Finite Group Databasebeta

← #3484×C181 #37531427

Subgroups — #3484×C181 #37531427

Order 23168.

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×H(5,𝔽2)×C181C211yesmaximal, characteristic, complemented
2C23×D4×C181C211yesmaximal, characteristic, complemented
3#546×C181C218yesmaximal, complemented
4D42×C181C218yesmaximal, complemented
5#535×C181C212yesmaximal, complemented
6#534×C181C214yesmaximal, complemented
7#525×C181C212yesmaximal, complemented
8C2×#120×C181C214yesmaximal, complemented
9#518×C181C211yesmaximal, characteristic, complemented
10C25×C181C2212yescomplemented
11H(5,𝔽2)×C181—28no—
12C2×#41×C181C2212yescomplemented
13C2×#41×C181C2214yescomplemented
14C22×D4×C181—28no—
15C22×D4×C181C2211yescharacteristic
16C22×D4×C181C2212yescomplemented
17C22×D4×C181C2211yescharacteristic, complemented
18C22×D4×C181C2218yescomplemented
19C22×D4×C181C2214yescomplemented
20C22×D4×C181C2214yescomplemented
21C22×D4×C181C2218yescomplemented
22C23×C4×C181C2211yescharacteristic, complemented
23#127×C181C2214yescomplemented
24#124×C181C2214yescomplemented
25#123×C181C2214yescomplemented
26#123×C181C2218yescomplemented
27C22⋊Q8×C181C2214yescomplemented
28#121×C181C2214yescomplemented
29#121×C181C22116yescomplemented
30#121×C181C2218yescomplemented
31#120×C181C2214yescomplemented
32#120×C181C2218yescomplemented
33#120×C181C22116yescomplemented
34#120×C181C2218yescomplemented
35C4×D4×C181C2218yescomplemented
36C4×D4×C181C2218yescomplemented
37#117×C181C2212yescomplemented
38C2×C22⋊C4×C181C2214yescomplemented
39C2×C22⋊C4×C181C2218yescomplemented
40C24×C181—28no—
41C24×C181—48no—
42C24×C181C2311yescharacteristic
43C24×C181C2318yes—
44C24×C181C2312yes—
45C24×C181C2312yes—
46C24×C181C2314yescomplemented
47#41×C181—216no—
48#41×C181—28no—
49C2×Q8×C181C2312yescomplemented
50C2×D4×C181—28no—
51C2×D4×C181—216no—
52C2×D4×C181—232no—
53C2×D4×C181—216no—
54C2×D4×C181—24no—
55C2×D4×C181—416no—
56C2×D4×C181D418yescomplemented
57C2×D4×C181C2318yes—
58C2×D4×C181C2314yes—
59C2×D4×C181C2318yes—
60C2×D4×C181C2314yes—
61C2×D4×C181C2314yes—
62C2×D4×C181C2318yescomplemented
63C2×D4×C181C2312yescomplemented
64C2×D4×C181C23116yescomplemented
65C22×C4×C181—24no—
66C22×C4×C181C2314yes—
67C22×C4×C181C2311yescharacteristic
68C22×C4×C181C2311yescharacteristic
69C22×C4×C181C2314yescomplemented
70C22×C4×C181C2314yescomplemented
71C22×C4×C181C2318yescomplemented
72C4⋊C4×C181C2314yescomplemented
73C4⋊C4×C181C2318yescomplemented
74C22⋊C4×C181C2314yes—
75C22⋊C4×C181C2318yes—
76C22⋊C4×C181C2318yescomplemented
77C22⋊C4×C181C23116yescomplemented
78C22⋊C4×C181C2318yescomplemented
79C42×C181C2314yescomplemented
80C23×C181—22no—
81C23×C181—24no—
82C23×C181—216no—
83C23×C181—24no—
84C23×C181—216no—
85C23×C181—28no—
86C23×C181—44no—
87C23×C181—48no—
88C23×C181—44no—
89C23×C181—48no—
90C23×C181—432no—
91C23×C181C2×D418yescomplemented
92C23×C181C2414yes—
93C23×C181C2414yes—
94C23×C181C2411yescharacteristic
95C23×C181C2414yes—
96C23×C181C2412yes—
97Q8×C181—24no—
98D4×C181—216no—
99D4×C181—28no—
100D4×C181—216no—
101D4×C181—216no—
102D4×C181—28no—
103D4×C181—24no—
104D4×C181—416no—
105D4×C181C2×D4116yescomplemented
106C2×C4×C181—22no—
107C2×C4×C181—28no—
108C2×C4×C181—28no—
109C2×C4×C181—28no—
110C2×C4×C181—48no—
111C2×C4×C181C2×D414yescomplemented
112C2×C4×C181C2418yes—
113C2×C4×C181C2414yes—
114C2×C4×C181C2412yes—
115C2×C4×C181C2412yes—
116C22×C181—28no—
117C22×C181—22no—
118C22×C181—28no—
119C22×C181—22no—
120C22×C181—22no—
121C22×C181—24no—
122C22×C181—24no—
123C22×C181—28no—
124C22×C181—28no—
125C22×C181—48no—
126C22×C181—432no—
127C22×C181—48no—
128C22×C181—88no—
129C22×C181C22×D412yes—
130C22×C181C22×D418yes—
131C22×C181H(5,𝔽2)14yescomplemented
132C22×C181C2511yescharacteristic
133C4×C181—22no—
134C4×C181—24no—
135C4×C181—28no—
136C4×C181C22×D414yes—
137C2×C181—22no—
138C2×C181—24no—
139C2×C181—28no—
140C2×C181—44no—
141C2×C181—44no—
142C2×C181C23×D411yescharacteristic
143C2×C181C2×H(5,𝔽2)12yes—
144C181#348411yescharacteristic, direct product factor, Sylow
145#3484C18111yesmaximal, characteristic, direct product factor, Sylow
146C2×H(5,𝔽2)C2×C18111yescharacteristic, complemented
147C23×D4C2×C18111yescharacteristic, complemented
148#546C2×C18118yescomplemented
149D42C2×C18118yescomplemented
150#535C2×C18112yescomplemented
151#534C2×C18114yescomplemented
152#525C2×C18112yescomplemented
153C2×#120C2×C18114yescomplemented
154#518C2×C18111yescharacteristic, complemented
155C25C22×C18112yescomplemented
156H(5,𝔽2)—28no—
157C2×#41C22×C18112yescomplemented
158C2×#41C22×C18114yescomplemented
159C22×D4—28no—
160C22×D4C22×C18111yescharacteristic
161C22×D4C22×C18112yescomplemented
162C22×D4C22×C18111yescharacteristic, complemented
163C22×D4C22×C18118yescomplemented
164C22×D4C22×C18114yescomplemented
165C22×D4C22×C18114yescomplemented
166C22×D4C22×C18118yescomplemented
167C23×C4C22×C18111yescharacteristic, complemented
168#127C22×C18114yescomplemented
169#124C22×C18114yescomplemented
170#123C22×C18114yescomplemented
171#123C22×C18118yescomplemented
172C22⋊Q8C22×C18114yescomplemented
173#121C22×C18114yescomplemented
174#121C22×C181116yescomplemented
175#121C22×C18118yescomplemented
176#120C22×C18114yescomplemented
177#120C22×C18118yescomplemented
178#120C22×C181116yescomplemented
179#120C22×C18118yescomplemented
180C4×D4C22×C18118yescomplemented
181C4×D4C22×C18118yescomplemented
182#117C22×C18112yescomplemented
183C2×C22⋊C4C22×C18114yescomplemented
184C2×C22⋊C4C22×C18118yescomplemented
185C24—28no—
186C24—48no—
187C24C23×C18111yescharacteristic
188C24C23×C18118yes—
189C24C23×C18112yes—
190C24C23×C18112yes—
191C24C23×C18114yescomplemented
192#41—216no—
193#41—28no—
194C2×Q8C23×C18112yescomplemented
195C2×D4—28no—
196C2×D4—216no—
197C2×D4—232no—
198C2×D4—216no—
199C2×D4—24no—
200C2×D4—416no—
201C2×D4D4×C18118yescomplemented
202C2×D4C23×C18118yes—
203C2×D4C23×C18114yes—
204C2×D4C23×C18118yes—
205C2×D4C23×C18114yes—
206C2×D4C23×C18114yes—
207C2×D4C23×C18118yescomplemented
208C2×D4C23×C18112yescomplemented
209C2×D4C23×C181116yescomplemented
210C22×C4—24no—
211C22×C4C23×C18114yes—
212C22×C4C23×C18111yescharacteristic
213C22×C4C23×C18111yescharacteristic
214C22×C4C23×C18114yescomplemented
215C22×C4C23×C18114yescomplemented
216C22×C4C23×C18118yescomplemented
217C4⋊C4C23×C18114yescomplemented
218C4⋊C4C23×C18118yescomplemented
219C22⋊C4C23×C18114yes—
220C22⋊C4C23×C18118yes—
221C22⋊C4C23×C18118yescomplemented
222C22⋊C4C23×C181116yescomplemented
223C22⋊C4C23×C18118yescomplemented
224C42C23×C18114yescomplemented
225C23—22no—
226C23—24no—
227C23—216no—
228C23—24no—
229C23—216no—
230C23—28no—
231C23—44no—
232C23—48no—
233C23—44no—
234C23—48no—
235C23—432no—
236C23C2×D4×C18118yescomplemented
237C23C24×C18114yes—
238C23C24×C18114yes—
239C23C24×C18111yescharacteristic
240C23C24×C18114yes—
241C23C24×C18112yes—
242Q8—24no—
243D4—216no—
244D4—28no—
245D4—216no—
246D4—216no—
247D4—28no—
248D4—24no—
249D4—416no—
250D4C2×D4×C181116yescomplemented
251C2×C4—22no—
252C2×C4—28no—
253C2×C4—28no—
254C2×C4—28no—
255C2×C4—48no—
256C2×C4C2×D4×C18114yescomplemented
257C2×C4C24×C18118yes—
258C2×C4C24×C18114yes—
259C2×C4C24×C18112yes—
260C2×C4C24×C18112yes—
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×C18112yes—
275C22C22×D4×C18118yes—
276C22H(5,𝔽2)×C18114yescomplemented
277C22C25×C18111yescharacteristic
278C4—22no—
279C4—24no—
280C4—28no—
281C4C22×D4×C18114yes—
282C2—22no—
283C2—24no—
284C2—28no—
285C2—44no—
286C2—44no—
287C2C23×D4×C18111yescharacteristic
288C2C2×H(5,𝔽2)×C18112yes—
subgroupG/H
center, socleC22×C181C25
commutator, Frattini, cosocleC22C25×C181
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C181 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×H(5,𝔽2)×C181C2semidirect
2. C23×D4×C181C2semidirect
3. #546×C181C2semidirect
4. D42×C181C2semidirect
5. #535×C181C2semidirect
6. #534×C181C2semidirect
7. #525×C181C2semidirect
8. C2×#120×C181C2semidirect
9. #518×C181C2semidirect
10. C25×C181C22semidirect
12. C2×#41×C181C22semidirect
13. C2×#41×C181C22semidirect
16. C22×D4×C181C22semidirect
17. C22×D4×C181C22semidirect
18. C22×D4×C181C22semidirect
19. C22×D4×C181C22semidirect
20. C22×D4×C181C22semidirect
21. C22×D4×C181C22semidirect
22. C23×C4×C181C22semidirect
23. #127×C181C22semidirect
24. #124×C181C22semidirect
25. #123×C181C22semidirect
26. #123×C181C22semidirect
27. C22⋊Q8×C181C22semidirect
28. #121×C181C22semidirect
29. #121×C181C22semidirect
30. #121×C181C22semidirect
31. #120×C181C22semidirect
32. #120×C181C22semidirect
33. #120×C181C22semidirect
34. #120×C181C22semidirect
35. C4×D4×C181C22semidirect
36. C4×D4×C181C22semidirect
37. #117×C181C22semidirect
38. C2×C22⋊C4×C181C22semidirect
39. C2×C22⋊C4×C181C22semidirect
46. C24×C181C23semidirect
49. C2×Q8×C181C23semidirect
56. C2×D4×C181D4semidirect
62. C2×D4×C181C23semidirect
63. C2×D4×C181C23semidirect
64. C2×D4×C181C23semidirect
69. C22×C4×C181C23semidirect
70. C22×C4×C181C23semidirect
71. C22×C4×C181C23semidirect
72. C4⋊C4×C181C23semidirect
73. C4⋊C4×C181C23semidirect
76. C22⋊C4×C181C23semidirect
77. C22⋊C4×C181C23semidirect
78. C22⋊C4×C181C23semidirect
79. C42×C181C23semidirect
91. C23×C181C2×D4semidirect
105. D4×C181C2×D4semidirect
111. C2×C4×C181C2×D4semidirect
131. C22×C181H(5,𝔽2)semidirect
144. C181#3484direct (N × H)
145. #3484C181direct (N × H)
146. C2×H(5,𝔽2)C2×C181semidirect
147. C23×D4C2×C181semidirect
148. #546C2×C181semidirect
149. D42C2×C181semidirect
150. #535C2×C181semidirect
151. #534C2×C181semidirect
152. #525C2×C181semidirect
153. C2×#120C2×C181semidirect
154. #518C2×C181semidirect
155. C25C22×C181semidirect
157. C2×#41C22×C181semidirect
158. C2×#41C22×C181semidirect
161. C22×D4C22×C181semidirect
162. C22×D4C22×C181semidirect
163. C22×D4C22×C181semidirect
164. C22×D4C22×C181semidirect
165. C22×D4C22×C181semidirect
166. C22×D4C22×C181semidirect
167. C23×C4C22×C181semidirect
168. #127C22×C181semidirect
169. #124C22×C181semidirect
170. #123C22×C181semidirect
171. #123C22×C181semidirect
172. C22⋊Q8C22×C181semidirect
173. #121C22×C181semidirect
174. #121C22×C181semidirect
175. #121C22×C181semidirect
176. #120C22×C181semidirect
177. #120C22×C181semidirect
178. #120C22×C181semidirect
179. #120C22×C181semidirect
180. C4×D4C22×C181semidirect
181. C4×D4C22×C181semidirect
182. #117C22×C181semidirect
183. C2×C22⋊C4C22×C181semidirect
184. C2×C22⋊C4C22×C181semidirect
191. C24C23×C181semidirect
194. C2×Q8C23×C181semidirect
201. C2×D4D4×C181semidirect
207. C2×D4C23×C181semidirect
208. C2×D4C23×C181semidirect
209. C2×D4C23×C181semidirect
214. C22×C4C23×C181semidirect
215. C22×C4C23×C181semidirect
216. C22×C4C23×C181semidirect
217. C4⋊C4C23×C181semidirect
218. C4⋊C4C23×C181semidirect
221. C22⋊C4C23×C181semidirect
222. C22⋊C4C23×C181semidirect
223. C22⋊C4C23×C181semidirect
224. C42C23×C181semidirect
236. C23C2×D4×C181semidirect
250. D4C2×D4×C181semidirect
256. C2×C4C2×D4×C181semidirect
276. C22H(5,𝔽2)×C181semidirect

Maximal subgroups

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

subgroupindex
C2×H(5,𝔽2)×C1812
C23×D4×C1812
#546×C1812
D42×C1812
#535×C1812
#534×C1812
#525×C1812
C2×#120×C1812
#518×C1812
#3484181