Finite Group Databasebeta

← #14644143

Subgroups — #14644143

Order 2816.

942 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 942 conjugacy classes of subgroups — too many to draw. Only its 155 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
1D11×#407C212yesmaximal
2D11×#381C211yesmaximal, characteristic
3#13066525C212yesmaximal, complemented
4#13066524C211yesmaximal, characteristic, complemented
5C11×#1306C211yesmaximal, characteristic, complemented
6C23×C4×D11C2211yescharacteristic
7C2×M16×D11—22no—
8C2×C22⋊C4×D11C412yes—
9C11×#407C2212yes—
10C11×#381C2211yescharacteristic
11#10622824C2211yescharacteristic
12#10622820C2212yes—
13#10622739—22no—
14#10622556C412yes—
15#10622339—22no—
16#10622339C414yescomplemented
17D11×C22⋊C8—22no—
18D11×C22⋊C8C414yescomplemented
19#10622277—22no—
20D11×#95—22no—
21C24×D11C2×C411yescharacteristic
22C23×C4×C11C2311yescharacteristic
23C23×Dic11C2×C411yescharacteristic
24C22×C4×D11—22no—
25C22×C4×D11—44no—
26C22×C4×D11C2×C412yes—
27C22×C4×D11C2×C412yes—
28C22×C4×D11D412yes—
29C22×C4×D11D412yes—
30C22×C4×D11D412yes—
31C22×C4×D11Q812yes—
32C2×C11×M16—22no—
33C2×C11×C22⋊C4C2×C412yes—
34C2×C22⋊Dic11C2×C412yes—
35C2×(C2×D11)⋊C4—22no—
36C2×#4318—22no—
37M16×D11—48no—
38C2×#4313—24no—
39C2×C8×D11—24no—
40C22⋊C4×D11—44no—
41C11×C22⋊C8—22no—
42C11×C22⋊C8C2×C414yescomplemented
43C11×#95—22no—
44C11⋊#95—22no—
45C11⋊#95—24no—
46C22⋊(C11⋊C8)—22no—
47C22⋊(C11⋊C8)C2×C414yescomplemented
48(C2×D11)⋊C8—24no—
49(C2×D11)⋊C8—24no—
50#8114—111nomaximal, Sylow
51C24×C11C22×C411yescharacteristic
52C23×D11—24no—
53C23×D11—44no—
54C23×D11C4212yes—
55C23×D11C22⋊C411yescharacteristic
56C23×D11C22⋊C411yescharacteristic
57C23×D11C4⋊C412yes—
58C22×C4×C11—22no—
59C22×C4×C11—42no—
60C22×C4×C11C22×C412yes—
61C22×C4×C11C2×D412yes—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×Q811yescharacteristic
64C22×Dic11—22no—
65C22×Dic11—42no—
66C22×Dic11C4211yescharacteristic
67C22×Dic11C4211yescharacteristic
68C22×Dic11C22⋊C412yes—
69C22×Dic11C4⋊C412yes—
70C2×C4×D11—28no—
71C2×C4×D11—44no—
72C2×C4×D11—44no—
73C2×C4×D11—44no—
74C2×C4×D11—44no—
75C2×C4×D11—44no—
76C2×C4×D11—44no—
77C2×C4×D11—48no—
78C2×C4×D11C22⋊C412yes—
79C2×C4×D11C22⋊C412yes—
80C2×C4×D11C22⋊C412yes—
81C2×C4×D11C22⋊C412yes—
82C2×C4×D11C4⋊C412yes—
83C2×C4×D11C4⋊C412yes—
84C2×C4×D11C4⋊C412yes—
85C2×C4×D11C4⋊C412yes—
86C11×M16—44no—
87C2×C8×C11—24no—
88C11×C22⋊C4—42no—
89C22⋊Dic11—42no—
90(C2×D11)⋊C4—44no—
91#4318—44no—
92C2×C11⋊C8—24no—
93#4313—48no—
94C8×D11—48no—
95C2×#407—112no—
96C2×#381—111no—
97#1306—112no—
98#1306—111no—
99#1306D1111yescharacteristic, complemented
100C23×C11—22no—
101C23×C11—42no—
102C23×C11C2×C4211yescharacteristic
103C23×C11C2×C22⋊C411yescharacteristic
104C23×C11C2×C4⋊C411yescharacteristic
105C22×D11—22no—
106C22×D11—24no—
107C22×D11—24no—
108C22×D11—24no—
109C22×D11—24no—
110C22×D11—24no—
111C22×D11—42no—
112C22×D11—42no—
113C22×D11—42no—
114C22×D11—416no—
115C22×D11#9512yes—
116C22×D11#9512yes—
117C22×D11#9914yes—
118C2×C4×C11—24no—
119C2×C4×C11—42no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—44no—
123C2×C4×C11—42no—
124C2×C4×C11C2×C22⋊C412yes—
125C2×C4×C11C2×C4⋊C412yes—
126C2×Dic11—24no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—42no—
130C2×Dic11—44no—
131C2×Dic11—42no—
132C2×Dic11#9512yes—
133C2×Dic11#9512yes—
134C4×D11—24no—
135C4×D11—24no—
136C4×D11—24no—
137C4×D11—24no—
138C4×D11—42no—
139C4×D11—42no—
140C4×D11—42no—
141C4×D11—42no—
142C4×D11—88no—
143C8×C11—44no—
144C11⋊C8—44no—
145C24×C4—111no—
146C22×M16—222no—
147C22×C22⋊C4—112no—
148#407—112no—
149#407—114no—
150#407—222no—
151#407—222no—
152#407C2×D1112yes—
153C2×C22⋊C8—114no—
154C2×C22⋊C8—222no—
155#381—111no—
156#381—112no—
157#381—222no—
158#381C2×D1111yescharacteristic
159C2×#95—222no—
160C22×C11—22no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—22no—
164C22×C11—22no—
165C22×C11—44no—
166C22×C11C2×#9511yescharacteristic
167C22×C11C2×#9912yes—
168C2×D11—28no—
169C2×D11—22no—
170C2×D11—22no—
171C2×D11—22no—
172C2×D11—22no—
173C2×D11—44no—
174C2×D11—48no—
175C2×D11—48no—
176C2×D11#34214yes—
177C2×D11#34414yes—
178C4×C11—22no—
179C4×C11—22no—
180C4×C11—82no—
181Dic11—22no—
182Dic11—22no—
183Dic11—82no—
184C25—111no—
185C23×C4—111no—
186C23×C4—112no—
187C23×C4—112no—
188C23×C4—112no—
189C23×C4—112no—
190C23×C4—112no—
191C23×C4—112no—
192C23×C4—222no—
193C23×C4—444no—
194C23×C4C22×D1111yescharacteristic
195C2×M16—22no—
196C2×M16—224no—
197C2×M16—222no—
198C2×M16—448no—
199C22×C8—224no—
200C2×C22⋊C4—112no—
201C2×C22⋊C4—222no—
202C2×C22⋊C4—444no—
203C2×C22⋊C4C4×D1112yes—
204C22⋊C8—22no—
205C22⋊C8—114no—
206C22⋊C8—224no—
207C22⋊C8—224no—
208C22⋊C8—222no—
209C22⋊C8C4×D1114yescomplemented
210#95—22no—
211#95—224no—
212#95—222no—
213C2×C11—22no—
214C2×C11—41no—
215C2×C11—41no—
216C2×C11C2×#34211yescharacteristic
217C2×C11C2×#34412yes—
218D11—24no—
219D11—24no—
220C24—111no—
221C24—111no—
222C24—112no—
223C24—112no—
224C24—224no—
225C24—444no—
226C24C2×C4×D1111yescharacteristic
227C22×C4—22no—
228C22×C4—42no—
229C22×C4—112no—
230C22×C4—111no—
231C22×C4—111no—
232C22×C4—112no—
233C22×C4—112no—
234C22×C4—112no—
235C22×C4—112no—
236C22×C4—112no—
237C22×C4—112no—
238C22×C4—112no—
239C22×C4—112no—
240C22×C4—112no—
241C22×C4—228no—
242C22×C4—222no—
243C22×C4—444no—
244C22×C4—444no—
245C22×C4—444no—
246C22×C4—444no—
247C22×C4—444no—
248C22×C4—444no—
249C22×C4—448no—
250C22×C4—442no—
251C22×C4C2×C4×D1112yes—
252C22×C4D4×D1112yes—
253C22×C4D4×D1111yescharacteristic
254C22×C4Q8×D1111yescharacteristic
255M16—44no—
256M16—448no—
257M16—444no—
258C2×C8—24no—
259C2×C8—224no—
260C2×C8—448no—
261C22⋊C4—42no—
262C22⋊C4—444no—
263C22⋊C4—442no—
264C11#811411yescharacteristic, complemented, Sylow
265C23—22no—
266C23—42no—
267C23—112no—
268C23—112no—
269C23—114no—
270C23—224no—
271C23—224no—
272C23—224no—
273C23—224no—
274C23—224no—
275C23—222no—
276C23—442no—
277C23—442no—
278C23—442no—
279C23—4416no—
280C23C42×D1111yescharacteristic
281C23C22⋊C4×D1111yescharacteristic
282C23C4⋊C4×D1111yescharacteristic
283C2×C4—24no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—44no—
288C2×C4—42no—
289C2×C4—112no—
290C2×C4—112no—
291C2×C4—224no—
292C2×C4—224no—
293C2×C4—224no—
294C2×C4—224no—
295C2×C4—224no—
296C2×C4—442no—
297C2×C4—442no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—442no—
303C2×C4—444no—
304C2×C4—442no—
305C2×C4—888no—
306C2×C4C22⋊C4×D1112yes—
307C2×C4C4⋊C4×D1112yes—
308C8—44no—
309C8—444no—
310C22—22no—
311C22—21no—
312C22—21no—
313C22—22no—
314C22—22no—
315C22—44no—
316C22—114no—
317C22—114no—
318C22—228no—
319C22—222no—
320C22—222no—
321C22—222no—
322C22—222no—
323C22—444no—
324C22—448no—
325C22—448no—
326C22D11×#9511yescharacteristic
327C22D11×#9912yes—
328C4—22no—
329C4—22no—
330C4—82no—
331C4—222no—
332C4—222no—
333C4—882no—
334C2—22no—
335C2—41no—
336C2—41no—
337C2—224no—
338C2—224no—
339C2D11×#34211yescharacteristic
340C2D11×#34412yes—
subgroupG/H
centerC22D11×#95
commutatorC23×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#1306C2
socleC22×C11C2×#95
prime radicalC24×D11C2×C4
cosocleC23×C4×C11C23
hypercenter#1306D11
hypocenterC11#8114
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
3. #13066525C2semidirect
4. #13066524C2semidirect
5. C11×#1306C2semidirect
16. #10622339C4semidirect
18. D11×C22⋊C8C4semidirect
42. C11×C22⋊C8C2×C4semidirect
47. C22⋊(C11⋊C8)C2×C4semidirect
99. #1306D11semidirect
209. C22⋊C8C4×D11semidirect
264. C11#8114semidirect

Maximal subgroups

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

subgroupindex
D11×#4072
D11×#3812
#130665252
#130665242
C11×#13062
#811411