Finite Group Databasebeta

← C61×#62817 #29566250

Subgroups — C61×#62817 #29566250

Order 15616.

9494 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3532C2124yesmaximal, complemented
2C61×#3490C2118yesmaximal, complemented
3C61×#3484C2118yesmaximal, complemented
4C22×#120×C61C213yesmaximal, complemented
5C26×C61C2211yescharacteristic, complemented
6C2×H(5,𝔽2)×C61C2216yescomplemented
7C23×D4×C61C2219yescomplemented
8C61×H(3,𝔽4)C2218yescomplemented
9C61×#560C22124yescomplemented
10C61×#551C22172yescomplemented
11C61×#546C221144yescomplemented
12D42×C61C22172yescomplemented
13C61×#543C2216yescomplemented
14C61×#538C22172yescomplemented
15C61×#535C22136yescomplemented
16C61×#534C22118yescomplemented
17C61×#534C22136yescomplemented
18C61×#525C22136yescomplemented
19C2×#120×C61C22136yescomplemented
20C2×#120×C61C22136yescomplemented
21C2×#120×C61C22112yescomplemented
22C61×#518C22118yescomplemented
23C22×C22⋊C4×C61C2219yescomplemented
24C25×C61—412no—
25C25×C61C2319yes—
26C25×C61C2316yes—
27C25×C61C2313yescomplemented
28H(5,𝔽2)×C61—424no—
29C2×#41×C61C23136yescomplemented
30C22×D4×C61—436no—
31C22×D4×C61C23118yes—
32C22×D4×C61C23118yescomplemented
33C22×D4×C61C23172yescomplemented
34C22×D4×C61C23136yescomplemented
35C23×C4×C61C2319yescomplemented
36#127×C61C23124yescomplemented
37#126×C61C23148yescomplemented
38#124×C61C23172yescomplemented
39#123×C61C23172yescomplemented
40#123×C61C23172yescomplemented
41C22⋊Q8×C61C23172yescomplemented
42#121×C61C231144yescomplemented
43#121×C61C23172yescomplemented
44#120×C61C23172yes—
45#120×C61C23172yescomplemented
46#120×C61C23124yescomplemented
47#120×C61C23124yescomplemented
48#120×C61C23172yescomplemented
49#120×C61C23124yescomplemented
50C4×D4×C61C231144yescomplemented
51#117×C61C23136yescomplemented
52C2×C22⋊C4×C61C23118yes—
53C2×C22⋊C4×C61C23118yescomplemented
54C2×C22⋊C4×C61C23172yescomplemented
55C2×C22⋊C4×C61C23136yescomplemented
56C24×C61—236no—
57C24×C61—436no—
58C24×C61—436no—
59C24×C61—418no—
60C24×C61—464no—
61C24×C61C2413yes—
62C24×C61C24118yes—
63C24×C61C2419yes—
64C24×C61C24118yes—
65C24×C61C2412yes—
66C24×C61C2413yes—
67C24×C61C2414yescomplemented
68#41×C61—472no—
69C2×Q8×C61C24112yescomplemented
70C2×D4×C61—272no—
71C2×D4×C61—436no—
72C2×D4×C61—4144no—
73C2×D4×C61—472no—
74C2×D4×C61C24172yes—
75C2×D4×C61C24172yes—
76C2×D4×C61C24136yescomplemented
77C22×C4×C61—418no—
78C22×C4×C61C24118yes—
79C22×C4×C61C24136yes—
80C22×C4×C61C24136yescomplemented
81C4⋊C4×C61C24172yescomplemented
82C22⋊C4×C61C24172yes—
83C22⋊C4×C61C24172yes—
84C22⋊C4×C61C24172yescomplemented
85C42×C61C24124yescomplemented
86C23×C61—218no—
87C23×C61—272no—
88C23×C61—218no—
89C23×C61—236no—
90C23×C61—46no—
91C23×C61—418no—
92C23×C61—418no—
93C23×C61—46no—
94C23×C61—436no—
95C23×C61—412no—
96C23×C61—4144no—
97C23×C61—496no—
98C23×C61—824no—
99C23×C61H(5,𝔽2)112yescomplemented
100C23×C61C2516yes—
101C23×C61C25112yes—
102C23×C61C2519yes—
103Q8×C61—412no—
104D4×C61—2144no—
105D4×C61—472no—
106D4×C61—436no—
107C2×C4×C61—236no—
108C2×C4×C61—436no—
109C2×C4×C61—436no—
110C2×C4×C61C25136yes—
111#62817C6111yesmaximal, characteristic, direct product factor, Sylow
112C22×C61—224no—
113C22×C61—218no—
114C22×C61—236no—
115C22×C61—218no—
116C22×C61—412no—
117C22×C61—472no—
118C22×C61—436no—
119C22×C61—48no—
120C22×C61—836no—
121C22×C61—164no—
122C22×C61C2×H(5,𝔽2)118yes—
123C22×C61C2611yescharacteristic
124C4×C61—236no—
125#3532C2×C61124yescomplemented
126#3490C2×C61118yescomplemented
127#3484C2×C61118yescomplemented
128C22×#120C2×C6113yescomplemented
129C2×C61—218no—
130C2×C61—46no—
131C2×C61—412no—
132C2×C61C22×H(5,𝔽2)13yes—
133C26C22×C6111yescharacteristic, complemented
134C2×H(5,𝔽2)C22×C6116yescomplemented
135C23×D4C22×C6119yescomplemented
136H(3,𝔽4)C22×C6118yescomplemented
137#560C22×C61124yescomplemented
138#551C22×C61172yescomplemented
139#546C22×C611144yescomplemented
140D42C22×C61172yescomplemented
141#543C22×C6116yescomplemented
142#538C22×C61172yescomplemented
143#535C22×C61136yescomplemented
144#534C22×C61118yescomplemented
145#534C22×C61136yescomplemented
146#525C22×C61136yescomplemented
147C2×#120C22×C61136yescomplemented
148C2×#120C22×C61136yescomplemented
149C2×#120C22×C61112yescomplemented
150#518C22×C61118yescomplemented
151C22×C22⋊C4C22×C6119yescomplemented
152C61#6281711yescharacteristic, direct product factor, Sylow
153C25—412no—
154C25C23×C6119yes—
155C25C23×C6116yes—
156C25C23×C6113yescomplemented
157H(5,𝔽2)—424no—
158C2×#41C23×C61136yescomplemented
159C22×D4—436no—
160C22×D4C23×C61118yes—
161C22×D4C23×C61118yescomplemented
162C22×D4C23×C61172yescomplemented
163C22×D4C23×C61136yescomplemented
164C23×C4C23×C6119yescomplemented
165#127C23×C61124yescomplemented
166#126C23×C61148yescomplemented
167#124C23×C61172yescomplemented
168#123C23×C61172yescomplemented
169#123C23×C61172yescomplemented
170C22⋊Q8C23×C61172yescomplemented
171#121C23×C611144yescomplemented
172#121C23×C61172yescomplemented
173#120C23×C61172yes—
174#120C23×C61124yescomplemented
175#120C23×C61172yescomplemented
176#120C23×C61124yescomplemented
177#120C23×C61172yescomplemented
178#120C23×C61124yescomplemented
179C4×D4C23×C611144yescomplemented
180#117C23×C61136yescomplemented
181C2×C22⋊C4C23×C61118yes—
182C2×C22⋊C4C23×C61118yescomplemented
183C2×C22⋊C4C23×C61172yescomplemented
184C2×C22⋊C4C23×C61136yescomplemented
185C24—236no—
186C24—436no—
187C24—436no—
188C24—418no—
189C24—464no—
190C24C24×C6113yes—
191C24C24×C61118yes—
192C24C24×C6119yes—
193C24C24×C61118yes—
194C24C24×C6112yes—
195C24C24×C6113yes—
196C24C24×C6114yescomplemented
197#41—472no—
198C2×Q8C24×C61112yescomplemented
199C2×D4—272no—
200C2×D4—436no—
201C2×D4—4144no—
202C2×D4—472no—
203C2×D4C24×C61172yes—
204C2×D4C24×C61172yes—
205C2×D4C24×C61136yescomplemented
206C22×C4—418no—
207C22×C4C24×C61118yes—
208C22×C4C24×C61136yes—
209C22×C4C24×C61136yescomplemented
210C4⋊C4C24×C61172yescomplemented
211C22⋊C4C24×C61172yes—
212C22⋊C4C24×C61172yes—
213C22⋊C4C24×C61172yescomplemented
214C42C24×C61124yescomplemented
215C23—218no—
216C23—272no—
217C23—218no—
218C23—236no—
219C23—46no—
220C23—418no—
221C23—418no—
222C23—46no—
223C23—436no—
224C23—412no—
225C23—4144no—
226C23—496no—
227C23—824no—
228C23H(5,𝔽2)×C61112yescomplemented
229C23C25×C6116yes—
230C23C25×C61112yes—
231C23C25×C6119yes—
232Q8—412no—
233D4—2144no—
234D4—472no—
235D4—436no—
236C2×C4—236no—
237C2×C4—436no—
238C2×C4—436no—
239C2×C4C25×C61136yes—
240C22—224no—
241C22—218no—
242C22—236no—
243C22—218no—
244C22—412no—
245C22—472no—
246C22—436no—
247C22—48no—
248C22—836no—
249C22—164no—
250C22C2×H(5,𝔽2)×C61118yes—
251C22C26×C6111yescharacteristic
252C4—236no—
253C2—218no—
254C2—46no—
255C2—412no—
256C2C22×H(5,𝔽2)×C6113yes—
subgroupG/H
center, socleC22×C61C26
commutator, Frattini, cosocleC22C26×C61
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3532C2semidirect
2. C61×#3490C2semidirect
3. C61×#3484C2semidirect
4. C22×#120×C61C2semidirect
5. C26×C61C22semidirect
6. C2×H(5,𝔽2)×C61C22semidirect
7. C23×D4×C61C22semidirect
8. C61×H(3,𝔽4)C22semidirect
9. C61×#560C22semidirect
10. C61×#551C22semidirect
11. C61×#546C22semidirect
12. D42×C61C22semidirect
13. C61×#543C22semidirect
14. C61×#538C22semidirect
15. C61×#535C22semidirect
16. C61×#534C22semidirect
17. C61×#534C22semidirect
18. C61×#525C22semidirect
19. C2×#120×C61C22semidirect
20. C2×#120×C61C22semidirect
21. C2×#120×C61C22semidirect
22. C61×#518C22semidirect
23. C22×C22⋊C4×C61C22semidirect
27. C25×C61C23semidirect
29. C2×#41×C61C23semidirect
32. C22×D4×C61C23semidirect
33. C22×D4×C61C23semidirect
34. C22×D4×C61C23semidirect
35. C23×C4×C61C23semidirect
36. #127×C61C23semidirect
37. #126×C61C23semidirect
38. #124×C61C23semidirect
39. #123×C61C23semidirect
40. #123×C61C23semidirect
41. C22⋊Q8×C61C23semidirect
42. #121×C61C23semidirect
43. #121×C61C23semidirect
45. #120×C61C23semidirect
46. #120×C61C23semidirect
47. #120×C61C23semidirect
48. #120×C61C23semidirect
49. #120×C61C23semidirect
50. C4×D4×C61C23semidirect
51. #117×C61C23semidirect
53. C2×C22⋊C4×C61C23semidirect
54. C2×C22⋊C4×C61C23semidirect
55. C2×C22⋊C4×C61C23semidirect
67. C24×C61C24semidirect
69. C2×Q8×C61C24semidirect
76. C2×D4×C61C24semidirect
80. C22×C4×C61C24semidirect
81. C4⋊C4×C61C24semidirect
84. C22⋊C4×C61C24semidirect
85. C42×C61C24semidirect
99. C23×C61H(5,𝔽2)semidirect
111. #62817C61direct (N × H)
125. #3532C2×C61semidirect
126. #3490C2×C61semidirect
127. #3484C2×C61semidirect
128. C22×#120C2×C61semidirect
133. C26C22×C61semidirect
134. C2×H(5,𝔽2)C22×C61semidirect
135. C23×D4C22×C61semidirect
136. H(3,𝔽4)C22×C61semidirect
137. #560C22×C61semidirect
138. #551C22×C61semidirect
139. #546C22×C61semidirect
140. D42C22×C61semidirect
141. #543C22×C61semidirect
142. #538C22×C61semidirect
143. #535C22×C61semidirect
144. #534C22×C61semidirect
145. #534C22×C61semidirect
146. #525C22×C61semidirect
147. C2×#120C22×C61semidirect
148. C2×#120C22×C61semidirect
149. C2×#120C22×C61semidirect
150. #518C22×C61semidirect
151. C22×C22⋊C4C22×C61semidirect
152. C61#62817direct (N × H)
156. C25C23×C61semidirect
158. C2×#41C23×C61semidirect
161. C22×D4C23×C61semidirect
162. C22×D4C23×C61semidirect
163. C22×D4C23×C61semidirect
164. C23×C4C23×C61semidirect
165. #127C23×C61semidirect
166. #126C23×C61semidirect
167. #124C23×C61semidirect
168. #123C23×C61semidirect
169. #123C23×C61semidirect
170. C22⋊Q8C23×C61semidirect
171. #121C23×C61semidirect
172. #121C23×C61semidirect
174. #120C23×C61semidirect
175. #120C23×C61semidirect
176. #120C23×C61semidirect
177. #120C23×C61semidirect
178. #120C23×C61semidirect
179. C4×D4C23×C61semidirect
180. #117C23×C61semidirect
182. C2×C22⋊C4C23×C61semidirect
183. C2×C22⋊C4C23×C61semidirect
184. C2×C22⋊C4C23×C61semidirect
196. C24C24×C61semidirect
198. C2×Q8C24×C61semidirect
205. C2×D4C24×C61semidirect
209. C22×C4C24×C61semidirect
210. C4⋊C4C24×C61semidirect
213. C22⋊C4C24×C61semidirect
214. C42C24×C61semidirect
228. C23H(5,𝔽2)×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#35322
C61×#34902
C61×#34842
C22×#120×C612
#6281761