Finite Group Databasebeta

← C11×#32890 #14610083

Subgroups — C11×#32890 #14610083

Order 2816.

3688 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#585C211yesmaximal, characteristic, complemented
2C2×C11×#454C212yesmaximal, complemented
3C2×C11×#453C212yesmaximal, complemented
4C11×#3006C212yesmaximal, complemented
5C11×#2431C211yesmaximal, characteristic, complemented
6C11×#1793C212yesmaximal, complemented
7C11×#1792C212yesmaximal, complemented
8C11×#1789C212yesmaximal, complemented
9C11×#1785C211yesmaximal, characteristic, complemented
10C11×#585—28no—
11C11×#585—28no—
12C2×C11×2−1+4—22no—
13C2×C11×2−1+4C2212yes—
14C2×C11×H(5,𝔽2)—22no—
15C2×C11×H(5,𝔽2)—22no—
16C2×C11×H(5,𝔽2)C2212yes—
17C22×C11×#41—24no—
18C22×C11×#41—22no—
19C22×C11×#41C2212yes—
20C22×C11×#41C2211yescharacteristic
21C2×C11×AGL(1,ℤ/8)C2214yescomplemented
22C2×C11×#127C2211yescharacteristic, complemented
23C2×C11×#124C2211yescharacteristic, complemented
24C2×C11×#121C2211yescharacteristic, complemented
25C11×#454—28no—
26C11×#453—28no—
27C11×#449—24no—
28C11×#448—22no—
29C11×#447—22no—
30C2×C11×#104C2214yescomplemented
31C2×C11×#104C2214yescomplemented
32C11×#417C2214yescomplemented
33C2×C11×#101C2212yescomplemented
34C2×C11×#100C2212yescomplemented
35C11×#407C2212yescomplemented
36C11×#392—22no—
37C11×#391C2211yescharacteristic, complemented
38C11×#390C2211yescharacteristic, complemented
39C11×#386—22no—
40C4×C11×C22⋊C4C2211yescharacteristic, complemented
41C11×2−1+4—232no—
42C11×2−1+4—28no—
43C11×2−1+4—24no—
44C11×2−1+4D418yescomplemented
45C11×H(5,𝔽2)—216no—
46C11×H(5,𝔽2)—232no—
47C11×H(5,𝔽2)—216no—
48C11×H(5,𝔽2)—28no—
49C11×H(5,𝔽2)—24no—
50C11×H(5,𝔽2)D418yescomplemented
51C2×C11×#41—24no—
52C2×C11×#41—28no—
53C2×C11×#41—24no—
54C2×C11×#41—232no—
55C2×C11×#41—232no—
56C2×C11×#41—216no—
57C2×C11×#41—216no—
58C2×C11×#41—28no—
59C2×C11×#41—28no—
60C2×C11×#41—24no—
61C2×C11×#41—24no—
62C2×C11×#41—24no—
63C2×C11×#41—24no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—24no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41D414yescomplemented
70C2×C11×#41C2314yes—
71C22×Q8×C11—22no—
72C22×Q8×C11—24no—
73C22×Q8×C11D412yescomplemented
74C22×Q8×C11C2311yescharacteristic
75C22×D4×C11—28no—
76C22×D4×C11—22no—
77C22×D4×C11—24no—
78C22×D4×C11—22no—
79C22×D4×C11—24no—
80C22×D4×C11—22no—
81C22×D4×C11—21no—
82C22×D4×C11D412yes—
83C22×D4×C11D412yescomplemented
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C23×C4×C11—24no—
87C23×C4×C11—22no—
88C23×C4×C11D412yes—
89C23×C4×C11C2311yescharacteristic
90C11×AGL(1,ℤ/8)—28no—
91C11×AGL(1,ℤ/8)—28no—
92C2×C11×SD16—24no—
93C2×C11×D8—24no—
94C2×C11×M16C2314yes—
95C11×#127—24no—
96C11×#124—24no—
97C11×#121—22no—
98C11×#121—22no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4—22no—
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C11×#104—28no—
107C11×#104—28no—
108C11×#103—24no—
109C11×#102—24no—
110C11×#101—24no—
111C11×#100—24no—
112C11×C22⋊C8—22no—
113C11×C22⋊C8—22no—
114C11×#95—21no—
115C11×#95—22no—
116#32890C1111yesmaximal, characteristic, direct product factor, Sylow
117C24×C11—24no—
118C24×C11—22no—
119C24×C11—21no—
120C24×C11C2×D412yes—
121C24×C11C2×D411yescharacteristic
122C11×#41—232no—
123C11×#41—28no—
124C11×#41—28no—
125C11×#41—216no—
126C11×#41—264no—
127C11×#41—232no—
128C11×#41—216no—
129C11×#41—216no—
130C11×#41—216no—
131C11×#41—216no—
132C11×#41—216no—
133C11×#41—28no—
134C11×#41—216no—
135C11×#41—28no—
136C11×#41—216no—
137C11×#41—216no—
138C11×#41—24no—
139C11×#41—24no—
140C11×#41C2×D418yes—
141C11×#41C2×D418yes—
142C2×Q8×C11—24no—
143C2×Q8×C11—216no—
144C2×Q8×C11—216no—
145C2×Q8×C11—216no—
146C2×Q8×C11—28no—
147C2×Q8×C11—22no—
148C2×Q8×C11—22no—
149C2×Q8×C11—22no—
150C2×Q8×C11C2×D414yes—
151C2×Q8×C11C2×D414yes—
152C2×D4×C11—28no—
153C2×D4×C11—24no—
154C2×D4×C11—264no—
155C2×D4×C11—216no—
156C2×D4×C11—216no—
157C2×D4×C11—28no—
158C2×D4×C11—28no—
159C2×D4×C11—216no—
160C2×D4×C11—24no—
161C2×D4×C11—24no—
162C2×D4×C11—216no—
163C2×D4×C11—24no—
164C2×D4×C11—24no—
165C2×D4×C11—216no—
166C2×D4×C11—28no—
167C2×D4×C11—22no—
168C2×D4×C11—24no—
169C2×D4×C11—22no—
170C2×D4×C11—22no—
171C2×D4×C11—22no—
172C2×D4×C11—22no—
173C2×D4×C11—22no—
174C2×D4×C11—44no—
175C2×D4×C11—42no—
176C2×D4×C11—44no—
177C2×D4×C11—82no—
178C2×D4×C11—82no—
179C2×D4×C11C2×D414yes—
180C2×D4×C11C2×D414yes—
181C22×C4×C11—24no—
182C22×C4×C11—28no—
183C22×C4×C11—232no—
184C22×C4×C11—216no—
185C22×C4×C11—22no—
186C22×C4×C11—24no—
187C22×C4×C11—24no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—24no—
191C22×C4×C11—24no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2411yescharacteristic
202C11×SD16—48no—
203C11×D8—48no—
204C11×M16—24no—
205C11×M16—24no—
206C2×C8×C11—24no—
207C11×C4⋊C4—22no—
208C11×C22⋊C4—42no—
209C11×C22⋊C4—41no—
210C11×C22⋊C4—41no—
211C11×C22⋊C4—44no—
212C11×C22⋊C4—82no—
213C42×C11—22no—
214C42×C11—22no—
215C2×#585C2×C1111yescharacteristic, complemented
216C2×#454C2×C1112yescomplemented
217C2×#453C2×C1112yescomplemented
218#3006C2×C1112yescomplemented
219#2431C2×C1111yescharacteristic, complemented
220#1793C2×C1112yescomplemented
221#1792C2×C1112yescomplemented
222#1789C2×C1112yescomplemented
223#1785C2×C1111yescharacteristic, complemented
224C23×C11—28no—
225C23×C11—216no—
226C23×C11—22no—
227C23×C11—24no—
228C23×C11—21no—
229C23×C11—22no—
230C23×C11—21no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—82no—
241C23×C11—82no—
242C23×C11—84no—
243C23×C11—84no—
244C23×C11#12012yes—
245C23×C11#12014yes—
246C23×C11C22×D411yescharacteristic
247Q8×C11—216no—
248Q8×C11—28no—
249Q8×C11—24no—
250Q8×C11—28no—
251Q8×C11#12018yes—
252D4×C11—232no—
253D4×C11—216no—
254D4×C11—216no—
255D4×C11—216no—
256D4×C11—28no—
257D4×C11—28no—
258D4×C11—28no—
259D4×C11—28no—
260D4×C11—24no—
261D4×C11—44no—
262D4×C11—88no—
263D4×C11—84no—
264D4×C11#12018yes—
265C2×C4×C11—216no—
266C2×C4×C11—28no—
267C2×C4×C11—216no—
268C2×C4×C11—28no—
269C2×C4×C11—232no—
270C2×C4×C11—28no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
274C2×C4×C11—24no—
275C2×C4×C11—22no—
276C2×C4×C11—24no—
277C2×C4×C11—28no—
278C2×C4×C11—28no—
279C2×C4×C11—24no—
280C2×C4×C11—22no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—42no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11#12014yes—
289C2×C4×C11#12011yescharacteristic
290C2×C4×C11#12011yescharacteristic
291C2×C4×C11C22×D412yes—
292C2×C4×C11C22×D412yes—
293C2×C4×C11C22×D412yes—
294C8×C11—44no—
295#585—28no—
296#585—28no—
297C2×2−1+4—22no—
298C2×2−1+4C22×C1112yes—
299C2×H(5,𝔽2)—22no—
300C2×H(5,𝔽2)—22no—
301C2×H(5,𝔽2)C22×C1112yes—
302C22×#41—24no—
303C22×#41—22no—
304C22×#41C22×C1112yes—
305C22×#41C22×C1111yescharacteristic
306C2×AGL(1,ℤ/8)C22×C1114yescomplemented
307C2×#127C22×C1111yescharacteristic, complemented
308C2×#124C22×C1111yescharacteristic, complemented
309C2×#121C22×C1111yescharacteristic, complemented
310#454—28no—
311#453—28no—
312#449—24no—
313#448—22no—
314#447—22no—
315C2×#104C22×C1114yescomplemented
316C2×#104C22×C1114yescomplemented
317#417C22×C1114yescomplemented
318C2×#101C22×C1112yescomplemented
319C2×#100C22×C1112yescomplemented
320#407C22×C1112yescomplemented
321#392—22no—
322#391C22×C1111yescharacteristic, complemented
323#390C22×C1111yescharacteristic, complemented
324#386—22no—
325C4×C22⋊C4C22×C1111yescharacteristic, complemented
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—22no—
329C22×C11—24no—
330C22×C11—28no—
331C22×C11—22no—
332C22×C11—22no—
333C22×C11—44no—
334C22×C11—42no—
335C22×C11—44no—
336C22×C11—42no—
337C22×C11—44no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11—82no—
341C22×C11—82no—
342C22×C11—82no—
343C22×C11—88no—
344C22×C11—816no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11C2×#12011yescharacteristic
349C22×C11C2×#12011yescharacteristic
350C22×C11C2×#12011yescharacteristic
351C4×C11—21no—
352C4×C11—28no—
353C4×C11—24no—
354C4×C11—21no—
355C4×C11—42no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11C2×#12014yes—
3592−1+4—232no—
3602−1+4—28no—
3612−1+4—24no—
3622−1+4D4×C1118yescomplemented
363H(5,𝔽2)—216no—
364H(5,𝔽2)—232no—
365H(5,𝔽2)—216no—
366H(5,𝔽2)—28no—
367H(5,𝔽2)—24no—
368H(5,𝔽2)D4×C1118yescomplemented
369C2×#41—24no—
370C2×#41—28no—
371C2×#41—24no—
372C2×#41—232no—
373C2×#41—232no—
374C2×#41—216no—
375C2×#41—216no—
376C2×#41—28no—
377C2×#41—28no—
378C2×#41—24no—
379C2×#41—24no—
380C2×#41—24no—
381C2×#41—24no—
382C2×#41—22no—
383C2×#41—22no—
384C2×#41—24no—
385C2×#41—22no—
386C2×#41—22no—
387C2×#41D4×C1114yescomplemented
388C2×#41C23×C1114yes—
389C22×Q8—22no—
390C22×Q8—24no—
391C22×Q8D4×C1112yescomplemented
392C22×Q8C23×C1111yescharacteristic
393C22×D4—28no—
394C22×D4—22no—
395C22×D4—24no—
396C22×D4—22no—
397C22×D4—24no—
398C22×D4—22no—
399C22×D4—21no—
400C22×D4D4×C1112yes—
401C22×D4D4×C1112yescomplemented
402C22×D4C23×C1111yescharacteristic
403C22×D4C23×C1111yescharacteristic
404C23×C4—24no—
405C23×C4—22no—
406C23×C4D4×C1112yes—
407C23×C4C23×C1111yescharacteristic
408AGL(1,ℤ/8)—28no—
409AGL(1,ℤ/8)—28no—
410C2×SD16—24no—
411C2×D8—24no—
412C2×M16C23×C1114yes—
413#127—24no—
414#124—24no—
415#121—22no—
416#121—22no—
417C2×C4⋊C4C23×C1111yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C42C23×C1111yescharacteristic
423C2×C42C23×C1111yescharacteristic
424#104—28no—
425#104—28no—
426#103—24no—
427#102—24no—
428#101—24no—
429#100—24no—
430C22⋊C8—22no—
431C22⋊C8—22no—
432#95—21no—
433#95—22no—
434C2×C11—21no—
435C2×C11—21no—
436C2×C11—42no—
437C2×C11—44no—
438C2×C11—48no—
439C2×C11—161no—
440C2×C11#284611yescharacteristic
441C2×C11#301811yescharacteristic
442C2×C11#302111yescharacteristic
443C24—24no—
444C24—22no—
445C24—21no—
446C24C2×D4×C1112yes—
447C24C2×D4×C1111yescharacteristic
448#41—232no—
449#41—28no—
450#41—28no—
451#41—216no—
452#41—264no—
453#41—232no—
454#41—216no—
455#41—216no—
456#41—216no—
457#41—216no—
458#41—216no—
459#41—28no—
460#41—216no—
461#41—28no—
462#41—216no—
463#41—216no—
464#41—24no—
465#41—24no—
466#41C2×D4×C1118yes—
467#41C2×D4×C1118yes—
468C2×Q8—24no—
469C2×Q8—216no—
470C2×Q8—216no—
471C2×Q8—216no—
472C2×Q8—28no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8C2×D4×C1114yes—
477C2×Q8C2×D4×C1114yes—
478C2×D4—28no—
479C2×D4—24no—
480C2×D4—264no—
481C2×D4—216no—
482C2×D4—216no—
483C2×D4—28no—
484C2×D4—28no—
485C2×D4—216no—
486C2×D4—24no—
487C2×D4—24no—
488C2×D4—216no—
489C2×D4—24no—
490C2×D4—24no—
491C2×D4—216no—
492C2×D4—28no—
493C2×D4—22no—
494C2×D4—24no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—44no—
501C2×D4—42no—
502C2×D4—44no—
503C2×D4—82no—
504C2×D4—82no—
505C2×D4C2×D4×C1114yes—
506C2×D4C2×D4×C1114yes—
507C22×C4—24no—
508C22×C4—28no—
509C22×C4—232no—
510C22×C4—216no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4C2×D4×C1111yescharacteristic
524C22×C4C2×D4×C1112yes—
525C22×C4C2×D4×C1112yes—
526C22×C4C2×D4×C1112yes—
527C22×C4C24×C1111yescharacteristic
528SD16—48no—
529D8—48no—
530M16—24no—
531M16—24no—
532C2×C8—24no—
533C4⋊C4—22no—
534C22⋊C4—42no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C22⋊C4—44no—
538C22⋊C4—82no—
539C42—22no—
540C42—22no—
541C11#3289011yescharacteristic, direct product factor, Sylow
542C23—28no—
543C23—216no—
544C23—22no—
545C23—24no—
546C23—21no—
547C23—22no—
548C23—21no—
549C23—41no—
550C23—41no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—82no—
559C23—82no—
560C23—84no—
561C23—84no—
562C23C11×#12012yes—
563C23C11×#12014yes—
564C23C22×D4×C1111yescharacteristic
565Q8—216no—
566Q8—28no—
567Q8—24no—
568Q8—28no—
569Q8C11×#12018yes—
570D4—232no—
571D4—216no—
572D4—216no—
573D4—216no—
574D4—28no—
575D4—28no—
576D4—28no—
577D4—28no—
578D4—24no—
579D4—44no—
580D4—88no—
581D4—84no—
582D4C11×#12018yes—
583C2×C4—216no—
584C2×C4—28no—
585C2×C4—216no—
586C2×C4—28no—
587C2×C4—232no—
588C2×C4—28no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—28no—
596C2×C4—28no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4C11×#12011yescharacteristic
607C2×C4C11×#12011yescharacteristic
608C2×C4C11×#12014yes—
609C2×C4C22×D4×C1112yes—
610C2×C4C22×D4×C1112yes—
611C2×C4C22×D4×C1112yes—
612C8—44no—
613C22—21no—
614C22—21no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—24no—
619C22—28no—
620C22—44no—
621C22—42no—
622C22—44no—
623C22—42no—
624C22—44no—
625C22—81no—
626C22—81no—
627C22—82no—
628C22—82no—
629C22—82no—
630C22—88no—
631C22—816no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22C2×C11×#12011yescharacteristic
636C22C2×C11×#12011yescharacteristic
637C22C2×C11×#12011yescharacteristic
638C4—21no—
639C4—28no—
640C4—24no—
641C4—21no—
642C4—42no—
643C4—81no—
644C4—81no—
645C4C2×C11×#12014yes—
646C2—21no—
647C2—21no—
648C2—42no—
649C2—44no—
650C2—48no—
651C2—161no—
652C2C11×#284611yescharacteristic
653C2C11×#301811yescharacteristic
654C2C11×#302111yescharacteristic
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. C2×C11×#585C2semidirect
2. C2×C11×#454C2semidirect
3. C2×C11×#453C2semidirect
4. C11×#3006C2semidirect
5. C11×#2431C2semidirect
6. C11×#1793C2semidirect
7. C11×#1792C2semidirect
8. C11×#1789C2semidirect
9. C11×#1785C2semidirect
21. C2×C11×AGL(1,ℤ/8)C22semidirect
22. C2×C11×#127C22semidirect
23. C2×C11×#124C22semidirect
24. C2×C11×#121C22semidirect
30. C2×C11×#104C22semidirect
31. C2×C11×#104C22semidirect
32. C11×#417C22semidirect
33. C2×C11×#101C22semidirect
34. C2×C11×#100C22semidirect
35. C11×#407C22semidirect
37. C11×#391C22semidirect
38. C11×#390C22semidirect
40. C4×C11×C22⋊C4C22semidirect
44. C11×2−1+4D4semidirect
50. C11×H(5,𝔽2)D4semidirect
69. C2×C11×#41D4semidirect
73. C22×Q8×C11D4semidirect
83. C22×D4×C11D4semidirect
116. #32890C11direct (N × H)
215. C2×#585C2×C11semidirect
216. C2×#454C2×C11semidirect
217. C2×#453C2×C11semidirect
218. #3006C2×C11semidirect
219. #2431C2×C11semidirect
220. #1793C2×C11semidirect
221. #1792C2×C11semidirect
222. #1789C2×C11semidirect
223. #1785C2×C11semidirect
306. C2×AGL(1,ℤ/8)C22×C11semidirect
307. C2×#127C22×C11semidirect
308. C2×#124C22×C11semidirect
309. C2×#121C22×C11semidirect
315. C2×#104C22×C11semidirect
316. C2×#104C22×C11semidirect
317. #417C22×C11semidirect
318. C2×#101C22×C11semidirect
319. C2×#100C22×C11semidirect
320. #407C22×C11semidirect
322. #391C22×C11semidirect
323. #390C22×C11semidirect
325. C4×C22⋊C4C22×C11semidirect
362. 2−1+4D4×C11semidirect
368. H(5,𝔽2)D4×C11semidirect
387. C2×#41D4×C11semidirect
391. C22×Q8D4×C11semidirect
401. C22×D4D4×C11semidirect
541. C11#32890direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5852
C2×C11×#4542
C2×C11×#4532
C11×#30062
C11×#24312
C11×#17932
C11×#17922
C11×#17892
C11×#17852
#3289011