Finite Group Databasebeta

← D29×#496 #16829922

Subgroups — D29×#496 #16829922

Order 3712.

668 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 145 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×SD16×D29C212yesmaximal, complemented
2C2×D8×D29C212yesmaximal, complemented
3#127×D29C211yesmaximal, characteristic, complemented
4#124×D29C211yesmaximal, characteristic, complemented
5#14271553C211yesmaximal, characteristic, complemented
6#14271552C211yesmaximal, characteristic, complemented
7#14271551C212yesmaximal, complemented
8#14271550C211yesmaximal, characteristic, complemented
9#14271549C212yesmaximal, complemented
10#97×D29C211yesmaximal, characteristic, complemented
11C29×#496C211yesmaximal, characteristic, complemented
12C2×Q8×D29C2211yescharacteristic
13C2×D4×D29—22no—
14C2×D4×D29C2211yescharacteristic
15C2×D4×D29C2212yes—
16C2×SD16×C29C2212yescomplemented
17C2×D8×C29C2212yescomplemented
18C29×#127C2211yescharacteristic, complemented
19C29×#124C2211yescharacteristic, complemented
20#11745309C2211yescharacteristic, complemented
21C2×#90784C2212yescomplemented
22#11745302—22no—
23#11745302C2212yescomplemented
24#11745298C2211yescharacteristic, complemented
25C2×#90783C2212yescomplemented
26C2×#90782C2212yescomplemented
27C2×#90782C2212yescomplemented
28SD16×D29—28no—
29D8×D29—28no—
30C2×D232C2212yescomplemented
31C2×#90773C2212yescomplemented
32C2×C8×D29C2212yes—
33#11745247—22no—
34C22⋊C4×D29—22no—
35#11745237C2211yescharacteristic, complemented
36#11745236C2211yescharacteristic, complemented
37C42×D29C2211yescharacteristic
38C29×#97C2211yescharacteristic, complemented
39#11745163C2212yescomplemented
40#11745151C2211yescharacteristic, complemented
41C23×D29—22no—
42C23×D29—21no—
43C2×Q8×C29C2311yescharacteristic
44C2×D4×C29—22no—
45C2×D4×C29C2311yescharacteristic
46C2×D4×C29C2312yes—
47C2×C22⋊D29—22no—
48C2×C22⋊D29—24no—
49C2×C22⋊D29—21no—
50Q8×D29—24no—
51D4×D29—24no—
52D4×D29—24no—
53D4×D29—24no—
54D4×D29—48no—
55C2×D116—22no—
56C2×D116C2311yescharacteristic
57C2×D116C2312yes—
58C2×C4×D29—21no—
59C2×C4×D29D412yes—
60C2×C4×D29C2311yescharacteristic
61C2×Dic58—21no—
62C2×Dic58C2311yescharacteristic
63SD16×C29—24no—
64D8×C29—24no—
65C2×C8×C29C2312yes—
66C22⋊C4×C29—22no—
67C42×C29C2311yescharacteristic
68C22⋊Dic29—22no—
69#90784—24no—
70#90783—24no—
71#90782—24no—
72#90782—24no—
73#90781—22no—
74#90781—22no—
75C4×Dic29D412yes—
76C4×Dic29C2311yescharacteristic
77C2×#6597C2312yes—
78D232—24no—
79#90773—24no—
80C8×D29D418yescomplemented
81C23×C29—21no—
82C23×C29—22no—
83C22×D29—21no—
84C22×D29—22no—
85C22×D29—42no—
86C22×D29—44no—
87C22×D29—48no—
88C22×D29—44no—
89C22×D29C2×D411yescharacteristic
90Q8×C29—22no—
91D4×C29—22no—
92D4×C29—22no—
93D4×C29—22no—
94D4×C29—44no—
95C2×C4×C29—21no—
96C2×C4×C29C2×D412yes—
97C2×C4×C29C2411yescharacteristic
98C22⋊D29—48no—
99C22⋊D29—42no—
100C22⋊D29—44no—
101C2×Dic29—21no—
102C2×Dic29C2×D412yes—
103C2×Dic29C2×D411yescharacteristic
104D116—22no—
105D116—22no—
106D116—22no—
107D116—44no—
108C4×D29—24no—
109C4×D29—42no—
110C4×D29C2×D414yes—
111Dic58—22no—
112Dic58—42no—
113C8×C29C2×D414yescomplemented
114#6597C2×D414yescomplemented
115C2×#496—291nomaximal, Sylow
116C22×C29—41no—
117C22×C29—42no—
118C22×C29—44no—
119C22×C29—42no—
120C22×C29C22×D411yescharacteristic
121C2×D29—42no—
122C2×D29—41no—
123C2×D29—44no—
124C2×D29—42no—
125C2×D29—88no—
126C2×D29—84no—
127C2×D29#12712yes—
128C2×D29AGL(1,ℤ/8)14yes—
129C4×C29—22no—
130C4×C29—41no—
131C4×C29C22×D412yes—
132Dic29—22no—
133Dic29—41no—
134Dic29#12712yes—
135C22×SD16—292no—
136C22×D8—292no—
137C2×#127—291no—
138C2×#124—291no—
139#496—292no—
140#496—292no—
141#496—291no—
142#496—291no—
143#496—291no—
144#496D2911yescharacteristic, direct product factor
145C2×#97—291no—
146C2×C29—82no—
147C2×C29—81no—
148C2×C29C2×#12711yescharacteristic
149C2×C29C2×AGL(1,ℤ/8)12yes—
150D29—82no—
151D29—81no—
152D29#49614yesdirect product factor
153C22×Q8—291no—
154C22×D4—291no—
155C22×D4—292no—
156C22×D4—582no—
157C2×SD16—292no—
158C2×SD16—292no—
159C2×SD16—292no—
160C2×SD16—588no—
161C2×SD16C2×D2912yescomplemented
162C2×D8—292no—
163C2×D8—292no—
164C2×D8—292no—
165C2×D8—588no—
166C2×D8C2×D2912yescomplemented
167C22×C8—292no—
168#127—292no—
169#127—291no—
170#127—582no—
171#127C2×D2911yescharacteristic, complemented
172#124—291no—
173#124—291no—
174#124—291no—
175#124—582no—
176#124C2×D2911yescharacteristic, complemented
177C2×C22⋊C4—582no—
178C2×C42—291no—
179#97—292no—
180#97—291no—
181#97C2×D2911yescharacteristic, complemented
182C29C2×#49611yescharacteristic, complemented, Sylow
183C24—581no—
184C24—582no—
185C2×Q8—291no—
186C2×Q8—581no—
187C2×Q8—584no—
188C2×Q8C22×D2911yescharacteristic
189C2×D4—22no—
190C2×D4—291no—
191C2×D4—292no—
192C2×D4—584no—
193C2×D4—584no—
194C2×D4—584no—
195C2×D4—581no—
196C2×D4—584no—
197C2×D4—582no—
198C2×D4—582no—
199C2×D4—1168no—
200C2×D4C22×D2911yescharacteristic
201C2×D4C22×D2912yes—
202C22×C4—291no—
203C22×C4—292no—
204C22×C4—581no—
205SD16—24no—
206SD16—584no—
207SD16—584no—
208SD16—584no—
209D8—24no—
210D8—584no—
211D8—584no—
212D8—584no—
213C2×C8—292no—
214C2×C8—298no—
215C2×C8C22×D2912yes—
216C22⋊C4—22no—
217C22⋊C4—582no—
218C22⋊C4—582no—
219C22⋊C4—582no—
220C42—292no—
221C42—291no—
222C42C22×D2911yescharacteristic
223C23—21no—
224C23—22no—
225C23—291no—
226C23—581no—
227C23—582no—
228C23—1162no—
229C23—1164no—
230C23—1168no—
231C23—1164no—
232Q8—22no—
233Q8—582no—
234Q8—1162no—
235D4—22no—
236D4—22no—
237D4—22no—
238D4—44no—
239D4—582no—
240D4—582no—
241D4—582no—
242D4—1164no—
243D4—1162no—
244D4—1164no—
245D4—1168no—
246C2×C4—21no—
247C2×C4—291no—
248C2×C4—294no—
249C2×C4—292no—
250C2×C4—584no—
251C2×C4—581no—
252C2×C4—1162no—
253C2×C4D4×D2912yes—
254C2×C4C23×D2911yescharacteristic
255C8—294no—
256C8D4×D2914yescomplemented
257C22—44no—
258C22—42no—
259C22—41no—
260C22—42no—
261C22—294no—
262C22—292no—
263C22—1164no—
264C22—1162no—
265C22—1161no—
266C22—1162no—
267C22—2328no—
268C22—2324no—
269C22C2×D4×D2911yescharacteristic
270C4—22no—
271C4—41no—
272C4—292no—
273C4—582no—
274C4—1161no—
275C4C2×D4×D2912yes—
276C2—82no—
277C2—81no—
278C2—294no—
279C2—2322no—
280C2—2321no—
281C2#127×D2911yescharacteristic
282C2AGL(1,ℤ/8)×D2912yes—
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#496C2
socleC22×C29C22×D4
hypercenter#496D29
hypocenterC29C2×#496
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D29C2semidirect
2. C2×D8×D29C2semidirect
3. #127×D29C2semidirect
4. #124×D29C2semidirect
5. #14271553C2semidirect
6. #14271552C2semidirect
7. #14271551C2semidirect
8. #14271550C2semidirect
9. #14271549C2semidirect
10. #97×D29C2semidirect
11. C29×#496C2semidirect
16. C2×SD16×C29C22semidirect
17. C2×D8×C29C22semidirect
18. C29×#127C22semidirect
19. C29×#124C22semidirect
20. #11745309C22semidirect
21. C2×#90784C22semidirect
23. #11745302C22semidirect
24. #11745298C22semidirect
25. C2×#90783C22semidirect
26. C2×#90782C22semidirect
27. C2×#90782C22semidirect
30. C2×D232C22semidirect
31. C2×#90773C22semidirect
35. #11745237C22semidirect
36. #11745236C22semidirect
38. C29×#97C22semidirect
39. #11745163C22semidirect
40. #11745151C22semidirect
80. C8×D29D4semidirect
113. C8×C29C2×D4semidirect
114. #6597C2×D4semidirect
144. #496D29direct (N × H)
152. D29#496direct (N × H)
161. C2×SD16C2×D29semidirect
166. C2×D8C2×D29semidirect
171. #127C2×D29semidirect
176. #124C2×D29semidirect
181. #97C2×D29semidirect
182. C29C2×#496semidirect
256. C8D4×D29semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D292
C2×D8×D292
#127×D292
#124×D292
#142715532
#142715522
#142715512
#142715502
#142715492
#97×D292
C29×#4962
C2×#49629