Finite Group Databasebeta

← #21448058

Subgroups — #21448058

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#16840146C211yesmaximal, characteristic
2#16839565C212yesmaximal, complemented
3#16839562C212yesmaximal
4#16839538C211yesmaximal, characteristic, complemented
5C61×#500C211yesmaximal, characteristic, complemented
6C2×Dic244C2211yescharacteristic
7C2×#11758190—21no—
8C2×D488C2211yescharacteristic
9#14519765—21no—
10C2×#11758185C2212yes—
11C4⋊Q8×C61—21no—
12#107×C61—21no—
13#107×C61C2212yes—
14C4×C8×C61C2211yescharacteristic
15C2×Q8×C61—41no—
16C2×D244—21no—
17C2×Dic122—21no—
18C2×C8×C61D411yescharacteristic
19C2×C8×C61C2311yescharacteristic
20C4⋊C4×C61—22no—
21C4⋊C4×C61—41no—
22C42×C61D411yescharacteristic
23#11758198—41no—
24#11758198—41no—
25Dic244—22no—
26D488—22no—
27#11758190—42no—
28#11758185—22no—
29C22×D61—41no—
30Q8×C61—82no—
31C2×C4×C61—42no—
32C2×C4×C61D811yescharacteristic
33C2×C4×C61D811yescharacteristic
34C2×C4×C61C2×D411yescharacteristic
35C2×Dic61—41no—
36D244—41no—
37D244—41no—
38Dic122—41no—
39Dic122—41no—
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—82no—
49C4×C61#12411yescharacteristic
50C4×C61C2×SD1611yescharacteristic
51Dic61—81no—
52#2243—611nomaximal, Sylow
53C2×C61#48611yescharacteristic
54C2×C61#50911yescharacteristic
55C2×C61#51011yescharacteristic
56D61—161no—
57#500D6111yescharacteristic, complemented
58#495—611no—
59#358—612no—
60#357—612no—
61#346—611no—
62C61#224311yescharacteristic, complemented, Sylow
63C2×Q16—611no—
64C2×SD16—1221no—
65C2×D8—611no—
66C4⋊Q8—21no—
67#124—1221no—
68C2×C16—612no—
69#107—21no—
70#107C2×D6112yes—
71C4×C8C2×D6111yescharacteristic
72C2×Q8—41no—
73C2×Q8—1221no—
74C2×D4—1221no—
75Q16—1222no—
76SD16—2442no—
77D8—1222no—
78C2×C8C22⋊D6111yescharacteristic
79C2×C8C22×D6111yescharacteristic
80C4⋊C4—22no—
81C4⋊C4—41no—
82C22⋊C4—2441no—
83C22⋊C4—2441no—
84C42C22⋊D6111yescharacteristic
85C16—1222no—
86C23—2441no—
87Q8—82no—
88Q8—2441no—
89Q8—2441no—
90D4—2441no—
91D4—2441no—
92C2×C4—42no—
93C2×C4—2441no—
94C2×C4#1175819911yescharacteristic
95C2×C4#1175819911yescharacteristic
96C2×C4C2×C22⋊D6111yescharacteristic
97C8#1175820112yes—
98C8#1175822612yes—
99C22—4881no—
100C22—4881no—
101C22—4881no—
102C22C2×#1175819911yescharacteristic
103C4—21no—
104C4—21no—
105C4—82no—
106C4—4881no—
107C4#1451976611yescharacteristic
108C4C2×#1175820111yescharacteristic
109C2—9761no—
110C2#1684011011yescharacteristic
111C2#1684019811yescharacteristic
112C2#1684020311yescharacteristic
subgroupG/H
centerC22C2×#11758199
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#500C2
socleC22×C61C2×D8
hypercenter#500D61
hypocenterC61#2243
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #500

Complements

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

NH ≅ G/Ntype
2. #16839565C2semidirect
4. #16839538C2semidirect
5. C61×#500C2semidirect
57. #500D61semidirect
62. C61#2243semidirect