Finite Group Databasebeta

← #21460723

Subgroups — #21460723

Order 7808.

192 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 42 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#16840733C211yesmaximal, characteristic
2#16840705C211yesmaximal, characteristic
3#16839724C211yesmaximal, characteristic
4C2×#11758213—21no—
5C2×C22⋊#6923C412yes—
6#14519834—21no—
7C22⋊#92420C412yescomplemented
8(C2×#6923)⋊C4—21no—
9(C2×#6923)⋊C4—21no—
10C22×C4×D61C2211yescharacteristic
11C2×#11758189—21no—
12C22⋊#92418C411yescharacteristic, complemented
13#14519689—21no—
14C22⋊C8×C61C411yescharacteristic, complemented
15C23×D61C2×C411yescharacteristic
16C22×#6923—22no—
17C22×C4×C61C2×C411yescharacteristic
18C22×Dic61C2×C411yescharacteristic
19C2×C4×D61—42no—
20C2×C4×D61D411yescharacteristic
21C2×C4×D61D411yescharacteristic
22C2×C4×D61D411yescharacteristic
23C2×C4×D61Q811yescharacteristic
24C22⋊#6923—42no—
25C2×#92420—22no—
26#11758213—42no—
27C2×C8×C61—21no—
28C2×#92418—21no—
29#11758189—42no—
30C23×C61C4211yescharacteristic
31C22×D61—22no—
32C22×D61—41no—
33C22×D61—41no—
34C22×D61C22⋊C411yescharacteristic
35C22×D61C4⋊C411yescharacteristic
36C2×#6923—42no—
37C2×#6923—42no—
38C2×#6923—42no—
39C2×C4×C61—41no—
40C2×C4×C61C22⋊C411yescharacteristic
41C2×C4×C61C4⋊C411yescharacteristic
42C2×Dic61—41no—
43C2×Dic61C22⋊C411yescharacteristic
44C2×Dic61C4⋊C411yescharacteristic
45C4×D61—22no—
46C4×D61—22no—
47C4×D61—41no—
48C4×D61—41no—
49#92420—42no—
50C8×C61—41no—
51#92418—41no—
52C22×C61—21no—
53C22×C61—21no—
54C22×C61—21no—
55C22×C61#9511yescharacteristic
56C2×D61—21no—
57C2×D61—21no—
58C2×D61—21no—
59C2×D61—21no—
60C2×D61—21no—
61C2×D61—44no—
62C2×D61#9912yes—
63#6923—82no—
64C4×C61—21no—
65C4×C61—21no—
66Dic61—21no—
67Dic61—21no—
68#1306—611nomaximal, Sylow
69C2×C61—41no—
70C2×C61#34211yescharacteristic
71C2×C61#34411yescharacteristic
72C2×C61#34411yescharacteristic
73D61—22no—
74D61—41no—
75#407—611no—
76#407—611no—
77#381—611no—
78C61#130611yescharacteristic, complemented, Sylow
79C23×C4—611no—
80C2×M16—1221no—
81C2×M16—1221no—
82C2×C22⋊C4—612no—
83C22⋊C8—612no—
84C22⋊C8—611no—
85C22⋊C8—1221no—
86C22⋊C8—1221no—
87C22⋊C8#692311yescharacteristic, complemented
88#95—1221no—
89#95—1221no—
90C24—611no—
91C22×C4—611no—
92C22×C4—611no—
93C22×C4—611no—
94C22×C4—611no—
95C22×C4—611no—
96C22×C4—1222no—
97C22×C4—2442no—
98C22×C4C2×#692311yescharacteristic
99M16—2442no—
100M16—2442no—
101C2×C8—21no—
102C2×C8—1222no—
103C2×C8—1221no—
104C22⋊C4—2442no—
105C23—611no—
106C23—611no—
107C23—1222no—
108C23—2441no—
109C23—2441no—
110C23C4×#692311yescharacteristic
111C2×C4—41no—
112C2×C4—611no—
113C2×C4—611no—
114C2×C4—1222no—
115C2×C4—1222no—
116C2×C4—2441no—
117C2×C4—2441no—
118C2×C4—2441no—
119C2×C4—2442no—
120C2×C4—2442no—
121C2×C4—2442no—
122C2×C4C4⋊#692311yescharacteristic
123C2×C4C22⋊#692311yescharacteristic
124C8—41no—
125C8—2441no—
126C8—2442no—
127C22—21no—
128C22—21no—
129C22—21no—
130C22—612no—
131C22—1221no—
132C22—1221no—
133C22—1221no—
134C22—1221no—
135C22—1221no—
136C22—2444no—
137C22(C2×#6923)⋊C411yescharacteristic
138C4—21no—
139C4—21no—
140C4—1221no—
141C4—1221no—
142C4—4882no—
143C2—41no—
144C2—1222no—
145C2—2441no—
146C2#1684063911yescharacteristic
147C2#1684064411yescharacteristic
148C2#1684064511yescharacteristic
subgroupG/H
centerC22(C2×#6923)⋊C4
commutatorC23×C61C42
FrattiniC22×C4C2×#6923
FittingC22⋊C8×C61C4
socleC22×C61#95
hypercenterC22⋊C8#6923
hypocenterC61#1306
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
7. C22⋊#92420C4semidirect
12. C22⋊#92418C4semidirect
14. C22⋊C8×C61C4semidirect
78. C61#1306semidirect
87. C22⋊C8#6923semidirect