Finite Group Databasebeta

← #21456265

Subgroups — #21456265

Order 7808.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C2×#14519799C214yesmaximal, complemented
2#16840312C212yesmaximal, complemented
3#16840156C214yesmaximal, complemented
4#16840151C214yesmaximal, complemented
5C2×#97×C61C211yesmaximal, characteristic, complemented
6C2×#11758222C2214yes—
7#14519799—216no—
8C2×Dic244C2214yes—
9C2×#11758190C2218yes—
10C2×D488C2214yes—
11#14519777C2212yes—
12#14519774C2212yes—
13#14519765C2214yes—
14#14519751—24no—
15C4×D244—24no—
16C22×C8×C61C2212yes—
17C2×C42×C61C2211yescharacteristic
18#97×C61C2214yes—
19C22×C4×C61D412yes—
20C22×C4×C61C2311yescharacteristic
21C2×C22⋊D61—24no—
22#11758222—216no—
23C2×D244—24no—
24C2×D244C2314yes—
25C2×C4×D61—24no—
26C2×Dic122C2314yes—
27C2×C8×C61D418yescomplemented
28C2×C8×C61C2314yes—
29C42×C61D412yes—
30C42×C61C2312yes—
31#11758198—28no—
32C4⋊Dic61—24no—
33Dic244—28no—
34D488—28no—
35#11758190—216no—
36C23×C61C2×D411yescharacteristic
37C22×D61—24no—
38C2×C4×C61—42no—
39C2×C4×C61C2×D414yes—
40C2×C4×C61C2×D411yescharacteristic
41C2×C4×C61C2×D414yes—
42C2×C4×C61C2411yescharacteristic
43C22⋊D61—48no—
44C2×Dic61—24no—
45D244—28no—
46D244—48no—
47C4×D61—48no—
48Dic122—28no—
49C8×C61C2×D418yes—
50C22×C61—22no—
51C22×C61#12712yes—
52C22×C61C22×D411yescharacteristic
53C2×D61—44no—
54C2×D61—48no—
55C4×C61—24no—
56C4×C61#12712yes—
57C4×C61C22×D412yes—
58Dic61—44no—
59#3150—611nomaximal, Sylow
60C2×C61—22no—
61C2×C61C2×#12711yescharacteristic
62C2×C61#57512yes—
63D61—84no—
64C2×#135—614no—
65#532—612no—
66#497—614no—
67#496—614no—
68C2×#97D6111yescharacteristic, complemented
69C61#315011yescharacteristic, complemented, Sylow
70C2×#41—614no—
71#135—12216no—
72C2×Q16—614no—
73C2×SD16—618no—
74C2×D8—614no—
75C22×C8C2×D6112yes—
76C4⋊Q8—612no—
77#127—612no—
78#124—614no—
79#121—1224no—
80C4×D4—1224no—
81C2×C42C2×D6111yescharacteristic
82#97C2×D6114yes—
83#41—12216no—
84C2×Q8—614no—
85C2×D4—614no—
86C2×D4—1224no—
87C2×D4—1224no—
88C22×C4—1224no—
89C22×C4D24412yes—
90C22×C4C22×D6111yescharacteristic
91Q16—1228no—
92SD16—12216no—
93D8—1228no—
94C2×C8D24418yescomplemented
95C2×C8C22×D6114yes—
96C4⋊C4—1224no—
97C22⋊C4—1228no—
98C42D24412yes—
99C42C22×D6112yes—
100C23—1224no—
101C23C2×D24411yescharacteristic
102Q8—1228no—
103D4—1228no—
104D4—2448no—
105D4—2448no—
106C2×C4—42no—
107C2×C4—1224no—
108C2×C4—2448no—
109C2×C4C2×D24414yes—
110C2×C4C2×D24414yes—
111C2×C4C2×D24411yescharacteristic
112C2×C4C23×D6111yescharacteristic
113C8C2×D24418yes—
114C22—22no—
115C22—2444no—
116C22—2448no—
117C22#1451977412yes—
118C22C22×D24411yescharacteristic
119C4—24no—
120C4—2444no—
121C4#1451977412yes—
122C4C22×D24412yes—
123C2—22no—
124C2—4884no—
125C2C2×#1451977411yescharacteristic
126C2#1684056212yes—
subgroupG/H
centerC2×C4C2×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#97×C61C2
socleC22×C61C22×D4
hypercenterC2×#97D61
hypocenterC61#3150
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
1. C2×#14519799C2semidirect
2. #16840312C2semidirect
3. #16840156C2semidirect
4. #16840151C2semidirect
5. C2×#97×C61C2semidirect
27. C2×C8×C61D4semidirect
68. C2×#97D61semidirect
69. C61#3150semidirect
94. C2×C8D244semidirect