Finite Group Databasebeta

← C22×#107×C251 #44547495

Subgroups — C22×#107×C251 #44547495

Order 32128.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C8×C251C211yesmaximal, characteristic
2C22×C4⋊C4×C251C212yesmaximal
3C2×#107×C251C2112yesmaximal, direct product factor
4C23×C4×C251—22no—
5C23×C4×C251C2211yescharacteristic
6C22×C8×C251C418yescomplemented
7C22×C8×C251C2216yes—
8C2×C4⋊C4×C251—26no—
9C2×C4⋊C4×C251C22112yes—
10#107×C251C22116yesdirect product factor
11C24×C251D411yescharacteristic
12C22×C4×C251—212no—
13C22×C4×C251—48no—
14C22×C4×C251C2×C414yes—
15C22×C4×C251D413yes—
16C22×C4×C251Q814yes—
17C22×C4×C251C2313yes—
18C2×C8×C251C2×C4124yescomplemented
19C2×C8×C251C2314yes—
20C4⋊C4×C251—212no—
21C4⋊C4×C251C2318yes—
22C23×C251C4⋊C414yes—
23C23×C251D814yes—
24C23×C251Q1614yes—
25C23×C251C2×D413yes—
26C2×C4×C251—28no—
27C2×C4×C251—424no—
28C2×C4×C251C4⋊C4112yes—
29C2×C4×C251C22×C416yes—
30C2×C4×C251C2×D413yes—
31C2×C4×C251C2×Q816yes—
32C2×C4×C251C2411yescharacteristic
33C8×C251C22×C418yescomplemented
34C22×C251#107116yesdirect product factor
35C22×C251C2×C4⋊C416yes—
36C22×C251C2×D816yes—
37C22×C251C2×Q1616yes—
38C22×C251C22×D411yescharacteristic
39C4×C251—48no—
40C4×C251C2×C4⋊C416yes—
41C4×C251C23×C411yescharacteristic
42C4×C251C22×Q811yescharacteristic
43C2×C251C2×#107112yesdirect product factor
44C2×C251C22×C4⋊C411yescharacteristic
45C2×C251C22×D811yescharacteristic
46C2×C251C22×Q1611yescharacteristic
47C251C22×#10711yescharacteristic, direct product factor, Sylow
48C22×#107C25111yesmaximal, characteristic, direct product factor, Sylow
49C23×C8C2×C25111yescharacteristic
50C22×C4⋊C4C2×C25112yes—
51C2×#107C2×C251112yesdirect product factor
52C23×C4—22no—
53C23×C4C22×C25111yescharacteristic
54C22×C8C4×C25118yescomplemented
55C22×C8C22×C25116yes—
56C2×C4⋊C4—26no—
57C2×C4⋊C4C22×C251112yes—
58#107C22×C251116yesdirect product factor
59C24D4×C25111yescharacteristic
60C22×C4—212no—
61C22×C4—48no—
62C22×C4C2×C4×C25114yes—
63C22×C4D4×C25113yes—
64C22×C4Q8×C25114yes—
65C22×C4C23×C25113yes—
66C2×C8C2×C4×C251124yescomplemented
67C2×C8C23×C25114yes—
68C4⋊C4—212no—
69C4⋊C4C23×C25118yes—
70C23C4⋊C4×C25114yes—
71C23D8×C25114yes—
72C23Q16×C25114yes—
73C23C2×D4×C25113yes—
74C2×C4—28no—
75C2×C4—424no—
76C2×C4C4⋊C4×C251112yes—
77C2×C4C22×C4×C25116yes—
78C2×C4C2×D4×C25113yes—
79C2×C4C2×Q8×C25116yes—
80C2×C4C24×C25111yescharacteristic
81C8C22×C4×C25118yescomplemented
82C22#107×C251116yesdirect product factor
83C22C2×C4⋊C4×C25116yes—
84C22C2×D8×C25116yes—
85C22C2×Q16×C25116yes—
86C22C22×D4×C25111yescharacteristic
87C4—48no—
88C4C2×C4⋊C4×C25116yes—
89C4C23×C4×C25111yescharacteristic
90C4C22×Q8×C25111yescharacteristic
91C2C2×#107×C251112yesdirect product factor
92C2C22×C4⋊C4×C25111yescharacteristic
93C2C22×D8×C25111yescharacteristic
94C2C22×Q16×C25111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C251D4
commutatorC4C23×C4×C251
Frattini, cosocleC2×C4C24×C251
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C251 ◁ C23×C4×C251 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#107×C251C2direct (N × H)
6. C22×C8×C251C4semidirect
10. #107×C251C22direct (N × H)
18. C2×C8×C251C2×C4semidirect
33. C8×C251C22×C4semidirect
34. C22×C251#107direct (N × H)
43. C2×C251C2×#107direct (N × H)
47. C251C22×#107direct (N × H)
48. C22×#107C251direct (N × H)
51. C2×#107C2×C251direct (N × H)
54. C22×C8C4×C251semidirect
58. #107C22×C251direct (N × H)
66. C2×C8C2×C4×C251semidirect
81. C8C22×C4×C251semidirect
82. C22#107×C251direct (N × H)
91. C2C2×#107×C251direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C8×C2512
C22×C4⋊C4×C2512
C2×#107×C2512
C22×#107251