Finite Group Databasebeta

← #18010494

Subgroups — #18010494

Order 4736.

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#14558476C212yesmaximal
2#14558411C214yesmaximal
3C2×#11924494C211yesmaximal, characteristic
4C2×C22⋊#3866C2214yes—
5(C2×#3866)⋊C4—24no—
6C22×C4×D37C2211yescharacteristic
7#11924494—24no—
8C2×C4⋊Dic37C411yescharacteristic, complemented
9C2×#10596938C2212yes—
10C2×C4×Dic37C412yescomplemented
11C2×C4⋊C4×C37C411yescharacteristic, complemented
12C23×D37C2311yescharacteristic
13C22×#3866—24no—
14C22×C4×C37C2×C412yes—
15C22×C4×C37C2×C411yescharacteristic
16C22×Dic37C2×C411yescharacteristic
17C22×Dic37C2×C412yes—
18C2×C4×D37—24no—
19C2×C4×D37D414yes—
20C22⋊#3866—28no—
21C4⋊C4×C37—22no—
22#10596938—24no—
23C4⋊Dic37—22no—
24C4×Dic37—24no—
25C23×C37C22×C411yescharacteristic
26C22×D37—41no—
27C22×D37—41no—
28C22×D37C2×D412yes—
29C22×D37#4114yes—
30C2×#3866—44no—
31C2×#3866—44no—
32C2×#3866—44no—
33C2×C4×C37—22no—
34C2×C4×C37—22no—
35C2×C4×C37—42no—
36C2×C4×C37C22⋊C412yes—
37C2×Dic37—22no—
38C2×Dic37—22no—
39C2×Dic37—42no—
40C2×Dic37C22⋊C412yes—
41C4×D37—28no—
42C22×C37—21no—
43C22×C37—21no—
44C22×C37C2×C22⋊C411yescharacteristic
45C22×C37#11712yes—
46C2×D37—22no—
47C2×D37—22no—
48C2×D37—44no—
49C2×D37#12314yes—
50#3866—84no—
51C4×C37—22no—
52C4×C37—42no—
53Dic37—22no—
54Dic37—42no—
55#1820—371nomaximal, Sylow
56C2×C37—22no—
57C2×C37#38111yescharacteristic
58C2×C37#41011yescharacteristic
59C2×C37#41011yescharacteristic
60D37—24no—
61C2×#117—371no—
62#381—372no—
63#342—374no—
64C37#182011yescharacteristic, complemented, Sylow
65C23×C4—371no—
66#117—744no—
67C2×C4⋊C4—371no—
68C2×C4⋊C4#386611yescharacteristic, complemented
69C2×C22⋊C4—372no—
70C2×C22⋊C4—374no—
71C2×C42—372no—
72#95—744no—
73C24—371no—
74C22×C4—371no—
75C22×C4—374no—
76C22×C4—372no—
77C22×C4—744no—
78C22×C4—744no—
79C22×C4C2×#386612yes—
80C22×C4C2×#386611yescharacteristic
81C4⋊C4—22no—
82C4⋊C4—742no—
83C22⋊C4—744no—
84C22⋊C4—748no—
85C42—744no—
86C23—372no—
87C23—374no—
88C23—1481no—
89C23—1481no—
90C23C22×#386611yescharacteristic
91C2×C4—22no—
92C2×C4—22no—
93C2×C4—42no—
94C2×C4—372no—
95C2×C4—748no—
96C2×C4—742no—
97C2×C4—742no—
98C2×C4—1484no—
99C2×C4—1484no—
100C2×C4—1484no—
101C2×C4—1482no—
102C2×C4C22⋊#386612yes—
103C22—21no—
104C22—21no—
105C22—374no—
106C22—742no—
107C22—742no—
108C22—1484no—
109C22C2×C22⋊#386611yescharacteristic
110C22#1192461512yes—
111C4—22no—
112C4—42no—
113C4—2964no—
114C4—742no—
115C4—1482no—
116C2—22no—
117C2—744no—
118C2#1455847611yescharacteristic
119C2#1455851311yescharacteristic
120C2#1455851411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C4⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radical, cosocleC23×D37C23
hypercenterC2×C4⋊C4#3866
hypocenterC37#1820
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
8. C2×C4⋊Dic37C4semidirect
10. C2×C4×Dic37C4semidirect
11. C2×C4⋊C4×C37C4semidirect
64. C37#1820semidirect
68. C2×C4⋊C4#3866semidirect

Maximal subgroups

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

subgroupindex
#145584762
#145584112
C2×#119244942
#182037