Finite Group Databasebeta

← #21462120

Subgroups — #21462120

Order 7808.

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

normal subgroups only

This group has 262 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#16840748C212yesmaximal, complemented
2#16840671C214yesmaximal, complemented
3#16840331C211yesmaximal, characteristic
4D61⋊M16—22no—
5#14519838C2214yescomplemented
6#14519837—22no—
7C2×#11758222C2211yescharacteristic
8C22×D244C411yescharacteristic
9#14519774C412yes—
10#14519765C2212yes—
11#14519752—22no—
12#14519747—22no—
13#117×C61C411yescharacteristic
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×D244C2×C411yescharacteristic
23C2×C4×D61D412yes—
24C2×Dic122C2311yescharacteristic
25#11758217—24no—
26#11758213—42no—
27D61⋊C8—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×D61C22⋊C412yes—
37C2×C4×C61—22no—
38C2×C4×C61—22no—
39C2×C4×C61C22⋊C411yescharacteristic
40C2×C4×C61C22×C411yescharacteristic
41C22⋊D61—42no—
42C2×Dic61C2×D412yes—
43D244—41no—
44D244—42no—
45D244—42no—
46D244—84no—
47C4×D61—22no—
48C4×D61—22no—
49Dic122—41no—
50#92420—44no—
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—
59C4×C61—21no—
60C4×C61—42no—
61C4×C61#9912yes—
62Dic61—22no—
63#2134—611nomaximal, Sylow
64C2×C61—21no—
65C2×C61—41no—
66C2×C61C2×#9911yescharacteristic
67D61—42no—
68D61—82no—
69#535—611no—
70#413—612no—
71#355—614no—
72C61#213411yescharacteristic, complemented, Sylow
73C2×#41—611no—
74C22×D4—611no—
75C2×M16—1222no—
76#127—612no—
77#124—612no—
78#121—1222no—
79#120—1222no—
80#117#692311yescharacteristic
81#101—614no—
82#100—1222no—
83C24—1221no—
84#41—2442no—
85C2×Q8—611no—
86C2×D4—612no—
87C2×D4—611no—
88C2×D4—612no—
89C2×D4—1224no—
90C2×D4—1221no—
91C2×D4—2442no—
92C22×C4—612no—
93C22×C4C2×#692311yescharacteristic
94M16—1224no—
95M16—2442no—
96C2×C8—2442no—
97C4⋊C4—21no—
98C22⋊C4—21no—
99C22⋊C4—1224no—
100C42C2×#692312yes—
101C23—612no—
102C23—1222no—
103C23—4882no—
104C23—2442no—
105C23C22⋊#692311yescharacteristic
106Q8—2441no—
107D4—4884no—
108D4—2441no—
109D4—2442no—
110D4—2442no—
111D4—2442no—
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—612no—
115C2×C4—1222no—
116C2×C4—1222no—
117C2×C4C22⋊#692311yescharacteristic
118C2×C4C22×#692311yescharacteristic
119C8—2444no—
120C22—21no—
121C22—41no—
122C22—1222no—
123C22—4884no—
124C22—2444no—
125C22—2442no—
126C22—2442no—
127C22C2×C22⋊#692311yescharacteristic
128C4—21no—
129C4—42no—
130C4—1222no—
131C4#1451983612yes—
132C2—21no—
133C2—41no—
134C2—4882no—
135C2—2442no—
136C2C2×#1451983611yescharacteristic
subgroupG/H
centerC2C2×#14519836
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#117×C61C4
socleC2×C61C2×#99
hypercenter#117#6923
hypocenterC61#2134
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. #16840748C2semidirect
2. #16840671C2semidirect
5. #14519838C22semidirect
72. C61#2134semidirect