Finite Group Databasebeta

← #21443744

Subgroups — #21443744

Order 7808.

116 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 37 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#16839728C211yesmaximal, characteristic
2C22⋊#11758185C211yesmaximal, characteristic, complemented
3C61×C22⋊C16C211yesmaximal, characteristic, complemented
4C2×#11758222C411yescharacteristic
5C2×#11758194C411yescharacteristic
6C2×#11758185—21no—
7#14519689—21no—
8#14519689—21no—
9C22×C8×C61C2211yescharacteristic
10C2×C16×C61—21no—
11C22×C4×C61C2×C411yescharacteristic
12C2×C22⋊D61—21no—
13#11758222—41no—
14#11758222—41no—
15C2×D244C811yescharacteristic
16C2×C4×D61—21no—
17C2×Dic122C811yescharacteristic
18C2×C8×C61—41no—
19C2×C8×C61D411yescharacteristic
20C2×C8×C61D411yescharacteristic
21#11758194—41no—
22C2×#92418—21no—
23C16×C61—41no—
24#11758185—41no—
25C23×C61M1611yescharacteristic
26C22×D61—21no—
27C2×C4×C61—21no—
28C2×C4×C61—21no—
29C2×C4×C61C22⋊C411yescharacteristic
30C2×C4×C61C2×C811yescharacteristic
31C22⋊D61—42no—
32C2×Dic61—21no—
33D244—41no—
34C4×D61—41no—
35C4×D61—41no—
36Dic122—41no—
37C8×C61—21no—
38C8×C61—21no—
39#92418—41no—
40C22×C61—21no—
41C22×C61—21no—
42C22×C61—21no—
43C22×C61C22⋊C811yescharacteristic
44C2×D61—41no—
45C2×D61—41no—
46C2×D61—41no—
47C4×C61—21no—
48C4×C61#9911yescharacteristic
49C4×C61#10011yescharacteristic
50Dic61—41no—
51#1315—611nomaximal, Sylow
52C2×C61—41no—
53C2×C61#32311yescharacteristic
54C2×C61#35011yescharacteristic
55C2×C61#35011yescharacteristic
56D61—81no—
57#408—611no—
58C22⋊C16—611no—
59C22⋊C16D6111yescharacteristic, complemented
60C61#131511yescharacteristic, complemented, Sylow
61C2×#41—611no—
62C2×M16—611no—
63C22×C8C2×D6111yescharacteristic
64C2×C16—21no—
65C2×C16—1221no—
66C22⋊C8—1221no—
67C22⋊C8—1221no—
68#41—2441no—
69#41—2441no—
70C2×Q8—611no—
71C2×D4—611no—
72C2×D4—1221no—
73C22×C4—1221no—
74C22×C4C4×D6111yescharacteristic
75M16—2441no—
76C2×C8—41no—
77C2×C8—1221no—
78C2×C8D24411yescharacteristic
79C2×C8C22⋊D6111yescharacteristic
80C16—41no—
81C16—2441no—
82C23—1221no—
83C23#1175818911yescharacteristic
84Q8—2441no—
85D4—2441no—
86D4—2442no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—1221no—
90C2×C4—2441no—
91C2×C4—2441no—
92C2×C4C8×D6111yescharacteristic
93C2×C4#1175819811yescharacteristic
94C8—21no—
95C8—21no—
96C8—2441no—
97C22—21no—
98C22—21no—
99C22—21no—
100C22—2441no—
101C22—2441no—
102C22—2441no—
103C22#1451968911yescharacteristic
104C4—21no—
105C4—2441no—
106C4#1451969111yescharacteristic
107C4#1451969311yescharacteristic
108C2—41no—
109C2—4881no—
110C2#1683948511yescharacteristic
111C2#1683954511yescharacteristic
112C2#1683954711yescharacteristic
subgroupG/H
centerC2×C4#11758198
commutatorC2×C4×C61C2×C8
FrattiniC22×C8C2×D61
FittingC61×C22⋊C16C2
socleC22×C61C22⋊C8
hypercenterC22⋊C16D61
hypocenterC61#1315
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
2. C22⋊#11758185C2semidirect
3. C61×C22⋊C16C2semidirect
59. C22⋊C16D61semidirect
60. C61#1315semidirect