Finite Group Databasebeta

← #14722349

Subgroups — #14722349

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic
2#13077244C212yesmaximal
3#13067352C214yesmaximal, complemented
4#13067331C214yesmaximal, complemented
5#13067281C211yesmaximal, characteristic, complemented
6#13067280C212yesmaximal, complemented
7C11×#1544C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9#10623259C2212yes—
10D11×C4⋊Q8C2212yes—
11#10623219C412yes—
12D11×#125C412yes—
13D11×C22⋊Q8—22no—
14#10623153—22no—
15#10623109—22no—
16C4×Q8×D11—22no—
17D11×#117C412yes—
18#10623048C412yes—
19C2×C42×D11C2211yescharacteristic
20#10623001C2211yescharacteristic
21C11×#431C2212yes—
22#10622538C2212yes—
23#10622450C2214yes—
24#10622448C2214yes—
25#10622339—22no—
26#10622332—22no—
27C4×#4313—22no—
28#10622298—22no—
29C11×#332C2214yescomplemented
30#10622185C2214yescomplemented
31#10622124C2214yescomplemented
32#10622120C2214yescomplemented
33C2×Q8×D11—22no—
34C22×C4×D11C2×C411yescharacteristic
35C22×C4×D11D412yes—
36C11×C4⋊Q8C2312yes—
37C11×#125C2×C412yes—
38C11×C22⋊Q8—22no—
39C4×Q8×C11—22no—
40C11×#117C2×C412yes—
41C2×C42×C11C2311yescharacteristic
42#66999—22no—
43Q8×Dic11—22no—
44#66997—22no—
45#66979C2×C412yes—
46#66977—22no—
47C2×C4×Dic11C2×C411yescharacteristic
48C2×C4×Dic11D412yes—
49C2×#4313—24no—
50#66950—22no—
51#66949—24no—
52#66945C2×C414yes—
53C4⋊C4×D11—24no—
54C4⋊C4×D11—22no—
55C4⋊C4×D11C2×C414yes—
56#66943C2×C414yes—
57#66942—24no—
58#66941—22no—
59#66941C2×C414yes—
60#66940—24no—
61#66940—22no—
62C22⋊C4×D11—22no—
63#66931—24no—
64#66930—22no—
65#66925—22no—
66C42×D11—22no—
67C42×D11C2×C411yescharacteristic
68C42×D11C2×C411yescharacteristic
69C42×D11D412yes—
70C42×D11D412yes—
71C42×D11C2311yescharacteristic
72C42×D11C2311yescharacteristic
73#66923C2×C412yes—
74#66922C2312yes—
75C4×Dic22—22no—
76C4×Dic22—24no—
77C11×C4⋊C8C2314yes—
78C11×C22⋊C8—22no—
79C4×C8×C11—22no—
80C22⋊(C11⋊C8)—22no—
81(C2×D11)⋊C8—24no—
82#66879—24no—
83Dic11⋊C8—24no—
84C4⋊(C11⋊C8)C2314yes—
85C4×C11⋊C8—22no—
86#17739—111nomaximal, Sylow
87C23×D11C22⋊C411yescharacteristic
88C2×Q8×C11—22no—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C2×D412yes—
91C22×Dic11C22⋊C411yescharacteristic
92C22×Dic11C22⋊C412yes—
93Q8×D11—48no—
94C2×C4×D11—24no—
95C2×C4×D11—24no—
96C2×C4×D11—44no—
97C2×C4×D11C22⋊C411yescharacteristic
98C2×C4×D11C22⋊C412yes—
99C2×C4×D11C22⋊C412yes—
100C2×C4×D11C22⋊C411yescharacteristic
101C2×C4×D11C22×C411yescharacteristic
102C2×C4×D11C22×C411yescharacteristic
103C2×C4×D11C2×D412yes—
104C2×C4×D11C2×D412yes—
105C2×Dic22—24no—
106C2×Dic22—22no—
107C2×C8×C11—24no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4C22×C414yes—
111C11×C22⋊C4—22no—
112C42×C11—22no—
113C42×C11C22×C411yescharacteristic
114C42×C11C2×D412yes—
115C42×C11C2411yescharacteristic
116C22⋊Dic11—22no—
117(C2×D11)⋊C4—24no—
118C4⋊Dic11—24no—
119C4⋊Dic11—22no—
120C4⋊Dic11C22×C414yes—
121Dic11⋊C4—24no—
122Dic11⋊C4—24no—
123Dic11⋊C4—24no—
124Dic11⋊C4—24no—
125C4×Dic11—24no—
126C4×Dic11—22no—
127C4×Dic11C22⋊C412yes—
128C4×Dic11C22⋊C412yes—
129C4×Dic11C22⋊C412yes—
130C4×Dic11C22×C411yescharacteristic
131C4×Dic11C22×C411yescharacteristic
132C4×Dic11C2×D412yes—
133C4×Dic11C2×D412yes—
134C2×C11⋊C8—24no—
135#4313—48no—
136C2×#533—111no—
137#2920—112no—
138#1561—114no—
139#1556—114no—
140#1544—112no—
141#1544—111no—
142#1544D1111yescharacteristic, complemented
143C23×C11C2×C22⋊C411yescharacteristic
144C22×D11—22no—
145C22×D11—42no—
146C22×D11C2×C22⋊C411yescharacteristic
147C22×D11C2×C22⋊C411yescharacteristic
148Q8×C11—44no—
149C2×C4×C11—24no—
150C2×C4×C11—22no—
151C2×C4×C11—24no—
152C2×C4×C11C2×C22⋊C412yes—
153C2×C4×C11C2×C22⋊C411yescharacteristic
154C2×C4×C11C23×C411yescharacteristic
155C2×C4×C11C22×D412yes—
156C2×Dic11—22no—
157C2×Dic11—24no—
158C2×Dic11—42no—
159C2×Dic11C2×C22⋊C412yes—
160C2×Dic11C2×C22⋊C412yes—
161C2×Dic11C2×C22⋊C411yescharacteristic
162C2×Dic11C2×C22⋊C411yescharacteristic
163C4×D11—22no—
164C4×D11—24no—
165C4×D11—24no—
166C4×D11—22no—
167C4×D11—22no—
168C4×D11—42no—
169C4×D11—42no—
170C4×D11—48no—
171C4×D11#10114yes—
172Dic22—48no—
173Dic22—44no—
174C8×C11—44no—
175C11⋊C8—44no—
176#533—112no—
177#533—112no—
178#533—112no—
179#533—111no—
180#533—222no—
181#533—222no—
182#533C2×D1111yescharacteristic
183C2×C4⋊Q8—112no—
184C2×#125—112no—
185C2×C22⋊Q8—222no—
186C2×C4×Q8—222no—
187C2×#117—112no—
188C22×C42—111no—
189#432—114no—
190#432—222no—
191#431—112no—
192#431—222no—
193#431C2×D1112yes—
194#423—114no—
195#407—222no—
196C4×M16—222no—
197#332—114no—
198#332—114no—
199#332—114no—
200#332C2×D1114yescomplemented
201C22×C11—21no—
202C22×C11—22no—
203C22×C11C22×C22⋊C411yescharacteristic
204C2×D11—22no—
205C2×D11—21no—
206C2×D11—22no—
207C2×D11—44no—
208C2×D11C2×#10112yes—
209C4×C11—21no—
210C4×C11—22no—
211C4×C11—44no—
212C4×C11C2×#10112yes—
213C4×C11#57514yes—
214Dic11—21no—
215Dic11—22no—
216Dic11—22no—
217Dic11—44no—
218Dic11C2×#10112yes—
219C22×Q8—222no—
220C23×C4—111no—
221C23×C4—112no—
222C2×M16—224no—
223C4⋊Q8—114no—
224C4⋊Q8—112no—
225C4⋊Q8—222no—
226C4⋊Q8—222no—
227C4⋊Q8C22×D1112yes—
228#125—114no—
229#125—112no—
230#125—224no—
231#125C4×D1112yes—
232C22⋊Q8—22no—
233C22⋊Q8—224no—
234C22⋊Q8—224no—
235C22⋊Q8—222no—
236C22⋊Q8—222no—
237C22⋊Q8—222no—
238C4×Q8—22no—
239C4×Q8—224no—
240C4×Q8—224no—
241C4×Q8—222no—
242C4×Q8—222no—
243C4×Q8—222no—
244#117—112no—
245#117—114no—
246#117—222no—
247#117—222no—
248#117C4×D1112yes—
249C2×C4⋊C4—114no—
250C2×C4⋊C4—224no—
251C2×C4⋊C4—222no—
252C2×C22⋊C4—222no—
253C2×C42—111no—
254C2×C42—112no—
255C2×C42—111no—
256C2×C42—111no—
257C2×C42—112no—
258C2×C42—112no—
259C2×C42—111no—
260C2×C42—111no—
261C2×C42—222no—
262C2×C42C22×D1111yescharacteristic
263C4⋊C8—114no—
264C4⋊C8—224no—
265C4⋊C8C22×D1114yes—
266C22⋊C8—22no—
267C22⋊C8—224no—
268C22⋊C8—222no—
269#97—224no—
270C4×C8—22no—
271C4×C8—222no—
272C2×C11—41no—
273C2×C11C22×#10111yescharacteristic
274C2×C11#289612yes—
275D11—22no—
276D11—41no—
277C24—111no—
278C2×Q8—22no—
279C2×Q8—224no—
280C2×Q8—222no—
281C2×Q8—448no—
282C22×C4—111no—
283C22×C4—111no—
284C22×C4—112no—
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—112no—
289C22×C4—112no—
290C22×C4—112no—
291C22×C4—112no—
292C22×C4—224no—
293C22×C4—224no—
294C22×C4—444no—
295C22×C4C2×C4×D1111yescharacteristic
296C22×C4D4×D1112yes—
297M16—448no—
298C2×C8—24no—
299C2×C8—224no—
300C4⋊C4—24no—
301C4⋊C4—22no—
302C4⋊C4—114no—
303C4⋊C4—224no—
304C4⋊C4—224no—
305C4⋊C4—224no—
306C4⋊C4—224no—
307C4⋊C4—224no—
308C4⋊C4—222no—
309C4⋊C4C2×C4×D1114yes—
310C22⋊C4—22no—
311C22⋊C4—224no—
312C22⋊C4—222no—
313C42—22no—
314C42—112no—
315C42—112no—
316C42—112no—
317C42—111no—
318C42—111no—
319C42—112no—
320C42—112no—
321C42—224no—
322C42—222no—
323C42C2×C4×D1111yescharacteristic
324C42D4×D1112yes—
325C42C23×D1111yescharacteristic
326C11#1773911yescharacteristic, complemented, Sylow
327C23—111no—
328C23—111no—
329C23—222no—
330C23—442no—
331C23C22⋊C4×D1111yescharacteristic
332Q8—44no—
333Q8—448no—
334Q8—444no—
335C2×C4—24no—
336C2×C4—22no—
337C2×C4—24no—
338C2×C4—111no—
339C2×C4—114no—
340C2×C4—111no—
341C2×C4—112no—
342C2×C4—112no—
343C2×C4—222no—
344C2×C4—222no—
345C2×C4—222no—
346C2×C4—224no—
347C2×C4—224no—
348C2×C4—222no—
349C2×C4—224no—
350C2×C4—442no—
351C2×C4—442no—
352C2×C4—448no—
353C2×C4—442no—
354C2×C4C22⋊C4×D1112yes—
355C2×C4C22⋊C4×D1111yescharacteristic
356C2×C4C22×C4×D1111yescharacteristic
357C2×C4C2×D4×D1112yes—
358C8—44no—
359C8—444no—
360C22—21no—
361C22—22no—
362C22—112no—
363C22—222no—
364C22—221no—
365C22—222no—
366C22—444no—
367C22C2×C22⋊C4×D1111yescharacteristic
368C4—21no—
369C4—22no—
370C4—44no—
371C4—112no—
372C4—221no—
373C4—222no—
374C4—222no—
375C4—444no—
376C4D11×#10112yes—
377C4#1062329914yes—
378C2—41no—
379C2—222no—
380C2—441no—
381C2C2×D11×#10111yescharacteristic
382C2#1307713112yes—
subgroupG/H
centerC2×C4C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1544C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1544D11
hypocenterC11#17739
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1544

Complements

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

NH ≅ G/Ntype
3. #13067352C2semidirect
4. #13067331C2semidirect
5. #13067281C2semidirect
6. #13067280C2semidirect
7. C11×#1544C2semidirect
29. C11×#332C22semidirect
30. #10622185C22semidirect
31. #10622124C22semidirect
32. #10622120C22semidirect
142. #1544D11semidirect
200. #332C2×D11semidirect
326. C11#17739semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
#130772442
#130673522
#130673312
#130672812
#130672802
C11×#15442
#1773911