Finite Group Databasebeta

← C22×#14519700 #21454308

Subgroups — C22×#14519700 #21454308

Order 7808.

816 conjugacy classes of subgroups; only the 349 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 349 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
1C23×Dic122C211yesmaximal, characteristic
2C23×#92418C211yesmaximal, characteristic
3C2×#14519700C2112yesmaximal, direct product factor
4C22×C4⋊C4×C61C211yesmaximal, characteristic
5C22×Dic122—23no—
6C22×Dic122—24no—
7C22×Dic122C418yescomplemented
8C22×Dic122C2216yes—
9C23×Dic61—21no—
10C22×#92418—24no—
11C22×#92418C2216yes—
12#14519700C22116yesdirect product factor
13C23×C4×C61—21no—
14C23×C4×C61C2211yescharacteristic
15C2×C4⋊C4×C61—23no—
16C2×C4⋊C4×C61C2216yes—
17C24×C61D411yescharacteristic
18C22×C4×C61—26no—
19C22×C4×C61—44no—
20C22×C4×C61C2×C414yes—
21C22×C4×C61D413yes—
22C22×C4×C61D414yes—
23C22×C4×C61C2313yes—
24C22×Dic61—28no—
25C22×Dic61—26no—
26C2×Dic122—224no—
27C2×Dic122—26no—
28C2×Dic122—212no—
29C2×Dic122C2×C4124yescomplemented
30C2×Dic122C2314yes—
31C4⋊C4×C61—26no—
32C4⋊C4×C61C2314yes—
33C2×#92418—212no—
34C2×#92418C2314yes—
35C23×C61C22⋊C414yes—
36C23×C61SD1614yes—
37C23×C61Q1614yes—
38C23×C61C2×D413yes—
39C2×C4×C61—24no—
40C2×C4×C61—412no—
41C2×C4×C61C22⋊C4112yes—
42C2×C4×C61C22×C416yes—
43C2×C4×C61C2×D413yes—
44C2×C4×C61C2×D416yes—
45C2×C4×C61C2411yescharacteristic
46C2×Dic61—224no—
47C2×Dic61—24no—
48Dic122—224no—
49Dic122—24no—
50Dic122C22×C418yescomplemented
51#92418—24no—
52C22×C61#103116yescomplemented
53C22×C61C2×C22⋊C416yes—
54C22×C61C2×SD1616yes—
55C22×C61C2×Q1616yes—
56C22×C61C22×D411yescharacteristic
57C4×C61—44no—
58C4×C61C2×C22⋊C416yes—
59C4×C61C23×C411yescharacteristic
60C4×C61C22×D411yescharacteristic
61Dic61—28no—
62C22×#103—611nomaximal, Sylow
63C2×C61C2×#103112yescomplemented
64C2×C61C22×C22⋊C411yescharacteristic
65C2×C61C22×SD1611yescharacteristic
66C2×C61C22×Q1611yescharacteristic
67C23×Q8—611no—
68C23×C8—611no—
69C22×C4⋊C4D6111yescharacteristic
70C2×#103—6112no—
71C61C22×#10311yescharacteristic, complemented, Sylow
72C22×Q8—618no—
73C22×Q8—616no—
74C22×Q8—1224no—
75C22×Q8—1223no—
76C23×C4—21no—
77C23×C4—1221no—
78C23×C4C2×D6111yescharacteristic
79C22×C8—616no—
80C22×C8—1224no—
81C2×C4⋊C4—23no—
82C2×C4⋊C4C2×D6116yes—
83#103—6116no—
84C24C22⋊D6111yescharacteristic
85C2×Q8—6124no—
86C2×Q8—614no—
87C2×Q8—12224no—
88C2×Q8—12212no—
89C2×Q8—1226no—
90C22×C4—26no—
91C22×C4—44no—
92C22×C4—1228no—
93C22×C4—1226no—
94C22×C4C4×D6114yes—
95C22×C4D24414yes—
96C22×C4C22⋊D6113yes—
97C22×C4C22×D6113yes—
98C2×C8—614no—
99C2×C8—12212no—
100C4⋊C4—26no—
101C4⋊C4C22×D6114yes—
102C23#1175819814yes—
103C23#1175820014yes—
104C23#1175820214yes—
105C23C2×C22⋊D6113yes—
106Q8—618no—
107Q8—1224no—
108Q8—12224no—
109C2×C4—24no—
110C2×C4—412no—
111C2×C4—1224no—
112C2×C4—12224no—
113C2×C4#11758198112yes—
114C2×C4C2×C4×D6116yes—
115C2×C4C2×D24416yes—
116C2×C4C2×C22⋊D6113yes—
117C2×C4C23×D6111yescharacteristic
118C8—1224no—
119C22#14519700116yesdirect product factor
120C22C2×#1175819816yes—
121C22C2×#1175820016yes—
122C22C2×#1175820216yes—
123C22C22×C22⋊D6111yescharacteristic
124C4—44no—
125C4—1228no—
126C4C2×#1175819816yes—
127C4C22×C4×D6111yescharacteristic
128C4C22×D24411yescharacteristic
129C2C2×#14519700112yesdirect product factor
130C2C22×#1175819811yescharacteristic
131C2C22×#1175820011yescharacteristic
132C2C22×#1175820211yescharacteristic
subgroupG/H
centerC24C22⋊D61
commutatorC4×C61C23×C4
FrattiniC2×C4C23×D61
FittingC22×C4⋊C4×C61C2
socleC24×C61D4
hypercenterC22×C4⋊C4D61
hypocenterC61C22×#103
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#14519700C2direct (N × H)
7. C22×Dic122C4semidirect
12. #14519700C22direct (N × H)
29. C2×Dic122C2×C4semidirect
50. Dic122C22×C4semidirect
52. C22×C61#103semidirect
63. C2×C61C2×#103semidirect
71. C61C22×#103semidirect
119. C22#14519700direct (N × H)
129. C2C2×#14519700direct (N × H)