Finite Group Databasebeta

← #21443831

Subgroups — #21443831

Order 7808.

116 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 41 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#16839525C211yesmaximal, characteristic
3C61×#467C211yesmaximal, characteristic
4C2×C4⋊Dic61—21no—
5C2×#11758185—21no—
6C2×Q16×C61C411yescharacteristic, complemented
7C22×C8×C61C2211yescharacteristic
8C22⋊Q8×C61—21no—
9#107×C61C411yescharacteristic, complemented
10#103×C61—21no—
11C2×Q8×C61—21no—
12C22×C4×C61D411yescharacteristic
13C22×Dic61—41no—
14Q16×C61—41no—
15C2×C8×C61—41no—
16C2×C8×C61C2×C411yescharacteristic
17C2×C8×C61D411yescharacteristic
18C4⋊C4×C61—21no—
19C4⋊C4×C61—41no—
20C22⋊C4×C61—41no—
21C4⋊Dic61—22no—
22C4⋊Dic61—41no—
23#11758185—41no—
24C23×C61D811yescharacteristic
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×C61SD1611yescharacteristic
33C2×Dic61—42no—
34C2×Dic61—81no—
35C2×Dic61—81no—
36C8×C61—21no—
37C8×C61—21no—
38C22×C61—21no—
39C22×C61—21no—
40C22×C61#10211yescharacteristic
41C22×C61SD3211yescharacteristic
42C22×C61Q3211yescharacteristic
43C4×C61—21no—
44C4×C61—81no—
45C4×C61—81no—
46C4×C61#9911yescharacteristic
47C4×C61#10411yescharacteristic
48Dic61—82no—
49#1348—611nomaximal, Sylow
50C2×C61—21no—
51C2×C61—21no—
52C2×C61#32711yescharacteristic
53C2×C61#35811yescharacteristic
54C2×C61#36011yescharacteristic
55#467D6111yescharacteristic
56C22⋊C16—611no—
57#340—611no—
58C61#134811yescharacteristic, complemented, Sylow
59C2×Q16Dic6111yescharacteristic, complemented
60C22×C8C2×D6111yescharacteristic
61C22⋊Q8—21no—
62C2×C4⋊C4—1221no—
63C2×C16—1221no—
64#107Dic6111yescharacteristic, complemented
65#103—21no—
66C2×Q8—21no—
67C22×C4—2441no—
68C22×C4C22⋊D6111yescharacteristic
69Q16—41no—
70C2×C8—41no—
71C2×C8C2×Dic6111yescharacteristic
72C2×C8C22⋊D6111yescharacteristic
73C4⋊C4—21no—
74C4⋊C4—41no—
75C4⋊C4—1222no—
76C4⋊C4—2441no—
77C22⋊C4—41no—
78C16—2441no—
79C23#1175819911yescharacteristic
80Q8—41no—
81Q8—41no—
82C2×C4—21no—
83C2×C4—21no—
84C2×C4—41no—
85C2×C4—41no—
86C2×C4—4881no—
87C2×C4—4881no—
88C2×C4—2442no—
89C2×C4#1175820011yescharacteristic
90C2×C4C22⋊Dic6111yescharacteristic
91C8—21no—
92C8—21no—
93C22—21no—
94C22—21no—
95C22#1451969811yescharacteristic
96C22#1451972011yescharacteristic
97C22#1451972311yescharacteristic
98C4—21no—
99C4—81no—
100C4—81no—
101C4—4882no—
102C4#1451969211yescharacteristic
103C4#1451970411yescharacteristic
104C2—21no—
105C2—21no—
106C2#1683949611yescharacteristic
107C2#1683956611yescharacteristic
108C2#1683957211yescharacteristic
subgroupG/H
centerC22#14519698
commutatorC2×C8×C61C2×C4
FrattiniC22×C8C2×D61
FittingC61×#467C2
socleC22×C61#102
hypercenter#467D61
hypocenterC61#1348
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
6. C2×Q16×C61C4semidirect
9. #107×C61C4semidirect
58. C61#1348semidirect
59. C2×Q16Dic61semidirect
64. #107Dic61semidirect