Finite Group Databasebeta

← #18009875

Subgroups — #18009875

Order 4736.

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

normal subgroups only

This group has 270 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#14558503C211yesmaximal, characteristic
2C2×C22⋊#64438C211yesmaximal, characteristic
3#14558379C212yesmaximal, complemented
4#14558378C212yesmaximal, complemented
5C2×#11924513C211yesmaximal, characteristic
6C2×#10596957—21no—
7C22×#64438—21no—
8C22⋊#64438—21no—
9C22⋊#64438—21no—
10C22⋊#64438C2212yes—
11C22⋊#64438C2212yes—
12C22×Dic74C411yescharacteristic
13C23×Dic37C2211yescharacteristic
14#11924513—21no—
15#11924513—21no—
16#11924513—21no—
17#11924513—21no—
18C2×C4⋊Dic37C2211yescharacteristic
19C2×#10596936C411yescharacteristic
20C2×#10596936C2211yescharacteristic
21C2×C22⋊Dic37C411yescharacteristic
22C2×C22⋊C4×C37C411yescharacteristic
23C24×C37C2×C411yescharacteristic
24C22×C4×C37C2×C411yescharacteristic
25C22×C4×C37C2×C411yescharacteristic
26C22×Dic37—42no—
27C22×Dic37C2×C411yescharacteristic
28C22×Dic37C2×C411yescharacteristic
29C22×Dic37C2×C411yescharacteristic
30C22×Dic37D411yescharacteristic
31C22×Dic37D411yescharacteristic
32C22×Dic37D411yescharacteristic
33C22×Dic37D411yescharacteristic
34C22×Dic37C2311yescharacteristic
35C2×Dic74—21no—
36C2×Dic74—21no—
37C2×Dic74—42no—
38#10596957—42no—
39C2×#64438—22no—
40C2×#64438—22no—
41C2×#64438—42no—
42C22⋊C4×C37—21no—
43C22⋊C4×C37—21no—
44C22⋊Dic37—21no—
45C22⋊Dic37—21no—
46C4⋊Dic37—21no—
47C4⋊Dic37—21no—
48#10596936—21no—
49#10596936—21no—
50#10596936—21no—
51#10596936—21no—
52C23×C37—22no—
53C23×C37—22no—
54C23×C37—41no—
55C23×C37C22⋊C411yescharacteristic
56C23×C37C22⋊C411yescharacteristic
57C23×C37C22×C411yescharacteristic
58C2×C4×C37—21no—
59C2×C4×C37—21no—
60C2×C4×C37—22no—
61C2×C4×C37—41no—
62C2×Dic37—22no—
63C2×Dic37—22no—
64C2×Dic37—22no—
65C2×Dic37—21no—
66C2×Dic37—21no—
67C2×Dic37—22no—
68C2×Dic37—41no—
69C2×Dic37—41no—
70C2×Dic37—41no—
71C2×Dic37—41no—
72C2×Dic37C22⋊C411yescharacteristic
73C2×Dic37C22⋊C411yescharacteristic
74C2×Dic37C2×D411yescharacteristic
75C2×Dic37C2×D411yescharacteristic
76Dic74—42no—
77Dic74—42no—
78#64438—42no—
79#64438—42no—
80C22×C37—21no—
81C22×C37—21no—
82C22×C37—21no—
83C22×C37—21no—
84C22×C37—21no—
85C22×C37—21no—
86C22×C37—21no—
87C22×C37—44no—
88C22×C37#10112yes—
89C22×C37C2×C22⋊C411yescharacteristic
90C22×C37#13112yes—
91C4×C37—41no—
92C4×C37—41no—
93Dic37—21no—
94Dic37—21no—
95Dic37—21no—
96Dic37—41no—
97Dic37—41no—
98Dic37#9912yes—
99#1472—371nomaximal, Sylow
100C2×C37—22no—
101C2×C37—22no—
102C2×C37—41no—
103C2×C37#40811yescharacteristic
104C2×C37C2×#9911yescharacteristic
105C2×C37C2×#10111yescharacteristic
106C2×C22⋊Q8—371no—
107#407—371no—
108C2×C22⋊C8—371no—
109#324—372no—
110#324—372no—
111C37#147211yescharacteristic, complemented, Sylow
112C22×Q8—371no—
113C23×C4—371no—
114C2×M16—741no—
115C22×C8—741no—
116C22⋊Q8—741no—
117C22⋊Q8—741no—
118C22⋊Q8—741no—
119C22⋊Q8—741no—
120C2×C4⋊C4—371no—
121C2×C4⋊C4—371no—
122C2×C4⋊C4—371no—
123C2×C22⋊C4—371no—
124C2×C22⋊C4#386611yescharacteristic
125C22⋊C8—372no—
126C22⋊C8—372no—
127C22⋊C8—741no—
128C22⋊C8—741no—
129C24C2×#386611yescharacteristic
130C2×Q8—741no—
131C2×Q8—741no—
132C2×Q8—1482no—
133C22×C4—371no—
134C22×C4—371no—
135C22×C4—371no—
136C22×C4—371no—
137C22×C4—371no—
138C22×C4—371no—
139C22×C4—371no—
140C22×C4—371no—
141C22×C4—1482no—
142C22×C4C2×#386611yescharacteristic
143C22×C4C2×#386611yescharacteristic
144M16—1482no—
145C2×C8—742no—
146C2×C8—742no—
147C2×C8—1482no—
148C4⋊C4—741no—
149C4⋊C4—741no—
150C4⋊C4—741no—
151C4⋊C4—741no—
152C4⋊C4—741no—
153C4⋊C4—741no—
154C22⋊C4—21no—
155C22⋊C4—21no—
156C22⋊C4—741no—
157C22⋊C4—741no—
158C23—22no—
159C23—22no—
160C23—41no—
161C23C22⋊#386611yescharacteristic
162C23C22⋊#386611yescharacteristic
163C23C22×#386611yescharacteristic
164Q8—1482no—
165Q8—1482no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—371no—
171C2×C4—371no—
172C2×C4—371no—
173C2×C4—371no—
174C2×C4—742no—
175C2×C4—742no—
176C2×C4—742no—
177C2×C4—741no—
178C2×C4—741no—
179C2×C4—742no—
180C2×C4—1481no—
181C2×C4—1481no—
182C2×C4—1481no—
183C2×C4—1481no—
184C8—1482no—
185C8—1482no—
186C22—21no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—44no—
194C22#1192459712yes—
195C22C2×C22⋊#386611yescharacteristic
196C22#1192462312yes—
197C4—41no—
198C4—41no—
199C4—372no—
200C4—741no—
201C4—741no—
202C4—741no—
203C4—1481no—
204C4—1481no—
205C2—22no—
206C2—22no—
207C2—41no—
208C2#1455850611yescharacteristic
209C2D37⋊#9911yescharacteristic
210C2C2×#1192459711yescharacteristic
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#1472
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #14558379C2semidirect
4. #14558378C2semidirect
111. C37#1472semidirect

Maximal subgroups

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

subgroupindex
#145585032
C2×C22⋊#644382
#145583792
#145583782
C2×#119245132
#147237