Finite Group Databasebeta

← #18009857

Subgroups — #18009857

Order 4736.

300 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 64 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#14558553C212yesmaximal, complemented
2#14558377C214yesmaximal, complemented
3C2×#11924498C211yesmaximal, characteristic
4#11924603—22no—
5C22⋊#64438C2214yes—
6#11924591—22no—
7C22×D148C411yescharacteristic
8C22×C4×D37C412yes—
9#11924498—22no—
10#11924498—22no—
11C2×#10596938C2212yes—
12C2×C4×Dic37C2211yescharacteristic
13C2×C4⋊C4×C37C411yescharacteristic
14C23×D37C2×C412yes—
15C22×C4×C37C2×C412yes—
16C22×C4×C37C2×C411yescharacteristic
17C22×Dic37C2×C411yescharacteristic
18C22×Dic37C2311yescharacteristic
19C2×D148—24no—
20C2×D148—22no—
21C2×C4×D37—22no—
22C2×C4×D37—22no—
23C2×C4×D37—44no—
24C2×#64438—24no—
25C4⋊C4×C37—22no—
26#10596938—24no—
27C4×Dic37D412yes—
28C4×Dic37D412yes—
29C23×C37C22×C411yescharacteristic
30C22×D37—22no—
31C22×D37—22no—
32C22×D37—42no—
33C22×D37—42no—
34C22×D37M1614yes—
35C2×C4×C37—22no—
36C2×C4×C37—22no—
37C2×C4×C37—42no—
38C2×C4×C37C22⋊C412yes—
39C2×Dic37—22no—
40C2×Dic37—41no—
41C2×Dic37C22⋊C411yescharacteristic
42C2×Dic37C22⋊C411yescharacteristic
43C2×Dic37C2×D412yes—
44D148—28no—
45C4×D37—44no—
46C4×D37—44no—
47#64438—44no—
48C22×C37—21no—
49C22×C37—21no—
50C22×C37C2×C22⋊C411yescharacteristic
51C22×C37C2×M1612yes—
52C2×D37—24no—
53C2×D37—44no—
54C2×D37—42no—
55C2×D37—42no—
56C2×D37—44no—
57C4×C37—22no—
58C4×C37—42no—
59Dic37—22no—
60Dic37—21no—
61Dic37#10012yes—
62#1466—371nomaximal, Sylow
63C2×C37—22no—
64C2×C37#40711yescharacteristic
65C2×C37#41011yescharacteristic
66C2×C37C2×#10011yescharacteristic
67D37—44no—
68C2×C4×D4—371no—
69#432—372no—
70#323—374no—
71C37#146611yescharacteristic, complemented, Sylow
72C22×D4—371no—
73C23×C4—372no—
74C4×D4—742no—
75C4×D4—742no—
76C2×C4⋊C4#386611yescharacteristic
77C2×C22⋊C4—372no—
78C2×C42—371no—
79C4⋊C8—742no—
80C22⋊C8—374no—
81#97—742no—
82C24—372no—
83C2×D4—744no—
84C2×D4—742no—
85C22×C4—371no—
86C22×C4—371no—
87C22×C4—742no—
88C22×C4—742no—
89C22×C4—1484no—
90C22×C4C2×#386612yes—
91C22×C4C2×#386611yescharacteristic
92C2×C8—744no—
93C4⋊C4—22no—
94C22⋊C4—744no—
95C42—372no—
96C42—372no—
97C23—374no—
98C23—742no—
99C23—742no—
100C23—1482no—
101C23—1482no—
102C23C22×#386611yescharacteristic
103D4—748no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—42no—
107C2×C4—371no—
108C2×C4—372no—
109C2×C4—371no—
110C2×C4—742no—
111C2×C4—1484no—
112C2×C4—1484no—
113C2×C4—1481no—
114C2×C4C22⋊#386612yes—
115C8—1484no—
116C22—21no—
117C22—21no—
118C22—744no—
119C22—1484no—
120C22—1484no—
121C22—1482no—
122C22—1482no—
123C22C2×C22⋊#386611yescharacteristic
124C22D37⋊M1612yes—
125C4—22no—
126C4—42no—
127C4—372no—
128C4—742no—
129C4—741no—
130C2—22no—
131C2—1484no—
132C2#1455850511yescharacteristic
133C2#1455851411yescharacteristic
134C2D37⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C4⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×D148C4
cosocleC22×Dic37C23
hypercenterC2×C4⋊C4#3866
hypocenterC37#1466
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #14558553C2semidirect
2. #14558377C2semidirect
71. C37#1466semidirect

Maximal subgroups

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

subgroupindex
#145585532
#145583772
C2×#119244982
#146637