Finite Group Databasebeta

← #15872183

Subgroups — #15872183

Order 3328.

1538 conjugacy classes of subgroups; only the 315 normal subgroups are shown.

normal subgroups only

This group has 1538 conjugacy classes of subgroups — too many to draw. Only its 315 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#13117434C212yesmaximal, complemented
2#13115673C218yesmaximal, complemented
3#13114751C214yesmaximal, complemented
4C2×C13×#534C211yesmaximal, characteristic
5C23×D4×C13C2212yes—
6C13×#534—28no—
7C2×C13×#123C414yescomplemented
8C2×C13×#121C2214yes—
9C2×C13×#120C414yescomplemented
10C22×C13×C22⋊C4C2211yescharacteristic
11#11718908C2214yes—
12C2×#88074C22116yescomplemented
13#11718873C2214yescomplemented
14C4×C22⋊Dic13C2214yescomplemented
15#11718612—28no—
16C25×C13C2×C412yes—
17C25×C13C2311yescharacteristic
18C22×D4×C13—28no—
19C22×D4×C13—48no—
20C22×D4×C13C2×C414yes—
21C22×D4×C13C2×C414yes—
22C22×D4×C13C2314yes—
23C23×C4×C13C2×C412yes—
24C23×C4×C13C2312yes—
25C13×#123—216no—
26C13×#121—28no—
27C13×#121—28no—
28C13×#120—216no—
29C2×C13×C4⋊C4C2×C414yes—
30C2×C13×C22⋊C4C2×C418yes—
31C2×C13×C22⋊C4C2×C414yes—
32C2×C13×C22⋊C4D418yes—
33C2×C22⋊Dic13—24no—
34C2×C22⋊Dic13—24no—
35C2×C22⋊Dic13C2318yes—
36C2×C4⋊Dic13—24no—
37C2×C4×Dic13—24no—
38#88074—416no—
39#88071—24no—
40#88071—24no—
41#21795—131nomaximal, Sylow
42C24×C13—24no—
43C24×C13—24no—
44C24×C13—44no—
45C24×C13—82no—
46C24×C13—84no—
47C24×C13C22×C414yes—
48C24×C13C22×C412yes—
49C24×C13C2×D414yes—
50C24×C13C2411yescharacteristic
51C2×D4×C13—28no—
52C2×D4×C13—28no—
53C2×D4×C13—216no—
54C2×D4×C13—28no—
55C2×D4×C13—48no—
56C2×D4×C13—432no—
57C2×D4×C13—84no—
58C22×C4×C13—24no—
59C22×C4×C13—44no—
60C22×C4×C13—82no—
61C22×C4×C13C22×C414yes—
62C22×C4×C13C22×C414yes—
63C22×C4×C13C2×D414yes—
64C22×C4×C13C2×D414yes—
65C22×Dic13—28no—
66C13×C4⋊C4—28no—
67C13×C22⋊C4—216no—
68C13×C22⋊C4C22⋊C4116yes—
69C22⋊Dic13—216no—
70C22⋊Dic13—84no—
71C22⋊Dic13—84no—
72C4⋊Dic13—84no—
73C4×Dic13—84no—
74C2×#534D1311yescharacteristic
75#2312—132no—
76#1964—138no—
77#1781—134no—
78C23×C13—24no—
79C23×C13—28no—
80C23×C13—24no—
81C23×C13—28no—
82C23×C13—42no—
83C23×C13—44no—
84C23×C13—44no—
85C23×C13—44no—
86C23×C13—48no—
87C23×C13—48no—
88C23×C13—88no—
89C23×C13—88no—
90C23×C13—816no—
91C23×C13C2×C22⋊C414yes—
92C23×C13C23×C411yescharacteristic
93C23×C13C22×D412yes—
94C23×C13H(5,𝔽2)14yes—
95D4×C13—416no—
96D4×C13—416no—
97D4×C13—88no—
98C2×C4×C13—24no—
99C2×C4×C13—28no—
100C2×C4×C13—44no—
101C2×C4×C13—44no—
102C2×C4×C13—44no—
103C2×C4×C13—48no—
104C2×C4×C13C2×C22⋊C418yes—
105C2×Dic13—48no—
106C2×Dic13—48no—
107C2×Dic13—48no—
108C23×D4C2×D1312yes—
109#534—28no—
110C2×#123Dic1314yescomplemented
111C2×#121C2×D1314yes—
112C2×#120Dic1314yescomplemented
113C22×C22⋊C4C2×D1311yescharacteristic
114C2×#99—1316no—
115#388—268no—
116#380—134no—
117#379—134no—
118C4×C22⋊C4—134no—
119C22×C13—22no—
120C22×C13—22no—
121C22×C13—22no—
122C22×C13—24no—
123C22×C13—28no—
124C22×C13—44no—
125C22×C13—48no—
126C22×C13—44no—
127C22×C13—48no—
128C22×C13—88no—
129C22×C13—88no—
130C22×C13—816no—
131C22×C13C22×C22⋊C411yescharacteristic
132C22×C13#51812yes—
133C22×C13#53514yes—
134C4×C13—28no—
135C4×C13—44no—
136Dic13—88no—
137C25C2×Dic1312yes—
138C25C22×D1311yescharacteristic
139C22×D4—28no—
140C22×D4—48no—
141C22×D4C2×Dic1314yes—
142C22×D4C2×Dic1314yes—
143C22×D4C22×D1314yes—
144C23×C4C2×Dic1312yes—
145C23×C4C22×D1312yes—
146#123—216no—
147#121—28no—
148#121—28no—
149#120—216no—
150C2×C4⋊C4—264no—
151C2×C4⋊C4C2×Dic1314yes—
152C2×C22⋊C4—138no—
153C2×C22⋊C4—264no—
154C2×C22⋊C4—264no—
155C2×C22⋊C4C2×Dic1318yes—
156C2×C22⋊C4C2×Dic1314yes—
157C2×C22⋊C4C22⋊D1318yes—
158C2×C42—264no—
159#99—5216no—
160#95—264no—
161#95—264no—
162C2×C13—24no—
163C2×C13—22no—
164C2×C13—44no—
165C2×C13—84no—
166C2×C13#230911yescharacteristic
167C2×C13#288312yes—
168C24—24no—
169C24—24no—
170C24—44no—
171C24—82no—
172C24—84no—
173C24C22×Dic1314yes—
174C24C22×Dic1312yes—
175C24C2×C22⋊D1314yes—
176C24C23×D1311yescharacteristic
177C2×D4—28no—
178C2×D4—216no—
179C2×D4—28no—
180C2×D4—28no—
181C2×D4—48no—
182C2×D4—432no—
183C2×D4—84no—
184C22×C4—24no—
185C22×C4—44no—
186C22×C4—82no—
187C22×C4—268no—
188C22×C4C22×Dic1314yes—
189C22×C4C22×Dic1314yes—
190C22×C4C2×C22⋊D1314yes—
191C22×C4C2×C22⋊D1314yes—
192C4⋊C4—28no—
193C4⋊C4—1044no—
194C22⋊C4—216no—
195C22⋊C4—2616no—
196C22⋊C4—1044no—
197C22⋊C4—1044no—
198C22⋊C4C22⋊Dic13116yes—
199C42—1044no—
200C13#2179511yescharacteristic, complemented, Sylow
201C23—24no—
202C23—28no—
203C23—24no—
204C23—28no—
205C23—42no—
206C23—44no—
207C23—44no—
208C23—44no—
209C23—48no—
210C23—48no—
211C23—88no—
212C23—88no—
213C23—816no—
214C23C2×C22⋊Dic1314yes—
215C23#8825114yes—
216C23C23×Dic1311yescharacteristic
217C23C22×C22⋊D1312yes—
218D4—416no—
219D4—416no—
220D4—88no—
221C2×C4—28no—
222C2×C4—24no—
223C2×C4—44no—
224C2×C4—44no—
225C2×C4—44no—
226C2×C4—48no—
227C2×C4—528no—
228C2×C4—528no—
229C2×C4—528no—
230C2×C4C2×C22⋊Dic1318yes—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—28no—
235C22—24no—
236C22—44no—
237C22—48no—
238C22—48no—
239C22—44no—
240C22—88no—
241C22—88no—
242C22—816no—
243C22#1171950312yes—
244C22#1171951014yes—
245C22C22×C22⋊Dic1311yescharacteristic
246C4—28no—
247C4—44no—
248C4—1048no—
249C2—24no—
250C2—22no—
251C2—44no—
252C2—84no—
253C2#1311741811yescharacteristic
254C2#1312329712yes—
subgroupG/H
centerC22C22×C22⋊Dic13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
Fitting, prime radicalC2×C13×#534C2
socleC22×C13C22×C22⋊C4
cosocleC24×C13C24
hypercenterC2×#534D13
hypocenterC13#21795
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C22⋊C4 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. #13117434C2semidirect
2. #13115673C2semidirect
3. #13114751C2semidirect
7. C2×C13×#123C4semidirect
9. C2×C13×#120C4semidirect
12. C2×#88074C22semidirect
13. #11718873C22semidirect
14. C4×C22⋊Dic13C22semidirect
110. C2×#123Dic13semidirect
112. C2×#120Dic13semidirect
200. C13#21795semidirect

Maximal subgroups

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

subgroupindex
#131174342
#131156732
#131147512
C2×C13×#5342
#2179513