Finite Group Databasebeta

← #14763246

Subgroups — #14763246

Order 2816.

914 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C211yesmaximal, characteristic
2#13077254C211yesmaximal, characteristic
3#13069609C212yesmaximal, complemented
4#13069608C212yesmaximal, complemented
5#13069605C212yesmaximal, complemented
6#13069604C212yesmaximal, complemented
7#13068697C212yesmaximal
8#13068694C212yesmaximal
9C11×#2921C211yesmaximal, characteristic
10C2×C11×#117C2211yescharacteristic
11C2×#66979C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13#10623050—24no—
14#10623050—24no—
15C2×#66943C412yes—
16C2×#66941C412yes—
17C2×#66931C412yes—
18C2×#66931C412yes—
19C2×#66923C2211yescharacteristic
20C2×#66923C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C11×#433—24no—
24C11×#423C2212yes—
25C11×#407C2212yes—
26C4×C11×M16C2212yes—
27#10622820C2212yes—
28#10622613—24no—
29#10622537C2212yes—
30C4×#4318C2212yes—
31#10622192C2214yes—
32#10622192C2214yes—
33#10622192C2214yes—
34#10622192C2214yes—
35C23×C4×C11C2311yescharacteristic
36C23×Dic11C2×C412yes—
37C22×Dic22C2×C412yes—
38C22×Dic22C2×C412yes—
39C2×C11×M16C2314yes—
40C11×#117D414yes—
41C11×#117D414yes—
42C2×C11×C4⋊C4C2×C411yescharacteristic
43C2×C11×C4⋊C4C2×C411yescharacteristic
44C2×C11×C22⋊C4C2×C411yescharacteristic
45C2×C11×C22⋊C4C2×C411yescharacteristic
46C2×C42×C11C2311yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C2×C22⋊Dic11C2×C412yes—
49#66979—22no—
50#66979—22no—
51C2×C4⋊Dic11—22no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11C2×C412yes—
54C2×C4⋊Dic11C2×C412yes—
55C2×C4⋊Dic11C2×C412yes—
56C2×C4⋊Dic11C2311yescharacteristic
57C2×C4⋊Dic11C2311yescharacteristic
58C2×C4⋊Dic11C2311yescharacteristic
59C2×C4⋊Dic11C2311yescharacteristic
60C2×Dic11⋊C4C2×C412yes—
61C2×Dic11⋊C4C2×C412yes—
62C2×Dic11⋊C4C2×C412yes—
63C2×Dic11⋊C4C2×C412yes—
64C2×C4×Dic11C2×C412yes—
65C2×#4318C2314yes—
66#66943—28no—
67#66941—28no—
68#66931—28no—
69#66931—28no—
70#66923—22no—
71#66923—22no—
72#66923—22no—
73#66923—22no—
74#66922—22no—
75#66922—22no—
76#66922—22no—
77#66922—22no—
78C11×C4⋊C8—24no—
79C11×C22⋊C8—24no—
80C11×#97—22no—
81C4×C8×C11—22no—
82C22⋊(C11⋊C8)—24no—
83C4⋊(C11⋊C8)—24no—
84#66867—22no—
85C4×C11⋊C8—22no—
86#21832—111nomaximal, Sylow
87C24×C11C22×C411yescharacteristic
88C22×C4×C11—24no—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2411yescharacteristic
97C22×Dic11—24no—
98C22×Dic11—82no—
99C22×Dic11C22×C412yes—
100C22×Dic11C22×C412yes—
101C22×Dic11C22×C412yes—
102C22×Dic11C22×C412yes—
103C2×Dic22—24no—
104C2×Dic22—24no—
105C2×Dic22—82no—
106C2×Dic22—82no—
107C11×M16—28no—
108C2×C8×C11—24no—
109C11×C4⋊C4C22⋊C414yes—
110C11×C4⋊C4C22⋊C414yes—
111C11×C22⋊C4C22⋊C414yes—
112C11×C22⋊C4C22⋊C414yes—
113C42×C11C2×D412yes—
114C42×C11C2×D412yes—
115C42×C11C2×D412yes—
116C42×C11C2×D412yes—
117C22⋊Dic11—24no—
118C4⋊Dic11—24no—
119C4⋊Dic11—24no—
120C4⋊Dic11—24no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129Dic11⋊C4—24no—
130Dic11⋊C4—24no—
131Dic11⋊C4—24no—
132Dic11⋊C4—24no—
133C4×Dic11—24no—
134#4318—28no—
135C2×C11⋊C8—24no—
136C2×#544—111no—
137#2921—111no—
138#2921D1111yescharacteristic
139#1998—112no—
140#1998—112no—
141#1997—112no—
142#1997—112no—
143#1822—112no—
144#1821—112no—
145C23×C11—22no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11C2×C22⋊C412yes—
149C23×C11C23×C411yescharacteristic
150C2×C4×C11—22no—
151C2×C4×C11—24no—
152C2×C4×C11—24no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11C2×C22⋊C412yes—
158C2×C4×C11C2×C22⋊C412yes—
159C2×C4×C11C2×C22⋊C412yes—
160C2×C4×C11C2×C22⋊C412yes—
161C2×C4×C11C2×C22⋊C412yes—
162C2×C4×C11C22×D411yescharacteristic
163C2×C4×C11C22×D411yescharacteristic
164C2×C4×C112−1+414yes—
165C2×Dic11—22no—
166C2×Dic11—22no—
167C2×Dic11—22no—
168C2×Dic11—22no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—84no—
174Dic22—84no—
175Dic22—84no—
176C8×C11—44no—
177C11⋊C8—44no—
178#544—224no—
179#544—224no—
180C2×C4⋊Q8—112no—
181C2×C4⋊Q8—111no—
182C2×C4⋊Q8—111no—
183C2×#125—112no—
184C2×#125—111no—
185C2×#125—111no—
186C2×C22⋊Q8—112no—
187C2×C22⋊Q8—112no—
188C2×#117—111no—
189C2×#117C2×D1111yescharacteristic
190C22×C4⋊C4—111no—
191#433—24no—
192#433—224no—
193#423—112no—
194#423C2×D1112yes—
195#407—112no—
196#407C2×D1112yes—
197C4×M16—112no—
198C4×M16C2×D1112yes—
199#343—114no—
200#343—114no—
201#343—114no—
202#343—114no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—44no—
209C22×C11C22×C22⋊C411yescharacteristic
210C22×C11#51912yes—
211C4×C11—22no—
212C4×C11—22no—
213C4×C11—22no—
214C4×C11—22no—
215C4×C11—22no—
216C4×C11#53612yes—
217C4×C11#53612yes—
218Dic11—42no—
219Dic11—42no—
220Dic11—42no—
221Dic11—42no—
222C22×Q8—112no—
223C22×Q8—112no—
224C23×C4—112no—
225C23×C4C22×D1111yescharacteristic
226C2×M16—114no—
227C2×M16C22×D1114yes—
228C4⋊Q8—228no—
229C4⋊Q8—222no—
230C4⋊Q8—222no—
231C4⋊Q8—222no—
232C4⋊Q8—222no—
233#125—228no—
234#125—222no—
235#125—222no—
236#125—222no—
237#125—222no—
238C22⋊Q8—228no—
239C22⋊Q8—228no—
240#117—222no—
241#117—222no—
242#117D4414yes—
243#117C22⋊D1114yes—
244C2×C4⋊C4—112no—
245C2×C4⋊C4—112no—
246C2×C4⋊C4—112no—
247C2×C4⋊C4—112no—
248C2×C4⋊C4—112no—
249C2×C4⋊C4—112no—
250C2×C4⋊C4—112no—
251C2×C4⋊C4—111no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4—111no—
254C2×C4⋊C4—111no—
255C2×C4⋊C4—222no—
256C2×C4⋊C4—222no—
257C2×C4⋊C4C4×D1111yescharacteristic
258C2×C4⋊C4C4×D1111yescharacteristic
259C2×C22⋊C4—112no—
260C2×C22⋊C4C4×D1111yescharacteristic
261C2×C22⋊C4C4×D1111yescharacteristic
262C2×C42—112no—
263C2×C42C22×D1111yescharacteristic
264C2×C42C22×D1111yescharacteristic
265C4⋊C8—24no—
266C4⋊C8—224no—
267C22⋊C8—24no—
268C22⋊C8—224no—
269#97—22no—
270#97—222no—
271C4×C8—22no—
272C4×C8—222no—
273C2×C11—22no—
274C2×C11—42no—
275C2×C11#231011yescharacteristic
276C2×C11#288811yescharacteristic
277C2×C11#288911yescharacteristic
278C24C2×C4×D1111yescharacteristic
279C2×Q8—224no—
280C2×Q8—224no—
281C2×Q8—882no—
282C2×Q8—882no—
283C22×C4—24no—
284C22×C4—112no—
285C22×C4—112no—
286C22×C4—112no—
287C22×C4—112no—
288C22×C4—224no—
289C22×C4—882no—
290C22×C4C2×C4×D1111yescharacteristic
291C22×C4C2×C4×D1111yescharacteristic
292C22×C4C2×C4×D1111yescharacteristic
293C22×C4C2×C4×D1111yescharacteristic
294C22×C4C2×C4×D1111yescharacteristic
295C22×C4C2×D4412yes—
296C22×C4C2×C22⋊D1112yes—
297C22×C4C23×D1111yescharacteristic
298M16—28no—
299M16—228no—
300C2×C8—24no—
301C2×C8—224no—
302C4⋊C4—224no—
303C4⋊C4—224no—
304C4⋊C4—224no—
305C4⋊C4—224no—
306C4⋊C4—224no—
307C4⋊C4—224no—
308C4⋊C4—224no—
309C4⋊C4—221no—
310C4⋊C4—221no—
311C4⋊C4—221no—
312C4⋊C4—221no—
313C4⋊C4—221no—
314C4⋊C4—221no—
315C4⋊C4—221no—
316C4⋊C4—221no—
317C4⋊C4(C2×D11)⋊C414yes—
318C4⋊C4(C2×D11)⋊C414yes—
319C22⋊C4—224no—
320C22⋊C4(C2×D11)⋊C414yes—
321C22⋊C4(C2×D11)⋊C414yes—
322C42—224no—
323C42C2×D4412yes—
324C42C2×D4412yes—
325C42C2×C22⋊D1112yes—
326C42C2×C22⋊D1112yes—
327C11#2183211yescharacteristic, complemented, Sylow
328C23—22no—
329C23—41no—
330C23—41no—
331C23C2×(C2×D11)⋊C412yes—
332C23C22×C4×D1111yescharacteristic
333Q8—884no—
334Q8—884no—
335C2×C4—22no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—222no—
343C2×C4—222no—
344C2×C4—222no—
345C2×C4—222no—
346C2×C4—442no—
347C2×C4—442no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—884no—
351C2×C4C2×(C2×D11)⋊C412yes—
352C2×C4C2×(C2×D11)⋊C412yes—
353C2×C4C2×(C2×D11)⋊C412yes—
354C2×C4C2×(C2×D11)⋊C412yes—
355C2×C4C2×(C2×D11)⋊C412yes—
356C2×C4C22×D4411yescharacteristic
357C2×C4#6704314yes—
358C2×C4C22×C22⋊D1111yescharacteristic
359C8—44no—
360C8—444no—
361C22—21no—
362C22—21no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—44no—
367C22#1062304712yes—
368C22C22×(C2×D11)⋊C411yescharacteristic
369C4—22no—
370C4—22no—
371C4—22no—
372C4—22no—
373C4—22no—
374C4—442no—
375C4—442no—
376C4—442no—
377C4—442no—
378C4#1062305712yes—
379C4#1062335612yes—
380C2—22no—
381C2—42no—
382C2#1307120011yescharacteristic
383C2#1307709411yescharacteristic
384C2#1307709811yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2921C2
socleC22×C11C22×C22⋊C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#2921D11
hypocenterC11#21832
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2921

Complements

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

NH ≅ G/Ntype
3. #13069609C2semidirect
4. #13069608C2semidirect
5. #13069605C2semidirect
6. #13069604C2semidirect
327. C11#21832semidirect

Maximal subgroups

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

subgroupindex
C2×#106230502
#130772542
#130696092
#130696082
#130696052
#130696042
#130686972
#130686942
C11×#29212
#2183211