Finite Group Databasebeta

← C23×#41×D43 #26010478

Subgroups — C23×#41×D43 #26010478

Order 11008.

65470 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#10621902C211yesmaximal, characteristic, complemented
2C23×#10621898C213yesmaximal, complemented
3C23×#10621900C213yesmaximal, complemented
4C22×#41×D43C21112yesmaximal, direct product factor
5C23×Q8×D43C211yesmaximal, characteristic, complemented
6C23×D4×D43C213yesmaximal, complemented
7C24×C4×D43C213yesmaximal, complemented
8C23×#41×C43C211yesmaximal, characteristic, complemented
9C25×D43C2213yes—
10C22×#10621902C22156yescomplemented
11C22×#10621898C221168yescomplemented
12C22×#10621900C221168yescomplemented
13C2×#41×D43C2211792yesdirect product factor
14C23×Dic86C2213yescomplemented
15C22×Q8×D43C22156yescomplemented
16C23×D172C2213yescomplemented
17C23×C22⋊D43C2216yescomplemented
18C22×D4×D43C221168yescomplemented
19C24×Dic43C2213yescomplemented
20C23×C4×D43C2211yescharacteristic
21C23×C4×D43C2213yes—
22C23×C4×D43C2213yescomplemented
23C23×C4×D43C2213yescomplemented
24C23×C4×D43C221168yescomplemented
25C22×#41×C43C22156yescomplemented
26C23×Q8×C43C2211yescharacteristic, complemented
27C23×D4×C43C2213yescomplemented
28C24×C4×C43C2213yescomplemented
29C24×D43—248no—
30C24×D43C23184yes—
31C24×D43C2313yes—
32C24×D43C2311yescharacteristic
33C2×#10621902C231448yescomplemented
34C2×#10621898C2311344yescomplemented
35C2×#10621900C2311344yescomplemented
36#41×D43C2314096yesdirect product factor
37C22×Dic86C23184yescomplemented
38C2×Q8×D43C231448yescomplemented
39C22×D172C23184yescomplemented
40C22×C22⋊D43C231168yescomplemented
41C2×D4×D43C2311344yescomplemented
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2313yes—
44C23×Dic43C23184yescomplemented
45C22×C4×D43C23128yes—
46C22×C4×D43C23184yes—
47C22×C4×D43C2311344yescomplemented
48C22×C4×D43C23184yescomplemented
49C22×C4×D43C23184yescomplemented
50C25×C43C2313yes—
51C2×#41×C43C231448yescomplemented
52C22×Q8×C43C23128yescomplemented
53C22×D4×C43C23184yescomplemented
54C23×C4×C43C2313yes—
55C23×C4×C43C2311yescharacteristic
56C23×C4×C43C23184yescomplemented
57C24×C43—224no—
58C24×C43C24142yes—
59C24×C43C2411yescharacteristic
60C23×D43—224no—
61C23×D43—2672no—
62C23×D43#41116yesdirect product factor
63C23×D43C241336yes—
64C23×D43C24142yes—
65C23×D43C24114yes—
66#41×C43C241512yescomplemented
67C2×Q8×C43C241112yescomplemented
68C2×D4×C43C241336yescomplemented
69C22×C4×C43C24114yes—
70C22×C4×C43C24142yes—
71C22×C4×C43C241336yescomplemented
72C2×C22⋊D43C241672yescomplemented
73C22×Dic43C24114yes—
74C22×Dic43C24142yes—
75C22×Dic43C241336yescomplemented
76#10621902C241512yescomplemented
77Q8×D43C241512yescomplemented
78#10621900C2411536yescomplemented
79D4×D43C2411536yescomplemented
80#10621898C2411536yescomplemented
81C2×D172C241336yescomplemented
82C2×C4×D43C241112yes—
83C2×C4×D43C241336yes—
84C2×C4×D43C2411536yescomplemented
85C2×C4×D43C241336yescomplemented
86C2×C4×D43C241336yescomplemented
87C2×Dic86C241336yescomplemented
88C23×C43—2168no—
89C23×C43C2×#4118yescomplemented
90C23×C43C25184yes—
91C23×C43C2517yes—
92C22×D43—2168no—
93C22×D43—21344no—
94C22×D43C2×#411112yesdirect product factor
95C22×D43C25184yes—
96C22×D43C251192yes—
97C22×D43C25128yes—
98Q8×C43C25164yescomplemented
99D4×C43C251192yescomplemented
100C2×C4×C43C25184yes—
101C2×C4×C43C25128yes—
102C2×C4×C43C251192yescomplemented
103C22⋊D43C251384yescomplemented
104C2×Dic43C25184yes—
105C2×Dic43C25128yes—
106C2×Dic43C251192yescomplemented
107D172C251192yescomplemented
108C4×D43C25164yes—
109C4×D43C251192yes—
110C4×D43C251192yescomplemented
111C4×D43C251192yescomplemented
112Dic86C251192yescomplemented
113C24×#41—431nomaximal, Sylow
114C22×C43—2168no—
115C22×C43C22×#41128yescomplemented
116C22×C43C26124yes—
117C22×C43C2617yes—
118C2×D43—2168no—
119C2×D43—2384no—
120C2×D43C22×#411112yesdirect product factor
121C2×D43C26124yes—
122C2×D43C2618yes—
123C4×C43C26124yes—
124C4×C43C2618yes—
125Dic43C26124yes—
126Dic43C2618yes—
127C23×#41—43112no—
128C23×#41—431no—
129C23×#41—433no—
130C23×#41—433no—
131C23×#41D4311yescharacteristic, direct product factor
132C24×Q8—431no—
133C24×D4—433no—
134C25×C4—433no—
135C2×C43—224no—
136C2×C43C23×#41114yescomplemented
137C2×C43C2711yescharacteristic
138D43—224no—
139D43C23×#41116yesdirect product factor
140C26—433no—
141C22×#41—431792no—
142C22×#41—4356no—
143C22×#41—43168no—
144C22×#41—43168no—
145C22×#41C2×D43156yesdirect product factor
146C23×Q8—4356no—
147C23×Q8—433no—
148C23×Q8C2×D4311yescharacteristic, complemented
149C23×D4—436no—
150C23×D4—43168no—
151C23×D4—433no—
152C23×D4C2×D4313yescomplemented
153C24×C4—433no—
154C24×C4—433no—
155C24×C4—433no—
156C24×C4—431no—
157C24×C4—433no—
158C24×C4—43168no—
159C24×C4C2×D4313yescomplemented
160C43C24×#4111yescharacteristic, complemented, Sylow
161C25—431no—
162C25—4384no—
163C25—433no—
164C25—8648no—
165C25C22×D4313yes—
166C2×#41—434096no—
167C2×#41—43448no—
168C2×#41—431344no—
169C2×#41—431344no—
170C2×#41C22×D431448yesdirect product factor
171C22×Q8—43448no—
172C22×Q8—4384no—
173C22×Q8C22×D43128yescomplemented
174C22×D4—43168no—
175C22×D4—431344no—
176C22×D4—4384no—
177C22×D4C22×D43184yescomplemented
178C23×C4—431no—
179C23×C4—433no—
180C23×C4—4384no—
181C23×C4—4328no—
182C23×C4—4384no—
183C23×C4—4384no—
184C23×C4—4384no—
185C23×C4—431344no—
186C23×C4C22×D4313yes—
187C23×C4C22×D4311yescharacteristic
188C23×C4C22×D43184yescomplemented
189C24—224no—
190C24—4316no—
191C24—4314no—
192C24—43336no—
193C24—4342no—
194C24—86672no—
195C24—8624no—
196C24C23×D43142yes—
197C24C23×D4311yescharacteristic
198#41—43512no—
199#41—431536no—
200#41—431536no—
201#41C23×D431512yesdirect product factor
202C2×Q8—43512no—
203C2×Q8—43336no—
204C2×Q8C23×D431112yescomplemented
205C2×D4—43672no—
206C2×D4—431536no—
207C2×D4—43336no—
208C2×D4C23×D431336yescomplemented
209C22×C4—4314no—
210C22×C4—4342no—
211C22×C4—43336no—
212C22×C4—43112no—
213C22×C4—43336no—
214C22×C4—43336no—
215C22×C4—43336no—
216C22×C4—431536no—
217C22×C4C23×D43114yes—
218C22×C4C23×D43142yes—
219C22×C4C23×D431336yescomplemented
220C23—2168no—
221C23—43112no—
222C23—4328no—
223C23—43192no—
224C23—4384no—
225C23—861344no—
226C23—86168no—
227C23#41×D4318yesdirect product factor
228C23C24×D43184yes—
229C23C24×D4317yes—
230Q8—43192no—
231Q8C24×D43164yescomplemented
232D4—43384no—
233D4—43192no—
234D4C24×D431192yescomplemented
235C2×C4—4328no—
236C2×C4—4384no—
237C2×C4—43192no—
238C2×C4—4364no—
239C2×C4—43192no—
240C2×C4—43192no—
241C2×C4—43192no—
242C2×C4C24×D43128yes—
243C2×C4C24×D43184yes—
244C2×C4C24×D431192yescomplemented
245C22—2168no—
246C22—43112no—
247C22—438no—
248C22—4324no—
249C22—86384no—
250C22—86168no—
251C22C2×#41×D43128yesdirect product factor
252C22C25×D43124yes—
253C22C25×D4317yes—
254C4—438no—
255C4—4324no—
256C4C25×D4318yes—
257C4C25×D43124yes—
258C2—224no—
259C2—4316no—
260C2—8624no—
261C2C22×#41×D43114yesdirect product factor
262C2C26×D4311yescharacteristic
subgroupG/H
centerC23×C4C22×D43
commutator, cosocleC2×C43C27
FrattiniC2C26×D43
FittingC23×#41×C43C2
socleC24×C43C24
hypercenterC23×#41D43
hypocenterC43C24×#41
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C23×#41

Complements

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

NH ≅ G/Ntype
1. C23×#10621902C2semidirect
2. C23×#10621898C2semidirect
3. C23×#10621900C2semidirect
4. C22×#41×D43C2direct (N × H)
5. C23×Q8×D43C2semidirect
6. C23×D4×D43C2semidirect
7. C24×C4×D43C2semidirect
8. C23×#41×C43C2semidirect
10. C22×#10621902C22semidirect
11. C22×#10621898C22semidirect
12. C22×#10621900C22semidirect
13. C2×#41×D43C22direct (N × H)
14. C23×Dic86C22semidirect
15. C22×Q8×D43C22semidirect
16. C23×D172C22semidirect
17. C23×C22⋊D43C22semidirect
18. C22×D4×D43C22semidirect
19. C24×Dic43C22semidirect
22. C23×C4×D43C22semidirect
23. C23×C4×D43C22semidirect
24. C23×C4×D43C22semidirect
25. C22×#41×C43C22semidirect
26. C23×Q8×C43C22semidirect
27. C23×D4×C43C22semidirect
28. C24×C4×C43C22semidirect
33. C2×#10621902C23semidirect
34. C2×#10621898C23semidirect
35. C2×#10621900C23semidirect
36. #41×D43C23direct (N × H)
37. C22×Dic86C23semidirect
38. C2×Q8×D43C23semidirect
39. C22×D172C23semidirect
40. C22×C22⋊D43C23semidirect
41. C2×D4×D43C23semidirect
44. C23×Dic43C23semidirect
47. C22×C4×D43C23semidirect
48. C22×C4×D43C23semidirect
49. C22×C4×D43C23semidirect
51. C2×#41×C43C23semidirect
52. C22×Q8×C43C23semidirect
53. C22×D4×C43C23semidirect
56. C23×C4×C43C23semidirect
62. C23×D43#41direct (N × H)
66. #41×C43C24semidirect
67. C2×Q8×C43C24semidirect
68. C2×D4×C43C24semidirect
71. C22×C4×C43C24semidirect
72. C2×C22⋊D43C24semidirect
75. C22×Dic43C24semidirect
76. #10621902C24semidirect
77. Q8×D43C24semidirect
78. #10621900C24semidirect
79. D4×D43C24semidirect
80. #10621898C24semidirect
81. C2×D172C24semidirect
84. C2×C4×D43C24semidirect
85. C2×C4×D43C24semidirect
86. C2×C4×D43C24semidirect
87. C2×Dic86C24semidirect
89. C23×C43C2×#41semidirect
94. C22×D43C2×#41direct (N × H)
98. Q8×C43C25semidirect
99. D4×C43C25semidirect
102. C2×C4×C43C25semidirect
103. C22⋊D43C25semidirect
106. C2×Dic43C25semidirect
107. D172C25semidirect
110. C4×D43C25semidirect
111. C4×D43C25semidirect
112. Dic86C25semidirect
115. C22×C43C22×#41semidirect
120. C2×D43C22×#41direct (N × H)
131. C23×#41D43direct (N × H)
136. C2×C43C23×#41semidirect
139. D43C23×#41direct (N × H)
145. C22×#41C2×D43direct (N × H)
148. C23×Q8C2×D43semidirect
152. C23×D4C2×D43semidirect
159. C24×C4C2×D43semidirect
160. C43C24×#41semidirect
170. C2×#41C22×D43direct (N × H)
173. C22×Q8C22×D43semidirect
177. C22×D4C22×D43semidirect
188. C23×C4C22×D43semidirect
201. #41C23×D43direct (N × H)
204. C2×Q8C23×D43semidirect
208. C2×D4C23×D43semidirect
219. C22×C4C23×D43semidirect
227. C23#41×D43direct (N × H)
231. Q8C24×D43semidirect
234. D4C24×D43semidirect
244. C2×C4C24×D43semidirect
251. C22C2×#41×D43direct (N × H)
261. C2C22×#41×D43direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#106219022
C23×#106218982
C23×#106219002
C22×#41×D432
C23×Q8×D432
C23×D4×D432
C24×C4×D432
C23×#41×C432
C24×#4143