Finite Group Databasebeta

← #21460705

Subgroups — #21460705

Order 7808.

150 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 50 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#16840766C211yesmaximal, characteristic
2C4×#11758213C211yesmaximal, characteristic
3#16839814C211yesmaximal, characteristic
4C2×#11758213—21no—
5C2×#11758213C412yes—
6C4⋊#92420—21no—
7C4⋊#92420—21no—
8#14519832C412yes—
9C4×#92420—21no—
10C42×D61C2211yescharacteristic
11C4⋊#92418C411yescharacteristic
12#14519689—21no—
13C8×Dic61—21no—
14C4⋊C8×C61C411yescharacteristic
15C2×C4×D61C2×C411yescharacteristic
16C2×C4×D61D411yescharacteristic
17C2×C4×D61Q811yescharacteristic
18C2×#92420—22no—
19C2×#92420—22no—
20#11758213—22no—
21#11758213—22no—
22#11758213—42no—
23C2×C8×C61—21no—
24C42×C61C2×C411yescharacteristic
25C4×Dic61C2×C411yescharacteristic
26C4×Dic61D411yescharacteristic
27C4×Dic61D411yescharacteristic
28C2×#92418—21no—
29C22×D61C4⋊C411yescharacteristic
30C2×C4×C61C4211yescharacteristic
31C2×C4×C61C22⋊C411yescharacteristic
32C2×C4×C61C4⋊C411yescharacteristic
33C2×Dic61C22⋊C411yescharacteristic
34C2×Dic61C22⋊C411yescharacteristic
35C2×Dic61C4⋊C411yescharacteristic
36C4×D61—21no—
37C4×D61—21no—
38C4×D61—21no—
39C4×D61—21no—
40C4×D61—21no—
41C4×D61—21no—
42#92420—24no—
43#92420—42no—
44C8×C61—41no—
45#92418—41no—
46C22×C61#9511yescharacteristic
47C2×D61—21no—
48C2×D61—21no—
49C2×D61—21no—
50C4×C61—21no—
51C4×C61#10411yescharacteristic
52C4×C61#10411yescharacteristic
53C4×C61#10811yescharacteristic
54C4×C61#10811yescharacteristic
55Dic61—21no—
56Dic61—21no—
57Dic61#10011yescharacteristic
58Dic61#10111yescharacteristic
59#1299—611nomaximal, Sylow
60C2×C61#33911yescharacteristic
61C2×C61#34111yescharacteristic
62C2×C61#34311yescharacteristic
63D61—41no—
64#431—611no—
65#423—611no—
66C4×M16—611no—
67C61#129911yescharacteristic, complemented, Sylow
68C2×M16—612no—
69C2×M16—1221no—
70C2×C42—611no—
71C4⋊C8—611no—
72C4⋊C8—1221no—
73C4⋊C8—1221no—
74C4⋊C8#692311yescharacteristic
75C22⋊C8—1221no—
76#97—612no—
77C4×C8—1221no—
78C4×C8—1221no—
79C22×C4—611no—
80C22×C4—611no—
81C22×C4—611no—
82M16—1222no—
83M16—1222no—
84M16—2442no—
85C2×C8—21no—
86C2×C8—1222no—
87C2×C8—1222no—
88C2×C8—1221no—
89C42—611no—
90C42—611no—
91C42—611no—
92C42C2×#692311yescharacteristic
93C23—611no—
94C2×C4—611no—
95C2×C4—611no—
96C2×C4—611no—
97C2×C4—1221no—
98C2×C4—1221no—
99C2×C4—1221no—
100C2×C4—1221no—
101C2×C4—1221no—
102C2×C4—1221no—
103C2×C4C4×#692311yescharacteristic
104C2×C4C4⋊#692311yescharacteristic
105C2×C4C22⋊#692311yescharacteristic
106C8—41no—
107C8—1224no—
108C8—2442no—
109C8—2441no—
110C22—1221no—
111C22—1221no—
112C22—1221no—
113C22(C2×#6923)⋊C411yescharacteristic
114C4—21no—
115C4—611no—
116C4—611no—
117C4—1221no—
118C4—1221no—
119C4#1451984111yescharacteristic
120C4#1451984211yescharacteristic
121C4#1451984711yescharacteristic
122C4#1451984811yescharacteristic
123C2—2441no—
124C2#1684063211yescharacteristic
125C2#1684063811yescharacteristic
126C2#1684064111yescharacteristic
subgroupG/H
centerC22(C2×#6923)⋊C4
commutatorC2×C4×C61C42
FrattiniC42C2×#6923
FittingC4⋊C8×C61C4
socleC22×C61#95
hypercenterC4⋊C8#6923
hypocenterC61#1299
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
67. C61#1299semidirect