Finite Group Databasebeta

← #21460808

Subgroups — #21460808

Order 7808.

116 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 32 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#16840657C211yesmaximal, characteristic
2#16840636C211yesmaximal, characteristic
3#16840004C211yesmaximal, characteristic
4C2×C4⋊#6923—21no—
5C2×#11758187—21no—
6C2×Dic244C411yescharacteristic, complemented
7C2×C8×D61C2211yescharacteristic
8#14519757—21no—
9#14519700—21no—
10#107×C61C411yescharacteristic, complemented
11C22×#6923—41no—
12C2×C4×D61D411yescharacteristic
13C2×Dic122—21no—
14C4⋊#6923—22no—
15C4⋊#6923—41no—
16C2×C8×C61C2×C411yescharacteristic
17C4⋊C4×C61—21no—
18#11758198—41no—
19C4⋊Dic61—41no—
20C2×#92418D411yescharacteristic
21Dic244—41no—
22C8×D61—41no—
23#11758187—41no—
24C22×D61D811yescharacteristic
25C2×#6923—42no—
26C2×#6923—81no—
27C2×#6923—81no—
28C2×C4×C61—41no—
29C2×C4×C61C22⋊C411yescharacteristic
30C2×Dic61—41no—
31C2×Dic61SD1611yescharacteristic
32C4×D61—21no—
33C4×D61—21no—
34Dic122—41no—
35Dic122—41no—
36C8×C61—21no—
37#92418—21no—
38C22×C61#10211yescharacteristic
39C2×D61—21no—
40C2×D61—21no—
41C2×D61SD3211yescharacteristic
42C2×D61Q3211yescharacteristic
43#6923—82no—
44C4×C61—81no—
45C4×C61#9911yescharacteristic
46C4×C61#10411yescharacteristic
47Dic61—21no—
48Dic61—81no—
49#1348—611nomaximal, Sylow
50C2×C61#32711yescharacteristic
51C2×C61#35811yescharacteristic
52C2×C61#36011yescharacteristic
53D61—21no—
54D61—21no—
55#467—611no—
56C22⋊C16—611no—
57#340—611no—
58C61#134811yescharacteristic, complemented, Sylow
59C2×Q16—611no—
60C22×C8—611no—
61C22⋊Q8—1221no—
62C2×C4⋊C4—1221no—
63C2×C16—1221no—
64#107#692311yescharacteristic, complemented
65#103—1221no—
66C2×Q8—1221no—
67C22×C4—611no—
68C22×C4—2441no—
69Q16—2441no—
70C2×C8—611no—
71C2×C8—2441no—
72C2×C8C2×#692311yescharacteristic
73C4⋊C4—21no—
74C4⋊C4—1222no—
75C4⋊C4—2441no—
76C4⋊C4—2441no—
77C22⋊C4—2441no—
78C16—2441no—
79C23—611no—
80Q8—2441no—
81Q8—2441no—
82C2×C4—41no—
83C2×C4—611no—
84C2×C4—1221no—
85C2×C4—1221no—
86C2×C4—4881no—
87C2×C4—4881no—
88C2×C4—2442no—
89C2×C4—2441no—
90C2×C4C22⋊#692311yescharacteristic
91C8—21no—
92C8—1221no—
93C22—611no—
94C22—611no—
95C22—1221no—
96C22—1221no—
97C22#1451983911yescharacteristic
98C4—81no—
99C4—1221no—
100C4—4882no—
101C4—4881no—
102C4#1451983611yescharacteristic
103C4#1451984211yescharacteristic
104C2—1221no—
105C2—1221no—
106C2#1684061411yescharacteristic
107C2#1684067511yescharacteristic
108C2#1684067811yescharacteristic
subgroupG/H
centerC22#14519839
commutatorC2×C8×C61C2×C4
FrattiniC2×C8C2×#6923
Fitting#107×C61C4
socleC22×C61#102
hypercenter#107#6923
hypocenterC61#1348
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
6. C2×Dic244C4semidirect
10. #107×C61C4semidirect
58. C61#1348semidirect
64. #107#6923semidirect