Finite Group Databasebeta

← #18004519

Subgroups — #18004519

Order 4736.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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#14558044C211yesmaximal, characteristic
2#14557868C212yesmaximal, complemented
3#14557863C212yesmaximal, complemented
4#14557851C212yesmaximal, complemented
5#14557846C212yesmaximal, complemented
6#14557573C212yesmaximal, complemented
7#14557532C212yesmaximal, complemented
8#14557497C211yesmaximal, characteristic, complemented
9C22×C4⋊C4×C37C211yesmaximal, characteristic, complemented
10C2×#10596962C2211yescharacteristic
11C2×#10596934C2212yes—
12#11924519—21no—
13#11924515C2211yescharacteristic
14#11924515C2211yescharacteristic
15#11924510C2211yescharacteristic
16#11924510C2211yescharacteristic
17#11924505—21no—
18C4×C22⋊D37—21no—
19C4×C22⋊D37—21no—
20#11924495C2211yescharacteristic
21#11924469C2214yescomplemented
22#11924467C2214yescomplemented
23#11924459C2214yescomplemented
24#11924456C2214yescomplemented
25C22⋊#64436C2212yes—
26C22⋊#64436C2212yes—
27C23×C4×C37—21no—
28C23×C4×C37C2211yescharacteristic
29C2×C4⋊C4×C37—21no—
30C2×C4⋊C4×C37—21no—
31C2×C4⋊C4×C37—21no—
32C2×C4⋊C4×C37C2212yes—
33C2×C4⋊C4×C37C2212yes—
34C2×C4⋊C4×C37C2212yes—
35C24×C37D411yescharacteristic
36C22×C4×C37—24no—
37C22×C4×C37—22no—
38C22×C4×C37—22no—
39C22×C4×C37—22no—
40C22×C4×C37—44no—
41C22×C4×C37D411yescharacteristic
42C22×C4×C37D411yescharacteristic
43C22×C4×C37D411yescharacteristic
44C22×C4×C37C2311yescharacteristic
45C22×C4×C37C2311yescharacteristic
46C22×C4×C37C2311yescharacteristic
47C2×C22⋊D37—21no—
48C2×C22⋊D37—21no—
49C2×C22⋊D37—21no—
50#10596962—24no—
51C2×D148C2311yescharacteristic
52C2×C4×D37—21no—
53C2×Dic74C2311yescharacteristic
54C4⋊C4×C37—22no—
55C4⋊C4×C37—22no—
56C4⋊C4×C37—22no—
57C4⋊C4×C37C2314yes—
58C22⋊Dic37—21no—
59C22⋊Dic37—21no—
60C22⋊Dic37—21no—
61#10596938—21no—
62#10596938—21no—
63C4⋊Dic37C2311yescharacteristic
64C4⋊Dic37C2311yescharacteristic
65#10596936—21no—
66#10596936—21no—
67C4×Dic37—21no—
68#10596934—24no—
69C2×#64436C2314yes—
70C23×C37—22no—
71C23×C37—22no—
72C23×C37—22no—
73C23×C37C2×D411yescharacteristic
74C23×C37C2×D411yescharacteristic
75C23×C37C2×D411yescharacteristic
76C22×D37—21no—
77C2×C4×C37—22no—
78C2×C4×C37—22no—
79C2×C4×C37—22no—
80C2×C4×C37—22no—
81C2×C4×C37—22no—
82C2×C4×C37—24no—
83C2×C4×C37—44no—
84C2×C4×C37—44no—
85C2×C4×C37—44no—
86C2×C4×C37C2×D411yescharacteristic
87C2×C4×C37C2×D411yescharacteristic
88C2×C4×C37C2×D411yescharacteristic
89C2×C4×C37#4114yes—
90C2×C4×C37C2411yescharacteristic
91C22⋊D37—42no—
92C22⋊D37—42no—
93C22⋊D37—42no—
94C2×Dic37—21no—
95C2×Dic37—21no—
96C2×Dic37—21no—
97D148—22no—
98C4×D37—42no—
99Dic74—22no—
100#64436—24no—
101C22×C37—28no—
102C22×C37—21no—
103C22×C37—21no—
104C22×C37—21no—
105C22×C37—21no—
106C22×C37—21no—
107C22×C37—21no—
108C22×C37#12312yes—
109C22×C37AGL(1,ℤ/8)12yes—
110C22×C37#13712yes—
111C22×C37C22×D411yescharacteristic
112C2×D37—41no—
113C2×D37—41no—
114C2×D37—41no—
115C4×C37—21no—
116C4×C37—21no—
117C4×C37—44no—
118C4×C37#12312yes—
119C4×C37C2×#4112yes—
120Dic37—41no—
121Dic37—41no—
122Dic37—41no—
123#3092—371nomaximal, Sylow
124C2×C37—22no—
125C2×C37—22no—
126C2×C37—22no—
127C2×C37C2×#12311yescharacteristic
128C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
129C2×C37C2×#13711yescharacteristic
130D37—81no—
131#525—371no—
132C22×C4⋊C4D3711yescharacteristic, complemented
133#484—372no—
134#483—372no—
135#481—372no—
136#480—372no—
137#428—372no—
138#417—372no—
139#407—371no—
140C37#309211yescharacteristic, complemented, Sylow
141C2×#41—371no—
142C23×C4—21no—
143C23×C4C2×D3711yescharacteristic
144C2×M16—372no—
145#123—741no—
146C22⋊Q8—371no—
147C22⋊Q8—371no—
148#121—371no—
149#121—371no—
150#120—741no—
151C4×D4—741no—
152C4×D4—741no—
153#117—371no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4C2×D3712yes—
158C2×C4⋊C4C2×D3712yes—
159C2×C4⋊C4C2×D3712yes—
160#107—374no—
161#106—374no—
162#103—374no—
163#102—374no—
164C22⋊C8—372no—
165C22⋊C8—372no—
166C24C22⋊D3711yescharacteristic
167#41—744no—
168C2×Q8—371no—
169C2×D4—371no—
170C2×D4—741no—
171C2×D4—741no—
172C2×D4—741no—
173C22×C4—24no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—44no—
178C22×C4—741no—
179C22×C4C22⋊D3711yescharacteristic
180C22×C4C22⋊D3711yescharacteristic
181C22×C4C22⋊D3711yescharacteristic
182C22×C4C22×D3711yescharacteristic
183C22×C4C22×D3711yescharacteristic
184C22×C4C22×D3711yescharacteristic
185M16—744no—
186C2×C8—374no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—371no—
191C4⋊C4—371no—
192C4⋊C4—741no—
193C4⋊C4—741no—
194C4⋊C4C22×D3714yes—
195C22⋊C4—741no—
196C22⋊C4—741no—
197C22⋊C4—741no—
198C22⋊C4—741no—
199C22⋊C4—741no—
200C42—741no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—741no—
205C23C2×C22⋊D3711yescharacteristic
206C23C2×C22⋊D3711yescharacteristic
207C23C2×C22⋊D3711yescharacteristic
208Q8—742no—
209D4—742no—
210D4—1482no—
211D4—1482no—
212D4—1482no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—24no—
219C2×C4—44no—
220C2×C4—44no—
221C2×C4—44no—
222C2×C4—741no—
223C2×C4—741no—
224C2×C4—741no—
225C2×C4—1482no—
226C2×C4#1059696214yes—
227C2×C4C2×C22⋊D3711yescharacteristic
228C2×C4C2×C22⋊D3711yescharacteristic
229C2×C4C2×C22⋊D3711yescharacteristic
230C2×C4C23×D3711yescharacteristic
231C8—744no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—1481no—
240C22—1481no—
241C22—1481no—
242C22#1192451912yes—
243C22#1192456212yes—
244C22#1192456712yes—
245C22C22×C22⋊D3711yescharacteristic
246C4—21no—
247C4—21no—
248C4—44no—
249C4—1481no—
250C4—1481no—
251C4—1481no—
252C4#1192451912yes—
253C4C2×#1059696212yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—2961no—
258C2C2×#1192451911yescharacteristic
259C2C2×#1192456211yescharacteristic
260C2C2×#1192456711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC22×C4⋊C4×C37C2
socleC22×C37C22×D4
prime radical#14558044C2
hypercenterC22×C4⋊C4D37
hypocenterC37#3092
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #14557868C2semidirect
3. #14557863C2semidirect
4. #14557851C2semidirect
5. #14557846C2semidirect
6. #14557573C2semidirect
7. #14557532C2semidirect
8. #14557497C2semidirect
9. C22×C4⋊C4×C37C2semidirect
21. #11924469C22semidirect
22. #11924467C22semidirect
23. #11924459C22semidirect
24. #11924456C22semidirect
132. C22×C4⋊C4D37semidirect
140. C37#3092semidirect

Maximal subgroups

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

subgroupindex
#145580442
#145578682
#145578632
#145578512
#145578462
#145575732
#145575322
#145574972
C22×C4⋊C4×C372
#309237