Finite Group Databasebeta

← C2×C11×#2012 #14600610

Subgroups — C2×C11×#2012 #14600610

Order 2816.

2382 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×SD16C211yesmaximal, characteristic, complemented
2C23×C11×D8C211yesmaximal, characteristic
3C22×C11×#124C211yesmaximal, characteristic, complemented
4C22×C11×#103C211yesmaximal, characteristic, complemented
5C22×C11×#102C211yesmaximal, characteristic, complemented
6C2×C11×#390C211yesmaximal, characteristic, complemented
7C11×#2012C218yesmaximal, direct product factor
8C2×C11×#336C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C22×C11×SD16—24no—
13C22×C11×SD16—24no—
14C22×C11×SD16—24no—
15C22×C11×SD16C2214yescomplemented
16C22×C11×D8—24no—
17C22×C11×D8—24no—
18C22×C11×D8—24no—
19C22×C11×D8C2214yes—
20C23×C8×C11C2211yescharacteristic
21C23×C8×C11C2211yescharacteristic
22C2×C11×#124—24no—
23C2×C11×#124—24no—
24C2×C11×#124—22no—
25C2×C11×#124C2214yescomplemented
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4—22no—
28C22×C11×C22⋊C4—22no—
29C22×C42×C11C2211yescharacteristic
30C2×C11×#103—24no—
31C2×C11×#103C2214yescomplemented
32C2×C11×#102—24no—
33C2×C11×#102C2214yescomplemented
34C11×#390—22no—
35C11×#390C2214yescomplemented
36C11×#336C2214yescomplemented
37C25×C11—21no—
38C25×C11—21no—
39C22×Q8×C11—22no—
40C22×Q8×C11—21no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11—22no—
45C22×Q8×C11D414yes—
46C22×Q8×C11C2312yes—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11—22no—
58C22×D4×C11—22no—
59C22×D4×C11D414yes—
60C22×D4×C11D414yes—
61C22×D4×C11C2312yes—
62C22×D4×C11C2312yes—
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11D412yes—
66C23×C4×C11C2311yescharacteristic
67C2×C11×SD16—232no—
68C2×C11×SD16—28no—
69C2×C11×SD16—28no—
70C2×C11×SD16—28no—
71C2×C11×D8—232no—
72C2×C11×D8—28no—
73C2×C11×D8—28no—
74C2×C11×D8—28no—
75C22×C8×C11—22no—
76C22×C8×C11—22no—
77C22×C8×C11—22no—
78C22×C8×C11—22no—
79C22×C8×C11D414yes—
80C22×C8×C11D414yes—
81C22×C8×C11C2312yes—
82C22×C8×C11C2312yes—
83C11×#124—216no—
84C11×#124—28no—
85C11×#124—28no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C22⋊C4—216no—
91C2×C11×C22⋊C4—28no—
92C2×C11×C22⋊C4—28no—
93C2×C11×C22⋊C4—48no—
94C2×C42×C11—22no—
95C2×C42×C11—22no—
96C2×C42×C11D412yes—
97C2×C42×C11C2312yes—
98C11×#103—28no—
99C11×#102—28no—
100C2×#2012C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11—24no—
102C24×C11—24no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—42no—
106C24×C11—42no—
107C24×C11—42no—
108C24×C11—42no—
109C24×C11—44no—
110C24×C11—44no—
111C24×C11—44no—
112C24×C11—44no—
113C24×C11C2×D411yescharacteristic
114C2×Q8×C11—24no—
115C2×Q8×C11—22no—
116C2×Q8×C11—28no—
117C2×Q8×C11—28no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—44no—
123C2×Q8×C11—42no—
124C2×Q8×C11—44no—
125C2×Q8×C11—42no—
126C2×Q8×C11C2×D414yes—
127C2×D4×C11—28no—
128C2×D4×C11—28no—
129C2×D4×C11—28no—
130C2×D4×C11—24no—
131C2×D4×C11—28no—
132C2×D4×C11—24no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—44no—
144C2×D4×C11—42no—
145C2×D4×C11—44no—
146C2×D4×C11—44no—
147C2×D4×C11—44no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11C2×D414yes—
152C2×D4×C11C2×D414yes—
153C22×C4×C11—24no—
154C22×C4×C11—24no—
155C22×C4×C11—24no—
156C22×C4×C11—24no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11—42no—
162C22×C4×C11—44no—
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D412yes—
170C22×C4×C11#4112yes—
171C22×C4×C11C2411yescharacteristic
172C11×SD16—232no—
173C11×D8—232no—
174C2×C8×C11—28no—
175C2×C8×C11—28no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11C2×D414yes—
181C2×C8×C11C2×D414yes—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—42no—
185C11×C22⋊C4—232no—
186C11×C22⋊C4—416no—
187C42×C11—24no—
188C42×C11—22no—
189C42×C11—22no—
190C23×SD16C2×C1111yescharacteristic, complemented
191C23×D8C2×C1111yescharacteristic
192C22×#124C2×C1111yescharacteristic, complemented
193C22×#103C2×C1111yescharacteristic, complemented
194C22×#102C2×C1111yescharacteristic, complemented
195C2×#390C2×C1111yescharacteristic, complemented
196#2012C2×C1118yesdirect product factor
197C2×#336C2×C1111yescharacteristic, complemented
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—44no—
205C23×C11—44no—
206C23×C11—44no—
207C23×C11—44no—
208C23×C11—48no—
209C23×C11—48no—
210C23×C11—416no—
211C23×C11—416no—
212C23×C11—88no—
213C23×C11—88no—
214C23×C11—84no—
215C23×C11—84no—
216C23×C11—84no—
217C23×C11—84no—
218C23×C11#12012yes—
219C23×C11#12112yes—
220C23×C11#12712yes—
221C23×C11#13514yes—
222C23×C11AGL(1,ℤ/8)14yes—
223C23×C11C22×D411yescharacteristic
224Q8×C11—24no—
225Q8×C11—24no—
226Q8×C11—42no—
227Q8×C11—42no—
228Q8×C11—48no—
229D4×C11—24no—
230D4×C11—24no—
231D4×C11—24no—
232D4×C11—24no—
233D4×C11—42no—
234D4×C11—42no—
235D4×C11—42no—
236D4×C11—42no—
237D4×C11—48no—
238D4×C11—48no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—48no—
246C2×C4×C11—48no—
247C2×C4×C11—42no—
248C2×C4×C11—44no—
249C2×C4×C11—84no—
250C2×C4×C11#12014yes—
251C2×C4×C11#12014yes—
252C2×C4×C11#12012yes—
253C2×C4×C11#12114yes—
254C2×C4×C11#12114yes—
255C2×C4×C11#12112yes—
256C2×C4×C11#12712yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C8×C11—24no—
264C8×C11—24no—
265C23×Q8C22×C1111yescharacteristic
266C23×D4C22×C1111yescharacteristic
267C23×D4C22×C1111yescharacteristic
268C22×SD16—24no—
269C22×SD16—24no—
270C22×SD16—24no—
271C22×SD16C22×C1114yescomplemented
272C22×D8—24no—
273C22×D8—24no—
274C22×D8—24no—
275C22×D8C22×C1114yes—
276C23×C8C22×C1111yescharacteristic
277C23×C8C22×C1111yescharacteristic
278C2×#124—24no—
279C2×#124—24no—
280C2×#124—22no—
281C2×#124C22×C1114yescomplemented
282C22×C4⋊C4C22×C1111yescharacteristic
283C22×C22⋊C4—22no—
284C22×C22⋊C4—22no—
285C22×C42C22×C1111yescharacteristic
286C2×#103—24no—
287C2×#103C22×C1114yescomplemented
288C2×#102—24no—
289C2×#102C22×C1114yescomplemented
290#390—22no—
291#390C22×C1114yescomplemented
292#336C22×C1114yescomplemented
293C22×C11—44no—
294C22×C11—44no—
295C22×C11—48no—
296C22×C11—48no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11—84no—
302C22×C11—84no—
303C22×C11—816no—
304C22×C11—816no—
305C22×C11#39214yes—
306C22×C11#44918yes—
307C22×C11#46318yes—
308C22×C11#49514yes—
309C22×C11#49614yes—
310C22×C11C2×#12011yescharacteristic
311C22×C11C2×#12111yescharacteristic
312C22×C11C2×#12711yescharacteristic
313C22×C11C2×#13512yes—
314C22×C11C2×AGL(1,ℤ/8)12yes—
315C4×C11—44no—
316C4×C11—44no—
317C4×C11—82no—
318C4×C11#39214yes—
319C4×C11C2×#12011yescharacteristic
320C4×C11C2×#12011yescharacteristic
321C4×C11C2×#12111yescharacteristic
322C4×C11C2×#12111yescharacteristic
323C25—21no—
324C25—21no—
325C22×Q8—22no—
326C22×Q8—21no—
327C22×Q8—22no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8D4×C1114yes—
332C22×Q8C23×C1112yes—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—21no—
342C22×D4—21no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4D4×C1114yes—
346C22×D4D4×C1114yes—
347C22×D4C23×C1112yes—
348C22×D4C23×C1112yes—
349C23×C4—21no—
350C23×C4—21no—
351C23×C4D4×C1112yes—
352C23×C4C23×C1111yescharacteristic
353C2×SD16—232no—
354C2×SD16—28no—
355C2×SD16—28no—
356C2×SD16—28no—
357C2×D8—232no—
358C2×D8—28no—
359C2×D8—28no—
360C2×D8—28no—
361C22×C8—22no—
362C22×C8—22no—
363C22×C8—22no—
364C22×C8—22no—
365C22×C8D4×C1114yes—
366C22×C8D4×C1114yes—
367C22×C8C23×C1112yes—
368C22×C8C23×C1112yes—
369#124—216no—
370#124—28no—
371#124—28no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4C23×C1112yes—
376C2×C22⋊C4—216no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—48no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42D4×C1112yes—
383C2×C42C23×C1112yes—
384#103—28no—
385#102—28no—
386C2×C11—84no—
387C2×C11—84no—
388C2×C11#201218yesdirect product factor
389C2×C11C2×#39211yescharacteristic
390C2×C11C2×#44912yes—
391C2×C11C2×#46312yes—
392C2×C11C2×#49511yescharacteristic
393C2×C11C2×#49611yescharacteristic
394C24—24no—
395C24—24no—
396C24—22no—
397C24—22no—
398C24—42no—
399C24—42no—
400C24—42no—
401C24—42no—
402C24—44no—
403C24—44no—
404C24—44no—
405C24—44no—
406C24C2×D4×C1111yescharacteristic
407C2×Q8—24no—
408C2×Q8—22no—
409C2×Q8—28no—
410C2×Q8—28no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—44no—
416C2×Q8—42no—
417C2×Q8—44no—
418C2×Q8—42no—
419C2×Q8C2×D4×C1114yes—
420C2×D4—28no—
421C2×D4—28no—
422C2×D4—28no—
423C2×D4—24no—
424C2×D4—28no—
425C2×D4—24no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—44no—
437C2×D4—42no—
438C2×D4—44no—
439C2×D4—44no—
440C2×D4—44no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4C2×D4×C1114yes—
445C2×D4C2×D4×C1114yes—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—44no—
456C22×C4C2×D4×C1114yes—
457C22×C4C2×D4×C1112yes—
458C22×C4C2×D4×C1112yes—
459C22×C4C2×D4×C1112yes—
460C22×C4C2×D4×C1111yescharacteristic
461C22×C4C2×D4×C1112yes—
462C22×C4C2×D4×C1112yes—
463C22×C4C11×#4112yes—
464C22×C4C24×C1111yescharacteristic
465SD16—232no—
466D8—232no—
467C2×C8—28no—
468C2×C8—28no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8C2×D4×C1114yes—
474C2×C8C2×D4×C1114yes—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—42no—
478C22⋊C4—232no—
479C22⋊C4—416no—
480C42—24no—
481C42—22no—
482C42—22no—
483C11C2×#201211yescharacteristic, direct product factor, Sylow
484C23—24no—
485C23—24no—
486C23—42no—
487C23—42no—
488C23—48no—
489C23—48no—
490C23—42no—
491C23—42no—
492C23—44no—
493C23—44no—
494C23—44no—
495C23—44no—
496C23—416no—
497C23—416no—
498C23—84no—
499C23—84no—
500C23—84no—
501C23—84no—
502C23—88no—
503C23—88no—
504C23C11×#12012yes—
505C23C11×#12112yes—
506C23C11×#12712yes—
507C23C11×#13514yes—
508C23C11×AGL(1,ℤ/8)14yes—
509C23C22×D4×C1111yescharacteristic
510Q8—24no—
511Q8—24no—
512Q8—42no—
513Q8—42no—
514Q8—48no—
515D4—24no—
516D4—24no—
517D4—24no—
518D4—24no—
519D4—42no—
520D4—42no—
521D4—42no—
522D4—42no—
523D4—48no—
524D4—48no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—42no—
530C2×C4—48no—
531C2×C4—42no—
532C2×C4—48no—
533C2×C4—42no—
534C2×C4—44no—
535C2×C4—84no—
536C2×C4C11×#12014yes—
537C2×C4C11×#12014yes—
538C2×C4C11×#12012yes—
539C2×C4C11×#12114yes—
540C2×C4C11×#12114yes—
541C2×C4C11×#12112yes—
542C2×C4C11×#12712yes—
543C2×C4C22×D4×C1111yescharacteristic
544C2×C4C22×D4×C1111yescharacteristic
545C2×C4C22×D4×C1111yescharacteristic
546C2×C4C22×D4×C1111yescharacteristic
547C2×C4C22×D4×C1111yescharacteristic
548C2×C4C2×C11×#4111yescharacteristic
549C8—24no—
550C8—24no—
551C22—44no—
552C22—44no—
553C22—48no—
554C22—48no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22—82no—
559C22—84no—
560C22—84no—
561C22—816no—
562C22—816no—
563C22C11×#39214yes—
564C22C11×#44918yes—
565C22C11×#46318yes—
566C22C11×#49514yes—
567C22C11×#49614yes—
568C22C2×C11×#12011yescharacteristic
569C22C2×C11×#12111yescharacteristic
570C22C2×C11×#12711yescharacteristic
571C22C2×C11×#13512yes—
572C22C2×C11×AGL(1,ℤ/8)12yes—
573C4—44no—
574C4—44no—
575C4—82no—
576C4C11×#39214yes—
577C4C2×C11×#12011yescharacteristic
578C4C2×C11×#12011yescharacteristic
579C4C2×C11×#12111yescharacteristic
580C4C2×C11×#12111yescharacteristic
581C2—84no—
582C2—84no—
583C2C11×#201218yesdirect product factor
584C2C2×C11×#39211yescharacteristic
585C2C2×C11×#44912yes—
586C2C2×C11×#46312yes—
587C2C2×C11×#49511yescharacteristic
588C2C2×C11×#49611yescharacteristic
subgroupG/H
center, socleC24×C11C2×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×C11×D8C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C11×SD16C2semidirect
3. C22×C11×#124C2semidirect
4. C22×C11×#103C2semidirect
5. C22×C11×#102C2semidirect
6. C2×C11×#390C2semidirect
7. C11×#2012C2direct (N × H)
8. C2×C11×#336C2semidirect
15. C22×C11×SD16C22semidirect
25. C2×C11×#124C22semidirect
31. C2×C11×#103C22semidirect
33. C2×C11×#102C22semidirect
35. C11×#390C22semidirect
36. C11×#336C22semidirect
100. C2×#2012C11direct (N × H)
190. C23×SD16C2×C11semidirect
192. C22×#124C2×C11semidirect
193. C22×#103C2×C11semidirect
194. C22×#102C2×C11semidirect
195. C2×#390C2×C11semidirect
196. #2012C2×C11direct (N × H)
197. C2×#336C2×C11semidirect
271. C22×SD16C22×C11semidirect
281. C2×#124C22×C11semidirect
287. C2×#103C22×C11semidirect
289. C2×#102C22×C11semidirect
291. #390C22×C11semidirect
292. #336C22×C11semidirect
388. C2×C11#2012direct (N × H)
483. C11C2×#2012direct (N × H)
583. C2C11×#2012direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C11×SD162
C23×C11×D82
C22×C11×#1242
C22×C11×#1032
C22×C11×#1022
C2×C11×#3902
C11×#20122
C2×C11×#3362
C2×#201211