Finite Group Databasebeta

← #17994583

Subgroups — #17994583

Order 4736.

380 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×#11924496C211yesmaximal, characteristic
2C2×#11924450C212yesmaximal
3#14557391C212yesmaximal, complemented
4#14557300C211yesmaximal, characteristic, complemented
5C37×#342C211yesmaximal, characteristic, complemented
6C22×C22⋊D37C2211yescharacteristic
7C23×Dic37C2211yescharacteristic
8C22×C4×D37C411yescharacteristic, complemented
9#11924496—22no—
10#11924496—22no—
11C2×#10596936—22no—
12C2×#10596936C411yescharacteristic, complemented
13C2×C22⋊Dic37C2212yes—
14C2×#10596938C411yescharacteristic, complemented
15C2×C4×Dic37C411yescharacteristic, complemented
16#11924450—24no—
17#11924443—22no—
18C2×C22⋊C4×C37C2212yes—
19C2×C22⋊C4×C37C2211yescharacteristic
20C24×C37C2311yescharacteristic
21C23×D37C2×C411yescharacteristic
22C22×C4×C37—22no—
23C22×C4×C37C2×C411yescharacteristic
24C22×C4×C37C2×C411yescharacteristic
25C2×C22⋊D37—22no—
26C2×C22⋊D37—22no—
27C2×C22⋊D37D412yes—
28C2×C22⋊D37Q812yes—
29C22×Dic37—22no—
30C22×Dic37—42no—
31C22×Dic37C2×C411yescharacteristic
32C22×Dic37C2×C411yescharacteristic
33C22×Dic37C2×C411yescharacteristic
34C22×Dic37D412yes—
35C22×Dic37D412yes—
36C2×C4×D37—21no—
37C2×C4×D37—21no—
38C2×C4×D37—42no—
39C22⋊C4×C37—22no—
40C22⋊C4×C37—22no—
41C22⋊C4×C37—22no—
42C22⋊Dic37—22no—
43C22⋊Dic37—22no—
44#10596938—22no—
45#10596936—22no—
46#10596936—44no—
47C4×Dic37—21no—
48C4×Dic37—21no—
49C23×C37—41no—
50C23×C37—41no—
51C23×C37C22×C411yescharacteristic
52C23×C37C2×D412yes—
53C23×C37C2×D411yescharacteristic
54C23×C37C2×Q811yescharacteristic
55C23×C37#4112yes—
56C22×D37—21no—
57C22×D37—21no—
58C22×D37—41no—
59C22×D37—41no—
60C22×D37C4⋊C412yescomplemented
61C2×C4×C37—21no—
62C2×C4×C37—21no—
63C2×C4×C37—41no—
64C2×C4×C37—41no—
65C2×C4×C37—42no—
66C2×C4×C37—42no—
67C2×C4×C37—42no—
68C22⋊D37—24no—
69C22⋊D37—24no—
70C2×Dic37—21no—
71C2×Dic37—21no—
72C2×Dic37—24no—
73C2×Dic37—22no—
74C2×Dic37—41no—
75C2×Dic37—42no—
76C2×Dic37—42no—
77C2×Dic37—42no—
78C2×Dic37—42no—
79C2×Dic37C22⋊C411yescharacteristic
80C2×Dic37C22⋊C412yes—
81C2×Dic37C22⋊C411yescharacteristic
82C2×Dic37C4⋊C412yescomplemented
83C4×D37—42no—
84C4×D37—42no—
85C22×C37—22no—
86C22×C37—21no—
87C22×C37—22no—
88C22×C37—21no—
89C22×C37—41no—
90C22×C37—41no—
91C22×C37—42no—
92C22×C37C2×C22⋊C411yescharacteristic
93C22×C37C2×C4⋊C411yescharacteristic
94C22×C37#11711yescharacteristic
95C22×C37#12112yes—
96C22×C37C22⋊Q812yes—
97C2×D37—22no—
98C2×D37—42no—
99C2×D37—41no—
100C2×D37—41no—
101C2×D37—42no—
102C4×C37—41no—
103C4×C37—41no—
104C4×C37—82no—
105Dic37—22no—
106Dic37—21no—
107Dic37—22no—
108Dic37—82no—
109Dic37#9912yescomplemented
110#1799—371nomaximal, Sylow
111C2×C37—22no—
112C2×C37—21no—
113C2×C37—21no—
114C2×C37—22no—
115C2×C37#38011yescharacteristic
116C2×C37C2×#9911yescharacteristic
117C2×C37#41011yescharacteristic
118D37—42no—
119C2×C4×D4—371no—
120C2×#99—372no—
121#380—372no—
122#342—371no—
123#342D3711yescharacteristic, complemented
124C37#179911yescharacteristic, complemented, Sylow
125C22×D4—371no—
126C23×C4—371no—
127C23×C4—371no—
128C4×D4—742no—
129C4×D4—742no—
130C2×C4⋊C4—371no—
131C2×C4⋊C4—742no—
132C2×C22⋊C4—371no—
133C2×C22⋊C4—372no—
134C2×C22⋊C4C2×D3712yes—
135C2×C22⋊C4C2×D3711yescharacteristic
136C2×C42—371no—
137#99—744no—
138#95—742no—
139C24—371no—
140C24C22×D3711yescharacteristic
141C2×D4—372no—
142C2×D4—372no—
143C2×D4—742no—
144C2×D4—742no—
145C22×C4—22no—
146C22×C4—371no—
147C22×C4—371no—
148C22×C4—372no—
149C22×C4—371no—
150C22×C4—372no—
151C22×C4—741no—
152C22×C4—741no—
153C22×C4—742no—
154C22×C4—1482no—
155C22×C4—1482no—
156C22×C4C4×D3711yescharacteristic
157C22×C4C4×D3711yescharacteristic
158C4⋊C4—742no—
159C4⋊C4—1484no—
160C22⋊C4—22no—
161C22⋊C4—22no—
162C22⋊C4—22no—
163C22⋊C4—742no—
164C22⋊C4—742no—
165C22⋊C4—742no—
166C42—741no—
167C42—741no—
168C23—41no—
169C23—41no—
170C23—372no—
171C23—741no—
172C23—741no—
173C23—1481no—
174C23—1481no—
175C23C2×C4×D3711yescharacteristic
176C23#1059696212yes—
177C23D4×D3712yes—
178C23D4×D3711yescharacteristic
179C23Q8×D3711yescharacteristic
180D4—744no—
181D4—744no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—371no—
190C2×C4—371no—
191C2×C4—372no—
192C2×C4—372no—
193C2×C4—744no—
194C2×C4—742no—
195C2×C4—741no—
196C2×C4—741no—
197C2×C4—1482no—
198C2×C4—1482no—
199C2×C4—1482no—
200C2×C4—1482no—
201C2×C4—1482no—
202C2×C4—1482no—
203C2×C4—1481no—
204C22—22no—
205C22—21no—
206C22—22no—
207C22—21no—
208C22—42no—
209C22—41no—
210C22—41no—
211C22—742no—
212C22—1482no—
213C22—1482no—
214C22—1481no—
215C22—1481no—
216C22C22⋊C4×D3711yescharacteristic
217C22C4⋊C4×D3711yescharacteristic
218C22#1192449311yescharacteristic
219C22#1192450912yes—
220C22#1192451412yes—
221C4—41no—
222C4—41no—
223C4—82no—
224C4—372no—
225C4—2962no—
226C4—741no—
227C4—742no—
228C4—742no—
229C2—22no—
230C2—21no—
231C2—21no—
232C2—22no—
233C2—1482no—
234C2#1455739211yescharacteristic
235C2#99×D3711yescharacteristic
236C2#1455750511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC23×C37C22×C4
FrattiniC24C22×D37
FittingC37×#342C2
socleC22×C37C2×C22⋊C4
prime radicalC22×C22⋊D37C22
cosocleC24×C37C23
hypercenter#342D37
hypocenterC37#1799
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. #14557391C2semidirect
4. #14557300C2semidirect
5. C37×#342C2semidirect
8. C22×C4×D37C4semidirect
12. C2×#10596936C4semidirect
14. C2×#10596938C4semidirect
15. C2×C4×Dic37C4semidirect
60. C22×D37C4⋊C4semidirect
82. C2×Dic37C4⋊C4semidirect
109. Dic37#99semidirect
123. #342D37semidirect
124. C37#1799semidirect

Maximal subgroups

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

subgroupindex
C2×#119244962
C2×#119244502
#145573912
#145573002
C37×#3422
#179937