Finite Group Databasebeta

← #18009877

Subgroups — #18009877

Order 4736.

214 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 58 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#14558554C211yesmaximal, characteristic, complemented
2#14558550C211yesmaximal, characteristic, complemented
3#14558378C212yesmaximal, complemented
4#14558376C212yesmaximal
5C2×#11924529C211yesmaximal, characteristic
6#11924603—21no—
7C4⋊#64438—21no—
8C22⋊#64438C2212yes—
9C22⋊#64438C2212yes—
10#11924591—21no—
11C4×#64438—21no—
12#11924529—21no—
13#11924529—21no—
14#11924529—21no—
15#11924529—21no—
16C2×C4⋊Dic37C2211yescharacteristic
17C2×#10596936C411yescharacteristic
18C2×#10596936C411yescharacteristic
19C2×C22⋊Dic37C411yescharacteristic
20C2×C22⋊Dic37C2211yescharacteristic
21C2×C4×Dic37C2211yescharacteristic
22C2×C22⋊C4×C37C411yescharacteristic
23C24×C37C2×C411yescharacteristic
24C22×C4×C37C2×C411yescharacteristic
25C22×C4×C37C2×C411yescharacteristic
26C22×Dic37C2×C411yescharacteristic
27C22×Dic37C2×C411yescharacteristic
28C22×Dic37C2×C411yescharacteristic
29C22×Dic37C2311yescharacteristic
30C2×#64438—22no—
31C2×#64438—22no—
32C22⋊C4×C37—21no—
33C22⋊C4×C37—21no—
34C22⋊Dic37—21no—
35C22⋊Dic37—21no—
36C22⋊Dic37—21no—
37C22⋊Dic37—21no—
38C4⋊Dic37—21no—
39C4⋊Dic37—21no—
40#10596936—21no—
41#10596936—21no—
42#10596936—21no—
43#10596936—21no—
44C4×Dic37D411yescharacteristic
45C4×Dic37D411yescharacteristic
46C4×Dic37D411yescharacteristic
47C4×Dic37D411yescharacteristic
48C23×C37—21no—
49C23×C37—22no—
50C23×C37—41no—
51C23×C37—41no—
52C23×C37C22×C411yescharacteristic
53C2×C4×C37—21no—
54C2×C4×C37—22no—
55C2×C4×C37—41no—
56C2×C4×C37C22⋊C411yescharacteristic
57C2×C4×C37C22⋊C411yescharacteristic
58C2×Dic37—22no—
59C2×Dic37—21no—
60C2×Dic37—21no—
61C2×Dic37—41no—
62C2×Dic37—41no—
63C2×Dic37—41no—
64C2×Dic37C22⋊C411yescharacteristic
65C2×Dic37C22⋊C411yescharacteristic
66C2×Dic37C2×D411yescharacteristic
67C2×Dic37C2×D411yescharacteristic
68#64438—42no—
69#64438—42no—
70C22×C37—21no—
71C22×C37—21no—
72C22×C37—41no—
73C22×C37—41no—
74C22×C37—41no—
75C22×C37—82no—
76C22×C37C2×C22⋊C411yescharacteristic
77C22×C37#13112yes—
78C4×C37—21no—
79C4×C37—21no—
80C4×C37—41no—
81Dic37—21no—
82Dic37—21no—
83Dic37—21no—
84Dic37—21no—
85Dic37—41no—
86Dic37—41no—
87#1473—371nomaximal, Sylow
88C2×C37—22no—
89C2×C37—81no—
90C2×C37#40811yescharacteristic
91C2×C37#41011yescharacteristic
92C2×C37#41311yescharacteristic
93C2×#126—371no—
94#432—371no—
95#431—371no—
96#324—372no—
97#323—372no—
98C37#147311yescharacteristic, complemented, Sylow
99#126—741no—
100#126—741no—
101#126—741no—
102#126—741no—
103C2×C4⋊C4—371no—
104C2×C4⋊C4—371no—
105C2×C4⋊C4—371no—
106C2×C22⋊C4—371no—
107C2×C22⋊C4—371no—
108C2×C22⋊C4#386611yescharacteristic
109C2×C42—371no—
110C4⋊C8—741no—
111C4⋊C8—741no—
112C22⋊C8—372no—
113C22⋊C8—372no—
114#97—741no—
115C4×C8—741no—
116C24C2×#386611yescharacteristic
117C22×C4—371no—
118C22×C4—371no—
119C22×C4—371no—
120C22×C4—371no—
121C22×C4C2×#386611yescharacteristic
122C22×C4C2×#386611yescharacteristic
123C2×C8—742no—
124C2×C8—742no—
125C4⋊C4—741no—
126C4⋊C4—741no—
127C4⋊C4—741no—
128C4⋊C4—741no—
129C4⋊C4—741no—
130C4⋊C4—741no—
131C22⋊C4—21no—
132C22⋊C4—21no—
133C22⋊C4—741no—
134C22⋊C4—741no—
135C22⋊C4—741no—
136C22⋊C4—741no—
137C42—371no—
138C42—371no—
139C42—371no—
140C42—371no—
141C23—21no—
142C23—22no—
143C23—41no—
144C23—41no—
145C23C22×#386611yescharacteristic
146C2×C4—21no—
147C2×C4—22no—
148C2×C4—41no—
149C2×C4—371no—
150C2×C4—371no—
151C2×C4—371no—
152C2×C4—371no—
153C2×C4—742no—
154C2×C4—741no—
155C2×C4—741no—
156C2×C4—1481no—
157C2×C4—1481no—
158C2×C4—1481no—
159C2×C4C22⋊#386611yescharacteristic
160C2×C4C22⋊#386611yescharacteristic
161C8—1482no—
162C8—1482no—
163C22—21no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22—82no—
169C22C2×C22⋊#386611yescharacteristic
170C22#1192462312yes—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—741no—
175C4—741no—
176C4—741no—
177C4—741no—
178C4—1481no—
179C4—1481no—
180C2—22no—
181C2—81no—
182C2#1455850711yescharacteristic
183C2#1455851211yescharacteristic
184C2#1455852011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C22⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC24×C37C2×C4
cosocleC22×Dic37C23
hypercenterC2×C22⋊C4#3866
hypocenterC37#1473
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #14558554C2semidirect
2. #14558550C2semidirect
3. #14558378C2semidirect
98. C37#1473semidirect

Maximal subgroups

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

subgroupindex
#145585542
#145585502
#145583782
#145583762
C2×#119245292
#147337