Finite Group Databasebeta

← #21462100

Subgroups — #21462100

Order 7808.

270 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 54 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#16840741C212yesmaximal, complemented
2#16840667C214yesmaximal, complemented
3#16840331C211yesmaximal, characteristic
4#14519856—22no—
5#14519836C2214yescomplemented
6#14519835—22no—
7C2×#11758222C2211yescharacteristic
8C22×D244C411yescharacteristic, complemented
9#14519774C2212yes—
10#14519765C412yescomplemented
11#14519752—22no—
12#14519747—22no—
13#117×C61C411yescharacteristic, complemented
14C23×D61—21no—
15C22×C4×C61C2×C411yescharacteristic
16C2×C22⋊D61D412yes—
17#11758222—42no—
18C2×D244—21no—
19C2×D244—24no—
20C2×D244—42no—
21C2×D244C2×C412yes—
22C2×D244C2311yescharacteristic
23C2×C4×D61D412yes—
24C2×Dic122C2×C411yescharacteristic
25C22⋊#6923—24no—
26C4⋊#6923—42no—
27C4×#6923—42no—
28C4⋊C4×C61—21no—
29C22⋊C4×C61—21no—
30C42×C61C2×C412yes—
31#11758198—24no—
32C23×C61C22⋊C411yescharacteristic
33C22×D61—22no—
34C22×D61—42no—
35C22×D61—82no—
36C22×D61C2×D412yes—
37C2×#6923—44no—
38C2×C4×C61—22no—
39C2×C4×C61—22no—
40C2×C4×C61C22⋊C411yescharacteristic
41C2×C4×C61C22×C411yescharacteristic
42C22⋊D61—42no—
43C2×Dic61C22⋊C412yes—
44D244—41no—
45D244—42no—
46D244—42no—
47D244—84no—
48C4×D61—22no—
49C4×D61—22no—
50Dic122—41no—
51C22×C61—21no—
52C22×C61—41no—
53C22×C61C2×C22⋊C411yescharacteristic
54C2×D61—22no—
55C2×D61—42no—
56C2×D61—44no—
57C2×D61—42no—
58C2×D61—84no—
59#6923—84no—
60C4×C61—21no—
61C4×C61—42no—
62C4×C61#9912yes—
63Dic61—22no—
64#2128—611nomaximal, Sylow
65C2×C61—21no—
66C2×C61—41no—
67C2×C61C2×#9911yescharacteristic
68D61—42no—
69D61—82no—
70#535—611no—
71#410—612no—
72#353—614no—
73C61#212811yescharacteristic, complemented, Sylow
74C2×#41—611no—
75C22×D4—611no—
76#127—612no—
77#124—612no—
78#121—1222no—
79#120—1222no—
80#117—1222no—
81#117#692311yescharacteristic, complemented
82#99—614no—
83#99—1222no—
84C24—1221no—
85#41—2442no—
86C2×Q8—611no—
87C2×D4—612no—
88C2×D4—611no—
89C2×D4—612no—
90C2×D4—1224no—
91C2×D4—1221no—
92C2×D4—2442no—
93C22×C4—612no—
94C22×C4C2×#692311yescharacteristic
95C4⋊C4—21no—
96C4⋊C4—2442no—
97C22⋊C4—21no—
98C22⋊C4—1224no—
99C22⋊C4—1224no—
100C42—2442no—
101C42C2×#692312yes—
102C23—612no—
103C23—1222no—
104C23—4882no—
105C23—2442no—
106C23C22⋊#692311yescharacteristic
107Q8—2441no—
108D4—4884no—
109D4—2441no—
110D4—2442no—
111D4—2442no—
112D4—2442no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—612no—
116C2×C4—1222no—
117C2×C4—1222no—
118C2×C4—2444no—
119C2×C4C22⋊#692311yescharacteristic
120C2×C4C22×#692311yescharacteristic
121C22—21no—
122C22—41no—
123C22—1222no—
124C22—4884no—
125C22—2444no—
126C22—2442no—
127C22—2442no—
128C22C2×C22⋊#692311yescharacteristic
129C4—21no—
130C4—42no—
131C4—1222no—
132C4—4884no—
133C4#1451983612yes—
134C2—21no—
135C2—41no—
136C2—4882no—
137C2—2442no—
138C2C2×#1451983611yescharacteristic
subgroupG/H
centerC2C2×#14519836
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#117×C61C4
socleC2×C61C2×#99
hypercenter#117#6923
hypocenterC61#2128
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #16840741C2semidirect
2. #16840667C2semidirect
5. #14519836C22semidirect
8. C22×D244C4semidirect
10. #14519765C4semidirect
13. #117×C61C4semidirect
73. C61#2128semidirect
81. #117#6923semidirect