Finite Group Databasebeta

← #442×D37 #18003385

Subgroups — #442×D37 #18003385

Order 4736.

608 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 183 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
2C4×D4×D37C212yesmaximal, complemented
3#14557646C211yesmaximal, characteristic, complemented
4#14557645C211yesmaximal, characteristic, complemented
5#14557644C211yesmaximal, characteristic, complemented
6#14557643C212yesmaximal, complemented
7#14557642C212yesmaximal, complemented
8#106×D37C211yesmaximal, characteristic, complemented
9#102×D37C212yesmaximal, complemented
10#97×D37C211yesmaximal, characteristic, complemented
11C37×#442C211yesmaximal, characteristic, complemented
12C2×D4×D37C2212yes—
13C22×C4×D37—22no—
14C2×D296C2211yescharacteristic
15C2×#10596939C2212yes—
16D8×D37C418yescomplemented
17C2×C8×D37C2211yescharacteristic
18C2×C8×D37C2211yescharacteristic
19C4×D148C2212yescomplemented
20D4×Dic37C2212yescomplemented
21#11924498C2212yescomplemented
22C4×C22⋊D37—22no—
23#11924496—22no—
24C4⋊C4×D37C2212yes—
25C22⋊C4×D37—22no—
26C42×D37C2211yescharacteristic
27#11924468C2211yescharacteristic, complemented
28#11924467C2212yescomplemented
29#11924458C2212yescomplemented
30#11924457C2212yescomplemented
31#11924456C2212yescomplemented
32#11924447C2211yescharacteristic, complemented
33#11924446C2211yescharacteristic, complemented
34#11924446C2211yescharacteristic, complemented
35C2×D8×C37C2211yescharacteristic
36C4×D4×C37C2212yescomplemented
37#106×C37C2211yescharacteristic, complemented
38#102×C37C2212yescomplemented
39#97×C37C2211yescharacteristic, complemented
40C23×D37—22no—
41C2×D4×C37C2312yes—
42C22×C4×C37—22no—
43C2×C22⋊D37—22no—
44C22×Dic37—22no—
45D4×D37—24no—
46D4×D37C2×C418yescomplemented
47C2×D148C2312yes—
48C2×C4×D37—22no—
49C2×C4×D37—22no—
50C2×C4×D37—22no—
51C2×C4×D37—48no—
52C2×C4×D37D412yes—
53C2×C4×D37C2311yescharacteristic
54D8×C37C2×C414yescomplemented
55C2×C8×C37C2311yescharacteristic
56C2×C8×C37C2311yescharacteristic
57C4⋊C4×C37C2312yes—
58C22⋊C4×C37—22no—
59C42×C37C2311yescharacteristic
60C22⋊Dic37—22no—
61#10596939C2×C418yescomplemented
62#10596938—22no—
63#10596938—22no—
64C4⋊Dic37C2312yes—
65#10596936—22no—
66C4×Dic37D412yes—
67C4×Dic37C2311yescharacteristic
68C2×#64436C2311yescharacteristic
69C2×#64436C2311yescharacteristic
70D296C2×C414yescomplemented
71C8×D37—22no—
72C8×D37C2×C414yescomplemented
73C23×C37—22no—
74C22×D37—22no—
75C22×D37—28no—
76C22×D37—44no—
77C22×D37—44no—
78C22×D37C2×D411yescharacteristic
79D4×C37—22no—
80D4×C37C22×C414yescomplemented
81C2×C4×C37—22no—
82C2×C4×C37—44no—
83C2×C4×C37C2×D412yes—
84C2×C4×C37C2411yescharacteristic
85C22⋊D37—28no—
86C2×Dic37—22no—
87C2×Dic37—44no—
88C2×Dic37C2×D412yes—
89C2×Dic37C2×D411yescharacteristic
90D148—22no—
91D148C22×C414yescomplemented
92C4×D37—24no—
93C4×D37—44no—
94C4×D37—44no—
95C4×D37—44no—
96C4×D37C22×C412yes—
97C4×D37#4112yes—
98C8×C37—21no—
99C8×C37C22×C412yescomplemented
100#64436—21no—
101#64436C22×C412yescomplemented
102C22×C37—24no—
103C22×C37—42no—
104C22×C37—42no—
105C22×C37C22×D411yescharacteristic
106C2×D37—24no—
107C2×D37—42no—
108C2×D37—42no—
109C2×D37—416no—
110C2×D37C4×D412yes—
111C2×D37AGL(1,ℤ/8)14yes—
112C4×C37—22no—
113C4×C37—42no—
114C4×C37C23×C411yescharacteristic
115C4×C37C2×#4111yescharacteristic
116Dic37—22no—
117Dic37—42no—
118Dic37C4×D412yes—
119C2×#442—371nomaximal, Sylow
120C2×C37—44no—
121C2×C37C2×C4×D411yescharacteristic
122C2×C37C2×AGL(1,ℤ/8)12yes—
123D37—44no—
124D37#44214yesdirect product factor
125C22×D8—371no—
126C2×C4×D4—372no—
127#442—371no—
128#442—372no—
129#442—371no—
130#442—372no—
131#442—371no—
132#442D3711yescharacteristic, direct product factor
133C2×#106—371no—
134C2×#102—372no—
135C2×#97—371no—
136C37C2×#44211yescharacteristic, complemented, Sylow
137C22×D4—372no—
138C23×C4—742no—
139C2×D8—372no—
140C2×D8—378no—
141C2×D8—371no—
142C2×D8C2×D3711yescharacteristic
143C22×C8—371no—
144C22×C8—371no—
145C4×D4—372no—
146C4×D4—372no—
147C4×D4—372no—
148C4×D4—742no—
149C4×D4—742no—
150C4×D4C2×D3712yescomplemented
151C2×C4⋊C4—372no—
152C2×C22⋊C4—742no—
153C2×C42—371no—
154#106—371no—
155#106—372no—
156#106C2×D3711yescharacteristic, complemented
157#102—372no—
158#102—372no—
159#102—372no—
160#102C2×D3712yescomplemented
161#97—371no—
162#97—371no—
163#97—371no—
164#97C2×D3711yescharacteristic, complemented
165C24—742no—
166C2×D4—378no—
167C2×D4—372no—
168C2×D4—744no—
169C2×D4—742no—
170C2×D4C22×D3712yes—
171C22×C4—22no—
172C22×C4—371no—
173C22×C4—372no—
174C22×C4—742no—
175C22×C4—742no—
176C22×C4—742no—
177C22×C4—742no—
178C22×C4—1488no—
179D8—378no—
180D8—374no—
181D8C4×D3714yescomplemented
182C2×C8—371no—
183C2×C8—374no—
184C2×C8—371no—
185C2×C8—742no—
186C2×C8C22×D3711yescharacteristic
187C2×C8C22×D3711yescharacteristic
188C4⋊C4—372no—
189C4⋊C4—742no—
190C4⋊C4C22×D3712yes—
191C22⋊C4—22no—
192C22⋊C4—742no—
193C22⋊C4—742no—
194C22⋊C4—742no—
195C42—372no—
196C42—371no—
197C42C22×D3711yescharacteristic
198C23—22no—
199C23—371no—
200C23—748no—
201C23—742no—
202C23—1484no—
203C23—1484no—
204D4—22no—
205D4—374no—
206D4—748no—
207D4—742no—
208D4C2×C4×D3714yescomplemented
209C2×C4—22no—
210C2×C4—44no—
211C2×C4—371no—
212C2×C4—372no—
213C2×C4—372no—
214C2×C4—372no—
215C2×C4—744no—
216C2×C4—742no—
217C2×C4—1484no—
218C2×C4—1484no—
219C2×C4—1484no—
220C2×C4—1484no—
221C2×C4D4×D3712yes—
222C2×C4C23×D3711yescharacteristic
223C8—21no—
224C8—372no—
225C8—741no—
226C8C2×C4×D3712yescomplemented
227C22—24no—
228C22—42no—
229C22—42no—
230C22—372no—
231C22—374no—
232C22—744no—
233C22—14816no—
234C22—1482no—
235C22—1482no—
236C22C2×D4×D3711yescharacteristic
237C4—22no—
238C4—42no—
239C4—372no—
240C4—742no—
241C4—1482no—
242C4C22×C4×D3711yescharacteristic
243C4#41×D3711yescharacteristic
244C2—44no—
245C2—374no—
246C2—1484no—
247C2C4×D4×D3711yescharacteristic
248C2AGL(1,ℤ/8)×D3712yes—
subgroupG/H
centerC22C2×D4×D37
commutatorC4×C37C23×C4
FrattiniC2×C4C23×D37
FittingC37×#442C2
socleC22×C37C22×D4
prime radicalC2×D8×D37C2
cosocleC2×C4×C37C24
hypercenter#442D37
hypocenterC37C2×#442
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. C4×D4×D37C2semidirect
3. #14557646C2semidirect
4. #14557645C2semidirect
5. #14557644C2semidirect
6. #14557643C2semidirect
7. #14557642C2semidirect
8. #106×D37C2semidirect
9. #102×D37C2semidirect
10. #97×D37C2semidirect
11. C37×#442C2semidirect
16. D8×D37C4semidirect
19. C4×D148C22semidirect
20. D4×Dic37C22semidirect
21. #11924498C22semidirect
27. #11924468C22semidirect
28. #11924467C22semidirect
29. #11924458C22semidirect
30. #11924457C22semidirect
31. #11924456C22semidirect
32. #11924447C22semidirect
33. #11924446C22semidirect
34. #11924446C22semidirect
36. C4×D4×C37C22semidirect
37. #106×C37C22semidirect
38. #102×C37C22semidirect
39. #97×C37C22semidirect
46. D4×D37C2×C4semidirect
54. D8×C37C2×C4semidirect
61. #10596939C2×C4semidirect
70. D296C2×C4semidirect
72. C8×D37C2×C4semidirect
80. D4×C37C22×C4semidirect
91. D148C22×C4semidirect
99. C8×C37C22×C4semidirect
101. #64436C22×C4semidirect
124. D37#442direct (N × H)
132. #442D37direct (N × H)
136. C37C2×#442semidirect
150. C4×D4C2×D37semidirect
156. #106C2×D37semidirect
160. #102C2×D37semidirect
164. #97C2×D37semidirect
181. D8C4×D37semidirect
208. D4C2×C4×D37semidirect
226. C8C2×C4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D372
C4×D4×D372
#145576462
#145576452
#145576442
#145576432
#145576422
#106×D372
#102×D372
#97×D372
C37×#4422
C2×#44237