Finite Group Databasebeta

← #13129738

Subgroups — #13129738

Order 1664.

200 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 44 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#11719136C211yesmaximal, characteristic
2#11719126C211yesmaximal, characteristic
3#11718387C211yesmaximal, characteristic
4C22×C4×D13C2211yescharacteristic
5C2×C22⋊#261C412yes—
6C2×#6122C412yescomplemented
7C2×C4⋊#261—21no—
8C2×#6094—21no—
9(C2×#261)⋊C4—21no—
10#88111—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—
25#6122—42no—
26C2×#1057—22no—
27C4⋊#261—42no—
28C2×C8×C13—21no—
29C2×#1055—21no—
30#6094—42no—
31#1305—131nomaximal, Sylow
32C23×C13C4211yescharacteristic
33C22×D13—21no—
34C22×D13—21no—
35C22×D13—41no—
36C22×D13—41no—
37C22×D13C22⋊C411yescharacteristic
38C22×D13C4⋊C411yescharacteristic
39C2×#261—42no—
40C2×#261—42no—
41C2×#261—42no—
42C2×C4×C13—41no—
43C2×C4×C13C22⋊C411yescharacteristic
44C2×C4×C13C4⋊C411yescharacteristic
45C2×Dic13—22no—
46C2×Dic13C22⋊C411yescharacteristic
47C2×Dic13C4⋊C411yescharacteristic
48C4×D13—22no—
49C4×D13—22no—
50C4×D13—41no—
51C4×D13—41no—
52#1057—42no—
53C8×C13—41no—
54#1055—41no—
55#407—131no—
56#407—131no—
57#380—131no—
58C22×C13—21no—
59C22×C13—21no—
60C22×C13—21no—
61C22×C13#9511yescharacteristic
62C2×D13—21no—
63C2×D13—21no—
64C2×D13—21no—
65C2×D13—21no—
66C2×D13—21no—
67C2×D13—42no—
68C2×D13—42no—
69C2×D13#10011yescharacteristic
70C2×D13#10111yescharacteristic
71#261—82no—
72C4×C13—21no—
73C4×C13—21no—
74Dic13—21no—
75Dic13#9912yes—
76C23×C4—131no—
77C2×M16—132no—
78C2×M16—261no—
79C2×C4⋊C4—261no—
80C2×C22⋊C4—132no—
81C22⋊C8—131no—
82C22⋊C8—261no—
83C22⋊C8—261no—
84C22⋊C8—261no—
85C22⋊C8#26111yescharacteristic, complemented
86#95—261no—
87C2×C13—41no—
88C2×C13#34211yescharacteristic
89C2×C13#34311yescharacteristic
90C2×C13#34411yescharacteristic
91D13—21no—
92D13—21no—
93D13—41no—
94C24—131no—
95C22×C4—131no—
96C22×C4—131no—
97C22×C4—131no—
98C22×C4—131no—
99C22×C4—131no—
100C22×C4—262no—
101C22×C4—522no—
102C22×C4C2×#26111yescharacteristic
103M16—522no—
104M16—522no—
105C2×C8—21no—
106C2×C8—262no—
107C2×C8—261no—
108C4⋊C4—522no—
109C22⋊C4—522no—
110C13#130511yescharacteristic, complemented, Sylow
111C23—131no—
112C23—131no—
113C23—261no—
114C23—261no—
115C23—521no—
116C23—521no—
117C23C4×#26111yescharacteristic
118C2×C4—41no—
119C2×C4—131no—
120C2×C4—131no—
121C2×C4—262no—
122C2×C4—262no—
123C2×C4—262no—
124C2×C4—521no—
125C2×C4—521no—
126C2×C4—522no—
127C2×C4—522no—
128C2×C4—522no—
129C2×C4C4⋊#26111yescharacteristic
130C2×C4C22⋊#26111yescharacteristic
131C8—41no—
132C8—521no—
133C8—522no—
134C22—21no—
135C22—21no—
136C22—21no—
137C22—131no—
138C22—131no—
139C22—261no—
140C22—261no—
141C22—261no—
142C22—261no—
143C22—261no—
144C22—522no—
145C22—522no—
146C22(C2×#261)⋊C411yescharacteristic
147C4—21no—
148C4—21no—
149C4—132no—
150C4—261no—
151C4—1042no—
152C2—41no—
153C2—261no—
154C2—261no—
155C2—521no—
156C2#1171823811yescharacteristic
157C2#1171826611yescharacteristic
158C2#1171827111yescharacteristic
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#1305
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
6. C2×#6122C4semidirect
12. C13×C22⋊C8C4semidirect
13. C22⋊#1055C4semidirect
85. C22⋊C8#261semidirect
110. C13#1305semidirect

Maximal subgroups

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

subgroupindex
#117191362
#117191262
#117183872
#130513