Finite Group Databasebeta

← #21447945

Subgroups — #21447945

Order 7808.

140 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C2×Dic488C211yesmaximal, characteristic, complemented
2#16840178C211yesmaximal, characteristic
3#16840038C212yesmaximal
4#16839577C212yesmaximal, complemented
5C61×#368C211yesmaximal, characteristic, complemented
6#14519810—22no—
7C2×Dic244C2212yes—
8#14519783C2211yescharacteristic
9Dic488—21no—
10Dic488—21no—
11#14519717C2211yescharacteristic
12#14519716—21no—
13C16×D61—21no—
14#14519695—22no—
15C2×C16×C61C2211yescharacteristic
16#108×C61C2212yes—
17#11758222D411yescharacteristic
18C2×Dic122—22no—
19M16×C61—22no—
20C2×C8×C61C2311yescharacteristic
21#11758194D411yescharacteristic
22Dic244—22no—
23Dic244—22no—
24Dic244—42no—
25#11758190—42no—
26#11758189—21no—
27C8×D61—21no—
28C16×C61D411yescharacteristic
29C16×C61D411yescharacteristic
30#11758185—21no—
31C2×C4×C61C2×D411yescharacteristic
32C22⋊D61—21no—
33C2×Dic61—42no—
34D244D811yescharacteristic
35C4×D61—21no—
36Dic122—42no—
37Dic122—42no—
38Dic122D811yescharacteristic
39C8×C61—42no—
40C8×C61C2×D411yescharacteristic
41C8×C61#4111yescharacteristic
42#92418—21no—
43C22×C61#13511yescharacteristic
44C2×D61—21no—
45C4×C61#12111yescharacteristic
46C4×C61C2×D811yescharacteristic
47Dic61—21no—
48Dic61—82no—
49#2222—611nomaximal, Sylow
50C2×C61—21no—
51C2×C61#46611yescharacteristic
52D61—41no—
53C2×Q32—611no—
54#504—611no—
55#473—612no—
56#368D6111yescharacteristic, complemented
57#362—612no—
58C61#222211yescharacteristic, complemented, Sylow
59#137—1222no—
60C2×Q16—612no—
61#131—611no—
62Q32—1221no—
63Q32—1221no—
64M32—611no—
65M32—1221no—
66C2×C16—1221no—
67C2×C16C2×D6111yescharacteristic
68#108C2×D6112yes—
69#101—1222no—
70#41—611no—
71C2×Q8—1222no—
72Q16—1222no—
73Q16—1222no—
74Q16—2442no—
75SD16—2442no—
76M16—22no—
77M16—611no—
78M16—1221no—
79C2×C8—1221no—
80C2×C8C22×D6111yescharacteristic
81C16—1221no—
82C16D24411yescharacteristic
83C16D24411yescharacteristic
84Q8—611no—
85Q8—2442no—
86Q8—2442no—
87D4—611no—
88D4—1221no—
89C2×C4—1221no—
90C2×C4—2442no—
91C2×C4D4×D6111yescharacteristic
92C8—42no—
93C8—1221no—
94C8C2×D24411yescharacteristic
95C8#1175822611yescharacteristic
96C22—1221no—
97C22#1451980011yescharacteristic
98C4—1221no—
99C4—4882no—
100C4#1451975211yescharacteristic
101C4D8×D6111yescharacteristic
102C2—21no—
103C2—2441no—
104C2#1683999911yescharacteristic
subgroupG/H
centerC2#16839999
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#368C2
socleC2×C61#466
hypercenter#368D61
hypocenterC61#2222
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #368

Complements

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

NH ≅ G/Ntype
1. C2×Dic488C2semidirect
4. #16839577C2semidirect
5. C61×#368C2semidirect
56. #368D61semidirect
58. C61#2222semidirect