Finite Group Databasebeta

← #18010571

Subgroups — #18010571

Order 4736.

432 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C23×#64438C211yesmaximal, characteristic, complemented
2C2×#11924593C212yesmaximal, complemented
3C2×C22⋊#64438C211yesmaximal, characteristic, complemented
4#14558399C212yesmaximal, complemented
5C2×#11924496C211yesmaximal, characteristic
6C22×#64438—22no—
7C22×#64438—24no—
8C22×#64438C2212yes—
9C22×#64438C2212yes—
10#11924593—24no—
11C22⋊#64438—22no—
12C22×C22⋊D37C411yescharacteristic
13C23×Dic37C2211yescharacteristic
14C22×C4×D37C2211yescharacteristic
15#11924496—22no—
16#11924496—22no—
17C2×#10596936C411yescharacteristic
18C2×#10596938C411yescharacteristic
19C2×C4×Dic37C2211yescharacteristic
20C2×C22⋊C4×C37C411yescharacteristic
21C24×C37C2×C411yescharacteristic
22C23×D37C2×C411yescharacteristic
23C22×C4×C37C2×C411yescharacteristic
24C22×C4×C37C2×C411yescharacteristic
25C2×C22⋊D37—22no—
26C2×C22⋊D37—22no—
27C2×C22⋊D37C814yescomplemented
28C22×Dic37—22no—
29C22×Dic37—22no—
30C22×Dic37C2×C411yescharacteristic
31C22×Dic37C2×C411yescharacteristic
32C22×Dic37D412yes—
33C22×Dic37D412yes—
34C22×Dic37C2311yescharacteristic
35C2×C4×D37—21no—
36C2×C4×D37—21no—
37C2×C4×D37—22no—
38C2×C4×D37—22no—
39C2×#64438—28no—
40C2×#64438—22no—
41C2×#64438—22no—
42C2×#64438—22no—
43C2×#64438—22no—
44C2×#64438—22no—
45C2×#64438D414yescomplemented
46C22⋊C4×C37—22no—
47#10596938—22no—
48#10596936—22no—
49C4×Dic37—21no—
50C4×Dic37—21no—
51C23×C37—22no—
52C23×C37—22no—
53C23×C37C22⋊C412yes—
54C23×C37C2×C812yes—
55C23×C37M1612yes—
56C23×C37C22×C411yescharacteristic
57C22×D37—21no—
58C22×D37—22no—
59C22×D37—21no—
60C22×D37—22no—
61C22×D37C2×C812yescomplemented
62C2×C4×C37—21no—
63C2×C4×C37—21no—
64C2×C4×C37—22no—
65C2×C4×C37—22no—
66C22⋊D37—28no—
67C2×Dic37—21no—
68C2×Dic37—22no—
69C2×Dic37—21no—
70C2×Dic37—22no—
71C2×Dic37—24no—
72C2×Dic37—22no—
73C2×Dic37C22⋊C412yes—
74C2×Dic37C2×C812yescomplemented
75C2×Dic37C2×D412yes—
76C2×Dic37C2×D411yescharacteristic
77C2×Dic37C2×D411yescharacteristic
78C2×Dic37#4112yes—
79C4×D37—41no—
80C4×D37—42no—
81C4×D37—41no—
82#64438—24no—
83#64438—42no—
84C22×C37—22no—
85C22×C37—22no—
86C22×C37—24no—
87C22×C37—24no—
88C22×C37C22⋊C814yescomplemented
89C22×C37C2×C22⋊C411yescharacteristic
90C22×C37C4×D412yes—
91C22×C37C22×C811yescharacteristic
92C22×C37C2×M1611yescharacteristic
93C22×C37#13112yes—
94C2×D37—22no—
95C2×D37—24no—
96C2×D37—41no—
97C2×D37—41no—
98C2×D37—42no—
99C4×C37—41no—
100C4×C37—41no—
101Dic37—22no—
102Dic37—22no—
103Dic37#12011yescharacteristic
104Dic37#12112yes—
105Dic37#12311yescharacteristic
106#1869—371nomaximal, Sylow
107C2×C37—24no—
108C2×C37#38611yescharacteristic
109C2×C37C2×C22⋊C811yescharacteristic
110C2×C37#40811yescharacteristic
111C2×C37C8×D412yes—
112C2×C37#43512yes—
113D37—42no—
114C23×C8—371no—
115C2×C4×D4—371no—
116C2×C22⋊C8—371no—
117C2×C22⋊C8—372no—
118#336—372no—
119C37#186911yescharacteristic, complemented, Sylow
120C22×D4—371no—
121C23×C4—371no—
122C23×C4—371no—
123C22×C8—372no—
124C22×C8—372no—
125C22×C8—744no—
126C22×C8—742no—
127C4×D4—742no—
128C4×D4—742no—
129C2×C4⋊C4—371no—
130C2×C22⋊C4—371no—
131C2×C22⋊C4#386611yescharacteristic
132C2×C42—371no—
133C22⋊C8—744no—
134C22⋊C8—742no—
135C24—371no—
136C24C2×#386611yescharacteristic
137C2×D4—374no—
138C2×D4—742no—
139C2×D4—742no—
140C22×C4—371no—
141C22×C4—372no—
142C22×C4—372no—
143C22×C4—371no—
144C22×C4—371no—
145C22×C4—742no—
146C22×C4—741no—
147C22×C4—741no—
148C22×C4—742no—
149C22×C4—742no—
150C22×C4—742no—
151C22×C4C2×#386611yescharacteristic
152C22×C4C2×#386611yescharacteristic
153C2×C8—374no—
154C2×C8—742no—
155C2×C8—742no—
156C2×C8—748no—
157C2×C8—742no—
158C2×C8—742no—
159C2×C8—742no—
160C4⋊C4—742no—
161C22⋊C4—22no—
162C22⋊C4—742no—
163C42—741no—
164C42—741no—
165C23—22no—
166C23—22no—
167C23—372no—
168C23—741no—
169C23—742no—
170C23—741no—
171C23—742no—
172C23D37⋊C812yes—
173C23#1059695312yes—
174C23C22⋊#386612yes—
175C23C22×#386611yescharacteristic
176D4—748no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—371no—
182C2×C4—371no—
183C2×C4—372no—
184C2×C4—372no—
185C2×C4—372no—
186C2×C4—372no—
187C2×C4—742no—
188C2×C4—744no—
189C2×C4—742no—
190C2×C4—741no—
191C2×C4—742no—
192C2×C4—741no—
193C2×C4—1481no—
194C2×C4—1482no—
195C2×C4—1481no—
196C8—744no—
197C8—1482no—
198C22—22no—
199C22—22no—
200C22—24no—
201C22—24no—
202C22—742no—
203C22—744no—
204C22—1481no—
205C22—1481no—
206C22—1482no—
207C22#1192459314yescomplemented
208C22C2×C22⋊#386611yescharacteristic
209C22D4×#386612yes—
210C22C2×D37⋊C811yescharacteristic
211C22C2×#1059695311yescharacteristic
212C22#1192462312yes—
213C4—41no—
214C4—41no—
215C4—371no—
216C4—372no—
217C4—371no—
218C4—742no—
219C4—742no—
220C2—24no—
221C2—1482no—
222C2#1455848111yescharacteristic
223C2C2×#1192459311yescharacteristic
224C2#1455850611yescharacteristic
225C2#1455856012yes—
226C2#1455856212yes—
subgroupG/H
center, FrattiniC23C22×#3866
commutatorC22×C37C22×C8
FittingC2×C22⋊C4×C37C4
socleC23×C37C22×C4
prime radicalC22×C22⋊D37C4
cosocleC22×Dic37C23
hypercenterC2×C22⋊C4#3866
hypocenterC37#1869
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×#64438C2semidirect
2. C2×#11924593C2semidirect
3. C2×C22⋊#64438C2semidirect
4. #14558399C2semidirect
27. C2×C22⋊D37C8semidirect
45. C2×#64438D4semidirect
61. C22×D37C2×C8semidirect
74. C2×Dic37C2×C8semidirect
88. C22×C37C22⋊C8semidirect
119. C37#1869semidirect
207. C22#11924593semidirect

Maximal subgroups

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

subgroupindex
C23×#644382
C2×#119245932
C2×C22⋊#644382
#145583992
C2×#119244962
#186937