Finite Group Databasebeta

← #21443764

Subgroups — #21443764

Order 7808.

134 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 37 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#16839631C211yesmaximal, characteristic
2#16839488C211yesmaximal, characteristic
3C61×#324C211yesmaximal, characteristic
4C2×C4⋊Dic61C411yescharacteristic
5C2×#11758196—21no—
6C2×#11758196—21no—
7C2×C4×Dic61C411yescharacteristic
8C22⋊#92418—21no—
9C2×C4⋊C4×C61C2211yescharacteristic
10C22⋊C8×C61—21no—
11C22×C4×C61C2×C411yescharacteristic
12C22×C4×C61D411yescharacteristic
13C22×C4×C61D411yescharacteristic
14C22×Dic61—21no—
15C22×Dic61—21no—
16C2×C8×C61—41no—
17C4⋊C4×C61—41no—
18C4⋊Dic61—41no—
19#11758196—42no—
20#11758196—42no—
21C4×Dic61—21no—
22C4×Dic61C812yescomplemented
23C2×#92418—41no—
24C23×C61C22⋊C411yescharacteristic
25C2×C4×C61—21no—
26C2×C4×C61—21no—
27C2×C4×C61—21no—
28C2×C4×C61—21no—
29C2×C4×C61—41no—
30C2×C4×C61—41no—
31C2×C4×C61C2×C811yescharacteristic
32C2×C4×C61M1611yescharacteristic
33C2×Dic61—22no—
34C2×Dic61—22no—
35C2×Dic61—22no—
36C2×Dic61—41no—
37C2×Dic61—41no—
38C2×Dic61—41no—
39C8×C61—81no—
40#92418—81no—
41C22×C61—21no—
42C22×C61—21no—
43C22×C61C22⋊C811yescharacteristic
44C22×C61#9911yescharacteristic
45C22×C61#10111yescharacteristic
46C4×C61—21no—
47C4×C61—21no—
48C4×C61—41no—
49C4×C61—41no—
50Dic61—24no—
51Dic61—81no—
52#1325—611nomaximal, Sylow
53C2×C61—21no—
54C2×C61—21no—
55C2×C61#32411yescharacteristic
56C2×C61#35311yescharacteristic
57C2×C61#35611yescharacteristic
58#384—611no—
59#324—611no—
60#324D6111yescharacteristic
61C61#132511yescharacteristic, complemented, Sylow
62C2×C4⋊C4—611no—
63C2×C4⋊C4—1221no—
64C2×C4⋊C4—1221no—
65C2×C4⋊C4C2×D6111yescharacteristic
66C2×C42—611no—
67C22⋊C8—21no—
68C22⋊C8—1221no—
69C22×C4—1221no—
70C22×C4—1221no—
71C22×C4C4×D6111yescharacteristic
72C22×C4D24411yescharacteristic
73C22×C4C22⋊D6111yescharacteristic
74C2×C8—41no—
75C2×C8—2441no—
76C4⋊C4—41no—
77C4⋊C4—2441no—
78C4⋊C4—2442no—
79C4⋊C4—2442no—
80C42—612no—
81C42—1221no—
82C23#1175819811yescharacteristic
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—41no—
88C2×C4—41no—
89C2×C4—1222no—
90C2×C4—1222no—
91C2×C4—1222no—
92C2×C4—2441no—
93C2×C4—2441no—
94C2×C4—2441no—
95C2×C4C8×D6111yescharacteristic
96C2×C4#1175818911yescharacteristic
97C8—81no—
98C8—4881no—
99C22—21no—
100C22—21no—
101C22#1451968911yescharacteristic
102C22#1451969111yescharacteristic
103C22#1451969511yescharacteristic
104C4—21no—
105C4—21no—
106C4—41no—
107C4—41no—
108C4—1224no—
109C4—4881no—
110C2—21no—
111C2—21no—
112C2#1683948711yescharacteristic
113C2#1683955411yescharacteristic
114C2#1683956011yescharacteristic
subgroupG/H
centerC22#14519691
commutatorC2×C4×C61C2×C8
FrattiniC2×C4⋊C4C2×D61
FittingC61×#324C2
socleC22×C61#99
hypercenter#324D61
hypocenterC61#1325
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
22. C4×Dic61C8semidirect
61. C61#1325semidirect