Finite Group Databasebeta

← #21443834

Subgroups — #21443834

Order 7808.

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

normal subgroups only

This group has 114 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, complemented
2#16839527C211yesmaximal, characteristic, complemented
3C61×#466C211yesmaximal, characteristic
4C2×#11758194—21no—
5C2×#11758185—21no—
6C2×D8×C61C411yescharacteristic
7C22×C8×C61C2211yescharacteristic
8#121×C61—21no—
9#107×C61C411yescharacteristic
10#102×C61—21no—
11C2×D4×C61—21no—
12C2×D4×C61—41no—
13C22×C4×C61D411yescharacteristic
14D8×C61—41no—
15C2×C8×C61—41no—
16C2×C8×C61C2×C411yescharacteristic
17C2×C8×C61D411yescharacteristic
18C4⋊C4×C61—21no—
19C22⋊C4×C61—41no—
20#11758194—22no—
21#11758194—41no—
22C2×#92418—41no—
23#11758185—41no—
24C23×C61—41no—
25C23×C61SD1611yescharacteristic
26D4×C61—41no—
27D4×C61—41no—
28D4×C61—82no—
29C2×C4×C61—21no—
30C2×C4×C61—21no—
31C2×C4×C61—41no—
32C2×C4×C61C22⋊C411yescharacteristic
33C2×C4×C61D811yescharacteristic
34C8×C61—21no—
35C8×C61—21no—
36#92418—42no—
37C22×C61—21no—
38C22×C61—21no—
39C22×C61—21no—
40C22×C61—81no—
41C22×C61—81no—
42C22×C61—81no—
43C22×C61#10211yescharacteristic
44C4×C61—21no—
45C4×C61—81no—
46C4×C61#9911yescharacteristic
47C4×C61#10411yescharacteristic
48#1349—611nomaximal, Sylow
49C2×C61—41no—
50C2×C61—161no—
51C2×C61#32711yescharacteristic
52C2×C61#35911yescharacteristic
53C2×C61#36111yescharacteristic
54#466D6111yescharacteristic
55C22⋊C16—611no—
56#341—611no—
57C61#134911yescharacteristic, complemented, Sylow
58C2×D8Dic6111yescharacteristic
59C2×M16—1221no—
60C22×C8C2×D6111yescharacteristic
61#121—21no—
62C2×C16—1221no—
63#107Dic6111yescharacteristic
64#102—21no—
65C2×D4—21no—
66C2×D4—41no—
67C22×C4C22⋊D6111yescharacteristic
68D8—41no—
69M16—1222no—
70M16—2441no—
71C2×C8—41no—
72C2×C8—2441no—
73C2×C8C2×Dic6111yescharacteristic
74C2×C8C22⋊D6111yescharacteristic
75C4⋊C4—21no—
76C22⋊C4—41no—
77C16—2441no—
78C23—41no—
79C23#1175820011yescharacteristic
80D4—41no—
81D4—41no—
82D4—82no—
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—41no—
86C2×C4#1175819911yescharacteristic
87C2×C4C22⋊Dic6111yescharacteristic
88C8—21no—
89C8—21no—
90C8—2442no—
91C22—21no—
92C22—21no—
93C22—21no—
94C22—81no—
95C22—81no—
96C22—81no—
97C22#1451969811yescharacteristic
98C4—21no—
99C4—81no—
100C4#1451969211yescharacteristic
101C4#1451970411yescharacteristic
102C2—41no—
103C2—161no—
104C2#1683949611yescharacteristic
105C2#1683956911yescharacteristic
106C2#1683957511yescharacteristic
subgroupG/H
centerC22#14519698
commutatorC2×C8×C61C2×C4
FrattiniC22×C8C2×D61
FittingC61×#466C2
socleC22×C61#102
hypercenter#466D61
hypocenterC61#1349
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C22⋊#11758185C2semidirect
2. #16839527C2semidirect
57. C61#1349semidirect