Finite Group Databasebeta

← #21447940

Subgroups — #21447940

Order 7808.

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

normal subgroups only

This group has 148 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×D976C211yesmaximal, characteristic, complemented
2#16840178C211yesmaximal, characteristic, complemented
3#16840033C212yesmaximal, complemented
4#16839574C212yesmaximal, complemented
5C61×#368C211yesmaximal, characteristic, complemented
6#14519805—22no—
7C2×D488C2212yes—
8#14519783C2211yescharacteristic
9D976—21no—
10D976—21no—
11#14519717C2211yescharacteristic
12#14519716—21no—
13C16×D61—21no—
14#14519693—22no—
15C2×C16×C61C2211yescharacteristic
16#108×C61C2212yes—
17#11758222D411yescharacteristic
18C2×D244—22no—
19M16×C61—22no—
20C2×C8×C61C2311yescharacteristic
21#11758194D411yescharacteristic
22D488—22no—
23D488—22no—
24D488—42no—
25#11758190—42no—
26#11758189—21no—
27C8×D61—21no—
28C16×C61D411yescharacteristic
29C16×C61D411yescharacteristic
30#11758185—21no—
31C22×D61—42no—
32C2×C4×C61C2×D411yescharacteristic
33C22⋊D61—21no—
34D244—42no—
35D244—42no—
36D244D811yescharacteristic
37C4×D61—21no—
38Dic122D811yescharacteristic
39C8×C61—42no—
40C8×C61C2×D411yescharacteristic
41C8×C61#4111yescharacteristic
42#92418—21no—
43C22×C61#13511yescharacteristic
44C2×D61—21no—
45C2×D61—82no—
46C2×D61—162no—
47C4×C61#12111yescharacteristic
48C4×C61C2×D811yescharacteristic
49Dic61—21no—
50#2221—611nomaximal, Sylow
51C2×C61—21no—
52C2×C61#46611yescharacteristic
53D61—41no—
54D61—162no—
55C2×D16—611no—
56#504—611no—
57#472—612no—
58#368D6111yescharacteristic, complemented
59#361—612no—
60C61#222111yescharacteristic, complemented, Sylow
61AGL(1,ℤ/8)—1222no—
62C2×D8—612no—
63#131—611no—
64D16—1221no—
65D16—1221no—
66M32—611no—
67M32—1221no—
68C2×C16—1221no—
69C2×C16C2×D6111yescharacteristic
70#108C2×D6112yes—
71#100—1222no—
72#41—611no—
73C2×D4—1222no—
74SD16—2442no—
75D8—1222no—
76D8—1222no—
77D8—2442no—
78M16—22no—
79M16—611no—
80M16—1221no—
81C2×C8—1221no—
82C2×C8C22×D6111yescharacteristic
83C16—1221no—
84C16D24411yescharacteristic
85C16D24411yescharacteristic
86C23—2442no—
87Q8—611no—
88D4—611no—
89D4—1221no—
90D4—2442no—
91D4—2442no—
92C2×C4—1221no—
93C2×C4D4×D6111yescharacteristic
94C8—42no—
95C8—1221no—
96C8C2×D24411yescharacteristic
97C8#1175822611yescharacteristic
98C22—1221no—
99C22—9762no—
100C22—4882no—
101C22#1451980011yescharacteristic
102C4—1221no—
103C4#1451975211yescharacteristic
104C4D8×D6111yescharacteristic
105C2—21no—
106C2—9762no—
107C2—2441no—
108C2#1683999911yescharacteristic
subgroupG/H
centerC2#16839999
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#368C2
socleC2×C61#466
hypercenter#368D61
hypocenterC61#2221
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×D976C2semidirect
2. #16840178C2semidirect
3. #16840033C2semidirect
4. #16839574C2semidirect
5. C61×#368C2semidirect
58. #368D61semidirect
60. C61#2221semidirect