Finite Group Databasebeta

← C11×#22503 #14599696

Subgroups — C11×#22503 #14599696

Order 2816.

1246 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#555C211yesmaximal, characteristic
2C2×C11×#436C211yesmaximal, characteristic, complemented
3D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
4C11×#1990C211yesmaximal, characteristic, complemented
5C11×#1987C211yesmaximal, characteristic, complemented
6C11×#1895C212yesmaximal, complemented
7C11×#1874C212yesmaximal, complemented
8C11×#1825C212yesmaximal, complemented
9C11×#1802C211yesmaximal, characteristic, complemented
10C4×C11×#102C211yesmaximal, characteristic, complemented
11C11×#1736C212yesmaximal, complemented
12C22×C11×M16C2212yes—
13C11×#555—24no—
14C11×#555C418yescomplemented
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#124—22no—
17C2×C11×#121—21no—
18C2×C11×#121C2212yes—
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117—21no—
23C2×C11×#117C2212yes—
24C22×C11×C4⋊C4C2212yes—
25C11×#436—24no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2212yes—
30C2×C11×C22⋊C8C2212yes—
31C2×C4×C8×C11C2211yescharacteristic
32C11×#389—21no—
33C11×#385—22no—
34C11×#384C2211yescharacteristic
35C11×#380C2212yes—
36C4×C11×C4⋊C4C2211yescharacteristic
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2211yescharacteristic
42C11×#340C2212yes—
43C11×#340C2211yescharacteristic
44C22×Q8×C11—21no—
45C22×D4×C11—22no—
46C22×D4×C11D411yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11—22no—
50C23×C4×C11C2312yes—
51C2×C11×M16—24no—
52C2×C11×M16—24no—
53C2×C11×M16—42no—
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2312yes—
56C22×C8×C11C2311yescharacteristic
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8C2×C414yescomplemented
59C11×#124—216no—
60C11×#121—28no—
61C11×#121—24no—
62C11×#121C2×C418yescomplemented
63C4×D4×C11—22no—
64C4×D4×C11—44no—
65C4×D4×C11C2×C414yes—
66C4×D4×C11C2×C414yescomplemented
67C4×D4×C11D414yes—
68C11×#117—24no—
69C11×#117—28no—
70C11×#117C2×C418yescomplemented
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—42no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4D412yes—
88C2×C42×C11—22no—
89C2×C42×C11—21no—
90C2×C42×C11C2311yescharacteristic
91C11×C4⋊C8—22no—
92C11×#102—22no—
93C11×#102—22no—
94C11×#102—42no—
95C11×C22⋊C8—24no—
96C4×C8×C11—22no—
97C11×#95—21no—
98C11×#95—22no—
99#22503C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11—21no—
101C24×C11C2×D412yes—
102C2×Q8×C11—24no—
103C2×Q8×C11—81no—
104C2×Q8×C11—81no—
105C2×D4×C11—28no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—82no—
114C2×D4×C11—82no—
115C2×D4×C11C22⋊C414yes—
116C2×D4×C11C22×C412yes—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—24no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—44no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11—44no—
131C22×C4×C11—82no—
132C22×C4×C11C22×C414yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D414yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C11×M16—48no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—22no—
142C2×C8×C11—21no—
143C2×C8×C11—22no—
144C2×C8×C11—21no—
145C2×C8×C11—22no—
146C2×C8×C11—21no—
147C2×C8×C11#4112yes—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—44no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—81no—
159C11×C4⋊C4C22⋊C414yes—
160C11×C4⋊C4C22×C412yes—
161C11×C4⋊C4C22×C414yes—
162C11×C4⋊C4#4112yes—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—28no—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—44no—
167C11×C22⋊C4C22⋊C418yes—
168C42×C11—28no—
169C42×C11—42no—
170C42×C11C22×C412yes—
171C42×C11C2×D412yes—
172C2×#555C2×C1111yescharacteristic
173C2×#436C2×C1111yescharacteristic, complemented
174D4×C4⋊C4C2×C1111yescharacteristic, complemented
175#1990C2×C1111yescharacteristic, complemented
176#1987C2×C1111yescharacteristic, complemented
177#1895C2×C1112yescomplemented
178#1874C2×C1112yescomplemented
179#1825C2×C1112yescomplemented
180#1802C2×C1111yescharacteristic, complemented
181C4×#102C2×C1111yescharacteristic, complemented
182#1736C2×C1112yescomplemented
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11C2×C22⋊C414yes—
197C23×C11C22×D411yescharacteristic
198Q8×C11—84no—
199D4×C11—22no—
200D4×C11—22no—
201D4×C11—28no—
202D4×C11—41no—
203D4×C11—41no—
204D4×C11—88no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—48no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11—88no—
230C2×C4×C11C2×C22⋊C414yes—
231C2×C4×C11C2×C22⋊C412yes—
232C2×C4×C11C2×C22⋊C412yes—
233C2×C4×C11AGL(1,ℤ/8)12yes—
234C2×C4×C11#13712yes—
235C2×C4×C11C23×C411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11H(5,𝔽2)11yescharacteristic
240C2×C4×C112−1+411yescharacteristic
241C8×C11—22no—
242C8×C11—42no—
243C8×C11—41no—
244C22×M16C22×C1112yes—
245#555—24no—
246#555C4×C1118yescomplemented
247C2×C4⋊Q8C22×C1111yescharacteristic
248C2×#124—22no—
249C2×#121—21no—
250C2×#121C22×C1112yes—
251C2×C4×D4—21no—
252C2×C4×D4C22×C1111yescharacteristic
253C2×C4×D4C22×C1111yescharacteristic
254C2×#117—21no—
255C2×#117C22×C1112yes—
256C22×C4⋊C4C22×C1112yes—
257#436—24no—
258C2×C4⋊C8C22×C1111yescharacteristic
259C2×#102C22×C1111yescharacteristic
260C2×#102C22×C1111yescharacteristic
261C2×#102C22×C1112yes—
262C2×C22⋊C8C22×C1112yes—
263C2×C4×C8C22×C1111yescharacteristic
264#389—21no—
265#385—22no—
266#384C22×C1111yescharacteristic
267#380C22×C1112yes—
268C4×C4⋊C4C22×C1111yescharacteristic
269#340C22×C1112yes—
270#340C22×C1111yescharacteristic
271#340C22×C1112yes—
272#340C22×C1112yes—
273#340C22×C1112yes—
274#340C22×C1112yes—
275#340C22×C1111yescharacteristic
276C22×C11—24no—
277C22×C11—24no—
278C22×C11—24no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11C22×C22⋊C411yescharacteristic
291C22×C11#54611yescharacteristic
292C22×C11#54711yescharacteristic
293C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
294C22×C11C2×#13711yescharacteristic
295C22×C11#57611yescharacteristic
296C22×C11#57711yescharacteristic
297C4×C11—24no—
298C4×C11—22no—
299C4×C11—42no—
300C4×C11—44no—
301C4×C11—42no—
302C4×C11—81no—
303C4×C11—82no—
304C4×C11#41714yes—
305C4×C11C4×#4111yescharacteristic
306C4×C11#52011yescharacteristic
307C4×C11#54611yescharacteristic
308C4×C11#54711yescharacteristic
309C22×Q8—21no—
310C22×D4—22no—
311C22×D4D4×C1111yescharacteristic
312C22×D4C23×C1111yescharacteristic
313C23×C4—21no—
314C23×C4—22no—
315C23×C4C23×C1112yes—
316C2×M16—24no—
317C2×M16—24no—
318C2×M16—42no—
319C22×C8C23×C1112yes—
320C22×C8C23×C1111yescharacteristic
321C22×C8C23×C1111yescharacteristic
322C4⋊Q8—22no—
323C4⋊Q8C2×C4×C1114yescomplemented
324#124—216no—
325#121—28no—
326#121—24no—
327#121C2×C4×C1118yescomplemented
328C4×D4—22no—
329C4×D4—44no—
330C4×D4C2×C4×C1114yes—
331C4×D4C2×C4×C1114yescomplemented
332C4×D4D4×C1114yes—
333#117—24no—
334#117—28no—
335#117C2×C4×C1118yescomplemented
336C2×C4⋊C4—21no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4D4×C1111yescharacteristic
343C2×C4⋊C4C23×C1112yes—
344C2×C4⋊C4C23×C1111yescharacteristic
345C2×C4⋊C4C23×C1111yescharacteristic
346C2×C4⋊C4C23×C1112yes—
347C2×C4⋊C4C23×C1111yescharacteristic
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4D4×C1112yes—
353C2×C42—22no—
354C2×C42—21no—
355C2×C42C23×C1111yescharacteristic
356C4⋊C8—22no—
357#102—22no—
358#102—22no—
359#102—42no—
360C22⋊C8—24no—
361C4×C8—22no—
362#95—21no—
363#95—22no—
364C2×C11—44no—
365C2×C11—82no—
366C2×C11#233911yescharacteristic
367C2×C11C2×#41711yescharacteristic
368C2×C11#289711yescharacteristic
369C2×C11#332511yescharacteristic
370C2×C11#332911yescharacteristic
371C2×C11#335411yescharacteristic
372C2×C11#335711yescharacteristic
373C24—21no—
374C24C2×D4×C1112yes—
375C2×Q8—24no—
376C2×Q8—81no—
377C2×Q8—81no—
378C2×D4—28no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—82no—
387C2×D4—82no—
388C2×D4C11×C22⋊C414yes—
389C2×D4C22×C4×C1112yes—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—44no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—44no—
404C22×C4—82no—
405C22×C4C22×C4×C1114yes—
406C22×C4C2×D4×C1112yes—
407C22×C4C2×D4×C1111yescharacteristic
408C22×C4C2×D4×C1114yes—
409C22×C4C2×D4×C1111yescharacteristic
410C22×C4C24×C1111yescharacteristic
411M16—48no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—22no—
416C2×C8—21no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—21no—
420C2×C8C11×#4112yes—
421C4⋊C4—24no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—44no—
430C4⋊C4—42no—
431C4⋊C4—81no—
432C4⋊C4C11×C22⋊C414yes—
433C4⋊C4C22×C4×C1112yes—
434C4⋊C4C22×C4×C1114yes—
435C4⋊C4C11×#4112yes—
436C22⋊C4—28no—
437C22⋊C4—28no—
438C22⋊C4—24no—
439C22⋊C4—44no—
440C22⋊C4C11×C22⋊C418yes—
441C42—28no—
442C42—42no—
443C42C22×C4×C1112yes—
444C42C2×D4×C1112yes—
445C11#2250311yescharacteristic, direct product factor, Sylow
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—22no—
452C23—22no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23—41no—
459C23C2×C11×C22⋊C414yes—
460C23C22×D4×C1111yescharacteristic
461Q8—84no—
462D4—22no—
463D4—22no—
464D4—28no—
465D4—41no—
466D4—41no—
467D4—88no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—48no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—88no—
493C2×C4C2×C11×C22⋊C414yes—
494C2×C4C2×C11×C22⋊C412yes—
495C2×C4C2×C11×C22⋊C412yes—
496C2×C4C11×AGL(1,ℤ/8)12yes—
497C2×C4C11×#13712yes—
498C2×C4C23×C4×C1111yescharacteristic
499C2×C4C22×D4×C1111yescharacteristic
500C2×C4C2×C11×#4111yescharacteristic
501C2×C4C2×C11×#4111yescharacteristic
502C2×C4C11×H(5,𝔽2)11yescharacteristic
503C2×C4C11×2−1+411yescharacteristic
504C8—22no—
505C8—42no—
506C8—41no—
507C22—24no—
508C22—24no—
509C22—24no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22C22×C11×C22⋊C411yescharacteristic
522C22C11×#54611yescharacteristic
523C22C11×#54711yescharacteristic
524C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
525C22C2×C11×#13711yescharacteristic
526C22C11×#57611yescharacteristic
527C22C11×#57711yescharacteristic
528C4—22no—
529C4—24no—
530C4—42no—
531C4—44no—
532C4—42no—
533C4—82no—
534C4—81no—
535C4C11×#41714yes—
536C4C4×C11×#4111yescharacteristic
537C4C11×#52011yescharacteristic
538C4C11×#54611yescharacteristic
539C4C11×#54711yescharacteristic
540C2—44no—
541C2—82no—
542C2C11×#233911yescharacteristic
543C2C2×C11×#41711yescharacteristic
544C2C11×#289711yescharacteristic
545C2C11×#332511yescharacteristic
546C2C11×#332911yescharacteristic
547C2C11×#335411yescharacteristic
548C2C11×#335711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#555C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#436C2semidirect
3. D4×C11×C4⋊C4C2semidirect
4. C11×#1990C2semidirect
5. C11×#1987C2semidirect
6. C11×#1895C2semidirect
7. C11×#1874C2semidirect
8. C11×#1825C2semidirect
9. C11×#1802C2semidirect
10. C4×C11×#102C2semidirect
11. C11×#1736C2semidirect
14. C11×#555C4semidirect
58. C11×C4⋊Q8C2×C4semidirect
62. C11×#121C2×C4semidirect
66. C4×D4×C11C2×C4semidirect
70. C11×#117C2×C4semidirect
99. #22503C11direct (N × H)
173. C2×#436C2×C11semidirect
174. D4×C4⋊C4C2×C11semidirect
175. #1990C2×C11semidirect
176. #1987C2×C11semidirect
177. #1895C2×C11semidirect
178. #1874C2×C11semidirect
179. #1825C2×C11semidirect
180. #1802C2×C11semidirect
181. C4×#102C2×C11semidirect
182. #1736C2×C11semidirect
246. #555C4×C11semidirect
323. C4⋊Q8C2×C4×C11semidirect
327. #121C2×C4×C11semidirect
331. C4×D4C2×C4×C11semidirect
335. #117C2×C4×C11semidirect
445. C11#22503direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5552
C2×C11×#4362
D4×C11×C4⋊C42
C11×#19902
C11×#19872
C11×#18952
C11×#18742
C11×#18252
C11×#18022
C4×C11×#1022
C11×#17362
#2250311