Finite Group Databasebeta

← C4×#14519835 #21461563

Subgroups — C4×#14519835 #21461563

Order 7808.

412 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C2×#14519835C212yesmaximal
2C4×C22⋊#6923C212yesmaximal, complemented
3#16840640C212yesmaximal, complemented
4C2×C4×C22⋊D61C211yesmaximal, characteristic
5C2×C22⋊#6923C2214yes—
6C2×C4×#6923—22no—
7#14519835C418yesdirect product factor
8(C2×#6923)⋊C4—22no—
9C22×C22⋊D61C2211yescharacteristic
10C22×C4×D61C2211yescharacteristic
11C4×C22⋊D61—22no—
12C4×C22⋊D61—22no—
13C2×#11758196C411yescharacteristic, complemented
14C2×C22⋊Dic61C411yescharacteristic, complemented
15C2×#11758198C2211yescharacteristic
16C2×C4×Dic61C411yescharacteristic, complemented
17C23×C4×C61C411yescharacteristic, complemented
18C24×C61C2×C411yescharacteristic
19C23×D61C2311yescharacteristic
20C22×#6923—24no—
21C22×C4×C61—21no—
22C22×C4×C61—21no—
23C22×C4×C61—42no—
24C22×C4×C61C2×C411yescharacteristic
25C22×C4×C61C2×C411yescharacteristic
26C2×C22⋊D61—22no—
27C2×C22⋊D61—22no—
28C2×C22⋊D61C2×C414yes—
29C22×Dic61C2×C411yescharacteristic
30C22×Dic61C2×C411yescharacteristic
31C22×Dic61C2×C411yescharacteristic
32C2×C4×D61—42no—
33C2×C4×D61D412yes—
34C2×C4×D61D412yes—
35C22⋊#6923—24no—
36C22⋊#6923C2×C418yescomplemented
37C4×#6923—44no—
38C22⋊Dic61—22no—
39#11758198—22no—
40#11758196—22no—
41C4×Dic61—21no—
42C4×Dic61—21no—
43C23×C61—21no—
44C23×C61—21no—
45C23×C61—41no—
46C23×C61—41no—
47C23×C61C4212yescomplemented
48C23×C61C22×C411yescharacteristic
49C22×D61—41no—
50C22×D61—41no—
51C22×D61C22×C412yes—
52C22×D61C2×D412yes—
53C22×D61#4112yes—
54C2×#6923—28no—
55C2×#6923—44no—
56C2×#6923—44no—
57C2×C4×C61—22no—
58C2×C4×C61—21no—
59C2×C4×C61—42no—
60C2×C4×C61—42no—
61C2×C4×C61—41no—
62C2×C4×C61C22⋊C411yescharacteristic
63C2×C4×C61C22⋊C411yescharacteristic
64C22⋊D61—28no—
65C2×Dic61—21no—
66C2×Dic61—21no—
67C2×Dic61—21no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61C4212yescomplemented
71C2×Dic61C22⋊C412yes—
72C4×D61—24no—
73C4×D61—42no—
74C22×C61—21no—
75C22×C61—21no—
76C22×C61—22no—
77C22×C61—42no—
78C22×C61—42no—
79C22×C61—41no—
80C22×C61—41no—
81C22×C61C2×C4211yescharacteristic
82C22×C61C2×C22⋊C411yescharacteristic
83C22×C61#11711yescharacteristic
84C2×D61—22no—
85C2×D61—22no—
86C2×D61—42no—
87C2×D61—42no—
88C2×D61C4×D414yes—
89#6923—48no—
90C4×C61—21no—
91C4×C61—41no—
92C4×C61#9912yescomplemented
93Dic61—22no—
94Dic61—22no—
95Dic61—41no—
96C4×#99—611nomaximal, Sylow
97C2×C61—21no—
98C2×C61—21no—
99C2×C61—42no—
100C2×C61C4×C22⋊C411yescharacteristic
101C2×C61C2×#9911yescharacteristic
102C2×C61#41011yescharacteristic
103D61—24no—
104C2×C4×D4—611no—
105C2×#99—612no—
106C4×C22⋊C4—612no—
107#342—612no—
108C61C4×#9911yescharacteristic, complemented, Sylow
109C22×D4—611no—
110C23×C4—611no—
111C23×C4#692311yescharacteristic, complemented
112C4×D4—1222no—
113C4×D4—1222no—
114C2×C4⋊C4—611no—
115C2×C22⋊C4—614no—
116C2×C22⋊C4—611no—
117C2×C22⋊C4—611no—
118C2×C42—611no—
119C2×C42—1222no—
120#99—618no—
121#95—1222no—
122C24—611no—
123C24C2×#692311yescharacteristic
124C2×D4—614no—
125C2×D4—1222no—
126C2×D4—1222no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—42no—
130C22×C4—611no—
131C22×C4—611no—
132C22×C4—612no—
133C22×C4—612no—
134C22×C4—611no—
135C22×C4—1224no—
136C22×C4—2442no—
137C22×C4C2×#692311yescharacteristic
138C22×C4C2×#692311yescharacteristic
139C4⋊C4—1222no—
140C22⋊C4—618no—
141C22⋊C4—1222no—
142C22⋊C4—1222no—
143C22⋊C4—1224no—
144C42—1221no—
145C42—1221no—
146C42—2444no—
147C23—21no—
148C23—21no—
149C23—41no—
150C23—41no—
151C23—612no—
152C23—612no—
153C23—612no—
154C23—2441no—
155C23—2441no—
156C23C4×#692312yescomplemented
157C23C22×#692311yescharacteristic
158D4—1228no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—41no—
164C2×C4—612no—
165C2×C4—612no—
166C2×C4—1221no—
167C2×C4—1221no—
168C2×C4—1224no—
169C2×C4—1228no—
170C2×C4—1221no—
171C2×C4—2442no—
172C2×C4—2441no—
173C2×C4—2444no—
174C2×C4—2444no—
175C2×C4—2441no—
176C2×C4C22⋊#692311yescharacteristic
177C2×C4C22⋊#692311yescharacteristic
178C22—21no—
179C22—21no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—41no—
184C22—41no—
185C22—614no—
186C22—1222no—
187C22—1222no—
188C22—2442no—
189C22—2442no—
190C22C2×C4×#692311yescharacteristic
191C22C2×C22⋊#692311yescharacteristic
192C22#1451985611yescharacteristic
193C4—21no—
194C4—41no—
195C4—1222no—
196C4—1222no—
197C4—2448no—
198C4—2441no—
199C4#1451983512yesdirect product factor
200C2—21no—
201C2—21no—
202C2—42no—
203C2—1224no—
204C2C4×C22⋊#692311yescharacteristic
205C2C2×#1451983511yescharacteristic
206C2#1684074111yescharacteristic
subgroupG/H
centerC2×C4C22⋊#6923
commutatorC22×C61C2×C42
FrattiniC23C22×#6923
FittingC23×C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC23×C4#6923
hypocenterC61C4×#99
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊#6923C2semidirect
3. #16840640C2semidirect
7. #14519835C4direct (N × H)
13. C2×#11758196C4semidirect
14. C2×C22⋊Dic61C4semidirect
16. C2×C4×Dic61C4semidirect
17. C23×C4×C61C4semidirect
36. C22⋊#6923C2×C4semidirect
47. C23×C61C42semidirect
70. C2×Dic61C42semidirect
92. C4×C61#99semidirect
108. C61C4×#99semidirect
111. C23×C4#6923semidirect
156. C23C4×#6923semidirect
199. C4#14519835direct (N × H)