Finite Group Databasebeta

← C2×#20268533 #27209264

Subgroups — C2×#20268533 #27209264

Order 13184.

1408 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 469 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
1#20268533C2116yesmaximal, direct product factor
2C2×#15693010C212yesmaximal, complemented
3C2×#15693009C212yesmaximal, complemented
4C2×#15693007C214yesmaximal, complemented
5C2×#15692991C214yesmaximal, complemented
6C2×#15692989C212yesmaximal, complemented
7C2×#124×C103C211yesmaximal, characteristic, complemented
8C24×D103C2212yescomplemented
9C22×Dic206C2212yescomplemented
10C22×D412C2212yes—
11C22×D412C2212yes—
12C22×C22⋊D103C2214yes—
13#15693010C22116yescomplemented
14#15693009C22116yescomplemented
15#15693007C22132yescomplemented
16#15692991C22132yescomplemented
17#15692989C22116yescomplemented
18C2×C22⋊Dic103C2212yescomplemented
19C2×(C2×D103)⋊C4C2214yescomplemented
20C2×(C2×D103)⋊C4C2214yescomplemented
21C2×(C2×D103)⋊C4C2214yescomplemented
22C2×C4×Dic103C2212yescomplemented
23C22×Q8×C103C2211yescharacteristic, complemented
24C22×D4×C103C2211yescharacteristic
25#124×C103C2218yescomplemented
26C2×C22⋊C4×C103C2214yescomplemented
27C2×C42×C103C2211yescharacteristic, complemented
28C23×D103—48no—
29C23×D103—44no—
30C23×D103C2314yes—
31C23×D103C2318yescomplemented
32C2×Dic206—44no—
33C2×Dic206C2318yescomplemented
34C2×D412—44no—
35C2×D412—44no—
36C2×D412C2318yes—
37C2×D412C2318yes—
38C2×C22⋊D103—48no—
39C2×C22⋊D103C23116yes—
40C22×Dic103C2314yes—
41C22⋊Dic103C2318yescomplemented
42(C2×D103)⋊C4C23116yescomplemented
43(C2×D103)⋊C4C23116yescomplemented
44(C2×D103)⋊C4C23116yescomplemented
45C4×Dic103C2318yescomplemented
46C24×C103C2312yes—
47C2×Q8×C103—42no—
48C2×Q8×C103C2314yescomplemented
49C2×D4×C103—42no—
50C2×D4×C103C2314yes—
51C22×C4×C103C2312yes—
52C22×C4×C103C2312yes—
53C22×C4×C103C2311yescharacteristic
54C22⋊C4×C103C23116yescomplemented
55C42×C103C2314yescomplemented
56C23×C103—24no—
57C23×C103—28no—
58C23×C103C2414yes—
59C23×C103C2411yescharacteristic
60C22×D103—28no—
61C22×D103—28no—
62C22×D103—28no—
63C22×D103—48no—
64C22×D103—416no—
65C22×D103—432no—
66C22×D103C2418yes—
67Q8×C103—44no—
68D4×C103—44no—
69C2×C4×C103—22no—
70C2×C4×C103—24no—
71C2×C4×C103—24no—
72C2×C4×C103C2414yes—
73C2×C4×C103C2412yes—
74C2×C4×C103C2414yes—
75C22⋊D103—416no—
76C2×Dic103—28no—
77C2×Dic103C2418yes—
78D412—48no—
79D412—48no—
80Dic206—48no—
81C22×C103—28no—
82C22×C103—24no—
83C22×C103—48no—
84C22×C103H(5,𝔽2)12yes—
85C22×C103H(5,𝔽2)14yes—
86C22×C103C2511yescharacteristic
87C2×D103—28no—
88C2×D103—28no—
89C2×D103—28no—
90C2×D103—432no—
91C2×D103—416no—
92C4×C103—24no—
93C4×C103—24no—
94C4×C103—22no—
95Dic103—28no—
96C2×C103—44no—
97C2×C103H(3,𝔽4)14yescomplemented
98C2×C103C2×H(5,𝔽2)11yescharacteristic
99C2×C103C2×H(5,𝔽2)12yes—
100D103—48no—
101C2×H(3,𝔽4)—1031nomaximal, Sylow
102C103C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
103H(3,𝔽4)—10316no—
104C2×#124—1032no—
105C2×#124—1034no—
106C2×#124—1032no—
107C2×#124D10311yescharacteristic, complemented
108C2×#120—1032no—
109C2×#120—1034no—
110C25—1032no—
111C22×Q8—1032no—
112C22×Q8C2×D10311yescharacteristic, complemented
113C22×D4—1034no—
114C22×D4—1032no—
115C22×D4—1032no—
116C22×D4C2×D10311yescharacteristic
117#124—10316no—
118#124—10332no—
119#124—10316no—
120#124C2×D10318yescomplemented
121#120—10316no—
122#120—10332no—
123C2×C22⋊C4—1032no—
124C2×C22⋊C4—1034no—
125C2×C22⋊C4—1034no—
126C2×C22⋊C4—1034no—
127C2×C22⋊C4C2×D10314yescomplemented
128C2×C42—1032no—
129C2×C42C2×D10311yescharacteristic, complemented
130C24—1038no—
131C24—1034no—
132C24—4124no—
133C24—4128no—
134C24C22×D10312yes—
135C2×Q8—42no—
136C2×Q8—1038no—
137C2×Q8—4124no—
138C2×Q8C22×D10314yescomplemented
139C2×D4—42no—
140C2×D4—10316no—
141C2×D4—1038no—
142C2×D4—1038no—
143C2×D4—4124no—
144C2×D4—4124no—
145C2×D4—4128no—
146C2×D4C22×D10314yes—
147C22×C4—1034no—
148C22×C4C22×D10312yes—
149C22×C4C22×D10311yescharacteristic
150C22×C4C22×D10312yes—
151C22⋊C4—1038no—
152C22⋊C4—10316no—
153C22⋊C4—10316no—
154C22⋊C4—10316no—
155C22⋊C4C22×D103116yescomplemented
156C42—1038no—
157C42C22×D10314yescomplemented
158C23—24no—
159C23—28no—
160C23—1038no—
161C23—4128no—
162C23—41216no—
163C23—41232no—
164C23—2068no—
165C23—2068no—
166C23—2068no—
167C23C23×D10314yes—
168C23C23×D10311yescharacteristic
169Q8—44no—
170Q8—4128no—
171D4—44no—
172D4—4128no—
173D4—4128no—
174D4—41216no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—1038no—
179C2×C4—2068no—
180C2×C4C23×D10314yes—
181C2×C4C23×D10312yes—
182C2×C4C23×D10314yes—
183C22—24no—
184C22—28no—
185C22—48no—
186C22—41232no—
187C22—41216no—
188C22—2068no—
189C22—2068no—
190C22—2068no—
191C22#1569306612yes—
192C22#1569306714yes—
193C22C24×D10311yescharacteristic
194C4—22no—
195C4—24no—
196C4—24no—
197C4—2068no—
198C2—44no—
199C2—4128no—
200C2#2026853314yesdirect product factor
201C2C2×#1569306611yescharacteristic
202C2C2×#1569306712yes—
subgroupG/H
centerC23C23×D103
commutator, cosocleC22×C103C25
FrattiniC22C24×D103
FittingC2×#124×C103C2
socleC23×C103C24
hypercenterC2×#124D103
hypocenterC103C2×H(3,𝔽4)
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #20268533C2direct (N × H)
2. C2×#15693010C2semidirect
3. C2×#15693009C2semidirect
4. C2×#15693007C2semidirect
5. C2×#15692991C2semidirect
6. C2×#15692989C2semidirect
7. C2×#124×C103C2semidirect
8. C24×D103C22semidirect
9. C22×Dic206C22semidirect
13. #15693010C22semidirect
14. #15693009C22semidirect
15. #15693007C22semidirect
16. #15692991C22semidirect
17. #15692989C22semidirect
18. C2×C22⋊Dic103C22semidirect
19. C2×(C2×D103)⋊C4C22semidirect
20. C2×(C2×D103)⋊C4C22semidirect
21. C2×(C2×D103)⋊C4C22semidirect
22. C2×C4×Dic103C22semidirect
23. C22×Q8×C103C22semidirect
25. #124×C103C22semidirect
26. C2×C22⋊C4×C103C22semidirect
27. C2×C42×C103C22semidirect
31. C23×D103C23semidirect
33. C2×Dic206C23semidirect
41. C22⋊Dic103C23semidirect
42. (C2×D103)⋊C4C23semidirect
43. (C2×D103)⋊C4C23semidirect
44. (C2×D103)⋊C4C23semidirect
45. C4×Dic103C23semidirect
48. C2×Q8×C103C23semidirect
54. C22⋊C4×C103C23semidirect
55. C42×C103C23semidirect
97. C2×C103H(3,𝔽4)semidirect
102. C103C2×H(3,𝔽4)semidirect
107. C2×#124D103semidirect
112. C22×Q8C2×D103semidirect
120. #124C2×D103semidirect
127. C2×C22⋊C4C2×D103semidirect
129. C2×C42C2×D103semidirect
138. C2×Q8C22×D103semidirect
155. C22⋊C4C22×D103semidirect
157. C42C22×D103semidirect
200. C2#20268533direct (N × H)

Maximal subgroups

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

subgroupindex
#202685332
C2×#156930102
C2×#156930092
C2×#156930072
C2×#156929912
C2×#156929892
C2×#124×C1032
C2×H(3,𝔽4)103