Finite Group Databasebeta

← D29×#442 #16828281

Subgroups — D29×#442 #16828281

Order 3712.

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×D29C211yesmaximal, characteristic
2C4×D4×D29C212yesmaximal, complemented
3#14271276C211yesmaximal, characteristic, complemented
4#14271275C211yesmaximal, characteristic, complemented
5#14271274C211yesmaximal, characteristic, complemented
6#14271273C212yesmaximal, complemented
7#14271272C212yesmaximal, complemented
8#106×D29C211yesmaximal, characteristic, complemented
9#102×D29C212yesmaximal, complemented
10#97×D29C211yesmaximal, characteristic, complemented
11C29×#442C211yesmaximal, characteristic, complemented
12C2×D4×D29C2212yes—
13C22×C4×D29—22no—
14C2×D8×C29C2211yescharacteristic
15C4×D4×C29C2212yescomplemented
16D4×Dic29C2212yescomplemented
17C2×#90782C2212yes—
18C4×C22⋊D29—22no—
19D8×D29C418yescomplemented
20C2×D232C2211yescharacteristic
21C2×C8×D29C2211yescharacteristic
22C2×C8×D29C2211yescharacteristic
23#11745255C2212yescomplemented
24C4⋊C4×D29C2212yes—
25#11745243—22no—
26C22⋊C4×D29—22no—
27C4×D116C2212yescomplemented
28C42×D29C2211yescharacteristic
29C29×#106C2211yescharacteristic, complemented
30C29×#102C2212yescomplemented
31C29×#97C2211yescharacteristic, complemented
32#11745180C2212yescomplemented
33#11745169C2212yescomplemented
34#11745165C2211yescharacteristic, complemented
35#11745163C2211yescharacteristic, complemented
36#11745163C2211yescharacteristic, complemented
37#11745157C2212yescomplemented
38#11745156C2212yescomplemented
39#11745151C2211yescharacteristic, complemented
40C23×D29—22no—
41C2×D4×C29C2312yes—
42C22×C4×C29—22no—
43C2×C22⋊D29—22no—
44C22×Dic29—22no—
45D4×D29—24no—
46D4×D29C2×C418yescomplemented
47C2×D116C2312yes—
48C2×C4×D29—22no—
49C2×C4×D29—22no—
50C2×C4×D29—22no—
51C2×C4×D29—48no—
52C2×C4×D29D412yes—
53C2×C4×D29C2311yescharacteristic
54D8×C29C2×C414yescomplemented
55C2×C8×C29C2311yescharacteristic
56C2×C8×C29C2311yescharacteristic
57C4⋊C4×C29C2312yes—
58C22⋊C4×C29—22no—
59C42×C29C2311yescharacteristic
60C22⋊Dic29—22no—
61#90782C2×C418yescomplemented
62#90781—22no—
63#90781—22no—
64C4⋊Dic29C2312yes—
65#90779—22no—
66C4×Dic29D412yes—
67C4×Dic29C2311yescharacteristic
68C2×#6597C2311yescharacteristic
69C2×#6597C2311yescharacteristic
70D232C2×C414yescomplemented
71C8×D29—22no—
72C8×D29C2×C414yescomplemented
73C23×C29—22no—
74C22×D29—22no—
75C22×D29—28no—
76C22×D29—44no—
77C22×D29—44no—
78C22×D29C2×D411yescharacteristic
79D4×C29—22no—
80D4×C29C22×C414yescomplemented
81C2×C4×C29—22no—
82C2×C4×C29—44no—
83C2×C4×C29C2×D412yes—
84C2×C4×C29C2411yescharacteristic
85C22⋊D29—28no—
86C2×Dic29—22no—
87C2×Dic29—44no—
88C2×Dic29C2×D412yes—
89C2×Dic29C2×D411yescharacteristic
90D116—22no—
91D116C22×C414yescomplemented
92C4×D29—24no—
93C4×D29—44no—
94C4×D29—44no—
95C4×D29—44no—
96C4×D29C22×C412yes—
97C4×D29#4112yes—
98C8×C29—21no—
99C8×C29C22×C412yescomplemented
100#6597—21no—
101#6597C22×C412yescomplemented
102C2×#442—291nomaximal, Sylow
103C22×C29—24no—
104C22×C29—42no—
105C22×C29—42no—
106C22×C29C22×D411yescharacteristic
107C2×D29—24no—
108C2×D29—42no—
109C2×D29—42no—
110C2×D29—416no—
111C2×D29C4×D412yes—
112C2×D29AGL(1,ℤ/8)14yes—
113C4×C29—22no—
114C4×C29—42no—
115C4×C29C23×C411yescharacteristic
116C4×C29C2×#4111yescharacteristic
117Dic29—22no—
118Dic29—42no—
119Dic29C4×D412yes—
120C22×D8—291no—
121C2×C4×D4—292no—
122#442—291no—
123#442—292no—
124#442—291no—
125#442—292no—
126#442—291no—
127#442D2911yescharacteristic, direct product factor
128C2×#106—291no—
129C2×#102—292no—
130C2×#97—291no—
131C2×C29—44no—
132C2×C29C2×C4×D411yescharacteristic
133C2×C29C2×AGL(1,ℤ/8)12yes—
134D29—44no—
135D29#44214yesdirect product factor
136C22×D4—292no—
137C23×C4—582no—
138C2×D8—292no—
139C2×D8—298no—
140C2×D8—291no—
141C2×D8C2×D2911yescharacteristic
142C22×C8—291no—
143C22×C8—291no—
144C4×D4—292no—
145C4×D4—292no—
146C4×D4—292no—
147C4×D4—582no—
148C4×D4—582no—
149C4×D4C2×D2912yescomplemented
150C2×C4⋊C4—292no—
151C2×C22⋊C4—582no—
152C2×C42—291no—
153#106—291no—
154#106—292no—
155#106C2×D2911yescharacteristic, complemented
156#102—292no—
157#102—292no—
158#102—292no—
159#102C2×D2912yescomplemented
160#97—291no—
161#97—291no—
162#97—291no—
163#97C2×D2911yescharacteristic, complemented
164C29C2×#44211yescharacteristic, complemented, Sylow
165C24—582no—
166C2×D4—298no—
167C2×D4—292no—
168C2×D4—584no—
169C2×D4—582no—
170C2×D4C22×D2912yes—
171C22×C4—22no—
172C22×C4—291no—
173C22×C4—292no—
174C22×C4—582no—
175C22×C4—582no—
176C22×C4—582no—
177C22×C4—582no—
178C22×C4—1168no—
179D8—298no—
180D8—294no—
181D8C4×D2914yescomplemented
182C2×C8—291no—
183C2×C8—294no—
184C2×C8—291no—
185C2×C8—582no—
186C2×C8C22×D2911yescharacteristic
187C2×C8C22×D2911yescharacteristic
188C4⋊C4—292no—
189C4⋊C4—582no—
190C4⋊C4C22×D2912yes—
191C22⋊C4—22no—
192C22⋊C4—582no—
193C22⋊C4—582no—
194C22⋊C4—582no—
195C42—292no—
196C42—291no—
197C42C22×D2911yescharacteristic
198C23—22no—
199C23—291no—
200C23—588no—
201C23—582no—
202C23—1164no—
203C23—1164no—
204D4—22no—
205D4—294no—
206D4—588no—
207D4—582no—
208D4C2×C4×D2914yescomplemented
209C2×C4—22no—
210C2×C4—44no—
211C2×C4—291no—
212C2×C4—292no—
213C2×C4—292no—
214C2×C4—292no—
215C2×C4—584no—
216C2×C4—582no—
217C2×C4—1164no—
218C2×C4—1164no—
219C2×C4—1164no—
220C2×C4—1164no—
221C2×C4D4×D2912yes—
222C2×C4C23×D2911yescharacteristic
223C8—21no—
224C8—292no—
225C8—581no—
226C8C2×C4×D2912yescomplemented
227C22—24no—
228C22—42no—
229C22—42no—
230C22—292no—
231C22—294no—
232C22—584no—
233C22—11616no—
234C22—1162no—
235C22—1162no—
236C22C2×D4×D2911yescharacteristic
237C4—22no—
238C4—42no—
239C4—292no—
240C4—582no—
241C4—1162no—
242C4C22×C4×D2911yescharacteristic
243C4#41×D2911yescharacteristic
244C2—44no—
245C2—294no—
246C2—1164no—
247C2C4×D4×D2911yescharacteristic
248C2AGL(1,ℤ/8)×D2912yes—
subgroupG/H
centerC22C2×D4×D29
commutatorC4×C29C23×C4
FrattiniC2×C4C23×D29
FittingC29×#442C2
socleC22×C29C22×D4
prime radicalC2×D8×D29C2
cosocleC2×C4×C29C24
hypercenter#442D29
hypocenterC29C2×#442
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. C4×D4×D29C2semidirect
3. #14271276C2semidirect
4. #14271275C2semidirect
5. #14271274C2semidirect
6. #14271273C2semidirect
7. #14271272C2semidirect
8. #106×D29C2semidirect
9. #102×D29C2semidirect
10. #97×D29C2semidirect
11. C29×#442C2semidirect
15. C4×D4×C29C22semidirect
16. D4×Dic29C22semidirect
19. D8×D29C4semidirect
23. #11745255C22semidirect
27. C4×D116C22semidirect
29. C29×#106C22semidirect
30. C29×#102C22semidirect
31. C29×#97C22semidirect
32. #11745180C22semidirect
33. #11745169C22semidirect
34. #11745165C22semidirect
35. #11745163C22semidirect
36. #11745163C22semidirect
37. #11745157C22semidirect
38. #11745156C22semidirect
39. #11745151C22semidirect
46. D4×D29C2×C4semidirect
54. D8×C29C2×C4semidirect
61. #90782C2×C4semidirect
70. D232C2×C4semidirect
72. C8×D29C2×C4semidirect
80. D4×C29C22×C4semidirect
91. D116C22×C4semidirect
99. C8×C29C22×C4semidirect
101. #6597C22×C4semidirect
127. #442D29direct (N × H)
135. D29#442direct (N × H)
149. C4×D4C2×D29semidirect
155. #106C2×D29semidirect
159. #102C2×D29semidirect
163. #97C2×D29semidirect
164. C29C2×#442semidirect
181. D8C4×D29semidirect
208. D4C2×C4×D29semidirect
226. C8C2×C4×D29semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D292
C4×D4×D292
#142712762
#142712752
#142712742
#142712732
#142712722
#106×D292
#102×D292
#97×D292
C29×#4422
C2×#44229