Finite Group Databasebeta

← C29×#3484 #16817198

Subgroups — C29×#3484 #16817198

Order 3712.

1900 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2C23×D4×C29C211yesmaximal, characteristic, complemented
3C29×#546C218yesmaximal, complemented
4D42×C29C218yesmaximal, complemented
5C29×#535C212yesmaximal, complemented
6C29×#534C214yesmaximal, complemented
7C29×#525C212yesmaximal, complemented
8C2×C29×#120C214yesmaximal, complemented
9C29×#518C211yesmaximal, characteristic, complemented
10C25×C29C2212yescomplemented
11C29×H(5,𝔽2)—28no—
12C2×#41×C29C2212yescomplemented
13C2×#41×C29C2214yescomplemented
14C22×D4×C29—28no—
15C22×D4×C29C2211yescharacteristic
16C22×D4×C29C2212yescomplemented
17C22×D4×C29C2211yescharacteristic, complemented
18C22×D4×C29C2218yescomplemented
19C22×D4×C29C2214yescomplemented
20C22×D4×C29C2214yescomplemented
21C22×D4×C29C2218yescomplemented
22C23×C4×C29C2211yescharacteristic, complemented
23C29×#127C2214yescomplemented
24C29×#124C2214yescomplemented
25C29×#123C2214yescomplemented
26C29×#123C2218yescomplemented
27C29×C22⋊Q8C2214yescomplemented
28C29×#121C2214yescomplemented
29C29×#121C22116yescomplemented
30C29×#121C2218yescomplemented
31C29×#120C2214yescomplemented
32C29×#120C2218yescomplemented
33C29×#120C22116yescomplemented
34C29×#120C2218yescomplemented
35C4×D4×C29C2218yescomplemented
36C4×D4×C29C2218yescomplemented
37C29×#117C2212yescomplemented
38C2×C22⋊C4×C29C2214yescomplemented
39C2×C22⋊C4×C29C2218yescomplemented
40C24×C29—28no—
41C24×C29—48no—
42C24×C29C2311yescharacteristic
43C24×C29C2318yes—
44C24×C29C2312yes—
45C24×C29C2312yes—
46C24×C29C2314yescomplemented
47#41×C29—216no—
48#41×C29—28no—
49C2×Q8×C29C2312yescomplemented
50C2×D4×C29—28no—
51C2×D4×C29—216no—
52C2×D4×C29—232no—
53C2×D4×C29—216no—
54C2×D4×C29—24no—
55C2×D4×C29—416no—
56C2×D4×C29D418yescomplemented
57C2×D4×C29C2318yes—
58C2×D4×C29C2314yes—
59C2×D4×C29C2318yes—
60C2×D4×C29C2314yes—
61C2×D4×C29C2314yes—
62C2×D4×C29C2318yescomplemented
63C2×D4×C29C2312yescomplemented
64C2×D4×C29C23116yescomplemented
65C22×C4×C29—24no—
66C22×C4×C29C2314yes—
67C22×C4×C29C2311yescharacteristic
68C22×C4×C29C2311yescharacteristic
69C22×C4×C29C2314yescomplemented
70C22×C4×C29C2314yescomplemented
71C22×C4×C29C2318yescomplemented
72C4⋊C4×C29C2314yescomplemented
73C4⋊C4×C29C2318yescomplemented
74C22⋊C4×C29C2314yes—
75C22⋊C4×C29C2318yes—
76C22⋊C4×C29C2318yescomplemented
77C22⋊C4×C29C23116yescomplemented
78C22⋊C4×C29C2318yescomplemented
79C42×C29C2314yescomplemented
80C23×C29—22no—
81C23×C29—24no—
82C23×C29—216no—
83C23×C29—24no—
84C23×C29—216no—
85C23×C29—28no—
86C23×C29—44no—
87C23×C29—48no—
88C23×C29—44no—
89C23×C29—48no—
90C23×C29—432no—
91C23×C29C2×D418yescomplemented
92C23×C29C2414yes—
93C23×C29C2414yes—
94C23×C29C2411yescharacteristic
95C23×C29C2414yes—
96C23×C29C2412yes—
97Q8×C29—24no—
98D4×C29—216no—
99D4×C29—28no—
100D4×C29—216no—
101D4×C29—216no—
102D4×C29—28no—
103D4×C29—24no—
104D4×C29—416no—
105D4×C29C2×D4116yescomplemented
106C2×C4×C29—22no—
107C2×C4×C29—28no—
108C2×C4×C29—28no—
109C2×C4×C29—28no—
110C2×C4×C29—48no—
111C2×C4×C29C2×D414yescomplemented
112C2×C4×C29C2418yes—
113C2×C4×C29C2414yes—
114C2×C4×C29C2412yes—
115C2×C4×C29C2412yes—
116#3484C2911yesmaximal, characteristic, direct product factor, Sylow
117C22×C29—28no—
118C22×C29—22no—
119C22×C29—28no—
120C22×C29—22no—
121C22×C29—22no—
122C22×C29—24no—
123C22×C29—24no—
124C22×C29—28no—
125C22×C29—28no—
126C22×C29—48no—
127C22×C29—432no—
128C22×C29—48no—
129C22×C29—88no—
130C22×C29C22×D412yes—
131C22×C29C22×D418yes—
132C22×C29H(5,𝔽2)14yescomplemented
133C22×C29C2511yescharacteristic
134C4×C29—22no—
135C4×C29—24no—
136C4×C29—28no—
137C4×C29C22×D414yes—
138C2×H(5,𝔽2)C2×C2911yescharacteristic, complemented
139C23×D4C2×C2911yescharacteristic, complemented
140#546C2×C2918yescomplemented
141D42C2×C2918yescomplemented
142#535C2×C2912yescomplemented
143#534C2×C2914yescomplemented
144#525C2×C2912yescomplemented
145C2×#120C2×C2914yescomplemented
146#518C2×C2911yescharacteristic, complemented
147C2×C29—22no—
148C2×C29—24no—
149C2×C29—28no—
150C2×C29—44no—
151C2×C29—44no—
152C2×C29C23×D411yescharacteristic
153C2×C29C2×H(5,𝔽2)12yes—
154C25C22×C2912yescomplemented
155H(5,𝔽2)—28no—
156C2×#41C22×C2912yescomplemented
157C2×#41C22×C2914yescomplemented
158C22×D4—28no—
159C22×D4C22×C2911yescharacteristic
160C22×D4C22×C2912yescomplemented
161C22×D4C22×C2911yescharacteristic, complemented
162C22×D4C22×C2918yescomplemented
163C22×D4C22×C2914yescomplemented
164C22×D4C22×C2914yescomplemented
165C22×D4C22×C2918yescomplemented
166C23×C4C22×C2911yescharacteristic, complemented
167#127C22×C2914yescomplemented
168#124C22×C2914yescomplemented
169#123C22×C2914yescomplemented
170#123C22×C2918yescomplemented
171C22⋊Q8C22×C2914yescomplemented
172#121C22×C2914yescomplemented
173#121C22×C29116yescomplemented
174#121C22×C2918yescomplemented
175#120C22×C2914yescomplemented
176#120C22×C2918yescomplemented
177#120C22×C29116yescomplemented
178#120C22×C2918yescomplemented
179C4×D4C22×C2918yescomplemented
180C4×D4C22×C2918yescomplemented
181#117C22×C2912yescomplemented
182C2×C22⋊C4C22×C2914yescomplemented
183C2×C22⋊C4C22×C2918yescomplemented
184C29#348411yescharacteristic, direct product factor, Sylow
185C24—28no—
186C24—48no—
187C24C23×C2911yescharacteristic
188C24C23×C2918yes—
189C24C23×C2912yes—
190C24C23×C2912yes—
191C24C23×C2914yescomplemented
192#41—216no—
193#41—28no—
194C2×Q8C23×C2912yescomplemented
195C2×D4—28no—
196C2×D4—216no—
197C2×D4—232no—
198C2×D4—216no—
199C2×D4—24no—
200C2×D4—416no—
201C2×D4D4×C2918yescomplemented
202C2×D4C23×C2918yes—
203C2×D4C23×C2914yes—
204C2×D4C23×C2918yes—
205C2×D4C23×C2914yes—
206C2×D4C23×C2914yes—
207C2×D4C23×C2918yescomplemented
208C2×D4C23×C2912yescomplemented
209C2×D4C23×C29116yescomplemented
210C22×C4—24no—
211C22×C4C23×C2914yes—
212C22×C4C23×C2911yescharacteristic
213C22×C4C23×C2911yescharacteristic
214C22×C4C23×C2914yescomplemented
215C22×C4C23×C2914yescomplemented
216C22×C4C23×C2918yescomplemented
217C4⋊C4C23×C2914yescomplemented
218C4⋊C4C23×C2918yescomplemented
219C22⋊C4C23×C2914yes—
220C22⋊C4C23×C2918yes—
221C22⋊C4C23×C2918yescomplemented
222C22⋊C4C23×C29116yescomplemented
223C22⋊C4C23×C2918yescomplemented
224C42C23×C2914yescomplemented
225C23—22no—
226C23—24no—
227C23—216no—
228C23—24no—
229C23—216no—
230C23—28no—
231C23—44no—
232C23—48no—
233C23—44no—
234C23—48no—
235C23—432no—
236C23C2×D4×C2918yescomplemented
237C23C24×C2914yes—
238C23C24×C2914yes—
239C23C24×C2911yescharacteristic
240C23C24×C2914yes—
241C23C24×C2912yes—
242Q8—24no—
243D4—216no—
244D4—28no—
245D4—216no—
246D4—216no—
247D4—28no—
248D4—24no—
249D4—416no—
250D4C2×D4×C29116yescomplemented
251C2×C4—22no—
252C2×C4—28no—
253C2×C4—28no—
254C2×C4—28no—
255C2×C4—48no—
256C2×C4C2×D4×C2914yescomplemented
257C2×C4C24×C2918yes—
258C2×C4C24×C2914yes—
259C2×C4C24×C2912yes—
260C2×C4C24×C2912yes—
261C22—28no—
262C22—22no—
263C22—28no—
264C22—22no—
265C22—22no—
266C22—24no—
267C22—24no—
268C22—28no—
269C22—28no—
270C22—48no—
271C22—432no—
272C22—48no—
273C22—88no—
274C22C22×D4×C2912yes—
275C22C22×D4×C2918yes—
276C22C29×H(5,𝔽2)14yescomplemented
277C22C25×C2911yescharacteristic
278C4—22no—
279C4—24no—
280C4—28no—
281C4C22×D4×C2914yes—
282C2—22no—
283C2—24no—
284C2—28no—
285C2—44no—
286C2—44no—
287C2C23×D4×C2911yescharacteristic
288C2C2×C29×H(5,𝔽2)12yes—
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. C2×C29×H(5,𝔽2)C2semidirect
2. C23×D4×C29C2semidirect
3. C29×#546C2semidirect
4. D42×C29C2semidirect
5. C29×#535C2semidirect
6. C29×#534C2semidirect
7. C29×#525C2semidirect
8. C2×C29×#120C2semidirect
9. C29×#518C2semidirect
10. C25×C29C22semidirect
12. C2×#41×C29C22semidirect
13. C2×#41×C29C22semidirect
16. C22×D4×C29C22semidirect
17. C22×D4×C29C22semidirect
18. C22×D4×C29C22semidirect
19. C22×D4×C29C22semidirect
20. C22×D4×C29C22semidirect
21. C22×D4×C29C22semidirect
22. C23×C4×C29C22semidirect
23. C29×#127C22semidirect
24. C29×#124C22semidirect
25. C29×#123C22semidirect
26. C29×#123C22semidirect
27. C29×C22⋊Q8C22semidirect
28. C29×#121C22semidirect
29. C29×#121C22semidirect
30. C29×#121C22semidirect
31. C29×#120C22semidirect
32. C29×#120C22semidirect
33. C29×#120C22semidirect
34. C29×#120C22semidirect
35. C4×D4×C29C22semidirect
36. C4×D4×C29C22semidirect
37. C29×#117C22semidirect
38. C2×C22⋊C4×C29C22semidirect
39. C2×C22⋊C4×C29C22semidirect
46. C24×C29C23semidirect
49. C2×Q8×C29C23semidirect
56. C2×D4×C29D4semidirect
62. C2×D4×C29C23semidirect
63. C2×D4×C29C23semidirect
64. C2×D4×C29C23semidirect
69. C22×C4×C29C23semidirect
70. C22×C4×C29C23semidirect
71. C22×C4×C29C23semidirect
72. C4⋊C4×C29C23semidirect
73. C4⋊C4×C29C23semidirect
76. C22⋊C4×C29C23semidirect
77. C22⋊C4×C29C23semidirect
78. C22⋊C4×C29C23semidirect
79. C42×C29C23semidirect
91. C23×C29C2×D4semidirect
105. D4×C29C2×D4semidirect
111. C2×C4×C29C2×D4semidirect
116. #3484C29direct (N × H)
132. C22×C29H(5,𝔽2)semidirect
138. C2×H(5,𝔽2)C2×C29semidirect
139. C23×D4C2×C29semidirect
140. #546C2×C29semidirect
141. D42C2×C29semidirect
142. #535C2×C29semidirect
143. #534C2×C29semidirect
144. #525C2×C29semidirect
145. C2×#120C2×C29semidirect
146. #518C2×C29semidirect
154. C25C22×C29semidirect
156. C2×#41C22×C29semidirect
157. C2×#41C22×C29semidirect
160. C22×D4C22×C29semidirect
161. C22×D4C22×C29semidirect
162. C22×D4C22×C29semidirect
163. C22×D4C22×C29semidirect
164. C22×D4C22×C29semidirect
165. C22×D4C22×C29semidirect
166. C23×C4C22×C29semidirect
167. #127C22×C29semidirect
168. #124C22×C29semidirect
169. #123C22×C29semidirect
170. #123C22×C29semidirect
171. C22⋊Q8C22×C29semidirect
172. #121C22×C29semidirect
173. #121C22×C29semidirect
174. #121C22×C29semidirect
175. #120C22×C29semidirect
176. #120C22×C29semidirect
177. #120C22×C29semidirect
178. #120C22×C29semidirect
179. C4×D4C22×C29semidirect
180. C4×D4C22×C29semidirect
181. #117C22×C29semidirect
182. C2×C22⋊C4C22×C29semidirect
183. C2×C22⋊C4C22×C29semidirect
184. C29#3484direct (N × H)
191. C24C23×C29semidirect
194. C2×Q8C23×C29semidirect
201. C2×D4D4×C29semidirect
207. C2×D4C23×C29semidirect
208. C2×D4C23×C29semidirect
209. C2×D4C23×C29semidirect
214. C22×C4C23×C29semidirect
215. C22×C4C23×C29semidirect
216. C22×C4C23×C29semidirect
217. C4⋊C4C23×C29semidirect
218. C4⋊C4C23×C29semidirect
221. C22⋊C4C23×C29semidirect
222. C22⋊C4C23×C29semidirect
223. C22⋊C4C23×C29semidirect
224. C42C23×C29semidirect
236. C23C2×D4×C29semidirect
250. D4C2×D4×C29semidirect
256. C2×C4C2×D4×C29semidirect
276. C22C29×H(5,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C2×C29×H(5,𝔽2)2
C23×D4×C292
C29×#5462
D42×C292
C29×#5352
C29×#5342
C29×#5252
C2×C29×#1202
C29×#5182
#348429