Finite Group Databasebeta

← #18009865

Subgroups — #18009865

Order 4736.

256 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 60 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#14558553C211yesmaximal, characteristic, complemented
2#14558549C211yesmaximal, characteristic, complemented
3#14558377C212yesmaximal, complemented
4#14558376C212yesmaximal, complemented
5C2×#11924522C211yesmaximal, characteristic
6#11924603—21no—
7C4⋊#64438—21no—
8C22⋊#64438C2212yes—
9C22⋊#64438C2212yes—
10#11924591—21no—
11C4×#64438—21no—
12C22×Dic74C411yescharacteristic
13C22×C22⋊D37C411yescharacteristic
14#11924522—21no—
15#11924522—21no—
16#11924522—21no—
17#11924522—21no—
18C2×C22⋊Dic37C2211yescharacteristic
19C2×#10596938C411yescharacteristic
20C2×#10596938C2211yescharacteristic
21C2×C4×Dic37C2211yescharacteristic
22C2×C22⋊C4×C37C411yescharacteristic
23C24×C37C2×C411yescharacteristic
24C23×D37C2×C411yescharacteristic
25C22×C4×C37C2×C411yescharacteristic
26C22×C4×C37C2×C411yescharacteristic
27C2×C22⋊D37—21no—
28C2×C22⋊D37—21no—
29C2×C22⋊D37—42no—
30C22×Dic37C2×C411yescharacteristic
31C22×Dic37C2×C411yescharacteristic
32C22×Dic37C2311yescharacteristic
33C2×Dic74—21no—
34C2×Dic74—21no—
35C2×Dic74—42no—
36C2×#64438—22no—
37C2×#64438—22no—
38C22⋊C4×C37—21no—
39C22⋊C4×C37—21no—
40C22⋊Dic37—21no—
41C22⋊Dic37—21no—
42#10596938—21no—
43#10596938—21no—
44#10596938—21no—
45#10596938—21no—
46C4×Dic37D411yescharacteristic
47C4×Dic37D411yescharacteristic
48C4×Dic37D411yescharacteristic
49C4×Dic37D411yescharacteristic
50C23×C37—21no—
51C23×C37—22no—
52C23×C37—41no—
53C23×C37—41no—
54C23×C37C22×C411yescharacteristic
55C22×D37—21no—
56C22×D37—22no—
57C22×D37—41no—
58C22×D37—41no—
59C2×C4×C37—22no—
60C2×C4×C37—21no—
61C2×C4×C37—41no—
62C2×C4×C37C22⋊C411yescharacteristic
63C2×C4×C37C22⋊C411yescharacteristic
64C22⋊D37—42no—
65C22⋊D37—42no—
66C2×Dic37—22no—
67C2×Dic37—21no—
68C2×Dic37—41no—
69C2×Dic37—41no—
70C2×Dic37C22⋊C411yescharacteristic
71C2×Dic37C22⋊C411yescharacteristic
72C2×Dic37C2×D411yescharacteristic
73C2×Dic37C2×D411yescharacteristic
74Dic74—42no—
75Dic74—42no—
76#64438—42no—
77#64438—42no—
78C22×C37—21no—
79C22×C37—21no—
80C22×C37—41no—
81C22×C37—41no—
82C22×C37—41no—
83C22×C37—82no—
84C22×C37C2×C22⋊C411yescharacteristic
85C22×C37#13112yes—
86C2×D37—41no—
87C2×D37—41no—
88C2×D37—41no—
89C2×D37—82no—
90C4×C37—21no—
91C4×C37—21no—
92C4×C37—41no—
93Dic37—21no—
94Dic37—21no—
95Dic37—21no—
96Dic37—41no—
97Dic37#10012yes—
98#1469—371nomaximal, Sylow
99C2×C37—22no—
100C2×C37—81no—
101C2×C37#40811yescharacteristic
102C2×C37#41011yescharacteristic
103C2×C37C2×#10011yescharacteristic
104D37—81no—
105C2×#124—371no—
106#432—371no—
107#431—371no—
108#323—372no—
109#323—372no—
110C37#146911yescharacteristic, complemented, Sylow
111C22×Q8—371no—
112C22×D4—371no—
113#124—741no—
114#124—741no—
115#124—741no—
116#124—741no—
117C2×C22⋊C4—371no—
118C2×C22⋊C4—371no—
119C2×C22⋊C4—371no—
120C2×C22⋊C4#386611yescharacteristic
121C2×C42—371no—
122C4⋊C8—741no—
123C4⋊C8—741no—
124C22⋊C8—372no—
125C22⋊C8—372no—
126#97—741no—
127C4×C8—741no—
128C24—371no—
129C24C2×#386611yescharacteristic
130C2×Q8—741no—
131C2×Q8—741no—
132C2×Q8—1482no—
133C2×D4—741no—
134C2×D4—741no—
135C2×D4—1482no—
136C22×C4—371no—
137C22×C4—371no—
138C22×C4—371no—
139C22×C4C2×#386611yescharacteristic
140C22×C4C2×#386611yescharacteristic
141C2×C8—742no—
142C2×C8—742no—
143C22⋊C4—21no—
144C22⋊C4—21no—
145C22⋊C4—741no—
146C22⋊C4—741no—
147C22⋊C4—741no—
148C22⋊C4—741no—
149C22⋊C4—741no—
150C22⋊C4—741no—
151C42—371no—
152C42—371no—
153C42—371no—
154C42—371no—
155C23—21no—
156C23—22no—
157C23—41no—
158C23—41no—
159C23—742no—
160C23—741no—
161C23—1481no—
162C23—1481no—
163C23C22×#386611yescharacteristic
164Q8—1482no—
165Q8—1482no—
166D4—1482no—
167D4—1482no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—371no—
172C2×C4—371no—
173C2×C4—371no—
174C2×C4—371no—
175C2×C4—742no—
176C2×C4—741no—
177C2×C4—1481no—
178C2×C4—1481no—
179C2×C4C22⋊#386611yescharacteristic
180C2×C4C22⋊#386611yescharacteristic
181C8—1482no—
182C8—1482no—
183C22—21no—
184C22—21no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—82no—
189C22—2962no—
190C22—1481no—
191C22—1481no—
192C22—1481no—
193C22C2×C22⋊#386611yescharacteristic
194C22#1192462312yes—
195C4—21no—
196C4—21no—
197C4—41no—
198C4—372no—
199C4—741no—
200C4—741no—
201C4—741no—
202C4—1481no—
203C2—22no—
204C2—81no—
205C2—2961no—
206C2#1455850611yescharacteristic
207C2#1455851211yescharacteristic
208C2D37⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C22⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×C22⋊D37C4
cosocleC22×Dic37C23
hypercenterC2×C22⋊C4#3866
hypocenterC37#1469
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. #14558553C2semidirect
2. #14558549C2semidirect
3. #14558377C2semidirect
4. #14558376C2semidirect
110. C37#1469semidirect

Maximal subgroups

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

subgroupindex
#145585532
#145585492
#145583772
#145583762
C2×#119245222
#146937