Finite Group Databasebeta

← #21460691

Subgroups — #21460691

Order 7808.

184 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 48 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#16840733C212yesmaximal
2C2×#14519689C211yesmaximal, characteristic
3C2×#11758213—22no—
4#14519834C414yes—
5C22⋊#92420—22no—
6C22×C4×D61C2211yescharacteristic
7C22×#92418C411yescharacteristic
8#14519689—22no—
9C22×C8×C61C411yescharacteristic
10C23×D61Q811yescharacteristic
11C22×C4×C61C2×C411yescharacteristic
12C22×Dic61D411yescharacteristic
13C2×C4×D61—41no—
14C2×C4×D61—41no—
15C2×C4×D61C2×C412yes—
16C2×C4×D61D412yes—
17C2×#92420—24no—
18#11758213—42no—
19#11758213—42no—
20C2×C8×C61—21no—
21C2×C8×C61—41no—
22C2×#92418—21no—
23C2×#92418—41no—
24C23×C61C4⋊C411yescharacteristic
25C22×D61—21no—
26C22×D61—21no—
27C22×D61—41no—
28C22×D61—41no—
29C22×D61C4⋊C412yes—
30C2×C4×C61—21no—
31C2×C4×C61—21no—
32C2×C4×C61C4211yescharacteristic
33C2×C4×C61C22⋊C411yescharacteristic
34C2×Dic61—41no—
35C2×Dic61C22⋊C412yes—
36C4×D61—22no—
37C4×D61—22no—
38C4×D61—42no—
39#92420—44no—
40C8×C61—41no—
41#92418—41no—
42C22×C61—21no—
43C22×C61—21no—
44C22×C61#9511yescharacteristic
45C22×C61#10811yescharacteristic
46C22×C61#10811yescharacteristic
47C2×D61—22no—
48C2×D61—22no—
49C2×D61—22no—
50C2×D61—42no—
51C2×D61—42no—
52C4×C61—21no—
53C4×C61#9911yescharacteristic
54C4×C61#9911yescharacteristic
55Dic61—22no—
56#1293—611nomaximal, Sylow
57C2×C61—21no—
58C2×C61—21no—
59C2×C61#33811yescharacteristic
60C2×C61#34111yescharacteristic
61C2×C61#34211yescharacteristic
62D61—42no—
63#407—612no—
64C2×C22⋊C8—611no—
65C61#129311yescharacteristic, complemented, Sylow
66C23×C4—611no—
67C2×M16—1222no—
68C22×C8—611no—
69C22×C8#692311yescharacteristic
70C22⋊C8—614no—
71C22⋊C8—1222no—
72C22⋊C8—1222no—
73C24—611no—
74C22×C4—611no—
75C22×C4—612no—
76C22×C4—612no—
77C22×C4—2441no—
78C22×C4—2441no—
79C22×C4C2×#692311yescharacteristic
80M16—2442no—
81M16—2442no—
82C2×C8—21no—
83C2×C8—41no—
84C2×C8—1224no—
85C2×C8—1221no—
86C2×C8—2441no—
87C23—612no—
88C23—1221no—
89C23—1221no—
90C23—2441no—
91C23—2441no—
92C23C4⋊#692311yescharacteristic
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—612no—
96C2×C4—1222no—
97C2×C4—1222no—
98C2×C4—2442no—
99C2×C4—2441no—
100C2×C4C4×#692311yescharacteristic
101C2×C4C22⋊#692311yescharacteristic
102C8—41no—
103C8—2444no—
104C8—2441no—
105C22—21no—
106C22—21no—
107C22—1222no—
108C22—1222no—
109C22—1222no—
110C22—2442no—
111C22—2442no—
112C22(C2×#6923)⋊C411yescharacteristic
113C22#1451984711yescharacteristic
114C22#1451984811yescharacteristic
115C4—21no—
116C4—1222no—
117C4#1451983511yescharacteristic
118C4#1451983611yescharacteristic
119C2—21no—
120C2—21no—
121C2—2442no—
122C2#1684063111yescharacteristic
123C2#1684063811yescharacteristic
124C2#1684064011yescharacteristic
subgroupG/H
centerC22(C2×#6923)⋊C4
commutatorC2×C4×C61C42
FrattiniC22×C4C2×#6923
FittingC22×C8×C61C4
socleC22×C61#95
hypercenterC22×C8#6923
hypocenterC61#1293
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
65. C61#1293semidirect