Finite Group Databasebeta

← #469×D37 #18004188

Subgroups — #469×D37 #18004188

Order 4736.

596 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 135 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×D8×D37C211yesmaximal, characteristic, complemented
2C2×M16×D37C211yesmaximal, characteristic, complemented
3#121×D37C212yesmaximal, complemented
4#14557787C211yesmaximal, characteristic, complemented
5#14557786C211yesmaximal, characteristic, complemented
6#14557785C212yesmaximal, complemented
7#14557784C212yesmaximal, complemented
8#14557783C211yesmaximal, characteristic, complemented
9#106×D37C211yesmaximal, characteristic, complemented
10#102×D37C212yesmaximal, complemented
11C37×#469C211yesmaximal, characteristic, complemented
12C2×D4×D37—22no—
13C2×D4×D37C2212yes—
14C22×C4×D37C2211yescharacteristic
15C2×D296C2211yescharacteristic, complemented
16C2×#10596939C2212yescomplemented
17D8×D37—24no—
18C2×#10596934C2211yescharacteristic, complemented
19C2×#10596929C2211yescharacteristic, complemented
20C2×#10596929C2211yescharacteristic, complemented
21M16×D37—24no—
22C2×C8×D37C2211yescharacteristic
23C2×C8×D37C2211yescharacteristic
24#11924511C2212yescomplemented
25#11924510C2212yescomplemented
26#11924509—22no—
27#11924508—22no—
28#11924507C2212yescomplemented
29C4⋊C4×D37C2212yes—
30C22⋊C4×D37—22no—
31#11924468C2211yescharacteristic, complemented
32#11924467C2212yescomplemented
33#11924458C2212yescomplemented
34#11924457C2212yescomplemented
35#11924456C2212yescomplemented
36C2×D8×C37C2211yescharacteristic, complemented
37C2×M16×C37C2211yescharacteristic, complemented
38#121×C37C2212yescomplemented
39#106×C37C2211yescharacteristic, complemented
40#102×C37C2212yescomplemented
41C23×D37—22no—
42C23×D37D411yescharacteristic
43C2×D4×C37—22no—
44C2×D4×C37C2312yes—
45C22×C4×C37C2311yescharacteristic
46C2×C22⋊D37—22no—
47C2×C22⋊D37—22no—
48C2×C22⋊D37—22no—
49C22×Dic37D411yescharacteristic
50D4×D37—24no—
51D4×D37—24no—
52D4×D37—48no—
53C2×D148—22no—
54C2×D148C2312yes—
55C2×C4×D37—22no—
56C2×C4×D37—22no—
57C2×C4×D37—22no—
58C2×C4×D37D411yescharacteristic
59C2×C4×D37D411yescharacteristic
60C2×C4×D37C2311yescharacteristic
61C2×C4×D37C2311yescharacteristic
62D8×C37—22no—
63M16×C37—22no—
64C2×C8×C37C2311yescharacteristic
65C2×C8×C37C2311yescharacteristic
66C4⋊C4×C37C2312yes—
67C22⋊C4×C37—22no—
68C22⋊Dic37—22no—
69#10596939—24no—
70#10596938—22no—
71#10596938—22no—
72C4⋊Dic37C2312yes—
73#10596936—22no—
74#10596934—22no—
75C2×#64436C2311yescharacteristic
76C2×#64436C2311yescharacteristic
77D296—22no—
78#10596929—22no—
79#10596929—22no—
80C8×D37—22no—
81C8×D37D414yescomplemented
82C23×C37—22no—
83C23×C37C2×D411yescharacteristic
84C22×D37—22no—
85C22×D37—24no—
86C22×D37—22no—
87C22×D37—44no—
88C22×D37—44no—
89C22×D37—44no—
90C22×D37C2×D411yescharacteristic
91C22×D37C2×D411yescharacteristic
92D4×C37—22no—
93D4×C37—22no—
94D4×C37—44no—
95C2×C4×C37—21no—
96C2×C4×C37—21no—
97C2×C4×C37—22no—
98C2×C4×C37C2×D411yescharacteristic
99C2×C4×C37C2411yescharacteristic
100C22⋊D37—44no—
101C22⋊D37—44no—
102C22⋊D37—44no—
103C2×Dic37—22no—
104C2×Dic37—22no—
105C2×Dic37C2×D411yescharacteristic
106C2×Dic37C2×D411yescharacteristic
107D148—22no—
108D148—22no—
109D148—44no—
110C4×D37—22no—
111C4×D37—21no—
112C4×D37—21no—
113C4×D37—22no—
114C4×D37—44no—
115C4×D37C2×D412yes—
116C4×D37#4112yes—
117C8×C37—21no—
118C8×C37C2×D412yescomplemented
119#64436—21no—
120#64436C2×D412yescomplemented
121C22×C37—21no—
122C22×C37—22no—
123C22×C37—42no—
124C22×C37—42no—
125C22×C37—42no—
126C22×C37C22×D411yescharacteristic
127C2×D37—21no—
128C2×D37—22no—
129C2×D37—44no—
130C2×D37—42no—
131C2×D37—42no—
132C2×D37—42no—
133C2×D37—88no—
134C2×D37#12112yes—
135C2×D37AGL(1,ℤ/8)14yes—
136C4×C37—21no—
137C4×C37—42no—
138C4×C37C22×D411yescharacteristic
139C4×C37C2×#4111yescharacteristic
140Dic37—21no—
141Dic37—42no—
142Dic37#12112yes—
143C2×#469—371nomaximal, Sylow
144C2×C37—41no—
145C2×C37—82no—
146C2×C37C2×#12111yescharacteristic
147C2×C37C2×AGL(1,ℤ/8)12yes—
148D37—41no—
149D37—82no—
150D37#46914yesdirect product factor
151C22×D8—371no—
152C22×M16—371no—
153C2×#121—372no—
154#469—371no—
155#469—371no—
156#469—372no—
157#469—371no—
158#469—372no—
159#469D3711yescharacteristic, direct product factor
160C2×#106—371no—
161C2×#102—372no—
162C37C2×#46911yescharacteristic, complemented, Sylow
163C22×D4—372no—
164C22×D4—742no—
165C23×C4—371no—
166C2×D8—372no—
167C2×D8—371no—
168C2×D8—744no—
169C2×D8C2×D3711yescharacteristic, complemented
170C2×M16—371no—
171C2×M16—371no—
172C2×M16—371no—
173C2×M16—744no—
174C2×M16C2×D3711yescharacteristic, complemented
175C22×C8—371no—
176C22×C8—371no—
177#121—372no—
178#121—372no—
179#121—372no—
180#121—742no—
181#121—742no—
182#121C2×D3712yescomplemented
183C2×C4⋊C4—372no—
184C2×C22⋊C4—742no—
185#106—371no—
186#106—372no—
187#106C2×D3711yescharacteristic, complemented
188#102—372no—
189#102—372no—
190#102—372no—
191#102C2×D3712yescomplemented
192C24—371no—
193C24—742no—
194C2×D4—22no—
195C2×D4—372no—
196C2×D4—742no—
197C2×D4—744no—
198C2×D4—744no—
199C2×D4—742no—
200C2×D4—742no—
201C2×D4—742no—
202C2×D4—1488no—
203C2×D4C22×D3712yes—
204C22×C4—371no—
205C22×C4—371no—
206C22×C4—371no—
207C22×C4—371no—
208C22×C4—371no—
209C22×C4—742no—
210C22×C4—742no—
211C22×C4—742no—
212C22×C4C22×D3711yescharacteristic
213D8—22no—
214D8—744no—
215D8—742no—
216M16—22no—
217M16—742no—
218M16—742no—
219M16—742no—
220C2×C8—371no—
221C2×C8—374no—
222C2×C8—371no—
223C2×C8—742no—
224C2×C8C22×D3711yescharacteristic
225C2×C8C22×D3711yescharacteristic
226C4⋊C4—372no—
227C4⋊C4—742no—
228C4⋊C4C22×D3712yes—
229C22⋊C4—22no—
230C22⋊C4—742no—
231C22⋊C4—742no—
232C22⋊C4—742no—
233C23—22no—
234C23—371no—
235C23—371no—
236C23—742no—
237C23—744no—
238C23—742no—
239C23—1484no—
240C23—1484no—
241C23—1484no—
242C23D4×D3711yescharacteristic
243D4—22no—
244D4—22no—
245D4—44no—
246D4—742no—
247D4—742no—
248D4—1484no—
249D4—1484no—
250D4—1484no—
251D4—1484no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—371no—
256C2×C4—372no—
257C2×C4—372no—
258C2×C4—371no—
259C2×C4—742no—
260C2×C4—742no—
261C2×C4—742no—
262C2×C4—741no—
263C2×C4—741no—
264C2×C4—742no—
265C2×C4—1484no—
266C2×C4D4×D3711yescharacteristic
267C2×C4C23×D3711yescharacteristic
268C8—21no—
269C8—372no—
270C8—741no—
271C8D4×D3712yescomplemented
272C22—21no—
273C22—22no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—372no—
278C22—374no—
279C22—2968no—
280C22—741no—
281C22—742no—
282C22—1484no—
283C22—1482no—
284C22—1482no—
285C22—1482no—
286C22C2×D4×D3711yescharacteristic
287C4—21no—
288C4—42no—
289C4—372no—
290C4—741no—
291C4—1482no—
292C4C2×D4×D3711yescharacteristic
293C4#41×D3711yescharacteristic
294C2—41no—
295C2—82no—
296C2—374no—
297C2—2962no—
298C2—1481no—
299C2#121×D3711yescharacteristic
300C2AGL(1,ℤ/8)×D3712yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#469C2
socleC22×C37C22×D4
hypercenter#469D37
hypocenterC37C2×#469
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×D8×D37C2semidirect
2. C2×M16×D37C2semidirect
3. #121×D37C2semidirect
4. #14557787C2semidirect
5. #14557786C2semidirect
6. #14557785C2semidirect
7. #14557784C2semidirect
8. #14557783C2semidirect
9. #106×D37C2semidirect
10. #102×D37C2semidirect
11. C37×#469C2semidirect
15. C2×D296C22semidirect
16. C2×#10596939C22semidirect
18. C2×#10596934C22semidirect
19. C2×#10596929C22semidirect
20. C2×#10596929C22semidirect
24. #11924511C22semidirect
25. #11924510C22semidirect
28. #11924507C22semidirect
31. #11924468C22semidirect
32. #11924467C22semidirect
33. #11924458C22semidirect
34. #11924457C22semidirect
35. #11924456C22semidirect
36. C2×D8×C37C22semidirect
37. C2×M16×C37C22semidirect
38. #121×C37C22semidirect
39. #106×C37C22semidirect
40. #102×C37C22semidirect
81. C8×D37D4semidirect
118. C8×C37C2×D4semidirect
120. #64436C2×D4semidirect
150. D37#469direct (N × H)
159. #469D37direct (N × H)
162. C37C2×#469semidirect
169. C2×D8C2×D37semidirect
174. C2×M16C2×D37semidirect
182. #121C2×D37semidirect
187. #106C2×D37semidirect
191. #102C2×D37semidirect
271. C8D4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D372
C2×M16×D372
#121×D372
#145577872
#145577862
#145577852
#145577842
#145577832
#106×D372
#102×D372
C37×#4692
C2×#46937