119C212yesmaximal, complemented
4#11719076C218yesmaximal, complemented
5C22×D52C411yescharacteristic
6C22×C4×D13C2212yes—
7C2×#6118C2218yescomplemented
8C2×C13×C4⋊C4C411yescharacteristic
9C2×#6103C412yes—
10C2×C4×Dic13C2211yescharacteristic
11#88147C414yes—
12#88147C2214yes—
13C22⋊#1057C2214yes—
14#88111C2218yescomplemented
15C4⋊#1057C2214yescomplemented
16C4×#1057C2214yescomplemented
17C23×D13C2×C412yes—
18C22×C4×C13C2×C412yes—
19C22×C4×C13C2×C411yescharacteristic
20C22×Dic13C2×C411yescharacteristic
21C22×Dic13C2311yescharacteristic
22C2×D52—24no—
23C2×D52C2×C414yes—
24C2×C4×D13—44no—
25C2×C4×D13C2×C414yes—
26C2×C4×D13C2314yes—
27C2×#1057C2318yes—
28#6118—48no—
29C13×C4⋊C4C2×C414yes—
30#6103C2×C418yes—
31C4×Dic13C2×C412yes—
32C4×Dic13C2312yes—
33#2975—131nomaximal, Sylow
34C23×C13C22×C411yescharacteristic
35C22×D13—24no—
36C22×D13—42no—
37C22×D13—42no—
38C22×D13C22×C414yes—
39C2×C4×C13—42no—
40C2×C4×C13M1614yescomplemented
41C2×C4×C13C22×C414yes—
42C2×C4×C13C22×C412yes—
43C2×Dic13—22no—
44C2×Dic13—41no—
45C2×Dic13C22×C411yescharacteristic
46C2×Dic13C22×C412yes—
47C2×Dic13C2411yescharacteristic
48D52—28no—
49C4×D13—28no—
50C4×D13—44no—
51#1057—28no—
52C2×C4×D4—131no—
53#436—138no—
54#431—132no—
55#407—134no—
56C22×C13—21no—
57C22×C13—21no—
58C22×C13C2×M1612yes—
59C22×C13C23×C411yescharacteristic
60C2×D13—24no—
61C2×D13—24no—
62C2×D13—24no—
63C2×D13—48no—
64C4×C13—24no—
65C4×C13C2×M1614yes—
66Dic13—21no—
67Dic13—22no—
68Dic13H(5,𝔽2)12yes—
69C22×D4—131no—
70C23×C4—132no—
71C2×M16—138no—
72C4×D4—134no—
73C4×D4—134no—
74C2×C4⋊C4#26111yescharacteristic
75C2×C22⋊C4—132no—
76C2×C42—131no—
77C4⋊C8—134no—
78C22⋊C8—138no—
79C22⋊C8—134no—
80C4×C8—134no—
81C2×C13—22no—
82C2×C13#51811yescharacteristic
83C2×C13C22×M1611yescharacteristic
84C2×C13#56811yescharacteristic
85D13—44no—
86C24—132no—
87C2×D4—134no—
88C2×D4—264no—
89C22×C4—131no—
90C22×C4—131no—
91C22×C4—134no—
92C22×C4—134no—
93C22×C4—524no—
94C22×C4C2×#26112yes—
95C22×C4C2×#26111yescharacteristic
96M16—528no—
97C2×C8—138no—
98C4⋊C4C2×#26114yes—
99C22⋊C4—138no—
100C42—132no—
101C42—132no—
102C13#297511yescharacteristic, complemented, Sylow
103C23—134no—
104C23—264no—
105C23—522no—
106C23—522no—
107C23C22×#26111yescharacteristic
108D4—268no—
109C2×C4—42no—
110C2×C4—131no—
111C2×C4—132no—
112C2×C4—131no—
113C2×C4—268no—
114C2×C4—262no—
115C2×C4—524no—
116C2×C4—521no—
117C2×C4#611814yescomplemented
118C2×C4C22×#26114yes—
119C2×C4C22×#26112yes—
120C8—268no—
121C22—21no—
122C22—21no—
123C22—264no—
124C22—264no—
125C22—264no—
126C22—528no—
127C22C2×#611812yes—
128C22C23×#26111yescharacteristic
129C4—24no—
130C4—132no—
131C4—261no—
132C4—262no—
133C4C2×#611814yes—
134C2—22no—
135C2—524no—
136C2C22×#611811yescharacteristic
137C2#1171962311yescharacteristic
138C2#1171962511yescharacteristic
subgroupG/H
center, FrattiniC22C23×#261
commutator, socleC22×C13C23×C4
FittingC2×C13×C4⋊C4C4
prime radicalC22×D52C4
cosocleC2×Dic13C24
hypercenterC2×C4⋊C4#261
hypocenterC13#2975
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11719127C2semidirect
3. #11719119C2semidirect
4. #11719076C2semidirect
7. C2×#6118C22semidirect
14. #88111C22semidirect
15. C4⋊#1057C22semidirect
16. C4×#1057C22semidirect
40. C2×C4×C13M16semidirect
102. C13#2975semidirect
117. C2×C4#6118semidirect

Maximal subgroups

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

subgroupindex
C2×#881472
#117191272
#117191192
#117190762
#297513