Finite Group Databasebeta

← #24905481

Subgroups — #24905481

Order 10624.

104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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
1C22⋊(C83⋊C16)C211yesmaximal, characteristic
2#19127466C211yesmaximal, characteristic
3#467×C83C211yesmaximal, characteristic
4C2×#13050574—21no—
5C2×C83⋊C16—21no—
6C2×Q16×C83C411yescharacteristic
7C22×C8×C83C2211yescharacteristic
8C22⋊Q8×C83—21no—
9#107×C83C411yescharacteristic
10#103×C83—21no—
11#13050574—22no—
12#13050574—41no—
13C2×C83⋊C8—41no—
14C83⋊C16—41no—
15C2×Q8×C83—21no—
16C22×C4×C83D411yescharacteristic
17Q16×C83—41no—
18C2×C8×C83—41no—
19C2×C8×C83C2×C411yescharacteristic
20C2×C8×C83D411yescharacteristic
21C4⋊C4×C83—21no—
22C4⋊C4×C83—41no—
23C22⋊C4×C83—41no—
24C23×C83SD1611yescharacteristic
25Q8×C83—41no—
26Q8×C83—41no—
27C2×C4×C83—21no—
28C2×C4×C83—21no—
29C2×C4×C83—41no—
30C2×C4×C83—41no—
31C2×C4×C83C22⋊C411yescharacteristic
32C2×C4×C83D811yescharacteristic
33C8×C83—21no—
34C8×C83—21no—
35C83⋊C8—42no—
36C22×C83—21no—
37C22×C83—21no—
38C22×C83—21no—
39C22×C83#10211yescharacteristic
40C4×C83—21no—
41C4×C83—81no—
42C4×C83—81no—
43C4×C83#9911yescharacteristic
44C4×C83#10411yescharacteristic
45C2×C83—41no—
46C2×C83#32711yescharacteristic
47C2×C83#35911yescharacteristic
48C2×C83#36211yescharacteristic
49#1350—831nomaximal, Sylow
50C83#135011yescharacteristic, complemented, Sylow
51#467D8311yescharacteristic
52C22⋊C16—831no—
53#341—831no—
54C2×Q16Dic8311yescharacteristic
55C2×M16—1661no—
56C22×C8C2×D8311yescharacteristic
57C22⋊Q8—21no—
58C2×C16—1661no—
59#107Dic8311yescharacteristic
60#103—21no—
61C2×Q8—21no—
62C22×C4C22⋊D8311yescharacteristic
63Q16—41no—
64M16—3321no—
65M16—1662no—
66C2×C8—41no—
67C2×C8—3321no—
68C2×C8C2×Dic8311yescharacteristic
69C2×C8C22⋊D8311yescharacteristic
70C4⋊C4—21no—
71C4⋊C4—41no—
72C22⋊C4—41no—
73C16—3321no—
74C23#1305057811yescharacteristic
75Q8—41no—
76Q8—41no—
77C2×C4—21no—
78C2×C4—21no—
79C2×C4—41no—
80C2×C4—41no—
81C2×C4C22⋊Dic8311yescharacteristic
82C2×C4#1305057511yescharacteristic
83C8—21no—
84C8—21no—
85C8—3322no—
86C22—21no—
87C22—21no—
88C22—21no—
89C22#1458171311yescharacteristic
90C4—21no—
91C4—81no—
92C4—81no—
93C4#1458170711yescharacteristic
94C4#1458171911yescharacteristic
95C2—41no—
96C2#1912743511yescharacteristic
97C2#1912750811yescharacteristic
98C2#1912751711yescharacteristic
subgroupG/H
centerC22#14581713
commutatorC2×C8×C83C2×C4
FrattiniC22×C8C2×D83
Fitting#467×C83C2
socleC22×C83#102
prime radicalC23×C83SD16
cosocleC22×C8×C83C22
hypercenter#467D83
hypocenterC83#1350
LCSG ▷ C2×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
50. C83#1350semidirect