Finite Group Databasebeta

← #18010576

Subgroups — #18010576

Order 4736.

408 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C22×#10596953C211yesmaximal, characteristic, complemented
2C2×#11924593C212yesmaximal, complemented
3C2×#11924593C211yesmaximal, characteristic, complemented
4#14558399C212yesmaximal, complemented
5C2×#11924498C211yesmaximal, characteristic
6C2×#10596953—22no—
7C2×#10596953—24no—
8C22×#64438C2212yes—
9C22×#64438C2212yes—
10#11924593—22no—
11#11924593—24no—
12C22×D148C411yescharacteristic
13C22×C4×D37C2211yescharacteristic
14C22×C4×D37C2211yescharacteristic
15#11924498—22no—
16#11924498—22no—
17C2×#10596938C411yescharacteristic
18C2×#10596938C411yescharacteristic
19C2×C4×Dic37C2211yescharacteristic
20C2×C4⋊C4×C37C411yescharacteristic
21C23×D37C2×C411yescharacteristic
22C23×D37C2×C411yescharacteristic
23C22×C4×C37C2×C411yescharacteristic
24C22×C4×C37C2×C411yescharacteristic
25C22×C4×C37C2×C411yescharacteristic
26C22×Dic37C2×C411yescharacteristic
27C22×Dic37C2311yescharacteristic
28C2×D148—22no—
29C2×D148—22no—
30C2×D148—22no—
31C2×C4×D37—22no—
32C2×C4×D37—22no—
33C2×C4×D37—21no—
34C2×C4×D37—21no—
35C2×C4×D37—22no—
36C2×C4×D37—22no—
37C2×C4×D37D412yes—
38C2×C4×D37D412yes—
39C2×#64438—22no—
40C2×#64438—22no—
41C2×#64438—22no—
42C2×#64438—22no—
43C2×#64438—22no—
44C2×#64438D414yescomplemented
45#10596953—28no—
46C4⋊C4×C37—22no—
47#10596938—22no—
48#10596938—22no—
49C4×Dic37—21no—
50C4×Dic37—21no—
51C23×C37C22×C411yescharacteristic
52C22×D37—21no—
53C22×D37—22no—
54C22×D37—22no—
55C22×D37—21no—
56C22×D37—21no—
57C22×D37—21no—
58C22×D37—22no—
59C22×D37—22no—
60C22×D37C22⋊C412yes—
61C22×D37M1612yescomplemented
62C2×C4×C37—21no—
63C2×C4×C37—22no—
64C2×C4×C37—21no—
65C2×C4×C37—21no—
66C2×C4×C37—22no—
67C2×C4×C37C22⋊C412yes—
68C2×C4×C37M1612yescomplemented
69C2×Dic37—21no—
70C2×Dic37—22no—
71C2×Dic37C2×D412yes—
72C2×Dic37C2×D411yescharacteristic
73C2×Dic37C2×D411yescharacteristic
74C2×Dic37#4112yes—
75D148—28no—
76C4×D37—22no—
77C4×D37—24no—
78C4×D37—22no—
79C4×D37—41no—
80C4×D37—42no—
81C4×D37—41no—
82#64438—24no—
83#64438—42no—
84C22×C37C2×C22⋊C411yescharacteristic
85C22×C37C4×D412yes—
86C22×C37C2×M1611yescharacteristic
87C22×C37C2×M1611yescharacteristic
88C22×C37#13112yes—
89C2×D37—22no—
90C2×D37—22no—
91C2×D37—22no—
92C2×D37—22no—
93C2×D37—24no—
94C2×D37—41no—
95C2×D37—41no—
96C2×D37—42no—
97C2×D37—42no—
98C2×D37—42no—
99C4×C37—22no—
100C4×C37—22no—
101C4×C37—41no—
102Dic37—41no—
103Dic37#12011yescharacteristic
104Dic37#12112yes—
105Dic37#12311yescharacteristic
106#1870—371nomaximal, Sylow
107C2×C37#38611yescharacteristic
108C2×C37#40711yescharacteristic
109C2×C37#40811yescharacteristic
110C2×C37#43512yes—
111C2×C37#43612yes—
112D37—42no—
113D37—42no—
114C22×M16—371no—
115C2×C4×D4—371no—
116C2×C22⋊C8—372no—
117C2×C22⋊C8—371no—
118#336—372no—
119C37#187011yescharacteristic, complemented, Sylow
120C22×D4—371no—
121C23×C4—371no—
122C23×C4—371no—
123C2×M16—744no—
124C2×M16—742no—
125C22×C8—372no—
126C22×C8—372no—
127C4×D4—742no—
128C4×D4—742no—
129C2×C4⋊C4#386611yescharacteristic
130C2×C22⋊C4—371no—
131C2×C22⋊C4—371no—
132C2×C42—371no—
133C22⋊C8—744no—
134C22⋊C8—742no—
135C24—371no—
136C24—371no—
137C2×D4—742no—
138C2×D4—742no—
139C2×D4—742no—
140C22×C4—371no—
141C22×C4—372no—
142C22×C4—372no—
143C22×C4—371no—
144C22×C4—742no—
145C22×C4—742no—
146C22×C4—742no—
147C22×C4—741no—
148C22×C4—741no—
149C22×C4—742no—
150C22×C4C2×#386611yescharacteristic
151C22×C4C2×#386611yescharacteristic
152C22×C4C2×#386611yescharacteristic
153M16—748no—
154C2×C8—374no—
155C2×C8—742no—
156C2×C8—742no—
157C2×C8—742no—
158C2×C8—742no—
159C2×C8—742no—
160C4⋊C4—22no—
161C22⋊C4—742no—
162C22⋊C4—742no—
163C42—741no—
164C42—741no—
165C23—372no—
166C23—372no—
167C23—741no—
168C23—742no—
169C23—742no—
170C23—741no—
171C23—741no—
172C23—741no—
173C23—742no—
174C23—742no—
175C23C22×#386611yescharacteristic
176D4—748no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—371no—
183C2×C4—371no—
184C2×C4—372no—
185C2×C4—372no—
186C2×C4—742no—
187C2×C4—744no—
188C2×C4—742no—
189C2×C4—741no—
190C2×C4—742no—
191C2×C4—1481no—
192C2×C4—1482no—
193C2×C4—1481no—
194C2×C4#1059695312yescomplemented
195C2×C4C22⋊#386612yes—
196C8—744no—
197C8—1482no—
198C22—742no—
199C22—742no—
200C22—742no—
201C22—742no—
202C22—744no—
203C22—1481no—
204C22—1481no—
205C22—1482no—
206C22—1482no—
207C22—1482no—
208C22C2×C22⋊#386611yescharacteristic
209C22D4×#386612yes—
210C22D37⋊M1611yescharacteristic
211C22C2×#1059695311yescharacteristic
212C22#1192462412yes—
213C4—22no—
214C4—22no—
215C4—41no—
216C4—371no—
217C4—372no—
218C4—371no—
219C4—1481no—
220C2—1482no—
221C2—1482no—
222C2#1455848111yescharacteristic
223C2#1455850411yescharacteristic
224C2#1455850811yescharacteristic
225C2#1455856312yes—
226C2#1455856712yes—
subgroupG/H
center, FrattiniC23C22×#3866
commutator, socleC23×C37C22×C4
FittingC2×C4⋊C4×C37C4
prime radicalC22×D148C4
cosocleC22×Dic37C23
hypercenterC2×C4⋊C4#3866
hypocenterC37#1870
LCSG ▷ C23×C37 ▷ C37
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#10596953C2semidirect
2. C2×#11924593C2semidirect
3. C2×#11924593C2semidirect
4. #14558399C2semidirect
44. C2×#64438D4semidirect
61. C22×D37M16semidirect
68. C2×C4×C37M16semidirect
119. C37#1870semidirect
194. C2×C4#10596953semidirect

Maximal subgroups

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

subgroupindex
C22×#105969532
C2×#119245932
#145583992
C2×#119244982
#187037