Finite Group Databasebeta

← D29×#483 #16829366

Subgroups — D29×#483 #16829366

Order 3712.

460 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 460 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
1C22⋊Q8×D29C211yesmaximal, characteristic
2C2×C4⋊C4×D29C211yesmaximal, characteristic
3#14271495C212yesmaximal, complemented
4#14271494C211yesmaximal, characteristic, complemented
5#14271493C211yesmaximal, characteristic, complemented
6#14271492C212yesmaximal, complemented
7#14271491C211yesmaximal, characteristic, complemented
8#106×D29C212yesmaximal, complemented
9#103×D29C212yesmaximal, complemented
10C22⋊C8×D29C211yesmaximal, characteristic
11C29×#483C211yesmaximal, characteristic, complemented
12C2×Q8×D29C2211yescharacteristic
13C22×C4×D29—21no—
14C22×C4×D29C2211yescharacteristic
15C29×C22⋊Q8C2211yescharacteristic
16C2×C4⋊C4×C29C2211yescharacteristic
17#11745308C2211yescharacteristic
18C2×C4⋊Dic29C2211yescharacteristic
19#11745286C2211yescharacteristic
20C2×#90779—21no—
21C2×C8×D29C2212yes—
22#11745259C2211yescharacteristic
23#11745258—21no—
24C4⋊C4×D29—21no—
25C4⋊C4×D29—21no—
26C4⋊C4×D29—21no—
27C4⋊C4×D29C2212yes—
28C4⋊C4×D29C2212yes—
29C4⋊C4×D29C2211yescharacteristic
30C22⋊C4×D29—21no—
31#11745240—21no—
32C29×#106C2212yescomplemented
33C29×#103C2212yescomplemented
34C29×C22⋊C8C2211yescharacteristic
35#11745183C2212yescomplemented
36C22⋊#6597C2211yescharacteristic
37#11745168C2212yes—
38#11745165C2212yescomplemented
39#11745164C2212yescomplemented
40#11745158C2212yescomplemented
41#11745156C2212yescomplemented
42#11745156C2212yescomplemented
43C23×D29D411yescharacteristic
44C2×Q8×C29C2311yescharacteristic
45C22×C4×C29—21no—
46C22×C4×C29C2311yescharacteristic
47C22×Dic29—21no—
48C22×Dic29D411yescharacteristic
49Q8×D29—24no—
50C2×C4×D29—24no—
51C2×C4×D29—22no—
52C2×C4×D29—22no—
53C2×C4×D29—21no—
54C2×C4×D29—21no—
55C2×C4×D29—44no—
56C2×C4×D29D411yescharacteristic
57C2×C4×D29D411yescharacteristic
58C2×C4×D29C2311yescharacteristic
59C2×C4×D29C2311yescharacteristic
60C2×Dic58—21no—
61C2×Dic58C2311yescharacteristic
62C2×C8×C29C2312yes—
63C4⋊C4×C29—21no—
64C4⋊C4×C29—21no—
65C4⋊C4×C29C2312yes—
66C4⋊C4×C29C2311yescharacteristic
67C22⋊C4×C29—21no—
68C22⋊Dic29—21no—
69#90781—21no—
70#90781—21no—
71C4⋊Dic29—21no—
72C4⋊Dic29—21no—
73C4⋊Dic29C2311yescharacteristic
74C4⋊Dic29C2312yes—
75#90779—21no—
76#90779—22no—
77#90779—22no—
78#90779—21no—
79#90779—21no—
80C2×#6597C2312yes—
81C8×D29—24no—
82C23×C29C2×D411yescharacteristic
83C22×D29—22no—
84C22×D29—22no—
85C22×D29SD1614yes—
86C22×D29C2×D411yescharacteristic
87C22×D29C2×D411yescharacteristic
88Q8×C29—22no—
89C2×C4×C29—22no—
90C2×C4×C29—22no—
91C2×C4×C29—21no—
92C2×C4×C29—21no—
93C2×C4×C29—42no—
94C2×C4×C29C2×D411yescharacteristic
95C2×C4×C29C2411yescharacteristic
96C2×Dic29—22no—
97C2×Dic29—21no—
98C2×Dic29—22no—
99C2×Dic29—21no—
100C2×Dic29—42no—
101C2×Dic29C2×D411yescharacteristic
102C2×Dic29C2×D411yescharacteristic
103C4×D29—22no—
104C4×D29—22no—
105C4×D29—22no—
106C4×D29—42no—
107C4×D29—44no—
108C4×D29—44no—
109C4×D29—42no—
110C4×D29#4114yes—
111Dic58—22no—
112Dic58—42no—
113C8×C29—22no—
114#6597—22no—
115C2×#483—291nomaximal, Sylow
116C22×C29—21no—
117C22×C29—21no—
118C22×C29C2×SD1612yes—
119C22×C29C22×D411yescharacteristic
120C2×D29—21no—
121C2×D29—21no—
122C2×D29—28no—
123C2×D29#12312yes—
124C2×D29C2×SD1612yes—
125C2×D29C2×SD1612yes—
126C2×D29#13712yes—
127C4×C29—21no—
128C4×C29—41no—
129C4×C29—42no—
130C4×C29—41no—
131C4×C29C2×#4112yes—
132Dic29—21no—
133Dic29—41no—
134Dic29—42no—
135Dic29—41no—
136Dic29#12312yes—
137C2×C22⋊Q8—291no—
138C22×C4⋊C4—291no—
139#483—291no—
140#483—291no—
141#483—292no—
142#483—292no—
143#483—291no—
144#483D2911yescharacteristic, direct product factor
145C2×#106—292no—
146C2×#103—292no—
147C2×C22⋊C8—291no—
148C2×C29—22no—
149C2×C29C2×#12311yescharacteristic
150C2×C29C22×SD1611yescharacteristic
151C2×C29C2×#13711yescharacteristic
152D29—22no—
153D29#48314yesdirect product factor
154C22×Q8—291no—
155C23×C4—291no—
156C23×C4—581no—
157C22×C8—292no—
158C22⋊Q8—291no—
159C22⋊Q8—291no—
160C22⋊Q8—291no—
161C22⋊Q8—581no—
162C22⋊Q8—581no—
163C22⋊Q8C2×D2911yescharacteristic
164C2×C4⋊C4—291no—
165C2×C4⋊C4—292no—
166C2×C4⋊C4—292no—
167C2×C4⋊C4—291no—
168C2×C4⋊C4—581no—
169C2×C4⋊C4—581no—
170C2×C4⋊C4—581no—
171C2×C4⋊C4—581no—
172C2×C4⋊C4C2×D2911yescharacteristic
173C2×C22⋊C4—581no—
174#106—292no—
175#106—292no—
176#106—292no—
177#106C2×D2912yescomplemented
178#103—292no—
179#103—292no—
180#103—292no—
181#103C2×D2912yescomplemented
182C22⋊C8—291no—
183C22⋊C8—292no—
184C22⋊C8C2×D2911yescharacteristic
185C29C2×#48311yescharacteristic, complemented, Sylow
186C24—291no—
187C2×Q8—291no—
188C2×Q8—581no—
189C2×Q8—584no—
190C2×Q8C22×D2911yescharacteristic
191C22×C4—21no—
192C22×C4—291no—
193C22×C4—291no—
194C22×C4—291no—
195C22×C4—291no—
196C22×C4—291no—
197C22×C4—584no—
198C22×C4—581no—
199C22×C4—581no—
200C22×C4—582no—
201C22×C4—582no—
202C22×C4—581no—
203C22×C4—1164no—
204C22×C4C22×D2911yescharacteristic
205C2×C8—292no—
206C2×C8—584no—
207C2×C8C22×D2912yes—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—292no—
211C4⋊C4—291no—
212C4⋊C4—582no—
213C4⋊C4—582no—
214C4⋊C4—581no—
215C4⋊C4—581no—
216C4⋊C4—581no—
217C4⋊C4—581no—
218C4⋊C4—581no—
219C4⋊C4C22×D2912yes—
220C4⋊C4C22×D2911yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—581no—
223C22⋊C4—581no—
224C22⋊C4—581no—
225C23—291no—
226C23—291no—
227C23—294no—
228C23—582no—
229C23—582no—
230C23D4×D2911yescharacteristic
231Q8—22no—
232Q8—582no—
233Q8—1162no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—291no—
240C2×C4—294no—
241C2×C4—291no—
242C2×C4—582no—
243C2×C4—582no—
244C2×C4—582no—
245C2×C4—582no—
246C2×C4—581no—
247C2×C4—581no—
248C2×C4—582no—
249C2×C4—1164no—
250C2×C4—1164no—
251C2×C4—1162no—
252C2×C4—1162no—
253C2×C4—1162no—
254C2×C4D4×D2911yescharacteristic
255C2×C4C23×D2911yescharacteristic
256C8—22no—
257C8—582no—
258C22—21no—
259C22—21no—
260C22—292no—
261C22—292no—
262C22—292no—
263C22—292no—
264C22—588no—
265C22—581no—
266C22—581no—
267C22SD16×D2912yes—
268C22C2×D4×D2911yescharacteristic
269C4—21no—
270C4—41no—
271C4—42no—
272C4—41no—
273C4—292no—
274C4—581no—
275C4—1161no—
276C4—1162no—
277C4—1161no—
278C4#41×D2912yes—
279C2—22no—
280C2—294no—
281C2—582no—
282C2#123×D2911yescharacteristic
283C2C2×SD16×D2911yescharacteristic
284C2#137×D2911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#483C2
socleC22×C29C22×D4
prime radicalC23×D29D4
hypercenter#483D29
hypocenterC29C2×#483
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #14271495C2semidirect
4. #14271494C2semidirect
5. #14271493C2semidirect
6. #14271492C2semidirect
7. #14271491C2semidirect
8. #106×D29C2semidirect
9. #103×D29C2semidirect
11. C29×#483C2semidirect
32. C29×#106C22semidirect
33. C29×#103C22semidirect
35. #11745183C22semidirect
38. #11745165C22semidirect
39. #11745164C22semidirect
40. #11745158C22semidirect
41. #11745156C22semidirect
42. #11745156C22semidirect
144. #483D29direct (N × H)
153. D29#483direct (N × H)
177. #106C2×D29semidirect
181. #103C2×D29semidirect
185. C29C2×#483semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D292
C2×C4⋊C4×D292
#142714952
#142714942
#142714932
#142714922
#142714912
#106×D292
#103×D292
C22⋊C8×D292
C29×#4832
C2×#48329