Finite Group Databasebeta

← #21460667

Subgroups — #21460667

Order 7808.

226 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 46 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#16840705C211yesmaximal, characteristic
3C4×#11758198C211yesmaximal, characteristic
4C2×#11758217—21no—
5C2×C22⋊#6923—21no—
6#14519834—21no—
7#14519834C412yescomplemented
8(C2×#6923)⋊C4—21no—
9(C2×#6923)⋊C4C412yescomplemented
10C22×C4×D61C2211yescharacteristic
11C2×#11758198—21no—
12C2×C4×Dic61C411yescharacteristic, complemented
13#14519684—21no—
14C2×C42×C61C411yescharacteristic, complemented
15C23×D61D411yescharacteristic
16C22×#6923—22no—
17C22×C4×C61—21no—
18C22×C4×C61C2×C411yescharacteristic
19C22×Dic61—21no—
20C22×Dic61D411yescharacteristic
21C2×C4×D61—41no—
22C2×C4×D61—41no—
23C2×C4×D61C2×C411yescharacteristic
24C2×C4×D61C2×C411yescharacteristic
25C2×C4×D61D411yescharacteristic
26C2×C4×D61Q811yescharacteristic
27C22⋊#6923—41no—
28C22⋊#6923—41no—
29#11758217—41no—
30#11758217—41no—
31C2×#92420—22no—
32C42×C61—41no—
33#11758198—24no—
34C4×Dic61—41no—
35C23×C61C22⋊C411yescharacteristic
36C22×D61—21no—
37C22×D61—21no—
38C22×D61—22no—
39C22×D61—41no—
40C22×D61C22⋊C411yescharacteristic
41C22×D61C4⋊C411yescharacteristic
42C2×#6923—42no—
43C2×#6923—42no—
44C2×#6923—42no—
45C2×C4×C61—21no—
46C2×C4×C61—21no—
47C2×C4×C61—22no—
48C2×C4×C61—41no—
49C2×C4×C61—41no—
50C2×C4×C61C4211yescharacteristic
51C2×C4×C61C4⋊C411yescharacteristic
52C2×Dic61—21no—
53C2×Dic61—21no—
54C2×Dic61—22no—
55C2×Dic61—41no—
56C2×Dic61—41no—
57C2×Dic61C22⋊C411yescharacteristic
58C2×Dic61C4⋊C411yescharacteristic
59C4×D61—41no—
60C4×D61—41no—
61C4×D61—41no—
62C4×D61—41no—
63#92420—42no—
64C22×C61—21no—
65C22×C61—21no—
66C22×C61#9511yescharacteristic
67C22×C61#9911yescharacteristic
68C22×C61#9911yescharacteristic
69C2×D61—21no—
70C2×D61—21no—
71C2×D61—21no—
72C2×D61—21no—
73C2×D61—21no—
74C2×D61—42no—
75C2×D61—42no—
76C2×D61#10412yes—
77#6923—82no—
78C4×C61—21no—
79C4×C61—21no—
80C4×C61—42no—
81Dic61—21no—
82Dic61—21no—
83Dic61—42no—
84#1284—611nomaximal, Sylow
85C2×C61—21no—
86C2×C61—21no—
87C2×C61H(3,ℤ/4)11yescharacteristic
88C2×C61#33911yescharacteristic
89C2×C61#34211yescharacteristic
90D61—22no—
91D61—41no—
92#407—611no—
93#381—611no—
94C4×C22⋊C4—611no—
95C61#128411yescharacteristic, complemented, Sylow
96C23×C4—611no—
97C2×M16—1221no—
98C2×C22⋊C4—1221no—
99C2×C22⋊C4—1221no—
100C2×C42—611no—
101C2×C42#692311yescharacteristic, complemented
102C22⋊C8—612no—
103C22⋊C8—1221no—
104#95—612no—
105#95—1221no—
106#95—1221no—
107C24—611no—
108C22×C4—21no—
109C22×C4—611no—
110C22×C4—611no—
111C22×C4—611no—
112C22×C4—611no—
113C22×C4—611no—
114C22×C4—1221no—
115C22×C4—1222no—
116C22×C4—2441no—
117C22×C4—2441no—
118C22×C4C2×#692311yescharacteristic
119M16—2441no—
120M16—2441no—
121C2×C8—1222no—
122C22⋊C4—1224no—
123C22⋊C4—2441no—
124C22⋊C4—2441no—
125C42—41no—
126C42—2441no—
127C23—611no—
128C23—611no—
129C23—1222no—
130C23—1221no—
131C23—1221no—
132C23—2441no—
133C23C22⋊#692311yescharacteristic
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—22no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—611no—
140C2×C4—611no—
141C2×C4—1221no—
142C2×C4—1221no—
143C2×C4—1222no—
144C2×C4—2441no—
145C2×C4—2441no—
146C2×C4—2441no—
147C2×C4—2441no—
148C2×C4—2442no—
149C2×C4—2442no—
150C2×C4—2442no—
151C2×C4—2441no—
152C2×C4—2441no—
153C2×C4C4×#692311yescharacteristic
154C2×C4C4⋊#692311yescharacteristic
155C8—2442no—
156C22—21no—
157C22—21no—
158C22—612no—
159C22—1221no—
160C22—1221no—
161C22—1221no—
162C22—1221no—
163C22—1221no—
164C22—2442no—
165C22—2442no—
166C22(C2×#6923)⋊C411yescharacteristic
167C22#1451983511yescharacteristic
168C22#1451983611yescharacteristic
169C4—21no—
170C4—21no—
171C4—42no—
172C4—1221no—
173C4—1221no—
174C4—4882no—
175C4—2442no—
176C2—21no—
177C2—21no—
178C2—1222no—
179C2—2441no—
180C2#1684062911yescharacteristic
181C2#1684063311yescharacteristic
182C2#1684064011yescharacteristic
subgroupG/H
centerC22(C2×#6923)⋊C4
commutatorC2×C4×C61C42
FrattiniC22×C4C2×#6923
FittingC2×C42×C61C4
socleC22×C61#95
hypercenterC2×C42#6923
hypocenterC61#1284
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
7. #14519834C4semidirect
9. (C2×#6923)⋊C4C4semidirect
12. C2×C4×Dic61C4semidirect
14. C2×C42×C61C4semidirect
95. C61#1284semidirect
101. C2×C42#6923semidirect