Finite Group Databasebeta

← #14651448

Subgroups — #14651448

Order 2816.

424 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 107 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#13077701C211yesmaximal, characteristic
2#13067243C212yesmaximal
3#13066960C211yesmaximal, characteristic
4#13066472C212yesmaximal
5C11×#2565C211yesmaximal, characteristic
6C2×C11×#125C2211yescharacteristic
7C2×C4×Q8×C11C2211yescharacteristic
8C11×#398—21no—
9C11×#398—21no—
10C11×#391C411yescharacteristic
11C11×#391C411yescharacteristic
12C11×#387—21no—
13C11×#387—21no—
14C11×#384C411yescharacteristic
15C11×#382C411yescharacteristic
16C4×C11×C4⋊C4C2211yescharacteristic
17#10622637—24no—
18#10622539—21no—
19#10622539C2212yes—
20#10622539C2212yes—
21#10622538—21no—
22#10622181—24no—
23#10622166—21no—
24#10622166—21no—
25C22×Q8×C11C2×C411yescharacteristic
26C11×#125—22no—
27C11×#125—22no—
28C4×Q8×C11—22no—
29C4×Q8×C11—22no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C42×C11C2×C411yescharacteristic
41C2×C42×C11C2×C411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×C42×C11D411yescharacteristic
44C2×C42×C11C2311yescharacteristic
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C22⋊(C11⋊C8)—22no—
53C22⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)—22no—
55C4⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)—22no—
57C4⋊(C11⋊C8)—22no—
58#66867—22no—
59#66867—22no—
60#66867D414yes—
61C4×C11⋊C8—22no—
62#9450—111nomaximal, Sylow
63C2×Q8×C11—22no—
64C2×Q8×C11—22no—
65C2×Q8×C11—41no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C11×C4⋊C4—22no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—42no—
84C11×C4⋊C4—42no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—42no—
87C11×C4⋊C4—41no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—21no—
92C42×C11—41no—
93C42×C11—41no—
94C42×C11C2×D412yes—
95C42×C11#4112yes—
96C2×C11⋊C8—24no—
97C2×C11⋊C8—42no—
98#2983—111no—
99#2565D1111yescharacteristic
100#1534—112no—
101#1467—111no—
102#1285—112no—
103C23×C11C2×C22⋊C411yescharacteristic
104Q8×C11—44no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—22no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—42no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11#10112yes—
130C2×C4×C11C4×D412yes—
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12112yes—
133C2×C4×C11#12311yescharacteristic
134C11⋊C8—44no—
135C11⋊C8—82no—
136C2×#125C2×D1111yescharacteristic
137C2×C4×Q8C2×D1111yescharacteristic
138#446—224no—
139#432—112no—
140#432—112no—
141#432—221no—
142#431—221no—
143#398—21no—
144#398—21no—
145#391Dic1111yescharacteristic
146#391Dic1111yescharacteristic
147#387—21no—
148#387—21no—
149#384Dic1111yescharacteristic
150#382Dic1111yescharacteristic
151C4×C4⋊C4C2×D1111yescharacteristic
152#330—224no—
153#324—221no—
154#324—221no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11#38611yescharacteristic
158C22×C11C2×#10111yescharacteristic
159C22×C11#41311yescharacteristic
160C4×C11—22no—
161C4×C11—22no—
162C4×C11—22no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—42no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—81no—
170C4×C11—81no—
171C4×C11—81no—
172C22×Q8C2×Dic1111yescharacteristic
173#125—22no—
174#125—22no—
175C4×Q8—22no—
176C4×Q8—22no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4C2×Dic1111yescharacteristic
183C2×C4⋊C4C2×Dic1111yescharacteristic
184C2×C4⋊C4C2×Dic1111yescharacteristic
185C2×C4⋊C4C22⋊D1111yescharacteristic
186C2×C4⋊C4C22⋊D1111yescharacteristic
187C2×C42C2×Dic1111yescharacteristic
188C2×C42C2×Dic1111yescharacteristic
189C2×C42C22⋊D1111yescharacteristic
190C2×C42C22⋊D1111yescharacteristic
191C2×C42C22×D1111yescharacteristic
192C4⋊C8—222no—
193C4⋊C8—222no—
194C4⋊C8—222no—
195C4⋊C8—222no—
196C22⋊C8—222no—
197C22⋊C8—222no—
198#97—114no—
199#97—222no—
200#97—222no—
201C4×C8—222no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209C2×C11—21no—
210C2×C11—21no—
211C2×C11#188411yescharacteristic
212C2×C11#190111yescharacteristic
213C2×C11#191211yescharacteristic
214C2×Q8—22no—
215C2×Q8—22no—
216C2×Q8—41no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4C22⋊Dic1111yescharacteristic
222C22×C4C22⋊Dic1111yescharacteristic
223C22×C4C22⋊Dic1111yescharacteristic
224C22×C4C22⋊Dic1111yescharacteristic
225C22×C4C22×Dic1111yescharacteristic
226C22×C4C2×C22⋊D1111yescharacteristic
227C22×C4C2×C22⋊D1111yescharacteristic
228C2×C8—224no—
229C2×C8—442no—
230C4⋊C4—22no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—41no—
246C42—41no—
247C42D4×D1112yes—
248C42#434112yes—
249C11#945011yescharacteristic, complemented, Sylow
250C23C2×C22⋊Dic1111yescharacteristic
251Q8—44no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4#6690012yes—
277C2×C4D4×Dic1112yes—
278C2×C4#6698811yescharacteristic
279C2×C4#6699011yescharacteristic
280C2×C4#6699212yes—
281C8—444no—
282C8—882no—
283C22—21no—
284C22—21no—
285C22#1062283311yescharacteristic
286C22C2×#6690011yescharacteristic
287C22#1062285011yescharacteristic
288C4—22no—
289C4—22no—
290C4—21no—
291C4—21no—
292C4—22no—
293C4—42no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—81no—
298C4—81no—
299C4—81no—
300C2—21no—
301C2—21no—
302C2#1306900011yescharacteristic
303C2#1306908511yescharacteristic
304C2#1306915411yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2565C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2565D11
hypocenterC11#9450
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2565

Complements

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

NH ≅ G/Ntype
249. C11#9450semidirect

Maximal subgroups

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

subgroupindex
#130777012
#130672432
#130669602
#130664722
C11×#25652
#945011