Finite Group Databasebeta

← C2×#15689086 #20251823

Subgroups — C2×#15689086 #20251823

Order 6016.

1008 conjugacy classes of subgroups; only the 285 normal subgroups are shown.

normal subgroups only

This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 285 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
1C23×C4×D47C211yesmaximal, characteristic
2C22×#10625329C211yesmaximal, characteristic, complemented
3#15689086C218yesmaximal, direct product factor
4C2×(C2×D47)⋊C8C214yesmaximal, complemented
5C22×M16×C47C211yesmaximal, characteristic, complemented
6C24×D47C411yescharacteristic
7C23×Dic47C411yescharacteristic
8C22×C4×D47—24no—
9C22×C4×D47—24no—
10C22×C4×D47C414yes—
11C22×C4×D47C412yes—
12C22×C4×D47C2212yes—
13C22×C4×D47C2214yes—
14C2×#10625329—24no—
15C2×#10625329C2214yescomplemented
16C22×C47⋊C8C2212yescomplemented
17(C2×D47)⋊C8C22116yescomplemented
18C23×C4×C47C2211yescharacteristic
19C2×M16×C47—24no—
20C2×M16×C47C2214yescomplemented
21C22×C8×C47C2212yescomplemented
22C24×C47C2×C411yescharacteristic
23C23×D47—24no—
24C23×D47—28no—
25C23×D47C2×C414yes—
26C23×D47C2×C412yes—
27C22×C4×C47C2×C412yes—
28C22×C4×C47C2×C411yescharacteristic
29C22×C4×C47D414yes—
30C22×C4×C47D414yes—
31C22×C4×C47C2312yes—
32C22×C4×C47C2311yescharacteristic
33C22×Dic47—24no—
34C22×Dic47C2×C414yes—
35C22×Dic47C2×C412yes—
36C2×C4×D47—216no—
37C2×C4×D47—28no—
38C2×C4×D47—24no—
39C2×C4×D47—28no—
40C2×C4×D47—24no—
41C2×C4×D47—28no—
42C2×C4×D47C2×C414yes—
43C2×C4×D47C2×C418yes—
44C2×C4×D47C2314yes—
45M16×C47—28no—
46C2×C8×C47—24no—
47C2×C8×C47C2314yescomplemented
48#10625329—28no—
49C2×C47⋊C8—24no—
50C2×C47⋊C8C2314yescomplemented
51C23×C47—24no—
52C23×C47C22⋊C414yes—
53C23×C47C22×C412yes—
54C23×C47C22×C411yescharacteristic
55C22×D47—232no—
56C22×D47—28no—
57C22×D47—24no—
58C22×D47—24no—
59C22×D47—216no—
60C22×D47M1618yescomplemented
61C22×D47C22×C414yes—
62C2×C4×C47C22⋊C418yes—
63C2×C4×C47C22⋊C414yes—
64C2×C4×C47C22×C412yes—
65C2×C4×C47C22×C411yescharacteristic
66C2×C4×C47C2×D412yes—
67C2×C4×C47C2×D414yes—
68C2×C4×C47C2×D412yes—
69C2×C4×C47C2×D414yes—
70C2×C4×C47C2411yescharacteristic
71C2×Dic47—28no—
72C2×Dic47—24no—
73C2×Dic47C22×C414yes—
74C4×D47—28no—
75C4×D47—216no—
76C4×D47—24no—
77C4×D47—24no—
78C8×C47—24no—
79C47⋊C8—24no—
80C22×C47—24no—
81C22×C47—28no—
82C22×C47C2×C22⋊C414yes—
83C22×C47C2×C22⋊C412yes—
84C22×C47C2×M1614yes—
85C22×C47C23×C411yescharacteristic
86C2×D47—232no—
87C2×D47—24no—
88C2×D47—24no—
89C2×D47—216no—
90C2×D47C2×M1618yescomplemented
91C4×C47C2×C22⋊C412yes—
92C4×C47C2×C22⋊C414yes—
93C4×C47C22×D411yescharacteristic
94C4×C47C22×D411yescharacteristic
95Dic47—24no—
96C2×#407—471nomaximal, Sylow
97C2×C47—24no—
98C2×C47#40714yescomplemented
99C2×C47C22×C22⋊C411yescharacteristic
100C2×C47C22×M1612yes—
101D47—28no—
102C24×C4—471no—
103C22×M16—471no—
104C22×M16D4711yescharacteristic, complemented
105#407—478no—
106C2×C22⋊C8—474no—
107C47C2×#40711yescharacteristic, complemented, Sylow
108C25—471no—
109C23×C4—471no—
110C23×C4—472no—
111C23×C4—474no—
112C23×C4—474no—
113C23×C4—472no—
114C23×C4—944no—
115C23×C4—944no—
116C23×C4C2×D4711yescharacteristic
117C2×M16—24no—
118C2×M16—474no—
119C2×M16—944no—
120C2×M16C2×D4714yescomplemented
121C22×C8—472no—
122C22×C8C2×D4712yescomplemented
123C22⋊C8—4716no—
124C24—472no—
125C24—474no—
126C24—948no—
127C24—944no—
128C24C4×D4711yescharacteristic
129C22×C4—474no—
130C22×C4—472no—
131C22×C4—478no—
132C22×C4—474no—
133C22×C4—474no—
134C22×C4—944no—
135C22×C4—9416no—
136C22×C4—948no—
137C22×C4—944no—
138C22×C4—948no—
139C22×C4—944no—
140C22×C4—948no—
141C22×C4C4×D4711yescharacteristic
142C22×C4C4×D4712yes—
143C22×C4D18814yes—
144C22×C4C22⋊D4714yes—
145C22×C4C22×D4712yes—
146C22×C4C22×D4711yescharacteristic
147M16—28no—
148M16—948no—
149C2×C8—24no—
150C2×C8—474no—
151C2×C8—944no—
152C2×C8C22×D4714yescomplemented
153C23—24no—
154C23—478no—
155C23—474no—
156C23—9416no—
157C23—9432no—
158C23—948no—
159C23—944no—
160C23—944no—
161C23(C2×D47)⋊C414yes—
162C23C2×C4×D4712yes—
163C23C2×C4×D4711yescharacteristic
164C2×C4—474no—
165C2×C4—948no—
166C2×C4—944no—
167C2×C4—9416no—
168C2×C4—948no—
169C2×C4—944no—
170C2×C4—944no—
171C2×C4(C2×D47)⋊C418yes—
172C2×C4(C2×D47)⋊C414yes—
173C2×C4C2×C4×D4712yes—
174C2×C4C2×C4×D4711yescharacteristic
175C2×C4C2×D18812yes—
176C2×C4C2×D18814yes—
177C2×C4C2×C22⋊D4712yes—
178C2×C4C2×C22⋊D4714yes—
179C2×C4C23×D4711yescharacteristic
180C8—24no—
181C8—944no—
182C22—28no—
183C22—24no—
184C22—478no—
185C22—9432no—
186C22—944no—
187C22—9416no—
188C22—944no—
189C22C2×(C2×D47)⋊C414yes—
190C22C2×(C2×D47)⋊C412yes—
191C22M16×D4714yes—
192C22C22×C4×D4711yescharacteristic
193C4—944no—
194C4C2×(C2×D47)⋊C414yes—
195C4C2×(C2×D47)⋊C412yes—
196C4C22×C22⋊D4711yescharacteristic
197C4C22×D18811yescharacteristic
198C2—24no—
199C2—948no—
200C2#1568908614yesdirect product factor
201C2C22×(C2×D47)⋊C411yescharacteristic
202C2C2×M16×D4712yes—
subgroupG/H
centerC22×C4C22×D47
commutatorC22×C47C23×C4
FrattiniC2×C4C23×D47
FittingC22×M16×C47C2
socleC23×C47C22×C4
hypercenterC22×M16D47
hypocenterC47C2×#407
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. C22×#10625329C2semidirect
3. #15689086C2direct (N × H)
4. C2×(C2×D47)⋊C8C2semidirect
5. C22×M16×C47C2semidirect
15. C2×#10625329C22semidirect
16. C22×C47⋊C8C22semidirect
17. (C2×D47)⋊C8C22semidirect
20. C2×M16×C47C22semidirect
21. C22×C8×C47C22semidirect
47. C2×C8×C47C23semidirect
50. C2×C47⋊C8C23semidirect
60. C22×D47M16semidirect
90. C2×D47C2×M16semidirect
98. C2×C47#407semidirect
104. C22×M16D47semidirect
107. C47C2×#407semidirect
120. C2×M16C2×D47semidirect
122. C22×C8C2×D47semidirect
152. C2×C8C22×D47semidirect
200. C2#15689086direct (N × H)