Finite Group Databasebeta

← #18009861

Subgroups — #18009861

Order 4736.

280 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 62 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, complemented
2C2×C22⋊#64438C211yesmaximal, characteristic, complemented
3#14558379C212yesmaximal, complemented
4#14558376C212yesmaximal, complemented
5C2×#11924517C211yesmaximal, characteristic
6C2×#10596957—21no—
7C22×#64438—21no—
8C22⋊#64438—21no—
9C22⋊#64438—21no—
10C22⋊#64438C2212yes—
11C22⋊#64438C2212yes—
12C23×Dic37C2211yescharacteristic
13#11924517—21no—
14#11924517—21no—
15#11924517—21no—
16#11924517—21no—
17C2×#10596936C411yescharacteristic
18C2×#10596936C2211yescharacteristic
19C2×C22⋊Dic37C411yescharacteristic
20C2×C22⋊Dic37C411yescharacteristic
21C2×C22⋊Dic37C2211yescharacteristic
22C22×D4×C37C411yescharacteristic
23C24×C37C2×C411yescharacteristic
24C24×C37C2×C411yescharacteristic
25C2×D4×C37—21no—
26C2×D4×C37—21no—
27C2×D4×C37—42no—
28C22×C4×C37C2×C411yescharacteristic
29C22×Dic37—42no—
30C22×Dic37C2×C411yescharacteristic
31C22×Dic37C2×C411yescharacteristic
32C22×Dic37C2×C411yescharacteristic
33C22×Dic37D411yescharacteristic
34C22×Dic37D411yescharacteristic
35C22×Dic37D411yescharacteristic
36C22×Dic37D411yescharacteristic
37C22×Dic37C2311yescharacteristic
38#10596957—42no—
39C2×#64438—22no—
40C2×#64438—22no—
41C2×#64438—42no—
42C22⋊Dic37—21no—
43C22⋊Dic37—21no—
44C22⋊Dic37—21no—
45C22⋊Dic37—21no—
46C22⋊Dic37—21no—
47C22⋊Dic37—21no—
48#10596936—21no—
49#10596936—21no—
50#10596936—21no—
51#10596936—21no—
52C23×C37—22no—
53C23×C37—22no—
54C23×C37—21no—
55C23×C37—22no—
56C23×C37—41no—
57C23×C37—41no—
58C23×C37—41no—
59C23×C37C22⋊C411yescharacteristic
60C23×C37C22⋊C411yescharacteristic
61C23×C37C22×C411yescharacteristic
62D4×C37—42no—
63D4×C37—42no—
64C2×C4×C37—21no—
65C2×C4×C37—41no—
66C2×Dic37—22no—
67C2×Dic37—22no—
68C2×Dic37—21no—
69C2×Dic37—21no—
70C2×Dic37—22no—
71C2×Dic37—41no—
72C2×Dic37—41no—
73C2×Dic37—41no—
74C2×Dic37—41no—
75C2×Dic37—41no—
76C2×Dic37C22⋊C411yescharacteristic
77C2×Dic37C22⋊C411yescharacteristic
78C2×Dic37C2×D411yescharacteristic
79C2×Dic37C2×D411yescharacteristic
80#64438—42no—
81#64438—42no—
82C22×C37—21no—
83C22×C37—21no—
84C22×C37—21no—
85C22×C37—21no—
86C22×C37—21no—
87C22×C37—21no—
88C22×C37—21no—
89C22×C37—44no—
90C22×C37—41no—
91C22×C37—41no—
92C22×C37—41no—
93C22×C37—82no—
94C22×C37#9912yes—
95C22×C37C2×C22⋊C411yescharacteristic
96C22×C37#13112yes—
97C4×C37—41no—
98Dic37—21no—
99Dic37—21no—
100Dic37—21no—
101Dic37—21no—
102Dic37—41no—
103Dic37—41no—
104#1468—371nomaximal, Sylow
105C2×C37—22no—
106C2×C37—22no—
107C2×C37—41no—
108C2×C37—81no—
109C2×C37#40811yescharacteristic
110C2×C37C2×#9911yescharacteristic
111C2×C37#41311yescharacteristic
112C2×#123—371no—
113#407—371no—
114C2×C22⋊C8—371no—
115#324—372no—
116#323—372no—
117C37#146811yescharacteristic, complemented, Sylow
118C22×D4#386611yescharacteristic
119C23×C4—371no—
120C2×M16—741no—
121C22×C8—741no—
122#123—741no—
123#123—741no—
124#123—741no—
125#123—741no—
126C2×C4⋊C4—371no—
127C2×C4⋊C4—371no—
128C2×C22⋊C4—371no—
129C2×C22⋊C4—371no—
130C2×C22⋊C4—371no—
131C22⋊C8—372no—
132C22⋊C8—372no—
133C22⋊C8—741no—
134C22⋊C8—741no—
135C24C2×#386611yescharacteristic
136C24C2×#386611yescharacteristic
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—42no—
140C22×C4—371no—
141C22×C4—371no—
142C22×C4—371no—
143C22×C4—371no—
144C22×C4—371no—
145C22×C4—371no—
146C22×C4—371no—
147C22×C4—371no—
148C22×C4—1482no—
149C22×C4C2×#386611yescharacteristic
150M16—1482no—
151C2×C8—742no—
152C2×C8—742no—
153C2×C8—1482no—
154C4⋊C4—741no—
155C4⋊C4—741no—
156C4⋊C4—741no—
157C4⋊C4—741no—
158C22⋊C4—741no—
159C22⋊C4—741no—
160C22⋊C4—741no—
161C22⋊C4—741no—
162C22⋊C4—741no—
163C22⋊C4—741no—
164C23—22no—
165C23—22no—
166C23—21no—
167C23—22no—
168C23—41no—
169C23—41no—
170C23—41no—
171C23C22⋊#386611yescharacteristic
172C23C22⋊#386611yescharacteristic
173C23C22×#386611yescharacteristic
174D4—42no—
175D4—42no—
176C2×C4—21no—
177C2×C4—41no—
178C2×C4—371no—
179C2×C4—371no—
180C2×C4—371no—
181C2×C4—371no—
182C2×C4—742no—
183C2×C4—742no—
184C2×C4—741no—
185C2×C4—741no—
186C2×C4—742no—
187C2×C4—1481no—
188C2×C4—1481no—
189C2×C4—1481no—
190C2×C4—1481no—
191C2×C4—1481no—
192C8—1482no—
193C8—1482no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—82no—
206C22#1192459412yes—
207C22C2×C22⋊#386611yescharacteristic
208C22#1192462312yes—
209C4—41no—
210C4—741no—
211C4—741no—
212C4—741no—
213C4—741no—
214C4—1481no—
215C4—1481no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—81no—
220C2#1455850611yescharacteristic
221C2C2×#1192459411yescharacteristic
222C2#1455852011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
Fitting, prime radicalC22×D4×C37C4
socleC22×C37C2×C22⋊C4
cosocleC22×Dic37C23
hypercenterC22×D4#3866
hypocenterC37#1468
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #14558503C2semidirect
2. C2×C22⋊#64438C2semidirect
3. #14558379C2semidirect
4. #14558376C2semidirect
117. C37#1468semidirect

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
#145583762
C2×#119245172
#146837