Finite Group Databasebeta

← #15839039

Subgroups — #15839039

Order 3328.

982 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 982 conjugacy classes of subgroups — too many to draw. Only its 179 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#13125210C211yesmaximal, characteristic
2#13124966C212yesmaximal, complemented
3#13114022C218yesmaximal, complemented
4#13113550C211yesmaximal, characteristic
5#13113283C212yesmaximal, complemented
6C2×C13×#559C211yesmaximal, characteristic
7C13×#559—22no—
8C13×#559—24no—
9C13×#559C2214yes—
10C2×C13×#127C2211yescharacteristic
11C2×C13×#124—22no—
12C2×C13×#123—22no—
13C2×C4×Q8×C13C2212yes—
14C2×C4×D4×C13—22no—
15#11719175C2211yescharacteristic
16#11718889—22no—
17#11718876—22no—
18#11718732—22no—
19#11718731C2214yes—
20#11718692C2214yescomplemented
21#11718691—24no—
22#11718681C2214yescomplemented
23#11718632—22no—
24#11718587C2212yes—
25C4×#6099C2211yescharacteristic
26#11718136C2214yes—
27Q8⋊#1055C2218yescomplemented
28C22×Q8×C13D412yes—
29C22×D4×C13—22no—
30C22×D4×C13D412yes—
31C23×C4×C13—22no—
32C13×#127—22no—
33C13×#127D412yes—
34C13×#127C2312yes—
35C13×#124—28no—
36C13×#124—28no—
37C13×#123—28no—
38C13×#123—28no—
39C4×Q8×C13—22no—
40C4×Q8×C13—22no—
41C4×Q8×C13D414yes—
42C4×Q8×C13C2314yes—
43C4×D4×C13—28no—
44C4×D4×C13—28no—
45C2×C13×C4⋊C4—22no—
46C2×C13×C4⋊C4D412yes—
47C2×C13×C22⋊C4—24no—
48C2×C13×C22⋊C4—22no—
49C2×C42×C13—22no—
50C2×C42×C13C2311yescharacteristic
51C2×#6107—24no—
52#88180—21no—
53#88178—22no—
54C2×#6099—21no—
55#88124—21no—
56#88123C2312yes—
57C4×Dic26—22no—
58#88075—24no—
59#88072—28no—
60C22⋊#1055—22no—
61#88050—24no—
62#88048—24no—
63C4⋊#1055C2314yes—
64#88043—22no—
65#88043—21no—
66C4×#1055C2312yes—
67#18531—131nomaximal, Sylow
68C24×C13—22no—
69C2×Q8×C13—22no—
70C2×Q8×C13—44no—
71C2×Q8×C13C2×D414yes—
72C2×D4×C13—24no—
73C2×D4×C13—22no—
74C2×D4×C13—24no—
75C2×D4×C13—48no—
76C2×D4×C13—44no—
77C2×D4×C13C2×D414yes—
78C22×C4×C13—22no—
79C22×C4×C13—22no—
80C22×C4×C13—28no—
81C22×C4×C13—84no—
82C22×C4×C13C2×D412yes—
83C22×C4×C13C2×D411yescharacteristic
84C2×Dic26—22no—
85C13×C4⋊C4—24no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—24no—
88C13×C4⋊C4C2×D414yes—
89C13×C22⋊C4—216no—
90C13×C22⋊C4—28no—
91C42×C13—24no—
92C42×C13—24no—
93C42×C13C2×D412yes—
94C42×C13C2×D411yescharacteristic
95C42×C13C2411yescharacteristic
96C22⋊Dic13—41no—
97#6107—48no—
98C4⋊Dic13—22no—
99C4⋊Dic13—22no—
100#6101—42no—
101C4×Dic13—41no—
102#6099—42no—
103C2×#1055—24no—
104C2×#1055—22no—
105C2×#559D1311yescharacteristic
106#3138—131no—
107#3113—132no—
108#1640—138no—
109#1555—131no—
110#1491—132no—
111C23×C13—24no—
112C23×C13—48no—
113C23×C13—44no—
114C23×C13#12011yescharacteristic
115Q8×C13—24no—
116Q8×C13—24no—
117Q8×C13—44no—
118D4×C13—48no—
119D4×C13—44no—
120D4×C13—48no—
121D4×C13—82no—
122C2×C4×C13—22no—
123C2×C4×C13—24no—
124C2×C4×C13—24no—
125C2×C4×C13—24no—
126C2×C4×C13—44no—
127C2×C4×C13—44no—
128C2×C4×C13—88no—
129C2×C4×C13#12011yescharacteristic
130C2×C4×C13#12012yes—
131C2×C4×C13C22×D411yescharacteristic
132C2×C4×C13C22×D412yes—
133C2×Dic13—42no—
134Dic26—44no—
135#1055—42no—
136#1055—44no—
137#559—22no—
138#559—24no—
139#559C2×D1314yes—
140#533—131no—
141C2×#127C2×D1311yescharacteristic
142C2×#124—22no—
143C2×#123—22no—
144C2×C4×Q8C2×D1312yes—
145C2×C4×D4—22no—
146#490—262no—
147#486—134no—
148#483—262no—
149#475—134no—
150#462—134no—
151#451—262no—
152#441—264no—
153#432—132no—
154#418—262no—
155C4×M16—131no—
156#331—134no—
157Q8⋊C8—138no—
158C22×C13—22no—
159C22×C13—48no—
160C22×C13—44no—
161C22×C13—88no—
162C22×C13#45512yes—
163C22×C13C2×#12011yescharacteristic
164C4×C13—22no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—44no—
168C4×C13—44no—
169C4×C13#57514yes—
170Dic13—82no—
171C22×Q8C22⋊D1312yes—
172C22×D4—22no—
173C22×D4C22⋊D1312yes—
174C23×C4—22no—
175C2×Q16—264no—
176C2×M16—261no—
177C4⋊Q8—132no—
178#127—22no—
179#127C22⋊D1312yes—
180#127C22×D1312yes—
181#125—261no—
182#124—28no—
183#124—28no—
184#123—28no—
185#123—28no—
186C22⋊Q8—262no—
187C4×Q8—22no—
188C4×Q8—22no—
189C4×Q8—262no—
190C4×Q8C22⋊D1314yes—
191C4×Q8C22×D1314yes—
192C4×D4—28no—
193C4×D4—28no—
194#117—261no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4C22⋊D1312yes—
197C2×C22⋊C4—24no—
198C2×C22⋊C4—22no—
199C2×C42—22no—
200C2×C42C22×D1311yescharacteristic
201#106—264no—
202C4⋊C8—134no—
203#103—264no—
204#103—264no—
205#102—268no—
206C22⋊C8—262no—
207#97—261no—
208#97—262no—
209C4×C8—132no—
210C2×C13—22no—
211C2×C13—84no—
212C2×C13#300512yes—
213C2×C13C2×#45511yescharacteristic
214C24—22no—
215C2×Q8—22no—
216C2×Q8—44no—
217C2×Q8—262no—
218C2×Q8C2×C22⋊D1314yes—
219C2×D4—24no—
220C2×D4—22no—
221C2×D4—24no—
222C2×D4—48no—
223C2×D4—44no—
224C2×D4C2×C22⋊D1314yes—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—28no—
228C22×C4—84no—
229C22×C4C2×C22⋊D1312yes—
230C22×C4C2×C22⋊D1311yescharacteristic
231Q16—528no—
232M16—522no—
233C2×C8—262no—
234C2×C8—264no—
235C4⋊C4—24no—
236C4⋊C4—22no—
237C4⋊C4—24no—
238C4⋊C4—262no—
239C4⋊C4—262no—
240C4⋊C4—522no—
241C4⋊C4C2×C22⋊D1314yes—
242C22⋊C4—216no—
243C22⋊C4—28no—
244C22⋊C4—521no—
245C42—24no—
246C42—24no—
247C42—521no—
248C42C2×C22⋊D1311yescharacteristic
249C42C2×C22⋊D1312yes—
250C42C23×D1311yescharacteristic
251C13#1853111yescharacteristic, complemented, Sylow
252C23—24no—
253C23—48no—
254C23—44no—
255C23#8820711yescharacteristic
256Q8—24no—
257Q8—24no—
258Q8—44no—
259Q8—524no—
260D4—44no—
261D4—48no—
262D4—48no—
263D4—82no—
264C2×C4—22no—
265C2×C4—24no—
266C2×C4—24no—
267C2×C4—24no—
268C2×C4—44no—
269C2×C4—44no—
270C2×C4—88no—
271C2×C4—522no—
272C2×C4#8820712yes—
273C2×C4#8820711yescharacteristic
274C2×C4C22×C22⋊D1311yescharacteristic
275C2×C4C22×C22⋊D1312yes—
276C8—522no—
277C8—524no—
278C22—22no—
279C22—44no—
280C22—48no—
281C22—88no—
282C22#1171890312yes—
283C22C2×#8820711yescharacteristic
284C4—21no—
285C4—21no—
286C4—22no—
287C4—44no—
288C4—44no—
289C4—1042no—
290C4#1171952714yes—
291C2—22no—
292C2—84no—
293C2#1312407812yes—
294C2C2×#1171890311yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#559C2
socleC22×C13C2×#120
prime radicalC2×C13×#127C22
hypercenterC2×#559D13
hypocenterC13#18531
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
2. #13124966C2semidirect
3. #13114022C2semidirect
5. #13113283C2semidirect
20. #11718692C22semidirect
22. #11718681C22semidirect
27. Q8⋊#1055C22semidirect
251. C13#18531semidirect

Maximal subgroups

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

subgroupindex
#131252102
#131249662
#131140222
#131135502
#131132832
C2×C13×#5592
#1853113