Finite Group Databasebeta

← #16835390

Subgroups — #16835390

Order 3712.

300 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 66 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#14272106C212yesmaximal
2#14272041C214yesmaximal
3C2×#11745254C211yesmaximal, characteristic
4C22×C4×D29C2211yescharacteristic
5C2×C22⋊#1181C2214yes—
6C2×C4⋊C4×C29C411yescharacteristic, complemented
7C2×#90781C2212yes—
8C2×C4⋊Dic29C411yescharacteristic, complemented
9C2×C4×Dic29C412yescomplemented
10#11745254—24no—
11(C2×#1181)⋊C4—24no—
12C23×D29C2311yescharacteristic
13C22×#1181—24no—
14C22×C4×C29C2×C412yes—
15C22×C4×C29C2×C411yescharacteristic
16C22×Dic29C2×C411yescharacteristic
17C22×Dic29C2×C412yes—
18C2×C4×D29—24no—
19C2×C4×D29D414yes—
20C22⋊#1181—28no—
21C4⋊C4×C29—22no—
22#90781—24no—
23C4⋊Dic29—22no—
24C4×Dic29—24no—
25C23×C29C22×C411yescharacteristic
26C22×D29—41no—
27C22×D29—41no—
28C22×D29C2×D412yes—
29C22×D29#4114yes—
30C2×#1181—44no—
31C2×#1181—44no—
32C2×#1181—44no—
33C2×C4×C29—22no—
34C2×C4×C29—22no—
35C2×C4×C29—42no—
36C2×C4×C29C22⋊C412yes—
37C2×Dic29—22no—
38C2×Dic29—22no—
39C2×Dic29—42no—
40C2×Dic29C22⋊C412yes—
41C4×D29—28no—
42#1820—291nomaximal, Sylow
43C22×C29—21no—
44C22×C29—21no—
45C22×C29C2×C22⋊C411yescharacteristic
46C22×C29#11712yes—
47C2×D29—22no—
48C2×D29—22no—
49C2×D29—44no—
50C2×D29#12314yes—
51#1181—84no—
52C4×C29—22no—
53C4×C29—42no—
54Dic29—22no—
55Dic29—42no—
56C2×#117—291no—
57#381—292no—
58#342—294no—
59C2×C29—22no—
60C2×C29#38111yescharacteristic
61C2×C29#41011yescharacteristic
62C2×C29#41011yescharacteristic
63D29—24no—
64C23×C4—291no—
65#117—584no—
66C2×C4⋊C4—291no—
67C2×C4⋊C4#118111yescharacteristic, complemented
68C2×C22⋊C4—292no—
69C2×C22⋊C4—294no—
70C2×C42—292no—
71#95—584no—
72C29#182011yescharacteristic, complemented, Sylow
73C24—291no—
74C22×C4—291no—
75C22×C4—294no—
76C22×C4—292no—
77C22×C4—584no—
78C22×C4—584no—
79C22×C4C2×#118112yes—
80C22×C4C2×#118111yescharacteristic
81C4⋊C4—22no—
82C4⋊C4—582no—
83C22⋊C4—584no—
84C22⋊C4—588no—
85C42—584no—
86C23—292no—
87C23—294no—
88C23—1161no—
89C23—1161no—
90C23C22×#118111yescharacteristic
91C2×C4—22no—
92C2×C4—22no—
93C2×C4—42no—
94C2×C4—292no—
95C2×C4—588no—
96C2×C4—582no—
97C2×C4—582no—
98C2×C4—1162no—
99C2×C4—1164no—
100C2×C4—1164no—
101C2×C4—1164no—
102C2×C4C22⋊#118112yes—
103C22—21no—
104C22—21no—
105C22—294no—
106C22—582no—
107C22—582no—
108C22—1164no—
109C22#1174534512yes—
110C22C2×C22⋊#118111yescharacteristic
111C4—22no—
112C4—42no—
113C4—582no—
114C4—1162no—
115C4—2324no—
116C2—22no—
117C2—584no—
118C2#1427210611yescharacteristic
119C2#1427214311yescharacteristic
120C2#1427214411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC2×C4⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radical, cosocleC23×D29C23
hypercenterC2×C4⋊C4#1181
hypocenterC29#1820
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. C2×C4⋊C4×C29C4semidirect
8. C2×C4⋊Dic29C4semidirect
9. C2×C4×Dic29C4semidirect
67. C2×C4⋊C4#1181semidirect
72. C29#1820semidirect

Maximal subgroups

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

subgroupindex
#142721062
#142720412
C2×#117452542
#182029