Finite Group Databasebeta

← #21443839

Subgroups — #21443839

Order 7808.

162 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 35 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#16839674C211yesmaximal, characteristic
2#16839486C211yesmaximal, characteristic
3C61×#342C211yesmaximal, characteristic
4C22×Dic122C411yescharacteristic, complemented
5C2×C22⋊Dic61—21no—
6C22⋊#92418—21no—
7#14519684—21no—
8#14519684C411yescharacteristic, complemented
9C2×C22⋊C4×C61—21no—
10C2×C22⋊C4×C61C2211yescharacteristic
11C24×C61D411yescharacteristic
12C22×C4×C61—41no—
13C22×C4×C61C2×C411yescharacteristic
14C22×C4×C61D411yescharacteristic
15C22×Dic61—21no—
16C22×Dic61—21no—
17C2×Dic122—41no—
18C2×Dic122—42no—
19C22⋊C4×C61—22no—
20C22⋊C4×C61—41no—
21C22⋊C4×C61—41no—
22C22⋊Dic61—42no—
23C2×#92418—41no—
24C23×C61—21no—
25C23×C61—21no—
26C23×C61—41no—
27C23×C61—41no—
28C23×C61C22⋊C411yescharacteristic
29C23×C61SD1611yescharacteristic
30C23×C61Q1611yescharacteristic
31C2×C4×C61—21no—
32C2×C4×C61—21no—
33C2×C4×C61—41no—
34C2×C4×C61—41no—
35C2×C4×C61—42no—
36C2×C4×C61—81no—
37C2×C4×C61—81no—
38C2×Dic61—22no—
39C2×Dic61—41no—
40C2×Dic61—41no—
41C2×Dic61—41no—
42C2×Dic61—41no—
43C2×Dic61—41no—
44Dic122—42no—
45Dic122—42no—
46#92418—81no—
47C22×C61—21no—
48C22×C61—21no—
49C22×C61—21no—
50C22×C61—21no—
51C22×C61—41no—
52C22×C61—41no—
53C22×C61—41no—
54C22×C61—41no—
55C22×C61—81no—
56C22×C61#9911yescharacteristic
57C22×C61#10311yescharacteristic
58C22×C61#10411yescharacteristic
59C4×C61—41no—
60C4×C61—41no—
61C4×C61—82no—
62Dic61—42no—
63Dic61—81no—
64#1351—611nomaximal, Sylow
65C2×C61—21no—
66C2×C61—21no—
67C2×C61—41no—
68C2×C61—41no—
69C2×C61#32811yescharacteristic
70C2×C61AΣL(1,𝔽16)11yescharacteristic
71C2×C61#35411yescharacteristic
72#393—611no—
73#342D6111yescharacteristic
74#323—611no—
75C61#135111yescharacteristic, complemented, Sylow
76C22×Q8—611no—
77C2×C22⋊C4—21no—
78C2×C22⋊C4—1221no—
79C2×C22⋊C4C2×D6111yescharacteristic
80C22⋊C8—1221no—
81#95—611no—
82#95—1221no—
83C24C22⋊D6111yescharacteristic
84C2×Q8—2441no—
85C2×Q8—2442no—
86C22×C4—41no—
87C22×C4—1221no—
88C22×C4—1221no—
89C22×C4C4×D6111yescharacteristic
90C22×C4D24411yescharacteristic
91C2×C8—2441no—
92C22⋊C4—22no—
93C22⋊C4—41no—
94C22⋊C4—41no—
95C22⋊C4—2442no—
96C23—21no—
97C23—21no—
98C23—41no—
99C23—41no—
100C23#1175819811yescharacteristic
101C23#1175820011yescharacteristic
102C23#1175820211yescharacteristic
103Q8—2442no—
104Q8—2442no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4—42no—
110C2×C4—81no—
111C2×C4—81no—
112C2×C4—1222no—
113C2×C4—2441no—
114C2×C4—2441no—
115C2×C4—2441no—
116C2×C4—2441no—
117C2×C4—2441no—
118C8—4881no—
119C22—21no—
120C22—21no—
121C22—21no—
122C22—21no—
123C22—41no—
124C22—41no—
125C22—41no—
126C22—41no—
127C22—81no—
128C22#1451969111yescharacteristic
129C22#1451970011yescharacteristic
130C22#1451970511yescharacteristic
131C4—41no—
132C4—41no—
133C4—82no—
134C4—4881no—
135C4—2442no—
136C2—21no—
137C2—21no—
138C2—41no—
139C2—41no—
140C2#1683949811yescharacteristic
141C2#1683954811yescharacteristic
142C2#1683955611yescharacteristic
subgroupG/H
centerC22#14519691
commutatorC22×C4×C61C2×C4
FrattiniC2×C22⋊C4C2×D61
FittingC61×#342C2
socleC22×C61#99
hypercenter#342D61
hypocenterC61#1351
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #342

Complements

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

NH ≅ G/Ntype
4. C22×Dic122C4semidirect
8. #14519684C4semidirect
75. C61#1351semidirect