Finite Group Databasebeta

← C29×#3532 #16817246

Subgroups — C29×#3532 #16817246

Order 3712.

1336 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×H(3,𝔽4)C211yesmaximal, characteristic, complemented
2C29×#560C213yesmaximal, complemented
3C29×#551C213yesmaximal, complemented
4C29×#546C216yesmaximal, complemented
5D42×C29C213yesmaximal, complemented
6C29×#538C216yesmaximal, complemented
7C29×#535C213yesmaximal, complemented
8C29×#534C213yesmaximal, complemented
9C2×C29×#120C213yesmaximal, complemented
10C25×C29C2211yescharacteristic, complemented
11C2×#41×C29C2213yescomplemented
12C22×D4×C29C2213yescomplemented
13C22×D4×C29C2216yescomplemented
14C22×D4×C29C2213yescomplemented
15C29×#127C2211yescharacteristic, complemented
16C29×#127C2213yescomplemented
17C29×#126C2212yescomplemented
18C29×#126C2216yescomplemented
19C29×#124C2213yescomplemented
20C29×#124C2213yescomplemented
21C29×#124C2216yescomplemented
22C29×#123C2213yescomplemented
23C29×#123C2213yescomplemented
24C29×#123C2216yescomplemented
25C29×#123C2216yescomplemented
26C29×C22⋊Q8C2216yescomplemented
27C29×#121C2216yescomplemented
28C29×#121C2216yescomplemented
29C29×#121C2216yescomplemented
30C29×#121C2216yescomplemented
31C29×#121C2216yescomplemented
32C29×#120C2213yes—
33C29×#120C2216yescomplemented
34C29×#120C2216yescomplemented
35C29×#120C2213yescomplemented
36C29×#120C2213yescomplemented
37C29×#120C2213yescomplemented
38C29×#120C2216yescomplemented
39C29×#120C2211yescharacteristic, complemented
40C29×#120C2213yescomplemented
41C4×D4×C29C2216yescomplemented
42C4×D4×C29C2216yescomplemented
43C29×#117C2213yescomplemented
44C2×C22⋊C4×C29C2213yescomplemented
45C2×C22⋊C4×C29C2216yescomplemented
46C2×C22⋊C4×C29C2213yescomplemented
47C24×C29—46no—
48C24×C29C2313yes—
49C24×C29C2313yes—
50C24×C29C2313yes—
51C24×C29C2311yescharacteristic
52C24×C29C2311yescharacteristic, complemented
53#41×C29—46no—
54C2×Q8×C29C2313yescomplemented
55C2×D4×C29—46no—
56C2×D4×C29—412no—
57C2×D4×C29—46no—
58C2×D4×C29C2316yes—
59C2×D4×C29C2316yes—
60C2×D4×C29C2313yes—
61C2×D4×C29C2313yes—
62C2×D4×C29C2316yes—
63C2×D4×C29C2313yes—
64C2×D4×C29C2316yes—
65C2×D4×C29C2313yes—
66C2×D4×C29C2313yescomplemented
67C2×D4×C29C2316yescomplemented
68C22×C4×C29C2313yes—
69C22×C4×C29C2316yes—
70C22×C4×C29C2316yescomplemented
71C22×C4×C29C2313yescomplemented
72C4⋊C4×C29C2316yescomplemented
73C4⋊C4×C29C2316yescomplemented
74C4⋊C4×C29C2316yescomplemented
75C22⋊C4×C29C2316yes—
76C22⋊C4×C29C2316yes—
77C22⋊C4×C29C2313yes—
78C22⋊C4×C29C2316yes—
79C22⋊C4×C29C2316yes—
80C22⋊C4×C29C2316yes—
81C22⋊C4×C29C2313yes—
82C22⋊C4×C29C2313yescomplemented
83C22⋊C4×C29C2313yescomplemented
84C22⋊C4×C29C2316yescomplemented
85C22⋊C4×C29C2316yescomplemented
86C42×C29C2311yescharacteristic, complemented
87C42×C29C2313yescomplemented
88C42×C29C2312yescomplemented
89C23×C29—212no—
90C23×C29—26no—
91C23×C29—26no—
92C23×C29—43no—
93C23×C29—46no—
94C23×C29—43no—
95C23×C29—46no—
96C23×C29—43no—
97C23×C29—416no—
98C23×C29C2413yes—
99C23×C29C2411yescharacteristic
100C23×C29C2413yes—
101C23×C29C2413yes—
102C23×C29C2413yes—
103Q8×C29—43no—
104D4×C29—212no—
105D4×C29—212no—
106D4×C29—43no—
107D4×C29—43no—
108D4×C29—43no—
109D4×C29—43no—
110D4×C29—46no—
111D4×C29—46no—
112D4×C29—46no—
113D4×C29—43no—
114C2×C4×C29—26no—
115C2×C4×C29—46no—
116C2×C4×C29—43no—
117C2×C4×C29—46no—
118C2×C4×C29C2413yes—
119C2×C4×C29C2416yes—
120C2×C4×C29C2416yes—
121C2×C4×C29C2413yes—
122#3532C2911yesmaximal, characteristic, direct product factor, Sylow
123C22×C29—26no—
124C22×C29—26no—
125C22×C29—23no—
126C22×C29—26no—
127C22×C29—23no—
128C22×C29—23no—
129C22×C29—26no—
130C22×C29—23no—
131C22×C29—412no—
132C22×C29—412no—
133C22×C29—44no—
134C22×C29—86no—
135C22×C29—82no—
136C22×C29H(5,𝔽2)16yes—
137C22×C29C2511yescharacteristic
138C4×C29—23no—
139C4×C29—23no—
140C4×C29—26no—
141C4×C29—26no—
142H(3,𝔽4)C2×C2911yescharacteristic, complemented
143#560C2×C2913yescomplemented
144#551C2×C2913yescomplemented
145#546C2×C2916yescomplemented
146D42C2×C2913yescomplemented
147#538C2×C2916yescomplemented
148#535C2×C2913yescomplemented
149#534C2×C2913yescomplemented
150C2×#120C2×C2913yescomplemented
151C2×C29—26no—
152C2×C29—43no—
153C2×C29—41no—
154C2×C29—43no—
155C2×C29—43no—
156C2×C29C2×H(5,𝔽2)13yes—
157C25C22×C2911yescharacteristic, complemented
158C2×#41C22×C2913yescomplemented
159C22×D4C22×C2913yescomplemented
160C22×D4C22×C2916yescomplemented
161C22×D4C22×C2913yescomplemented
162#127C22×C2911yescharacteristic, complemented
163#127C22×C2913yescomplemented
164#126C22×C2912yescomplemented
165#126C22×C2916yescomplemented
166#124C22×C2913yescomplemented
167#124C22×C2913yescomplemented
168#124C22×C2916yescomplemented
169#123C22×C2913yescomplemented
170#123C22×C2913yescomplemented
171#123C22×C2916yescomplemented
172#123C22×C2916yescomplemented
173C22⋊Q8C22×C2916yescomplemented
174#121C22×C2916yescomplemented
175#121C22×C2916yescomplemented
176#121C22×C2916yescomplemented
177#121C22×C2916yescomplemented
178#121C22×C2916yescomplemented
179#120C22×C2913yes—
180#120C22×C2916yescomplemented
181#120C22×C2916yescomplemented
182#120C22×C2913yescomplemented
183#120C22×C2913yescomplemented
184#120C22×C2913yescomplemented
185#120C22×C2916yescomplemented
186#120C22×C2911yescharacteristic, complemented
187#120C22×C2913yescomplemented
188C4×D4C22×C2916yescomplemented
189C4×D4C22×C2916yescomplemented
190#117C22×C2913yescomplemented
191C2×C22⋊C4C22×C2913yescomplemented
192C2×C22⋊C4C22×C2916yescomplemented
193C2×C22⋊C4C22×C2913yescomplemented
194C29#353211yescharacteristic, direct product factor, Sylow
195C24—46no—
196C24C23×C2913yes—
197C24C23×C2913yes—
198C24C23×C2913yes—
199C24C23×C2911yescharacteristic
200C24C23×C2911yescharacteristic, complemented
201#41—46no—
202C2×Q8C23×C2913yescomplemented
203C2×D4—46no—
204C2×D4—412no—
205C2×D4—46no—
206C2×D4C23×C2916yes—
207C2×D4C23×C2916yes—
208C2×D4C23×C2913yes—
209C2×D4C23×C2913yes—
210C2×D4C23×C2916yes—
211C2×D4C23×C2913yes—
212C2×D4C23×C2916yes—
213C2×D4C23×C2913yes—
214C2×D4C23×C2913yescomplemented
215C2×D4C23×C2916yescomplemented
216C22×C4C23×C2913yes—
217C22×C4C23×C2916yes—
218C22×C4C23×C2916yescomplemented
219C22×C4C23×C2913yescomplemented
220C4⋊C4C23×C2916yescomplemented
221C4⋊C4C23×C2916yescomplemented
222C4⋊C4C23×C2916yescomplemented
223C22⋊C4C23×C2916yes—
224C22⋊C4C23×C2916yes—
225C22⋊C4C23×C2913yes—
226C22⋊C4C23×C2916yes—
227C22⋊C4C23×C2916yes—
228C22⋊C4C23×C2916yes—
229C22⋊C4C23×C2913yes—
230C22⋊C4C23×C2913yescomplemented
231C22⋊C4C23×C2913yescomplemented
232C22⋊C4C23×C2916yescomplemented
233C22⋊C4C23×C2916yescomplemented
234C42C23×C2911yescharacteristic, complemented
235C42C23×C2913yescomplemented
236C42C23×C2912yescomplemented
237C23—212no—
238C23—26no—
239C23—26no—
240C23—43no—
241C23—46no—
242C23—43no—
243C23—46no—
244C23—43no—
245C23—416no—
246C23C24×C2913yes—
247C23C24×C2911yescharacteristic
248C23C24×C2913yes—
249C23C24×C2913yes—
250C23C24×C2913yes—
251Q8—43no—
252D4—212no—
253D4—212no—
254D4—43no—
255D4—43no—
256D4—43no—
257D4—43no—
258D4—46no—
259D4—46no—
260D4—46no—
261D4—43no—
262C2×C4—26no—
263C2×C4—46no—
264C2×C4—43no—
265C2×C4—46no—
266C2×C4C24×C2913yes—
267C2×C4C24×C2916yes—
268C2×C4C24×C2916yes—
269C2×C4C24×C2913yes—
270C22—26no—
271C22—26no—
272C22—23no—
273C22—26no—
274C22—23no—
275C22—23no—
276C22—26no—
277C22—23no—
278C22—412no—
279C22—412no—
280C22—44no—
281C22—86no—
282C22—82no—
283C22C29×H(5,𝔽2)16yes—
284C22C25×C2911yescharacteristic
285C4—23no—
286C4—23no—
287C4—26no—
288C4—26no—
289C2—26no—
290C2—43no—
291C2—41no—
292C2—43no—
293C2—43no—
294C2C2×C29×H(5,𝔽2)13yes—
subgroupG/H
center, socleC22×C29C25
commutator, Frattini, cosocleC22C25×C29
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×H(3,𝔽4)C2semidirect
2. C29×#560C2semidirect
3. C29×#551C2semidirect
4. C29×#546C2semidirect
5. D42×C29C2semidirect
6. C29×#538C2semidirect
7. C29×#535C2semidirect
8. C29×#534C2semidirect
9. C2×C29×#120C2semidirect
10. C25×C29C22semidirect
11. C2×#41×C29C22semidirect
12. C22×D4×C29C22semidirect
13. C22×D4×C29C22semidirect
14. C22×D4×C29C22semidirect
15. C29×#127C22semidirect
16. C29×#127C22semidirect
17. C29×#126C22semidirect
18. C29×#126C22semidirect
19. C29×#124C22semidirect
20. C29×#124C22semidirect
21. C29×#124C22semidirect
22. C29×#123C22semidirect
23. C29×#123C22semidirect
24. C29×#123C22semidirect
25. C29×#123C22semidirect
26. C29×C22⋊Q8C22semidirect
27. C29×#121C22semidirect
28. C29×#121C22semidirect
29. C29×#121C22semidirect
30. C29×#121C22semidirect
31. C29×#121C22semidirect
33. C29×#120C22semidirect
34. C29×#120C22semidirect
35. C29×#120C22semidirect
36. C29×#120C22semidirect
37. C29×#120C22semidirect
38. C29×#120C22semidirect
39. C29×#120C22semidirect
40. C29×#120C22semidirect
41. C4×D4×C29C22semidirect
42. C4×D4×C29C22semidirect
43. C29×#117C22semidirect
44. C2×C22⋊C4×C29C22semidirect
45. C2×C22⋊C4×C29C22semidirect
46. C2×C22⋊C4×C29C22semidirect
52. C24×C29C23semidirect
54. C2×Q8×C29C23semidirect
66. C2×D4×C29C23semidirect
67. C2×D4×C29C23semidirect
70. C22×C4×C29C23semidirect
71. C22×C4×C29C23semidirect
72. C4⋊C4×C29C23semidirect
73. C4⋊C4×C29C23semidirect
74. C4⋊C4×C29C23semidirect
82. C22⋊C4×C29C23semidirect
83. C22⋊C4×C29C23semidirect
84. C22⋊C4×C29C23semidirect
85. C22⋊C4×C29C23semidirect
86. C42×C29C23semidirect
87. C42×C29C23semidirect
88. C42×C29C23semidirect
122. #3532C29direct (N × H)
142. H(3,𝔽4)C2×C29semidirect
143. #560C2×C29semidirect
144. #551C2×C29semidirect
145. #546C2×C29semidirect
146. D42C2×C29semidirect
147. #538C2×C29semidirect
148. #535C2×C29semidirect
149. #534C2×C29semidirect
150. C2×#120C2×C29semidirect
157. C25C22×C29semidirect
158. C2×#41C22×C29semidirect
159. C22×D4C22×C29semidirect
160. C22×D4C22×C29semidirect
161. C22×D4C22×C29semidirect
162. #127C22×C29semidirect
163. #127C22×C29semidirect
164. #126C22×C29semidirect
165. #126C22×C29semidirect
166. #124C22×C29semidirect
167. #124C22×C29semidirect
168. #124C22×C29semidirect
169. #123C22×C29semidirect
170. #123C22×C29semidirect
171. #123C22×C29semidirect
172. #123C22×C29semidirect
173. C22⋊Q8C22×C29semidirect
174. #121C22×C29semidirect
175. #121C22×C29semidirect
176. #121C22×C29semidirect
177. #121C22×C29semidirect
178. #121C22×C29semidirect
180. #120C22×C29semidirect
181. #120C22×C29semidirect
182. #120C22×C29semidirect
183. #120C22×C29semidirect
184. #120C22×C29semidirect
185. #120C22×C29semidirect
186. #120C22×C29semidirect
187. #120C22×C29semidirect
188. C4×D4C22×C29semidirect
189. C4×D4C22×C29semidirect
190. #117C22×C29semidirect
191. C2×C22⋊C4C22×C29semidirect
192. C2×C22⋊C4C22×C29semidirect
193. C2×C22⋊C4C22×C29semidirect
194. C29#3532direct (N × H)
200. C24C23×C29semidirect
202. C2×Q8C23×C29semidirect
214. C2×D4C23×C29semidirect
215. C2×D4C23×C29semidirect
218. C22×C4C23×C29semidirect
219. C22×C4C23×C29semidirect
220. C4⋊C4C23×C29semidirect
221. C4⋊C4C23×C29semidirect
222. C4⋊C4C23×C29semidirect
230. C22⋊C4C23×C29semidirect
231. C22⋊C4C23×C29semidirect
232. C22⋊C4C23×C29semidirect
233. C22⋊C4C23×C29semidirect
234. C42C23×C29semidirect
235. C42C23×C29semidirect
236. C42C23×C29semidirect

Maximal subgroups

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

subgroupindex
C29×H(3,𝔽4)2
C29×#5602
C29×#5512
C29×#5462
D42×C292
C29×#5382
C29×#5352
C29×#5342
C2×C29×#1202
#353229