Finite Group Databasebeta

← #18004536

Subgroups — #18004536

Order 4736.

462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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×#11924510C211yesmaximal, characteristic
2#14557857C214yesmaximal, complemented
3#14557851C212yesmaximal, complemented
4#14557846C212yesmaximal, complemented
5#14557576C212yesmaximal, complemented
6#14557537C212yesmaximal, complemented
7#14557497C211yesmaximal, characteristic, complemented
8C2×#117×C37C211yesmaximal, characteristic, complemented
9C22×D148C2211yescharacteristic
10C22×C22⋊D37—21no—
11C2×#10596934C2212yes—
12#11924510—21no—
13#11924510—21no—
14#11924510C2212yes—
15#11924510C2212yes—
16C2×C4⋊Dic37C2211yescharacteristic
17C2×#10596938—21no—
18#11924469C2214yescomplemented
19#11924467C2214yescomplemented
20#11924456C2214yescomplemented
21#11924456C2214yescomplemented
22C22⋊#64436C2212yescomplemented
23C22⋊#64436C2212yescomplemented
24C23×C4×C37C2211yescharacteristic
25#117×C37—21no—
26#117×C37—21no—
27#117×C37C2212yes—
28#117×C37C2212yescomplemented
29C2×C4⋊C4×C37C2211yescharacteristic, complemented
30C2×C4⋊C4×C37C2211yescharacteristic, complemented
31C2×C22⋊C4×C37—21no—
32C2×C42×C37—21no—
33C24×C37D411yescharacteristic
34C23×D37—21no—
35C22×C4×C37—24no—
36C22×C4×C37—21no—
37C22×C4×C37—21no—
38C22×C4×C37D411yescharacteristic
39C22×C4×C37D411yescharacteristic
40C22×C4×C37D411yescharacteristic
41C22×C4×C37C2311yescharacteristic
42C22×C4×C37C2311yescharacteristic
43C22×C4×C37C2311yescharacteristic
44C2×C22⋊D37—22no—
45C2×C22⋊D37—22no—
46C2×C22⋊D37—44no—
47C22×Dic37—21no—
48C2×D148—24no—
49C2×D148—21no—
50C2×D148C2312yes—
51C4⋊C4×C37—21no—
52C4⋊C4×C37—21no—
53C4⋊C4×C37C2312yes—
54C4⋊C4×C37C2312yes—
55C22⋊C4×C37—22no—
56C22⋊C4×C37—22no—
57C42×C37—22no—
58C42×C37—22no—
59#10596938—22no—
60#10596938—22no—
61C4⋊Dic37—21no—
62C4⋊Dic37C2312yes—
63#10596934—24no—
64C2×#64436C2314yes—
65C23×C37—22no—
66C23×C37—22no—
67C23×C37—41no—
68C23×C37C2×D411yescharacteristic
69C23×C37C2×D411yescharacteristic
70C23×C37C2×D411yescharacteristic
71C22×D37—22no—
72C22×D37—42no—
73C22×D37—42no—
74C22×D37—42no—
75C2×C4×C37—22no—
76C2×C4×C37—22no—
77C2×C4×C37—22no—
78C2×C4×C37—22no—
79C2×C4×C37—22no—
80C2×C4×C37—22no—
81C2×C4×C37—22no—
82C2×C4×C37—42no—
83C2×C4×C37—42no—
84C2×C4×C37C2×D411yescharacteristic
85C2×C4×C37C2×D411yescharacteristic
86C2×C4×C37C2×D411yescharacteristic
87C2×C4×C37#4114yes—
88C2×C4×C37C2411yescharacteristic
89C22⋊D37—44no—
90C22⋊D37—44no—
91C2×Dic37—22no—
92C2×Dic37—42no—
93D148—24no—
94D148—42no—
95#64436—24no—
96C22×C37—21no—
97C22×C37—21no—
98C22×C37—21no—
99C22×C37—21no—
100C22×C37—21no—
101C22×C37—21no—
102C22×C37—21no—
103C22×C37—44no—
104C22×C37#12312yes—
105C22×C37AGL(1,ℤ/8)12yes—
106C22×C37C22×D411yescharacteristic
107C2×D37—42no—
108C2×D37—42no—
109C2×D37—42no—
110C2×D37—84no—
111C4×C37—21no—
112C4×C37—21no—
113C4×C37—42no—
114C4×C37—42no—
115C4×C37#12312yes—
116C4×C37C2×#4112yes—
117Dic37—42no—
118#3094—371nomaximal, Sylow
119C2×C37—22no—
120C2×C37—22no—
121C2×C37—41no—
122C2×C37C2×#12311yescharacteristic
123C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
124C2×C37#57511yescharacteristic
125D37—82no—
126C2×#121—371no—
127C2×#117D3711yescharacteristic, complemented
128#482—374no—
129#481—372no—
130#480—372no—
131#428—372no—
132#418—372no—
133#407—371no—
134C37#309411yescharacteristic, complemented, Sylow
135C22×D4—371no—
136C22×D4—741no—
137C23×C4C2×D3711yescharacteristic
138C2×M16—372no—
139#121—372no—
140#121—372no—
141#121—741no—
142#121—741no—
143#117—21no—
144#117—21no—
145#117C2×D3712yes—
146#117C2×D3712yescomplemented
147C2×C4⋊C4—371no—
148C2×C4⋊C4C2×D3711yescharacteristic, complemented
149C2×C4⋊C4C2×D3711yescharacteristic, complemented
150C2×C22⋊C4—21no—
151C2×C22⋊C4—741no—
152C2×C42—21no—
153#107—374no—
154#106—374no—
155#102—374no—
156#102—374no—
157C22⋊C8—372no—
158C22⋊C8—372no—
159C24—741no—
160C24C22⋊D3711yescharacteristic
161C2×D4—372no—
162C2×D4—742no—
163C2×D4—742no—
164C2×D4—744no—
165C2×D4—741no—
166C2×D4—1484no—
167C22×C4—24no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—741no—
171C22×C4C22⋊D3711yescharacteristic
172C22×C4C22⋊D3711yescharacteristic
173C22×C4C22⋊D3711yescharacteristic
174C22×C4C22×D3711yescharacteristic
175C22×C4C22×D3711yescharacteristic
176C22×C4C22×D3711yescharacteristic
177M16—744no—
178C2×C8—374no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—372no—
182C4⋊C4—741no—
183C4⋊C4C22×D3712yes—
184C4⋊C4C22×D3712yes—
185C22⋊C4—22no—
186C22⋊C4—22no—
187C22⋊C4—742no—
188C22⋊C4—742no—
189C42—22no—
190C42—22no—
191C23—22no—
192C23—22no—
193C23—41no—
194C23—742no—
195C23—1482no—
196C23—1482no—
197C23—1482no—
198C23C2×C22⋊D3711yescharacteristic
199C23C2×C22⋊D3711yescharacteristic
200C23C2×C22⋊D3711yescharacteristic
201D4—744no—
202D4—1484no—
203D4—1484no—
204D4—1482no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—742no—
215C2×C4—1482no—
216C2×C4#1059696214yes—
217C2×C4C2×C22⋊D3711yescharacteristic
218C2×C4C2×C22⋊D3711yescharacteristic
219C2×C4C2×C22⋊D3711yescharacteristic
220C2×C4C23×D3711yescharacteristic
221C8—744no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—44no—
230C22—2964no—
231C22—1482no—
232C22—1482no—
233C22—1482no—
234C22#1192451912yes—
235C22#1192456112yes—
236C22C22×C22⋊D3711yescharacteristic
237C4—21no—
238C4—21no—
239C4—42no—
240C4—42no—
241C4—1482no—
242C4#1192451912yes—
243C4C2×#1059696212yes—
244C2—22no—
245C2—22no—
246C2—41no—
247C2—2962no—
248C2C2×#1192451911yescharacteristic
249C2C2×#1192456111yescharacteristic
250C2#1455833111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#117×C37C2
socleC22×C37C22×D4
prime radicalC2×#11924510C2
hypercenterC2×#117D37
hypocenterC37#3094
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #14557857C2semidirect
3. #14557851C2semidirect
4. #14557846C2semidirect
5. #14557576C2semidirect
6. #14557537C2semidirect
7. #14557497C2semidirect
8. C2×#117×C37C2semidirect
18. #11924469C22semidirect
19. #11924467C22semidirect
20. #11924456C22semidirect
21. #11924456C22semidirect
22. C22⋊#64436C22semidirect
23. C22⋊#64436C22semidirect
28. #117×C37C22semidirect
29. C2×C4⋊C4×C37C22semidirect
30. C2×C4⋊C4×C37C22semidirect
127. C2×#117D37semidirect
134. C37#3094semidirect
146. #117C2×D37semidirect
148. C2×C4⋊C4C2×D37semidirect
149. C2×C4⋊C4C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245102
#145578572
#145578512
#145578462
#145575762
#145575372
#145574972
C2×#117×C372
#309437