Finite Group Databasebeta

← #21443837

Subgroups — #21443837

Order 7808.

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⋊#11758185C211yesmaximal, characteristic
2#16839527C211yesmaximal, characteristic
3C61×#467C211yesmaximal, characteristic
4C2×#11758194—21no—
5C2×#11758185—21no—
6C2×Q16×C61C411yescharacteristic
7C22×C8×C61C2211yescharacteristic
8C22⋊Q8×C61—21no—
9#107×C61C411yescharacteristic
10#103×C61—21no—
11C2×Q8×C61—21no—
12C22×C4×C61D411yescharacteristic
13Q16×C61—41no—
14C2×C8×C61—41no—
15C2×C8×C61C2×C411yescharacteristic
16C2×C8×C61D411yescharacteristic
17C4⋊C4×C61—21no—
18C4⋊C4×C61—41no—
19C22⋊C4×C61—41no—
20#11758194—22no—
21#11758194—41no—
22C2×#92418—41no—
23#11758185—41no—
24C23×C61SD1611yescharacteristic
25Q8×C61—41no—
26Q8×C61—41no—
27C2×C4×C61—21no—
28C2×C4×C61—21no—
29C2×C4×C61—41no—
30C2×C4×C61—41no—
31C2×C4×C61C22⋊C411yescharacteristic
32C2×C4×C61D811yescharacteristic
33C8×C61—21no—
34C8×C61—21no—
35#92418—42no—
36C22×C61—21no—
37C22×C61—21no—
38C22×C61—21no—
39C22×C61#10211yescharacteristic
40C4×C61—21no—
41C4×C61—81no—
42C4×C61—81no—
43C4×C61#9911yescharacteristic
44C4×C61#10411yescharacteristic
45#1350—611nomaximal, Sylow
46C2×C61—41no—
47C2×C61#32711yescharacteristic
48C2×C61#35911yescharacteristic
49C2×C61#36211yescharacteristic
50#467D6111yescharacteristic
51C22⋊C16—611no—
52#341—611no—
53C61#135011yescharacteristic, complemented, Sylow
54C2×Q16Dic6111yescharacteristic
55C2×M16—1221no—
56C22×C8C2×D6111yescharacteristic
57C22⋊Q8—21no—
58C2×C16—1221no—
59#107Dic6111yescharacteristic
60#103—21no—
61C2×Q8—21no—
62C22×C4C22⋊D6111yescharacteristic
63Q16—41no—
64M16—1222no—
65M16—2441no—
66C2×C8—41no—
67C2×C8—2441no—
68C2×C8C2×Dic6111yescharacteristic
69C2×C8C22⋊D6111yescharacteristic
70C4⋊C4—21no—
71C4⋊C4—41no—
72C22⋊C4—41no—
73C16—2441no—
74C23#1175820011yescharacteristic
75Q8—41no—
76Q8—41no—
77C2×C4—21no—
78C2×C4—21no—
79C2×C4—41no—
80C2×C4—41no—
81C2×C4#1175819911yescharacteristic
82C2×C4C22⋊Dic6111yescharacteristic
83C8—21no—
84C8—21no—
85C8—2442no—
86C22—21no—
87C22—21no—
88C22—21no—
89C22#1451969811yescharacteristic
90C4—21no—
91C4—81no—
92C4—81no—
93C4#1451969211yescharacteristic
94C4#1451970411yescharacteristic
95C2—41no—
96C2#1683949611yescharacteristic
97C2#1683956911yescharacteristic
98C2#1683957811yescharacteristic
subgroupG/H
centerC22#14519698
commutatorC2×C8×C61C2×C4
FrattiniC22×C8C2×D61
FittingC61×#467C2
socleC22×C61#102
hypercenter#467D61
hypocenterC61#1350
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
53. C61#1350semidirect