Finite Group Databasebeta

← #14729893

Subgroups — #14729893

Order 2816.

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#13078990C211yesmaximal, characteristic
2#13078746C212yesmaximal, complemented
3#13067802C218yesmaximal, complemented
4#13067330C211yesmaximal, characteristic
5#13067063C212yesmaximal, complemented
6C2×C11×#559C211yesmaximal, characteristic
7C11×#559—22no—
8C11×#559—24no—
9C11×#559C2214yes—
10C2×C11×#127C2211yescharacteristic
11C2×C11×#124—22no—
12C2×C11×#123—22no—
13C2×C4×Q8×C11C2212yes—
14C2×C4×D4×C11—22no—
15#10623001C2211yescharacteristic
16#10622841—22no—
17#10622828—22no—
18#10622684—22no—
19#10622683C2214yes—
20#10622644C2214yescomplemented
21#10622643—24no—
22#10622633C2214yescomplemented
23#10622584—22no—
24#10622539C2212yes—
25C4×#4318C2211yescharacteristic
26#10622182C2214yes—
27Q8⋊(C11⋊C8)C2218yescomplemented
28C22×Q8×C11D412yes—
29C22×D4×C11—22no—
30C22×D4×C11D412yes—
31C23×C4×C11—22no—
32C11×#127—22no—
33C11×#127D412yes—
34C11×#127C2312yes—
35C11×#124—28no—
36C11×#124—28no—
37C11×#123—28no—
38C11×#123—28no—
39C4×Q8×C11—22no—
40C4×Q8×C11—22no—
41C4×Q8×C11D414yes—
42C4×Q8×C11C2314yes—
43C4×D4×C11—28no—
44C4×D4×C11—28no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4D412yes—
47C2×C11×C22⋊C4—24no—
48C2×C11×C22⋊C4—22no—
49C2×C42×C11—22no—
50C2×C42×C11C2311yescharacteristic
51C2×#4326—24no—
52#66979—21no—
53#66977—22no—
54C2×#4318—21no—
55#66923—21no—
56#66922C2312yes—
57C4×Dic22—22no—
58#66899—24no—
59#66896—28no—
60C22⋊(C11⋊C8)—22no—
61#66874—24no—
62#66872—24no—
63C4⋊(C11⋊C8)C2314yes—
64#66867—21no—
65#66867—22no—
66C4×C11⋊C8C2312yes—
67#18531—111nomaximal, Sylow
68C24×C11—22no—
69C2×Q8×C11—22no—
70C2×Q8×C11—44no—
71C2×Q8×C11C2×D414yes—
72C2×D4×C11—24no—
73C2×D4×C11—22no—
74C2×D4×C11—24no—
75C2×D4×C11—48no—
76C2×D4×C11—44no—
77C2×D4×C11C2×D414yes—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—28no—
81C22×C4×C11—84no—
82C22×C4×C11C2×D412yes—
83C22×C4×C11C2×D411yescharacteristic
84C2×Dic22—22no—
85C11×C4⋊C4—24no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—24no—
88C11×C4⋊C4C2×D414yes—
89C11×C22⋊C4—216no—
90C11×C22⋊C4—28no—
91C42×C11—24no—
92C42×C11—24no—
93C42×C11C2×D412yes—
94C42×C11C2×D411yescharacteristic
95C42×C11C2411yescharacteristic
96C22⋊Dic11—41no—
97#4326—48no—
98C4⋊Dic11—22no—
99C4⋊Dic11—22no—
100Dic11⋊C4—42no—
101C4×Dic11—41no—
102#4318—42no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—24no—
105C2×#559D1111yescharacteristic
106#3138—111no—
107#3113—112no—
108#1640—118no—
109#1555—111no—
110#1491—112no—
111C23×C11—24no—
112C23×C11—48no—
113C23×C11—44no—
114C23×C11#12011yescharacteristic
115Q8×C11—24no—
116Q8×C11—24no—
117Q8×C11—44no—
118D4×C11—44no—
119D4×C11—48no—
120D4×C11—48no—
121D4×C11—82no—
122C2×C4×C11—22no—
123C2×C4×C11—24no—
124C2×C4×C11—24no—
125C2×C4×C11—24no—
126C2×C4×C11—44no—
127C2×C4×C11—44no—
128C2×C4×C11—88no—
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12012yes—
131C2×C4×C11C22×D411yescharacteristic
132C2×C4×C11C22×D412yes—
133C2×Dic11—42no—
134Dic22—44no—
135C11⋊C8—42no—
136C11⋊C8—44no—
137#559—22no—
138#559—24no—
139#559C2×D1114yes—
140#533—111no—
141C2×#127C2×D1111yescharacteristic
142C2×#124—22no—
143C2×#123—22no—
144C2×C4×Q8C2×D1112yes—
145C2×C4×D4—22no—
146#490—222no—
147#486—114no—
148#483—222no—
149#475—114no—
150#462—114no—
151#451—222no—
152#441—224no—
153#432—112no—
154#418—222no—
155C4×M16—111no—
156#331—114no—
157Q8⋊C8—118no—
158C22×C11—22no—
159C22×C11—48no—
160C22×C11—44no—
161C22×C11—88no—
162C22×C11#45512yes—
163C22×C11C2×#12011yescharacteristic
164C4×C11—22no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—44no—
168C4×C11—44no—
169C4×C11#57514yes—
170Dic11—82no—
171C22×Q8C22⋊D1112yes—
172C22×D4—22no—
173C22×D4C22⋊D1112yes—
174C23×C4—22no—
175C2×Q16—224no—
176C2×M16—221no—
177C4⋊Q8—112no—
178#127—22no—
179#127C22⋊D1112yes—
180#127C22×D1112yes—
181#125—221no—
182#124—28no—
183#124—28no—
184#123—28no—
185#123—28no—
186C22⋊Q8—222no—
187C4×Q8—22no—
188C4×Q8—22no—
189C4×Q8—222no—
190C4×Q8C22⋊D1114yes—
191C4×Q8C22×D1114yes—
192C4×D4—28no—
193C4×D4—28no—
194#117—221no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4C22⋊D1112yes—
197C2×C22⋊C4—24no—
198C2×C22⋊C4—22no—
199C2×C42—22no—
200C2×C42C22×D1111yescharacteristic
201#106—224no—
202C4⋊C8—114no—
203#103—224no—
204#103—224no—
205#102—228no—
206C22⋊C8—222no—
207#97—221no—
208#97—222no—
209C4×C8—112no—
210C2×C11—22no—
211C2×C11—84no—
212C2×C11#300512yes—
213C2×C11C2×#45511yescharacteristic
214C24—22no—
215C2×Q8—22no—
216C2×Q8—44no—
217C2×Q8—222no—
218C2×Q8C2×C22⋊D1114yes—
219C2×D4—24no—
220C2×D4—22no—
221C2×D4—24no—
222C2×D4—48no—
223C2×D4—44no—
224C2×D4C2×C22⋊D1114yes—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—28no—
228C22×C4—84no—
229C22×C4C2×C22⋊D1112yes—
230C22×C4C2×C22⋊D1111yescharacteristic
231Q16—448no—
232M16—442no—
233C2×C8—222no—
234C2×C8—224no—
235C4⋊C4—24no—
236C4⋊C4—22no—
237C4⋊C4—24no—
238C4⋊C4—222no—
239C4⋊C4—222no—
240C4⋊C4—442no—
241C4⋊C4C2×C22⋊D1114yes—
242C22⋊C4—216no—
243C22⋊C4—28no—
244C22⋊C4—441no—
245C42—24no—
246C42—24no—
247C42—441no—
248C42C2×C22⋊D1111yescharacteristic
249C42C2×C22⋊D1112yes—
250C42C23×D1111yescharacteristic
251C11#1853111yescharacteristic, complemented, Sylow
252C23—24no—
253C23—48no—
254C23—44no—
255C23#6700611yescharacteristic
256Q8—24no—
257Q8—24no—
258Q8—44no—
259Q8—444no—
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—442no—
272C2×C4#6700612yes—
273C2×C4#6700611yescharacteristic
274C2×C4C22×C22⋊D1111yescharacteristic
275C2×C4C22×C22⋊D1112yes—
276C8—442no—
277C8—444no—
278C22—22no—
279C22—48no—
280C22—44no—
281C22—88no—
282C22#1062285512yes—
283C22C2×#6700611yescharacteristic
284C4—22no—
285C4—21no—
286C4—21no—
287C4—44no—
288C4—44no—
289C4—882no—
290C4#1062335314yes—
291C2—22no—
292C2—84no—
293C2#1307785812yes—
294C2C2×#1062285511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#559C2
socleC22×C11C2×#120
prime radicalC2×C11×#127C22
hypercenterC2×#559D11
hypocenterC11#18531
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
2. #13078746C2semidirect
3. #13067802C2semidirect
5. #13067063C2semidirect
20. #10622644C22semidirect
22. #10622633C22semidirect
27. Q8⋊(C11⋊C8)C22semidirect
251. C11#18531semidirect

Maximal subgroups

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

subgroupindex
#130789902
#130787462
#130678022
#130673302
#130670632
C2×C11×#5592
#1853111