Finite Group Databasebeta

← D29×#481 #16829388

Subgroups — D29×#481 #16829388

Order 3712.

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

normal subgroups only

This group has 512 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
1#121×D29C211yesmaximal, characteristic
2C2×C4⋊C4×D29C211yesmaximal, characteristic, complemented
3#14271483C212yesmaximal, complemented
4#14271482C211yesmaximal, characteristic, complemented
5#14271481C211yesmaximal, characteristic, complemented
6#14271480C212yesmaximal, complemented
7#14271479C211yesmaximal, characteristic, complemented
8#106×D29C212yesmaximal, complemented
9#102×D29C212yesmaximal, complemented
10C22⋊C8×D29C211yesmaximal, characteristic, complemented
11C29×#481C211yesmaximal, characteristic, complemented
12C2×D4×D29—21no—
13C2×D4×D29C2211yescharacteristic
14C22×C4×D29—21no—
15C22×C4×D29C2211yescharacteristic
16C29×#121C2211yescharacteristic
17C2×C4⋊C4×C29C2211yescharacteristic, complemented
18#11745301—21no—
19#11745300C2211yescharacteristic
20#11745292C2211yescharacteristic
21C2×C4⋊Dic29C2211yescharacteristic, complemented
22C2×#90779—21no—
23C2×C8×D29C2212yes—
24#11745257C2211yescharacteristic
25C4⋊C4×D29—21no—
26C4⋊C4×D29—21no—
27C4⋊C4×D29C2212yes—
28C4⋊C4×D29C2211yescharacteristic
29C4⋊C4×D29C2212yescomplemented
30#11745246—21no—
31C22⋊C4×D29—21no—
32C29×#106C2212yescomplemented
33C29×#102C2212yescomplemented
34C29×C22⋊C8C2211yescharacteristic, complemented
35#11745180C2212yescomplemented
36C22⋊#6597C2211yescharacteristic, complemented
37#11745169C2212yescomplemented
38#11745168C2212yescomplemented
39#11745165C2212yescomplemented
40#11745157C2212yescomplemented
41#11745156C2212yescomplemented
42#11745156C2212yescomplemented
43C23×D29—21no—
44C23×D29D411yescharacteristic
45C2×D4×C29—21no—
46C2×D4×C29C2311yescharacteristic
47C22×C4×C29—21no—
48C22×C4×C29C2311yescharacteristic
49C2×C22⋊D29—21no—
50C2×C22⋊D29—21no—
51C2×C22⋊D29—21no—
52C22×Dic29—21no—
53C22×Dic29D411yescharacteristic
54D4×D29—24no—
55D4×D29—44no—
56C2×D116—21no—
57C2×D116C2311yescharacteristic
58C2×C4×D29—24no—
59C2×C4×D29—22no—
60C2×C4×D29—22no—
61C2×C4×D29—21no—
62C2×C4×D29—44no—
63C2×C4×D29D411yescharacteristic
64C2×C4×D29D411yescharacteristic
65C2×C4×D29C2311yescharacteristic
66C2×C4×D29C2311yescharacteristic
67C2×C8×C29C2312yes—
68C4⋊C4×C29—21no—
69C4⋊C4×C29C2312yes—
70C4⋊C4×C29C2311yescharacteristic
71C22⋊C4×C29—21no—
72C22⋊Dic29—21no—
73#90781—21no—
74#90781—21no—
75C4⋊Dic29—21no—
76C4⋊Dic29C2312yes—
77C4⋊Dic29C2311yescharacteristic
78#90779—22no—
79#90779—22no—
80#90779—21no—
81C2×#6597C2312yes—
82C8×D29—24no—
83C23×C29—21no—
84C23×C29C2×D411yescharacteristic
85C22×D29—22no—
86C22×D29—22no—
87C22×D29—21no—
88C22×D29—42no—
89C22×D29—42no—
90C22×D29—42no—
91C22×D29SD1614yes—
92C22×D29C2×D411yescharacteristic
93C22×D29C2×D411yescharacteristic
94D4×C29—22no—
95D4×C29—42no—
96C2×C4×C29—22no—
97C2×C4×C29—22no—
98C2×C4×C29—21no—
99C2×C4×C29—42no—
100C2×C4×C29C2×D411yescharacteristic
101C2×C4×C29C2411yescharacteristic
102C22⋊D29—42no—
103C22⋊D29—42no—
104C22⋊D29—42no—
105C2×Dic29—22no—
106C2×Dic29—22no—
107C2×Dic29—21no—
108C2×Dic29—42no—
109C2×Dic29C2×D411yescharacteristic
110C2×Dic29C2×D411yescharacteristic
111D116—22no—
112D116—42no—
113C4×D29—22no—
114C4×D29—22no—
115C4×D29—22no—
116C4×D29—44no—
117C4×D29—42no—
118C4×D29—44no—
119C4×D29#4114yes—
120C8×C29—22no—
121#6597—22no—
122C2×#481—291nomaximal, Sylow
123C22×C29—21no—
124C22×C29—21no—
125C22×C29—41no—
126C22×C29—41no—
127C22×C29—41no—
128C22×C29C2×SD1612yes—
129C22×C29C22×D411yescharacteristic
130C2×D29—21no—
131C2×D29—21no—
132C2×D29—28no—
133C2×D29—41no—
134C2×D29—41no—
135C2×D29—41no—
136C2×D29—84no—
137C2×D29#12312yes—
138C2×D29C2×SD1612yes—
139C2×D29C2×SD1612yes—
140C2×D29AGL(1,ℤ/8)12yes—
141C4×C29—21no—
142C4×C29—41no—
143C4×C29—42no—
144C4×C29C2×#4112yes—
145Dic29—21no—
146Dic29—41no—
147Dic29—42no—
148Dic29#12312yes—
149C2×#121—291no—
150C22×C4⋊C4—291no—
151#481—291no—
152#481—291no—
153#481—292no—
154#481—292no—
155#481—291no—
156#481D2911yescharacteristic, direct product factor
157C2×#106—292no—
158C2×#102—292no—
159C2×C22⋊C8—291no—
160C2×C29—22no—
161C2×C29—81no—
162C2×C29C2×#12311yescharacteristic
163C2×C29C22×SD1611yescharacteristic
164C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
165D29—22no—
166D29—81no—
167D29#48114yesdirect product factor
168C22×D4—291no—
169C22×D4—581no—
170C23×C4—291no—
171C23×C4—581no—
172C22×C8—292no—
173#121—291no—
174#121—291no—
175#121—291no—
176#121—581no—
177#121—581no—
178#121C2×D2911yescharacteristic
179C2×C4⋊C4—291no—
180C2×C4⋊C4—292no—
181C2×C4⋊C4—292no—
182C2×C4⋊C4—291no—
183C2×C4⋊C4—581no—
184C2×C4⋊C4—581no—
185C2×C4⋊C4—581no—
186C2×C4⋊C4C2×D2911yescharacteristic, complemented
187C2×C22⋊C4—581no—
188#106—292no—
189#106—292no—
190#106—292no—
191#106C2×D2912yescomplemented
192#102—292no—
193#102—292no—
194#102—292no—
195#102C2×D2912yescomplemented
196C22⋊C8—291no—
197C22⋊C8—292no—
198C22⋊C8C2×D2911yescharacteristic, complemented
199C29C2×#48111yescharacteristic, complemented, Sylow
200C24—291no—
201C24—581no—
202C2×D4—21no—
203C2×D4—291no—
204C2×D4—581no—
205C2×D4—584no—
206C2×D4—581no—
207C2×D4—581no—
208C2×D4—581no—
209C2×D4—1164no—
210C2×D4C22×D2911yescharacteristic
211C22×C4—21no—
212C22×C4—291no—
213C22×C4—291no—
214C22×C4—291no—
215C22×C4—291no—
216C22×C4—291no—
217C22×C4—584no—
218C22×C4—581no—
219C22×C4—582no—
220C22×C4—582no—
221C22×C4—581no—
222C22×C4—1164no—
223C22×C4C22×D2911yescharacteristic
224C2×C8—292no—
225C2×C8—584no—
226C2×C8C22×D2912yes—
227C4⋊C4—21no—
228C4⋊C4—292no—
229C4⋊C4—291no—
230C4⋊C4—582no—
231C4⋊C4—582no—
232C4⋊C4—581no—
233C4⋊C4—581no—
234C4⋊C4C22×D2912yes—
235C4⋊C4C22×D2911yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—581no—
238C22⋊C4—581no—
239C22⋊C4—581no—
240C23—21no—
241C23—291no—
242C23—291no—
243C23—294no—
244C23—582no—
245C23—582no—
246C23—581no—
247C23—1162no—
248C23—1162no—
249C23—1162no—
250C23D4×D2911yescharacteristic
251D4—22no—
252D4—42no—
253D4—582no—
254D4—1162no—
255D4—1162no—
256D4—1162no—
257D4—1162no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—291no—
263C2×C4—294no—
264C2×C4—291no—
265C2×C4—582no—
266C2×C4—582no—
267C2×C4—582no—
268C2×C4—582no—
269C2×C4—581no—
270C2×C4—582no—
271C2×C4—1164no—
272C2×C4—1162no—
273C2×C4—1164no—
274C2×C4—1162no—
275C2×C4D4×D2911yescharacteristic
276C2×C4C23×D2911yescharacteristic
277C8—22no—
278C8—582no—
279C22—21no—
280C22—21no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—292no—
285C22—292no—
286C22—292no—
287C22—292no—
288C22—588no—
289C22—581no—
290C22—581no—
291C22—1161no—
292C22—1161no—
293C22—1161no—
294C22—2324no—
295C22SD16×D2912yes—
296C22C2×D4×D2911yescharacteristic
297C4—21no—
298C4—41no—
299C4—42no—
300C4—292no—
301C4—581no—
302C4—1161no—
303C4—1162no—
304C4#41×D2912yes—
305C2—22no—
306C2—81no—
307C2—294no—
308C2—582no—
309C2—2321no—
310C2#123×D2911yescharacteristic
311C2C2×SD16×D2911yescharacteristic
312C2AGL(1,ℤ/8)×D2911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#481C2
socleC22×C29C22×D4
prime radical#121×D29C2
hypercenter#481D29
hypocenterC29C2×#481
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D29C2semidirect
3. #14271483C2semidirect
4. #14271482C2semidirect
5. #14271481C2semidirect
6. #14271480C2semidirect
7. #14271479C2semidirect
8. #106×D29C2semidirect
9. #102×D29C2semidirect
10. C22⋊C8×D29C2semidirect
11. C29×#481C2semidirect
17. C2×C4⋊C4×C29C22semidirect
21. C2×C4⋊Dic29C22semidirect
29. C4⋊C4×D29C22semidirect
32. C29×#106C22semidirect
33. C29×#102C22semidirect
34. C29×C22⋊C8C22semidirect
35. #11745180C22semidirect
36. C22⋊#6597C22semidirect
37. #11745169C22semidirect
38. #11745168C22semidirect
39. #11745165C22semidirect
40. #11745157C22semidirect
41. #11745156C22semidirect
42. #11745156C22semidirect
156. #481D29direct (N × H)
167. D29#481direct (N × H)
186. C2×C4⋊C4C2×D29semidirect
191. #106C2×D29semidirect
195. #102C2×D29semidirect
198. C22⋊C8C2×D29semidirect
199. C29C2×#481semidirect

Maximal subgroups

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

subgroupindex
#121×D292
C2×C4⋊C4×D292
#142714832
#142714822
#142714812
#142714802
#142714792
#106×D292
#102×D292
C22⋊C8×D292
C29×#4812
C2×#48129