Finite Group Databasebeta

← #18004512

Subgroups — #18004512

Order 4736.

420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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#14558046C211yesmaximal, characteristic
2C2×#11924494C211yesmaximal, characteristic, complemented
3#14557873C212yesmaximal, complemented
4#14557861C211yesmaximal, characteristic, complemented
5#14557860C212yesmaximal, complemented
6#14557851C211yesmaximal, characteristic, complemented
7#14557847C211yesmaximal, characteristic, complemented
8#14557570C212yesmaximal, complemented
9#14557528C212yesmaximal, complemented
10C22⋊C8×D37C211yesmaximal, characteristic, complemented
11C37×#484C211yesmaximal, characteristic, complemented
12C2×#10596966C2211yescharacteristic
13C22×C4×D37C2211yescharacteristic
14C2×C8×D37C2212yes—
15#11924521—21no—
16#11924512C2211yescharacteristic
17#11924511C2211yescharacteristic
18#11924510C2211yescharacteristic
19#11924506—21no—
20#11924498—21no—
21#11924496—21no—
22#11924494—21no—
23#11924494—21no—
24#11924494C2212yes—
25#11924494C2212yes—
26#11924494C2211yescharacteristic
27C2×C4⋊Dic37C2211yescharacteristic
28C2×#10596938—21no—
29C2×C4×Dic37—21no—
30#11924470C2212yescomplemented
31#11924467C2212yescomplemented
32#11924467C2212yescomplemented
33#11924460C2212yescomplemented
34#11924458C2212yescomplemented
35#11924456C2212yescomplemented
36C22⋊#64436C2211yescharacteristic
37#11924448C2212yes—
38C22⋊Q8×C37C2211yescharacteristic
39C2×C4⋊C4×C37C2211yescharacteristic
40#107×C37C2212yescomplemented
41#103×C37C2212yescomplemented
42C22⋊C8×C37C2211yescharacteristic
43C23×D37D411yescharacteristic
44C2×Q8×C37C2311yescharacteristic
45C22×C4×C37—21no—
46C22×C4×C37C2311yescharacteristic
47C2×C22⋊D37—21no—
48C22×Dic37—21no—
49C22×Dic37D411yescharacteristic
50#10596966—24no—
51C2×D148—21no—
52C2×D148—21no—
53C2×D148C2311yescharacteristic
54C2×C4×D37—24no—
55C2×C4×D37—21no—
56C2×C4×D37D411yescharacteristic
57C2×C4×D37D411yescharacteristic
58C2×C4×D37C2311yescharacteristic
59C2×C4×D37C2311yescharacteristic
60C2×C8×C37C2312yes—
61C4⋊C4×C37—21no—
62C4⋊C4×C37—21no—
63C4⋊C4×C37C2312yes—
64C4⋊C4×C37C2311yescharacteristic
65C22⋊C4×C37—21no—
66#10596938—22no—
67#10596938—22no—
68#10596938—21no—
69#10596938—21no—
70#10596938—21no—
71#10596938—21no—
72C4⋊Dic37—21no—
73C4⋊Dic37C2312yes—
74C4⋊Dic37C2311yescharacteristic
75#10596936—21no—
76C4×Dic37—22no—
77C4×Dic37—22no—
78C4×Dic37—21no—
79C2×#64436C2312yes—
80C8×D37—24no—
81C23×C37C2×D411yescharacteristic
82C22×D37—22no—
83C22×D37—22no—
84C22×D37—21no—
85C22×D37—41no—
86C22×D37C2×D411yescharacteristic
87C22×D37C2×D411yescharacteristic
88Q8×C37—22no—
89C2×C4×C37—22no—
90C2×C4×C37—22no—
91C2×C4×C37—21no—
92C2×C4×C37—21no—
93C2×C4×C37—42no—
94C2×C4×C37C2×D411yescharacteristic
95C2×C4×C37C2411yescharacteristic
96C22⋊D37—42no—
97C2×Dic37—22no—
98C2×Dic37—22no—
99C2×Dic37—21no—
100C2×Dic37—42no—
101C2×Dic37C2×D411yescharacteristic
102C2×Dic37C2×D411yescharacteristic
103D148—22no—
104D148—42no—
105D148—42no—
106C4×D37—22no—
107C4×D37—22no—
108C4×D37—22no—
109C4×D37—42no—
110C4×D37#4114yes—
111C8×C37—22no—
112#64436—22no—
113C22×C37—21no—
114C22×C37—21no—
115C22×C37#13512yes—
116C22×C37C22×D411yescharacteristic
117C2×D37—21no—
118C2×D37—21no—
119C2×D37—21no—
120C2×D37—21no—
121C2×D37—21no—
122C2×D37—44no—
123C2×D37—41no—
124C2×D37—41no—
125C2×D37—41no—
126C2×D37#12312yes—
127C4×C37—21no—
128C4×C37—41no—
129C4×C37—41no—
130C4×C37—42no—
131C4×C37C2×#4112yes—
132Dic37—21no—
133Dic37—42no—
134Dic37—41no—
135Dic37#12312yes—
136#3091—371nomaximal, Sylow
137C2×C37—22no—
138C2×C37C2×#12311yescharacteristic
139C2×C37C2×#13511yescharacteristic
140C2×C37#57511yescharacteristic
141D37—22no—
142D37—41no—
143D37—81no—
144#525—371no—
145C2×#117—371no—
146#485—372no—
147#484D3711yescharacteristic, complemented
148#483—371no—
149#482—372no—
150#481—371no—
151#480—371no—
152#427—372no—
153#416—372no—
154C2×C22⋊C8—371no—
155C37#309111yescharacteristic, complemented, Sylow
156C2×#41—371no—
157C23×C4—371no—
158C22×C8—372no—
159#123—741no—
160C22⋊Q8—371no—
161C22⋊Q8C2×D3711yescharacteristic
162#121—371no—
163#121—371no—
164#120—741no—
165C4×D4—741no—
166C4×D4—741no—
167#117—372no—
168#117—372no—
169#117—371no—
170#117—741no—
171#117—741no—
172C2×C4⋊C4—371no—
173C2×C4⋊C4C2×D3711yescharacteristic
174C2×C22⋊C4—741no—
175C2×C42—741no—
176#107—372no—
177#107C2×D3712yescomplemented
178#106—372no—
179#106—372no—
180#103—372no—
181#103C2×D3712yescomplemented
182#102—372no—
183#102—372no—
184C22⋊C8—371no—
185C22⋊C8—372no—
186C22⋊C8C2×D3711yescharacteristic
187C24—371no—
188#41—744no—
189C2×Q8C22×D3711yescharacteristic
190C2×D4—371no—
191C2×D4—741no—
192C2×D4—741no—
193C2×D4—741no—
194C22×C4—21no—
195C22×C4—371no—
196C22×C4—371no—
197C22×C4—371no—
198C22×C4—371no—
199C22×C4—371no—
200C22×C4—744no—
201C22×C4—741no—
202C22×C4—741no—
203C22×C4C22×D3711yescharacteristic
204C2×C8—372no—
205C2×C8—744no—
206C2×C8C22×D3712yes—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—372no—
210C4⋊C4—371no—
211C4⋊C4—741no—
212C4⋊C4—741no—
213C4⋊C4C22×D3712yes—
214C4⋊C4C22×D3711yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—741no—
217C22⋊C4—742no—
218C22⋊C4—742no—
219C22⋊C4—741no—
220C22⋊C4—741no—
221C22⋊C4—741no—
222C42—742no—
223C42—742no—
224C42—741no—
225C23—371no—
226C23—371no—
227C23—742no—
228C23—742no—
229C23—741no—
230C23—1481no—
231C23D4×D3711yescharacteristic
232Q8—22no—
233D4—742no—
234D4—1482no—
235D4—1482no—
236D4—1482no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—371no—
243C2×C4—374no—
244C2×C4—371no—
245C2×C4—742no—
246C2×C4—742no—
247C2×C4—742no—
248C2×C4—742no—
249C2×C4—742no—
250C2×C4—741no—
251C2×C4—1482no—
252C2×C4—1482no—
253C2×C4D4×D3711yescharacteristic
254C2×C4C23×D3711yescharacteristic
255C8—22no—
256C8—742no—
257C22—21no—
258C22—21no—
259C22—372no—
260C22—741no—
261C22—741no—
262C22—741no—
263C22—741no—
264C22—741no—
265C22—1484no—
266C22—1481no—
267C22—1481no—
268C22—1481no—
269C22#1192455912yes—
270C22C2×D4×D3711yescharacteristic
271C4—21no—
272C4—41no—
273C4—42no—
274C4—41no—
275C4—372no—
276C4—741no—
277C4—1482no—
278C4—1481no—
279C4#41×D3712yes—
280C2—22no—
281C2—2961no—
282C2—742no—
283C2—1481no—
284C2#123×D3711yescharacteristic
285C2C2×#1192455911yescharacteristic
286C2#1455832911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#484C2
socleC22×C37C22×D4
prime radical#14558046C2
hypercenter#484D37
hypocenterC37#3091
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C2×#11924494C2semidirect
3. #14557873C2semidirect
4. #14557861C2semidirect
5. #14557860C2semidirect
6. #14557851C2semidirect
7. #14557847C2semidirect
8. #14557570C2semidirect
9. #14557528C2semidirect
10. C22⋊C8×D37C2semidirect
11. C37×#484C2semidirect
30. #11924470C22semidirect
31. #11924467C22semidirect
32. #11924467C22semidirect
33. #11924460C22semidirect
34. #11924458C22semidirect
35. #11924456C22semidirect
40. #107×C37C22semidirect
41. #103×C37C22semidirect
147. #484D37semidirect
155. C37#3091semidirect
177. #107C2×D37semidirect
181. #103C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580462
C2×#119244942
#145578732
#145578612
#145578602
#145578512
#145578472
#145575702
#145575282
C22⋊C8×D372
C37×#4842
#309137