Finite Group Databasebeta

← #14666344

Subgroups — #14666344

Order 2816.

472 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 63 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#13069840C211yesmaximal, characteristic
2#13067584C212yesmaximal
3#13066646C212yesmaximal, complemented
4#13066562C211yesmaximal, characteristic, complemented
5C11×#2551C211yesmaximal, characteristic, complemented
6C2×C11×C4⋊Q8—22no—
7#10623041C2211yescharacteristic
8C11×#395—21no—
9C11×#395C2212yes—
10C11×#389—22no—
11C11×#384C2211yescharacteristic
12C4×C11×C4⋊C4—21no—
13#10622840—22no—
14#10622579—21no—
15C2×#66869—21no—
16#10622168C2211yescharacteristic
17#10622166C2212yes—
18#10622089—22no—
19C22×Q8×C11—21no—
20C22×Q8×C11D412yes—
21C2×#4339—21no—
22C11×C4⋊Q8—48no—
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4—21no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4C2311yescharacteristic
30C2×C42×C11—22no—
31C2×C42×C11D411yescharacteristic
32C2×#4325—42no—
33#66983—22no—
34C2×#4318—21no—
35#66950—41no—
36#66948—41no—
37C11×#95—21no—
38C11×#95—22no—
39C11×#95D412yes—
40#66899—42no—
41C22⋊(C11⋊C8)—22no—
42#66874—41no—
43#66873—41no—
44#66869—42no—
45#12180—111nomaximal, Sylow
46C2×Q8×C11—44no—
47C2×Q8×C11—44no—
48C2×Q8×C11—42no—
49C2×Q8×C11—81no—
50C22×C4×C11—21no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—21no—
54C22×C4×C11C2×D411yescharacteristic
55C22×C4×C11C2×D412yes—
56C2×C22⋊D11—41no—
57#4339—41no—
58#4339—41no—
59#4339—41no—
60#4339—41no—
61C2×D44—21no—
62C2×D44—22no—
63C2×C4×D11—41no—
64C2×Dic22—21no—
65C11×C4⋊C4—24no—
66C11×C4⋊C4—24no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—44no—
69C11×C4⋊C4—44no—
70C11×C4⋊C4—44no—
71C11×C4⋊C4—41no—
72C42×C11—21no—
73C42×C11—44no—
74C42×C11SD1612yescomplemented
75#4325—84no—
76(C2×D11)⋊C4—42no—
77C4⋊Dic11—22no—
78#4318—41no—
79#4318—41no—
80C2×C11⋊C8—41no—
81C2×C11⋊C8—42no—
82#2551D1111yescharacteristic, complemented
83#2039—111no—
84#1604—112no—
85#1354—112no—
86#1325—111no—
87C23×C11#12011yescharacteristic
88C22×D11—41no—
89Q8×C11—44no—
90Q8×C11—82no—
91Q8×C11—84no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—24no—
98C2×C4×C11—24no—
99C2×C4×C11—22no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—41no—
107C2×C4×C11C2×SD1611yescharacteristic
108C2×C4×C11#13711yescharacteristic
109C22⋊D11—81no—
110C22⋊D11—81no—
111C2×Dic11—41no—
112D44—41no—
113D44—41no—
114D44—82no—
115C4×D11—81no—
116C4×D11—81no—
117Dic22—41no—
118Dic22—41no—
119C11⋊C8—81no—
120C11⋊C8—82no—
121#537—111no—
122C2×C4⋊Q8—22no—
123#448—222no—
124C2×#104—221no—
125#417—221no—
126#395—21no—
127#395C2×D1112yes—
128#389—22no—
129#384C2×D1111yescharacteristic
130C4×C4⋊C4—21no—
131#343—111no—
132#327—222no—
133#324—112no—
134C22×C11—21no—
135C22×C11—21no—
136C22×C11#44811yescharacteristic
137C22×C11#45411yescharacteristic
138C22×C11B(4,𝔽2)11yescharacteristic
139C2×D11—81no—
140C2×D11—81no—
141C2×D11—81no—
142C4×C11—24no—
143C4×C11—21no—
144C4×C11—21no—
145C4×C11—44no—
146C4×C11—44no—
147C4×C11—42no—
148C4×C11—81no—
149Dic11—81no—
150C2×#41—221no—
151C22×Q8—21no—
152C22×Q8C22⋊D1112yes—
153C2×SD16—442no—
154C2×M16—221no—
155C4⋊Q8—48no—
156C22⋊Q8—441no—
157#121—222no—
158#121—441no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4C22⋊D1111yescharacteristic
165C2×C4⋊C4C22×D1111yescharacteristic
166C2×C42—22no—
167C2×C42C22⋊D1111yescharacteristic
168#104—442no—
169#103—441no—
170#103—442no—
171#102—441no—
172C22⋊C8—222no—
173#95—21no—
174#95—22no—
175#95C22⋊D1112yes—
176C2×C11—21no—
177C2×C11—21no—
178C2×C11#159911yescharacteristic
179C2×C11#219611yescharacteristic
180C2×C11#220511yescharacteristic
181D11—161no—
182#41—441no—
183#41—441no—
184#41—441no—
185#41—441no—
186C2×Q8—44no—
187C2×Q8—44no—
188C2×Q8—42no—
189C2×Q8—81no—
190C2×Q8—221no—
191C2×D4—221no—
192C2×D4—222no—
193C2×D4—441no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—21no—
198C22×C4—441no—
199C22×C4C2×C22⋊D1111yescharacteristic
200C22×C4C2×C22⋊D1112yes—
201SD16—884no—
202M16—441no—
203M16—441no—
204C2×C8—442no—
205C2×C8—441no—
206C4⋊C4—24no—
207C4⋊C4—24no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—44no—
211C4⋊C4—44no—
212C4⋊C4—44no—
213C4⋊C4—222no—
214C22⋊C4—442no—
215C42—21no—
216C42—44no—
217C42#432512yescomplemented
218C11#1218011yescharacteristic, complemented, Sylow
219C23—441no—
220C23#6700611yescharacteristic
221Q8—44no—
222Q8—82no—
223Q8—84no—
224Q8—441no—
225Q8—441no—
226D4—441no—
227D4—441no—
228D4—882no—
229D4—881no—
230D4—881no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—24no—
237C2×C4—24no—
238C2×C4—22no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—441no—
247C2×C4—881no—
248C2×C4—881no—
249C2×C4C2×#432511yescharacteristic
250C2×C4#6699511yescharacteristic
251C8—881no—
252C8—882no—
253C22—21no—
254C22—21no—
255C22—881no—
256C22—881no—
257C22—881no—
258C22#1062284011yescharacteristic
259C22#1062285711yescharacteristic
260C22#1062285811yescharacteristic
261C4—24no—
262C4—21no—
263C4—21no—
264C4—44no—
265C4—42no—
266C4—44no—
267C4—81no—
268C4—881no—
269C2—21no—
270C2—21no—
271C2—1761no—
272C2#1306755611yescharacteristic
273C2#1307060011yescharacteristic
274C2#1307064611yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2551C2
socleC22×C11B(4,𝔽2)
prime radical#10623041C22
hypercenter#2551D11
hypocenterC11#12180
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2551

Complements

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

NH ≅ G/Ntype
3. #13066646C2semidirect
4. #13066562C2semidirect
5. C11×#2551C2semidirect
74. C42×C11SD16semidirect
82. #2551D11semidirect
217. C42#4325semidirect
218. C11#12180semidirect

Maximal subgroups

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

subgroupindex
#130698402
#130675842
#130666462
#130665622
C11×#25512
#1218011