Finite Group Databasebeta

← #21460811

Subgroups — #21460811

Order 7808.

104 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 30 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#16840638C211yesmaximal, characteristic
3#16840000C211yesmaximal, characteristic
4C2×#11758213—21no—
5C2×#11758187—21no—
6C2×C8×D61C2211yescharacteristic
7#14519753—21no—
8#14519711C411yescharacteristic
9#14519701—21no—
10C2×Q16×C61C411yescharacteristic
11C2×Q8×C61—21no—
12C2×C4×D61D411yescharacteristic
13C2×#92420—41no—
14#11758213—22no—
15#11758213—41no—
16Q16×C61—41no—
17C2×C8×C61C2×C411yescharacteristic
18#11758198—41no—
19C4⋊Dic61—21no—
20#11758196—41no—
21C2×#92418D411yescharacteristic
22C8×D61—41no—
23#11758187—41no—
24C22×D61SD1611yescharacteristic
25Q8×C61—41no—
26Q8×C61—41no—
27C2×C4×C61—41no—
28C2×C4×C61C22⋊C411yescharacteristic
29C2×Dic61—41no—
30C2×Dic61D811yescharacteristic
31C4×D61—21no—
32C4×D61—21no—
33#92420—42no—
34C8×C61—21no—
35#92418—21no—
36C22×C61#10211yescharacteristic
37C2×D61—21no—
38C2×D61—21no—
39C2×D61—21no—
40C4×C61—81no—
41C4×C61#9911yescharacteristic
42C4×C61#10411yescharacteristic
43Dic61—21no—
44Dic61—81no—
45#1350—611nomaximal, Sylow
46C2×C61#32711yescharacteristic
47C2×C61#35911yescharacteristic
48C2×C61#36211yescharacteristic
49D61—41no—
50#467—611no—
51C22⋊C16—611no—
52#341—611no—
53C61#135011yescharacteristic, complemented, Sylow
54C2×Q16#692311yescharacteristic
55C2×M16—1221no—
56C22×C8—611no—
57C22⋊Q8—1221no—
58C2×C16—1221no—
59#107—611no—
60#103—1221no—
61C2×Q8—21no—
62C22×C4—611no—
63Q16—41no—
64M16—1222no—
65M16—2441no—
66C2×C8—611no—
67C2×C8—2441no—
68C2×C8—2441no—
69C2×C8C2×#692311yescharacteristic
70C4⋊C4—1221no—
71C4⋊C4—2441no—
72C22⋊C4—2441no—
73C16—2441no—
74C23—611no—
75Q8—41no—
76Q8—41no—
77C2×C4—41no—
78C2×C4—611no—
79C2×C4—1221no—
80C2×C4—1221no—
81C2×C4—2441no—
82C2×C4C22⋊#692311yescharacteristic
83C8—21no—
84C8—1221no—
85C8—2442no—
86C22—1221no—
87C22—1221no—
88C22—1221no—
89C22#1451983911yescharacteristic
90C4—81no—
91C4—1221no—
92C4—4881no—
93C4#1451983511yescharacteristic
94C4#1451984111yescharacteristic
95C2—2441no—
96C2#1684061311yescharacteristic
97C2#1684067711yescharacteristic
98C2#1684068111yescharacteristic
subgroupG/H
centerC22#14519839
commutatorC2×C8×C61C2×C4
FrattiniC2×C8C2×#6923
FittingC2×Q16×C61C4
socleC22×C61#102
hypercenterC2×Q16#6923
hypocenterC61#1350
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
53. C61#1350semidirect