Finite Group Databasebeta

← C11×#32880 #14610073

Subgroups — C11×#32880 #14610073

Order 2816.

4004 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
1C23×C11×#41C211yesmaximal, characteristic, complemented
2C2×C11×#449C214yesmaximal, complemented
3C2×C11×#448C211yesmaximal, characteristic, complemented
4C2×C11×#447C211yesmaximal, characteristic, complemented
5C11×#2847C211yesmaximal, characteristic, complemented
6C11×#1788C214yesmaximal, complemented
7C11×#1787C211yesmaximal, characteristic, complemented
8C11×#1786C211yesmaximal, characteristic, complemented
9C11×#1779C211yesmaximal, characteristic, complemented
10C22×C11×#41—216no—
11C22×C11×#41—24no—
12C22×C11×#41—24no—
13C22×C11×#41—22no—
14C22×C11×#41C2214yes—
15C23×Q8×C11C2211yescharacteristic
16C23×D4×C11—21no—
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11—21no—
19C24×C4×C11C2211yescharacteristic
20C22×C11×SD16C2212yescomplemented
21C22×C11×D8C2212yescomplemented
22C2×C11×#121C2211yescharacteristic
23C2×C11×#121C2212yescomplemented
24C2×C11×#120—21no—
25C11×#449—216no—
26C11×#448—24no—
27C11×#447—24no—
28C2×C11×#103C2212yescomplemented
29C2×C11×#103C2214yescomplemented
30C2×C11×#102C2212yescomplemented
31C2×C11×#102C2214yescomplemented
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×C22⋊C8C2214yescomplemented
35C11×#386—22no—
36C11×#386—21no—
37C11×#380C2211yescharacteristic
38C11×#380C2212yescomplemented
39C25×C11—21no—
40C25×C11D411yescharacteristic
41C2×C11×#41—264no—
42C2×C11×#41—264no—
43C2×C11×#41—216no—
44C2×C11×#41—216no—
45C2×C11×#41—216no—
46C2×C11×#41—28no—
47C2×C11×#41—28no—
48C2×C11×#41—28no—
49C2×C11×#41—28no—
50C2×C11×#41—28no—
51C2×C11×#41D4116yescomplemented
52C22×Q8×C11—28no—
53C22×Q8×C11—22no—
54C22×Q8×C11—21no—
55C22×Q8×C11D414yescomplemented
56C22×Q8×C11C2312yes—
57C22×D4×C11—216no—
58C22×D4×C11—28no—
59C22×D4×C11—24no—
60C22×D4×C11—28no—
61C22×D4×C11—21no—
62C22×D4×C11—22no—
63C22×D4×C11—21no—
64C22×D4×C11—22no—
65C22×D4×C11D414yescomplemented
66C22×D4×C11C2311yescharacteristic
67C22×D4×C11C2312yes—
68C23×C4×C11—216no—
69C23×C4×C11—28no—
70C23×C4×C11—21no—
71C23×C4×C11—24no—
72C23×C4×C11—22no—
73C23×C4×C11—22no—
74C23×C4×C11—28no—
75C23×C4×C11D411yescharacteristic
76C23×C4×C11D412yes—
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2312yes—
79C2×C11×SD16—24no—
80C2×C11×SD16—28no—
81C2×C11×D8—24no—
82C2×C11×D8—28no—
83C22×C8×C11C2312yes—
84C22×C8×C11C2312yes—
85C11×#121—22no—
86C11×#121—22no—
87C11×#121—28no—
88C11×#120—44no—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—22no—
95C11×#103—24no—
96C11×#103—28no—
97C11×#102—24no—
98C11×#102—28no—
99C11×C22⋊C8—22no—
100C11×C22⋊C8—22no—
101C11×C22⋊C8—28no—
102C11×#95—21no—
103C11×#95—22no—
104#32880C1111yesmaximal, characteristic, direct product factor, Sylow
105C24×C11—28no—
106C24×C11—24no—
107C24×C11—22no—
108C24×C11—24no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—21no—
113C24×C11—42no—
114C24×C11—44no—
115C24×C11—42no—
116C24×C11—42no—
117C24×C11C2×D412yes—
118C24×C11C2×D411yescharacteristic
119C11×#41—2128no—
120C11×#41—232no—
121C11×#41—232no—
122C11×#41—232no—
123C11×#41—232no—
124C2×Q8×C11—216no—
125C2×Q8×C11—28no—
126C2×Q8×C11—216no—
127C2×Q8×C11—24no—
128C2×Q8×C11—24no—
129C2×Q8×C11—22no—
130C2×Q8×C11C2×D418yes—
131C2×Q8×C11C2×D414yes—
132C2×D4×C11—264no—
133C2×D4×C11—216no—
134C2×D4×C11—216no—
135C2×D4×C11—28no—
136C2×D4×C11—216no—
137C2×D4×C11—216no—
138C2×D4×C11—216no—
139C2×D4×C11—24no—
140C2×D4×C11—22no—
141C2×D4×C11—24no—
142C2×D4×C11—21no—
143C2×D4×C11—24no—
144C2×D4×C11—21no—
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×D418yes—
152C2×D4×C11C2×D414yes—
153C22×C4×C11—28no—
154C22×C4×C11—264no—
155C22×C4×C11—216no—
156C22×C4×C11—216no—
157C22×C4×C11—216no—
158C22×C4×C11—216no—
159C22×C4×C11—22no—
160C22×C4×C11—24no—
161C22×C4×C11—24no—
162C22×C4×C11—22no—
163C22×C4×C11—24no—
164C22×C4×C11—216no—
165C22×C4×C11—24no—
166C22×C4×C11—24no—
167C22×C4×C11—24no—
168C22×C4×C11—22no—
169C22×C4×C11—24no—
170C22×C4×C11—22no—
171C22×C4×C11—21no—
172C22×C4×C11—22no—
173C22×C4×C11C2×D412yes—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D418yes—
178C22×C4×C11C2411yescharacteristic
179C11×SD16—48no—
180C11×D8—48no—
181C2×C8×C11—22no—
182C2×C8×C11—24no—
183C2×C8×C11—24no—
184C2×C8×C11—22no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—21no—
188C11×C22⋊C4—44no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—44no—
191C11×C22⋊C4—42no—
192C23×#41C2×C1111yescharacteristic, complemented
193C2×#449C2×C1114yescomplemented
194C2×#448C2×C1111yescharacteristic, complemented
195C2×#447C2×C1111yescharacteristic, complemented
196#2847C2×C1111yescharacteristic, complemented
197#1788C2×C1114yescomplemented
198#1787C2×C1111yescharacteristic, complemented
199#1786C2×C1111yescharacteristic, complemented
200#1779C2×C1111yescharacteristic, complemented
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—28no—
204C23×C11—216no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—24no—
208C23×C11—28no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—48no—
214C23×C11—48no—
215C23×C11—416no—
216C23×C11—44no—
217C23×C11—48no—
218C23×C11—416no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—44no—
222C23×C11—44no—
223C23×C11—48no—
224C23×C11—41no—
225C23×C11—42no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—42no—
229C23×C11#12014yes—
230C23×C11#12012yes—
231C23×C11#13512yes—
232C23×C11AGL(1,ℤ/8)12yes—
233C23×C11C22×D411yescharacteristic
234Q8×C11—216no—
235Q8×C11—24no—
236Q8×C11—28no—
237Q8×C11#12018yescomplemented
238D4×C11—264no—
239D4×C11—216no—
240D4×C11—28no—
241D4×C11—24no—
242D4×C11—42no—
243D4×C11—42no—
244D4×C11—88no—
245D4×C11—84no—
246D4×C11#12018yescomplemented
247C2×C4×C11—28no—
248C2×C4×C11—216no—
249C2×C4×C11—264no—
250C2×C4×C11—216no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—28no—
255C2×C4×C11—22no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—28no—
259C2×C4×C11—28no—
260C2×C4×C11—41no—
261C2×C4×C11—42no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11#12014yes—
267C2×C4×C11#12012yes—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D414yes—
270C2×C4×C11C22×D411yescharacteristic
271C8×C11—42no—
272C8×C11—42no—
273C22×#41—216no—
274C22×#41—24no—
275C22×#41—24no—
276C22×#41—22no—
277C22×#41C22×C1114yes—
278C23×Q8C22×C1111yescharacteristic
279C23×D4—21no—
280C23×D4C22×C1111yescharacteristic
281C24×C4—21no—
282C24×C4C22×C1111yescharacteristic
283C22×SD16C22×C1112yescomplemented
284C22×D8C22×C1112yescomplemented
285C2×#121C22×C1111yescharacteristic
286C2×#121C22×C1112yescomplemented
287C2×#120—21no—
288#449—216no—
289#448—24no—
290#447—24no—
291C2×#103C22×C1112yescomplemented
292C2×#103C22×C1114yescomplemented
293C2×#102C22×C1112yescomplemented
294C2×#102C22×C1114yescomplemented
295C2×C22⋊C8C22×C1111yescharacteristic
296C2×C22⋊C8C22×C1111yescharacteristic
297C2×C22⋊C8C22×C1114yescomplemented
298#386—22no—
299#386—21no—
300#380C22×C1111yescharacteristic
301#380C22×C1112yescomplemented
302C22×C11—22no—
303C22×C11—24no—
304C22×C11—22no—
305C22×C11—24no—
306C22×C11—24no—
307C22×C11—28no—
308C22×C11—24no—
309C22×C11—24no—
310C22×C11—416no—
311C22×C11—432no—
312C22×C11—42no—
313C22×C11—44no—
314C22×C11—42no—
315C22×C11—48no—
316C22×C11—42no—
317C22×C11—44no—
318C22×C11—42no—
319C22×C11—48no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—82no—
323C22×C11—81no—
324C22×C11—82no—
325C22×C11#44914yescomplemented
326C22×C11C2×#12011yescharacteristic
327C22×C11C2×#12012yes—
328C22×C11C2×#13511yescharacteristic
329C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
330C22×C11#57512yes—
331C4×C11—24no—
332C4×C11—28no—
333C4×C11—22no—
334C4×C11—81no—
335C4×C11—82no—
336C4×C11C2×#12012yes—
337C4×C11C2×#12012yes—
338C25—21no—
339C25D4×C1111yescharacteristic
340C2×#41—264no—
341C2×#41—264no—
342C2×#41—216no—
343C2×#41—216no—
344C2×#41—216no—
345C2×#41—28no—
346C2×#41—28no—
347C2×#41—28no—
348C2×#41—28no—
349C2×#41—28no—
350C2×#41D4×C11116yescomplemented
351C22×Q8—28no—
352C22×Q8—22no—
353C22×Q8—21no—
354C22×Q8D4×C1114yescomplemented
355C22×Q8C23×C1112yes—
356C22×D4—216no—
357C22×D4—28no—
358C22×D4—24no—
359C22×D4—28no—
360C22×D4—21no—
361C22×D4—22no—
362C22×D4—21no—
363C22×D4—22no—
364C22×D4D4×C1114yescomplemented
365C22×D4C23×C1111yescharacteristic
366C22×D4C23×C1112yes—
367C23×C4—216no—
368C23×C4—28no—
369C23×C4—21no—
370C23×C4—24no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—28no—
374C23×C4D4×C1111yescharacteristic
375C23×C4D4×C1112yes—
376C23×C4C23×C1111yescharacteristic
377C23×C4C23×C1112yes—
378C2×SD16—24no—
379C2×SD16—28no—
380C2×D8—24no—
381C2×D8—28no—
382C22×C8C23×C1112yes—
383C22×C8C23×C1112yes—
384#121—22no—
385#121—22no—
386#121—28no—
387#120—44no—
388C2×C4⋊C4C23×C1111yescharacteristic
389C2×C4⋊C4C23×C1112yes—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—22no—
394#103—24no—
395#103—28no—
396#102—24no—
397#102—28no—
398C22⋊C8—22no—
399C22⋊C8—22no—
400C22⋊C8—28no—
401#95—21no—
402#95—22no—
403C2×C11—24no—
404C2×C11—44no—
405C2×C11—48no—
406C2×C11—161no—
407C2×C11#284611yescharacteristic
408C2×C11C2×#44911yescharacteristic
409C2×C11#300212yes—
410C2×C11#300511yescharacteristic
411C2×C11#300612yes—
412C24—28no—
413C24—24no—
414C24—22no—
415C24—24no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—21no—
420C24—42no—
421C24—44no—
422C24—42no—
423C24—42no—
424C24C2×D4×C1112yes—
425C24C2×D4×C1111yescharacteristic
426#41—2128no—
427#41—232no—
428#41—232no—
429#41—232no—
430#41—232no—
431C2×Q8—216no—
432C2×Q8—28no—
433C2×Q8—216no—
434C2×Q8—24no—
435C2×Q8—24no—
436C2×Q8—22no—
437C2×Q8C2×D4×C1118yes—
438C2×Q8C2×D4×C1114yes—
439C2×D4—264no—
440C2×D4—216no—
441C2×D4—216no—
442C2×D4—28no—
443C2×D4—216no—
444C2×D4—216no—
445C2×D4—216no—
446C2×D4—24no—
447C2×D4—22no—
448C2×D4—24no—
449C2×D4—21no—
450C2×D4—24no—
451C2×D4—21no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4—44no—
455C2×D4—42no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4C2×D4×C1118yes—
459C2×D4C2×D4×C1114yes—
460C22×C4—28no—
461C22×C4—264no—
462C22×C4—216no—
463C22×C4—216no—
464C22×C4—216no—
465C22×C4—216no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—216no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4C2×D4×C1112yes—
481C22×C4C2×D4×C1111yescharacteristic
482C22×C4C2×D4×C1112yes—
483C22×C4C2×D4×C1112yes—
484C22×C4C2×D4×C1118yes—
485C22×C4C24×C1111yescharacteristic
486SD16—48no—
487D8—48no—
488C2×C8—22no—
489C2×C8—24no—
490C2×C8—24no—
491C2×C8—22no—
492C4⋊C4—21no—
493C4⋊C4—24no—
494C4⋊C4—21no—
495C22⋊C4—44no—
496C22⋊C4—42no—
497C22⋊C4—44no—
498C22⋊C4—42no—
499C11#3288011yescharacteristic, direct product factor, Sylow
500C23—22no—
501C23—22no—
502C23—28no—
503C23—216no—
504C23—22no—
505C23—22no—
506C23—24no—
507C23—28no—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—48no—
513C23—48no—
514C23—416no—
515C23—44no—
516C23—48no—
517C23—416no—
518C23—42no—
519C23—42no—
520C23—44no—
521C23—44no—
522C23—48no—
523C23—41no—
524C23—42no—
525C23—41no—
526C23—41no—
527C23—42no—
528C23C11×#12014yes—
529C23C11×#12012yes—
530C23C11×#13512yes—
531C23C11×AGL(1,ℤ/8)12yes—
532C23C22×D4×C1111yescharacteristic
533Q8—216no—
534Q8—24no—
535Q8—28no—
536Q8C11×#12018yescomplemented
537D4—264no—
538D4—216no—
539D4—28no—
540D4—24no—
541D4—42no—
542D4—42no—
543D4—88no—
544D4—84no—
545D4C11×#12018yescomplemented
546C2×C4—28no—
547C2×C4—216no—
548C2×C4—264no—
549C2×C4—216no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—28no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—28no—
558C2×C4—28no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4C11×#12014yes—
566C2×C4C11×#12012yes—
567C2×C4C22×D4×C1111yescharacteristic
568C2×C4C22×D4×C1114yes—
569C2×C4C22×D4×C1111yescharacteristic
570C8—42no—
571C8—42no—
572C22—24no—
573C22—22no—
574C22—24no—
575C22—22no—
576C22—24no—
577C22—24no—
578C22—24no—
579C22—28no—
580C22—416no—
581C22—432no—
582C22—42no—
583C22—44no—
584C22—42no—
585C22—48no—
586C22—42no—
587C22—44no—
588C22—42no—
589C22—48no—
590C22—81no—
591C22—82no—
592C22—81no—
593C22—82no—
594C22—81no—
595C22C11×#44914yescomplemented
596C22C2×C11×#12011yescharacteristic
597C22C2×C11×#12012yes—
598C22C2×C11×#13511yescharacteristic
599C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
600C22C11×#57512yes—
601C4—24no—
602C4—28no—
603C4—22no—
604C4—81no—
605C4—82no—
606C4C2×C11×#12012yes—
607C4C2×C11×#12012yes—
608C2—24no—
609C2—44no—
610C2—48no—
611C2—161no—
612C2C11×#284611yescharacteristic
613C2C2×C11×#44911yescharacteristic
614C2C11×#300212yes—
615C2C11×#300511yescharacteristic
616C2C11×#300612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C11×#41C2semidirect
2. C2×C11×#449C2semidirect
3. C2×C11×#448C2semidirect
4. C2×C11×#447C2semidirect
5. C11×#2847C2semidirect
6. C11×#1788C2semidirect
7. C11×#1787C2semidirect
8. C11×#1786C2semidirect
9. C11×#1779C2semidirect
20. C22×C11×SD16C22semidirect
21. C22×C11×D8C22semidirect
23. C2×C11×#121C22semidirect
28. C2×C11×#103C22semidirect
29. C2×C11×#103C22semidirect
30. C2×C11×#102C22semidirect
31. C2×C11×#102C22semidirect
34. C2×C11×C22⋊C8C22semidirect
38. C11×#380C22semidirect
51. C2×C11×#41D4semidirect
55. C22×Q8×C11D4semidirect
65. C22×D4×C11D4semidirect
104. #32880C11direct (N × H)
192. C23×#41C2×C11semidirect
193. C2×#449C2×C11semidirect
194. C2×#448C2×C11semidirect
195. C2×#447C2×C11semidirect
196. #2847C2×C11semidirect
197. #1788C2×C11semidirect
198. #1787C2×C11semidirect
199. #1786C2×C11semidirect
200. #1779C2×C11semidirect
237. Q8×C11#120semidirect
246. D4×C11#120semidirect
283. C22×SD16C22×C11semidirect
284. C22×D8C22×C11semidirect
286. C2×#121C22×C11semidirect
291. C2×#103C22×C11semidirect
292. C2×#103C22×C11semidirect
293. C2×#102C22×C11semidirect
294. C2×#102C22×C11semidirect
297. C2×C22⋊C8C22×C11semidirect
301. #380C22×C11semidirect
325. C22×C11#449semidirect
350. C2×#41D4×C11semidirect
354. C22×Q8D4×C11semidirect
364. C22×D4D4×C11semidirect
499. C11#32880direct (N × H)
536. Q8C11×#120semidirect
545. D4C11×#120semidirect
595. C22C11×#449semidirect

Maximal subgroups

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

subgroupindex
C23×C11×#412
C2×C11×#4492
C2×C11×#4482
C2×C11×#4472
C11×#28472
C11×#17882
C11×#17872
C11×#17862
C11×#17792
#3288011