Finite Group Databasebeta

← #21460790

Subgroups — #21460790

Order 7808.

114 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 26 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#16840659C211yesmaximal, characteristic, complemented
2#16840630C211yesmaximal, characteristic, complemented
3#16840016C211yesmaximal, characteristic
4#14519856—21no—
5#14519851—21no—
6C2×D488C411yescharacteristic, complemented
7C2×#11758189C2211yescharacteristic
8#14519752—21no—
9#14519697—21no—
10#106×C61C411yescharacteristic, complemented
11C2×D244—21no—
12C2×D244—41no—
13C2×C4×D61D411yescharacteristic
14C22⋊#6923—41no—
15C4⋊#6923—41no—
16C4×#6923—22no—
17C2×C8×C61C2×C411yescharacteristic
18C4⋊C4×C61—21no—
19#11758198—41no—
20C2×#92418D411yescharacteristic
21D488—41no—
22#11758189—41no—
23#11758187—41no—
24C22×D61—41no—
25C22×D61D811yescharacteristic
26C2×#6923—42no—
27C2×C4×C61—41no—
28C2×C4×C61C22⋊C411yescharacteristic
29C2×Dic61SD1611yescharacteristic
30D244—41no—
31D244—41no—
32D244—82no—
33C4×D61—21no—
34C4×D61—21no—
35C8×C61—21no—
36#92418—21no—
37C22×C61#10211yescharacteristic
38C2×D61—21no—
39C2×D61—41no—
40C2×D61—81no—
41C2×D61—81no—
42C2×D61—81no—
43#6923—82no—
44C4×C61—81no—
45C4×C61#9911yescharacteristic
46C4×C61#10411yescharacteristic
47Dic61—21no—
48#1339—611nomaximal, Sylow
49C2×C61—21no—
50C2×C61#32711yescharacteristic
51D61—41no—
52D61—161no—
53#469—611no—
54#349—611no—
55H(3,ℤ/4)—611no—
56C61#133911yescharacteristic, complemented, Sylow
57C2×D8—611no—
58C2×M16—611no—
59#121—1221no—
60#117—1221no—
61M32—1221no—
62#106#692311yescharacteristic, complemented
63#102—1221no—
64C2×D4—1221no—
65C2×D4—2441no—
66C22×C4—611no—
67D8—2441no—
68M16—2441no—
69C2×C8—611no—
70C2×C8C2×#692311yescharacteristic
71C4⋊C4—21no—
72C4⋊C4—2441no—
73C22⋊C4—2441no—
74C22⋊C4—2441no—
75C42—1222no—
76C16—2441no—
77C23—611no—
78C23—2441no—
79D4—4882no—
80D4—2441no—
81D4—2441no—
82C2×C4—41no—
83C2×C4—611no—
84C2×C4—1221no—
85C2×C4—1221no—
86C2×C4—2442no—
87C2×C4C22⋊#692311yescharacteristic
88C8—21no—
89C8—1221no—
90C22—1221no—
91C22—4881no—
92C22—4881no—
93C22—4881no—
94C22—2441no—
95C22#1451983911yescharacteristic
96C4—81no—
97C4—1221no—
98C4—4882no—
99C4#1451983611yescharacteristic
100C4#1451984211yescharacteristic
101C2—21no—
102C2—9761no—
103C2—2441no—
104C2#1684061411yescharacteristic
subgroupG/H
centerC2#16840614
commutatorC2×C8×C61C2×C4
FrattiniC2×C8C2×#6923
Fitting#106×C61C4
socleC2×C61#327
hypercenter#106#6923
hypocenterC61#1339
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
1. #16840659C2semidirect
2. #16840630C2semidirect
6. C2×D488C4semidirect
10. #106×C61C4semidirect
56. C61#1339semidirect
62. #106#6923semidirect