Finite Group Databasebeta

← #18009850

Subgroups — #18009850

Order 4736.

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

normal subgroups only

This group has 252 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#14558554C212yesmaximal, complemented
2#14558378C212yesmaximal, complemented
3#14558377C212yesmaximal
4C2×#11924494C211yesmaximal, characteristic
5C4⋊#64438—22no—
6C22⋊#64438C2214yes—
7#11924591—22no—
8C22×C4×D37C411yescharacteristic
9#11924494—22no—
10#11924494—22no—
11C2×C4⋊Dic37C2211yescharacteristic
12C2×#10596938C411yescharacteristic
13C2×#10596938C2211yescharacteristic
14C2×C4×Dic37C411yescharacteristic
15C2×C4×Dic37C2211yescharacteristic
16C2×C4⋊C4×C37C411yescharacteristic
17C23×D37C2×C411yescharacteristic
18C22×C4×C37C2×C411yescharacteristic
19C22×C4×C37C2×C411yescharacteristic
20C22×C4×C37C2×C411yescharacteristic
21C22×Dic37C2×C411yescharacteristic
22C22×Dic37C2×C411yescharacteristic
23C22×Dic37C2311yescharacteristic
24C2×C4×D37—22no—
25C2×C4×D37—22no—
26C2×C4×D37—21no—
27C2×C4×D37—21no—
28C2×#64438—24no—
29C4⋊C4×C37—22no—
30#10596938—22no—
31#10596938—22no—
32C4⋊Dic37—22no—
33C4×Dic37—21no—
34C4×Dic37—21no—
35C4×Dic37D412yes—
36C4×Dic37D412yes—
37C23×C37C22×C411yescharacteristic
38C22×D37—21no—
39C22×D37—21no—
40C22×D37—41no—
41C22×D37—41no—
42C22×D37M1612yes—
43C2×C4×C37—21no—
44C2×C4×C37—21no—
45C2×C4×C37—21no—
46C2×C4×C37—41no—
47C2×C4×C37—41no—
48C2×C4×C37C22⋊C412yes—
49C2×C4×C37M1612yes—
50C2×Dic37—21no—
51C2×Dic37—21no—
52C2×Dic37—21no—
53C2×Dic37—41no—
54C2×Dic37—41no—
55C2×Dic37C22⋊C411yescharacteristic
56C2×Dic37C22⋊C411yescharacteristic
57C2×Dic37C2×D412yes—
58C4×D37—24no—
59C4×D37—24no—
60#64438—44no—
61C22×C37—21no—
62C22×C37—21no—
63C22×C37C2×C22⋊C411yescharacteristic
64C22×C37C2×M1611yescharacteristic
65C22×C37C2×M1611yescharacteristic
66C2×D37—22no—
67C2×D37—42no—
68C2×D37—41no—
69C2×D37—41no—
70C2×D37—42no—
71C4×C37—22no—
72C4×C37—22no—
73C4×C37—41no—
74Dic37—21no—
75Dic37—21no—
76Dic37—22no—
77Dic37—41no—
78#1464—371nomaximal, Sylow
79C2×C37—21no—
80C2×C37—21no—
81C2×C37#40711yescharacteristic
82C2×C37#41011yescharacteristic
83C2×C37#41311yescharacteristic
84D37—42no—
85C2×#117—371no—
86#432—372no—
87#324—372no—
88#323—372no—
89C37#146411yescharacteristic, complemented, Sylow
90C23×C4—371no—
91#117—742no—
92#117—742no—
93C2×C4⋊C4—371no—
94C2×C4⋊C4#386611yescharacteristic
95C2×C22⋊C4—371no—
96C2×C22⋊C4—371no—
97C2×C42—371no—
98C2×C42—371no—
99C4⋊C8—742no—
100C22⋊C8—374no—
101#97—742no—
102C24—371no—
103C22×C4—371no—
104C22×C4—371no—
105C22×C4—371no—
106C22×C4—741no—
107C22×C4—741no—
108C22×C4—742no—
109C22×C4—742no—
110C22×C4C2×#386611yescharacteristic
111C22×C4C2×#386611yescharacteristic
112C22×C4C2×#386611yescharacteristic
113C2×C8—744no—
114C4⋊C4—22no—
115C4⋊C4—742no—
116C22⋊C4—742no—
117C22⋊C4—742no—
118C42—372no—
119C42—372no—
120C42—741no—
121C42—741no—
122C23—372no—
123C23—741no—
124C23—741no—
125C23—1481no—
126C23—1481no—
127C23C22×#386611yescharacteristic
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—371no—
134C2×C4—371no—
135C2×C4—372no—
136C2×C4—744no—
137C2×C4—744no—
138C2×C4—741no—
139C2×C4—741no—
140C2×C4—741no—
141C2×C4—1481no—
142C2×C4—1481no—
143C2×C4#1059695312yes—
144C2×C4C22⋊#386612yes—
145C8—1484no—
146C22—21no—
147C22—21no—
148C22—742no—
149C22—1482no—
150C22—1482no—
151C22—1481no—
152C22—1481no—
153C22C2×C22⋊#386611yescharacteristic
154C22D37⋊M1611yescharacteristic
155C22C2×#1059695311yescharacteristic
156C4—22no—
157C4—22no—
158C4—41no—
159C4—741no—
160C4—741no—
161C4—742no—
162C4—1481no—
163C2—21no—
164C2—21no—
165C2—1482no—
166C2#1455850411yescharacteristic
167C2#1455851411yescharacteristic
168C2#1455852011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C4⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC23×D37C2×C4
cosocleC22×Dic37C23
hypercenterC2×C4⋊C4#3866
hypocenterC37#1464
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. #14558554C2semidirect
2. #14558378C2semidirect
89. C37#1464semidirect

Maximal subgroups

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

subgroupindex
#145585542
#145583782
#145583772
C2×#119244942
#146437