Finite Group Databasebeta

← C2×#15689940 #20258155

Subgroups — C2×#15689940 #20258155

Order 6016.

1408 conjugacy classes of subgroups; only the 549 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 549 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×#13094071C212yesmaximal, complemented
2#15689940C2116yesmaximal, direct product factor
3C2×#13094057C216yesmaximal, complemented
4C2×#13094046C213yesmaximal, complemented
5C22×Dic188C213yesmaximal, complemented
6C2×#131×C47C211yesmaximal, characteristic, complemented
7#13094071—28no—
8#13094071C22116yescomplemented
9C2×#10625350C2216yes—
10C2×#10625352—26no—
11C22×Dic94C2216yes—
12C2×Q8×D47—22no—
13#13094057C22148yescomplemented
14#13094046C22124yescomplemented
15C2×Dic188C2213yes—
16C2×Dic188C2216yes—
17C2×Dic188C22124yescomplemented
18C2×#10625325C2216yes—
19C2×D376C2211yescharacteristic
20C2×#41×C47C2211yescharacteristic
21#131×C47C2218yescomplemented
22C2×M16×C47C2213yes—
23C22×C8×C47C2213yes—
24#41×C47D414yes—
25#41×C47C2314yes—
26C2×Q8×C47D411yescharacteristic
27C2×D4×C47D413yes—
28C22×C4×C47C2313yes—
29C2×C22⋊D47—26no—
30C22×Dic47—26no—
31Q8×D47—216no—
32#10625352—248no—
33#10625350—212no—
34#10625350C23124yes—
35C2×D188C2312yes—
36C2×C4×D47—26no—
37C2×Dic94—26no—
38C2×Dic94—212no—
39C2×Dic94C2316yes—
40C2×Dic94C23124yes—
41M16×C47C23112yes—
42C2×C8×C47C2311yescharacteristic
43C2×C8×C47C2313yes—
44C2×C8×C47C23112yes—
45Dic188C23112yes—
46Dic188C23124yes—
47D376C2314yes—
48#10625325C23124yes—
49C23×C47C2×D413yes—
50C22×D47—22no—
51Q8×C47C2×D414yes—
52D4×C47C2×D4112yes—
53C2×C4×C47C2×D413yes—
54C2×C4×C47C2×D416yes—
55C2×C4×C47C2411yescharacteristic
56C2×C4×C47C2416yes—
57C22⋊D47—224no—
58C2×Dic47—26no—
59C2×Dic47—224no—
60D188—22no—
61D188C2414yes—
62C4×D47—224no—
63Dic94—26no—
64Dic94—224no—
65Dic94C24112yes—
66C8×C47C2416yes—
67C8×C47C2412yes—
68C22×C47—26no—
69C22×C47C22×D416yes—
70C22×C47C22×D411yescharacteristic
71C2×D47—24no—
72C2×D47—44no—
73C4×C47C22×D411yescharacteristic
74C4×C47C22×D416yes—
75C4×C47C2511yescharacteristic
76Dic47—212no—
77C2×#578—471nomaximal, Sylow
78C2×C47—26no—
79C2×C47#57812yescomplemented
80C2×C47C23×D411yescharacteristic
81D47—44no—
82C2×2−1+4—472no—
83#578—4716no—
84C2×#137—476no—
85C2×#135—473no—
86C22×Q16—473no—
87C2×#131D4711yescharacteristic, complemented
88C47C2×#57811yescharacteristic, complemented, Sylow
892−1+4—4716no—
902−1+4—948no—
91C2×#41—476no—
92C2×#41—946no—
93C2×#41C2×D4711yescharacteristic
94C22×Q8—476no—
95C22×Q8—942no—
96#137—4748no—
97#135—4724no—
98C2×Q16—473no—
99C2×Q16—476no—
100C2×Q16—4724no—
101C2×SD16—476no—
102C2×D8—471no—
103#131C2×D4718yescomplemented
104C2×M16C2×D4713yes—
105C22×C8C2×D4713yes—
106#41—4724no—
107#41—9448no—
108#41—9412no—
109#41D18814yes—
110#41C22×D4714yes—
111C2×Q8—476no—
112C2×Q8—4724no—
113C2×Q8—9416no—
114C2×Q8—946no—
115C2×Q8—9412no—
116C2×Q8D18811yescharacteristic
117C2×D4—472no—
118C2×D4—946no—
119C2×D4D18813yes—
120C22×C4—946no—
121C22×C4—946no—
122C22×C4C22×D4713yes—
123Q16—4712no—
124Q16—4724no—
125SD16—4724no—
126D8—474no—
127M16C22×D47112yes—
128C2×C8C22×D4711yescharacteristic
129C2×C8C22×D4713yes—
130C2×C8C22×D47112yes—
131C23—942no—
132C23C2×D18813yes—
133Q8—4712no—
134Q8—9424no—
135Q8—946no—
136Q8C2×D18814yes—
137D4—474no—
138D4—9424no—
139D4—942no—
140D4C2×D188112yes—
141C2×C4—9424no—
142C2×C4—946no—
143C2×C4—9424no—
144C2×C4C2×D18816yes—
145C2×C4C2×D18813yes—
146C2×C4C23×D4716yes—
147C2×C4C23×D4711yescharacteristic
148C8C23×D4712yes—
149C8C23×D4716yes—
150C22—26no—
151C22—944no—
152C22—1884no—
153C22C22×D18816yes—
154C22C22×D18811yescharacteristic
155C4—9412no—
156C4C22×D18816yes—
157C4C22×D18811yescharacteristic
158C4C24×D4711yescharacteristic
159C2—26no—
160C2—1884no—
161C2#1568994012yesdirect product factor
162C2C23×D18811yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC4×C47C25
FrattiniC4C24×D47
FittingC2×#131×C47C2
socleC22×C47C22×D4
hypercenterC2×#131D47
hypocenterC47C2×#578
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. C2×#13094071C2semidirect
2. #15689940C2direct (N × H)
3. C2×#13094057C2semidirect
4. C2×#13094046C2semidirect
5. C22×Dic188C2semidirect
6. C2×#131×C47C2semidirect
8. #13094071C22semidirect
13. #13094057C22semidirect
14. #13094046C22semidirect
17. C2×Dic188C22semidirect
21. #131×C47C22semidirect
79. C2×C47#578semidirect
87. C2×#131D47semidirect
88. C47C2×#578semidirect
103. #131C2×D47semidirect
161. C2#15689940direct (N × H)