Finite Group Databasebeta

← #21461066

Subgroups — #21461066

Order 7808.

440 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 70 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#16840732C212yesmaximal, complemented
2#16840606C214yesmaximal, complemented
3C22×#11758198C211yesmaximal, characteristic
4C2×#11758217—22no—
5C22⋊#92420—22no—
6C22⋊#92420C2214yescomplemented
7C24×D61C411yescharacteristic
8C23×Dic61C2211yescharacteristic
9C2×#11758198—22no—
10C2×#11758198—22no—
11C2×#11758198C412yes—
12C2×#11758198C2212yes—
13C23×C4×C61C411yescharacteristic
14C24×C61C2×C411yescharacteristic
15C23×D61—21no—
16C23×D61—21no—
17C23×D61—24no—
18C23×D61—42no—
19C23×D61—42no—
20C23×D61C2×C412yes—
21C22×C4×C61—21no—
22C22×C4×C61—21no—
23C22×C4×C61—42no—
24C22×C4×C61C2×C412yes—
25C22×Dic61—42no—
26C22×Dic61C2×C411yescharacteristic
27C22×Dic61D412yes—
28C22×Dic61D412yes—
29C22×Dic61C2311yescharacteristic
30#11758217—44no—
31C2×#92420—24no—
32#11758198—24no—
33#11758198—24no—
34C23×C61—22no—
35C23×C61—22no—
36C23×C61—22no—
37C23×C61C22⋊C411yescharacteristic
38C23×C61C22⋊C411yescharacteristic
39C23×C61C22×C411yescharacteristic
40C22×D61—24no—
41C22×D61—24no—
42C22×D61—22no—
43C22×D61—22no—
44C22×D61—416no—
45C22×D61—42no—
46C22×D61—42no—
47C22×D61—42no—
48C22×D61—42no—
49C22×D61—42no—
50C22×D61—42no—
51C22×D61M1614yescomplemented
52C2×C4×C61—22no—
53C2×C4×C61—42no—
54C2×C4×C61—42no—
55C2×C4×C61—42no—
56C2×Dic61—24no—
57C2×Dic61—41no—
58C2×Dic61—42no—
59C2×Dic61—41no—
60C2×Dic61C22⋊C412yes—
61C2×Dic61C2×D412yes—
62#92420—44no—
63C22×C61—28no—
64C22×C61—21no—
65C22×C61—21no—
66C22×C61—21no—
67C22×C61—21no—
68C22×C61—21no—
69C22×C61—21no—
70C22×C61#9912yes—
71C22×C61#10012yes—
72C22×C61C2×C22⋊C411yescharacteristic
73C22×C61C2×M1612yes—
74C2×D61—24no—
75C2×D61—48no—
76C2×D61—48no—
77C2×D61—44no—
78C2×D61—42no—
79C2×D61—42no—
80C2×D61—44no—
81C4×C61—42no—
82Dic61—22no—
83Dic61—22no—
84#1462—611nomaximal, Sylow
85C2×C61—22no—
86C2×C61—22no—
87C2×C61—22no—
88C2×C61#40711yescharacteristic
89C2×C61C2×#9911yescharacteristic
90C2×C61C2×#10011yescharacteristic
91D61—44no—
92C22×C22⋊C4—611no—
93#407—612no—
94#323—614no—
95C61#146211yescharacteristic, complemented, Sylow
96C25—611no—
97C23×C4—611no—
98C23×C4#692311yescharacteristic
99C2×M16—1222no—
100C2×C22⋊C4—612no—
101C2×C22⋊C4—612no—
102C2×C22⋊C4—1222no—
103C2×C22⋊C4—1222no—
104C22⋊C8—614no—
105C22⋊C8—1222no—
106C24—612no—
107C24—1224no—
108C24—1221no—
109C24—1221no—
110C24—2442no—
111C24—2442no—
112C24C2×#692311yescharacteristic
113C22×C4—21no—
114C22×C4—21no—
115C22×C4—42no—
116C22×C4—612no—
117C22×C4—612no—
118C22×C4—611no—
119C22×C4—611no—
120C22×C4—2442no—
121C22×C4C2×#692312yes—
122M16—2444no—
123C2×C8—1224no—
124C22⋊C4—1224no—
125C22⋊C4—1224no—
126C23—22no—
127C23—22no—
128C23—22no—
129C23—614no—
130C23—1224no—
131C23—1224no—
132C23—1222no—
133C23—1222no—
134C23—2442no—
135C23—2442no—
136C23—24416no—
137C23—2442no—
138C23—2442no—
139C23—2442no—
140C23—2442no—
141C23C22⋊#692311yescharacteristic
142C23C22⋊#692311yescharacteristic
143C23C22×#692311yescharacteristic
144C2×C4—22no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4—612no—
149C2×C4—612no—
150C2×C4—1224no—
151C2×C4—2441no—
152C2×C4—2442no—
153C2×C4—2441no—
154C8—2444no—
155C22—28no—
156C22—21no—
157C22—21no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—1224no—
163C22—2444no—
164C22—2448no—
165C22—2448no—
166C22—2444no—
167C22—2442no—
168C22—2442no—
169C22#1451983612yes—
170C22#1451983712yes—
171C22C2×C22⋊#692311yescharacteristic
172C22D61⋊M1612yes—
173C4—42no—
174C4—1222no—
175C4—1222no—
176C2—22no—
177C2—22no—
178C2—22no—
179C2—2444no—
180C2#1684073411yescharacteristic
181C2C2×#1451983611yescharacteristic
182C2C2×#1451983711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC23×C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC23×C4#6923
hypocenterC61#1462
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. #16840732C2semidirect
2. #16840606C2semidirect
6. C22⋊#92420C22semidirect
51. C22×D61M16semidirect
95. C61#1462semidirect