Finite Group Databasebeta

← #21461719

Subgroups — #21461719

Order 7808.

316 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 70 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#16840734C212yesmaximal
2#16840642C214yesmaximal, complemented
3C2×C4⋊C4×D61C211yesmaximal, characteristic
4C2×#11758217C2214yes—
5#14519834—22no—
6#14519834—22no—
7C22×C4×D61C412yes—
8C22×C4×D61C2211yescharacteristic
9C2×C4⋊Dic61C411yescharacteristic
10C2×#11758196C2212yes—
11C4⋊C4×D61—22no—
12C4⋊C4×D61—22no—
13C2×C4⋊C4×C61C411yescharacteristic
14C23×D61C2×C411yescharacteristic
15C22×C4×C61C2×C411yescharacteristic
16C22×C4×C61C2×C412yes—
17C22×Dic61C2×C412yes—
18C22×Dic61C2311yescharacteristic
19C2×C4×D61—24no—
20C2×C4×D61—22no—
21C2×C4×D61—22no—
22C2×C4×D61—44no—
23C2×C4×D61D412yes—
24C2×C4×D61D412yes—
25#11758217—28no—
26C2×#92420—24no—
27C4⋊C4×C61—22no—
28C4⋊Dic61—22no—
29#11758196—24no—
30C23×C61C22×C411yescharacteristic
31C22×D61—22no—
32C22×D61—22no—
33C22×D61—22no—
34C22×D61C22⋊C411yescharacteristic
35C22×D61C22⋊C411yescharacteristic
36C2×C4×C61—22no—
37C2×C4×C61—22no—
38C2×C4×C61—42no—
39C2×C4×C61C22⋊C412yes—
40C2×Dic61—22no—
41C2×Dic61—42no—
42C2×Dic61C2×D412yes—
43C2×Dic61#4114yes—
44C4×D61—24no—
45C4×D61—24no—
46C4×D61—44no—
47C4×D61—44no—
48#92420—44no—
49C22×C61—21no—
50C22×C61—21no—
51C22×C61C2×C22⋊C411yescharacteristic
52C22×C61#11712yes—
53C2×D61—28no—
54C2×D61—21no—
55C2×D61—21no—
56C2×D61—21no—
57C2×D61—21no—
58C2×D61#10012yes—
59C2×D61#10112yes—
60C4×C61—22no—
61C4×C61—42no—
62Dic61—42no—
63Dic61#12314yes—
64#1821—611nomaximal, Sylow
65C2×C61—22no—
66C2×C61#38111yescharacteristic
67C2×C61C2×#10011yescharacteristic
68C2×C61C2×#10111yescharacteristic
69D61—22no—
70D61—22no—
71C22×C4⋊C4—611no—
72#407—612no—
73#343—614no—
74C61#182111yescharacteristic, complemented, Sylow
75C23×C4—611no—
76C23×C4—612no—
77C2×M16—614no—
78C2×C4⋊C4—612no—
79C2×C4⋊C4—611no—
80C2×C4⋊C4—1222no—
81C2×C4⋊C4—1222no—
82C2×C4⋊C4#692311yescharacteristic
83C22⋊C8—1222no—
84C22⋊C8—1222no—
85C24—611no—
86C22×C4—611no—
87C22×C4—612no—
88C22×C4—612no—
89C22×C4—612no—
90C22×C4—1224no—
91C22×C4—1222no—
92C22×C4—1222no—
93C22×C4—2444no—
94C22×C4C2×#692312yes—
95C22×C4C2×#692311yescharacteristic
96M16—1228no—
97C2×C8—1224no—
98C4⋊C4—22no—
99C4⋊C4—1224no—
100C4⋊C4—1222no—
101C23—611no—
102C23—611no—
103C23—1222no—
104C23—1222no—
105C23—1222no—
106C23C22×#692311yescharacteristic
107C2×C4—22no—
108C2×C4—22no—
109C2×C4—42no—
110C2×C4—612no—
111C2×C4—614no—
112C2×C4—1224no—
113C2×C4—1224no—
114C2×C4—1222no—
115C2×C4—2444no—
116C2×C4—2444no—
117C2×C4—2442no—
118C2×C4C22⋊#692312yes—
119C8—2444no—
120C22—21no—
121C22—21no—
122C22—612no—
123C22—612no—
124C22—1228no—
125C22—1221no—
126C22—1221no—
127C22—1221no—
128C22—1221no—
129C22C2×C22⋊#692311yescharacteristic
130C22#1451985612yes—
131C4—22no—
132C4—42no—
133C4—614no—
134C4—2442no—
135C2—22no—
136C2—1222no—
137C2—1222no—
138C2#1684070511yescharacteristic
139C2D61⋊#10011yescharacteristic
140C2D61⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC2×C4⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C4#6923
hypocenterC61#1821
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #16840642C2semidirect
74. C61#1821semidirect