Finite Group Databasebeta

← #21460688

Subgroups — #21460688

Order 7808.

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

normal subgroups only

This group has 152 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#16840767C211yesmaximal, characteristic
2D61⋊(C4⋊C8)C211yesmaximal, characteristic
3#16839784C211yesmaximal, characteristic
4C2×#11758213—21no—
5C2×D61⋊C8C412yes—
6#14519844—21no—
7#14519844—21no—
8#14519844C412yes—
9C4⋊#92420—21no—
10C2×#11758189—21no—
11C42×D61C2211yescharacteristic
12C4⋊#92418C411yescharacteristic
13#14519706—21no—
14C4⋊C8×C61C411yescharacteristic
15C2×C4×D61C2×C411yescharacteristic
16C2×C4×D61D411yescharacteristic
17C2×C4×D61Q811yescharacteristic
18C2×#92420—22no—
19C2×#92420—22no—
20#11758213—41no—
21#11758213—41no—
22D61⋊C8—42no—
23C2×C8×C61—21no—
24C42×C61C2×C411yescharacteristic
25C4×Dic61C2×C411yescharacteristic
26C4×Dic61D411yescharacteristic
27C4×Dic61D411yescharacteristic
28C2×#92418—21no—
29#11758189—41no—
30#11758189—41no—
31C22×D61C4⋊C411yescharacteristic
32C2×C4×C61C4211yescharacteristic
33C2×C4×C61C22⋊C411yescharacteristic
34C2×C4×C61C4⋊C411yescharacteristic
35C2×Dic61C22⋊C411yescharacteristic
36C2×Dic61C22⋊C411yescharacteristic
37C2×Dic61C4⋊C411yescharacteristic
38C4×D61—21no—
39C4×D61—21no—
40C4×D61—41no—
41C4×D61D811yescharacteristic
42C4×D61SD1611yescharacteristic
43C4×D61SD1611yescharacteristic
44C4×D61Q1611yescharacteristic
45#92420—42no—
46#92420—42no—
47C8×C61—41no—
48#92418—41no—
49C22×C61#9511yescharacteristic
50C2×D61—21no—
51C2×D61—21no—
52C2×D61#10611yescharacteristic
53C2×D61#10711yescharacteristic
54C4×C61—21no—
55C4×C61—21no—
56C4×C61#10211yescharacteristic
57C4×C61#10311yescharacteristic
58Dic61—21no—
59Dic61#10011yescharacteristic
60Dic61#10111yescharacteristic
61Dic61#10211yescharacteristic
62Dic61#10311yescharacteristic
63#1292—611nomaximal, Sylow
64C2×C61#33811yescharacteristic
65C2×C61#34011yescharacteristic
66C2×C61#34311yescharacteristic
67D61—21no—
68D61—21no—
69#423—611no—
70#423—611no—
71C2×C4⋊C8—611no—
72C61#129211yescharacteristic, complemented, Sylow
73C2×M16—1221no—
74C2×M16—1221no—
75C22×C8—612no—
76C2×C42—611no—
77C4⋊C8—612no—
78C4⋊C8—611no—
79C4⋊C8—1221no—
80C4⋊C8—1221no—
81C4⋊C8—1221no—
82C4⋊C8—1221no—
83C4⋊C8#692311yescharacteristic
84C22×C4—611no—
85C22×C4—611no—
86C22×C4—611no—
87M16—2441no—
88M16—2441no—
89M16—2441no—
90M16—2441no—
91C2×C8—21no—
92C2×C8—1222no—
93C2×C8—1222no—
94C2×C8—1221no—
95C2×C8—2442no—
96C42—611no—
97C42—611no—
98C42—611no—
99C42C2×#692311yescharacteristic
100C23—611no—
101C2×C4—611no—
102C2×C4—611no—
103C2×C4—611no—
104C2×C4—611no—
105C2×C4—611no—
106C2×C4—611no—
107C2×C4—611no—
108C2×C4—1221no—
109C2×C4—1221no—
110C2×C4—2441no—
111C2×C4C4×#692311yescharacteristic
112C2×C4C4⋊#692311yescharacteristic
113C2×C4C22⋊#692311yescharacteristic
114C8—41no—
115C8—2442no—
116C8—2442no—
117C8—2441no—
118C22—611no—
119C22—611no—
120C22—1221no—
121C22—1221no—
122C22(C2×#6923)⋊C411yescharacteristic
123C4—21no—
124C4—21no—
125C4—611no—
126C4—611no—
127C4—611no—
128C4—611no—
129C4—1221no—
130C4#1451983911yescharacteristic
131C4#1451984011yescharacteristic
132C2—1221no—
133C2—1221no—
134C2#1684063111yescharacteristic
135C2#1684063511yescharacteristic
136C2#1684064111yescharacteristic
subgroupG/H
centerC22(C2×#6923)⋊C4
commutatorC2×C4×C61C42
FrattiniC42C2×#6923
FittingC4⋊C8×C61C4
socleC22×C61#95
hypercenterC4⋊C8#6923
hypocenterC61#1292
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
72. C61#1292semidirect