Finite Group Databasebeta

← C2×#16810559 #20277963

Subgroups — C2×#16810559 #20277963

Order 6784.

908 conjugacy classes of subgroups; only the 261 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 261 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
1C22×C4⋊Dic53C211yesmaximal, characteristic, complemented
2C22×#11719919C212yesmaximal, complemented
3C22×C22⋊Dic53C212yesmaximal
4#16810559C218yesmaximal, direct product factor
5C2×#13133124C211yesmaximal, characteristic, complemented
6C22×C22⋊C4×C53C211yesmaximal, characteristic
7C23×Dic53C2212yes—
8C23×Dic53C2212yes—
9C2×C4⋊Dic53—24no—
10C2×C4⋊Dic53C2214yescomplemented
11C2×#11719919—28no—
12C2×#11719919C2218yescomplemented
13C2×C22⋊Dic53—28no—
14C2×C22⋊Dic53C2218yes—
15#13133124C2214yescomplemented
16C25×C53C2211yescharacteristic
17C23×C4×C53C2211yescharacteristic
18C23×C4×C53C2211yescharacteristic
19C2×C22⋊C4×C53—24no—
20C2×C22⋊C4×C53C2214yes—
21C24×C53—22no—
22C24×C53—24no—
23C24×C53—22no—
24C24×C53—24no—
25C24×C53Q814yes—
26C24×C53C2312yes—
27C24×C53C2311yescharacteristic
28C22×C4×C53—24no—
29C22×C4×C53—22no—
30C22×C4×C53—24no—
31C22×C4×C53D414yes—
32C22×C4×C53C2312yes—
33C22×C4×C53C2312yes—
34C22×Dic53—24no—
35C22×Dic53—24no—
36C22×Dic53—24no—
37C22×Dic53—24no—
38C22×Dic53—24no—
39C22×Dic53D418yes—
40C22×Dic53C2314yes—
41C22×Dic53C2314yes—
42C22⋊C4×C53—28no—
43C22⋊Dic53—216no—
44C4⋊Dic53—28no—
45#11719919—216no—
46C23×C53—216no—
47C23×C53—28no—
48C23×C53—24no—
49C23×C53—22no—
50C23×C53—24no—
51C23×C53—22no—
52C23×C53—44no—
53C23×C53—48no—
54C23×C53—44no—
55C23×C53C2×D414yes—
56C23×C53C2×D412yes—
57C23×C53C2×Q814yes—
58C23×C53C2×Q812yes—
59C23×C53#4112yes—
60C23×C53#4114yes—
61C23×C53C2411yescharacteristic
62C2×C4×C53—28no—
63C2×C4×C53—24no—
64C2×C4×C53—24no—
65C2×C4×C53—22no—
66C2×C4×C53—44no—
67C2×C4×C53C2×D414yes—
68C2×Dic53—216no—
69C2×Dic53—24no—
70C2×Dic53—24no—
71C2×Dic53—24no—
72C2×Dic53—24no—
73C2×Dic53—24no—
74C2×Dic53—48no—
75C2×Dic53C2×D418yes—
76C22×C53—28no—
77C22×C53—24no—
78C22×C53—42no—
79C22×C53—44no—
80C22×C53—42no—
81C22×C53—416no—
82C22×C53C22⋊Q818yes—
83C22×C53C22⋊Q814yes—
84C22×C53#12314yes—
85C22×C53#12318yes—
86C22×C53#12714yes—
87C22×C53C22×D412yes—
88C22×C53C22×D411yescharacteristic
89C22×C53C22×Q811yescharacteristic
90C22×C53C2×#4112yes—
91C22×C53C2×#4111yescharacteristic
92C4×C53—24no—
93C4×C53—42no—
94Dic53—28no—
95Dic53—44no—
96C2×#399—531nomaximal, Sylow
97C2×C53—44no—
98C2×C53#39918yescomplemented
99C2×C53C2×C22⋊Q812yes—
100C2×C53C2×C22⋊Q811yescharacteristic
101C2×C53C2×#12311yescharacteristic
102C2×C53C2×#12312yes—
103C2×C53C2×#12711yescharacteristic
104C22×C4⋊C4—532no—
105C22×C4⋊C4—531no—
106C22×C22⋊C4—532no—
107C22×C22⋊C4D5311yescharacteristic
108#399—538no—
109C2×#95—531no—
110C53C2×#39911yescharacteristic, complemented, Sylow
111C25C2×D5311yescharacteristic
112C23×C4—532no—
113C23×C4—532no—
114C23×C4C2×D5311yescharacteristic
115C23×C4C2×D5311yescharacteristic
116C2×C4⋊C4—538no—
117C2×C4⋊C4—534no—
118C2×C4⋊C4—1068no—
119C2×C4⋊C4—1064no—
120C2×C22⋊C4—24no—
121C2×C22⋊C4—538no—
122C2×C22⋊C4—1068no—
123C2×C22⋊C4C2×D5314yes—
124#95—534no—
125C24—22no—
126C24—24no—
127C24—24no—
128C24—22no—
129C24Dic10614yes—
130C24C22×D5312yes—
131C24C22×D5311yescharacteristic
132C22×C4—24no—
133C22×C4—24no—
134C22×C4—22no—
135C22×C4—538no—
136C22×C4—534no—
137C22×C4—534no—
138C22×C4—1064no—
139C22×C4—1064no—
140C22×C4—1064no—
141C22×C4—1064no—
142C22×C4—1064no—
143C22×C4C22⋊D5314yes—
144C22×C4C22×D5312yes—
145C22×C4C22×D5312yes—
146C4⋊C4—10616no—
147C4⋊C4—1068no—
148C22⋊C4—28no—
149C22⋊C4—10616no—
150C23—216no—
151C23—28no—
152C23—24no—
153C23—22no—
154C23—24no—
155C23—22no—
156C23—44no—
157C23—48no—
158C23—44no—
159C23C2×Dic10614yes—
160C23C2×Dic10612yes—
161C23#1171994512yes—
162C23D4×D5314yes—
163C23#1171994714yes—
164C23C2×C22⋊D5312yes—
165C23C23×D5311yescharacteristic
166C2×C4—28no—
167C2×C4—24no—
168C2×C4—24no—
169C2×C4—22no—
170C2×C4—44no—
171C2×C4—538no—
172C2×C4—10616no—
173C2×C4—1064no—
174C2×C4—1064no—
175C2×C4—1064no—
176C2×C4—1064no—
177C2×C4—1064no—
178C2×C4—2128no—
179C2×C4C2×C22⋊D5314yes—
180C22—28no—
181C22—24no—
182C22—416no—
183C22—42no—
184C22—44no—
185C22—42no—
186C22#1313319418yes—
187C22#1313319614yes—
188C22#1313319814yes—
189C22#1313319918yes—
190C22#1313321314yes—
191C22C2×D4×D5312yes—
192C22C22×C22⋊D5311yescharacteristic
193C22C22×Dic10611yescharacteristic
194C22C2×#1171994712yes—
195C22C2×#1171994511yescharacteristic
196C4—24no—
197C4—42no—
198C4—1068no—
199C4—2124no—
200C2—44no—
201C2#1681055918yesdirect product factor
202C2C2×#1313319412yes—
203C2C2×#1313319611yescharacteristic
204C2C2×#1313319811yescharacteristic
205C2C2×#1313319912yes—
206C2C2×#1313321311yescharacteristic
subgroupG/H
centerC24C22×D53
commutatorC23×C53C24
FrattiniC23C23×D53
FittingC22×C22⋊C4×C53C2
socleC24×C53C23
hypercenterC22×C22⋊C4D53
hypocenterC53C2×#399
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊Dic53C2semidirect
2. C22×#11719919C2semidirect
4. #16810559C2direct (N × H)
5. C2×#13133124C2semidirect
10. C2×C4⋊Dic53C22semidirect
12. C2×#11719919C22semidirect
15. #13133124C22semidirect
98. C2×C53#399semidirect
110. C53C2×#399semidirect
201. C2#16810559direct (N × H)