Finite Group Databasebeta

← C22×#107 #2908

Subgroups — C22×#107 #2908

Order 128.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C8C211yesmaximal, characteristic
2C22×C4⋊C4C212yesmaximal
3C2×#107C2112yesmaximal, direct product factor
4C23×C4—22no—
5C23×C4C2211yescharacteristic
6C22×C8C418yescomplemented
7C22×C8C2216yes—
8C2×C4⋊C4—26no—
9C2×C4⋊C4C22112yes—
10#107C22116yesdirect product factor
11C24D411yescharacteristic
12C22×C4—212no—
13C22×C4—48no—
14C22×C4C2×C414yes—
15C22×C4D413yes—
16C22×C4Q814yes—
17C22×C4C2313yes—
18C2×C8C2×C4124yescomplemented
19C2×C8C2314yes—
20C4⋊C4—212no—
21C4⋊C4C2318yes—
22C23C4⋊C414yes—
23C23D814yes—
24C23Q1614yes—
25C23C2×D413yes—
26C2×C4—28no—
27C2×C4—424no—
28C2×C4C4⋊C4112yes—
29C2×C4C22×C416yes—
30C2×C4C2×D413yes—
31C2×C4C2×Q816yes—
32C2×C4C2411yescharacteristic
33C8C22×C418yescomplemented
34C22#107116yesdirect product factor
35C22C2×C4⋊C416yes—
36C22C2×D816yes—
37C22C2×Q1616yes—
38C22C22×D411yescharacteristic
39C4—48no—
40C4C2×C4⋊C416yes—
41C4C23×C411yescharacteristic
42C4C22×Q811yescharacteristic
43C2C2×#107112yesdirect product factor
44C2C22×C4⋊C411yescharacteristic
45C2C22×D811yescharacteristic
46C2C22×Q1611yescharacteristic
subgroupG/H
center, socle, prime radicalC24D4
commutatorC4C23×C4
Frattini, cosocleC2×C4C24
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×C4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#107C2direct (N × H)
6. C22×C8C4semidirect
10. #107C22direct (N × H)
18. C2×C8C2×C4semidirect
33. C8C22×C4semidirect
34. C22#107direct (N × H)
43. C2C2×#107direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C82
C22×C4⋊C42
C2×#1072