Finite Group Databasebeta

← C11×#24211 #14601404

Subgroups — C11×#24211 #14601404

Order 2816.

2118 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#127C211yesmaximal, characteristic
2C2×C11×#460C212yesmaximal, complemented
3C2×C11×#450C212yesmaximal, complemented
4C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
5C11×#2041C212yesmaximal, complemented
6C11×#2014C212yesmaximal, complemented
7C11×#1982C212yesmaximal, complemented
8C11×#1797C211yesmaximal, characteristic, complemented
9C11×#1786C212yesmaximal, complemented
10C23×D4×C11—21no—
11C23×D4×C11—21no—
12C23×D4×C11C2212yes—
13C22×C11×SD16C2214yescomplemented
14C2×C11×#127—28no—
15C2×C11×#127—21no—
16C2×C11×#127—21no—
17C2×C11×#127C2212yes—
18C2×C11×#127C2212yes—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic, complemented
21C22×C42×C11C2211yescharacteristic
22C11×#460—28no—
23C11×#450—28no—
24C2×C11×C4⋊C8C2212yescomplemented
25C2×C11×#102C2214yescomplemented
26C2×C11×#102C2214yescomplemented
27C2×C11×#102C2214yescomplemented
28C2×C11×C22⋊C8C2212yes—
29C11×#391C2211yescharacteristic, complemented
30C11×#389C2211yescharacteristic, complemented
31C11×#387—21no—
32C11×#385—21no—
33C11×#380C2211yescharacteristic
34C4×C11×C4⋊C4—21no—
35C4×C11×C4⋊C4C2211yescharacteristic, complemented
36C4×C11×C22⋊C4—21no—
37C11×#336C2212yescomplemented
38C25×C11—22no—
39C22×Q8×C11C2311yescharacteristic
40C22×D4×C11—28no—
41C22×D4×C11—28no—
42C22×D4×C11—28no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—24no—
49C22×D4×C11—24no—
50C22×D4×C11—44no—
51C22×D4×C11—44no—
52C22×D4×C11—44no—
53C22×D4×C11—44no—
54C22×D4×C11—44no—
55C22×D4×C11C2314yes—
56C23×C4×C11D411yescharacteristic
57C23×C4×C11D411yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C2×C11×SD16—28no—
60C2×C11×SD16—28no—
61C2×C11×SD16—44no—
62C22×C8×C11C2314yes—
63C11×#127—28no—
64C11×#127—28no—
65C11×#127—28no—
66C11×#127—24no—
67C11×#127D418yes—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8D414yescomplemented
70C4×Q8×C11—24no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C42×C11—24no—
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C42×C11D411yescharacteristic
83C2×C42×C11D411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C11×C4⋊C8—24no—
87C11×#102—28no—
88C11×#102—28no—
89C11×#102—44no—
90C11×C22⋊C8—24no—
91C11×#95—21no—
92C11×#95—21no—
93C11×#95—21no—
94C11×#95—21no—
95C11×#95—21no—
96#24211C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11—28no—
98C24×C11—24no—
99C24×C11—44no—
100C24×C11—44no—
101C24×C11—44no—
102C24×C11—44no—
103C24×C11—44no—
104C24×C11—44no—
105C24×C11C2×D411yescharacteristic
106C2×Q8×C11—21no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11C2×D412yescomplemented
110C2×D4×C11—28no—
111C2×D4×C11—28no—
112C2×D4×C11—28no—
113C2×D4×C11—28no—
114C2×D4×C11—28no—
115C2×D4×C11—24no—
116C2×D4×C11—24no—
117C2×D4×C11—24no—
118C2×D4×C11—24no—
119C2×D4×C11—24no—
120C2×D4×C11—416no—
121C2×D4×C11—416no—
122C2×D4×C11—432no—
123C2×D4×C11—44no—
124C2×D4×C11—44no—
125C2×D4×C11—44no—
126C2×D4×C11—44no—
127C2×D4×C11—44no—
128C2×D4×C11—432no—
129C2×D4×C11—44no—
130C2×D4×C11—44no—
131C2×D4×C11—44no—
132C2×D4×C11—44no—
133C2×D4×C11—44no—
134C2×D4×C11C2×D418yes—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11SD1614yescomplemented
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4112yes—
154C22×C4×C11C2411yescharacteristic
155C11×SD16—416no—
156C2×C8×C11—24no—
157C2×C8×C11—24no—
158C2×C8×C11—24no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4C2×D412yescomplemented
166C11×C22⋊C4—24no—
167C11×C22⋊C4—42no—
168C42×C11—22no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11—42no—
172C42×C11—42no—
173C42×C11C2×D414yes—
174C22×#127C2×C1111yescharacteristic
175C2×#460C2×C1112yescomplemented
176C2×#450C2×C1112yescomplemented
177C4×C22⋊Q8C2×C1111yescharacteristic, complemented
178#2041C2×C1112yescomplemented
179#2014C2×C1112yescomplemented
180#1982C2×C1112yescomplemented
181#1797C2×C1111yescharacteristic, complemented
182#1786C2×C1112yescomplemented
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—28no—
188C23×C11—416no—
189C23×C11—416no—
190C23×C11—416no—
191C23×C11—44no—
192C23×C11—44no—
193C23×C11—44no—
194C23×C11—44no—
195C23×C11—44no—
196C23×C11—44no—
197C23×C11—88no—
198C23×C11—88no—
199C23×C11—88no—
200C23×C11—88no—
201C23×C11#12112yes—
202C23×C11C2×SD1612yes—
203C23×C11AGL(1,ℤ/8)12yes—
204C23×C11C22×D411yescharacteristic
205Q8×C11—24no—
206Q8×C11—42no—
207D4×C11—28no—
208D4×C11—28no—
209D4×C11—416no—
210D4×C11—416no—
211D4×C11—416no—
212D4×C11—416no—
213D4×C11—44no—
214D4×C11—44no—
215D4×C11—416no—
216C2×C4×C11—28no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—28no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11#12012yes—
241C2×C4×C11#12012yes—
242C2×C4×C11#12112yes—
243C2×C4×C11C2×SD1612yes—
244C2×C4×C11C2×SD1612yes—
245C2×C4×C11AGL(1,ℤ/8)12yes—
246C2×C4×C11AGL(1,ℤ/8)12yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D412yes—
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11H(5,𝔽2)12yes—
251C8×C11—44no—
252C23×D4—21no—
253C23×D4—21no—
254C23×D4C22×C1112yes—
255C22×SD16C22×C1114yescomplemented
256C2×#127—28no—
257C2×#127—21no—
258C2×#127—21no—
259C2×#127C22×C1112yes—
260C2×#127C22×C1112yes—
261C2×C22⋊Q8C22×C1111yescharacteristic
262C2×C4×Q8C22×C1111yescharacteristic, complemented
263C22×C42C22×C1111yescharacteristic
264#460—28no—
265#450—28no—
266C2×C4⋊C8C22×C1112yescomplemented
267C2×#102C22×C1114yescomplemented
268C2×#102C22×C1114yescomplemented
269C2×#102C22×C1114yescomplemented
270C2×C22⋊C8C22×C1112yes—
271#391C22×C1111yescharacteristic, complemented
272#389C22×C1111yescharacteristic, complemented
273#387—21no—
274#385—21no—
275#380C22×C1111yescharacteristic
276C4×C4⋊C4—21no—
277C4×C4⋊C4C22×C1111yescharacteristic, complemented
278C4×C22⋊C4—21no—
279#336C22×C1112yescomplemented
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—48no—
287C22×C11—48no—
288C22×C11—48no—
289C22×C11—832no—
290C22×C11—84no—
291C22×C11—84no—
292C22×C11—84no—
293C22×C11—84no—
294C22×C11#46014yescomplemented
295C22×C11C2×#12011yescharacteristic
296C22×C11C2×#12111yescharacteristic
297C22×C11#53511yescharacteristic
298C22×C11C22×SD1611yescharacteristic
299C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
301C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
302C4×C11—22no—
303C4×C11—22no—
304C4×C11—22no—
305C4×C11—22no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11—81no—
309C4×C11—81no—
310C4×C11#45014yescomplemented
311C4×C11D4212yes—
312C4×C11#54612yes—
313C25—22no—
314C22×Q8C23×C1111yescharacteristic
315C22×D4—28no—
316C22×D4—28no—
317C22×D4—28no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—24no—
324C22×D4—24no—
325C22×D4—44no—
326C22×D4—44no—
327C22×D4—44no—
328C22×D4—44no—
329C22×D4—44no—
330C22×D4C23×C1114yes—
331C23×C4D4×C1111yescharacteristic
332C23×C4D4×C1111yescharacteristic
333C23×C4C23×C1111yescharacteristic
334C2×SD16—28no—
335C2×SD16—28no—
336C2×SD16—44no—
337C22×C8C23×C1114yes—
338#127—28no—
339#127—28no—
340#127—28no—
341#127—24no—
342#127D4×C1118yes—
343C22⋊Q8—22no—
344C22⋊Q8D4×C1114yescomplemented
345C4×Q8—24no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4C23×C1111yescharacteristic
350C2×C4⋊C4C23×C1111yescharacteristic
351C2×C4⋊C4C23×C1111yescharacteristic
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C42—24no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42D4×C1111yescharacteristic
358C2×C42D4×C1111yescharacteristic
359C2×C42C23×C1111yescharacteristic
360C2×C42C23×C1111yescharacteristic
361C4⋊C8—24no—
362#102—28no—
363#102—28no—
364#102—44no—
365C22⋊C8—24no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371C2×C11—24no—
372C2×C11—88no—
373C2×C11#240811yescharacteristic
374C2×C11C2×#45011yescharacteristic
375C2×C11#300311yescharacteristic
376C2×C11C2×#46011yescharacteristic
377C2×C11#303811yescharacteristic
378C2×C11#320811yescharacteristic
379C2×C11#321711yescharacteristic
380C24—28no—
381C24—24no—
382C24—44no—
383C24—44no—
384C24—44no—
385C24—44no—
386C24—44no—
387C24—44no—
388C24C2×D4×C1111yescharacteristic
389C2×Q8—21no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8C2×D4×C1112yescomplemented
393C2×D4—28no—
394C2×D4—28no—
395C2×D4—28no—
396C2×D4—28no—
397C2×D4—28no—
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—24no—
401C2×D4—24no—
402C2×D4—24no—
403C2×D4—416no—
404C2×D4—416no—
405C2×D4—432no—
406C2×D4—44no—
407C2×D4—44no—
408C2×D4—44no—
409C2×D4—44no—
410C2×D4—44no—
411C2×D4—432no—
412C2×D4—44no—
413C2×D4—44no—
414C2×D4—44no—
415C2×D4—44no—
416C2×D4—44no—
417C2×D4C2×D4×C1118yes—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4C11×SD1614yescomplemented
430C22×C4C2×D4×C1111yescharacteristic
431C22×C4C2×D4×C1111yescharacteristic
432C22×C4C2×D4×C1112yes—
433C22×C4C2×D4×C1111yescharacteristic
434C22×C4C2×D4×C1111yescharacteristic
435C22×C4C2×D4×C1111yescharacteristic
436C22×C4C11×#4112yes—
437C22×C4C24×C1111yescharacteristic
438SD16—416no—
439C2×C8—24no—
440C2×C8—24no—
441C2×C8—24no—
442C4⋊C4—24no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—42no—
447C4⋊C4—42no—
448C4⋊C4C2×D4×C1112yescomplemented
449C22⋊C4—24no—
450C22⋊C4—42no—
451C42—22no—
452C42—22no—
453C42—22no—
454C42—42no—
455C42—42no—
456C42C2×D4×C1114yes—
457C11#2421111yescharacteristic, direct product factor, Sylow
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—28no—
463C23—416no—
464C23—416no—
465C23—416no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—44no—
470C23—44no—
471C23—44no—
472C23—88no—
473C23—88no—
474C23—88no—
475C23—88no—
476C23C11×#12112yes—
477C23C2×C11×SD1612yes—
478C23C11×AGL(1,ℤ/8)12yes—
479C23C22×D4×C1111yescharacteristic
480Q8—24no—
481Q8—42no—
482D4—28no—
483D4—28no—
484D4—416no—
485D4—416no—
486D4—416no—
487D4—416no—
488D4—44no—
489D4—44no—
490D4—416no—
491C2×C4—28no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—28no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4C11×#12012yes—
516C2×C4C11×#12012yes—
517C2×C4C11×#12112yes—
518C2×C4C2×C11×SD1612yes—
519C2×C4C2×C11×SD1612yes—
520C2×C4C11×AGL(1,ℤ/8)12yes—
521C2×C4C11×AGL(1,ℤ/8)12yes—
522C2×C4C22×D4×C1111yescharacteristic
523C2×C4C22×D4×C1112yes—
524C2×C4C2×C11×#4111yescharacteristic
525C2×C4C11×H(5,𝔽2)12yes—
526C8—44no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—48no—
534C22—48no—
535C22—48no—
536C22—832no—
537C22—84no—
538C22—84no—
539C22—84no—
540C22—84no—
541C22C11×#46014yescomplemented
542C22C2×C11×#12011yescharacteristic
543C22C2×C11×#12111yescharacteristic
544C22C11×#53511yescharacteristic
545C22C22×C11×SD1611yescharacteristic
546C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
547C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
548C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
549C4—22no—
550C4—22no—
551C4—22no—
552C4—22no—
553C4—42no—
554C4—42no—
555C4—81no—
556C4—81no—
557C4C11×#45014yescomplemented
558C4D42×C1112yes—
559C4C11×#54612yes—
560C2—24no—
561C2—88no—
562C2C11×#240811yescharacteristic
563C2C2×C11×#45011yescharacteristic
564C2C11×#300311yescharacteristic
565C2C2×C11×#46011yescharacteristic
566C2C11×#303811yescharacteristic
567C2C11×#320811yescharacteristic
568C2C11×#321711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#127C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#460C2semidirect
3. C2×C11×#450C2semidirect
4. C4×C11×C22⋊Q8C2semidirect
5. C11×#2041C2semidirect
6. C11×#2014C2semidirect
7. C11×#1982C2semidirect
8. C11×#1797C2semidirect
9. C11×#1786C2semidirect
13. C22×C11×SD16C22semidirect
20. C2×C4×Q8×C11C22semidirect
24. C2×C11×C4⋊C8C22semidirect
25. C2×C11×#102C22semidirect
26. C2×C11×#102C22semidirect
27. C2×C11×#102C22semidirect
29. C11×#391C22semidirect
30. C11×#389C22semidirect
35. C4×C11×C4⋊C4C22semidirect
37. C11×#336C22semidirect
69. C11×C22⋊Q8D4semidirect
96. #24211C11direct (N × H)
109. C2×Q8×C11C2×D4semidirect
146. C22×C4×C11SD16semidirect
165. C11×C4⋊C4C2×D4semidirect
175. C2×#460C2×C11semidirect
176. C2×#450C2×C11semidirect
177. C4×C22⋊Q8C2×C11semidirect
178. #2041C2×C11semidirect
179. #2014C2×C11semidirect
180. #1982C2×C11semidirect
181. #1797C2×C11semidirect
182. #1786C2×C11semidirect
255. C22×SD16C22×C11semidirect
262. C2×C4×Q8C22×C11semidirect
266. C2×C4⋊C8C22×C11semidirect
267. C2×#102C22×C11semidirect
268. C2×#102C22×C11semidirect
269. C2×#102C22×C11semidirect
271. #391C22×C11semidirect
272. #389C22×C11semidirect
277. C4×C4⋊C4C22×C11semidirect
279. #336C22×C11semidirect
294. C22×C11#460semidirect
310. C4×C11#450semidirect
344. C22⋊Q8D4×C11semidirect
392. C2×Q8C2×D4×C11semidirect
429. C22×C4C11×SD16semidirect
448. C4⋊C4C2×D4×C11semidirect
457. C11#24211direct (N × H)
541. C22C11×#460semidirect
557. C4C11×#450semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1272
C2×C11×#4602
C2×C11×#4502
C4×C11×C22⋊Q82
C11×#20412
C11×#20142
C11×#19822
C11×#17972
C11×#17862
#2421111