Finite Group Databasebeta

← #18009843

Subgroups — #18009843

Order 4736.

440 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 70 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#14558503C212yesmaximal, complemented
2#14558377C214yesmaximal, complemented
3C22×#10596938C211yesmaximal, characteristic
4C2×#10596957—22no—
5C22⋊#64438—22no—
6C22⋊#64438C2214yescomplemented
7C24×D37C411yescharacteristic
8C23×Dic37C2211yescharacteristic
9C2×#10596938—22no—
10C2×#10596938—22no—
11C2×#10596938C412yes—
12C2×#10596938C2212yes—
13C23×C4×C37C411yescharacteristic
14C24×C37C2×C411yescharacteristic
15C23×D37—21no—
16C23×D37—21no—
17C23×D37—24no—
18C23×D37—42no—
19C23×D37—42no—
20C23×D37C2×C412yes—
21C22×C4×C37—21no—
22C22×C4×C37—21no—
23C22×C4×C37—42no—
24C22×C4×C37C2×C412yes—
25C22×Dic37—42no—
26C22×Dic37C2×C411yescharacteristic
27C22×Dic37D412yes—
28C22×Dic37D412yes—
29C22×Dic37C2311yescharacteristic
30#10596957—44no—
31C2×#64438—24no—
32#10596938—24no—
33#10596938—24no—
34C23×C37—22no—
35C23×C37—22no—
36C23×C37—22no—
37C23×C37C22⋊C411yescharacteristic
38C23×C37C22⋊C411yescharacteristic
39C23×C37C22×C411yescharacteristic
40C22×D37—24no—
41C22×D37—24no—
42C22×D37—22no—
43C22×D37—22no—
44C22×D37—416no—
45C22×D37—42no—
46C22×D37—42no—
47C22×D37—42no—
48C22×D37—42no—
49C22×D37—42no—
50C22×D37—42no—
51C22×D37M1614yescomplemented
52C2×C4×C37—22no—
53C2×C4×C37—42no—
54C2×C4×C37—42no—
55C2×C4×C37—42no—
56C2×Dic37—24no—
57C2×Dic37—41no—
58C2×Dic37—42no—
59C2×Dic37—41no—
60C2×Dic37C22⋊C412yes—
61C2×Dic37C2×D412yes—
62#64438—44no—
63C22×C37—28no—
64C22×C37—21no—
65C22×C37—21no—
66C22×C37—21no—
67C22×C37—21no—
68C22×C37—21no—
69C22×C37—21no—
70C22×C37#9912yes—
71C22×C37#10012yes—
72C22×C37C2×C22⋊C411yescharacteristic
73C22×C37C2×M1612yes—
74C2×D37—24no—
75C2×D37—48no—
76C2×D37—48no—
77C2×D37—44no—
78C2×D37—42no—
79C2×D37—42no—
80C2×D37—44no—
81C4×C37—42no—
82Dic37—22no—
83Dic37—22no—
84#1462—371nomaximal, Sylow
85C2×C37—22no—
86C2×C37—22no—
87C2×C37—22no—
88C2×C37#40711yescharacteristic
89C2×C37C2×#9911yescharacteristic
90C2×C37C2×#10011yescharacteristic
91D37—44no—
92C22×C22⋊C4—371no—
93#407—372no—
94#323—374no—
95C37#146211yescharacteristic, complemented, Sylow
96C25—371no—
97C23×C4—371no—
98C23×C4#386611yescharacteristic
99C2×M16—742no—
100C2×C22⋊C4—372no—
101C2×C22⋊C4—372no—
102C2×C22⋊C4—742no—
103C2×C22⋊C4—742no—
104C22⋊C8—374no—
105C22⋊C8—742no—
106C24—372no—
107C24—744no—
108C24—741no—
109C24—741no—
110C24—1482no—
111C24—1482no—
112C24C2×#386611yescharacteristic
113C22×C4—21no—
114C22×C4—21no—
115C22×C4—42no—
116C22×C4—372no—
117C22×C4—372no—
118C22×C4—371no—
119C22×C4—371no—
120C22×C4—1482no—
121C22×C4C2×#386612yes—
122M16—1484no—
123C2×C8—744no—
124C22⋊C4—744no—
125C22⋊C4—744no—
126C23—22no—
127C23—22no—
128C23—22no—
129C23—374no—
130C23—744no—
131C23—744no—
132C23—742no—
133C23—742no—
134C23—1482no—
135C23—1482no—
136C23—14816no—
137C23—1482no—
138C23—1482no—
139C23—1482no—
140C23—1482no—
141C23C22⋊#386611yescharacteristic
142C23C22⋊#386611yescharacteristic
143C23C22×#386611yescharacteristic
144C2×C4—22no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4—372no—
149C2×C4—372no—
150C2×C4—744no—
151C2×C4—1481no—
152C2×C4—1482no—
153C2×C4—1481no—
154C8—1484no—
155C22—28no—
156C22—21no—
157C22—21no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—744no—
163C22—1484no—
164C22—1488no—
165C22—1488no—
166C22—1484no—
167C22—1482no—
168C22—1482no—
169C22#1192459512yes—
170C22#1192459612yes—
171C22C2×C22⋊#386611yescharacteristic
172C22D37⋊M1612yes—
173C4—42no—
174C4—742no—
175C4—742no—
176C2—22no—
177C2—22no—
178C2—22no—
179C2—1484no—
180C2#1455850511yescharacteristic
181C2C2×#1192459511yescharacteristic
182C2C2×#1192459611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC23×C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC24×D37C4
cosocleC22×Dic37C23
hypercenterC23×C4#3866
hypocenterC37#1462
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. #14558503C2semidirect
2. #14558377C2semidirect
6. C22⋊#64438C22semidirect
51. C22×D37M16semidirect
95. C37#1462semidirect

Maximal subgroups

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

subgroupindex
#145585032
#145583772
C22×#105969382
#146237