Finite Group Databasebeta

← #21460833

Subgroups — #21460833

Order 7808.

118 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 34 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#16840626C211yesmaximal, characteristic, complemented
3#16840137C211yesmaximal, characteristic
4C2×#11758187—21no—
5C4⋊#92420—21no—
6C2×D488C411yescharacteristic
7C2×#11758199—21no—
8#14519773—21no—
9C8×Dic61C2211yescharacteristic
10C2×D8×C61C411yescharacteristic
11C2×D4×C61—21no—
12C2×C22⋊D61—41no—
13C2×C22⋊D61—41no—
14C2×D244—21no—
15C2×#92420—41no—
16D8×C61—41no—
17C2×C8×C61C2×C411yescharacteristic
18#11758199—41no—
19#11758199—41no—
20C4×Dic61D411yescharacteristic
21C2×#92418D411yescharacteristic
22D488—41no—
23#11758187—41no—
24C23×C61—41no—
25C22×D61—41no—
26D4×C61—41no—
27D4×C61—41no—
28C2×C4×C61C22⋊C411yescharacteristic
29C22⋊D61—82no—
30C22⋊D61—81no—
31C22⋊D61—81no—
32C2×Dic61D811yescharacteristic
33C2×Dic61SD1611yescharacteristic
34D244—41no—
35D244—41no—
36#92420—81no—
37C8×C61—21no—
38#92418D811yescharacteristic
39#92418SD1611yescharacteristic
40C22×C61—81no—
41C22×C61—81no—
42C22×C61—81no—
43C22×C61#10211yescharacteristic
44C2×D61—81no—
45C2×D61—81no—
46C2×D61—81no—
47C4×C61#10011yescharacteristic
48C4×C61#10211yescharacteristic
49Dic61—21no—
50Dic61D1611yescharacteristic
51Dic61SD3211yescharacteristic
52#1361—611nomaximal, Sylow
53C2×C61—161no—
54C2×C61#33111yescharacteristic
55C2×C61#35711yescharacteristic
56C2×C61#36111yescharacteristic
57D61—161no—
58#493—611no—
59C4⋊C16—611no—
60#335—611no—
61C61#136111yescharacteristic, complemented, Sylow
62C2×D8—611no—
63C2×D8—1221no—
64C2×D8#692311yescharacteristic
65#127—1221no—
66C2×C16—1221no—
67C4⋊C8—1221no—
68C4×C8—611no—
69C2×D4—21no—
70C2×D4—1221no—
71C2×D4—2441no—
72C2×D4—2441no—
73D8—41no—
74D8—2441no—
75D8—2441no—
76D8—2441no—
77C2×C8—611no—
78C2×C8—2441no—
79C2×C8C2×#692311yescharacteristic
80C42—611no—
81C16—2441no—
82C23—41no—
83C23—2441no—
84D4—41no—
85D4—41no—
86D4—4881no—
87D4—4881no—
88D4—4882no—
89D4—2441no—
90D4—2441no—
91C2×C4—611no—
92C2×C4—611no—
93C2×C4C22⋊#692311yescharacteristic
94C8—21no—
95C8—611no—
96C8—611no—
97C8—4881no—
98C22—81no—
99C22—81no—
100C22—81no—
101C22—4881no—
102C22—4881no—
103C22—4881no—
104C22#1451983911yescharacteristic
105C4—611no—
106C4—611no—
107C4—1221no—
108C4#1451983711yescharacteristic
109C4#1451983911yescharacteristic
110C2—161no—
111C2—9761no—
112C2#1684062011yescharacteristic
113C2#1684067411yescharacteristic
114C2#1684068011yescharacteristic
subgroupG/H
centerC22#14519839
commutatorC2×C8×C61C2×C4
FrattiniC2×C8C2×#6923
FittingC2×D8×C61C4
socleC22×C61#102
hypercenterC2×D8#6923
hypocenterC61#1361
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. #16840626C2semidirect
61. C61#1361semidirect