Finite Group Databasebeta

← D29×#469 #16829084

Subgroups — D29×#469 #16829084

Order 3712.

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×D29C211yesmaximal, characteristic, complemented
2C2×M16×D29C211yesmaximal, characteristic, complemented
3#121×D29C212yesmaximal, complemented
4#14271417C211yesmaximal, characteristic, complemented
5#14271416C211yesmaximal, characteristic, complemented
6#14271415C212yesmaximal, complemented
7#14271414C212yesmaximal, complemented
8#14271413C211yesmaximal, characteristic, complemented
9#106×D29C211yesmaximal, characteristic, complemented
10#102×D29C212yesmaximal, complemented
11C29×#469C211yesmaximal, characteristic, complemented
12C2×D4×D29—22no—
13C2×D4×D29C2212yes—
14C22×C4×D29C2211yescharacteristic
15C2×D8×C29C2211yescharacteristic, complemented
16C2×M16×C29C2211yescharacteristic, complemented
17C29×#121C2212yescomplemented
18#11745301—22no—
19#11745300C2212yescomplemented
20C2×#90782C2212yescomplemented
21#11745292C2212yescomplemented
22C2×#90777C2211yescharacteristic, complemented
23D8×D29—24no—
24M16×D29—24no—
25C2×D232C2211yescharacteristic, complemented
26C2×#90772C2211yescharacteristic, complemented
27C2×#90772C2211yescharacteristic, complemented
28C2×C8×D29C2211yescharacteristic
29C2×C8×D29C2211yescharacteristic
30#11745257C2212yescomplemented
31C4⋊C4×D29C2212yes—
32#11745246—22no—
33C22⋊C4×D29—22no—
34C29×#106C2211yescharacteristic, complemented
35C29×#102C2212yescomplemented
36#11745180C2212yescomplemented
37#11745169C2212yescomplemented
38#11745165C2211yescharacteristic, complemented
39#11745157C2212yescomplemented
40#11745156C2212yescomplemented
41C23×D29—22no—
42C23×D29D411yescharacteristic
43C2×D4×C29—22no—
44C2×D4×C29C2312yes—
45C22×C4×C29C2311yescharacteristic
46C2×C22⋊D29—22no—
47C2×C22⋊D29—22no—
48C2×C22⋊D29—22no—
49C22×Dic29D411yescharacteristic
50D4×D29—24no—
51D4×D29—24no—
52D4×D29—48no—
53C2×D116—22no—
54C2×D116C2312yes—
55C2×C4×D29—22no—
56C2×C4×D29—22no—
57C2×C4×D29—22no—
58C2×C4×D29D411yescharacteristic
59C2×C4×D29D411yescharacteristic
60C2×C4×D29C2311yescharacteristic
61C2×C4×D29C2311yescharacteristic
62D8×C29—22no—
63M16×C29—22no—
64C2×C8×C29C2311yescharacteristic
65C2×C8×C29C2311yescharacteristic
66C4⋊C4×C29C2312yes—
67C22⋊C4×C29—22no—
68C22⋊Dic29—22no—
69#90782—24no—
70#90781—22no—
71#90781—22no—
72C4⋊Dic29C2312yes—
73#90779—22no—
74#90777—22no—
75C2×#6597C2311yescharacteristic
76C2×#6597C2311yescharacteristic
77D232—22no—
78#90772—22no—
79#90772—22no—
80C8×D29—22no—
81C8×D29D414yescomplemented
82C23×C29—22no—
83C23×C29C2×D411yescharacteristic
84C22×D29—22no—
85C22×D29—24no—
86C22×D29—22no—
87C22×D29—44no—
88C22×D29—44no—
89C22×D29—44no—
90C22×D29C2×D411yescharacteristic
91C22×D29C2×D411yescharacteristic
92D4×C29—22no—
93D4×C29—22no—
94D4×C29—44no—
95C2×C4×C29—21no—
96C2×C4×C29—21no—
97C2×C4×C29—22no—
98C2×C4×C29C2×D411yescharacteristic
99C2×C4×C29C2411yescharacteristic
100C22⋊D29—44no—
101C22⋊D29—44no—
102C22⋊D29—44no—
103C2×Dic29—22no—
104C2×Dic29—22no—
105C2×Dic29C2×D411yescharacteristic
106C2×Dic29C2×D411yescharacteristic
107D116—22no—
108D116—22no—
109D116—44no—
110C4×D29—22no—
111C4×D29—21no—
112C4×D29—21no—
113C4×D29—22no—
114C4×D29—44no—
115C4×D29C2×D412yes—
116C4×D29#4112yes—
117C8×C29—21no—
118C8×C29C2×D412yescomplemented
119#6597—21no—
120#6597C2×D412yescomplemented
121C2×#469—291nomaximal, Sylow
122C22×C29—21no—
123C22×C29—22no—
124C22×C29—42no—
125C22×C29—42no—
126C22×C29—42no—
127C22×C29C22×D411yescharacteristic
128C2×D29—21no—
129C2×D29—22no—
130C2×D29—44no—
131C2×D29—42no—
132C2×D29—42no—
133C2×D29—42no—
134C2×D29—88no—
135C2×D29#12112yes—
136C2×D29AGL(1,ℤ/8)14yes—
137C4×C29—21no—
138C4×C29—42no—
139C4×C29C22×D411yescharacteristic
140C4×C29C2×#4111yescharacteristic
141Dic29—21no—
142Dic29—42no—
143Dic29#12112yes—
144C22×D8—291no—
145C22×M16—291no—
146C2×#121—292no—
147#469—291no—
148#469—291no—
149#469—292no—
150#469—291no—
151#469—292no—
152#469D2911yescharacteristic, direct product factor
153C2×#106—291no—
154C2×#102—292no—
155C2×C29—41no—
156C2×C29—82no—
157C2×C29C2×#12111yescharacteristic
158C2×C29C2×AGL(1,ℤ/8)12yes—
159D29—41no—
160D29—82no—
161D29#46914yesdirect product factor
162C22×D4—292no—
163C22×D4—582no—
164C23×C4—291no—
165C2×D8—292no—
166C2×D8—291no—
167C2×D8—584no—
168C2×D8C2×D2911yescharacteristic, complemented
169C2×M16—291no—
170C2×M16—291no—
171C2×M16—291no—
172C2×M16—584no—
173C2×M16C2×D2911yescharacteristic, complemented
174C22×C8—291no—
175C22×C8—291no—
176#121—292no—
177#121—292no—
178#121—292no—
179#121—582no—
180#121—582no—
181#121C2×D2912yescomplemented
182C2×C4⋊C4—292no—
183C2×C22⋊C4—582no—
184#106—291no—
185#106—292no—
186#106C2×D2911yescharacteristic, complemented
187#102—292no—
188#102—292no—
189#102—292no—
190#102C2×D2912yescomplemented
191C29C2×#46911yescharacteristic, complemented, Sylow
192C24—291no—
193C24—582no—
194C2×D4—22no—
195C2×D4—292no—
196C2×D4—582no—
197C2×D4—584no—
198C2×D4—584no—
199C2×D4—582no—
200C2×D4—582no—
201C2×D4—582no—
202C2×D4—1168no—
203C2×D4C22×D2912yes—
204C22×C4—291no—
205C22×C4—291no—
206C22×C4—291no—
207C22×C4—291no—
208C22×C4—291no—
209C22×C4—582no—
210C22×C4—582no—
211C22×C4—582no—
212C22×C4C22×D2911yescharacteristic
213D8—22no—
214D8—584no—
215D8—582no—
216M16—22no—
217M16—582no—
218M16—582no—
219M16—582no—
220C2×C8—291no—
221C2×C8—294no—
222C2×C8—291no—
223C2×C8—582no—
224C2×C8C22×D2911yescharacteristic
225C2×C8C22×D2911yescharacteristic
226C4⋊C4—292no—
227C4⋊C4—582no—
228C4⋊C4C22×D2912yes—
229C22⋊C4—22no—
230C22⋊C4—582no—
231C22⋊C4—582no—
232C22⋊C4—582no—
233C23—22no—
234C23—291no—
235C23—291no—
236C23—582no—
237C23—584no—
238C23—582no—
239C23—1164no—
240C23—1164no—
241C23—1164no—
242C23D4×D2911yescharacteristic
243D4—22no—
244D4—22no—
245D4—44no—
246D4—582no—
247D4—582no—
248D4—1164no—
249D4—1164no—
250D4—1164no—
251D4—1164no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—291no—
256C2×C4—292no—
257C2×C4—292no—
258C2×C4—291no—
259C2×C4—582no—
260C2×C4—582no—
261C2×C4—582no—
262C2×C4—581no—
263C2×C4—581no—
264C2×C4—582no—
265C2×C4—1164no—
266C2×C4D4×D2911yescharacteristic
267C2×C4C23×D2911yescharacteristic
268C8—21no—
269C8—292no—
270C8—581no—
271C8D4×D2912yescomplemented
272C22—21no—
273C22—22no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—292no—
278C22—294no—
279C22—581no—
280C22—582no—
281C22—1164no—
282C22—1162no—
283C22—1162no—
284C22—1162no—
285C22—2328no—
286C22C2×D4×D2911yescharacteristic
287C4—21no—
288C4—42no—
289C4—292no—
290C4—581no—
291C4—1162no—
292C4C2×D4×D2911yescharacteristic
293C4#41×D2911yescharacteristic
294C2—41no—
295C2—82no—
296C2—294no—
297C2—1161no—
298C2—2322no—
299C2#121×D2911yescharacteristic
300C2AGL(1,ℤ/8)×D2912yes—
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#469C2
socleC22×C29C22×D4
hypercenter#469D29
hypocenterC29C2×#469
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×D8×D29C2semidirect
2. C2×M16×D29C2semidirect
3. #121×D29C2semidirect
4. #14271417C2semidirect
5. #14271416C2semidirect
6. #14271415C2semidirect
7. #14271414C2semidirect
8. #14271413C2semidirect
9. #106×D29C2semidirect
10. #102×D29C2semidirect
11. C29×#469C2semidirect
15. C2×D8×C29C22semidirect
16. C2×M16×C29C22semidirect
17. C29×#121C22semidirect
19. #11745300C22semidirect
20. C2×#90782C22semidirect
21. #11745292C22semidirect
22. C2×#90777C22semidirect
25. C2×D232C22semidirect
26. C2×#90772C22semidirect
27. C2×#90772C22semidirect
30. #11745257C22semidirect
34. C29×#106C22semidirect
35. C29×#102C22semidirect
36. #11745180C22semidirect
37. #11745169C22semidirect
38. #11745165C22semidirect
39. #11745157C22semidirect
40. #11745156C22semidirect
81. C8×D29D4semidirect
118. C8×C29C2×D4semidirect
120. #6597C2×D4semidirect
152. #469D29direct (N × H)
161. D29#469direct (N × H)
168. C2×D8C2×D29semidirect
173. C2×M16C2×D29semidirect
181. #121C2×D29semidirect
186. #106C2×D29semidirect
190. #102C2×D29semidirect
191. C29C2×#469semidirect
271. C8D4×D29semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D292
C2×M16×D292
#121×D292
#142714172
#142714162
#142714152
#142714142
#142714132
#106×D292
#102×D292
C29×#4692
C2×#46929