Finite Group Databasebeta

← #21448056

Subgroups — #21448056

Order 7808.

142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 53 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#16840167C211yesmaximal, characteristic, complemented
2#16840146C211yesmaximal, characteristic
3#16839567C212yesmaximal, complemented
4#16839564C212yesmaximal
5C61×#346C211yesmaximal, characteristic, complemented
6C2×Dic244C2211yescharacteristic
7C2×#11758190—21no—
8C2×D488C2211yescharacteristic
9#14519777—21no—
10#14519765—21no—
11#14519711—21no—
12#14519711C2212yes—
13C2×C16×C61C2212yes—
14C4×C8×C61C2211yescharacteristic
15C2×D244—21no—
16C2×Dic122—21no—
17C2×Dic122—41no—
18C2×C8×C61D411yescharacteristic
19C2×C8×C61C2311yescharacteristic
20C42×C61D411yescharacteristic
21#11758198—41no—
22#11758198—41no—
23C4⋊Dic61—22no—
24C4⋊Dic61—41no—
25Dic244—22no—
26D488—22no—
27#11758190—42no—
28C16×C61—22no—
29C22×D61—41no—
30C2×C4×C61D811yescharacteristic
31C2×C4×C61D811yescharacteristic
32C2×C4×C61C2×D411yescharacteristic
33C2×Dic61—42no—
34C2×Dic61—41no—
35D244—41no—
36D244—41no—
37Dic122—41no—
38Dic122—41no—
39Dic122—82no—
40C8×C61SD1612yes—
41C8×C61#4112yes—
42C22×C61C2×D811yescharacteristic
43C2×D61—81no—
44C2×D61—81no—
45C2×D61—81no—
46C4×C61—21no—
47C4×C61—21no—
48C4×C61#12411yescharacteristic
49C4×C61C2×SD1611yescharacteristic
50Dic61—81no—
51Dic61—82no—
52#2243—611nomaximal, Sylow
53C2×C61#48611yescharacteristic
54C2×C61#50911yescharacteristic
55C2×C61#51011yescharacteristic
56D61—161no—
57#500—611no—
58#495—611no—
59#358—612no—
60#357—612no—
61#346D6111yescharacteristic, complemented
62C61#224311yescharacteristic, complemented, Sylow
63C2×Q16—611no—
64C2×SD16—1221no—
65C2×D8—611no—
66C4⋊Q8—1221no—
67#124—1221no—
68C2×C16C2×D6112yes—
69#107—612no—
70#107—1221no—
71C4×C8C2×D6111yescharacteristic
72C2×Q8—1221no—
73C2×Q8—2441no—
74C2×D4—1221no—
75Q16—1222no—
76SD16—2442no—
77D8—1222no—
78C2×C8D24411yescharacteristic
79C2×C8C22×D6111yescharacteristic
80C4⋊C4—1222no—
81C4⋊C4—2441no—
82C22⋊C4—2441no—
83C22⋊C4—2441no—
84C42D24411yescharacteristic
85C16—22no—
86C23—2441no—
87Q8—4882no—
88Q8—2441no—
89Q8—2441no—
90D4—2441no—
91D4—2441no—
92C2×C4—2441no—
93C2×C4—2442no—
94C2×C4D48811yescharacteristic
95C2×C4D48811yescharacteristic
96C2×C4C2×D24411yescharacteristic
97C8#1175819012yes—
98C8#1175822212yes—
99C22—4881no—
100C22—4881no—
101C22—4881no—
102C22C2×D48811yescharacteristic
103C4—21no—
104C4—21no—
105C4—4882no—
106C4—4881no—
107C4#1451976511yescharacteristic
108C4C2×#1175819011yescharacteristic
109C2—9761no—
110C2#1684010911yescharacteristic
111C2#1684020011yescharacteristic
112C2#1684020511yescharacteristic
subgroupG/H
centerC22C2×D488
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#346C2
socleC22×C61C2×D8
hypercenter#346D61
hypocenterC61#2243
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #346

Complements

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

NH ≅ G/Ntype
1. #16840167C2semidirect
3. #16839567C2semidirect
5. C61×#346C2semidirect
61. #346D61semidirect
62. C61#2243semidirect