Finite Group Databasebeta

← #18005072

Subgroups — #18005072

Order 4736.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#11924569C211yesmaximal, characteristic, complemented
2C2×#11924564C211yesmaximal, characteristic, complemented
3C2×#11924558C211yesmaximal, characteristic, complemented
4C22×#10596930C211yesmaximal, characteristic, complemented
5#14558109C211yesmaximal, characteristic, complemented
6#14558102C211yesmaximal, characteristic, complemented
7#14557927C212yesmaximal, complemented
8#14557922C212yesmaximal, complemented
9#14557917C212yesmaximal, complemented
10#14557906C212yesmaximal, complemented
11C37×#405C211yesmaximal, characteristic, complemented
12C2×#10596962C2211yescharacteristic
13C2×#10596962C2211yescharacteristic
14C22×Dic74C2211yescharacteristic
15C22×D148C2211yescharacteristic
16#11924569—24no—
17#11924564—24no—
18#11924558—24no—
19C2×Dic148C2211yescharacteristic, complemented
20C2×Dic148C2212yescomplemented
21C2×#10596930—24no—
22C2×#10596930C2212yes—
23C2×#10596930C2212yes—
24C2×#10596930C2212yes—
25C2×#10596930C2211yescharacteristic, complemented
26C2×#10596930C2211yescharacteristic, complemented
27C2×#10596930C2212yescomplemented
28C2×D296C2212yes—
29C2×D296C2211yescharacteristic, complemented
30#11924536C2212yescomplemented
31#11924533C2212yes—
32#11924524C2212yes—
33#11924524C2212yescomplemented
34#11924520—22no—
35#11924516—22no—
36#11924511—22no—
37#11924506—22no—
38C2×M16×C37C2211yescharacteristic
39C22×C8×C37C2211yescharacteristic
40#117×C37C2211yescharacteristic
41#97×C37C2212yescomplemented
42C4×C8×C37C2212yescomplemented
43C23×D37—21no—
44C22×C4×C37C2311yescharacteristic
45C2×C22⋊D37—21no—
46C2×C22⋊D37—21no—
47C22×Dic37—21no—
48#10596962—22no—
49#10596962—22no—
50#10596962—22no—
51#10596962—22no—
52C2×D148—22no—
53C2×D148—22no—
54C2×D148—21no—
55C2×D148—24no—
56C2×D148C2312yes—
57C2×D148C2311yescharacteristic
58C2×D148C2311yescharacteristic
59C2×C4×D37—21no—
60C2×C4×D37—21no—
61C2×Dic74—22no—
62C2×Dic74—22no—
63C2×Dic74—21no—
64C2×Dic74C2311yescharacteristic
65C2×Dic74C2312yes—
66C2×Dic74C2311yescharacteristic
67M16×C37D414yescomplemented
68C2×C8×C37D414yescomplemented
69C2×C8×C37C2312yes—
70C2×C8×C37C2311yescharacteristic
71C2×C8×C37C2311yescharacteristic
72C4⋊C4×C37D412yes—
73C22⋊C4×C37D412yes—
74C42×C37C2312yes—
75#10596938—24no—
76#10596938—24no—
77C4⋊Dic37—24no—
78Dic148—22no—
79Dic148—24no—
80D296—24no—
81D296—22no—
82#10596930—24no—
83#10596930—24no—
84#10596930—24no—
85#10596930—22no—
86#10596930—22no—
87#10596930—24no—
88C23×C37C2×D411yescharacteristic
89C22×D37—21no—
90C22×D37—22no—
91C22×D37—21no—
92C22×D37—42no—
93C22×D37—82no—
94C2×C4×C37C2×D414yes—
95C2×C4×C37C2×D411yescharacteristic
96C2×C4×C37C2×D412yes—
97C2×C4×C37C2×D412yes—
98C2×C4×C37C2411yescharacteristic
99C22⋊D37—42no—
100C22⋊D37—42no—
101C2×Dic37—21no—
102C2×Dic37—22no—
103C2×Dic37—21no—
104C2×Dic37—42no—
105D148—22no—
106D148—21no—
107D148—22no—
108D148—21no—
109D148—21no—
110D148—21no—
111D148—42no—
112D148—84no—
113C4×D37—42no—
114C4×D37—42no—
115Dic74—22no—
116Dic74—21no—
117Dic74—22no—
118Dic74—21no—
119Dic74—21no—
120Dic74—21no—
121Dic74—42no—
122C8×C37C2×D412yes—
123C8×C37C2×D412yes—
124C8×C37C2×D414yes—
125C22×C37—22no—
126C22×C37#12712yes—
127C22×C37C22×D411yescharacteristic
128C2×D37—41no—
129C2×D37—41no—
130C2×D37—42no—
131C2×D37—42no—
132C2×D37—44no—
133C2×D37—42no—
134C2×D37—84no—
135C4×C37—24no—
136C4×C37#12712yes—
137C4×C37C22×D411yescharacteristic
138C4×C37C22×D411yescharacteristic
139Dic37—42no—
140Dic37—41no—
141Dic37—41no—
142#3154—371nomaximal, Sylow
143C2×C37—22no—
144C2×C37C2×#12711yescharacteristic
145C2×C37#57712yes—
146D37—81no—
147D37—81no—
148D37—82no—
149C2×#137—371no—
150C2×AGL(1,ℤ/8)—371no—
151C2×#135—371no—
152C22×SD16—371no—
153#536—371no—
154#535—371no—
155#497—372no—
156#496—372no—
157#495—372no—
158#492—372no—
159#405D3711yescharacteristic, complemented
160C37#315411yescharacteristic, complemented, Sylow
161C2×#41—371no—
162C2×#41—371no—
163C22×Q8—371no—
164C22×D4—371no—
165#137—744no—
166AGL(1,ℤ/8)—744no—
167#135—744no—
168C2×Q16—371no—
169C2×Q16—372no—
170C2×SD16—372no—
171C2×SD16—372no—
172C2×SD16—371no—
173C2×SD16—371no—
174C2×SD16—372no—
175C2×SD16—372no—
176C2×SD16—744no—
177C2×D8—371no—
178C2×D8—372no—
179C2×M16C2×D3711yescharacteristic
180C22×C8C2×D3711yescharacteristic
181C4⋊Q8—372no—
182#127—372no—
183#124—372no—
184#124—372no—
185#123—742no—
186C22⋊Q8—742no—
187#121—742no—
188#120—742no—
189#117C2×D3711yescharacteristic
190#97C2×D3712yescomplemented
191C4×C8C2×D3712yescomplemented
192C24—741no—
193#41—742no—
194#41—742no—
195#41—742no—
196#41—742no—
197C2×Q8—371no—
198C2×Q8—372no—
199C2×Q8—371no—
200C2×Q8—741no—
201C2×Q8—742no—
202C2×Q8—742no—
203C2×D4—371no—
204C2×D4—372no—
205C2×D4—371no—
206C2×D4—741no—
207C2×D4—741no—
208C2×D4—744no—
209C2×D4—742no—
210C2×D4—742no—
211C2×D4—741no—
212C22×C4—741no—
213C22×C4—741no—
214C22×C4—741no—
215C22×C4C22×D3711yescharacteristic
216Q16—742no—
217Q16—744no—
218SD16—744no—
219SD16—744no—
220SD16—742no—
221SD16—742no—
222SD16—744no—
223SD16—744no—
224D8—742no—
225D8—744no—
226M16D14814yescomplemented
227C2×C8D14814yescomplemented
228C2×C8C22×D3711yescharacteristic
229C2×C8C22×D3712yes—
230C2×C8C22×D3711yescharacteristic
231C4⋊C4—744no—
232C4⋊C4D14812yes—
233C22⋊C4—744no—
234C22⋊C4—744no—
235C22⋊C4D14812yes—
236C42C22×D3712yes—
237C23—2962no—
238C23—741no—
239C23—742no—
240C23—741no—
241C23—1482no—
242C23C2×D14811yescharacteristic
243Q8—742no—
244Q8—741no—
245Q8—742no—
246Q8—741no—
247Q8—741no—
248Q8—741no—
249Q8—1482no—
250D4—2964no—
251D4—741no—
252D4—742no—
253D4—741no—
254D4—741no—
255D4—742no—
256D4—741no—
257D4—1482no—
258D4—1482no—
259D4—1482no—
260C2×C4—741no—
261C2×C4—742no—
262C2×C4—741no—
263C2×C4—1482no—
264C2×C4—1482no—
265C2×C4—1482no—
266C2×C4C2×D14814yes—
267C2×C4C2×D14811yescharacteristic
268C2×C4C2×D14812yes—
269C2×C4C2×D14812yes—
270C2×C4C23×D3711yescharacteristic
271C8C2×D14812yes—
272C8C2×D14812yes—
273C8C2×D14814yes—
274C22—22no—
275C22—2964no—
276C22—1481no—
277C22—1481no—
278C22—1482no—
279C22—1482no—
280C22—1484no—
281C22—1482no—
282C22#1192453312yes—
283C22C22×D14811yescharacteristic
284C4—24no—
285C4—1481no—
286C4—1481no—
287C4—1482no—
288C4#1192453312yes—
289C4C22×D14811yescharacteristic
290C4C22×D14811yescharacteristic
291C2—22no—
292C2—2962no—
293C2—2961no—
294C2—2961no—
295C2C2×#1192453311yescharacteristic
296C2#1455834512yes—
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#405C2
socleC22×C37C22×D4
hypercenter#405D37
hypocenterC37#3154
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
1. C2×#11924569C2semidirect
2. C2×#11924564C2semidirect
3. C2×#11924558C2semidirect
4. C22×#10596930C2semidirect
5. #14558109C2semidirect
6. #14558102C2semidirect
7. #14557927C2semidirect
8. #14557922C2semidirect
9. #14557917C2semidirect
10. #14557906C2semidirect
11. C37×#405C2semidirect
19. C2×Dic148C22semidirect
20. C2×Dic148C22semidirect
25. C2×#10596930C22semidirect
26. C2×#10596930C22semidirect
27. C2×#10596930C22semidirect
29. C2×D296C22semidirect
30. #11924536C22semidirect
33. #11924524C22semidirect
41. #97×C37C22semidirect
42. C4×C8×C37C22semidirect
67. M16×C37D4semidirect
68. C2×C8×C37D4semidirect
159. #405D37semidirect
160. C37#3154semidirect
190. #97C2×D37semidirect
191. C4×C8C2×D37semidirect
226. M16D148semidirect
227. C2×C8D148semidirect

Maximal subgroups

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

subgroupindex
C2×#119245692
C2×#119245642
C2×#119245582
C22×#105969302
#145581092
#145581022
#145579272
#145579222
#145579172
#145579062
C37×#4052
#315437