Finite Group Databasebeta

← #14721519

Subgroups — #14721519

Order 2816.

1202 conjugacy classes of subgroups; only the 355 normal subgroups are shown.

normal subgroups only

This group has 1202 conjugacy classes of subgroups — too many to draw. Only its 355 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#13082387C211yesmaximal, characteristic
2#13077697C211yesmaximal, characteristic, complemented
3#13067175C216yesmaximal, complemented
4#13067110C216yesmaximal, complemented
5C11×#2351C211yesmaximal, characteristic, complemented
6C2×#67040—21no—
7C2×C4×Q8×C11—21no—
8C2×C4×Q8×C11C2211yescharacteristic
9#10623108C414yescomplemented
10#10623107—24no—
11Q8×D44C414yescomplemented
12#10623041—23no—
13#10623008C2216yes—
14C11×#389—23no—
15C11×#382C2213yes—
16C4×C11×C4⋊C4C2213yes—
17Q8×C11⋊C8—24no—
18#10622538C2216yes—
19#10622089C2214yes—
20#10622089C22112yes—
21C22×Q8×C11D411yescharacteristic
22#67040—44no—
23#67040—44no—
24C2×#4343—24no—
25C2×Q8×D11—24no—
26C2×#4339—26no—
27C4×Q8×C11—44no—
28C4×Q8×C11C2×C414yes—
29C4×Q8×C11D414yes—
30C2×C11×C4⋊C4—23no—
31C2×C11×C4⋊C4—23no—
32C2×C11×C4⋊C4D413yes—
33C2×C42×C11—23no—
34C2×C42×C11C2313yes—
35#66983—26no—
36#66983C2314yes—
37#66950—212no—
38#66948—212no—
39#66928—26no—
40#66927C2×C416yes—
41C4×D44—26no—
42C4×D44C2×C4112yes—
43#66922C2×C416yes—
44C11×#95—23no—
45C11×#95C2311yescharacteristic
46C11×#95C2313yes—
47C22⋊(C11⋊C8)C2314yes—
48C4⋊(C11⋊C8)—26no—
49C4×C11⋊C8—26no—
50#17618—111nomaximal, Sylow
51C2×Q8×C11C22⋊C414yes—
52C2×Q8×C11D814yes—
53C2×Q8×C11SD1614yes—
54C22×C4×C11—21no—
55C22×C4×C11—23no—
56C22×C4×C11C2×D413yes—
57C22×C4×C11C2×D413yes—
58C22×C4×C11C2411yescharacteristic
59C2×C22⋊D11—24no—
60#4343—416no—
61Q8×D11—416no—
62#4339—412no—
63#4339—412no—
64C2×D44—26no—
65C2×D44—26no—
66C2×D44C22×C414yes—
67C2×C4×D11—212no—
68C2×Dic22—26no—
69C11×C4⋊C4—46no—
70C11×C4⋊C4—46no—
71C11×C4⋊C4C22⋊C4112yes—
72C42×C11—46no—
73C42×C11C22×C416yes—
74C42×C11C2×D416yes—
75(C2×D11)⋊C4—212no—
76(C2×D11)⋊C4—24no—
77C4⋊Dic11—26no—
78C4⋊Dic11C22×C414yes—
79C2×C11⋊C8—24no—
80#3497—111no—
81#2982—111no—
82#2351D1111yescharacteristic, complemented
83#1517—116no—
84#1502—116no—
85C23×C11C22×D411yescharacteristic
86C22×D11—24no—
87Q8×C11#102116yes—
88C2×C4×C11—22no—
89C2×C4×C11—43no—
90C2×C4×C11—41no—
91C2×C4×C11—41no—
92C2×C4×C11—41no—
93C2×C4×C11—43no—
94C2×C4×C11—43no—
95C2×C4×C11—43no—
96C2×C4×C11C2×C22⋊C416yes—
97C2×C4×C11C2×C22⋊C416yes—
98C2×C4×C11C2×D816yes—
99C2×C4×C11C2×SD1616yes—
100C2×C4×C11C23×C411yescharacteristic
101C2×C4×C11C22×D411yescharacteristic
102C22⋊D11—44no—
103C22⋊D11—44no—
104C2×Dic11—24no—
105D44—44no—
106D44—412no—
107D44—86no—
108C4×D11—424no—
109Dic22—412no—
110C11⋊C8—44no—
111C2×2−1+4—221no—
112#550—114no—
113D4×Q8—114no—
114#548—224no—
115#537—223no—
116#532—116no—
117C2×C4×Q8—21no—
118C2×C4×Q8C2×D1111yescharacteristic
119C8×Q8—224no—
120#431—116no—
121#389—23no—
122#382C2×D1113yes—
123C4×C4⋊C4C2×D1113yes—
124#327—114no—
125#327—1112no—
126C22×C11—21no—
127C22×C11—21no—
128C22×C11C22×C22⋊C411yescharacteristic
129C22×C11C22×D811yescharacteristic
130C22×C11C22×SD1611yescharacteristic
131C2×D11—44no—
132C2×D11—44no—
133C2×D11—44no—
134C4×C11—21no—
135C4×C11—21no—
136C4×C11—26no—
137C4×C11—42no—
138C4×C11—83no—
139C4×C11C2×#102112yes—
140Dic11—44no—
1412−1+4—444no—
1422−1+4—444no—
143C2×#41—224no—
144C2×#41—226no—
145C22×Q8—224no—
146C22×Q8C22⋊D1111yescharacteristic
147C4⋊Q8—116no—
148#127—116no—
149#124—226no—
150C22⋊Q8—2212no—
151#121—114no—
152#121—226no—
153#121—2212no—
154C4×Q8—44no—
155C4×Q8C4×D1114yes—
156C4×Q8D4414yes—
157C4×D4—1112no—
158C4×D4—226no—
159C2×C4⋊C4—23no—
160C2×C4⋊C4—23no—
161C2×C4⋊C4C22⋊D1113yes—
162C2×C42—23no—
163C2×C42C22×D1113yes—
164C4⋊C8—226no—
165C22⋊C8—114no—
166C4×C8—226no—
167#95—23no—
168#95C22×D1111yescharacteristic
169#95C22×D1113yes—
170C2×C11—21no—
171C2×C11—21no—
172C2×C11#288411yescharacteristic
173C2×C11C22×#10211yescharacteristic
174C2×C11#290111yescharacteristic
175D11—84no—
176#41—4416no—
177#41—4412no—
178#41—4412no—
179C2×Q8—226no—
180C2×Q8—4416no—
181C2×Q8(C2×D11)⋊C414yes—
182C2×Q8#432314yes—
183C2×Q8#432514yes—
184C2×D4—114no—
185C2×D4—224no—
186C2×D4—226no—
187C2×D4—226no—
188C22×C4—21no—
189C22×C4—23no—
190C22×C4—2212no—
191C22×C4C2×C22⋊D1113yes—
192C22×C4C2×C22⋊D1113yes—
193C22×C4C23×D1111yescharacteristic
194C2×C8—224no—
195C4⋊C4—46no—
196C4⋊C4—46no—
197C4⋊C4—114no—
198C4⋊C4—226no—
199C4⋊C4(C2×D11)⋊C4112yes—
200C22⋊C4—2212no—
201C22⋊C4—224no—
202C42—46no—
203C42C2×C4×D1116yes—
204C42C2×D4416yes—
205C11#1761811yescharacteristic, complemented, Sylow
206C23—224no—
207C23C22×C22⋊D1111yescharacteristic
208Q8—4412no—
209Q8#66873116yes—
210D4—444no—
211D4—444no—
212D4—444no—
213D4—4412no—
214D4—886no—
215C2×C4—22no—
216C2×C4—43no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—43no—
221C2×C4—43no—
222C2×C4—43no—
223C2×C4—224no—
224C2×C4—4424no—
225C2×C4C2×(C2×D11)⋊C416yes—
226C2×C4C2×(C2×D11)⋊C416yes—
227C2×C4C2×#432316yes—
228C2×C4C2×#432516yes—
229C2×C4C22×C4×D1111yescharacteristic
230C2×C4C22×D4411yescharacteristic
231C8—444no—
232C22—21no—
233C22—21no—
234C22—444no—
235C22—444no—
236C22—444no—
237C22C22×(C2×D11)⋊C411yescharacteristic
238C22C22×#432311yescharacteristic
239C22C22×#432511yescharacteristic
240C4—21no—
241C4—21no—
242C4—26no—
243C4—42no—
244C4—83no—
245C4—444no—
246C4C2×#66873112yes—
247C2—21no—
248C2—21no—
249C2—884no—
250C2#1307707911yescharacteristic
251C2C22×#6687311yescharacteristic
252C2#1307716411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2351C2
socleC22×C11C22×C22⋊C4
prime radical#13082387C2
cosocleC22×C4×C11C24
hypercenter#2351D11
hypocenterC11#17618
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #2351

Complements

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

NH ≅ G/Ntype
2. #13077697C2semidirect
3. #13067175C2semidirect
4. #13067110C2semidirect
5. C11×#2351C2semidirect
9. #10623108C4semidirect
11. Q8×D44C4semidirect
82. #2351D11semidirect
205. C11#17618semidirect

Maximal subgroups

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

subgroupindex
#130823872
#130776972
#130671752
#130671102
C11×#23512
#1761811