Finite Group Databasebeta

← #14735828

Subgroups — #14735828

Order 2816.

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

normal subgroups only

This group has 936 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
1#13083016C211yesmaximal, characteristic
2#13079012C212yesmaximal, complemented
3#13067937C218yesmaximal, complemented
4#13067211C211yesmaximal, characteristic, complemented
5#13067207C212yesmaximal, complemented
6C11×#3139C211yesmaximal, characteristic, complemented
7C11×#533C2211yescharacteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623257—22no—
10#10623231C2214yes—
11#10623160—24no—
12#10623110—22no—
13#10623108—22no—
14#10623066—22no—
15#10623008C2212yes—
16C11×#491C2214yes—
17C11×#487—22no—
18C11×#419—22no—
19C4×C11×M16C2211yescharacteristic
20#10622706—22no—
21#10622702C2218yes—
22#10622701—22no—
23#10622579—24no—
24C4×#4318C2212yes—
25#10622181C2214yes—
26#10622102C2218yes—
27C22×Q8×C11—21no—
28C2×#4343—24no—
29C2×#4339D414yes—
30C2×C11×M16—21no—
31C11×C4⋊Q8—22no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8D412yes—
34C11×C4⋊Q8C2312yes—
35C11×#125C2312yes—
36C11×C22⋊Q8—22no—
37C4×Q8×C11—22no—
38C11×#117D412yes—
39C2×C11×C4⋊C4—22no—
40C2×C42×C11C2311yescharacteristic
41#66999—24no—
42#66983—22no—
43#66983—22no—
44C2×#4318—22no—
45#66949—28no—
46#66948—24no—
47#66948—28no—
48#66947—28no—
49C4⋊C4×D11—24no—
50#66937—28no—
51#66928C2314yes—
52#66927—22no—
53#66927D412yes—
54C4×D44—24no—
55C4×D44—22no—
56C4×D44—22no—
57#66923—22no—
58#66922D412yes—
59C11×#103—28no—
60C11×#97C2312yes—
61C4×C8×C11—21no—
62#66874—28no—
63#66873—28no—
64#66867C2314yes—
65C4×C11⋊C8—22no—
66#19080—111nomaximal, Sylow
67C2×Q8×C11—22no—
68C2×Q8×C11—22no—
69C2×Q8×C11—44no—
70C2×Q8×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11C2×D412yes—
73C22×C4×C11C2×D411yescharacteristic
74C2×C22⋊D11—24no—
75#4343—88no—
76#4339—48no—
77C2×D44—28no—
78C2×D44—22no—
79C2×D44—22no—
80C2×D44C2×D414yes—
81C2×C4×D11—28no—
82C2×C4×D11—24no—
83C2×Dic22C2×D414yes—
84C11×M16—42no—
85C2×C8×C11—22no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—24no—
88C11×C4⋊C4—24no—
89C11×C4⋊C4—42no—
90C11×C4⋊C4C2×D414yes—
91C11×C22⋊C4—22no—
92C42×C11—22no—
93C42×C11C2×D412yes—
94C42×C11C2×D411yescharacteristic
95C42×C11C2411yescharacteristic
96(C2×D11)⋊C4—28no—
97(C2×D11)⋊C4—24no—
98(C2×D11)⋊C4—24no—
99C4⋊Dic11—22no—
100C4⋊Dic11—22no—
101Dic11⋊C4—28no—
102#4318—44no—
103C2×C11⋊C8—24no—
104#3548—111no—
105#3141—112no—
106#3139D1111yescharacteristic, complemented
107#1662—118no—
108#1526—111no—
109#1525—112no—
110C23×C11#12011yescharacteristic
111C22×D11—24no—
112Q8×C11—44no—
113Q8×C11—44no—
114Q8×C11—82no—
115C2×C4×C11—22no—
116C2×C4×C11—24no—
117C2×C4×C11—24no—
118C2×C4×C11—42no—
119C2×C4×C11—82no—
120C2×C4×C11#12011yescharacteristic
121C2×C4×C11#12012yes—
122C2×C4×C11C22×D412yes—
123C2×C4×C11C22×D411yescharacteristic
124C22⋊D11—84no—
125C2×Dic11—24no—
126D44—44no—
127D44—44no—
128D44—44no—
129D44—88no—
130C4×D11—48no—
131C4×D11—88no—
132Dic22—44no—
133C8×C11—42no—
134C11⋊C8—44no—
135#562—114no—
136#554—222no—
137#550—222no—
138#547—222no—
139#540—222no—
140#537—224no—
141#533C2×D1111yescharacteristic
142#532—112no—
143C2×C4⋊Q8C2×D1111yescharacteristic
144#491C2×D1114yes—
145#489—118no—
146#487—22no—
147#487—222no—
148#486—222no—
149#419—22no—
150#417—224no—
151C4×M16—112no—
152C4×M16C2×D1111yescharacteristic
153#330—114no—
154#329—118no—
155C22×C11—22no—
156C22×C11—21no—
157C22×C11C2×#12011yescharacteristic
158C2×D11—44no—
159C2×D11—44no—
160C2×D11—44no—
161C4×C11—22no—
162C4×C11—21no—
163C4×C11—44no—
164C4×C11—82no—
165C4×C11#45412yes—
166C4×C11#45514yes—
167Dic11—44no—
168C2×#41—114no—
169C2×#41—224no—
170C22×Q8—21no—
171C2×M16—21no—
172C2×M16—222no—
173C4⋊Q8—22no—
174C4⋊Q8—21no—
175C4⋊Q8—112no—
176C4⋊Q8C22⋊D1112yes—
177C4⋊Q8C22×D1112yes—
178#127—112no—
179#127—222no—
180#125—222no—
181#125C22×D1112yes—
182#124—114no—
183#123—228no—
184C22⋊Q8—22no—
185C22⋊Q8—228no—
186C22⋊Q8—224no—
187#121—228no—
188#121—228no—
189#121—224no—
190#121—222no—
191#121—222no—
192C4×Q8—22no—
193C4×D4—224no—
194C4×D4—222no—
195C4×D4—222no—
196#117C22⋊D1112yes—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—224no—
199C2×C42C22×D1111yescharacteristic
200#103—28no—
201#103—228no—
202#102—228no—
203#97—114no—
204#97C22×D1112yes—
205C4×C8—21no—
206C4×C8—222no—
207C2×C11—41no—
208C2×C11C2×#45512yes—
209C2×C11C2×#45411yescharacteristic
210D11—84no—
211#41—448no—
212#41—888no—
213C2×Q8—22no—
214C2×Q8—22no—
215C2×Q8—44no—
216C2×Q8—41no—
217C2×Q8—114no—
218C2×D4—114no—
219C2×D4—228no—
220C2×D4—224no—
221C2×D4—222no—
222C2×D4—222no—
223C22×C4—41no—
224C22×C4—228no—
225C22×C4—224no—
226C22×C4D4×D1112yes—
227C22×C4C2×C22⋊D1111yescharacteristic
228M16—42no—
229M16—444no—
230C2×C8—22no—
231C2×C8—224no—
232C4⋊C4—22no—
233C4⋊C4—24no—
234C4⋊C4—24no—
235C4⋊C4—42no—
236C4⋊C4—228no—
237C4⋊C4—222no—
238C4⋊C4—222no—
239C4⋊C4C2×C22⋊D1114yes—
240C22⋊C4—22no—
241C22⋊C4—228no—
242C22⋊C4—224no—
243C22⋊C4—224no—
244C42—22no—
245C42D4×D1112yes—
246C42C2×C22⋊D1111yescharacteristic
247C42C23×D1111yescharacteristic
248C11#1908011yescharacteristic, complemented, Sylow
249C23—224no—
250C23#6699011yescharacteristic
251Q8—44no—
252Q8—44no—
253Q8—82no—
254Q8—444no—
255D4—444no—
256D4—444no—
257D4—444no—
258D4—888no—
259D4—884no—
260C2×C4—24no—
261C2×C4—22no—
262C2×C4—24no—
263C2×C4—42no—
264C2×C4—82no—
265C2×C4—224no—
266C2×C4—448no—
267C2×C4—888no—
268C2×C4#6699012yes—
269C2×C4#6699011yescharacteristic
270C2×C4C2×D4×D1112yes—
271C2×C4C22×C22⋊D1111yescharacteristic
272C8—42no—
273C8—444no—
274C22—22no—
275C22—21no—
276C22—444no—
277C22—444no—
278C22—444no—
279C22C2×#6699011yescharacteristic
280C4—22no—
281C4—21no—
282C4—44no—
283C4—82no—
284C4—444no—
285C4#1062267512yes—
286C4#1062281514yes—
287C2—41no—
288C2—884no—
289C2C2×#1062281512yes—
290C2C2×#1062267511yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3139C2
socleC22×C11C2×#120
prime radical#13083016C2
hypercenter#3139D11
hypocenterC11#19080
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

Complements

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

NH ≅ G/Ntype
2. #13079012C2semidirect
3. #13067937C2semidirect
4. #13067211C2semidirect
5. #13067207C2semidirect
6. C11×#3139C2semidirect
106. #3139D11semidirect
248. C11#19080semidirect

Maximal subgroups

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

subgroupindex
#130830162
#130790122
#130679372
#130672112
#130672072
C11×#31392
#1908011