Finite Group Databasebeta

← #21443830

Subgroups — #21443830

Order 7808.

116 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 39 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
1#16840003C211yesmaximal, characteristic
2C22⋊#11758185C211yesmaximal, characteristic
3C61×#340C211yesmaximal, characteristic
4C2×Dic244C411yescharacteristic, complemented
5#14519756—21no—
6C2×#11758185—21no—
7#14519711C411yescharacteristic, complemented
8#14519702—21no—
9C22×C8×C61C2211yescharacteristic
10C2×C4⋊C4×C61—21no—
11C22×C4×C61—41no—
12C22×C4×C61D411yescharacteristic
13C2×Dic122—21no—
14C2×C8×C61—41no—
15C2×C8×C61C2×C411yescharacteristic
16C2×C8×C61D411yescharacteristic
17C4⋊C4×C61—22no—
18C4⋊C4×C61—41no—
19C22⋊Dic61—41no—
20C4⋊Dic61—21no—
21#11758196—41no—
22Dic244—41no—
23#11758185—41no—
24C23×C61D811yescharacteristic
25C2×C4×C61—21no—
26C2×C4×C61—21no—
27C2×C4×C61—42no—
28C2×C4×C61—81no—
29C2×C4×C61—81no—
30C2×C4×C61C22⋊C411yescharacteristic
31C2×C4×C61SD1611yescharacteristic
32C2×Dic61—41no—
33C2×Dic61—41no—
34Dic122—41no—
35Dic122—41no—
36C8×C61—21no—
37C8×C61—21no—
38C22×C61—21no—
39C22×C61—21no—
40C22×C61#10211yescharacteristic
41C22×C61SD3211yescharacteristic
42C22×C61Q3211yescharacteristic
43C4×C61—21no—
44C4×C61—82no—
45C4×C61#9911yescharacteristic
46C4×C61#10411yescharacteristic
47Dic61—81no—
48Dic61—81no—
49#1348—611nomaximal, Sylow
50C2×C61—21no—
51C2×C61—21no—
52C2×C61#32711yescharacteristic
53C2×C61#35811yescharacteristic
54C2×C61#36011yescharacteristic
55#467—611no—
56C22⋊C16—611no—
57#340D6111yescharacteristic
58C61#134811yescharacteristic, complemented, Sylow
59C2×Q16—611no—
60C22×C8C2×D6111yescharacteristic
61C22⋊Q8—1221no—
62C2×C4⋊C4—21no—
63C2×C16—1221no—
64#107—611no—
65#103—1221no—
66C2×Q8—1221no—
67C22×C4—41no—
68C22×C4C22⋊D6111yescharacteristic
69Q16—2441no—
70C2×C8—41no—
71C2×C8C4×D6111yescharacteristic
72C2×C8D24411yescharacteristic
73C4⋊C4—22no—
74C4⋊C4—41no—
75C4⋊C4—1221no—
76C4⋊C4—2441no—
77C22⋊C4—2441no—
78C16—2441no—
79C23#1175819911yescharacteristic
80Q8—2441no—
81Q8—2441no—
82C2×C4—21no—
83C2×C4—21no—
84C2×C4—42no—
85C2×C4—81no—
86C2×C4—81no—
87C2×C4—2441no—
88C2×C4—2441no—
89C2×C4#1175819811yescharacteristic
90C2×C4#1175820111yescharacteristic
91C8—21no—
92C8—21no—
93C22—21no—
94C22—21no—
95C22#1451969711yescharacteristic
96C22#1451972111yescharacteristic
97C22#1451972311yescharacteristic
98C4—21no—
99C4—82no—
100C4—4881no—
101C4—4881no—
102C4#1451969111yescharacteristic
103C4#1451970511yescharacteristic
104C2—21no—
105C2—21no—
106C2#1683949511yescharacteristic
107C2#1683956511yescharacteristic
108C2#1683957111yescharacteristic
subgroupG/H
centerC22#14519697
commutatorC2×C8×C61C2×C4
FrattiniC22×C8C2×D61
FittingC61×#340C2
socleC22×C61#102
hypercenter#340D61
hypocenterC61#1348
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #340

Complements

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

NH ≅ G/Ntype
4. C2×Dic244C4semidirect
7. #14519711C4semidirect
58. C61#1348semidirect