Finite Group Databasebeta

← #21448090

Subgroups — #21448090

Order 7808.

178 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 61 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×Dic488C212yesmaximal, complemented
2C2×#14519722C212yesmaximal
3#16840146C211yesmaximal, characteristic
4#16840142C211yesmaximal, characteristic, complemented
5C61×#346C211yesmaximal, characteristic, complemented
6C2×Dic244—21no—
7C2×Dic244C2212yes—
8C2×Dic244C2211yescharacteristic
9C2×#11758190—21no—
10C2×D488C2211yescharacteristic
11#14519777—21no—
12#14519765—21no—
13Dic488—24no—
14#14519722—24no—
15C2×C16×C61C2212yes—
16C4×C8×C61C2211yescharacteristic
17C2×D244—21no—
18C2×Dic122—21no—
19C2×Dic122—22no—
20C2×C8×C61D411yescharacteristic
21C2×C8×C61C2311yescharacteristic
22C42×C61D411yescharacteristic
23#11758198—42no—
24C4⋊Dic61—42no—
25Dic244—22no—
26Dic244—22no—
27Dic244—22no—
28Dic244—42no—
29D488—22no—
30#11758190—42no—
31C16×C61D414yes—
32C22×D61—41no—
33C2×C4×C61D812yes—
34C2×C4×C61C2×D411yescharacteristic
35C2×Dic61—42no—
36C2×Dic61—41no—
37D244—41no—
38D244—41no—
39Dic122—42no—
40Dic122—41no—
41Dic122—41no—
42Dic122—42no—
43C8×C61D812yes—
44C8×C61C2×D412yes—
45C22×C61C2×D811yescharacteristic
46C2×D61—81no—
47C2×D61—82no—
48C4×C61—22no—
49C4×C61#12711yescharacteristic
50C4×C61C2×D811yescharacteristic
51Dic61—81no—
52Dic61—82no—
53#2251—611nomaximal, Sylow
54C2×C61#49311yescharacteristic
55C2×C61#51012yes—
56D61—161no—
57C2×Q32—612no—
58C2×SD32—612no—
59#495—611no—
60#494—611no—
61#346D6111yescharacteristic, complemented
62C61#225111yescharacteristic, complemented, Sylow
63C2×Q16—612no—
64C2×Q16—611no—
65C2×Q16—1221no—
66C2×SD16—1221no—
67C2×D8—611no—
68C4⋊Q8—1221no—
69#124—1221no—
70Q32—1224no—
71SD32—1224no—
72C2×C16C2×D6112yes—
73C4×C8C2×D6111yescharacteristic
74C2×Q8—1221no—
75C2×Q8—1222no—
76C2×D4—1221no—
77Q16—1222no—
78Q16—1222no—
79Q16—1222no—
80Q16—2442no—
81SD16—2442no—
82D8—1222no—
83C2×C8D24411yescharacteristic
84C2×C8C22×D6111yescharacteristic
85C4⋊C4—2442no—
86C22⋊C4—2442no—
87C42D24411yescharacteristic
88C16D24414yes—
89C23—2441no—
90Q8—2442no—
91Q8—2441no—
92Q8—2441no—
93Q8—2442no—
94D4—2441no—
95D4—2441no—
96C2×C4—2441no—
97C2×C4—2442no—
98C2×C4D48812yes—
99C2×C4C2×D24411yescharacteristic
100C8D48812yes—
101C8C2×D24412yes—
102C22—4882no—
103C22—4881no—
104C22C2×D48811yescharacteristic
105C4—22no—
106C4—4881no—
107C4—4882no—
108C4#1451977411yescharacteristic
109C4C2×D48811yescharacteristic
110C2—9761no—
111C2#1684013911yescharacteristic
112C2#1684020512yes—
subgroupG/H
centerC22C2×D488
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#346C2
socleC22×C61C2×D8
hypercenter#346D61
hypocenterC61#2251
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. C2×Dic488C2semidirect
4. #16840142C2semidirect
5. C61×#346C2semidirect
61. #346D61semidirect
62. C61#2251semidirect