Finite Group Databasebeta

← #21460799

Subgroups — #21460799

Order 7808.

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

normal subgroups only

This group has 146 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#16840640C211yesmaximal, characteristic
2#16840606C211yesmaximal, characteristic
3#16839688C211yesmaximal, characteristic
4C2×C22⋊#6923—21no—
5C22⋊#92420—21no—
6C2×#11758198—21no—
7C2×#11758198C2211yescharacteristic
8#14519684—21no—
9#14519684C411yescharacteristic, complemented
10C2×C4⋊C4×C61C411yescharacteristic, complemented
11C23×D61D411yescharacteristic
12C22×#6923—41no—
13C22×C4×C61—21no—
14C22×C4×C61C2×C411yescharacteristic
15C22×Dic61—21no—
16C22×Dic61D411yescharacteristic
17C22⋊#6923—22no—
18C22⋊#6923—41no—
19C2×#92420—41no—
20C4⋊C4×C61—41no—
21#11758198—41no—
22#11758198—41no—
23#11758198—41no—
24C23×C61C22⋊C411yescharacteristic
25C22×D61—21no—
26C22×D61—21no—
27C22×D61—41no—
28C22×D61—41no—
29C22×D61D811yescharacteristic
30C22×D61SD1611yescharacteristic
31C2×#6923—42no—
32C2×#6923—81no—
33C2×#6923—81no—
34C2×C4×C61—21no—
35C2×C4×C61—41no—
36C2×C4×C61—41no—
37C2×C4×C61—41no—
38C2×C4×C61—41no—
39C2×Dic61—21no—
40C2×Dic61—41no—
41C2×Dic61—41no—
42C2×Dic61—41no—
43C2×Dic61—41no—
44#92420—81no—
45C22×C61—21no—
46C22×C61—21no—
47C22×C61#9911yescharacteristic
48C22×C61#10211yescharacteristic
49C22×C61#10411yescharacteristic
50C2×D61—21no—
51C2×D61—21no—
52C2×D61—41no—
53C2×D61—41no—
54C2×D61—41no—
55C2×D61—41no—
56C2×D61—81no—
57#6923—82no—
58C4×C61—41no—
59C4×C61—81no—
60Dic61—41no—
61Dic61—81no—
62#1344—611nomaximal, Sylow
63C2×C61—21no—
64C2×C61—21no—
65C2×C61#32711yescharacteristic
66C2×C61#35211yescharacteristic
67C2×C61#35411yescharacteristic
68D61—41no—
69D61—41no—
70#397—611no—
71#342—611no—
72#323—611no—
73C61#134411yescharacteristic, complemented, Sylow
74C2×C4⋊C4#692311yescharacteristic, complemented
75C2×C22⋊C4—611no—
76C2×C22⋊C4—1221no—
77C2×C22⋊C4—1221no—
78C22⋊C8—1221no—
79#95—611no—
80#95—1221no—
81C24—611no—
82C22×C4—21no—
83C22×C4—611no—
84C22×C4—1221no—
85C22×C4—2441no—
86C22×C4C2×#692311yescharacteristic
87C2×C8—2441no—
88C4⋊C4—41no—
89C22⋊C4—1222no—
90C22⋊C4—2441no—
91C22⋊C4—2441no—
92C22⋊C4—2441no—
93C22⋊C4—2441no—
94C23—611no—
95C23—611no—
96C23—1221no—
97C23—1221no—
98C23—2441no—
99C23—2441no—
100C23C22⋊#692311yescharacteristic
101C2×C4—21no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—1221no—
107C2×C4—4881no—
108C2×C4—4881no—
109C2×C4—2441no—
110C2×C4—2441no—
111C2×C4—2442no—
112C2×C4—2441no—
113C2×C4—2441no—
114C8—4881no—
115C22—21no—
116C22—21no—
117C22—1221no—
118C22—1221no—
119C22—4881no—
120C22—2441no—
121C22—2441no—
122C22—2441no—
123C22—2441no—
124C22#1451983511yescharacteristic
125C22#1451983911yescharacteristic
126C22#1451984111yescharacteristic
127C4—41no—
128C4—81no—
129C4—4881no—
130C4—4882no—
131C4—2441no—
132C2—21no—
133C2—21no—
134C2—2441no—
135C2—2441no—
136C2#1684061311yescharacteristic
137C2#1684066411yescharacteristic
138C2#1684066811yescharacteristic
subgroupG/H
centerC22#14519835
commutatorC22×C4×C61C2×C4
FrattiniC22×C4C2×#6923
FittingC2×C4⋊C4×C61C4
socleC22×C61#99
hypercenterC2×C4⋊C4#6923
hypocenterC61#1344
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
9. #14519684C4semidirect
10. C2×C4⋊C4×C61C4semidirect
73. C61#1344semidirect
74. C2×C4⋊C4#6923semidirect