Finite Group Databasebeta

← C2×#120×D103 #27208358

Subgroups — C2×#120×D103 #27208358

Order 13184.

4544 conjugacy classes of subgroups; only the 661 normal subgroups are shown.

normal subgroups only

This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 661 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×D103C211yesmaximal, characteristic, complemented
2C22×D4×D103C213yesmaximal, complemented
3C2×#15692991C213yesmaximal, complemented
4C2×#15692990C211yesmaximal, characteristic, complemented
5C2×#15692989C213yesmaximal, complemented
6#120×D103C2116yesmaximal, direct product factor
7C2×C22⋊C4×D103C213yesmaximal, complemented
8C2×#120×C103C211yesmaximal, characteristic, complemented
9C24×D103—224no—
10C24×D103C2213yes—
11C24×D103C2213yescomplemented
12C24×D103C2218yescomplemented
13C24×D103C2211yescharacteristic, complemented
14C22×D412C2213yescomplemented
15C22×C22⋊D103C2213yescomplemented
16C22×C22⋊D103C2213yescomplemented
17C2×D4×D103—224no—
18C2×D4×D103C22124yescomplemented
19C22×C4×D103C2213yescomplemented
20#15692991C22124yescomplemented
21#15692990C2218yescomplemented
22#15692989C22124yescomplemented
23C2×C22⋊Dic103C2213yescomplemented
24C2×(C2×D103)⋊C4C2216yescomplemented
25C22⋊C4×D103C22124yescomplemented
26C25×C103C2211yescharacteristic, complemented
27C22×D4×C103C2213yescomplemented
28#120×C103C2218yescomplemented
29C2×C22⋊C4×C103C2213yescomplemented
30C23×D103—2128no—
31C23×D103—212no—
32C23×D103—224no—
33C23×D103—224no—
34C23×D103—296no—
35C23×D103—212no—
36C23×D103D4124yescomplemented
37C23×D103C23112yes—
38C23×D103C2313yes—
39C23×D103C2311yescharacteristic
40C23×D103C23112yescomplemented
41C23×D103C2314yescomplemented
42C23×D103C2311yescharacteristic, complemented
43C2×D412—212no—
44C2×D412C23112yescomplemented
45C2×C22⋊D103—212no—
46C2×C22⋊D103—212no—
47C2×C22⋊D103C23112yescomplemented
48C2×C22⋊D103C23112yescomplemented
49D4×D103—296no—
50C22×Dic103C2313yescomplemented
51C2×C4×D103—212no—
52C2×C4×D103C23112yescomplemented
53C22⋊Dic103C23112yescomplemented
54(C2×D103)⋊C4C23124yescomplemented
55C24×C103—212no—
56C24×C103C2313yes—
57C24×C103C2314yescomplemented
58C24×C103C2311yescharacteristic, complemented
59C2×D4×C103—212no—
60C2×D4×C103C23112yescomplemented
61C22×C4×C103C2313yescomplemented
62C22⋊C4×C103C23112yescomplemented
63C23×C103—232no—
64C23×C103—212no—
65C23×C103—224no—
66C23×C103—26no—
67C23×C103C2×D4112yescomplemented
68C23×C103C2416yes—
69C23×C103C2411yescharacteristic
70C23×C103C2412yescomplemented
71C22×D103—296no—
72C22×D103—2256no—
73C22×D103—212no—
74C22×D103—224no—
75C22×D103—296no—
76C22×D103—248no—
77C22×D103—248no—
78C22×D103—26no—
79C22×D103—224no—
80C22×D103—416no—
81C22×D103C2×D4112yes—
82C22×D103C2×D4148yescomplemented
83C22×D103C2×D4112yescomplemented
84C22×D103C2416yes—
85C22×D103C2412yes—
86C22×D103C2412yescomplemented
87D4×C103—224no—
88C2×C4×C103—26no—
89C2×C4×C103C2416yescomplemented
90C22⋊D103—224no—
91C22⋊D103—224no—
92C2×Dic103—26no—
93C2×Dic103C2416yescomplemented
94D412—224no—
95C4×D103—224no—
96C22×C103—232no—
97C22×C103—224no—
98C22×C103—212no—
99C22×C103—26no—
100C22×C103—44no—
101C22×C103C22×D416yes—
102C22×C103C22×D4112yescomplemented
103C22×C103C2511yescharacteristic
104C2×D103—296no—
105C2×D103—224no—
106C2×D103—212no—
107C2×D103—296no—
108C2×D103—26no—
109C2×D103—44no—
110C2×D103—416no—
111C2×D103#120116yesdirect product factor
112C2×D103C22×D4112yes—
113C2×D103C22×D4112yescomplemented
114C4×C103—26no—
115Dic103—26no—
116C2×C103—212no—
117C2×C103—42no—
118C2×C103C2×#12014yescomplemented
119C2×C103C23×D413yes—
120D103—212no—
121D103—42no—
122D103C2×#12018yesdirect product factor
123C22×#120—1031nomaximal, Sylow
124C103C22×#12011yescharacteristic, complemented, Sylow
125C26—1031no—
126C23×D4—1033no—
127C2×#120—1031no—
128C2×#120—1033no—
129C2×#120—10316no—
130C2×#120—1033no—
131C2×#120D10311yescharacteristic, direct product factor
132C22×C22⋊C4—1033no—
133C25—1033no—
134C25—1033no—
135C25—1038no—
136C25—1031no—
137C25—20624no—
138C25C2×D10311yescharacteristic, complemented
139C22×D4—1033no—
140C22×D4—1033no—
141C22×D4—10324no—
142C22×D4—1033no—
143C22×D4—20624no—
144C22×D4C2×D10313yescomplemented
145C23×C4—1033no—
146#120—1038no—
147#120—10324no—
148#120—10324no—
149#120C2×D10318yesdirect product factor
150C2×C22⋊C4—1033no—
151C2×C22⋊C4—1036no—
152C2×C22⋊C4—10324no—
153C2×C22⋊C4C2×D10313yescomplemented
154C24—212no—
155C24—1031no—
156C24—10324no—
157C24—10312no—
158C24—1033no—
159C24—10312no—
160C24—1031no—
161C24—1034no—
162C24—20612no—
163C24—20624no—
164C24—20624no—
165C24—20696no—
166C24—206128no—
167C24—20612no—
168C24C22×D10313yes—
169C24C22×D10314yescomplemented
170C24C22×D10311yescharacteristic, complemented
171C2×D4—212no—
172C2×D4—10312no—
173C2×D4—10312no—
174C2×D4—10312no—
175C2×D4—20612no—
176C2×D4—20696no—
177C2×D4—20612no—
178C2×D4—20612no—
179C2×D4C22×D103112yescomplemented
180C22×C4—1033no—
181C22×C4—10312no—
182C22×C4—20612no—
183C22×C4C22×D10313yescomplemented
184C22⋊C4—10312no—
185C22⋊C4—10324no—
186C22⋊C4C22×D103112yescomplemented
187C23—232no—
188C23—212no—
189C23—224no—
190C23—26no—
191C23—10312no—
192C23—1032no—
193C23—10312no—
194C23—10348no—
195C23—1036no—
196C23—1032no—
197C23—41216no—
198C23—20624no—
199C23—20648no—
200C23—20648no—
201C23—20696no—
202C23—206256no—
203C23—20696no—
204C23—2066no—
205C23—20612no—
206C23—20624no—
207C23D4×D103112yescomplemented
208C23C23×D10316yes—
209C23C23×D10311yescharacteristic
210C23C23×D10312yescomplemented
211D4—224no—
212D4—20624no—
213D4—20624no—
214D4—20624no—
215C2×C4—26no—
216C2×C4—1036no—
217C2×C4—20624no—
218C2×C4—2066no—
219C2×C4C23×D10316yescomplemented
220C22—232no—
221C22—212no—
222C22—224no—
223C22—26no—
224C22—44no—
225C22—10312no—
226C22—10316no—
227C22—10312no—
228C22—41216no—
229C22—4124no—
230C22—20696no—
231C22—20696no—
232C22—2066no—
233C22—20612no—
234C22—20624no—
235C22C2×D4×D10316yes—
236C22C2×D4×D103112yescomplemented
237C22C24×D10311yescharacteristic
238C4—26no—
239C4—2066no—
240C2—212no—
241C2—42no—
242C2—1038no—
243C2—4122no—
244C2—20612no—
245C2#120×D10314yesdirect product factor
246C2C22×D4×D10313yes—
subgroupG/H
centerC23C23×D103
commutator, cosocleC22×C103C25
FrattiniC22C24×D103
FittingC2×#120×C103C2
socleC23×C103C24
hypercenterC2×#120D103
hypocenterC103C22×#120
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C25×D103C2semidirect
2. C22×D4×D103C2semidirect
3. C2×#15692991C2semidirect
4. C2×#15692990C2semidirect
5. C2×#15692989C2semidirect
6. #120×D103C2direct (N × H)
7. C2×C22⋊C4×D103C2semidirect
8. C2×#120×C103C2semidirect
11. C24×D103C22semidirect
12. C24×D103C22semidirect
13. C24×D103C22semidirect
14. C22×D412C22semidirect
15. C22×C22⋊D103C22semidirect
16. C22×C22⋊D103C22semidirect
18. C2×D4×D103C22semidirect
19. C22×C4×D103C22semidirect
20. #15692991C22semidirect
21. #15692990C22semidirect
22. #15692989C22semidirect
23. C2×C22⋊Dic103C22semidirect
24. C2×(C2×D103)⋊C4C22semidirect
25. C22⋊C4×D103C22semidirect
26. C25×C103C22semidirect
27. C22×D4×C103C22semidirect
28. #120×C103C22semidirect
29. C2×C22⋊C4×C103C22semidirect
36. C23×D103D4semidirect
40. C23×D103C23semidirect
41. C23×D103C23semidirect
42. C23×D103C23semidirect
44. C2×D412C23semidirect
47. C2×C22⋊D103C23semidirect
48. C2×C22⋊D103C23semidirect
50. C22×Dic103C23semidirect
52. C2×C4×D103C23semidirect
53. C22⋊Dic103C23semidirect
54. (C2×D103)⋊C4C23semidirect
57. C24×C103C23semidirect
58. C24×C103C23semidirect
60. C2×D4×C103C23semidirect
61. C22×C4×C103C23semidirect
62. C22⋊C4×C103C23semidirect
67. C23×C103C2×D4semidirect
70. C23×C103C24semidirect
82. C22×D103C2×D4semidirect
83. C22×D103C2×D4semidirect
86. C22×D103C24semidirect
89. C2×C4×C103C24semidirect
93. C2×Dic103C24semidirect
102. C22×C103C22×D4semidirect
111. C2×D103#120direct (N × H)
113. C2×D103C22×D4semidirect
118. C2×C103C2×#120semidirect
122. D103C2×#120direct (N × H)
124. C103C22×#120semidirect
131. C2×#120D103direct (N × H)
138. C25C2×D103semidirect
144. C22×D4C2×D103semidirect
149. #120C2×D103direct (N × H)
153. C2×C22⋊C4C2×D103semidirect
169. C24C22×D103semidirect
170. C24C22×D103semidirect
179. C2×D4C22×D103semidirect
183. C22×C4C22×D103semidirect
186. C22⋊C4C22×D103semidirect
207. C23D4×D103semidirect
210. C23C23×D103semidirect
219. C2×C4C23×D103semidirect
236. C22C2×D4×D103semidirect
245. C2#120×D103direct (N × H)

Maximal subgroups

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

subgroupindex
C25×D1032
C22×D4×D1032
C2×#156929912
C2×#156929902
C2×#156929892
#120×D1032
C2×C22⋊C4×D1032
C2×#120×C1032
C22×#120103