Finite Group Databasebeta

← C22×#20269411 #41001188

Subgroups — C22×#20269411 #41001188

Order 26816.

890 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20269411C2124yesmaximal, direct product factor
2C22×Dic838C211yesmaximal, characteristic, complemented
3C22×D1676C211yesmaximal, characteristic, complemented
4C22×C22⋊D419C212yesmaximal, complemented
5C22×C4×D419C212yesmaximal, complemented
6C23×C4×C419C211yesmaximal, characteristic, complemented
7C23×D419C2212yes—
8#20269411C22164yesdirect product factor
9C2×Dic838C22112yescomplemented
10C2×D1676C22112yescomplemented
11C2×C22⋊D419C22124yescomplemented
12C22×Dic419C2212yes—
13C2×C4×D419C22124yescomplemented
14C24×C419C2211yescharacteristic
15C22×C4×C419C2211yescharacteristic
16C22×C4×C419C2211yescharacteristic
17C22×C4×C419C22112yescomplemented
18C22×D419—28no—
19C22×D419C23112yes—
20Dic838C23116yescomplemented
21D1676C23116yescomplemented
22C22⋊D419C23132yescomplemented
23C2×Dic419C23112yes—
24C4×D419C23132yescomplemented
25C23×C419—24no—
26C23×C419C2316yes—
27C23×C419C2311yescharacteristic
28C2×C4×C419C2316yes—
29C2×C4×C419C2316yes—
30C2×C4×C419C23116yescomplemented
31C22×C419—212no—
32C22×C419#4114yescomplemented
33C22×C419C2414yes—
34C22×C419C2413yes—
35C2×D419—224no—
36C2×D419C2418yes—
37C4×C419C2414yes—
38C4×C419C2414yes—
39Dic419C2418yes—
40C2×C419—24no—
41C2×C419C2×#4116yescomplemented
42C2×C419C2511yescharacteristic
43D419—28no—
44C419C22×#4111yescharacteristic, complemented, Sylow
45C22×#41—4191nomaximal, Sylow
46C2×#41—41924no—
47C22×Q8—4191no—
48C22×D4—4192no—
49C22×D4—4191no—
50C23×C4—4192no—
51C23×C4D41911yescharacteristic, complemented
52C24—4192no—
53C24C2×D41911yescharacteristic
54#41—41964no—
55C2×Q8—41912no—
56C2×D4—41924no—
57C2×D4—41912no—
58C22×C4—4192no—
59C22×C4—41924no—
60C22×C4C2×D41911yescharacteristic
61C22×C4C2×D41911yescharacteristic
62C22×C4C2×D419112yescomplemented
63C23—24no—
64C23—8388no—
65C23—41912no—
66C23C22×D41916yes—
67C23C22×D41911yescharacteristic
68Q8—41916no—
69D4—41932no—
70D4—41916no—
71C2×C4—41912no—
72C2×C4—41932no—
73C2×C4C22×D41916yes—
74C2×C4C22×D41916yes—
75C2×C4C22×D419116yescomplemented
76C22—212no—
77C22—83824no—
78C22—4198no—
79C22#2026941114yesdirect product factor
80C22C23×D41914yes—
81C22C23×D41913yes—
82C4—4198no—
83C4C23×D41914yes—
84C4C23×D41914yes—
85C2—24no—
86C2—8388no—
87C2C2×#2026941116yesdirect product factor
88C2C24×D41911yescharacteristic
subgroupG/H
centerC22×C4C2×D419
commutator, cosocleC2×C419C25
FrattiniC2C24×D419
FittingC23×C4×C419C2
socleC23×C419C23
hypercenterC23×C4D419
hypocenterC419C22×#41
LCSG ▷ C2×C419 ▷ C419
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#20269411C2direct (N × H)
2. C22×Dic838C2semidirect
3. C22×D1676C2semidirect
4. C22×C22⋊D419C2semidirect
5. C22×C4×D419C2semidirect
6. C23×C4×C419C2semidirect
8. #20269411C22direct (N × H)
9. C2×Dic838C22semidirect
10. C2×D1676C22semidirect
11. C2×C22⋊D419C22semidirect
13. C2×C4×D419C22semidirect
17. C22×C4×C419C22semidirect
20. Dic838C23semidirect
21. D1676C23semidirect
22. C22⋊D419C23semidirect
24. C4×D419C23semidirect
30. C2×C4×C419C23semidirect
32. C22×C419#41semidirect
41. C2×C419C2×#41semidirect
44. C419C22×#41semidirect
51. C23×C4D419semidirect
62. C22×C4C2×D419semidirect
75. C2×C4C22×D419semidirect
79. C22#20269411direct (N × H)
87. C2C2×#20269411direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#202694112
C22×Dic8382
C22×D16762
C22×C22⋊D4192
C22×C4×D4192
C23×C4×C4192
C22×#41419