Finite Group Databasebeta

← C2×#11719403 #13128197

Subgroups — C2×#11719403 #13128197

Order 1664.

1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.

normal subgroups only

This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 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×C13×#125C211yesmaximal, characteristic, complemented
2#11719403C2116yesmaximal, direct product factor
3C2×#88149C214yesmaximal, complemented
4C2×#88149C212yesmaximal, complemented
5C2×#88148C214yesmaximal, complemented
6C2×#88147C212yesmaximal, complemented
7C2×#88128C211yesmaximal, characteristic, complemented
8C2×#88126C211yesmaximal, characteristic, complemented
9C22×D52C2212yes—
10C22×D52C2214yes—
11C22×D52C2214yes—
12C22×C4×D13C2211yescharacteristic
13C22×C4×D13C2214yes—
14C13×#125C2218yescomplemented
15C2×C13×C4⋊C4C2212yes—
16C2×C13×C4⋊C4C2214yes—
17C2×C42×C13C2211yescharacteristic
18C2×#6103C2212yes—
19C2×#6103C2214yes—
20C2×#6103C2214yes—
21C2×#6101C2212yes—
22C2×C4×Dic13C2211yescharacteristic
23#88149C22132yescomplemented
24#88149C22116yescomplemented
25#88148C22132yescomplemented
26#88147C22116yescomplemented
27#88128C2218yescomplemented
28#88126C2218yescomplemented
29C23×D13C2311yescharacteristic
30C23×D13C2314yes—
31C22×C4×C13C2312yes—
32C22×C4×C13C2314yes—
33C22×C4×C13C2311yescharacteristic
34C22×Dic13C2312yes—
35C22×Dic13C2311yescharacteristic
36C2×D52—28no—
37C2×D52—48no—
38C2×D52—48no—
39C2×D52C2318yes—
40C2×D52C23116yes—
41C2×D52C23116yes—
42C2×C4×D13—24no—
43C2×C4×D13—48no—
44C2×C4×D13C2314yes—
45C2×C4×D13C23116yes—
46C13×C4⋊C4C2318yes—
47C13×C4⋊C4C23116yes—
48C42×C13C2314yes—
49#6103C2318yes—
50#6103C23116yes—
51#6103C23116yes—
52#6101C2318yes—
53C4×Dic13C2314yes—
54C2×#540—131nomaximal, Sylow
55C23×C13C2411yescharacteristic
56C22×D13—22no—
57C22×D13—28no—
58C22×D13—28no—
59C22×D13—24no—
60C22×D13—28no—
61C22×D13C2412yes—
62C22×D13C2418yes—
63C2×C4×C13—28no—
64C2×C4×C13—24no—
65C2×C4×C13#4114yes—
66C2×C4×C13C2414yes—
67C2×C4×C13C2418yes—
68C2×C4×C13C2412yes—
69C2×Dic13—22no—
70C2×Dic13—24no—
71C2×Dic13C2414yes—
72C2×Dic13C2412yes—
73D52—216no—
74D52—416no—
75D52—416no—
76C4×D13—28no—
77C4×D13—416no—
78#540—1316no—
79C2×#127—131no—
80C2×#125D1311yescharacteristic, complemented
81C2×#123—134no—
82C2×#121—134no—
83C2×#121—132no—
84C2×C4×D4—132no—
85C2×#117—131no—
86C22×C13C2×#4112yes—
87C22×C13H(5,𝔽2)14yes—
88C22×C13C2511yescharacteristic
89C2×D13—22no—
90C2×D13—28no—
91C2×D13—28no—
92C2×D13—24no—
93C2×D13—28no—
94C2×D13—44no—
95C2×D13—416no—
96C4×C13—28no—
97C4×C13—24no—
98C4×C13C2×#4114yes—
99Dic13—22no—
100Dic13—24no—
101C22×D4—132no—
102C22×D4—134no—
103C22×D4—134no—
104C23×C4—131no—
105C23×C4—134no—
106#127—138no—
107#125C2×D1318yescomplemented
108#123—1332no—
109#121—1332no—
110#121—1316no—
111C4×D4—1316no—
112#117—138no—
113C2×C4⋊C4—132no—
114C2×C4⋊C4C2×D1312yes—
115C2×C4⋊C4C2×D1314yes—
116C2×C22⋊C4—132no—
117C2×C22⋊C4—134no—
118C2×C22⋊C4—134no—
119C2×C42—131no—
120C2×C42C2×D1311yescharacteristic
121C2×C13#54014yescomplemented
122C2×C13C22×#4111yescharacteristic
123C2×C13C2×H(5,𝔽2)12yes—
124D13—42no—
125D13—48no—
126C24—131no—
127C24—134no—
128C2×D4—138no—
129C2×D4—1316no—
130C2×D4—1316no—
131C2×D4—268no—
132C2×D4—528no—
133C2×D4—528no—
134C22×C4—132no—
135C22×C4—131no—
136C22×C4—134no—
137C22×C4—1316no—
138C22×C4—264no—
139C22×C4—528no—
140C22×C4C22×D1312yes—
141C22×C4C22×D1314yes—
142C22×C4C22×D1311yescharacteristic
143C4⋊C4—138no—
144C4⋊C4C22×D1318yes—
145C4⋊C4C22×D13116yes—
146C22⋊C4—138no—
147C22⋊C4—1316no—
148C22⋊C4—1316no—
149C42—134no—
150C42C22×D1314yes—
151C13C2×#54011yescharacteristic, complemented, Sylow
152C23—132no—
153C23—138no—
154C23—262no—
155C23—268no—
156C23—268no—
157C23—264no—
158C23—268no—
159C23C23×D1311yescharacteristic
160D4—2616no—
161D4—5216no—
162D4—5216no—
163C2×C4—28no—
164C2×C4—24no—
165C2×C4—134no—
166C2×C4—132no—
167C2×C4—262no—
168C2×C4—264no—
169C2×C4—268no—
170C2×C4—5216no—
171C2×C4#613114yes—
172C2×C4C23×D1314yes—
173C2×C4C23×D1318yes—
174C2×C4C23×D1312yes—
175C22—262no—
176C22—268no—
177C22—268no—
178C22—264no—
179C22—268no—
180C22—524no—
181C22—5216no—
182C22C2×#613112yes—
183C22#8825614yes—
184C22C24×D1311yescharacteristic
185C4—28no—
186C4—24no—
187C4—262no—
188C4—264no—
189C4C2×#613114yes—
190C2—522no—
191C2—528no—
192C2#1171940314yesdirect product factor
193C2C22×#613111yescharacteristic
194C2C2×#8825612yes—
subgroupG/H
centerC23C23×D13
commutator, cosocleC22×C13C25
FrattiniC22C24×D13
FittingC2×C13×#125C2
socleC23×C13C24
hypercenterC2×#125D13
hypocenterC13C2×#540
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C13×#125C2semidirect
2. #11719403C2direct (N × H)
3. C2×#88149C2semidirect
4. C2×#88149C2semidirect
5. C2×#88148C2semidirect
6. C2×#88147C2semidirect
7. C2×#88128C2semidirect
8. C2×#88126C2semidirect
14. C13×#125C22semidirect
23. #88149C22semidirect
24. #88149C22semidirect
25. #88148C22semidirect
26. #88147C22semidirect
27. #88128C22semidirect
28. #88126C22semidirect
80. C2×#125D13semidirect
107. #125C2×D13semidirect
121. C2×C13#540semidirect
151. C13C2×#540semidirect
192. C2#11719403direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C13×#1252
#117194032
C2×#881492
C2×#881482
C2×#881472
C2×#881282
C2×#881262
C2×#54013