Finite Group Databasebeta

← C11×#24520 #14601713

Subgroups — C11×#24520 #14601713

Order 2816.

1002 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3094C211yesmaximal, characteristic, complemented
2C2×C11×#447C211yesmaximal, characteristic
3C11×#2924C211yesmaximal, characteristic, complemented
4C2×C11×#418C211yesmaximal, characteristic, complemented
5C11×#2063C212yesmaximal, complemented
6C11×#2045C212yesmaximal, complemented
7C11×#1978C212yesmaximal, complemented
8C11×#1931C212yesmaximal, complemented
9C11×#1900C211yesmaximal, characteristic, complemented
10C11×#1855C211yesmaximal, characteristic, complemented
11C11×#1783C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C22×C11×D8C2212yes—
14C22×C11×M16C2211yescharacteristic
15C2×C11×#121C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C11×#482—21no—
18C11×#482—21no—
19C11×#481—21no—
20C11×#480—21no—
21C11×#447—21no—
22C11×#447—21no—
23C11×#447—22no—
24C11×#433—22no—
25C11×#432—21no—
26C11×#431—21no—
27C2×C11×#108C2212yescomplemented
28C11×#428C2211yescharacteristic, complemented
29C11×#428C2211yescharacteristic, complemented
30C11×#424C2212yescomplemented
31C11×#418—21no—
32C11×#418—21no—
33C11×#418C2212yes—
34C11×#418C2212yes—
35C11×#418C2211yescharacteristic, complemented
36C11×#418C2211yescharacteristic, complemented
37C2×C11×#102—21no—
38C2×C11×#102—21no—
39C2×C11×#102C2212yes—
40C2×C11×#100C2212yes—
41C2×C11×#100C2212yes—
42C2×C11×#100C2212yescomplemented
43C11×#407C2211yescharacteristic
44C11×#407C2211yescharacteristic
45C2×C11×C22⋊C8C2211yescharacteristic
46C11×#405C2212yescomplemented
47C11×#343C2212yescomplemented
48C11×#341C2212yescomplemented
49C25×C11—21no—
50C22×D4×C11—24no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11—42no—
58C22×D4×C11C2311yescharacteristic
59C22×D4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C2×C11×D8—24no—
62C2×C11×D8—22no—
63C2×C11×D8—22no—
64C2×C11×D8—42no—
65C2×C11×M16—21no—
66C2×C11×M16—42no—
67C2×C11×M16C2311yescharacteristic
68C2×C11×M16C2312yes—
69C2×C11×M16C2312yes—
70C2×C11×M16C2311yescharacteristic
71C22×C8×C11—21no—
72C22×C8×C11C2312yes—
73C11×#121—21no—
74C11×#121—21no—
75C11×#121—21no—
76C11×#121—21no—
77C11×#117—21no—
78C11×#117—21no—
79C11×#117D411yescharacteristic
80C11×#117D411yescharacteristic
81C11×#117C2311yescharacteristic
82C11×#117C2311yescharacteristic
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C42×C11—21no—
89C11×#108—42no—
90C11×#107—21no—
91C11×#107—21no—
92C11×#106—21no—
93C11×#106—21no—
94C11×C4⋊C8—22no—
95C11×C4⋊C8—22no—
96C11×#102—22no—
97C11×#102—22no—
98C11×#102—22no—
99C11×#102—22no—
100C11×#102—22no—
101C11×#102—22no—
102C11×#102—21no—
103C11×#102—21no—
104C11×#102—21no—
105C11×#102—21no—
106C11×#100—24no—
107C11×#100—42no—
108C11×#100—42no—
109C11×C22⋊C8—21no—
110C11×C22⋊C8—21no—
111C11×C22⋊C8—21no—
112C11×C22⋊C8—21no—
113C11×C22⋊C8D411yescharacteristic
114C11×C22⋊C8D411yescharacteristic
115C11×C22⋊C8D412yes—
116C11×#97—22no—
117C4×C8×C11—22no—
118#24520C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11—22no—
120C24×C11—21no—
121C24×C11—44no—
122C24×C11—41no—
123C24×C11—41no—
124C24×C11—82no—
125C24×C11—82no—
126C24×C11#4111yescharacteristic
127C2×D4×C11—24no—
128C2×D4×C11—24no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—44no—
139C2×D4×C11—44no—
140C2×D4×C11—44no—
141C2×D4×C11—42no—
142C2×D4×C11—42no—
143C2×D4×C11—41no—
144C2×D4×C11—41no—
145C2×D4×C11—41no—
146C2×D4×C11—41no—
147C2×D4×C11—82no—
148C2×D4×C11#4114yes—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C11×D8—44no—
161C11×D8—44no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—22no—
167C11×M16—22no—
168C11×M16—42no—
169C2×C8×C11—22no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—42no—
176C2×C8×C11C2×D412yes—
177C2×C8×C11C2×D412yes—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4C2×D411yescharacteristic
183C11×C4⋊C4C2×D411yescharacteristic
184C11×C4⋊C4C2×D411yescharacteristic
185C11×C4⋊C4C2×D411yescharacteristic
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—41no—
191C11×C22⋊C4—41no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196#3094C2×C1111yescharacteristic, complemented
197C2×#447C2×C1111yescharacteristic
198#2924C2×C1111yescharacteristic, complemented
199C2×#418C2×C1111yescharacteristic, complemented
200#2063C2×C1112yescomplemented
201#2045C2×C1112yescomplemented
202#1978C2×C1112yescomplemented
203#1931C2×C1112yescomplemented
204#1900C2×C1111yescharacteristic, complemented
205#1855C2×C1111yescharacteristic, complemented
206#1783C2×C1111yescharacteristic, complemented
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—24no—
210C23×C11—41no—
211C23×C11—44no—
212C23×C11—44no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—41no—
216C23×C11—42no—
217C23×C11—82no—
218C23×C11—82no—
219C23×C11—82no—
220C23×C11—82no—
221C23×C11—82no—
222C23×C11—81no—
223C23×C11—81no—
224C23×C11—816no—
225C23×C11—82no—
226C23×C11#12111yescharacteristic
227C23×C11#12111yescharacteristic
228C23×C11C2×#4111yescharacteristic
229D4×C11—24no—
230D4×C11—24no—
231D4×C11—44no—
232D4×C11—44no—
233D4×C11—41no—
234D4×C11—42no—
235D4×C11—41no—
236D4×C11—42no—
237D4×C11—42no—
238D4×C11—82no—
239D4×C11—82no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—42no—
252C2×C4×C11—41no—
253C2×C4×C11—81no—
254C2×C4×C11—81no—
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C2×#4112yes—
260C2×C4×C11H(5,𝔽2)12yes—
261C8×C11—22no—
262C8×C11—22no—
263C8×C11—41no—
264C8×C11—42no—
265C8×C11—41no—
266C8×C11—42no—
267C23×D4C22×C1111yescharacteristic
268C22×D8C22×C1112yes—
269C22×M16C22×C1111yescharacteristic
270C2×#121C22×C1111yescharacteristic
271C2×#117C22×C1111yescharacteristic
272#482—21no—
273#482—21no—
274#481—21no—
275#480—21no—
276#447—21no—
277#447—21no—
278#447—22no—
279#433—22no—
280#432—21no—
281#431—21no—
282C2×#108C22×C1112yescomplemented
283#428C22×C1111yescharacteristic, complemented
284#428C22×C1111yescharacteristic, complemented
285#424C22×C1112yescomplemented
286#418—21no—
287#418—21no—
288#418C22×C1112yes—
289#418C22×C1112yes—
290#418C22×C1111yescharacteristic, complemented
291#418C22×C1111yescharacteristic, complemented
292C2×#102—21no—
293C2×#102—21no—
294C2×#102C22×C1112yes—
295C2×#100C22×C1112yes—
296C2×#100C22×C1112yes—
297C2×#100C22×C1112yescomplemented
298#407C22×C1111yescharacteristic
299#407C22×C1111yescharacteristic
300C2×C22⋊C8C22×C1111yescharacteristic
301#405C22×C1112yescomplemented
302#343C22×C1112yescomplemented
303#341C22×C1112yescomplemented
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—21no—
311C22×C11—44no—
312C22×C11—44no—
313C22×C11—84no—
314C22×C11—84no—
315C22×C11—88no—
316C22×C11—88no—
317C22×C11—82no—
318C22×C11—82no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—162no—
323C22×C11#47212yes—
324C22×C11C2×#12111yescharacteristic
325C22×C11#55112yes—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—81no—
333C4×C11#52511yescharacteristic
334C4×C11#53511yescharacteristic
335C4×C11#54612yes—
336C25—21no—
337C22×D4—24no—
338C22×D4—21no—
339C22×D4—21no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4—21no—
343C22×D4—21no—
344C22×D4—42no—
345C22×D4C23×C1111yescharacteristic
346C22×D4C23×C1112yes—
347C23×C4C23×C1111yescharacteristic
348C2×D8—24no—
349C2×D8—22no—
350C2×D8—22no—
351C2×D8—42no—
352C2×M16—21no—
353C2×M16—42no—
354C2×M16C23×C1112yes—
355C2×M16C23×C1111yescharacteristic
356C2×M16C23×C1112yes—
357C2×M16C23×C1111yescharacteristic
358C22×C8—21no—
359C22×C8C23×C1112yes—
360#121—21no—
361#121—21no—
362#121—21no—
363#121—21no—
364#117—21no—
365#117—21no—
366#117D4×C1111yescharacteristic
367#117D4×C1111yescharacteristic
368#117C23×C1111yescharacteristic
369#117C23×C1111yescharacteristic
370C2×C4⋊C4D4×C1111yescharacteristic
371C2×C4⋊C4D4×C1111yescharacteristic
372C2×C4⋊C4C23×C1111yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C42—21no—
376#108—42no—
377#107—21no—
378#107—21no—
379#106—21no—
380#106—21no—
381C4⋊C8—22no—
382C4⋊C8—22no—
383#102—22no—
384#102—22no—
385#102—22no—
386#102—22no—
387#102—22no—
388#102—22no—
389#102—21no—
390#102—21no—
391#102—21no—
392#102—21no—
393#100—24no—
394#100—42no—
395#100—42no—
396C22⋊C8—21no—
397C22⋊C8—21no—
398C22⋊C8—21no—
399C22⋊C8—21no—
400C22⋊C8D4×C1111yescharacteristic
401C22⋊C8D4×C1111yescharacteristic
402C22⋊C8D4×C1112yes—
403#97—22no—
404C4×C8—22no—
405C2×C11—22no—
406C2×C11—22no—
407C2×C11—41no—
408C2×C11—84no—
409C2×C11—161no—
410C2×C11#241111yescharacteristic
411C2×C11C2×#47211yescharacteristic
412C2×C11#306811yescharacteristic
413C24—22no—
414C24—21no—
415C24—44no—
416C24—41no—
417C24—41no—
418C24—82no—
419C24—82no—
420C24C11×#4111yescharacteristic
421C2×D4—24no—
422C2×D4—24no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—82no—
442C2×D4C11×#4114yes—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4C2×D4×C1111yescharacteristic
449C22×C4C2×D4×C1111yescharacteristic
450C22×C4C2×D4×C1111yescharacteristic
451C22×C4C2×D4×C1111yescharacteristic
452C22×C4C11×#4111yescharacteristic
453C22×C4C24×C1111yescharacteristic
454D8—44no—
455D8—44no—
456M16—22no—
457M16—22no—
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—42no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—22no—
469C2×C8—42no—
470C2×C8C2×D4×C1112yes—
471C2×C8C2×D4×C1112yes—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4C2×D4×C1111yescharacteristic
477C4⋊C4C2×D4×C1111yescharacteristic
478C4⋊C4C2×D4×C1111yescharacteristic
479C4⋊C4C2×D4×C1111yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C11#2452011yescharacteristic, direct product factor, Sylow
491C23—22no—
492C23—22no—
493C23—24no—
494C23—41no—
495C23—44no—
496C23—44no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—42no—
501C23—82no—
502C23—82no—
503C23—82no—
504C23—82no—
505C23—82no—
506C23—81no—
507C23—81no—
508C23—816no—
509C23—82no—
510C23C11×#12111yescharacteristic
511C23C11×#12111yescharacteristic
512C23C2×C11×#4111yescharacteristic
513D4—24no—
514D4—24no—
515D4—44no—
516D4—44no—
517D4—41no—
518D4—42no—
519D4—41no—
520D4—42no—
521D4—42no—
522D4—82no—
523D4—82no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—81no—
538C2×C4—81no—
539C2×C4C11×#12111yescharacteristic
540C2×C4C11×#12111yescharacteristic
541C2×C4C22×D4×C1111yescharacteristic
542C2×C4C22×D4×C1111yescharacteristic
543C2×C4C2×C11×#4112yes—
544C2×C4C11×H(5,𝔽2)12yes—
545C8—22no—
546C8—22no—
547C8—41no—
548C8—42no—
549C8—41no—
550C8—42no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—44no—
559C22—44no—
560C22—84no—
561C22—84no—
562C22—88no—
563C22—88no—
564C22—82no—
565C22—82no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—162no—
570C22C11×#47212yes—
571C22C2×C11×#12111yescharacteristic
572C22C11×#55112yes—
573C4—21no—
574C4—21no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—81no—
580C4C11×#52511yescharacteristic
581C4C11×#53511yescharacteristic
582C4C11×#54612yes—
583C2—22no—
584C2—22no—
585C2—41no—
586C2—84no—
587C2—161no—
588C2C11×#241111yescharacteristic
589C2C2×C11×#47211yescharacteristic
590C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#447C2
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×#3094C2semidirect
3. C11×#2924C2semidirect
4. C2×C11×#418C2semidirect
5. C11×#2063C2semidirect
6. C11×#2045C2semidirect
7. C11×#1978C2semidirect
8. C11×#1931C2semidirect
9. C11×#1900C2semidirect
10. C11×#1855C2semidirect
11. C11×#1783C2semidirect
27. C2×C11×#108C22semidirect
28. C11×#428C22semidirect
29. C11×#428C22semidirect
30. C11×#424C22semidirect
35. C11×#418C22semidirect
36. C11×#418C22semidirect
42. C2×C11×#100C22semidirect
46. C11×#405C22semidirect
47. C11×#343C22semidirect
48. C11×#341C22semidirect
118. #24520C11direct (N × H)
196. #3094C2×C11semidirect
198. #2924C2×C11semidirect
199. C2×#418C2×C11semidirect
200. #2063C2×C11semidirect
201. #2045C2×C11semidirect
202. #1978C2×C11semidirect
203. #1931C2×C11semidirect
204. #1900C2×C11semidirect
205. #1855C2×C11semidirect
206. #1783C2×C11semidirect
282. C2×#108C22×C11semidirect
283. #428C22×C11semidirect
284. #428C22×C11semidirect
285. #424C22×C11semidirect
290. #418C22×C11semidirect
291. #418C22×C11semidirect
297. C2×#100C22×C11semidirect
301. #405C22×C11semidirect
302. #343C22×C11semidirect
303. #341C22×C11semidirect
490. C11#24520direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30942
C2×C11×#4472
C11×#29242
C2×C11×#4182
C11×#20632
C11×#20452
C11×#19782
C11×#19312
C11×#19002
C11×#18552
C11×#17832
#2452011