Finite Group Databasebeta

← D31×#442 #16854500

Subgroups — D31×#442 #16854500

Order 3968.

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×D31C211yesmaximal, characteristic
2C4×D4×D31C212yesmaximal, complemented
3#14521162C211yesmaximal, characteristic, complemented
4#14521161C211yesmaximal, characteristic, complemented
5#14521160C211yesmaximal, characteristic, complemented
6#14521159C212yesmaximal, complemented
7#14521158C212yesmaximal, complemented
8#106×D31C211yesmaximal, characteristic, complemented
9#102×D31C212yesmaximal, complemented
10#97×D31C211yesmaximal, characteristic, complemented
11C31×#442C211yesmaximal, characteristic, complemented
12C2×D4×D31C2212yes—
13C22×C4×D31—22no—
14C2×D8×C31C2211yescharacteristic
15C4×D4×C31C2212yescomplemented
16D4×Dic31C2212yescomplemented
17C2×#92479C2212yes—
18C4×C22⋊D31—22no—
19D8×D31C418yescomplemented
20C2×D248C2211yescharacteristic
21C2×C8×D31C2211yescharacteristic
22C2×C8×D31C2211yescharacteristic
23#11758470C2212yescomplemented
24C4⋊C4×D31C2212yes—
25(C22⋊D31)⋊C4—22no—
26C22⋊C4×D31—22no—
27C4×D124C2212yescomplemented
28C42×D31C2211yescharacteristic
29C31×#106C2211yescharacteristic, complemented
30C31×#102C2212yescomplemented
31C31×#97C2211yescharacteristic, complemented
32#11758420C2212yescomplemented
33#11758409C2212yescomplemented
34#11758405C2211yescharacteristic, complemented
35#11758403C2211yescharacteristic, complemented
36#11758403C2211yescharacteristic, complemented
37#11758397C2212yescomplemented
38#11758396C2212yescomplemented
39#11758391C2211yescharacteristic, complemented
40C23×D31—22no—
41C2×D4×C31C2312yes—
42C22×C4×C31—22no—
43C2×C22⋊D31—22no—
44C22×Dic31—22no—
45D4×D31—24no—
46D4×D31C2×C418yescomplemented
47C2×D124C2312yes—
48C2×C4×D31—22no—
49C2×C4×D31—22no—
50C2×C4×D31—22no—
51C2×C4×D31—48no—
52C2×C4×D31D412yes—
53C2×C4×D31C2311yescharacteristic
54D8×C31C2×C414yescomplemented
55C2×C8×C31C2311yescharacteristic
56C2×C8×C31C2311yescharacteristic
57C4⋊C4×C31C2312yes—
58C22⋊C4×C31—22no—
59C42×C31C2311yescharacteristic
60C22⋊Dic31—22no—
61#92479C2×C418yescomplemented
62(C2×D31)⋊C4—22no—
63(C2×D31)⋊C4—22no—
64C4⋊Dic31C2312yes—
65Dic31⋊C4—22no—
66C4×Dic31D412yes—
67C4×Dic31C2311yescharacteristic
68C2×C31⋊C8C2311yescharacteristic
69C2×C31⋊C8C2311yescharacteristic
70D248C2×C414yescomplemented
71C8×D31—22no—
72C8×D31C2×C414yescomplemented
73C23×C31—22no—
74C22×D31—22no—
75C22×D31—28no—
76C22×D31—44no—
77C22×D31—44no—
78C22×D31C2×D411yescharacteristic
79D4×C31—22no—
80D4×C31C22×C414yescomplemented
81C2×C4×C31—22no—
82C2×C4×C31—44no—
83C2×C4×C31C2×D412yes—
84C2×C4×C31C2411yescharacteristic
85C22⋊D31—28no—
86C2×Dic31—22no—
87C2×Dic31—44no—
88C2×Dic31C2×D412yes—
89C2×Dic31C2×D411yescharacteristic
90D124—22no—
91D124C22×C414yescomplemented
92C4×D31—24no—
93C4×D31—44no—
94C4×D31—44no—
95C4×D31—44no—
96C4×D31C22×C412yes—
97C4×D31#4112yes—
98C8×C31—21no—
99C8×C31C22×C412yescomplemented
100C31⋊C8—21no—
101C31⋊C8C22×C412yescomplemented
102C2×#442—311nomaximal, Sylow
103C22×C31—24no—
104C22×C31—42no—
105C22×C31—42no—
106C22×C31C22×D411yescharacteristic
107C2×D31—24no—
108C2×D31—42no—
109C2×D31—42no—
110C2×D31—416no—
111C2×D31C4×D412yes—
112C2×D31AGL(1,ℤ/8)14yes—
113C4×C31—22no—
114C4×C31—42no—
115C4×C31C23×C411yescharacteristic
116C4×C31C2×#4111yescharacteristic
117Dic31—22no—
118Dic31—42no—
119Dic31C4×D412yes—
120C22×D8—311no—
121C2×C4×D4—312no—
122#442—311no—
123#442—312no—
124#442—311no—
125#442—312no—
126#442—311no—
127#442D3111yescharacteristic, direct product factor
128C2×#106—311no—
129C2×#102—312no—
130C2×#97—311no—
131C2×C31—44no—
132C2×C31C2×C4×D411yescharacteristic
133C2×C31C2×AGL(1,ℤ/8)12yes—
134D31—44no—
135D31#44214yesdirect product factor
136C22×D4—312no—
137C23×C4—622no—
138C2×D8—312no—
139C2×D8—318no—
140C2×D8—311no—
141C2×D8C2×D3111yescharacteristic
142C22×C8—311no—
143C22×C8—311no—
144C4×D4—312no—
145C4×D4—312no—
146C4×D4—312no—
147C4×D4—622no—
148C4×D4—622no—
149C4×D4C2×D3112yescomplemented
150C2×C4⋊C4—312no—
151C2×C22⋊C4—622no—
152C2×C42—311no—
153#106—311no—
154#106—312no—
155#106C2×D3111yescharacteristic, complemented
156#102—312no—
157#102—312no—
158#102—312no—
159#102C2×D3112yescomplemented
160#97—311no—
161#97—311no—
162#97—311no—
163#97C2×D3111yescharacteristic, complemented
164C31C2×#44211yescharacteristic, complemented, Sylow
165C24—622no—
166C2×D4—318no—
167C2×D4—312no—
168C2×D4—624no—
169C2×D4—622no—
170C2×D4C22×D3112yes—
171C22×C4—22no—
172C22×C4—311no—
173C22×C4—312no—
174C22×C4—622no—
175C22×C4—622no—
176C22×C4—622no—
177C22×C4—622no—
178C22×C4—1248no—
179D8—318no—
180D8—314no—
181D8C4×D3114yescomplemented
182C2×C8—311no—
183C2×C8—314no—
184C2×C8—311no—
185C2×C8—622no—
186C2×C8C22×D3111yescharacteristic
187C2×C8C22×D3111yescharacteristic
188C4⋊C4—312no—
189C4⋊C4—622no—
190C4⋊C4C22×D3112yes—
191C22⋊C4—22no—
192C22⋊C4—622no—
193C22⋊C4—622no—
194C22⋊C4—622no—
195C42—312no—
196C42—311no—
197C42C22×D3111yescharacteristic
198C23—22no—
199C23—311no—
200C23—628no—
201C23—622no—
202C23—1244no—
203C23—1244no—
204D4—22no—
205D4—314no—
206D4—628no—
207D4—622no—
208D4C2×C4×D3114yescomplemented
209C2×C4—22no—
210C2×C4—44no—
211C2×C4—311no—
212C2×C4—312no—
213C2×C4—312no—
214C2×C4—312no—
215C2×C4—624no—
216C2×C4—622no—
217C2×C4—1244no—
218C2×C4—1244no—
219C2×C4—1244no—
220C2×C4—1244no—
221C2×C4D4×D3112yes—
222C2×C4C23×D3111yescharacteristic
223C8—21no—
224C8—312no—
225C8—621no—
226C8C2×C4×D3112yescomplemented
227C22—24no—
228C22—42no—
229C22—42no—
230C22—312no—
231C22—314no—
232C22—624no—
233C22—12416no—
234C22—1242no—
235C22—1242no—
236C22C2×D4×D3111yescharacteristic
237C4—22no—
238C4—42no—
239C4—312no—
240C4—622no—
241C4—1242no—
242C4C22×C4×D3111yescharacteristic
243C4#41×D3111yescharacteristic
244C2—44no—
245C2—314no—
246C2—1244no—
247C2C4×D4×D3111yescharacteristic
248C2AGL(1,ℤ/8)×D3112yes—
subgroupG/H
centerC22C2×D4×D31
commutatorC4×C31C23×C4
FrattiniC2×C4C23×D31
FittingC31×#442C2
socleC22×C31C22×D4
prime radicalC2×D8×D31C2
cosocleC2×C4×C31C24
hypercenter#442D31
hypocenterC31C2×#442
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. C4×D4×D31C2semidirect
3. #14521162C2semidirect
4. #14521161C2semidirect
5. #14521160C2semidirect
6. #14521159C2semidirect
7. #14521158C2semidirect
8. #106×D31C2semidirect
9. #102×D31C2semidirect
10. #97×D31C2semidirect
11. C31×#442C2semidirect
15. C4×D4×C31C22semidirect
16. D4×Dic31C22semidirect
19. D8×D31C4semidirect
23. #11758470C22semidirect
27. C4×D124C22semidirect
29. C31×#106C22semidirect
30. C31×#102C22semidirect
31. C31×#97C22semidirect
32. #11758420C22semidirect
33. #11758409C22semidirect
34. #11758405C22semidirect
35. #11758403C22semidirect
36. #11758403C22semidirect
37. #11758397C22semidirect
38. #11758396C22semidirect
39. #11758391C22semidirect
46. D4×D31C2×C4semidirect
54. D8×C31C2×C4semidirect
61. #92479C2×C4semidirect
70. D248C2×C4semidirect
72. C8×D31C2×C4semidirect
80. D4×C31C22×C4semidirect
91. D124C22×C4semidirect
99. C8×C31C22×C4semidirect
101. C31⋊C8C22×C4semidirect
127. #442D31direct (N × H)
135. D31#442direct (N × H)
149. C4×D4C2×D31semidirect
155. #106C2×D31semidirect
159. #102C2×D31semidirect
163. #97C2×D31semidirect
164. C31C2×#442semidirect
181. D8C4×D31semidirect
208. D4C2×C4×D31semidirect
226. C8C2×C4×D31semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D312
C4×D4×D312
#145211622
#145211612
#145211602
#145211592
#145211582
#106×D312
#102×D312
#97×D312
C31×#4422
C2×#44231