Finite Group Databasebeta

← #18004521

Subgroups — #18004521

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
2C22×C4⋊Dic37C211yesmaximal, characteristic, complemented
3#14557869C212yesmaximal, complemented
4#14557864C212yesmaximal, complemented
5#14557852C212yesmaximal, complemented
6#14557847C212yesmaximal, complemented
7#14557575C212yesmaximal, complemented
8#14557535C212yesmaximal, complemented
9C37×#407C211yesmaximal, characteristic, complemented
10C2×#10596962C2211yescharacteristic
11C23×Dic37—21no—
12#11924519—21no—
13#11924515C2211yescharacteristic
14#11924515C2211yescharacteristic
15#11924510C2211yescharacteristic
16#11924510C2211yescharacteristic
17#11924505—21no—
18C4×C22⋊D37—21no—
19C4×C22⋊D37—21no—
20#11924495C2211yescharacteristic
21C2×C4⋊Dic37—21no—
22C2×C4⋊Dic37—21no—
23C2×C4⋊Dic37—21no—
24C2×C4⋊Dic37C2212yes—
25C2×C4⋊Dic37C2212yes—
26C2×C4⋊Dic37C2212yes—
27#11924470C2214yescomplemented
28#11924468C2214yescomplemented
29#11924461C2214yescomplemented
30#11924458C2214yescomplemented
31C23×C4×C37C2211yescharacteristic
32C2×M16×C37C2212yes—
33C22⋊C8×C37C2212yes—
34C22⋊C8×C37C2212yes—
35C24×C37D411yescharacteristic
36C22×C4×C37—24no—
37C22×C4×C37D411yescharacteristic
38C22×C4×C37D411yescharacteristic
39C22×C4×C37D411yescharacteristic
40C22×C4×C37C2311yescharacteristic
41C22×C4×C37C2311yescharacteristic
42C22×C4×C37C2311yescharacteristic
43C2×C22⋊D37—21no—
44C2×C22⋊D37—21no—
45C2×C22⋊D37—21no—
46C22×Dic37—22no—
47C22×Dic37—22no—
48C22×Dic37—22no—
49C22×Dic37—44no—
50#10596962—24no—
51C2×D148C2311yescharacteristic
52C2×C4×D37—21no—
53C2×Dic74C2311yescharacteristic
54M16×C37—24no—
55C2×C8×C37C2314yes—
56C22⋊Dic37—21no—
57C22⋊Dic37—21no—
58C22⋊Dic37—21no—
59#10596938—21no—
60#10596938—21no—
61C4⋊Dic37—22no—
62C4⋊Dic37—22no—
63C4⋊Dic37—22no—
64C4⋊Dic37C2314yes—
65C4⋊Dic37C2311yescharacteristic
66C4⋊Dic37C2311yescharacteristic
67#10596936—21no—
68#10596936—21no—
69C4×Dic37—21no—
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×C37C2×D411yescharacteristic
83C2×C4×C37C2×D411yescharacteristic
84C2×C4×C37C2×D411yescharacteristic
85C2×C4×C37#4114yes—
86C2×C4×C37C2411yescharacteristic
87C22⋊D37—42no—
88C22⋊D37—42no—
89C22⋊D37—42no—
90C2×Dic37—21no—
91C2×Dic37—21no—
92C2×Dic37—21no—
93C2×Dic37—24no—
94C2×Dic37—44no—
95C2×Dic37—44no—
96C2×Dic37—44no—
97D148—22no—
98C4×D37—42no—
99Dic74—22no—
100C8×C37—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#12312yes—
118C4×C37C2×#4112yes—
119Dic37—41no—
120Dic37—44no—
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⋊C4—371no—
133#484—372no—
134#483—372no—
135#481—372no—
136#480—372no—
137#428—372no—
138#417—372no—
139#407D3711yescharacteristic, complemented
140C37#309211yescharacteristic, complemented, Sylow
141C2×#41—371no—
142C23×C4—741no—
143C23×C4C2×D3711yescharacteristic
144C2×M16C2×D3712yes—
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—372no—
155C2×C4⋊C4—372no—
156C2×C4⋊C4—372no—
157C2×C4⋊C4—741no—
158C2×C4⋊C4—741no—
159C2×C4⋊C4—741no—
160#107—374no—
161#106—374no—
162#103—374no—
163#102—374no—
164C22⋊C8C2×D3712yes—
165C22⋊C8C2×D3712yes—
166C24D14811yescharacteristic
167#41—744no—
168C2×Q8—371no—
169C2×D4—371no—
170C2×D4—741no—
171C2×D4—741no—
172C2×D4—741no—
173C22×C4—24no—
174C22×C4—742no—
175C22×C4—742no—
176C22×C4—742no—
177C22×C4—741no—
178C22×C4—1484no—
179C22×C4D14811yescharacteristic
180C22×C4D14811yescharacteristic
181C22×C4D14811yescharacteristic
182C22×C4C22×D3711yescharacteristic
183C22×C4C22×D3711yescharacteristic
184C22×C4C22×D3711yescharacteristic
185M16—24no—
186C2×C8C22×D3714yes—
187C4⋊C4—374no—
188C4⋊C4—371no—
189C4⋊C4—371no—
190C4⋊C4—741no—
191C4⋊C4—741no—
192C4⋊C4—742no—
193C4⋊C4—742no—
194C4⋊C4—742no—
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×D14811yescharacteristic
206C23C2×D14811yescharacteristic
207C23C2×D14811yescharacteristic
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—741no—
219C2×C4—741no—
220C2×C4—741no—
221C2×C4—744no—
222C2×C4—1484no—
223C2×C4—1484no—
224C2×C4—1484no—
225C2×C4—1482no—
226C2×C4C2×D14811yescharacteristic
227C2×C4C2×D14811yescharacteristic
228C2×C4C2×D14811yescharacteristic
229C2×C4#1059696414yes—
230C2×C4C23×D3711yescharacteristic
231C8—24no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—1481no—
240C22—1481no—
241C22—1481no—
242C22#1192452012yes—
243C22#1192456412yes—
244C22#1192456912yes—
245C22C22×D14811yescharacteristic
246C4—21no—
247C4—21no—
248C4—1481no—
249C4—1484no—
250C4—1481no—
251C4—1481no—
252C4#1192452012yes—
253C4C2×#1059696412yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—2961no—
258C2C2×#1192452011yescharacteristic
259C2C2×#1192456411yescharacteristic
260C2C2×#1192456911yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#407C2
socleC22×C37C22×D4
prime radical#14558044C2
hypercenter#407D37
hypocenterC37#3092
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. C22×C4⋊Dic37C2semidirect
3. #14557869C2semidirect
4. #14557864C2semidirect
5. #14557852C2semidirect
6. #14557847C2semidirect
7. #14557575C2semidirect
8. #14557535C2semidirect
9. C37×#407C2semidirect
27. #11924470C22semidirect
28. #11924468C22semidirect
29. #11924461C22semidirect
30. #11924458C22semidirect
139. #407D37semidirect
140. C37#3092semidirect

Maximal subgroups

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

subgroupindex
#145580442
C22×C4⋊Dic372
#145578692
#145578642
#145578522
#145578472
#145575752
#145575352
C37×#4072
#309237