Finite Group Databasebeta

← #21460721

Subgroups — #21460721

Order 7808.

200 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 44 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#16840734C211yesmaximal, characteristic
2#16840704C211yesmaximal, characteristic
3#16839724C211yesmaximal, characteristic
4C2×#11758217C412yescomplemented
5C2×C4⋊#6923—21no—
6C2×C22⋊#6923C412yes—
7#14519834—21no—
8#14519834—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—
25#11758217—42no—
26C2×#92420—22no—
27C4⋊#6923—42no—
28C2×C8×C61—21no—
29C2×#92418—21no—
30#11758189—42no—
31C23×C61C4211yescharacteristic
32C22×D61—21no—
33C22×D61—21no—
34C22×D61—41no—
35C22×D61—41no—
36C22×D61C22⋊C411yescharacteristic
37C22×D61C4⋊C411yescharacteristic
38C2×#6923—42no—
39C2×#6923—42no—
40C2×#6923—42no—
41C2×C4×C61—41no—
42C2×C4×C61C22⋊C411yescharacteristic
43C2×C4×C61C4⋊C411yescharacteristic
44C2×Dic61—22no—
45C2×Dic61C22⋊C411yescharacteristic
46C2×Dic61C4⋊C411yescharacteristic
47C4×D61—22no—
48C4×D61—22no—
49C4×D61—41no—
50C4×D61—41no—
51#92420—42no—
52C8×C61—41no—
53#92418—41no—
54C22×C61—21no—
55C22×C61—21no—
56C22×C61—21no—
57C22×C61#9511yescharacteristic
58C2×D61—21no—
59C2×D61—21no—
60C2×D61—21no—
61C2×D61—21no—
62C2×D61—21no—
63C2×D61—42no—
64C2×D61—42no—
65C2×D61#10011yescharacteristic
66C2×D61#10111yescharacteristic
67#6923—82no—
68C4×C61—21no—
69C4×C61—21no—
70Dic61—21no—
71Dic61#9912yes—
72#1305—611nomaximal, Sylow
73C2×C61—41no—
74C2×C61#34211yescharacteristic
75C2×C61#34311yescharacteristic
76C2×C61#34411yescharacteristic
77D61—21no—
78D61—21no—
79D61—41no—
80#407—611no—
81#407—611no—
82#380—611no—
83C61#130511yescharacteristic, complemented, Sylow
84C23×C4—611no—
85C2×M16—612no—
86C2×M16—1221no—
87C2×C4⋊C4—1221no—
88C2×C22⋊C4—612no—
89C22⋊C8—611no—
90C22⋊C8—1221no—
91C22⋊C8—1221no—
92C22⋊C8—1221no—
93C22⋊C8#692311yescharacteristic, complemented
94#95—1221no—
95C24—611no—
96C22×C4—611no—
97C22×C4—611no—
98C22×C4—611no—
99C22×C4—611no—
100C22×C4—611no—
101C22×C4—1222no—
102C22×C4—2442no—
103C22×C4C2×#692311yescharacteristic
104M16—2442no—
105M16—2442no—
106C2×C8—21no—
107C2×C8—1222no—
108C2×C8—1221no—
109C4⋊C4—2442no—
110C22⋊C4—2442no—
111C23—611no—
112C23—611no—
113C23—1221no—
114C23—1221no—
115C23—2441no—
116C23—2441no—
117C23C4×#692311yescharacteristic
118C2×C4—41no—
119C2×C4—611no—
120C2×C4—611no—
121C2×C4—1222no—
122C2×C4—1222no—
123C2×C4—1222no—
124C2×C4—2441no—
125C2×C4—2441no—
126C2×C4—2442no—
127C2×C4—2442no—
128C2×C4—2442no—
129C2×C4C4⋊#692311yescharacteristic
130C2×C4C22⋊#692311yescharacteristic
131C8—41no—
132C8—2441no—
133C8—2442no—
134C22—21no—
135C22—21no—
136C22—21no—
137C22—611no—
138C22—611no—
139C22—1221no—
140C22—1221no—
141C22—1221no—
142C22—1221no—
143C22—1221no—
144C22—2442no—
145C22—2442no—
146C22(C2×#6923)⋊C411yescharacteristic
147C4—21no—
148C4—21no—
149C4—612no—
150C4—1221no—
151C4—4882no—
152C2—41no—
153C2—1221no—
154C2—1221no—
155C2—2441no—
156C2#1684063911yescharacteristic
157C2#1684064111yescharacteristic
158C2#1684064411yescharacteristic
subgroupG/H
centerC22(C2×#6923)⋊C4
commutatorC23×C61C42
FrattiniC22×C4C2×#6923
FittingC22⋊C8×C61C4
socleC22×C61#95
hypercenterC22⋊C8#6923
hypocenterC61#1305
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
4. C2×#11758217C4semidirect
12. C22⋊#92418C4semidirect
14. C22⋊C8×C61C4semidirect
83. C61#1305semidirect
93. C22⋊C8#6923semidirect