Finite Group Databasebeta

← #14722359

Subgroups — #14722359

Order 2816.

1866 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#127C211yesmaximal, characteristic
2#13077246C212yesmaximal, complemented
3#13067330C211yesmaximal, characteristic, complemented
4#13067329C212yesmaximal, complemented
5#13067282C218yesmaximal, complemented
6C11×#1555C211yesmaximal, characteristic, complemented
7C22×D4×D11—22no—
8C22×D4×D11C412yes—
9C2×C11×#127C2211yescharacteristic
10C2×#66993—22no—
11C2×#66993C412yes—
12D11×#127—22no—
13D11×#127—22no—
14D11×#127C414yes—
15D11×#127C2214yes—
16C2×#66927C2211yescharacteristic
17C2×C42×D11C2211yescharacteristic
18C11×#432C2212yescomplemented
19#10622539C2212yescomplemented
20#10622450C2214yescomplemented
21#10622446C2214yescomplemented
22#10622339—22no—
23#10622331—22no—
24#10622320—22no—
25#10622318—22no—
26C11×#331C2214yescomplemented
27#10622182C2214yescomplemented
28#10622123C2218yescomplemented
29C24×D11—22no—
30C22×D4×C11—22no—
31C22×D4×C11C2×C412yes—
32C22×C22⋊D11—22no—
33C22×C22⋊D11—24no—
34C2×D4×D11—24no—
35C2×D4×D11—24no—
36C2×D4×D11—24no—
37C2×D4×D11—24no—
38C2×D4×D11—24no—
39C2×D4×D11—416no—
40C2×D4×D11—48no—
41C2×D4×D11C2×C418yes—
42C22×D44—22no—
43C22×D44C2×C412yes—
44C22×C4×D11C2×C411yescharacteristic
45C22×C4×D11D412yes—
46C11×#127—22no—
47C11×#127C2×C412yes—
48C11×#127C2312yes—
49C2×C42×C11C2311yescharacteristic
50#66993—22no—
51#66993—22no—
52#66993—24no—
53#66993—24no—
54#66993—24no—
55#66993—24no—
56#66993C2×C418yes—
57C2×C4×Dic11C2×C411yescharacteristic
58C2×C4×Dic11D412yes—
59C2×#4313—24no—
60#66927—22no—
61#66927C2×C412yes—
62#66927C2312yes—
63C42×D11C2×C412yes—
64C42×D11D412yes—
65C42×D11D412yes—
66C42×D11C2312yes—
67C11×C4⋊C8C2314yescomplemented
68C11×C22⋊C8—22no—
69C11×#97—22no—
70C22⋊(C11⋊C8)—22no—
71(C2×D11)⋊C8—24no—
72Dic11⋊C8—24no—
73C8×Dic11—24no—
74C4⋊(C11⋊C8)C2314yescomplemented
75#66867—22no—
76#17741—111nomaximal, Sylow
77C24×C11—22no—
78C23×D11—22no—
79C23×D11—28no—
80C23×D11—48no—
81C23×D11—416no—
82C23×D11C22⋊C411yescharacteristic
83C2×D4×C11—22no—
84C2×D4×C11—24no—
85C2×D4×C11—24no—
86C2×D4×C11—48no—
87C2×D4×C11—44no—
88C2×D4×C11C22×C414yes—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C2×D412yes—
91C2×C22⋊D11—28no—
92C2×C22⋊D11—28no—
93C2×C22⋊D11—28no—
94C2×C22⋊D11—416no—
95C2×C22⋊D11—48no—
96C22×Dic11C22⋊C412yes—
97C22×Dic11C22⋊C411yescharacteristic
98D4×D11—416no—
99D4×D11—416no—
100D4×D11—416no—
101D4×D11—416no—
102D4×D11—416no—
103D4×D11—416no—
104C2×D44—22no—
105C2×D44—24no—
106C2×D44—24no—
107C2×D44—48no—
108C2×D44—44no—
109C2×D44C22×C414yes—
110C2×C4×D11—24no—
111C2×C4×D11—28no—
112C2×C4×D11C22⋊C412yes—
113C2×C4×D11C22⋊C412yes—
114C2×C4×D11C22⋊C412yes—
115C2×C4×D11C22×C412yes—
116C2×C4×D11C2×D412yes—
117C2×C4×D11C2×D412yes—
118C2×C8×C11—24no—
119C42×C11C22×C411yescharacteristic
120C42×C11C2×D412yes—
121C42×C11C2411yescharacteristic
122C4×Dic11C22⋊C412yes—
123C4×Dic11C22⋊C412yes—
124C4×Dic11C22⋊C411yescharacteristic
125C4×Dic11C22⋊C411yescharacteristic
126C4×Dic11C22×C412yes—
127C4×Dic11C2×D412yes—
128C4×Dic11C2×D412yes—
129C2×C11⋊C8—24no—
130#4313—48no—
131C22×#127—111no—
132#2920—112no—
133#1555—112no—
134#1555—111no—
135#1555D1111yescharacteristic, complemented
136#1545—118no—
137C23×C11—24no—
138C23×C11—48no—
139C23×C11—44no—
140C23×C11C2×C22⋊C411yescharacteristic
141C22×D11—22no—
142C22×D11—24no—
143C22×D11—24no—
144C22×D11—416no—
145C22×D11—416no—
146C22×D11—48no—
147C22×D11—44no—
148C22×D11—416no—
149C22×D11—832no—
150C22×D11C2×C22⋊C412yes—
151D4×C11—44no—
152D4×C11—44no—
153D4×C11—48no—
154D4×C11—48no—
155C2×C4×C11—22no—
156C2×C4×C11—24no—
157C2×C4×C11C2×C22⋊C412yes—
158C2×C4×C11C2×C22⋊C411yescharacteristic
159C2×C4×C11C23×C411yescharacteristic
160C2×C4×C11C22×D412yes—
161C22⋊D11—416no—
162C22⋊D11—416no—
163C22⋊D11—416no—
164C2×Dic11—24no—
165C2×Dic11#10014yes—
166C2×Dic11C2×C22⋊C412yes—
167C2×Dic11C2×C22⋊C412yes—
168C2×Dic11C2×C22⋊C412yes—
169D44—44no—
170D44—44no—
171D44—48no—
172D44—48no—
173C4×D11—24no—
174C4×D11—24no—
175C4×D11—24no—
176C4×D11—24no—
177C4×D11—24no—
178C4×D11AGL(1,ℤ/8)18yes—
179C8×C11—44no—
180C11⋊C8—44no—
181C23×D4—112no—
182C23×D4—222no—
183C2×#127—112no—
184C2×#127—114no—
185C2×#127—114no—
186C2×#127—111no—
187C2×#127—222no—
188C2×#127—222no—
189C2×#127—222no—
190C2×#127C2×D1111yescharacteristic
191C22×C42—111no—
192#432—112no—
193#432—222no—
194#432C2×D1112yescomplemented
195#431—114no—
196#431—222no—
197#423—114no—
198#407—222no—
199C4×M16—222no—
200#331—114no—
201#331—118no—
202#331C2×D1114yescomplemented
203C22×C11—22no—
204C22×C11—44no—
205C22×C11—48no—
206C22×C11—88no—
207C22×C11C2×#10012yes—
208C22×C11C22×C22⋊C411yescharacteristic
209C2×D11—28no—
210C2×D11—22no—
211C2×D11—22no—
212C2×D11—44no—
213C2×D11—48no—
214C2×D11—832no—
215C2×D11—88no—
216C2×D11#41814yes—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—22no—
220C4×C11C2×AGL(1,ℤ/8)14yes—
221Dic11—22no—
222Dic11C2×#10014yes—
223Dic11#41814yes—
224C25—222no—
225C22×D4—22no—
226C22×D4—118no—
227C22×D4—112no—
228C22×D4—224no—
229C22×D4—224no—
230C22×D4—224no—
231C22×D4—224no—
232C22×D4—224no—
233C22×D4—224no—
234C22×D4—222no—
235C22×D4—222no—
236C22×D4—4416no—
237C22×D4—448no—
238C22×D4C4×D1112yes—
239C23×C4—111no—
240C23×C4—112no—
241C2×M16—224no—
242#127—22no—
243#127—118no—
244#127—112no—
245#127—112no—
246#127—222no—
247#127—222no—
248#127—224no—
249#127—224no—
250#127—224no—
251#127—224no—
252#127—222no—
253#127C4×D1112yes—
254#127C22×D1112yes—
255C2×C42—111no—
256C2×C42—112no—
257C2×C42—112no—
258C2×C42—112no—
259C2×C42—112no—
260C2×C42—112no—
261C2×C42C22×D1111yescharacteristic
262C4⋊C8—114no—
263C4⋊C8—224no—
264C4⋊C8C22×D1114yescomplemented
265C22⋊C8—22no—
266C22⋊C8—224no—
267C22⋊C8—222no—
268#97—22no—
269#97—222no—
270C4×C8—224no—
271C2×C11—22no—
272C2×C11—84no—
273C2×C11C22×#10011yescharacteristic
274C2×C11C2×#41812yes—
275D11—24no—
276D11—84no—
277C24—22no—
278C24—111no—
279C24—228no—
280C24—222no—
281C24—4416no—
282C24—448no—
283C2×D4—22no—
284C2×D4—24no—
285C2×D4—24no—
286C2×D4—44no—
287C2×D4—48no—
288C2×D4—114no—
289C2×D4—228no—
290C2×D4—228no—
291C2×D4—228no—
292C2×D4—224no—
293C2×D4—222no—
294C2×D4—224no—
295C2×D4—444no—
296C2×D4—448no—
297C2×D4—4416no—
298C2×D4—448no—
299C2×D4—4416no—
300C2×D4—4416no—
301C2×D4—4416no—
302C2×D4—4416no—
303C2×D4—4416no—
304C2×D4—4416no—
305C2×D4C2×C4×D1114yes—
306C22×C4—111no—
307C22×C4—112no—
308C22×C4—112no—
309C22×C4—112no—
310C22×C4—112no—
311C22×C4—112no—
312C22×C4—112no—
313C22×C4—112no—
314C22×C4—224no—
315C22×C4—228no—
316C22×C4C2×C4×D1111yescharacteristic
317C22×C4D4×D1112yes—
318M16—448no—
319C2×C8—24no—
320C2×C8—224no—
321C42—112no—
322C42—111no—
323C42—112no—
324C42—111no—
325C42—112no—
326C42—112no—
327C42—112no—
328C42C2×C4×D1111yescharacteristic
329C42D4×D1112yes—
330C42C23×D1111yescharacteristic
331C11#1774111yescharacteristic, complemented, Sylow
332C23—24no—
333C23—48no—
334C23—44no—
335C23—112no—
336C23—224no—
337C23—222no—
338C23—224no—
339C23—448no—
340C23—4416no—
341C23—4416no—
342C23—4416no—
343C23—444no—
344C23—8832no—
345C23C22⋊C4×D1111yescharacteristic
346D4—44no—
347D4—44no—
348D4—48no—
349D4—48no—
350D4—444no—
351D4—444no—
352D4—448no—
353D4—4416no—
354D4—4416no—
355D4—4416no—
356D4—448no—
357C2×C4—22no—
358C2×C4—24no—
359C2×C4—112no—
360C2×C4—112no—
361C2×C4—114no—
362C2×C4—118no—
363C2×C4—112no—
364C2×C4—224no—
365C2×C4—224no—
366C2×C4—224no—
367C2×C4—224no—
368C2×C4—224no—
369C2×C4—224no—
370C2×C4C22⋊C4×D1112yes—
371C2×C4C22⋊C4×D1111yescharacteristic
372C2×C4C22×C4×D1111yescharacteristic
373C2×C4C2×D4×D1112yes—
374C8—44no—
375C8—444no—
376C22—22no—
377C22—44no—
378C22—48no—
379C22—88no—
380C22—114no—
381C22—228no—
382C22—222no—
383C22—222no—
384C22—444no—
385C22—448no—
386C22—888no—
387C22—8832no—
388C22D11×#10012yes—
389C22C2×C22⋊C4×D1111yescharacteristic
390C4—21no—
391C4—21no—
392C4—22no—
393C4—114no—
394C4—114no—
395C4—222no—
396C4D11×AGL(1,ℤ/8)14yes—
397C2—22no—
398C2—84no—
399C2—224no—
400C2—884no—
401C2C2×D11×#10011yescharacteristic
402C2D11×#41812yes—
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1555C2
socleC22×C11C22×C22⋊C4
prime radicalC2×D11×#127C2
cosocleC42×C11C24
hypercenter#1555D11
hypocenterC11#17741
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1555

Complements

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

NH ≅ G/Ntype
2. #13077246C2semidirect
3. #13067330C2semidirect
4. #13067329C2semidirect
5. #13067282C2semidirect
6. C11×#1555C2semidirect
18. C11×#432C22semidirect
19. #10622539C22semidirect
20. #10622450C22semidirect
21. #10622446C22semidirect
26. C11×#331C22semidirect
27. #10622182C22semidirect
28. #10622123C22semidirect
67. C11×C4⋊C8C23semidirect
74. C4⋊(C11⋊C8)C23semidirect
135. #1555D11semidirect
194. #432C2×D11semidirect
202. #331C2×D11semidirect
264. C4⋊C8C22×D11semidirect
331. C11#17741semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1272
#130772462
#130673302
#130673292
#130672822
C11×#15552
#1774111