Finite Group Databasebeta

← #17994671

Subgroups — #17994671

Order 4736.

300 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 85 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×#11924495C211yesmaximal, characteristic
2#14557396C211yesmaximal, characteristic
3#14557299C214yesmaximal
4C37×#381C211yesmaximal, characteristic
5#11924495—22no—
6#11924495—22no—
7C2×C4⋊Dic37C412yescomplemented
8C2×C22⋊Dic37C2212yes—
9C2×C22⋊Dic37C2212yes—
10C2×C4×Dic37C412yescomplemented
11#11924443—22no—
12C23×C4×C37C2211yescharacteristic
13C2×C22⋊C4×C37C2212yes—
14#95×C37—22no—
15C24×C37C2311yescharacteristic
16C22×C4×C37—24no—
17C22×C4×C37—22no—
18C22×C4×C37C2×C411yescharacteristic
19C22×C4×C37C2×C411yescharacteristic
20C22×C4×C37D412yes—
21C22×C4×C37D412yes—
22C22×Dic37—22no—
23C22×Dic37C2×C414yes—
24C22⋊C4×C37—24no—
25C22⋊Dic37—22no—
26C22⋊Dic37—22no—
27C22⋊Dic37—24no—
28C4⋊Dic37—24no—
29C4×Dic37—24no—
30C23×C37—42no—
31C23×C37C22×C411yescharacteristic
32C23×C37C2×D411yescharacteristic
33C23×C37C2×D411yescharacteristic
34C23×C37#4114yes—
35C2×C4×C37—22no—
36C2×C4×C37—22no—
37C2×C4×C37—24no—
38C2×C4×C37—24no—
39C2×C4×C37—44no—
40C2×C4×C37—42no—
41C2×C4×C37C22⋊C412yes—
42C2×C4×C37C22⋊C412yes—
43C2×Dic37—24no—
44C2×Dic37—44no—
45C2×Dic37—44no—
46C2×Dic37—42no—
47C22×C37—22no—
48C22×C37—22no—
49C22×C37—22no—
50C22×C37—44no—
51C22×C37C2×C22⋊C411yescharacteristic
52C22×C37#11712yes—
53C22×C37#12312yes—
54C22×C37#12312yes—
55C4×C37—22no—
56C4×C37—22no—
57C4×C37—82no—
58Dic37—44no—
59Dic37—82no—
60#1820—371nomaximal, Sylow
61C2×C37—22no—
62C2×C37—22no—
63C2×C37—22no—
64C2×C37#38111yescharacteristic
65C2×C37#41012yes—
66C2×#117—371no—
67#381—371no—
68#381D3711yescharacteristic
69#342—374no—
70C37#182011yescharacteristic, complemented, Sylow
71C23×C4C2×D3711yescharacteristic
72#117—742no—
73#117—742no—
74C2×C4⋊C4—372no—
75C2×C22⋊C4—372no—
76C2×C22⋊C4—372no—
77C2×C22⋊C4C2×D3712yes—
78C2×C42—372no—
79#95—22no—
80#95—742no—
81C24C22×D3711yescharacteristic
82C22×C4—24no—
83C22×C4—22no—
84C22×C4—374no—
85C22×C4—742no—
86C22×C4C4×D3711yescharacteristic
87C22×C4C4×D3711yescharacteristic
88C22×C4D14812yes—
89C22×C4C22⋊D3712yes—
90C4⋊C4—744no—
91C22⋊C4—24no—
92C22⋊C4—742no—
93C22⋊C4—742no—
94C22⋊C4—744no—
95C42—744no—
96C23—42no—
97C23C2×C4×D3711yescharacteristic
98C23C2×D14811yescharacteristic
99C23#1059696414yes—
100C23C2×C22⋊D3711yescharacteristic
101C2×C4—22no—
102C2×C4—22no—
103C2×C4—24no—
104C2×C4—24no—
105C2×C4—44no—
106C2×C4—42no—
107C2×C4—744no—
108C2×C4—1484no—
109C2×C4—1482no—
110C2×C4—1484no—
111C2×C4#1059693812yes—
112C2×C4#1059693812yes—
113C22—22no—
114C22—22no—
115C22—22no—
116C22—44no—
117C22C2×#1059693811yescharacteristic
118C22#1192449212yes—
119C22#1192451712yes—
120C22#1192452012yes—
121C4—22no—
122C4—22no—
123C4—82no—
124C4—2962no—
125C4—1484no—
126C2—22no—
127C2—22no—
128C2—22no—
129C2#1455739411yescharacteristic
130C2#1455750612yes—
subgroupG/H
centerC22C2×#10596938
commutatorC23×C37C22×C4
FrattiniC24C22×D37
FittingC37×#381C2
socleC22×C37C2×C22⋊C4
prime radical, cosocleC24×C37C23
hypercenter#381D37
hypocenterC37#1820
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
7. C2×C4⋊Dic37C4semidirect
10. C2×C4×Dic37C4semidirect
70. C37#1820semidirect

Maximal subgroups

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

subgroupindex
C2×#119244952
#145573962
#145572992
C37×#3812
#182037