Finite Group Databasebeta

← #18009847

Subgroups — #18009847

Order 4736.

252 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 252 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#14558553C212yesmaximal, complemented
2#14558378C212yesmaximal, complemented
3#14558376C212yesmaximal
4C2×#11924495C211yesmaximal, characteristic
5#11924603—22no—
6C22⋊#64438C2214yes—
7#11924591—22no—
8#11924495—22no—
9#11924495—22no—
10C2×C4⋊Dic37C411yescharacteristic
11C2×C4⋊Dic37C2211yescharacteristic
12C2×C22⋊Dic37C411yescharacteristic
13C2×C22⋊Dic37C2211yescharacteristic
14C2×C4×Dic37C411yescharacteristic
15C2×C4×Dic37C2211yescharacteristic
16C23×C4×C37C411yescharacteristic
17C24×C37C2×C411yescharacteristic
18C22×C4×C37—22no—
19C22×C4×C37—21no—
20C22×C4×C37—21no—
21C22×C4×C37—22no—
22C22×C4×C37C2×C411yescharacteristic
23C22×C4×C37C2×C411yescharacteristic
24C22×Dic37C2×C411yescharacteristic
25C22×Dic37C2×C411yescharacteristic
26C22×Dic37C2×C411yescharacteristic
27C22×Dic37C2311yescharacteristic
28C2×#64438—24no—
29C22⋊Dic37—22no—
30C22⋊Dic37—22no—
31C4⋊Dic37—22no—
32C4⋊Dic37—22no—
33C4×Dic37—21no—
34C4×Dic37—21no—
35C4×Dic37D412yes—
36C4×Dic37D412yes—
37C23×C37—21no—
38C23×C37—21no—
39C23×C37—41no—
40C23×C37—41no—
41C23×C37M1612yes—
42C23×C37C22×C411yescharacteristic
43C2×C4×C37—24no—
44C2×C4×C37—24no—
45C2×C4×C37—21no—
46C2×C4×C37—21no—
47C2×C4×C37—21no—
48C2×C4×C37—21no—
49C2×C4×C37C22⋊C411yescharacteristic
50C2×C4×C37C22⋊C411yescharacteristic
51C2×C4×C37M1612yes—
52C2×Dic37—21no—
53C2×Dic37—21no—
54C2×Dic37—41no—
55C2×Dic37—41no—
56C2×Dic37—41no—
57C2×Dic37—41no—
58C2×Dic37C22⋊C412yes—
59C2×Dic37C2×D412yes—
60#64438—44no—
61C22×C37—21no—
62C22×C37—21no—
63C22×C37—22no—
64C22×C37—42no—
65C22×C37—42no—
66C22×C37—41no—
67C22×C37—41no—
68C22×C37C2×C22⋊C411yescharacteristic
69C22×C37C2×M1611yescharacteristic
70C22×C37C2×M1611yescharacteristic
71C4×C37—21no—
72C4×C37—21no—
73C4×C37—22no—
74Dic37—22no—
75Dic37—22no—
76Dic37—41no—
77Dic37—41no—
78#1464—371nomaximal, Sylow
79C2×C37—21no—
80C2×C37—21no—
81C2×C37—42no—
82C2×C37#40711yescharacteristic
83C2×C37#41011yescharacteristic
84C2×C37#41311yescharacteristic
85C2×#117—371no—
86#432—372no—
87#324—372no—
88#323—372no—
89C37#146411yescharacteristic, complemented, Sylow
90C23×C4#386611yescharacteristic
91#117—742no—
92#117—742no—
93C2×C4⋊C4—371no—
94C2×C4⋊C4—371no—
95C2×C22⋊C4—371no—
96C2×C22⋊C4—371no—
97C2×C42—371no—
98C2×C42—371no—
99C4⋊C8—742no—
100C22⋊C8—374no—
101#97—742no—
102C24C2×#386611yescharacteristic
103C22×C4—22no—
104C22×C4—22no—
105C22×C4—21no—
106C22×C4—21no—
107C22×C4—371no—
108C22×C4—371no—
109C22×C4—371no—
110C22×C4—371no—
111C22×C4C2×#386611yescharacteristic
112C22×C4C2×#386611yescharacteristic
113C2×C8—744no—
114C4⋊C4—742no—
115C4⋊C4—742no—
116C22⋊C4—742no—
117C22⋊C4—742no—
118C42—372no—
119C42—372no—
120C42—741no—
121C42—741no—
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23#1059695712yes—
127C23C22×#386611yescharacteristic
128C2×C4—24no—
129C2×C4—24no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—372no—
135C2×C4—372no—
136C2×C4—741no—
137C2×C4—741no—
138C2×C4—1481no—
139C2×C4—1481no—
140C2×C4—1481no—
141C2×C4—1481no—
142C2×C4#1059695712yes—
143C2×C4C22⋊#386611yescharacteristic
144C2×C4C22⋊#386611yescharacteristic
145C8—1484no—
146C22—21no—
147C22—21no—
148C22—22no—
149C22—42no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22C2×C22⋊#386611yescharacteristic
154C22C2×#1059695711yescharacteristic
155C22C2×#1059695711yescharacteristic
156C4—22no—
157C4—21no—
158C4—21no—
159C4—742no—
160C4—742no—
161C4—1481no—
162C4—1481no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#1455850311yescharacteristic
167C2#1455851211yescharacteristic
168C2#1455851911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC23×C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC24×C37C2×C4
cosocleC22×Dic37C23
hypercenterC23×C4#3866
hypocenterC37#1464
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. #14558553C2semidirect
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
#145585532
#145583782
#145583762
C2×#119244952
#146437