Finite Group Databasebeta

← #17994694

Subgroups — #17994694

Order 4736.

306 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 79 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#117×D37C211yesmaximal, characteristic
2#14557496C211yesmaximal, characteristic
3C4×#10596938C211yesmaximal, characteristic
4#14557294C211yesmaximal, characteristic, complemented
5#14557293C211yesmaximal, characteristic, complemented
6#14557292C211yesmaximal, characteristic, complemented
7C37×#339C211yesmaximal, characteristic, complemented
8C22×C4×D37C2211yescharacteristic
9C2×#10596934C2211yescharacteristic
10#11924495C2211yescharacteristic
11#11924494C411yescharacteristic, complemented
12#11924494C411yescharacteristic, complemented
13#11924493—21no—
14#11924492—21no—
15C4⋊C4×D37C411yescharacteristic, complemented
16C4⋊C4×D37C411yescharacteristic, complemented
17C2×#10596938—21no—
18C22⋊C4×D37—21no—
19C2×C4×Dic37C2211yescharacteristic
20C42×D37—21no—
21#11924448—21no—
22#11924448—21no—
23#11924443—21no—
24C2×M16×C37C2211yescharacteristic
25#117×C37C2211yescharacteristic
26C2×C42×C37C2211yescharacteristic
27C23×D37D411yescharacteristic
28C22×C4×C37—21no—
29C22×C4×C37C2311yescharacteristic
30C22×Dic37—21no—
31C22×Dic37D411yescharacteristic
32C2×C4×D37—21no—
33C2×C4×D37—21no—
34C2×C4×D37—21no—
35C2×C4×D37—21no—
36C2×C4×D37—21no—
37C2×C4×D37—21no—
38C2×C4×D37C2×C411yescharacteristic
39C2×C4×D37C2×C411yescharacteristic
40C2×C4×D37D411yescharacteristic
41C2×C4×D37D411yescharacteristic
42M16×C37—21no—
43M16×C37—21no—
44C2×C8×C37—21no—
45C4⋊C4×C37C2×C411yescharacteristic
46C4⋊C4×C37C2×C411yescharacteristic
47C22⋊C4×C37—21no—
48C42×C37—21no—
49C42×C37—21no—
50C42×C37—21no—
51C22⋊Dic37—21no—
52#10596938—24no—
53#10596938—21no—
54#10596938—21no—
55C4⋊Dic37C2×C411yescharacteristic
56C4⋊Dic37C2×C411yescharacteristic
57#10596936—21no—
58#10596936—21no—
59C4×Dic37—21no—
60C4×Dic37—21no—
61C4×Dic37—21no—
62C4×Dic37—21no—
63C4×Dic37—21no—
64#10596934—21no—
65#10596934—21no—
66C2×#64436—21no—
67C23×C37C2×D411yescharacteristic
68C22×D37—21no—
69C22×D37—21no—
70C22×D37—22no—
71C22×D37—41no—
72C22×D37C22⋊C411yescharacteristic
73C22×D37C22⋊C411yescharacteristic
74C2×C4×C37—22no—
75C2×C4×C37—21no—
76C2×C4×C37—21no—
77C2×C4×C37—41no—
78C2×C4×C37—41no—
79C2×C4×C37C22×C411yescharacteristic
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37#4111yescharacteristic
82C2×C4×C37#4111yescharacteristic
83C2×C4×C37#4111yescharacteristic
84C2×C4×C37#4111yescharacteristic
85C2×Dic37—21no—
86C2×Dic37—21no—
87C2×Dic37—22no—
88C2×Dic37—21no—
89C2×Dic37—21no—
90C2×Dic37—41no—
91C2×Dic37—41no—
92C2×Dic37C22⋊C411yescharacteristic
93C2×Dic37C22⋊C411yescharacteristic
94C4×D37—21no—
95C4×D37—21no—
96C4×D37—21no—
97C4×D37—21no—
98C4×D37—21no—
99C4×D37—21no—
100C4×D37—21no—
101C4×D37—21no—
102C4×D37—42no—
103C4×D37—42no—
104C8×C37—41no—
105#64436—41no—
106C22×C37—21no—
107C22×C37—21no—
108C22×C37C2×C22⋊C411yescharacteristic
109C22×C37#12311yescharacteristic
110C22×C37#12311yescharacteristic
111C2×D37—21no—
112C2×D37—21no—
113C2×D37—21no—
114C2×D37—21no—
115C2×D37—21no—
116C2×D37—42no—
117C2×D37—42no—
118C2×D37#10412yes—
119C4×C37—42no—
120C4×C37—41no—
121C4×C37—41no—
122C4×C37#11711yescharacteristic
123C4×C37#11711yescharacteristic
124C4×C37#12311yescharacteristic
125C4×C37#12311yescharacteristic
126Dic37—21no—
127Dic37—21no—
128Dic37—42no—
129Dic37—41no—
130Dic37—41no—
131#1826—371nomaximal, Sylow
132C2×C37—21no—
133C2×C37—21no—
134C2×C37#38111yescharacteristic
135C2×C37C2×#10411yescharacteristic
136C2×C37#42111yescharacteristic
137D37—22no—
138D37—41no—
139C2×#117—371no—
140#407—371no—
141C4×C22⋊C4—371no—
142#339—371no—
143#339—371no—
144#339—371no—
145#339D3711yescharacteristic, complemented
146C37#182611yescharacteristic, complemented, Sylow
147C23×C4—371no—
148C2×M16—371no—
149C2×M16C2×D3711yescharacteristic
150#117—371no—
151#117—371no—
152#117—371no—
153#117—741no—
154#117—741no—
155#117C2×D3711yescharacteristic
156C2×C4⋊C4—371no—
157C2×C4⋊C4—371no—
158C2×C22⋊C4—741no—
159C2×C22⋊C4—741no—
160C2×C42—371no—
161C2×C42—741no—
162C2×C42C2×D3711yescharacteristic
163C22⋊C8—741no—
164C22⋊C8—741no—
165#95—741no—
166C24—371no—
167C22×C4—21no—
168C22×C4—371no—
169C22×C4—371no—
170C22×C4—371no—
171C22×C4—371no—
172C22×C4—371no—
173C22×C4—741no—
174C22×C4—741no—
175C22×C4—741no—
176C22×C4—741no—
177C22×C4—741no—
178C22×C4—741no—
179C22×C4—741no—
180C22×C4C22×D3711yescharacteristic
181M16—21no—
182M16—21no—
183M16—741no—
184M16—741no—
185C2×C8—21no—
186C2×C8—741no—
187C4⋊C4—371no—
188C4⋊C4—371no—
189C4⋊C4—741no—
190C4⋊C4—741no—
191C4⋊C4C4×D3711yescharacteristic
192C4⋊C4C4×D3711yescharacteristic
193C22⋊C4—21no—
194C22⋊C4—741no—
195C22⋊C4—741no—
196C22⋊C4—744no—
197C22⋊C4—741no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—741no—
202C42—741no—
203C42—741no—
204C42—741no—
205C42—741no—
206C23—371no—
207C23—371no—
208C23—742no—
209C23—741no—
210C23—741no—
211C23—1481no—
212C23D4×D3711yescharacteristic
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—371no—
219C2×C4—371no—
220C2×C4—741no—
221C2×C4—741no—
222C2×C4—741no—
223C2×C4—741no—
224C2×C4—741no—
225C2×C4—741no—
226C2×C4—741no—
227C2×C4—741no—
228C2×C4—741no—
229C2×C4—741no—
230C2×C4—742no—
231C2×C4—741no—
232C2×C4—741no—
233C2×C4—1482no—
234C2×C4—1482no—
235C2×C4—1481no—
236C2×C4—1481no—
237C2×C4C2×C4×D3711yescharacteristic
238C2×C4#1059696211yescharacteristic
239C2×C4#1059696211yescharacteristic
240C2×C4D4×D3711yescharacteristic
241C2×C4#1059696411yescharacteristic
242C2×C4#1059696611yescharacteristic
243C8—41no—
244C8—1481no—
245C22—21no—
246C22—21no—
247C22—372no—
248C22—741no—
249C22—741no—
250C22—741no—
251C22—741no—
252C22—741no—
253C22—1482no—
254C22—1482no—
255C22C22⋊C4×D3711yescharacteristic
256C22#1192451811yescharacteristic
257C22#1192452111yescharacteristic
258C4—42no—
259C4—41no—
260C4—41no—
261C4—741no—
262C4—741no—
263C4—1482no—
264C4—1481no—
265C4—1481no—
266C4#1192449311yescharacteristic
267C4#1192449411yescharacteristic
268C4#1192451811yescharacteristic
269C4#1192452111yescharacteristic
270C2—21no—
271C2—21no—
272C2—742no—
273C2—1481no—
274C2#1455739511yescharacteristic
275C2#104×D3711yescharacteristic
276C2#1455754811yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#339C2
socleC22×C37C2×C22⋊C4
prime radicalC23×D37D4
cosocleC22×C4×C37C23
hypercenter#339D37
hypocenterC37#1826
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
4. #14557294C2semidirect
5. #14557293C2semidirect
6. #14557292C2semidirect
7. C37×#339C2semidirect
11. #11924494C4semidirect
12. #11924494C4semidirect
15. C4⋊C4×D37C4semidirect
16. C4⋊C4×D37C4semidirect
145. #339D37semidirect
146. C37#1826semidirect

Maximal subgroups

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

subgroupindex
#117×D372
#145574962
C4×#105969382
#145572942
#145572932
#145572922
C37×#3392
#182637