Finite Group Databasebeta

← #18004537

Subgroups — #18004537

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
2C2×#11924495C211yesmaximal, characteristic, complemented
3#14557858C214yesmaximal, complemented
4#14557852C212yesmaximal, complemented
5#14557847C212yesmaximal, complemented
6#14557575C212yesmaximal, complemented
7#14557539C212yesmaximal, complemented
8C37×#407C211yesmaximal, characteristic, complemented
9C22×D148C2211yescharacteristic
10C22×C22⋊D37—21no—
11#11924510—21no—
12#11924510—21no—
13#11924510C2212yes—
14#11924510C2212yes—
15#11924495—21no—
16#11924495—21no—
17#11924495C2212yes—
18#11924495C2212yescomplemented
19C2×C4⋊Dic37C2211yescharacteristic
20C2×C4⋊Dic37C2211yescharacteristic, complemented
21C2×C4⋊Dic37C2211yescharacteristic, complemented
22C2×C22⋊Dic37—21no—
23C2×#10596938—21no—
24C2×C4×Dic37—21no—
25#11924470C2214yescomplemented
26#11924468C2214yescomplemented
27#11924458C2214yescomplemented
28#11924458C2214yescomplemented
29C23×C4×C37C2211yescharacteristic
30C2×M16×C37C2212yes—
31C22⋊C8×C37C2212yescomplemented
32C22⋊C8×C37C2212yescomplemented
33C24×C37D411yescharacteristic
34C23×D37—21no—
35C22×C4×C37—24no—
36C22×C4×C37D411yescharacteristic
37C22×C4×C37D411yescharacteristic
38C22×C4×C37D411yescharacteristic
39C22×C4×C37C2311yescharacteristic
40C22×C4×C37C2311yescharacteristic
41C22×C4×C37C2311yescharacteristic
42C2×C22⋊D37—22no—
43C2×C22⋊D37—22no—
44C2×C22⋊D37—44no—
45C22×Dic37—21no—
46C22×Dic37—21no—
47C22×Dic37—21no—
48C2×D148—24no—
49C2×D148—21no—
50C2×D148C2312yes—
51M16×C37—24no—
52C2×C8×C37C2314yes—
53C22⋊Dic37—22no—
54C22⋊Dic37—22no—
55#10596938—22no—
56#10596938—22no—
57C4⋊Dic37—21no—
58C4⋊Dic37—21no—
59C4⋊Dic37—21no—
60C4⋊Dic37C2312yes—
61C4⋊Dic37C2312yes—
62C4⋊Dic37C2312yes—
63C4×Dic37—22no—
64C4×Dic37—22no—
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×C37C2×D411yescharacteristic
81C2×C4×C37C2×D411yescharacteristic
82C2×C4×C37C2×D411yescharacteristic
83C2×C4×C37#4114yes—
84C2×C4×C37C2411yescharacteristic
85C22⋊D37—44no—
86C22⋊D37—44no—
87C2×Dic37—22no—
88C2×Dic37—22no—
89C2×Dic37—22no—
90C2×Dic37—42no—
91C2×Dic37—42no—
92C2×Dic37—42no—
93D148—24no—
94D148—42no—
95C8×C37—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#12312yes—
114C4×C37C2×#4112yes—
115Dic37—42no—
116Dic37—42no—
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×#117—371no—
128#482—374no—
129#481—372no—
130#480—372no—
131#428—372no—
132#418—372no—
133#407D3711yescharacteristic, complemented
134C37#309411yescharacteristic, complemented, Sylow
135C22×D4—371no—
136C22×D4—741no—
137C23×C4C2×D3711yescharacteristic
138C2×M16C2×D3712yes—
139#121—372no—
140#121—372no—
141#121—741no—
142#121—741no—
143#117—372no—
144#117—372no—
145#117—741no—
146#117—741no—
147C2×C4⋊C4—371no—
148C2×C4⋊C4—371no—
149C2×C4⋊C4—371no—
150C2×C22⋊C4—741no—
151C2×C22⋊C4—741no—
152C2×C42—741no—
153#107—374no—
154#106—374no—
155#102—374no—
156#102—374no—
157C22⋊C8C2×D3712yescomplemented
158C22⋊C8C2×D3712yescomplemented
159C24—741no—
160C24D14811yescharacteristic
161C2×D4—372no—
162C2×D4—742no—
163C2×D4—742no—
164C2×D4—741no—
165C2×D4—744no—
166C2×D4—1484no—
167C22×C4—24no—
168C22×C4—741no—
169C22×C4—741no—
170C22×C4—741no—
171C22×C4D14811yescharacteristic
172C22×C4D14811yescharacteristic
173C22×C4D14811yescharacteristic
174C22×C4C22×D3711yescharacteristic
175C22×C4C22×D3711yescharacteristic
176C22×C4C22×D3711yescharacteristic
177M16—24no—
178C2×C8C22×D3714yes—
179C4⋊C4—372no—
180C4⋊C4—372no—
181C4⋊C4—372no—
182C4⋊C4—741no—
183C4⋊C4—741no—
184C4⋊C4—741no—
185C22⋊C4—742no—
186C22⋊C4—742no—
187C22⋊C4—742no—
188C22⋊C4—742no—
189C42—742no—
190C42—742no—
191C23—22no—
192C23—22no—
193C23—41no—
194C23—742no—
195C23—1482no—
196C23—1482no—
197C23—1482no—
198C23C2×D14811yescharacteristic
199C23C2×D14811yescharacteristic
200C23C2×D14811yescharacteristic
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—742no—
211C2×C4—742no—
212C2×C4—742no—
213C2×C4—1482no—
214C2×C4—1482no—
215C2×C4—1482no—
216C2×C4C2×D14811yescharacteristic
217C2×C4C2×D14811yescharacteristic
218C2×C4C2×D14811yescharacteristic
219C2×C4#1059696414yes—
220C2×C4C23×D3711yescharacteristic
221C8—24no—
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#1192452012yes—
235C22#1192456412yes—
236C22C22×D14811yescharacteristic
237C4—21no—
238C4—21no—
239C4—1482no—
240C4—1482no—
241C4—1482no—
242C4#1192452012yes—
243C4C2×#1059696412yes—
244C2—22no—
245C2—22no—
246C2—41no—
247C2—2962no—
248C2C2×#1192452011yescharacteristic
249C2C2×#1192456411yescharacteristic
250C2#1455833311yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#407C2
socleC22×C37C22×D4
prime radicalC2×#11924510C2
hypercenter#407D37
hypocenterC37#3094
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#11924495C2semidirect
3. #14557858C2semidirect
4. #14557852C2semidirect
5. #14557847C2semidirect
6. #14557575C2semidirect
7. #14557539C2semidirect
8. C37×#407C2semidirect
18. #11924495C22semidirect
20. C2×C4⋊Dic37C22semidirect
21. C2×C4⋊Dic37C22semidirect
25. #11924470C22semidirect
26. #11924468C22semidirect
27. #11924458C22semidirect
28. #11924458C22semidirect
31. C22⋊C8×C37C22semidirect
32. C22⋊C8×C37C22semidirect
133. #407D37semidirect
134. C37#3094semidirect
157. C22⋊C8C2×D37semidirect
158. C22⋊C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245102
C2×#119244952
#145578582
#145578522
#145578472
#145575752
#145575392
C37×#4072
#309437