Finite Group Databasebeta

← C11×#24357 #14601550

Subgroups — C11×#24357 #14601550

Order 2816.

1526 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×SD16C211yesmaximal, characteristic
2C2×C11×#464C212yesmaximal, complemented
3C2×C11×#451C211yesmaximal, characteristic, complemented
4C11×#2435C211yesmaximal, characteristic
5Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
6C11×#2055C212yesmaximal, complemented
7C11×#2015C212yesmaximal, complemented
8C11×#1892C211yesmaximal, characteristic, complemented
9C11×#1880C212yesmaximal, complemented
10C11×#1850C211yesmaximal, characteristic, complemented
11C11×#1786C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C22×C11×Q16C2211yescharacteristic, complemented
15C22×C11×Q16C2211yescharacteristic, complemented
16C22×C11×SD16—24no—
17C22×C11×SD16—28no—
18C22×C11×SD16C2212yes—
19C22×C11×SD16C2212yes—
20C23×C8×C11C2211yescharacteristic
21C2×C11×#124C2212yes—
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C4×Q8×C11C2212yescomplemented
24C11×#464—28no—
25C11×#451—24no—
26C2×C11×C4⋊C8C2212yescomplemented
27C2×C11×#103C2211yescharacteristic, complemented
28C2×C11×#103C2212yescomplemented
29C2×C11×#103C2211yescharacteristic, complemented
30C2×C11×#102C2212yes—
31C2×C11×#102C2212yes—
32C2×C11×C22⋊C8C2211yescharacteristic
33C11×#394—22no—
34C11×#391—22no—
35C11×#391C2212yescomplemented
36C11×#390C2212yes—
37C11×#380—21no—
38C11×#380C2211yescharacteristic
39C11×#379—21no—
40C11×#379—21no—
41C4×C11×C22⋊C4—21no—
42C4×C11×C22⋊C4C2211yescharacteristic
43C11×#340C2212yescomplemented
44C11×#336C2212yescomplemented
45C25×C11—21no—
46C22×Q8×C11—21no—
47C22×Q8×C11—22no—
48C22×Q8×C11—24no—
49C22×Q8×C11—42no—
50C22×Q8×C11D414yes—
51C22×Q8×C11C2311yescharacteristic
52C22×Q8×C11C2311yescharacteristic
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11—24no—
55C22×D4×C11—22no—
56C22×D4×C11—21no—
57C22×D4×C11—22no—
58C22×D4×C11—42no—
59C22×D4×C11C2312yes—
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C2×C11×Q16—22no—
63C2×C11×Q16—22no—
64C2×C11×Q16—24no—
65C2×C11×Q16—42no—
66C2×C11×SD16—232no—
67C2×C11×SD16—24no—
68C2×C11×SD16—24no—
69C2×C11×SD16—24no—
70C2×C11×SD16—24no—
71C2×C11×SD16—24no—
72C2×C11×SD16D418yes—
73C22×C8×C11—22no—
74C22×C8×C11—24no—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2312yes—
78C11×#124—24no—
79C11×#124—42no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C4×Q8×C11—24no—
83C4×Q8×C11—42no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C11×C22⋊C4D411yescharacteristic
96C2×C42×C11—22no—
97C2×C42×C11C2312yes—
98C11×C4⋊C8—24no—
99C11×#103—22no—
100C11×#103—22no—
101C11×#103—24no—
102C11×#102—24no—
103C11×#102—42no—
104C11×C22⋊C8—22no—
105C11×#95—22no—
106C11×#95—22no—
107C11×#95—21no—
108C11×#95D412yes—
109#24357C1111yesmaximal, characteristic, direct product factor, Sylow
110C24×C11—22no—
111C24×C11—44no—
112C24×C11—42no—
113C24×C11—42no—
114C24×C11—42no—
115C24×C11—82no—
116C24×C11C2×D411yescharacteristic
117C2×Q8×C11—24no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—22no—
121C2×Q8×C11—28no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—44no—
129C2×Q8×C11—44no—
130C2×Q8×C11—48no—
131C2×Q8×C11C2×D412yes—
132C2×Q8×C11C2×D412yes—
133C2×Q8×C11C2×D414yes—
134C2×D4×C11—28no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—48no—
141C2×D4×C11—44no—
142C2×D4×C11—44no—
143C2×D4×C11—42no—
144C2×D4×C11C2×D414yes—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—24no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—44no—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D412yes—
158C22×C4×C11#4112yes—
159C22×C4×C11C2411yescharacteristic
160C11×Q16—44no—
161C11×Q16—44no—
162C11×SD16—216no—
163C11×SD16—216no—
164C2×C8×C11—28no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11C2×D414yes—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—44no—
177C11×C4⋊C4—42no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—44no—
181C11×C22⋊C4—44no—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—82no—
185C11×C22⋊C4—82no—
186C42×C11—22no—
187C42×C11—22no—
188C42×C11—44no—
189C23×SD16C2×C1111yescharacteristic
190C2×#464C2×C1112yescomplemented
191C2×#451C2×C1111yescharacteristic, complemented
192#2435C2×C1111yescharacteristic
193Q8×C22⋊C4C2×C1111yescharacteristic, complemented
194#2055C2×C1112yescomplemented
195#2015C2×C1112yescomplemented
196#1892C2×C1111yescharacteristic, complemented
197#1880C2×C1112yescomplemented
198#1850C2×C1111yescharacteristic, complemented
199#1786C2×C1111yescharacteristic
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—24no—
203C23×C11—48no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—88no—
211C23×C11—88no—
212C23×C11—84no—
213C23×C11—84no—
214C23×C11#12112yes—
215C23×C11#13512yes—
216C23×C11#13712yes—
217C23×C11C22×D411yescharacteristic
218Q8×C11—22no—
219Q8×C11—24no—
220Q8×C11—22no—
221Q8×C11—22no—
222Q8×C11—48no—
223Q8×C11—42no—
224Q8×C11—41no—
225Q8×C11—41no—
226Q8×C11—42no—
227Q8×C11#12014yes—
228D4×C11—24no—
229D4×C11—24no—
230D4×C11—48no—
231D4×C11—42no—
232D4×C11—42no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—48no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11#12112yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D412yes—
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)12yes—
260C8×C11—24no—
261C8×C11—41no—
262C8×C11—41no—
263C23×Q8C22×C1111yescharacteristic
264C23×D4C22×C1111yescharacteristic
265C22×Q16C22×C1111yescharacteristic, complemented
266C22×Q16C22×C1111yescharacteristic, complemented
267C22×SD16—24no—
268C22×SD16—28no—
269C22×SD16C22×C1112yes—
270C22×SD16C22×C1112yes—
271C23×C8C22×C1111yescharacteristic
272C2×#124C22×C1112yes—
273C2×C22⋊Q8C22×C1111yescharacteristic
274C2×C4×Q8C22×C1112yescomplemented
275#464—28no—
276#451—24no—
277C2×C4⋊C8C22×C1112yescomplemented
278C2×#103C22×C1111yescharacteristic, complemented
279C2×#103C22×C1111yescharacteristic, complemented
280C2×#103C22×C1112yescomplemented
281C2×#102C22×C1112yes—
282C2×#102C22×C1112yes—
283C2×C22⋊C8C22×C1111yescharacteristic
284#394—22no—
285#391—22no—
286#391C22×C1112yescomplemented
287#390C22×C1112yes—
288#380—21no—
289#380C22×C1111yescharacteristic
290#379—21no—
291#379—21no—
292C4×C22⋊C4—21no—
293C4×C22⋊C4C22×C1111yescharacteristic
294#340C22×C1112yescomplemented
295#336C22×C1112yescomplemented
296C22×C11—22no—
297C22×C11—24no—
298C22×C11—24no—
299C22×C11—22no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—816no—
304C22×C11—82no—
305C22×C11—82no—
306C22×C11—82no—
307C22×C11—82no—
308C22×C11#46414yescomplemented
309C22×C11C2×#12111yescharacteristic
310C22×C11D4212yes—
311C22×C11C2×#13511yescharacteristic
312C22×C11C2×#13711yescharacteristic
313C22×C11#57712yes—
314C4×C11—22no—
315C4×C11—24no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11—42no—
319C4×C11—81no—
320C4×C11—82no—
321C4×C11—81no—
322C4×C11C2×#12011yescharacteristic
323C4×C11#53411yescharacteristic
324C4×C11#54612yes—
325C25—21no—
326C22×Q8—21no—
327C22×Q8—22no—
328C22×Q8—24no—
329C22×Q8—42no—
330C22×Q8D4×C1114yes—
331C22×Q8C23×C1111yescharacteristic
332C22×Q8C23×C1111yescharacteristic
333C22×Q8C23×C1111yescharacteristic
334C22×D4—24no—
335C22×D4—22no—
336C22×D4—21no—
337C22×D4—22no—
338C22×D4—42no—
339C22×D4C23×C1112yes—
340C23×C4—21no—
341C23×C4C23×C1111yescharacteristic
342C2×Q16—22no—
343C2×Q16—22no—
344C2×Q16—24no—
345C2×Q16—42no—
346C2×SD16—232no—
347C2×SD16—24no—
348C2×SD16—24no—
349C2×SD16—24no—
350C2×SD16—24no—
351C2×SD16—24no—
352C2×SD16D4×C1118yes—
353C22×C8—22no—
354C22×C8—24no—
355C22×C8C23×C1111yescharacteristic
356C22×C8C23×C1111yescharacteristic
357C22×C8C23×C1112yes—
358#124—24no—
359#124—42no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C4×Q8—24no—
363C4×Q8—42no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4C23×C1112yes—
367C2×C4⋊C4C23×C1111yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4D4×C1111yescharacteristic
375C2×C22⋊C4D4×C1111yescharacteristic
376C2×C42—22no—
377C2×C42C23×C1112yes—
378C4⋊C8—24no—
379#103—22no—
380#103—22no—
381#103—24no—
382#102—24no—
383#102—42no—
384C22⋊C8—22no—
385#95—22no—
386#95—22no—
387#95—21no—
388#95D4×C1112yes—
389C2×C11—24no—
390C2×C11—84no—
391C2×C11#241011yescharacteristic
392C2×C11C2×#46411yescharacteristic
393C2×C11#304311yescharacteristic
394C2×C11#326612yes—
395C2×C11#328212yes—
396C24—22no—
397C24—44no—
398C24—42no—
399C24—42no—
400C24—42no—
401C24—82no—
402C24C2×D4×C1111yescharacteristic
403C2×Q8—24no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—22no—
407C2×Q8—28no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—44no—
415C2×Q8—44no—
416C2×Q8—48no—
417C2×Q8C2×D4×C1112yes—
418C2×Q8C2×D4×C1112yes—
419C2×Q8C2×D4×C1114yes—
420C2×D4—28no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—48no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—42no—
430C2×D4C2×D4×C1114yes—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—44no—
440C22×C4C2×D4×C1112yes—
441C22×C4C2×D4×C1112yes—
442C22×C4C2×D4×C1111yescharacteristic
443C22×C4C2×D4×C1112yes—
444C22×C4C11×#4112yes—
445C22×C4C24×C1111yescharacteristic
446Q16—44no—
447Q16—44no—
448SD16—216no—
449SD16—216no—
450C2×C8—28no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8C2×D4×C1114yes—
458C4⋊C4—22no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—44no—
463C4⋊C4—42no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—44no—
467C22⋊C4—44no—
468C22⋊C4—42no—
469C22⋊C4—42no—
470C22⋊C4—82no—
471C22⋊C4—82no—
472C42—22no—
473C42—22no—
474C42—44no—
475C11#2435711yescharacteristic, direct product factor, Sylow
476C23—22no—
477C23—22no—
478C23—24no—
479C23—48no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—88no—
487C23—88no—
488C23—84no—
489C23—84no—
490C23C11×#12112yes—
491C23C11×#13512yes—
492C23C11×#13712yes—
493C23C22×D4×C1111yescharacteristic
494Q8—22no—
495Q8—24no—
496Q8—22no—
497Q8—22no—
498Q8—48no—
499Q8—42no—
500Q8—41no—
501Q8—41no—
502Q8—42no—
503Q8C11×#12014yes—
504D4—24no—
505D4—24no—
506D4—48no—
507D4—42no—
508D4—42no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—48no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4C11×#12112yes—
532C2×C4C22×D4×C1111yescharacteristic
533C2×C4C22×D4×C1112yes—
534C2×C4C2×C11×#4111yescharacteristic
535C2×C4C11×H(5,𝔽2)12yes—
536C8—24no—
537C8—41no—
538C8—41no—
539C22—22no—
540C22—24no—
541C22—24no—
542C22—22no—
543C22—44no—
544C22—44no—
545C22—44no—
546C22—816no—
547C22—82no—
548C22—82no—
549C22—82no—
550C22—82no—
551C22C11×#46414yescomplemented
552C22C2×C11×#12111yescharacteristic
553C22D42×C1112yes—
554C22C2×C11×#13511yescharacteristic
555C22C2×C11×#13711yescharacteristic
556C22C11×#57712yes—
557C4—22no—
558C4—24no—
559C4—42no—
560C4—42no—
561C4—42no—
562C4—81no—
563C4—82no—
564C4—81no—
565C4C2×C11×#12011yescharacteristic
566C4C11×#53411yescharacteristic
567C4C11×#54612yes—
568C2—24no—
569C2—84no—
570C2C11×#241011yescharacteristic
571C2C2×C11×#46411yescharacteristic
572C2C11×#304311yescharacteristic
573C2C11×#326612yes—
574C2C11×#328212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#464C2semidirect
3. C2×C11×#451C2semidirect
5. Q8×C11×C22⋊C4C2semidirect
6. C11×#2055C2semidirect
7. C11×#2015C2semidirect
8. C11×#1892C2semidirect
9. C11×#1880C2semidirect
10. C11×#1850C2semidirect
14. C22×C11×Q16C22semidirect
15. C22×C11×Q16C22semidirect
23. C2×C4×Q8×C11C22semidirect
26. C2×C11×C4⋊C8C22semidirect
27. C2×C11×#103C22semidirect
28. C2×C11×#103C22semidirect
29. C2×C11×#103C22semidirect
35. C11×#391C22semidirect
43. C11×#340C22semidirect
44. C11×#336C22semidirect
109. #24357C11direct (N × H)
190. C2×#464C2×C11semidirect
191. C2×#451C2×C11semidirect
193. Q8×C22⋊C4C2×C11semidirect
194. #2055C2×C11semidirect
195. #2015C2×C11semidirect
196. #1892C2×C11semidirect
197. #1880C2×C11semidirect
198. #1850C2×C11semidirect
265. C22×Q16C22×C11semidirect
266. C22×Q16C22×C11semidirect
274. C2×C4×Q8C22×C11semidirect
277. C2×C4⋊C8C22×C11semidirect
278. C2×#103C22×C11semidirect
279. C2×#103C22×C11semidirect
280. C2×#103C22×C11semidirect
286. #391C22×C11semidirect
294. #340C22×C11semidirect
295. #336C22×C11semidirect
308. C22×C11#464semidirect
475. C11#24357direct (N × H)
551. C22C11×#464semidirect

Maximal subgroups

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

subgroupindex
C23×C11×SD162
C2×C11×#4642
C2×C11×#4512
C11×#24352
Q8×C11×C22⋊C42
C11×#20552
C11×#20152
C11×#18922
C11×#18802
C11×#18502
C11×#17862
#2435711