Finite Group Databasebeta

← C11×#23950 #14601143

Subgroups — C11×#23950 #14601143

Order 2816.

1242 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3493C211yesmaximal, characteristic, complemented
2C11×#3005C212yesmaximal, complemented
3C11×#2297C211yesmaximal, characteristic, complemented
4C11×#2028C211yesmaximal, characteristic, complemented
5C11×#2027C211yesmaximal, characteristic, complemented
6C11×#2007C211yesmaximal, characteristic, complemented
7C11×#2006C211yesmaximal, characteristic, complemented
8C11×#1896C212yesmaximal, complemented
9C11×#1883C212yesmaximal, complemented
10C11×#1882C212yesmaximal, complemented
11C11×#1822C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C2×C11×#137C2212yes—
14C2×C11×AGL(1,ℤ/8)C2212yes—
15C11×#556—22no—
16C11×#555—22no—
17C11×#553—22no—
18C11×#552—22no—
19C11×#544C2211yescharacteristic
20C11×#538—22no—
21C11×#537C2211yescharacteristic
22C11×#529—22no—
23C11×#525C2212yes—
24C11×#520C2212yes—
25C2×C11×#117C2211yescharacteristic
26C22×C42×C11C2211yescharacteristic
27C11×#452—22no—
28C11×#452—22no—
29C11×#449—22no—
30C11×#449—22no—
31C2×C11×#104C2212yes—
32C2×C11×#104C2212yes—
33C11×#419C2212yes—
34C11×#418C2212yes—
35C11×#407C2212yes—
36C11×#391C2211yescharacteristic
37C11×#391C2211yescharacteristic
38C11×#390C2211yescharacteristic
39C11×#390C2211yescharacteristic
40C11×#386—22no—
41C4×C11×C22⋊C4—22no—
42C11×#343C2212yes—
43C11×#343C2211yescharacteristic
44C11×#343C2211yescharacteristic
45C11×#339C2212yes—
46C11×#339C2212yes—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41—42no—
52C2×C11×#41C2312yes—
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11—21no—
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11—21no—
57C23×C4×C11—21no—
58C23×C4×C11C2311yescharacteristic
59C11×#137—24no—
60C11×#137—42no—
61C11×AGL(1,ℤ/8)—24no—
62C11×AGL(1,ℤ/8)—42no—
63C2×C11×Q16—22no—
64C2×C11×SD16—22no—
65C2×C11×SD16—22no—
66C2×C11×D8—22no—
67C2×C11×M16C2312yes—
68C2×C11×M16C2312yes—
69C11×C4⋊Q8—22no—
70C11×#126—24no—
71C11×#126—24no—
72C11×#125—22no—
73C11×#125—22no—
74C11×#124—22no—
75C11×#124—24no—
76C11×#123—24no—
77C11×#123—22no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8D412yes—
81C11×C22⋊Q8D412yes—
82C11×#121—24no—
83C11×#121—22no—
84C11×#121—22no—
85C11×#121D412yes—
86C11×#121D412yes—
87C11×#120—22no—
88C4×Q8×C11—22no—
89C4×Q8×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—24no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C11×#117—24no—
96C11×#117—22no—
97C11×#117—22no—
98C11×#117—22no—
99C11×#117C2312yes—
100C2×C11×C4⋊C4—22no—
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4D412yes—
106C2×C42×C11—21no—
107C2×C42×C11—42no—
108C2×C42×C11D412yes—
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C11×#104—42no—
112C11×#104—42no—
113C11×#103—22no—
114C11×#103—22no—
115C11×#102—22no—
116C11×#102—22no—
117C11×C22⋊C8—22no—
118C11×C22⋊C8—22no—
119C11×#95—22no—
120C11×#95—22no—
121#23950C1111yesmaximal, characteristic, direct product factor, Sylow
122C24×C11—21no—
123C24×C11C2×D411yescharacteristic
124C11×#41—22no—
125C11×#41—22no—
126C11×#41—22no—
127C11×#41—22no—
128C11×#41—44no—
129C11×#41—44no—
130C11×#41—44no—
131C11×#41—44no—
132C2×Q8×C11—22no—
133C2×Q8×C11—21no—
134C2×Q8×C11—22no—
135C2×Q8×C11—22no—
136C2×Q8×C11C2×D412yes—
137C2×Q8×C11#4112yes—
138C2×D4×C11—24no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—21no—
145C2×D4×C11—22no—
146C2×D4×C11—42no—
147C2×D4×C11—42no—
148C2×D4×C11C2×D412yes—
149C2×D4×C11#4112yes—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—24no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—24no—
158C22×C4×C11—22no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—41no—
164C22×C4×C11—41no—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D412yes—
170C22×C4×C11C2411yescharacteristic
171C11×Q16—44no—
172C11×SD16—44no—
173C11×SD16—44no—
174C11×D8—44no—
175C11×M16—22no—
176C11×M16—22no—
177C11×M16—22no—
178C11×M16—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4C2×D412yes—
190C11×C4⋊C4C2×D412yes—
191C11×C22⋊C4—24no—
192C11×C22⋊C4—24no—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—44no—
200C11×C22⋊C4—44no—
201C42×C11—24no—
202C42×C11—22no—
203C42×C11—22no—
204C42×C11—22no—
205C42×C11—22no—
206C42×C11—22no—
207C42×C11—42no—
208#3493C2×C1111yescharacteristic, complemented
209#3005C2×C1112yescomplemented
210#2297C2×C1111yescharacteristic, complemented
211#2028C2×C1111yescharacteristic, complemented
212#2027C2×C1111yescharacteristic, complemented
213#2007C2×C1111yescharacteristic, complemented
214#2006C2×C1111yescharacteristic, complemented
215#1896C2×C1112yescomplemented
216#1883C2×C1112yescomplemented
217#1882C2×C1112yescomplemented
218#1822C2×C1111yescharacteristic, complemented
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11#12012yes—
230C23×C11C22×D411yescharacteristic
231Q8×C11—22no—
232Q8×C11—24no—
233Q8×C11—22no—
234Q8×C11—42no—
235Q8×C11—82no—
236D4×C11—22no—
237D4×C11—24no—
238D4×C11—22no—
239D4×C11—48no—
240D4×C11—42no—
241D4×C11—42no—
242D4×C11—42no—
243D4×C11—82no—
244D4×C11—82no—
245D4×C11—82no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—44no—
261C2×C4×C11—44no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—48no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—84no—
274C2×C4×C11#12011yescharacteristic
275C2×C4×C11#12011yescharacteristic
276C2×C4×C11C22×D412yes—
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11H(5,𝔽2)12yes—
280C8×C11—42no—
281C8×C11—42no—
282C22×#41C22×C1111yescharacteristic
283C2×#137C22×C1112yes—
284C2×AGL(1,ℤ/8)C22×C1112yes—
285#556—22no—
286#555—22no—
287#553—22no—
288#552—22no—
289#544C22×C1111yescharacteristic
290#538—22no—
291#537C22×C1111yescharacteristic
292#529—22no—
293#525C22×C1112yes—
294#520C22×C1112yes—
295C2×#117C22×C1111yescharacteristic
296C22×C42C22×C1111yescharacteristic
297#452—22no—
298#452—22no—
299#449—22no—
300#449—22no—
301C2×#104C22×C1112yes—
302C2×#104C22×C1112yes—
303#419C22×C1112yes—
304#418C22×C1112yes—
305#407C22×C1112yes—
306#391C22×C1111yescharacteristic
307#391C22×C1111yescharacteristic
308#390C22×C1111yescharacteristic
309#390C22×C1111yescharacteristic
310#386—22no—
311C4×C22⋊C4—22no—
312#343C22×C1112yes—
313#343C22×C1111yescharacteristic
314#343C22×C1111yescharacteristic
315#339C22×C1112yes—
316#339C22×C1112yes—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—44no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—82no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11C2×#12011yescharacteristic
333C22×C11#52511yescharacteristic
334C22×C11#53511yescharacteristic
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—42no—
338C4×C11—42no—
339C4×C11—42no—
340C4×C11—42no—
341C4×C11—42no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11#54612yes—
346C4×C11#54612yes—
347C2×#41—22no—
348C2×#41—22no—
349C2×#41—22no—
350C2×#41—22no—
351C2×#41—42no—
352C2×#41C23×C1112yes—
353C22×Q8C23×C1111yescharacteristic
354C22×D4—21no—
355C22×D4C23×C1111yescharacteristic
356C23×C4—21no—
357C23×C4—21no—
358C23×C4C23×C1111yescharacteristic
359#137—24no—
360#137—42no—
361AGL(1,ℤ/8)—24no—
362AGL(1,ℤ/8)—42no—
363C2×Q16—22no—
364C2×SD16—22no—
365C2×SD16—22no—
366C2×D8—22no—
367C2×M16C23×C1112yes—
368C2×M16C23×C1112yes—
369C4⋊Q8—22no—
370#126—24no—
371#126—24no—
372#125—22no—
373#125—22no—
374#124—22no—
375#124—24no—
376#123—24no—
377#123—22no—
378C22⋊Q8—22no—
379C22⋊Q8—22no—
380C22⋊Q8D4×C1112yes—
381C22⋊Q8D4×C1112yes—
382#121—24no—
383#121—22no—
384#121—22no—
385#121D4×C1112yes—
386#121D4×C1112yes—
387#120—22no—
388C4×Q8—22no—
389C4×Q8—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—24no—
393C4×D4—22no—
394C4×D4—22no—
395#117—24no—
396#117—22no—
397#117—22no—
398#117—22no—
399#117C23×C1112yes—
400C2×C4⋊C4—22no—
401C2×C4⋊C4C23×C1111yescharacteristic
402C2×C4⋊C4C23×C1111yescharacteristic
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4D4×C1112yes—
406C2×C42—21no—
407C2×C42—42no—
408C2×C42D4×C1112yes—
409C2×C42C23×C1111yescharacteristic
410C2×C42C23×C1111yescharacteristic
411#104—42no—
412#104—42no—
413#103—22no—
414#103—22no—
415#102—22no—
416#102—22no—
417C22⋊C8—22no—
418C22⋊C8—22no—
419#95—22no—
420#95—22no—
421C2×C11—21no—
422C2×C11—21no—
423C2×C11—42no—
424C2×C11—82no—
425C2×C11—82no—
426C2×C11#240411yescharacteristic
427C2×C11#301811yescharacteristic
428C2×C11#301811yescharacteristic
429C24—21no—
430C24C2×D4×C1111yescharacteristic
431#41—22no—
432#41—22no—
433#41—22no—
434#41—22no—
435#41—44no—
436#41—44no—
437#41—44no—
438#41—44no—
439C2×Q8—22no—
440C2×Q8—21no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8C2×D4×C1112yes—
444C2×Q8C11×#4112yes—
445C2×D4—24no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—22no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4C2×D4×C1112yes—
456C2×D4C11×#4112yes—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4C2×D4×C1111yescharacteristic
473C22×C4C2×D4×C1112yes—
474C22×C4C2×D4×C1112yes—
475C22×C4C2×D4×C1112yes—
476C22×C4C2×D4×C1112yes—
477C22×C4C24×C1111yescharacteristic
478Q16—44no—
479SD16—44no—
480SD16—44no—
481D8—44no—
482M16—22no—
483M16—22no—
484M16—22no—
485M16—22no—
486C2×C8—22no—
487C2×C8—22no—
488C4⋊C4—24no—
489C4⋊C4—24no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4C2×D4×C1112yes—
497C4⋊C4C2×D4×C1112yes—
498C22⋊C4—24no—
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—44no—
507C22⋊C4—44no—
508C42—24no—
509C42—22no—
510C42—22no—
511C42—22no—
512C42—22no—
513C42—22no—
514C42—42no—
515C11#2395011yescharacteristic, direct product factor, Sylow
516C23—21no—
517C23—21no—
518C23—22no—
519C23—22no—
520C23—41no—
521C23—41no—
522C23—42no—
523C23—42no—
524C23—41no—
525C23—41no—
526C23C11×#12012yes—
527C23C22×D4×C1111yescharacteristic
528Q8—22no—
529Q8—24no—
530Q8—22no—
531Q8—42no—
532Q8—82no—
533D4—22no—
534D4—24no—
535D4—22no—
536D4—48no—
537D4—42no—
538D4—42no—
539D4—42no—
540D4—82no—
541D4—82no—
542D4—82no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—48no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—84no—
571C2×C4C11×#12011yescharacteristic
572C2×C4C11×#12011yescharacteristic
573C2×C4C22×D4×C1112yes—
574C2×C4C2×C11×#4111yescharacteristic
575C2×C4C2×C11×#4111yescharacteristic
576C2×C4C11×H(5,𝔽2)12yes—
577C8—42no—
578C8—42no—
579C22—21no—
580C22—21no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—42no—
585C22—42no—
586C22—44no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—82no—
592C22—81no—
593C22—81no—
594C22C2×C11×#12011yescharacteristic
595C22C11×#52511yescharacteristic
596C22C11×#53511yescharacteristic
597C4—21no—
598C4—21no—
599C4—42no—
600C4—42no—
601C4—42no—
602C4—42no—
603C4—42no—
604C4—42no—
605C4—42no—
606C4—42no—
607C4C11×#54612yes—
608C4C11×#54612yes—
609C2—21no—
610C2—21no—
611C2—42no—
612C2—82no—
613C2—82no—
614C2C11×#240411yescharacteristic
615C2C11×#301811yescharacteristic
616C2C11×#301811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3493C2semidirect
2. C11×#3005C2semidirect
3. C11×#2297C2semidirect
4. C11×#2028C2semidirect
5. C11×#2027C2semidirect
6. C11×#2007C2semidirect
7. C11×#2006C2semidirect
8. C11×#1896C2semidirect
9. C11×#1883C2semidirect
10. C11×#1882C2semidirect
11. C11×#1822C2semidirect
121. #23950C11direct (N × H)
208. #3493C2×C11semidirect
209. #3005C2×C11semidirect
210. #2297C2×C11semidirect
211. #2028C2×C11semidirect
212. #2027C2×C11semidirect
213. #2007C2×C11semidirect
214. #2006C2×C11semidirect
215. #1896C2×C11semidirect
216. #1883C2×C11semidirect
217. #1882C2×C11semidirect
218. #1822C2×C11semidirect
515. C11#23950direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34932
C11×#30052
C11×#22972
C11×#20282
C11×#20272
C11×#20072
C11×#20062
C11×#18962
C11×#18832
C11×#18822
C11×#18222
#2395011