Finite Group Databasebeta

← #21460804

Subgroups — #21460804

Order 7808.

124 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 30 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#16840642C211yesmaximal, characteristic
2#16840608C211yesmaximal, characteristic
3#16839694C211yesmaximal, characteristic
4C2×#11758217—21no—
5C22⋊#92420—21no—
6C2×C4⋊Dic61—21no—
7C2×C4⋊Dic61C411yescharacteristic
8C2×#11758196C2211yescharacteristic
9#14519684—21no—
10#95×C61C411yescharacteristic
11C22×C4×C61—21no—
12C22×C4×C61C2×C411yescharacteristic
13C22×Dic61—21no—
14C22×Dic61D411yescharacteristic
15C22×Dic61D411yescharacteristic
16#11758217—22no—
17#11758217—41no—
18C2×#92420—41no—
19C2×#92420—41no—
20C4⋊Dic61—41no—
21C4⋊Dic61—41no—
22C4⋊Dic61—41no—
23#11758196—41no—
24C23×C61C22⋊C411yescharacteristic
25C2×C4×C61—22no—
26C2×C4×C61—21no—
27C2×C4×C61—41no—
28C2×C4×C61—41no—
29C2×C4×C61—41no—
30C2×Dic61—21no—
31C2×Dic61—21no—
32C2×Dic61—21no—
33C2×Dic61—41no—
34C2×Dic61—41no—
35C2×Dic61—41no—
36C2×Dic61—41no—
37C2×Dic61D811yescharacteristic
38C2×Dic61SD1611yescharacteristic
39#92420—42no—
40#92420—81no—
41C22×C61—21no—
42C22×C61—21no—
43C22×C61#9911yescharacteristic
44C22×C61#10211yescharacteristic
45C22×C61#10411yescharacteristic
46C4×C61—42no—
47C4×C61—41no—
48Dic61—21no—
49Dic61—21no—
50Dic61—41no—
51Dic61—81no—
52#1346—611nomaximal, Sylow
53C2×C61—21no—
54C2×C61—21no—
55C2×C61#32711yescharacteristic
56C2×C61#35211yescharacteristic
57C2×C61#35611yescharacteristic
58#398—611no—
59#343—611no—
60#324—611no—
61C61#134611yescharacteristic, complemented, Sylow
62C2×M16—1221no—
63C2×C4⋊C4—611no—
64C2×C4⋊C4—611no—
65C2×C4⋊C4—1221no—
66C22⋊C8—1221no—
67#95—1221no—
68#95#692311yescharacteristic
69C22×C4—21no—
70C22×C4—611no—
71C22×C4—611no—
72C22×C4—1221no—
73C22×C4C2×#692311yescharacteristic
74M16—1222no—
75M16—2441no—
76C2×C8—2441no—
77C2×C8—2441no—
78C4⋊C4—2441no—
79C4⋊C4—2441no—
80C4⋊C4—2441no—
81C4⋊C4—2441no—
82C23C22⋊#692311yescharacteristic
83C2×C4—22no—
84C2×C4—21no—
85C2×C4—41no—
86C2×C4—41no—
87C2×C4—41no—
88C2×C4—611no—
89C2×C4—611no—
90C2×C4—1221no—
91C2×C4—1221no—
92C2×C4—1221no—
93C2×C4—2441no—
94C2×C4—2441no—
95C2×C4—2441no—
96C2×C4—2441no—
97C8—4881no—
98C8—2442no—
99C22—21no—
100C22—21no—
101C22#1451983611yescharacteristic
102C22#1451983911yescharacteristic
103C22#1451984211yescharacteristic
104C4—42no—
105C4—41no—
106C4—1221no—
107C4—1221no—
108C4—4881no—
109C4—2441no—
110C2—21no—
111C2—21no—
112C2#1684061411yescharacteristic
113C2#1684066511yescharacteristic
114C2#1684067311yescharacteristic
subgroupG/H
centerC22#14519836
commutatorC22×C4×C61C2×C4
FrattiniC22×C4C2×#6923
Fitting#95×C61C4
socleC22×C61#99
hypercenter#95#6923
hypocenterC61#1346
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
61. C61#1346semidirect