Finite Group Databasebeta

← C2×#126×D47 #20256642

Subgroups — C2×#126×D47 #20256642

Order 6016.

1320 conjugacy classes of subgroups; only the 517 normal subgroups are shown.

normal subgroups only

This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 517 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
1C2×#13094019C213yesmaximal, complemented
2C2×#13094018C211yesmaximal, characteristic, complemented
3C2×#13094017C213yesmaximal, complemented
4#126×D47C2116yesmaximal, direct product factor
5C2×C4⋊C4×D47C213yesmaximal, complemented
6C2×C22⋊C4×D47C213yesmaximal
7C2×C42×D47C211yesmaximal, characteristic, complemented
8C2×#126×C47C211yesmaximal, characteristic, complemented
9C24×D47C2211yescharacteristic
10C22×C4×D47C2213yes—
11C22×C4×D47C2213yes—
12#13094019C22124yescomplemented
13#13094018C2218yescomplemented
14#13094017C22124yescomplemented
15C2×C4⋊Dic47C2213yescomplemented
16C2×Dic47⋊C4C2213yescomplemented
17C2×Dic47⋊C4C2213yescomplemented
18C4⋊C4×D47C22124yescomplemented
19C2×C22⋊Dic47C2213yes—
20C2×(C2×D47)⋊C4C2213yes—
21C2×(C2×D47)⋊C4C2213yes—
22C22⋊C4×D47C22124yes—
23C2×C4×Dic47C2213yescomplemented
24C42×D47C2218yescomplemented
25#126×C47C2218yescomplemented
26C2×C4⋊C4×C47C2213yescomplemented
27C2×C22⋊C4×C47C2213yes—
28C2×C42×C47C2211yescharacteristic, complemented
29C24×C47C2311yescharacteristic
30C23×D47—212no—
31C23×D47C2314yes—
32C23×D47C2311yescharacteristic
33C23×D47C2311yescharacteristic
34C22×C4×C47C2313yes—
35C22×C4×C47C2313yes—
36C22×Dic47C2313yes—
37C22×Dic47C2313yes—
38C2×C4×D47—212no—
39C2×C4×D47—212no—
40C2×C4×D47C23112yes—
41C2×C4×D47C23112yes—
42C4⋊C4×C47C23112yescomplemented
43C22⋊C4×C47C23112yes—
44C42×C47C2314yescomplemented
45C22⋊Dic47C23112yes—
46(C2×D47)⋊C4C23112yes—
47(C2×D47)⋊C4C23112yes—
48C4⋊Dic47C23112yescomplemented
49Dic47⋊C4C23112yescomplemented
50Dic47⋊C4C23112yescomplemented
51C4×Dic47C23112yescomplemented
52C23×C47—26no—
53C23×C47C2412yes—
54C23×C47C2411yescharacteristic
55C22×D47—26no—
56C22×D47—224no—
57C22×D47—416no—
58C22×D47#41112yes—
59C22×D47C2412yes—
60C22×D47C2412yes—
61C2×C4×C47—26no—
62C2×C4×C47—26no—
63C2×C4×C47C2416yes—
64C2×C4×C47C2416yes—
65C2×Dic47—26no—
66C2×Dic47—26no—
67C2×Dic47C2416yes—
68C2×Dic47C2416yes—
69C4×D47—224no—
70C4×D47—224no—
71C22×C47—26no—
72C22×C47—44no—
73C22×C47C2×#4116yes—
74C22×C47C2511yescharacteristic
75C2×D47—26no—
76C2×D47—44no—
77C2×D47—416no—
78C2×D47#126116yesdirect product factor
79C2×D47C2×#41112yes—
80C4×C47—26no—
81C4×C47—26no—
82Dic47—26no—
83Dic47—26no—
84C22×#126—471nomaximal, Sylow
85C2×C47—42no—
86C2×C47C2×#12614yescomplemented
87C2×C47C22×#4113yes—
88D47—42no—
89D47C2×#12618yesdirect product factor
90C2×#126—4716no—
91C2×#126—473no—
92C2×#126—473no—
93C2×#126—471no—
94C2×#126D4711yescharacteristic, direct product factor
95C22×C4⋊C4—473no—
96C22×C22⋊C4—473no—
97C22×C42—471no—
98C47C22×#12611yescharacteristic, complemented, Sylow
99C25—471no—
100C23×C4—473no—
101C23×C4—473no—
102#126—4724no—
103#126—4724no—
104#126—478no—
105#126C2×D4718yesdirect product factor
106C2×C4⋊C4—473no—
107C2×C4⋊C4—473no—
108C2×C4⋊C4—473no—
109C2×C4⋊C4—4724no—
110C2×C4⋊C4C2×D4713yescomplemented
111C2×C22⋊C4—473no—
112C2×C22⋊C4—473no—
113C2×C22⋊C4—473no—
114C2×C22⋊C4—4724no—
115C2×C22⋊C4C2×D4713yes—
116C2×C42—473no—
117C2×C42—478no—
118C2×C42C2×D4711yescharacteristic, complemented
119C24—471no—
120C24—474no—
121C24—471no—
122C24—9412no—
123C24C22×D4711yescharacteristic
124C22×C4—473no—
125C22×C4—473no—
126C22×C4—4712no—
127C22×C4—4712no—
128C22×C4—9412no—
129C22×C4—9412no—
130C22×C4C22×D4713yes—
131C22×C4C22×D4713yes—
132C4⋊C4—4712no—
133C4⋊C4—4712no—
134C4⋊C4—4712no—
135C4⋊C4C22×D47112yescomplemented
136C22⋊C4—4712no—
137C22⋊C4—4712no—
138C22⋊C4—4712no—
139C22⋊C4C22×D47112yes—
140C42—4712no—
141C42C22×D4714yescomplemented
142C23—26no—
143C23—4712no—
144C23—472no—
145C23—472no—
146C23—9424no—
147C23—946no—
148C23—18816no—
149C23C23×D4712yes—
150C23C23×D4711yescharacteristic
151C2×C4—26no—
152C2×C4—26no—
153C2×C4—476no—
154C2×C4—476no—
155C2×C4—9424no—
156C2×C4—9424no—
157C2×C4—946no—
158C2×C4—946no—
159C2×C4C23×D4716yes—
160C2×C4C23×D4716yes—
161C22—26no—
162C22—44no—
163C22—4716no—
164C22—4712no—
165C22—946no—
166C22—18816no—
167C22—1884no—
168C22#41×D4716yes—
169C22C24×D4711yescharacteristic
170C4—26no—
171C4—26no—
172C4—946no—
173C4—946no—
174C2—42no—
175C2—478no—
176C2—1882no—
177C2#126×D4714yesdirect product factor
178C2C2×#41×D4713yes—
subgroupG/H
centerC23C23×D47
commutatorC22×C47C25
FrattiniC22C24×D47
FittingC2×#126×C47C2
socleC23×C47C24
hypercenterC2×#126D47
hypocenterC47C22×#126
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×#13094019C2semidirect
2. C2×#13094018C2semidirect
3. C2×#13094017C2semidirect
4. #126×D47C2direct (N × H)
5. C2×C4⋊C4×D47C2semidirect
7. C2×C42×D47C2semidirect
8. C2×#126×C47C2semidirect
12. #13094019C22semidirect
13. #13094018C22semidirect
14. #13094017C22semidirect
15. C2×C4⋊Dic47C22semidirect
16. C2×Dic47⋊C4C22semidirect
17. C2×Dic47⋊C4C22semidirect
18. C4⋊C4×D47C22semidirect
23. C2×C4×Dic47C22semidirect
24. C42×D47C22semidirect
25. #126×C47C22semidirect
26. C2×C4⋊C4×C47C22semidirect
28. C2×C42×C47C22semidirect
42. C4⋊C4×C47C23semidirect
44. C42×C47C23semidirect
48. C4⋊Dic47C23semidirect
49. Dic47⋊C4C23semidirect
50. Dic47⋊C4C23semidirect
51. C4×Dic47C23semidirect
78. C2×D47#126direct (N × H)
86. C2×C47C2×#126semidirect
89. D47C2×#126direct (N × H)
94. C2×#126D47direct (N × H)
98. C47C22×#126semidirect
105. #126C2×D47direct (N × H)
110. C2×C4⋊C4C2×D47semidirect
118. C2×C42C2×D47semidirect
135. C4⋊C4C22×D47semidirect
141. C42C22×D47semidirect
177. C2#126×D47direct (N × H)