Finite Group Databasebeta

← #13129740

Subgroups — #13129740

Order 1664.

192 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 42 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#11719135C211yesmaximal, characteristic
2#11719127C211yesmaximal, characteristic
3#11718387C211yesmaximal, characteristic
4C22×C4×D13C2211yescharacteristic
5C2×C22⋊#261C412yes—
6C2×#6118—21no—
7C2×#6094—21no—
8C22⋊#1057C412yescomplemented
9(C2×#261)⋊C4—21no—
10(C2×#261)⋊C4—21no—
11#88111—21no—
12C13×C22⋊C8C411yescharacteristic, complemented
13C22⋊#1055C411yescharacteristic, complemented
14#88060—21no—
15C23×D13C2×C411yescharacteristic
16C22×#261—22no—
17C22×C4×C13C2×C411yescharacteristic
18C22×Dic13C2×C411yescharacteristic
19C2×C4×D13—42no—
20C2×C4×D13D411yescharacteristic
21C2×C4×D13D411yescharacteristic
22C2×C4×D13D411yescharacteristic
23C2×C4×D13Q811yescharacteristic
24C22⋊#261—42no—
25C2×#1057—22no—
26#6118—42no—
27C2×C8×C13—21no—
28C2×#1055—21no—
29#6094—42no—
30#1306—131nomaximal, Sylow
31C23×C13C4211yescharacteristic
32C22×D13—22no—
33C22×D13—41no—
34C22×D13—41no—
35C22×D13C22⋊C411yescharacteristic
36C22×D13C4⋊C411yescharacteristic
37C2×#261—42no—
38C2×#261—42no—
39C2×#261—42no—
40C2×C4×C13—41no—
41C2×C4×C13C22⋊C411yescharacteristic
42C2×C4×C13C4⋊C411yescharacteristic
43C2×Dic13—41no—
44C2×Dic13C22⋊C411yescharacteristic
45C2×Dic13C4⋊C411yescharacteristic
46C4×D13—22no—
47C4×D13—22no—
48C4×D13—41no—
49C4×D13—41no—
50#1057—42no—
51C8×C13—41no—
52#1055—41no—
53#407—131no—
54#407—131no—
55#381—131no—
56C22×C13—21no—
57C22×C13—21no—
58C22×C13—21no—
59C22×C13#9511yescharacteristic
60C2×D13—21no—
61C2×D13—21no—
62C2×D13—21no—
63C2×D13—21no—
64C2×D13—21no—
65C2×D13—44no—
66C2×D13#9912yes—
67#261—82no—
68C4×C13—21no—
69C4×C13—21no—
70Dic13—21no—
71Dic13—21no—
72C23×C4—131no—
73C2×M16—261no—
74C2×M16—261no—
75C2×C22⋊C4—132no—
76C22⋊C8—132no—
77C22⋊C8—131no—
78C22⋊C8—261no—
79C22⋊C8—261no—
80C22⋊C8#26111yescharacteristic, complemented
81#95—261no—
82#95—261no—
83C2×C13—41no—
84C2×C13#34211yescharacteristic
85C2×C13#34411yescharacteristic
86C2×C13#34411yescharacteristic
87D13—22no—
88D13—41no—
89C24—131no—
90C22×C4—131no—
91C22×C4—131no—
92C22×C4—131no—
93C22×C4—131no—
94C22×C4—131no—
95C22×C4—262no—
96C22×C4—522no—
97C22×C4C2×#26111yescharacteristic
98M16—522no—
99M16—522no—
100C2×C8—21no—
101C2×C8—262no—
102C2×C8—261no—
103C22⋊C4—522no—
104C13#130611yescharacteristic, complemented, Sylow
105C23—131no—
106C23—131no—
107C23—262no—
108C23—521no—
109C23—521no—
110C23C4×#26111yescharacteristic
111C2×C4—41no—
112C2×C4—131no—
113C2×C4—131no—
114C2×C4—262no—
115C2×C4—262no—
116C2×C4—521no—
117C2×C4—521no—
118C2×C4—521no—
119C2×C4—522no—
120C2×C4—522no—
121C2×C4—522no—
122C2×C4C4⋊#26111yescharacteristic
123C2×C4C22⋊#26111yescharacteristic
124C8—41no—
125C8—521no—
126C8—522no—
127C22—21no—
128C22—21no—
129C22—21no—
130C22—132no—
131C22—261no—
132C22—261no—
133C22—261no—
134C22—261no—
135C22—261no—
136C22—524no—
137C22(C2×#261)⋊C411yescharacteristic
138C4—21no—
139C4—21no—
140C4—261no—
141C4—261no—
142C4—1042no—
143C2—41no—
144C2—262no—
145C2—521no—
146C2#1171823811yescharacteristic
147C2#1171826611yescharacteristic
148C2#1171827411yescharacteristic
subgroupG/H
centerC22(C2×#261)⋊C4
commutatorC23×C13C42
FrattiniC22×C4C2×#261
FittingC13×C22⋊C8C4
socleC22×C13#95
prime radicalC23×D13C2×C4
cosocleC22×C4×D13C22
hypercenterC22⋊C8#261
hypocenterC13#1306
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
8. C22⋊#1057C4semidirect
12. C13×C22⋊C8C4semidirect
13. C22⋊#1055C4semidirect
80. C22⋊C8#261semidirect
104. C13#1306semidirect

Maximal subgroups

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

subgroupindex
#117191352
#117191272
#117183872
#130613