Finite Group Databasebeta

← #21460831

Subgroups — #21460831

Order 7808.

102 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 32 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#16840683C211yesmaximal, characteristic, complemented
2#16840624C211yesmaximal, characteristic, complemented
3#16840145C211yesmaximal, characteristic
4C2×#11758187—21no—
5C4⋊#92420—21no—
6C2×Dic244C411yescharacteristic
7C2×#11758200—21no—
8#14519764—21no—
9C8×Dic61C2211yescharacteristic
10C2×D8×C61C411yescharacteristic
11C2×D4×C61—21no—
12C2×Dic122—21no—
13C2×#92420—41no—
14D8×C61—41no—
15C2×C8×C61C2×C411yescharacteristic
16C22⋊Dic61—41no—
17C22⋊Dic61—41no—
18#11758200—41no—
19#11758200—41no—
20C4×Dic61D411yescharacteristic
21C2×#92418D411yescharacteristic
22Dic244—41no—
23#11758187—41no—
24C23×C61—41no—
25D4×C61—41no—
26D4×C61—41no—
27C2×C4×C61C22⋊C411yescharacteristic
28C2×Dic61—41no—
29C2×Dic61D811yescharacteristic
30C2×Dic61SD1611yescharacteristic
31Dic122—41no—
32Dic122—41no—
33#92420—81no—
34C8×C61—21no—
35#92418D811yescharacteristic
36#92418SD1611yescharacteristic
37C22×C61—81no—
38C22×C61—81no—
39C22×C61—81no—
40C22×C61#10211yescharacteristic
41C4×C61#10011yescharacteristic
42C4×C61#10211yescharacteristic
43Dic61—21no—
44Dic61—21no—
45Dic61—81no—
46#1360—611nomaximal, Sylow
47C2×C61—161no—
48C2×C61#33111yescharacteristic
49C2×C61#35911yescharacteristic
50C2×C61#36011yescharacteristic
51#495—611no—
52C4⋊C16—611no—
53#334—611no—
54C61#136011yescharacteristic, complemented, Sylow
55C2×Q16—611no—
56C2×SD16—1221no—
57C2×D8#692311yescharacteristic
58#124—1221no—
59C2×C16—1221no—
60C4⋊C8—1221no—
61C4×C8—611no—
62C2×Q8—1221no—
63C2×D4—21no—
64Q16—2441no—
65SD16—2441no—
66SD16—2441no—
67D8—41no—
68C2×C8—611no—
69C2×C8—2441no—
70C2×C8C2×#692311yescharacteristic
71C22⋊C4—2441no—
72C22⋊C4—2441no—
73C42—611no—
74C16—2441no—
75C23—41no—
76Q8—2441no—
77Q8—2441no—
78D4—41no—
79D4—41no—
80C2×C4—611no—
81C2×C4—611no—
82C2×C4—2441no—
83C2×C4C22⋊#692311yescharacteristic
84C8—21no—
85C8—611no—
86C8—611no—
87C8—4881no—
88C22—81no—
89C22—81no—
90C22—81no—
91C22#1451983911yescharacteristic
92C4—1221no—
93C4—1221no—
94C4—4881no—
95C4#1451983711yescharacteristic
96C4#1451983911yescharacteristic
97C2—161no—
98C2#1684062011yescharacteristic
99C2#1684067611yescharacteristic
100C2#1684067811yescharacteristic
subgroupG/H
centerC22#14519839
commutatorC2×C8×C61C2×C4
FrattiniC2×C8C2×#6923
FittingC2×D8×C61C4
socleC22×C61#102
hypercenterC2×D8#6923
hypocenterC61#1360
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #16840683C2semidirect
2. #16840624C2semidirect
54. C61#1360semidirect