Finite Group Databasebeta

← #21443756

Subgroups — #21443756

Order 7808.

112 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 33 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#16839730C211yesmaximal, characteristic
2#16839544C211yesmaximal, characteristic, complemented
3C61×#349C211yesmaximal, characteristic, complemented
4C2×#11758222C411yescharacteristic
5C22×#92418C411yescharacteristic
6#14519717—21no—
7#14519689—21no—
8#14519689—21no—
9C2×M16×C61C2211yescharacteristic
10M32×C61—21no—
11C22×C4×C61C2×C411yescharacteristic
12C2×C22⋊D61—21no—
13#11758222—41no—
14#11758222—41no—
15C2×D244C811yescharacteristic
16C2×C4×D61—21no—
17C2×Dic122C811yescharacteristic
18M16×C61—41no—
19C2×C8×C61D411yescharacteristic
20C2×C8×C61D411yescharacteristic
21C2×#92418—21no—
22C2×#92418—41no—
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—41no—
42C22×C61C22⋊C811yescharacteristic
43C2×D61—42no—
44C2×D61—41no—
45C4×C61—21no—
46C4×C61#9911yescharacteristic
47C4×C61#10011yescharacteristic
48Dic61—41no—
49#1321—611nomaximal, Sylow
50C2×C61—21no—
51C2×C61—41no—
52C2×C61#32311yescharacteristic
53D61—81no—
54#408—611no—
55#349—611no—
56#349D6111yescharacteristic, complemented
57C61#132111yescharacteristic, complemented, Sylow
58C2×#41—611no—
59C2×M16C2×D6111yescharacteristic
60C22×C8—611no—
61M32—21no—
62M32—1221no—
63C22⋊C8—1221no—
64C22⋊C8—1221no—
65#41—2441no—
66#41—2441no—
67C2×Q8—611no—
68C2×D4—611no—
69C2×D4—1221no—
70C22×C4—1221no—
71C22×C4C4×D6111yescharacteristic
72M16—41no—
73C2×C8—1221no—
74C2×C8—2441no—
75C2×C8D24411yescharacteristic
76C2×C8C22⋊D6111yescharacteristic
77C16—41no—
78C16—2441no—
79C23—1221no—
80C23#1175818911yescharacteristic
81Q8—2441no—
82D4—2441no—
83D4—2442no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—1221no—
87C2×C4—2441no—
88C2×C4—2441no—
89C2×C4C8×D6111yescharacteristic
90C2×C4#1175819811yescharacteristic
91C8—21no—
92C8—21no—
93C8—2441no—
94C22—21no—
95C22—41no—
96C22—2442no—
97C22—2441no—
98C22#1451968911yescharacteristic
99C4—21no—
100C4—2441no—
101C4#1451969111yescharacteristic
102C4#1451969311yescharacteristic
103C2—21no—
104C2—41no—
105C2—4881no—
106C2#1683948511yescharacteristic
subgroupG/H
centerC4#14519691
commutatorC2×C4×C61C2×C8
FrattiniC2×M16C2×D61
FittingC61×#349C2
socleC2×C61#323
hypercenter#349D61
hypocenterC61#1321
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
2. #16839544C2semidirect
3. C61×#349C2semidirect
56. #349D61semidirect
57. C61#1321semidirect