Finite Group Databasebeta

← #14729891

Subgroups — #14729891

Order 2816.

982 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 982 conjugacy classes of subgroups — too many to draw. Only its 163 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×#10623244C211yesmaximal, characteristic
2#13078742C212yesmaximal, complemented
3#13067799C218yesmaximal, complemented
4#13067330C211yesmaximal, characteristic
5#13067064C212yesmaximal, complemented
6C11×#3138C211yesmaximal, characteristic
7C11×#533C2211yescharacteristic
8C2×C11×#127C2211yescharacteristic
9C2×#66989—22no—
10C2×#66988—22no—
11C2×D4×Dic11—22no—
12#10623244—22no—
13#10623244—24no—
14#10623244C2214yes—
15C2×C4×Dic22C2212yes—
16C11×#490—22no—
17C11×#486C2214yes—
18C11×#418—22no—
19C4×C11×M16C2211yescharacteristic
20#10622707C2214yescomplemented
21#10622703C2214yescomplemented
22#10622663—22no—
23#10622656—22no—
24#10622643—24no—
25#10622539C2212yes—
26#10622182C2214yes—
27#10622094C2218yescomplemented
28C22×D4×C11—22no—
29C22×D4×C11D412yes—
30C23×Dic11—22no—
31C22×Dic22D412yes—
32C2×C11×M16—21no—
33C11×C4⋊Q8C2312yes—
34C11×#127—22no—
35C11×#127D412yes—
36C11×#127C2312yes—
37C11×#125—21no—
38C11×C22⋊Q8—22no—
39C4×Q8×C11—22no—
40C11×#117—21no—
41C2×C42×C11C2311yescharacteristic
42C2×C22⋊Dic11—24no—
43C2×C22⋊Dic11—22no—
44C2×#4326—24no—
45#66989—28no—
46#66989—28no—
47#66988—28no—
48#66988—28no—
49D4×Dic11—28no—
50D4×Dic11—28no—
51C2×C4⋊Dic11D412yes—
52C2×Dic11⋊C4—22no—
53C2×C4×Dic11—22no—
54C4×Dic22—22no—
55C4×Dic22—22no—
56C4×Dic22D414yes—
57C4×Dic22C2314yes—
58C11×#102—28no—
59C11×#97—21no—
60C4×C8×C11C2312yes—
61#66899—24no—
62C22⋊(C11⋊C8)—22no—
63#66874—24no—
64#66872—24no—
65C4⋊(C11⋊C8)C2314yes—
66#66867—22no—
67#18531—111nomaximal, Sylow
68C24×C11—22no—
69C2×Q8×C11—22no—
70C2×D4×C11—24no—
71C2×D4×C11—22no—
72C2×D4×C11—24no—
73C2×D4×C11—48no—
74C2×D4×C11—44no—
75C2×D4×C11C2×D414yes—
76C22×C4×C11C2×D412yes—
77C22×C4×C11C2×D411yescharacteristic
78C22×Dic11—28no—
79C22×Dic11—22no—
80C22×Dic11—22no—
81C22×Dic11—84no—
82C2×Dic22—22no—
83C2×Dic22—44no—
84C2×Dic22C2×D414yes—
85C11×M16—42no—
86C2×C8×C11—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—42no—
90C11×C22⋊C4—41no—
91C42×C11—41no—
92C42×C11C2×D412yes—
93C42×C11C2×D411yescharacteristic
94C42×C11C2411yescharacteristic
95C22⋊Dic11—216no—
96C22⋊Dic11—28no—
97#4326—48no—
98C4⋊Dic11—22no—
99C4⋊Dic11C2×D414yes—
100Dic11⋊C4—24no—
101Dic11⋊C4—24no—
102C4×Dic11—24no—
103C4×Dic11—24no—
104C2×C11⋊C8—24no—
105C2×#559—111no—
106#3138D1111yescharacteristic
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—44no—
116D4×C11—44no—
117D4×C11—48no—
118D4×C11—48no—
119D4×C11—82no—
120C2×C4×C11—22no—
121C2×C4×C11—24no—
122C2×C4×C11—42no—
123C2×C4×C11#12012yes—
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11C22×D412yes—
126C2×C4×C11C22×D411yescharacteristic
127C2×Dic11—24no—
128C2×Dic11—24no—
129C2×Dic11—44no—
130C2×Dic11—44no—
131C2×Dic11—88no—
132Dic22—24no—
133Dic22—24no—
134Dic22—44no—
135C8×C11—42no—
136C11⋊C8—44no—
137#559—114no—
138#559—224no—
139#559—222no—
140#533C2×D1111yescharacteristic
141C2×#127C2×D1111yescharacteristic
142C2×#124—222no—
143C2×#123—222no—
144C2×C4×Q8—112no—
145C2×C4×D4—222no—
146#490—22no—
147#486C2×D1114yes—
148#483—222no—
149#475—114no—
150#462—114no—
151#451—222no—
152#441—224no—
153#432—112no—
154#418—22no—
155C4×M16C2×D1111yescharacteristic
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—82no—
168C4×C11#57514yes—
169Dic11—44no—
170Dic11—44no—
171C22×Q8—112no—
172C22×D4—22no—
173C22×D4C22⋊D1112yes—
174C23×C4—222no—
175C2×Q16—224no—
176C2×M16—21no—
177C4⋊Q8C22×D1112yes—
178#127—22no—
179#127C22⋊D1112yes—
180#127C22×D1112yes—
181#125—21no—
182#124—228no—
183#124—228no—
184#123—228no—
185#123—228no—
186C22⋊Q8—22no—
187C4×Q8—22no—
188C4×Q8—114no—
189C4×Q8—114no—
190C4×Q8—222no—
191C4×Q8—222no—
192C4×D4—228no—
193C4×D4—228no—
194#117—21no—
195C2×C4⋊C4—112no—
196C2×C4⋊C4—222no—
197C2×C22⋊C4—224no—
198C2×C22⋊C4—222no—
199C2×C42—222no—
200C2×C42C22×D1111yescharacteristic
201#106—224no—
202C4⋊C8—114no—
203#103—224no—
204#103—224no—
205#102—28no—
206C22⋊C8—222no—
207#97—21no—
208#97—222no—
209C4×C8C22×D1112yes—
210C2×C11—22no—
211C2×C11—84no—
212C2×C11#300512yes—
213C2×C11C2×#45511yescharacteristic
214C24—22no—
215C2×Q8—22no—
216C2×Q8—114no—
217C2×Q8—222no—
218C2×Q8—444no—
219C2×D4—24no—
220C2×D4—22no—
221C2×D4—24no—
222C2×D4—48no—
223C2×D4—44no—
224C2×D4C2×C22⋊D1114yes—
225C22×C4—222no—
226C22×C4—222no—
227C22×C4—228no—
228C22×C4—884no—
229C22×C4D4×D1112yes—
230C22×C4C2×C22⋊D1111yescharacteristic
231Q16—448no—
232M16—42no—
233C2×C8—22no—
234C2×C8—224no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—42no—
238C4⋊C4—114no—
239C4⋊C4—222no—
240C4⋊C4—224no—
241C4⋊C4—224no—
242C22⋊C4—41no—
243C22⋊C4—2216no—
244C22⋊C4—228no—
245C42—41no—
246C42—224no—
247C42—224no—
248C42D4×D1112yes—
249C42C2×C22⋊D1111yescharacteristic
250C42C23×D1111yescharacteristic
251C11#1853111yescharacteristic, complemented, Sylow
252C23—24no—
253C23—48no—
254C23—44no—
255C23#6699011yescharacteristic
256Q8—44no—
257Q8—224no—
258Q8—224no—
259Q8—444no—
260D4—44no—
261D4—48no—
262D4—48no—
263D4—82no—
264C2×C4—22no—
265C2×C4—24no—
266C2×C4—42no—
267C2×C4—224no—
268C2×C4—224no—
269C2×C4—444no—
270C2×C4—444no—
271C2×C4—888no—
272C2×C4#6699011yescharacteristic
273C2×C4#6699012yes—
274C2×C4C2×D4×D1112yes—
275C2×C4C22×C22⋊D1111yescharacteristic
276C8—42no—
277C8—444no—
278C22—22no—
279C22—48no—
280C22—44no—
281C22—88no—
282C22#1062267412yes—
283C22C2×#6699011yescharacteristic
284C4—22no—
285C4—21no—
286C4—21no—
287C4—82no—
288C4—444no—
289C4—444no—
290C4#1062330414yes—
291C2—22no—
292C2—84no—
293C2#1307785512yes—
294C2C2×#1062267411yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3138C2
socleC22×C11C2×#120
prime radicalC2×C11×#127C22
hypercenter#3138D11
hypocenterC11#18531
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3138

Complements

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

NH ≅ G/Ntype
2. #13078742C2semidirect
3. #13067799C2semidirect
5. #13067064C2semidirect
20. #10622707C22semidirect
21. #10622703C22semidirect
27. #10622094C22semidirect
251. C11#18531semidirect

Maximal subgroups

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

subgroupindex
C2×#106232442
#130787422
#130677992
#130673302
#130670642
C11×#31382
#1853111