Finite Group Databasebeta

← #534×AGL(1,𝔽11) #72269552

Subgroups — #534×AGL(1,𝔽11) #72269552

Order 7040.

3968 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72269545C214yesmaximal, complemented
2#72269473C211yesmaximal, characteristic, complemented
3#72248981C214yesmaximal, complemented
4#72248966C212yesmaximal, complemented
5#72248937C214yesmaximal, complemented
6C11⋊C5×#534C211yesmaximal, characteristic, complemented
7#121×AGL(1,𝔽11)C214yesmaximal, complemented
8#123×AGL(1,𝔽11)C214yesmaximal, complemented
9C2×C22⋊C4×AGL(1,𝔽11)C211yesmaximal, characteristic, complemented
10#120×AGL(1,𝔽11)C214yesmaximal, complemented
11C22×D4×AGL(1,𝔽11)C212yesmaximal, complemented
12C24×AGL(1,𝔽11)C2211yescharacteristic
13C24×AGL(1,𝔽11)C2212yescomplemented
14C22×D4×C11⋊C5C2212yescomplemented
15C22×C22⋊AGL(1,𝔽11)C2212yescomplemented
16C22×C22⋊AGL(1,𝔽11)C2212yescomplemented
17C2×D4×AGL(1,𝔽11)—216no—
18C2×D4×AGL(1,𝔽11)C2214yes—
19C2×D4×AGL(1,𝔽11)C2214yescomplemented
20C2×D4×AGL(1,𝔽11)C2214yescomplemented
21C2×D4×AGL(1,𝔽11)C2214yescomplemented
22C2×D4×AGL(1,𝔽11)C2214yescomplemented
23C22×C4⋊AGL(1,𝔽11)C2212yescomplemented
24C22×C4×AGL(1,𝔽11)C2212yescomplemented
25C22×C4×AGL(1,𝔽11)C2212yescomplemented
26#123×C11⋊C5C2214yescomplemented
27#121×C11⋊C5C2214yescomplemented
28#120×C11⋊C5C2214yescomplemented
29C2×C22⋊C4×C11⋊C5C2211yescharacteristic, complemented
30#67006⋊C5C2214yescomplemented
31C2×C22⋊(Dic11⋊C5)C2211yescharacteristic, complemented
32#66991⋊C5C2214yescomplemented
33#66990⋊C5C2218yescomplemented
34#66990⋊C5C2214yescomplemented
35#66988⋊C5C2214yescomplemented
36#66992⋊C5C2218yescomplemented
37#66983⋊C5C2214yescomplemented
38#66982⋊C5C2214yescomplemented
39C2×((C2×D11)⋊C4)⋊C5C2212yescomplemented
40#66948⋊C5C2214yescomplemented
41#66947⋊C5C2218yescomplemented
42C4⋊C4×AGL(1,𝔽11)C2214yescomplemented
43#66939⋊C5C2214yescomplemented
44#66937⋊C5C2218yescomplemented
45#66936⋊C5C2218yescomplemented
46#66935⋊C5C2218yescomplemented
47#66935⋊C5C2214yescomplemented
48C22⋊C4×AGL(1,𝔽11)C2218yescomplemented
49C22⋊C4×AGL(1,𝔽11)C2214yescomplemented
50C22⋊C4×AGL(1,𝔽11)C2214yescomplemented
51D11×#534C511yesmaximal, characteristic, complemented, Hall
52C24×C11⋊C5C2311yescharacteristic
53C24×C11⋊C5C2312yescomplemented
54C23×AGL(1,𝔽11)—28no—
55C23×AGL(1,𝔽11)—44no—
56C23×AGL(1,𝔽11)—48no—
57C23×AGL(1,𝔽11)D418yescomplemented
58C23×AGL(1,𝔽11)C2314yes—
59C23×AGL(1,𝔽11)C2312yes—
60C23×AGL(1,𝔽11)C2311yescharacteristic
61C23×AGL(1,𝔽11)C2312yes—
62C23×AGL(1,𝔽11)C2311yescharacteristic
63C23×AGL(1,𝔽11)C2312yescomplemented
64C23×AGL(1,𝔽11)C2314yescomplemented
65C2×D4×C11⋊C5—28no—
66C2×D4×C11⋊C5C2314yes—
67C2×D4×C11⋊C5C2314yescomplemented
68C2×D4×C11⋊C5C2314yescomplemented
69C22×C4×C11⋊C5C2312yescomplemented
70C22×C4×C11⋊C5C2312yescomplemented
71C2×C22⋊AGL(1,𝔽11)—28no—
72C2×C22⋊AGL(1,𝔽11)—28no—
73C2×C22⋊AGL(1,𝔽11)C2314yes—
74C2×C22⋊AGL(1,𝔽11)C2314yes—
75C2×C22⋊AGL(1,𝔽11)C2314yescomplemented
76C2×C22⋊AGL(1,𝔽11)C2314yescomplemented
77C2×C22⋊AGL(1,𝔽11)C2318yescomplemented
78C22×Dic11⋊C5C2312yescomplemented
79C22×Dic11⋊C5C2312yescomplemented
80D4×AGL(1,𝔽11)—216no—
81D4×AGL(1,𝔽11)—216no—
82D4×AGL(1,𝔽11)—216no—
83D4×AGL(1,𝔽11)—216no—
84D4×AGL(1,𝔽11)—48no—
85C2×C4⋊AGL(1,𝔽11)—28no—
86C2×C4⋊AGL(1,𝔽11)C2314yes—
87C2×C4⋊AGL(1,𝔽11)C2314yescomplemented
88C2×C4⋊AGL(1,𝔽11)C2314yescomplemented
89C2×C4×AGL(1,𝔽11)—28no—
90C2×C4×AGL(1,𝔽11)—44no—
91C2×C4×AGL(1,𝔽11)C2314yes—
92C2×C4×AGL(1,𝔽11)C2314yes—
93C2×C4×AGL(1,𝔽11)C2314yescomplemented
94C2×C4×AGL(1,𝔽11)C2314yescomplemented
95C4⋊C4×C11⋊C5C2314yescomplemented
96C22⋊C4×C11⋊C5C2314yescomplemented
97C22⋊C4×C11⋊C5C2318yescomplemented
98C22⋊(Dic11⋊C5)C2314yescomplemented
99C22⋊(Dic11⋊C5)C2318yescomplemented
100((C2×D11)⋊C4)⋊C5C2318yescomplemented
101((C2×D11)⋊C4)⋊C5C2318yescomplemented
102((C2×D11)⋊C4)⋊C5C2318yescomplemented
103C4⋊(Dic11⋊C5)C2314yescomplemented
104(Dic11⋊C4)⋊C5C2318yescomplemented
105C22×D4×D11C2×C512yescomplemented
106C11×#534C2×C511yescharacteristic, complemented
107#10623335C2×C512yescomplemented
108#10623184C2×C514yescomplemented
109D11×#123C2×C514yescomplemented
110#10623136C2×C514yescomplemented
111D11×#121C2×C514yescomplemented
112#10623120C2×C514yescomplemented
113D11×#120C2×C514yescomplemented
114#10623024C2×C511yescharacteristic, complemented
115C2×C22⋊C4×D11C2×C511yescharacteristic, complemented
116C2×C5×#534—111nomaximal, Hall
117C23×C11⋊C5—24no—
118C23×C11⋊C5—42no—
119C23×C11⋊C5—44no—
120C23×C11⋊C5C2×D414yescomplemented
121C23×C11⋊C5C2414yes—
122C23×C11⋊C5C2412yes—
123C23×C11⋊C5C2411yescharacteristic
124C22×AGL(1,𝔽11)—24no—
125C22×AGL(1,𝔽11)—28no—
126C22×AGL(1,𝔽11)—24no—
127C22×AGL(1,𝔽11)—28no—
128C22×AGL(1,𝔽11)—28no—
129C22×AGL(1,𝔽11)—216no—
130C22×AGL(1,𝔽11)—416no—
131C22×AGL(1,𝔽11)—44no—
132C22×AGL(1,𝔽11)—42no—
133C22×AGL(1,𝔽11)—48no—
134C22×AGL(1,𝔽11)—44no—
135C22×AGL(1,𝔽11)—432no—
136C22×AGL(1,𝔽11)C2×D418yes—
137C22×AGL(1,𝔽11)C2×D414yes—
138C22×AGL(1,𝔽11)C2×D418yescomplemented
139C22×AGL(1,𝔽11)C2×D414yescomplemented
140C22×AGL(1,𝔽11)C2414yes—
141C22×AGL(1,𝔽11)C2412yes—
142C22×AGL(1,𝔽11)C2411yescharacteristic
143C22×AGL(1,𝔽11)C2411yescharacteristic
144D4×C11⋊C5—28no—
145D4×C11⋊C5—28no—
146D4×C11⋊C5—44no—
147C2×C4×C11⋊C5—24no—
148C2×C4×C11⋊C5—42no—
149C2×C4×C11⋊C5C2414yes—
150C2×C4×C11⋊C5C2414yes—
151C22⋊AGL(1,𝔽11)—28no—
152C22⋊AGL(1,𝔽11)—28no—
153C22⋊AGL(1,𝔽11)—28no—
154C22⋊AGL(1,𝔽11)—28no—
155C22⋊AGL(1,𝔽11)—48no—
156C2×Dic11⋊C5—24no—
157C2×Dic11⋊C5—42no—
158C2×Dic11⋊C5C2414yes—
159C2×Dic11⋊C5C2414yes—
160C4⋊AGL(1,𝔽11)—28no—
161C4⋊AGL(1,𝔽11)—28no—
162C4⋊AGL(1,𝔽11)—44no—
163C4×AGL(1,𝔽11)—28no—
164C4×AGL(1,𝔽11)—28no—
165C4×AGL(1,𝔽11)—28no—
166C4×AGL(1,𝔽11)—44no—
167C24×D11C22×C511yescharacteristic
168C24×D11C22×C512yescomplemented
169C22×D4×C11C22×C512yescomplemented
170C22×C22⋊D11C22×C512yescomplemented
171C22×C22⋊D11C22×C512yescomplemented
172C2×D4×D11—216no—
173C2×D4×D11C22×C514yes—
174C2×D4×D11C22×C514yescomplemented
175C2×D4×D11C22×C514yescomplemented
176C2×D4×D11C22×C514yescomplemented
177C2×D4×D11C22×C514yescomplemented
178C22×D44C22×C512yescomplemented
179C22×C4×D11C22×C512yescomplemented
180C22×C4×D11C22×C512yescomplemented
181C11×#123C22×C514yescomplemented
182C11×#121C22×C514yescomplemented
183C11×#120C22×C514yescomplemented
184C2×C11×C22⋊C4C22×C511yescharacteristic, complemented
185#67006C22×C514yescomplemented
186C2×C22⋊Dic11C22×C511yescharacteristic, complemented
187#66992C22×C518yescomplemented
188#66991C22×C514yescomplemented
189#66990C22×C518yescomplemented
190#66990C22×C514yescomplemented
191#66988C22×C514yescomplemented
192#66983C22×C514yescomplemented
193#66982C22×C514yescomplemented
194C2×(C2×D11)⋊C4C22×C512yescomplemented
195#66948C22×C514yescomplemented
196#66947C22×C518yescomplemented
197C4⋊C4×D11C22×C514yescomplemented
198#66939C22×C514yescomplemented
199#66937C22×C518yescomplemented
200#66936C22×C518yescomplemented
201#66935C22×C518yescomplemented
202#66935C22×C514yescomplemented
203C22⋊C4×D11C22×C514yescomplemented
204C22⋊C4×D11C22×C518yescomplemented
205C22⋊C4×D11C22×C514yescomplemented
206C23×C5×D4—112no—
207C5×#534—112no—
208C5×#534—114no—
209C5×#534—114no—
210C5×#534—114no—
211C5×#534—111no—
212C5×#534—221no—
213C2×C5×#123—114no—
214C2×C5×#121—114no—
215C2×C5×#120—114no—
216C22×C5×C22⋊C4—111no—
217C22×C11⋊C5—22no—
218C22×C11⋊C5—24no—
219C22×C11⋊C5—24no—
220C22×C11⋊C5—28no—
221C22×C11⋊C5—44no—
222C22×C11⋊C5—48no—
223C22×C11⋊C5C22×D414yes—
224C22×C11⋊C5C22×D412yes—
225C22×C11⋊C5C2511yescharacteristic
226C2×AGL(1,𝔽11)—22no—
227C2×AGL(1,𝔽11)—24no—
228C2×AGL(1,𝔽11)—216no—
229C2×AGL(1,𝔽11)—28no—
230C2×AGL(1,𝔽11)—24no—
231C2×AGL(1,𝔽11)—28no—
232C2×AGL(1,𝔽11)—44no—
233C2×AGL(1,𝔽11)—48no—
234C2×AGL(1,𝔽11)—416no—
235C2×AGL(1,𝔽11)—48no—
236C2×AGL(1,𝔽11)—416no—
237C2×AGL(1,𝔽11)C22×D414yes—
238C2×AGL(1,𝔽11)C22×D412yes—
239C2×AGL(1,𝔽11)C22×D412yes—
240C2×AGL(1,𝔽11)H(5,𝔽2)14yes—
241C4×C11⋊C5—24no—
242C4×C11⋊C5—24no—
243Dic11⋊C5—24no—
244Dic11⋊C5—24no—
245C24×C11C23×C511yescharacteristic
246C24×C11C23×C512yescomplemented
247C23×D11—28no—
248C23×D11—44no—
249C23×D11—48no—
250C23×D11C5×D418yescomplemented
251C23×D11C23×C514yes—
252C23×D11C23×C512yes—
253C23×D11C23×C511yescharacteristic
254C23×D11C23×C512yes—
255C23×D11C23×C511yescharacteristic
256C23×D11C23×C512yescomplemented
257C23×D11C23×C514yescomplemented
258C2×D4×C11—28no—
259C2×D4×C11C23×C514yes—
260C2×D4×C11C23×C514yescomplemented
261C2×D4×C11C23×C514yescomplemented
262C22×C4×C11C23×C512yescomplemented
263C22×C4×C11C23×C512yescomplemented
264C2×C22⋊D11—28no—
265C2×C22⋊D11—28no—
266C2×C22⋊D11C23×C514yes—
267C2×C22⋊D11C23×C514yes—
268C2×C22⋊D11C23×C514yescomplemented
269C2×C22⋊D11C23×C514yescomplemented
270C2×C22⋊D11C23×C518yescomplemented
271C22×Dic11C23×C512yescomplemented
272C22×Dic11C23×C512yescomplemented
273D4×D11—216no—
274D4×D11—216no—
275D4×D11—216no—
276D4×D11—216no—
277D4×D11—48no—
278C2×D44—28no—
279C2×D44C23×C514yes—
280C2×D44C23×C514yescomplemented
281C2×D44C23×C514yescomplemented
282C2×C4×D11—28no—
283C2×C4×D11—44no—
284C2×C4×D11C23×C514yes—
285C2×C4×D11C23×C514yes—
286C2×C4×D11C23×C514yescomplemented
287C2×C4×D11C23×C514yescomplemented
288C11×C4⋊C4C23×C514yescomplemented
289C11×C22⋊C4C23×C514yescomplemented
290C11×C22⋊C4C23×C518yescomplemented
291C22⋊Dic11C23×C514yescomplemented
292C22⋊Dic11C23×C518yescomplemented
293(C2×D11)⋊C4C23×C518yescomplemented
294(C2×D11)⋊C4C23×C518yescomplemented
295(C2×D11)⋊C4C23×C518yescomplemented
296C4⋊Dic11C23×C514yescomplemented
297Dic11⋊C4C23×C518yescomplemented
298C25×C5—111no—
299C25×C5—112no—
300C22×C5×D4—112no—
301C22×C5×D4—112no—
302C22×C5×D4—114no—
303C22×C5×D4—114no—
304C22×C5×D4—114no—
305C22×C5×D4—114no—
306C22×C5×D4—114no—
307C22×C5×D4—112no—
308C22×C5×D4—2216no—
309C22×C5×D4—222no—
310C23×C4×C5—112no—
311C23×C4×C5—112no—
312C5×#123—114no—
313C5×#123—114no—
314C5×#123—118no—
315C5×#123—118no—
316C5×#123—114no—
317C5×#123—224no—
318C5×#121—118no—
319C5×#121—114no—
320C5×#121—114no—
321C5×#121—114no—
322C5×#121—118no—
323C5×#121—224no—
324C5×#120—114no—
325C5×#120—114no—
326C5×#120—118no—
327C5×#120—118no—
328C5×#120—114no—
329C5×#120—224no—
330C2×C5×C4⋊C4—114no—
331C2×C5×C22⋊C4—111no—
332C2×C5×C22⋊C4—112no—
333C2×C5×C22⋊C4—114no—
334C2×C5×C22⋊C4—114no—
335C2×C5×C22⋊C4—118no—
336C2×C5×C22⋊C4—221no—
337C2×#534—111noSylow
338C2×C11⋊C5—24no—
339C2×C11⋊C5—22no—
340C2×C11⋊C5—44no—
341C2×C11⋊C5C23×D411yescharacteristic
342C2×C11⋊C5C2×H(5,𝔽2)12yes—
343AGL(1,𝔽11)—24no—
344AGL(1,𝔽11)—22no—
345AGL(1,𝔽11)—44no—
346AGL(1,𝔽11)#53414yesdirect product factor
347C23×C11—24no—
348C23×C11—42no—
349C23×C11—44no—
350C23×C11C2×C5×D414yescomplemented
351C23×C11C24×C514yes—
352C23×C11C24×C512yes—
353C23×C11C24×C511yescharacteristic
354C22×D11—24no—
355C22×D11—28no—
356C22×D11—24no—
357C22×D11—28no—
358C22×D11—28no—
359C22×D11—216no—
360C22×D11—416no—
361C22×D11—42no—
362C22×D11—44no—
363C22×D11—48no—
364C22×D11—44no—
365C22×D11—432no—
366C22×D11C2×C5×D418yes—
367C22×D11C2×C5×D414yes—
368C22×D11C2×C5×D418yescomplemented
369C22×D11C2×C5×D414yescomplemented
370C22×D11C24×C514yes—
371C22×D11C24×C512yes—
372C22×D11C24×C511yescharacteristic
373C22×D11C24×C511yescharacteristic
374D4×C11—28no—
375D4×C11—28no—
376D4×C11—44no—
377C2×C4×C11—24no—
378C2×C4×C11—42no—
379C2×C4×C11C24×C514yes—
380C2×C4×C11C24×C514yes—
381C22⋊D11—28no—
382C22⋊D11—28no—
383C22⋊D11—28no—
384C22⋊D11—28no—
385C22⋊D11—48no—
386C2×Dic11—24no—
387C2×Dic11—42no—
388C2×Dic11C24×C514yes—
389C2×Dic11C24×C514yes—
390D44—28no—
391D44—28no—
392D44—44no—
393C4×D11—28no—
394C4×D11—28no—
395C4×D11—28no—
396C4×D11—44no—
397C24×C5—112no—
398C24×C5—111no—
399C24×C5—111no—
400C24×C5—112no—
401C24×C5—118no—
402C24×C5—114no—
403C24×C5—114no—
404C24×C5—112no—
405C24×C5—228no—
406C24×C5—221no—
407C24×C5—222no—
408C24×C5—444no—
409C24×C5—448no—
410C2×C5×D4—114no—
411C2×C5×D4—114no—
412C2×C5×D4—114no—
413C2×C5×D4—114no—
414C2×C5×D4—118no—
415C2×C5×D4—114no—
416C2×C5×D4—114no—
417C2×C5×D4—114no—
418C2×C5×D4—228no—
419C2×C5×D4—228no—
420C2×C5×D4—2216no—
421C2×C5×D4—2216no—
422C2×C5×D4—2216no—
423C2×C5×D4—2216no—
424C2×C5×D4—228no—
425C2×C5×D4—224no—
426C2×C5×D4—224no—
427C2×C5×D4—224no—
428C2×C5×D4—448no—
429C2×C5×D4—448no—
430C22×C4×C5—112no—
431C22×C4×C5—112no—
432C22×C4×C5—114no—
433C22×C4×C5—114no—
434C22×C4×C5—114no—
435C22×C4×C5—114no—
436C22×C4×C5—228no—
437C22×C4×C5—222no—
438C22×C4×C5—222no—
439C22×C4×C5—444no—
440C5×C4⋊C4—118no—
441C5×C4⋊C4—114no—
442C5×C4⋊C4—224no—
443C5×C22⋊C4—114no—
444C5×C22⋊C4—118no—
445C5×C22⋊C4—118no—
446C5×C22⋊C4—118no—
447C5×C22⋊C4—118no—
448C5×C22⋊C4—224no—
449C5×C22⋊C4—228no—
450C23×D4—112no—
451#534—112no—
452#534—114no—
453#534—114no—
454#534—114no—
455#534—111no—
456#534AGL(1,𝔽11)11yescharacteristic, direct product factor
457C2×#123—114no—
458C2×#121—114no—
459C2×#120—114no—
460C22×C22⋊C4—111no—
461C11⋊C5C2×#53411yescharacteristic, complemented, Hall
462C22×C11—22no—
463C22×C11—24no—
464C22×C11—24no—
465C22×C11—28no—
466C22×C11—44no—
467C22×C11—48no—
468C22×C11C22×C5×D414yes—
469C22×C11C22×C5×D412yes—
470C22×C11C25×C511yescharacteristic
471C2×D11—24no—
472C2×D11—22no—
473C2×D11—216no—
474C2×D11—28no—
475C2×D11—24no—
476C2×D11—28no—
477C2×D11—44no—
478C2×D11—48no—
479C2×D11—416no—
480C2×D11—48no—
481C2×D11—416no—
482C2×D11C22×C5×D414yes—
483C2×D11C22×C5×D412yes—
484C2×D11C22×C5×D412yes—
485C2×D11C5×H(5,𝔽2)14yes—
486C4×C11—24no—
487C4×C11—24no—
488Dic11—24no—
489Dic11—24no—
490C23×C5—111no—
491C23×C5—118no—
492C23×C5—114no—
493C23×C5—112no—
494C23×C5—111no—
495C23×C5—114no—
496C23×C5—118no—
497C23×C5—114no—
498C23×C5—224no—
499C23×C5—228no—
500C23×C5—228no—
501C23×C5—228no—
502C23×C5—2216no—
503C23×C5—224no—
504C23×C5—224no—
505C23×C5—222no—
506C23×C5—221no—
507C23×C5—224no—
508C23×C5—444no—
509C23×C5—4416no—
510C23×C5—444no—
511C23×C5—442no—
512C23×C5—448no—
513C23×C5—444no—
514C23×C5—4432no—
515C23×C5—882no—
516C23×C5—884no—
517C5×D4—228no—
518C5×D4—228no—
519C5×D4—228no—
520C5×D4—228no—
521C5×D4—228no—
522C5×D4—228no—
523C5×D4—448no—
524C5×D4—448no—
525C5×D4—448no—
526C5×D4—444no—
527C5×D4—884no—
528C2×C4×C5—114no—
529C2×C4×C5—114no—
530C2×C4×C5—224no—
531C2×C4×C5—228no—
532C2×C4×C5—228no—
533C2×C4×C5—228no—
534C2×C4×C5—224no—
535C2×C4×C5—224no—
536C2×C4×C5—444no—
537C2×C4×C5—442no—
538C2×C4×C5—444no—
539C2×C4×C5—882no—
540C25—111no—
541C25—112no—
542C22×D4—112no—
543C22×D4—112no—
544C22×D4—114no—
545C22×D4—114no—
546C22×D4—114no—
547C22×D4—114no—
548C22×D4—114no—
549C22×D4—112no—
550C22×D4—2216no—
551C22×D4C2×AGL(1,𝔽11)12yescomplemented
552C23×C4—112no—
553C23×C4—112no—
554#123—114no—
555#123—114no—
556#123—118no—
557#123—118no—
558#123—114no—
559#123C2×AGL(1,𝔽11)14yescomplemented
560#121—114no—
561#121—118no—
562#121—114no—
563#121—114no—
564#121—118no—
565#121C2×AGL(1,𝔽11)14yescomplemented
566#120—114no—
567#120—114no—
568#120—118no—
569#120—118no—
570#120—114no—
571#120C2×AGL(1,𝔽11)14yescomplemented
572C2×C4⋊C4—114no—
573C2×C22⋊C4—111no—
574C2×C22⋊C4—112no—
575C2×C22⋊C4—114no—
576C2×C22⋊C4—114no—
577C2×C22⋊C4—118no—
578C2×C22⋊C4C2×AGL(1,𝔽11)11yescharacteristic, complemented
579C2×C11—24no—
580C2×C11—22no—
581C2×C11—44no—
582C2×C11C23×C5×D411yescharacteristic
583C2×C11C2×C5×H(5,𝔽2)12yes—
584D11—24no—
585D11—22no—
586D11—44no—
587D11C5×#53414yescomplemented
588C22×C5—112no—
589C22×C5—114no—
590C22×C5—114no—
591C22×C5—112no—
592C22×C5—2216no—
593C22×C5—228no—
594C22×C5—222no—
595C22×C5—224no—
596C22×C5—224no—
597C22×C5—228no—
598C22×C5—224no—
599C22×C5—222no—
600C22×C5—221no—
601C22×C5—442no—
602C22×C5—444no—
603C22×C5—444no—
604C22×C5—448no—
605C22×C5—4416no—
606C22×C5—444no—
607C22×C5—448no—
608C22×C5—4416no—
609C22×C5—448no—
610C22×C5—884no—
611C22×C5—888no—
612C4×C5—224no—
613C4×C5—224no—
614C4×C5—444no—
615C4×C5—444no—
616C24—112no—
617C24—111no—
618C24—118no—
619C24—111no—
620C24—112no—
621C24—114no—
622C24—114no—
623C24—112no—
624C24—228no—
625C24—444no—
626C24—448no—
627C24C22×AGL(1,𝔽11)11yescharacteristic
628C24C22×AGL(1,𝔽11)12yescomplemented
629C2×D4—28no—
630C2×D4—114no—
631C2×D4—114no—
632C2×D4—114no—
633C2×D4—114no—
634C2×D4—118no—
635C2×D4—114no—
636C2×D4—114no—
637C2×D4—114no—
638C2×D4—228no—
639C2×D4—2216no—
640C2×D4—2216no—
641C2×D4—2216no—
642C2×D4—2216no—
643C2×D4—228no—
644C2×D4—228no—
645C2×D4—448no—
646C2×D4C22×AGL(1,𝔽11)14yes—
647C2×D4C22×AGL(1,𝔽11)14yescomplemented
648C2×D4C22×AGL(1,𝔽11)14yescomplemented
649C22×C4—112no—
650C22×C4—112no—
651C22×C4—114no—
652C22×C4—114no—
653C22×C4—114no—
654C22×C4—114no—
655C22×C4—228no—
656C22×C4—444no—
657C22×C4C22×AGL(1,𝔽11)12yescomplemented
658C22×C4C22×AGL(1,𝔽11)12yescomplemented
659C4⋊C4—118no—
660C4⋊C4—114no—
661C4⋊C4C22×AGL(1,𝔽11)14yescomplemented
662C22⋊C4—114no—
663C22⋊C4—118no—
664C22⋊C4—118no—
665C22⋊C4—118no—
666C22⋊C4—118no—
667C22⋊C4C22×AGL(1,𝔽11)14yescomplemented
668C22⋊C4C22×AGL(1,𝔽11)18yescomplemented
669C11C2×C5×#53411yescharacteristic, complemented, Sylow
670C2×C5—114no—
671C2×C5—224no—
672C2×C5—222no—
673C2×C5—221no—
674C2×C5—222no—
675C2×C5—444no—
676C2×C5—442no—
677C2×C5—444no—
678C2×C5—884no—
679C23—24no—
680C23—42no—
681C23—44no—
682C23—111no—
683C23—118no—
684C23—114no—
685C23—112no—
686C23—111no—
687C23—114no—
688C23—118no—
689C23—114no—
690C23—224no—
691C23—228no—
692C23—228no—
693C23—228no—
694C23—2216no—
695C23—224no—
696C23—442no—
697C23—444no—
698C23—444no—
699C23—448no—
700C23—4416no—
701C23—4432no—
702C23D4×AGL(1,𝔽11)14yescomplemented
703C23C23×AGL(1,𝔽11)14yes—
704C23C23×AGL(1,𝔽11)12yes—
705C23C23×AGL(1,𝔽11)11yescharacteristic
706D4—28no—
707D4—28no—
708D4—44no—
709D4—228no—
710D4—228no—
711D4—228no—
712D4—228no—
713D4—228no—
714D4—228no—
715D4—444no—
716D4—448no—
717C2×C4—24no—
718C2×C4—42no—
719C2×C4—114no—
720C2×C4—114no—
721C2×C4—228no—
722C2×C4—228no—
723C2×C4—228no—
724C2×C4—224no—
725C2×C4—444no—
726C2×C4—442no—
727C2×C4C23×AGL(1,𝔽11)14yes—
728C2×C4C23×AGL(1,𝔽11)14yes—
729C5—221noSylow
730C22—22no—
731C22—24no—
732C22—24no—
733C22—28no—
734C22—44no—
735C22—48no—
736C22—112no—
737C22—114no—
738C22—114no—
739C22—112no—
740C22—2216no—
741C22—228no—
742C22—222no—
743C22—224no—
744C22—224no—
745C22—228no—
746C22—448no—
747C22—444no—
748C22—448no—
749C22—4416no—
750C22—4416no—
751C22C2×D4×AGL(1,𝔽11)14yes—
752C22C2×D4×AGL(1,𝔽11)12yes—
753C22C24×AGL(1,𝔽11)11yescharacteristic
754C4—24no—
755C4—24no—
756C4—224no—
757C4—224no—
758C2—24no—
759C2—22no—
760C2—44no—
761C2—114no—
762C2—224no—
763C2—222no—
764C2—444no—
765C2C22×D4×AGL(1,𝔽11)11yescharacteristic
766C2H(5,𝔽2)×AGL(1,𝔽11)12yes—
subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽11)
commutator, socle, cosocleC22×C11C25×C5
FittingC11×#534C2×C5
hypercenter#534AGL(1,𝔽11)
hypocenterC11C2×C5×#534
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #72269545C2semidirect
2. #72269473C2semidirect
3. #72248981C2semidirect
4. #72248966C2semidirect
5. #72248937C2semidirect
6. C11⋊C5×#534C2semidirect
7. #121×AGL(1,𝔽11)C2semidirect
8. #123×AGL(1,𝔽11)C2semidirect
9. C2×C22⋊C4×AGL(1,𝔽11)C2semidirect
10. #120×AGL(1,𝔽11)C2semidirect
11. C22×D4×AGL(1,𝔽11)C2semidirect
13. C24×AGL(1,𝔽11)C22semidirect
14. C22×D4×C11⋊C5C22semidirect
15. C22×C22⋊AGL(1,𝔽11)C22semidirect
16. C22×C22⋊AGL(1,𝔽11)C22semidirect
19. C2×D4×AGL(1,𝔽11)C22semidirect
20. C2×D4×AGL(1,𝔽11)C22semidirect
21. C2×D4×AGL(1,𝔽11)C22semidirect
22. C2×D4×AGL(1,𝔽11)C22semidirect
23. C22×C4⋊AGL(1,𝔽11)C22semidirect
24. C22×C4×AGL(1,𝔽11)C22semidirect
25. C22×C4×AGL(1,𝔽11)C22semidirect
26. #123×C11⋊C5C22semidirect
27. #121×C11⋊C5C22semidirect
28. #120×C11⋊C5C22semidirect
29. C2×C22⋊C4×C11⋊C5C22semidirect
30. #67006⋊C5C22semidirect
31. C2×C22⋊(Dic11⋊C5)C22semidirect
32. #66991⋊C5C22semidirect
33. #66990⋊C5C22semidirect
34. #66990⋊C5C22semidirect
35. #66988⋊C5C22semidirect
36. #66992⋊C5C22semidirect
37. #66983⋊C5C22semidirect
38. #66982⋊C5C22semidirect
39. C2×((C2×D11)⋊C4)⋊C5C22semidirect
40. #66948⋊C5C22semidirect
41. #66947⋊C5C22semidirect
42. C4⋊C4×AGL(1,𝔽11)C22semidirect
43. #66939⋊C5C22semidirect
44. #66937⋊C5C22semidirect
45. #66936⋊C5C22semidirect
46. #66935⋊C5C22semidirect
47. #66935⋊C5C22semidirect
48. C22⋊C4×AGL(1,𝔽11)C22semidirect
49. C22⋊C4×AGL(1,𝔽11)C22semidirect
50. C22⋊C4×AGL(1,𝔽11)C22semidirect
51. D11×#534C5semidirect
53. C24×C11⋊C5C23semidirect
57. C23×AGL(1,𝔽11)D4semidirect
63. C23×AGL(1,𝔽11)C23semidirect
64. C23×AGL(1,𝔽11)C23semidirect
67. C2×D4×C11⋊C5C23semidirect
68. C2×D4×C11⋊C5C23semidirect
69. C22×C4×C11⋊C5C23semidirect
70. C22×C4×C11⋊C5C23semidirect
75. C2×C22⋊AGL(1,𝔽11)C23semidirect
76. C2×C22⋊AGL(1,𝔽11)C23semidirect
77. C2×C22⋊AGL(1,𝔽11)C23semidirect
78. C22×Dic11⋊C5C23semidirect
79. C22×Dic11⋊C5C23semidirect
87. C2×C4⋊AGL(1,𝔽11)C23semidirect
88. C2×C4⋊AGL(1,𝔽11)C23semidirect
93. C2×C4×AGL(1,𝔽11)C23semidirect
94. C2×C4×AGL(1,𝔽11)C23semidirect
95. C4⋊C4×C11⋊C5C23semidirect
96. C22⋊C4×C11⋊C5C23semidirect
97. C22⋊C4×C11⋊C5C23semidirect
98. C22⋊(Dic11⋊C5)C23semidirect
99. C22⋊(Dic11⋊C5)C23semidirect
100. ((C2×D11)⋊C4)⋊C5C23semidirect
101. ((C2×D11)⋊C4)⋊C5C23semidirect
102. ((C2×D11)⋊C4)⋊C5C23semidirect
103. C4⋊(Dic11⋊C5)C23semidirect
104. (Dic11⋊C4)⋊C5C23semidirect
105. C22×D4×D11C2×C5semidirect
106. C11×#534C2×C5semidirect
107. #10623335C2×C5semidirect
108. #10623184C2×C5semidirect
109. D11×#123C2×C5semidirect
110. #10623136C2×C5semidirect
111. D11×#121C2×C5semidirect
112. #10623120C2×C5semidirect
113. D11×#120C2×C5semidirect
114. #10623024C2×C5semidirect
115. C2×C22⋊C4×D11C2×C5semidirect
120. C23×C11⋊C5C2×D4semidirect
138. C22×AGL(1,𝔽11)C2×D4semidirect
139. C22×AGL(1,𝔽11)C2×D4semidirect
168. C24×D11C22×C5semidirect
169. C22×D4×C11C22×C5semidirect
170. C22×C22⋊D11C22×C5semidirect
171. C22×C22⋊D11C22×C5semidirect
174. C2×D4×D11C22×C5semidirect
175. C2×D4×D11C22×C5semidirect
176. C2×D4×D11C22×C5semidirect
177. C2×D4×D11C22×C5semidirect
178. C22×D44C22×C5semidirect
179. C22×C4×D11C22×C5semidirect
180. C22×C4×D11C22×C5semidirect
181. C11×#123C22×C5semidirect
182. C11×#121C22×C5semidirect
183. C11×#120C22×C5semidirect
184. C2×C11×C22⋊C4C22×C5semidirect
185. #67006C22×C5semidirect
186. C2×C22⋊Dic11C22×C5semidirect
187. #66992C22×C5semidirect
188. #66991C22×C5semidirect
189. #66990C22×C5semidirect
190. #66990C22×C5semidirect
191. #66988C22×C5semidirect
192. #66983C22×C5semidirect
193. #66982C22×C5semidirect
194. C2×(C2×D11)⋊C4C22×C5semidirect
195. #66948C22×C5semidirect
196. #66947C22×C5semidirect
197. C4⋊C4×D11C22×C5semidirect
198. #66939C22×C5semidirect
199. #66937C22×C5semidirect
200. #66936C22×C5semidirect
201. #66935C22×C5semidirect
202. #66935C22×C5semidirect
203. C22⋊C4×D11C22×C5semidirect
204. C22⋊C4×D11C22×C5semidirect
205. C22⋊C4×D11C22×C5semidirect
246. C24×C11C23×C5semidirect
250. C23×D11C5×D4semidirect
256. C23×D11C23×C5semidirect
257. C23×D11C23×C5semidirect
260. C2×D4×C11C23×C5semidirect
261. C2×D4×C11C23×C5semidirect
262. C22×C4×C11C23×C5semidirect
263. C22×C4×C11C23×C5semidirect
268. C2×C22⋊D11C23×C5semidirect
269. C2×C22⋊D11C23×C5semidirect
270. C2×C22⋊D11C23×C5semidirect
271. C22×Dic11C23×C5semidirect
272. C22×Dic11C23×C5semidirect
280. C2×D44C23×C5semidirect
281. C2×D44C23×C5semidirect
286. C2×C4×D11C23×C5semidirect
287. C2×C4×D11C23×C5semidirect
288. C11×C4⋊C4C23×C5semidirect
289. C11×C22⋊C4C23×C5semidirect
290. C11×C22⋊C4C23×C5semidirect
291. C22⋊Dic11C23×C5semidirect
292. C22⋊Dic11C23×C5semidirect
293. (C2×D11)⋊C4C23×C5semidirect
294. (C2×D11)⋊C4C23×C5semidirect
295. (C2×D11)⋊C4C23×C5semidirect
296. C4⋊Dic11C23×C5semidirect
297. Dic11⋊C4C23×C5semidirect
346. AGL(1,𝔽11)#534direct (N × H)
350. C23×C11C2×C5×D4semidirect
368. C22×D11C2×C5×D4semidirect
369. C22×D11C2×C5×D4semidirect
456. #534AGL(1,𝔽11)direct (N × H)
461. C11⋊C5C2×#534semidirect
551. C22×D4C2×AGL(1,𝔽11)semidirect
559. #123C2×AGL(1,𝔽11)semidirect
565. #121C2×AGL(1,𝔽11)semidirect
571. #120C2×AGL(1,𝔽11)semidirect
578. C2×C22⋊C4C2×AGL(1,𝔽11)semidirect
587. D11C5×#534semidirect
628. C24C22×AGL(1,𝔽11)semidirect
647. C2×D4C22×AGL(1,𝔽11)semidirect
648. C2×D4C22×AGL(1,𝔽11)semidirect
657. C22×C4C22×AGL(1,𝔽11)semidirect
658. C22×C4C22×AGL(1,𝔽11)semidirect
661. C4⋊C4C22×AGL(1,𝔽11)semidirect
667. C22⋊C4C22×AGL(1,𝔽11)semidirect
668. C22⋊C4C22×AGL(1,𝔽11)semidirect
669. C11C2×C5×#534semidirect
702. C23D4×AGL(1,𝔽11)semidirect

Maximal subgroups

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

subgroupindex
#722695452
#722694732
#722489812
#722489662
#722489372
C11⋊C5×#5342
#121×AGL(1,𝔽11)2
#123×AGL(1,𝔽11)2
C2×C22⋊C4×AGL(1,𝔽11)2
#120×AGL(1,𝔽11)2
C22×D4×AGL(1,𝔽11)2
D11×#5345
C2×C5×#53411