Finite Group Databasebeta

← #18003987

Subgroups — #18003987

Order 4736.

766 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 145 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#14558369C211yesmaximal, characteristic, complemented
2#14558044C212yesmaximal, complemented
3#14557722C214yesmaximal, complemented
4#14557719C214yesmaximal, complemented
5#14557507C211yesmaximal, characteristic, complemented
6#14557506C212yesmaximal, complemented
7C37×#525C211yesmaximal, characteristic, complemented
8#11924584—21no—
9#11924583—22no—
10#11924582—22no—
11#11924581—21no—
12#11924581C2214yes—
13C2×#10596962—22no—
14C2×#10596962C2212yes—
15#41×D37—24no—
16#11924519C2214yescomplemented
17#11924515—22no—
18#11924510—22no—
19#11924505C2214yescomplemented
20C4×C22⋊D37—24no—
21#11924495C2212yescomplemented
22#11924451C2214yescomplemented
23#11924450C2218yescomplemented
24C2×#41×C37C2211yescharacteristic
25C23×C4×C37C2211yescharacteristic, complemented
26#123×C37C2212yescomplemented
27C22⋊Q8×C37—21no—
28#121×C37—21no—
29#120×C37C2212yescomplemented
30C4×D4×C37—22no—
31#117×C37C2211yescharacteristic, complemented
32C24×C37C2311yescharacteristic
33#41×C37—22no—
34#41×C37—22no—
35C2×Q8×C37D411yescharacteristic, complemented
36C2×D4×C37—22no—
37C2×D4×C37D411yescharacteristic, complemented
38C2×D4×C37C2312yes—
39C22×C4×C37—22no—
40C22×C4×C37—22no—
41C22×C4×C37—21no—
42C22×C4×C37—21no—
43C22×C4×C37D412yescomplemented
44C22×C4×C37C2311yescharacteristic
45C22×C4×C37C2311yescharacteristic
46C2×C22⋊D37—24no—
47C2×C22⋊D37—24no—
48C2×C22⋊D37C2314yes—
49#10596966—24no—
50Q8×D37—24no—
51#10596964—24no—
52#10596964—28no—
53D4×D37—24no—
54D4×D37—28no—
55#10596962—24no—
56#10596962—24no—
57#10596962—22no—
58#10596962—22no—
59#10596962—24no—
60#10596962—22no—
61#10596962—22no—
62C2×D148—22no—
63C2×D148D412yescomplemented
64C2×C4×D37—24no—
65C2×C4×D37D414yescomplemented
66C2×Dic74—22no—
67C2×Dic74D412yescomplemented
68C4⋊C4×C37—21no—
69C4⋊C4×C37—22no—
70C22⋊C4×C37—22no—
71C22⋊C4×C37—22no—
72C22⋊C4×C37C2312yes—
73C42×C37—21no—
74C22⋊Dic37—24no—
75C22⋊Dic37C2314yes—
76#10596938—24no—
77C4⋊Dic37—22no—
78#10596936—24no—
79C4×Dic37—22no—
80C23×C37—22no—
81C23×C37—21no—
82C23×C37—42no—
83C23×C37C2×D412yes—
84C23×C37C2411yescharacteristic
85C22×D37—24no—
86C22×D37C2×D414yes—
87Q8×C37—22no—
88D4×C37—24no—
89D4×C37—22no—
90D4×C37—44no—
91C2×C4×C37—22no—
92C2×C4×C37—22no—
93C2×C4×C37—22no—
94C2×C4×C37—22no—
95C2×C4×C37—21no—
96C2×C4×C37—41no—
97C2×C4×C37—42no—
98C2×C4×C37—41no—
99C2×C4×C37C2×D412yes—
100C2×C4×C37C2×D412yes—
101C2×C4×C37C2×D412yes—
102C2×C4×C37C2×D411yescharacteristic
103C2×C4×C37C2×D411yescharacteristic
104C22⋊D37—28no—
105C22⋊D37—24no—
106C22⋊D37—24no—
107C22⋊D37—48no—
108C2×Dic37—24no—
109C2×Dic37—24no—
110C2×Dic37C2×D414yes—
111D148—24no—
112D148—22no—
113D148—22no—
114C4×D37—28no—
115C4×D37—24no—
116C4×D37—24no—
117Dic74—24no—
118Dic74—22no—
119Dic74—22no—
120C22×C37—24no—
121C22×C37—22no—
122C22×C37—22no—
123C22×C37—41no—
124C22×C37—42no—
125C22×C37—42no—
126C22×C37—41no—
127C22×C37—41no—
128C22×C37C22×D412yes—
129C22×C37C22×D411yescharacteristic
130C2×D37—24no—
131C2×D37—44no—
132C2×D37—84no—
133C4×C37—22no—
134C4×C37—42no—
135C4×C37—41no—
136C4×C37#12011yescharacteristic
137C4×C37#12012yes—
138C4×C37#12011yescharacteristic
139Dic37—24no—
140Dic37—44no—
141#3025—371nomaximal, Sylow
142C2×C37—22no—
143C2×C37—21no—
144C2×C37—42no—
145C2×C37—42no—
146C2×C37C2×#12011yescharacteristic
147D37—44no—
148#585—371no—
149#525—372no—
150#525D3711yescharacteristic, complemented
151#458—374no—
152B(4,𝔽2)—374no—
153#410—371no—
154#410—372no—
155C37#302511yescharacteristic, complemented, Sylow
1562−1+4—742no—
1572−1+4—741no—
158H(5,𝔽2)—374no—
159H(5,𝔽2)—742no—
160H(5,𝔽2)—741no—
161C2×#41—372no—
162C2×#41—744no—
163C2×#41—742no—
164C2×#41C2×D3711yescharacteristic
165C23×C4C2×D3711yescharacteristic, complemented
166#123—374no—
167#123C2×D3712yescomplemented
168C22⋊Q8—21no—
169C22⋊Q8—742no—
170#121—21no—
171#121—742no—
172#120—374no—
173#120C2×D3712yescomplemented
174C4×D4—22no—
175C4×D4—744no—
176#117—372no—
177#117C2×D3711yescharacteristic, complemented
178#99—374no—
179#99—378no—
180C24C22×D3711yescharacteristic
181#41—22no—
182#41—22no—
183#41—744no—
184#41—744no—
185#41—748no—
186#41—744no—
187#41—744no—
188#41—742no—
189#41—742no—
190#41—742no—
191#41—742no—
192#41—744no—
193C2×Q8—372no—
194C2×Q8—742no—
195C2×Q8—744no—
196C2×Q8C22⋊D3711yescharacteristic, complemented
197C2×D4—22no—
198C2×D4—374no—
199C2×D4—372no—
200C2×D4—742no—
201C2×D4—748no—
202C2×D4—744no—
203C2×D4—744no—
204C2×D4—744no—
205C2×D4C22⋊D3711yescharacteristic, complemented
206C2×D4C22×D3712yes—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—374no—
212C22×C4—744no—
213C22×C4C22⋊D3712yescomplemented
214C22×C4C22×D3711yescharacteristic
215C22×C4C22×D3711yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—22no—
218C4⋊C4—744no—
219C4⋊C4—742no—
220C22⋊C4—22no—
221C22⋊C4—22no—
222C22⋊C4—374no—
223C22⋊C4—744no—
224C22⋊C4—744no—
225C22⋊C4C22×D3712yes—
226C42—21no—
227C42—742no—
228C23—22no—
229C23—21no—
230C23—42no—
231C23—374no—
232C23—744no—
233C23C2×C22⋊D3712yes—
234C23C23×D3711yescharacteristic
235Q8—22no—
236Q8—744no—
237Q8—742no—
238Q8—742no—
239D4—24no—
240D4—22no—
241D4—44no—
242D4—744no—
243D4—748no—
244D4—744no—
245D4—744no—
246D4—742no—
247D4—742no—
248D4—1488no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—374no—
258C2×C4—748no—
259C2×C4—744no—
260C2×C4—744no—
261C2×C4—744no—
262C2×C4—744no—
263C2×C4D4×D3712yes—
264C2×C4D4×D3712yes—
265C2×C4C2×C22⋊D3712yes—
266C2×C4C2×C22⋊D3711yescharacteristic
267C2×C4C2×C22⋊D3711yescharacteristic
268C22—22no—
269C22—24no—
270C22—22no—
271C22—41no—
272C22—42no—
273C22—41no—
274C22—42no—
275C22—41no—
276C22—2964no—
277C22—744no—
278C22—1484no—
279C22C2×D4×D3712yes—
280C22C22×C22⋊D3711yescharacteristic
281C4—22no—
282C4—42no—
283C4—41no—
284C4—744no—
285C4—1484no—
286C4#1192450411yescharacteristic
287C4#1192450412yes—
288C4#1192450411yescharacteristic
289C2—21no—
290C2—22no—
291C2—42no—
292C2—42no—
293C2—1484no—
294C2C2×#1192450411yescharacteristic
subgroupG/H
centerC4#11924504
commutator, cosocleC23×C37C24
FrattiniC23C23×D37
FittingC37×#525C2
socleC2×C37C2×#120
hypercenter#525D37
hypocenterC37#3025
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #14558369C2semidirect
2. #14558044C2semidirect
3. #14557722C2semidirect
4. #14557719C2semidirect
5. #14557507C2semidirect
6. #14557506C2semidirect
7. C37×#525C2semidirect
16. #11924519C22semidirect
19. #11924505C22semidirect
21. #11924495C22semidirect
22. #11924451C22semidirect
23. #11924450C22semidirect
25. C23×C4×C37C22semidirect
26. #123×C37C22semidirect
29. #120×C37C22semidirect
31. #117×C37C22semidirect
35. C2×Q8×C37D4semidirect
37. C2×D4×C37D4semidirect
43. C22×C4×C37D4semidirect
63. C2×D148D4semidirect
65. C2×C4×D37D4semidirect
67. C2×Dic74D4semidirect
150. #525D37semidirect
155. C37#3025semidirect
165. C23×C4C2×D37semidirect
167. #123C2×D37semidirect
173. #120C2×D37semidirect
177. #117C2×D37semidirect
196. C2×Q8C22⋊D37semidirect
205. C2×D4C22⋊D37semidirect
213. C22×C4C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145583692
#145580442
#145577222
#145577192
#145575072
#145575062
C37×#5252
#302537