Finite Group Databasebeta

← C11×#24501 #14601694

Subgroups — C11×#24501 #14601694

Order 2816.

1208 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#450C211yesmaximal, characteristic
2C2×C11×#431C211yesmaximal, characteristic, complemented
3C11×#2855C211yesmaximal, characteristic, complemented
4C2×C11×#390C211yesmaximal, characteristic
5C11×#2065C212yesmaximal, complemented
6C11×#2055C212yesmaximal, complemented
7C11×#1968C212yesmaximal, complemented
8C11×#1934C212yesmaximal, complemented
9C11×#1872C211yesmaximal, characteristic, complemented
10C11×#1853C211yesmaximal, characteristic, complemented
11C11×#1786C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C2×C11×C22⋊Q8C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4—21no—
17C22×C11×C22⋊C4—21no—
18C22×C42×C11C2211yescharacteristic
19C11×#450—24no—
20C11×#431—24no—
21C2×C11×#106C2212yescomplemented
22C2×C11×C4⋊C8C2212yescomplemented
23C2×C11×#103C2212yescomplemented
24C2×C11×#102C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C4×C8×C11C2212yescomplemented
30C11×#391C2211yescharacteristic, complemented
31C11×#391C2211yescharacteristic, complemented
32C11×#390—21no—
33C11×#390—21no—
34C11×#390C2212yes—
35C11×#390C2212yes—
36C11×#389C2211yescharacteristic, complemented
37C11×#389C2211yescharacteristic, complemented
38C11×#387—21no—
39C11×#387—21no—
40C11×#385—21no—
41C11×#381—21no—
42C11×#380C2211yescharacteristic
43C11×#340C2212yescomplemented
44C11×#340C2212yescomplemented
45C25×C11—21no—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—24no—
48C22×D4×C11—21no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—42no—
52C22×D4×C11C2312yes—
53C23×C4×C11—21no—
54C23×C4×C11D411yescharacteristic
55C23×C4×C11D411yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C2×C11×SD16—24no—
58C2×C11×SD16—24no—
59C2×C11×SD16—42no—
60C22×C8×C11C2312yes—
61C22×C8×C11C2312yes—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—42no—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—44no—
80C2×C11×C22⋊C4—44no—
81C2×C42×C11—22no—
82C2×C42×C11—22no—
83C2×C42×C11D411yescharacteristic
84C2×C42×C11D411yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C11×#106—42no—
88C11×C4⋊C8—24no—
89C11×#103—42no—
90C11×#102—24no—
91C11×#102—24no—
92C11×#102—42no—
93C11×C22⋊C8—22no—
94C11×C22⋊C8D414yes—
95C4×C8×C11—24no—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103#24501C1111yesmaximal, characteristic, direct product factor, Sylow
104C24×C11—24no—
105C24×C11—22no—
106C24×C11—42no—
107C24×C11—42no—
108C24×C11—42no—
109C24×C11—42no—
110C24×C11—42no—
111C24×C11—42no—
112C24×C11C2×D411yescharacteristic
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×D4×C11—24no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—48no—
124C2×D4×C11—48no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11#4114yes—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—41no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11SD1614yescomplemented
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4112yes—
151C22×C4×C11C2411yescharacteristic
152C11×SD16—48no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11C2×D414yes—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4—42no—
169C11×C22⋊C4—44no—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—42no—
172C11×C22⋊C4—44no—
173C11×C22⋊C4—44no—
174C11×C22⋊C4—44no—
175C42×C11—22no—
176C42×C11—22no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C2×#450C2×C1111yescharacteristic
182C2×#431C2×C1111yescharacteristic, complemented
183#2855C2×C1111yescharacteristic, complemented
184C2×#390C2×C1111yescharacteristic
185#2065C2×C1112yescomplemented
186#2055C2×C1112yescomplemented
187#1968C2×C1112yescomplemented
188#1934C2×C1112yescomplemented
189#1872C2×C1111yescharacteristic, complemented
190#1853C2×C1111yescharacteristic, complemented
191#1786C2×C1111yescharacteristic
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—24no—
197C23×C11—48no—
198C23×C11—48no—
199C23×C11—48no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—84no—
207C23×C11—84no—
208C23×C11—84no—
209C23×C11—84no—
210C23×C11#12112yes—
211C23×C11C2×SD1612yes—
212C23×C11#13512yes—
213C23×C11C22×D411yescharacteristic
214Q8×C11—42no—
215Q8×C11—42no—
216D4×C11—24no—
217D4×C11—24no—
218D4×C11—48no—
219D4×C11—42no—
220D4×C11—42no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—28no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—44no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—84no—
252C2×C4×C11#12112yes—
253C2×C4×C11C2×SD1612yes—
254C2×C4×C11C2×SD1612yes—
255C2×C4×C11AGL(1,ℤ/8)12yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C2×#4112yes—
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)12yes—
260C8×C11—24no—
261C8×C11—42no—
262C23×D4C22×C1111yescharacteristic
263C22×SD16C22×C1112yes—
264C2×C22⋊Q8C22×C1111yescharacteristic
265C22×C4⋊C4C22×C1111yescharacteristic
266C22×C22⋊C4—21no—
267C22×C22⋊C4—21no—
268C22×C42C22×C1111yescharacteristic
269#450—24no—
270#431—24no—
271C2×#106C22×C1112yescomplemented
272C2×C4⋊C8C22×C1112yescomplemented
273C2×#103C22×C1112yescomplemented
274C2×#102C22×C1112yes—
275C2×#102C22×C1112yes—
276C2×#102C22×C1112yes—
277C2×C22⋊C8C22×C1111yescharacteristic
278C2×C22⋊C8C22×C1111yescharacteristic
279C2×C4×C8C22×C1112yescomplemented
280#391C22×C1111yescharacteristic, complemented
281#391C22×C1111yescharacteristic, complemented
282#390—21no—
283#390—21no—
284#390C22×C1112yes—
285#390C22×C1112yes—
286#389C22×C1111yescharacteristic, complemented
287#389C22×C1111yescharacteristic, complemented
288#387—21no—
289#387—21no—
290#385—21no—
291#381—21no—
292#380C22×C1111yescharacteristic
293#340C22×C1112yescomplemented
294#340C22×C1112yescomplemented
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—22no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—816no—
305C22×C11—82no—
306C22×C11—82no—
307C22×C11—82no—
308C22×C11—82no—
309C22×C11#46514yes—
310C22×C11C2×#12111yescharacteristic
311C22×C11#52511yescharacteristic
312C22×C11#53511yescharacteristic
313C22×C11C22×SD1611yescharacteristic
314C22×C11C2×#13511yescharacteristic
315C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
316C22×C11#57511yescharacteristic
317C4×C11—22no—
318C4×C11—22no—
319C4×C11—22no—
320C4×C11—22no—
321C4×C11—41no—
322C4×C11—81no—
323C4×C11—81no—
324C4×C11—82no—
325C4×C11—81no—
326C4×C11—81no—
327C4×C11#54612yes—
328C4×C11#55112yes—
329C25—21no—
330C22×Q8C23×C1111yescharacteristic
331C22×D4—24no—
332C22×D4—21no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—42no—
336C22×D4C23×C1112yes—
337C23×C4—21no—
338C23×C4D4×C1111yescharacteristic
339C23×C4D4×C1111yescharacteristic
340C23×C4C23×C1111yescharacteristic
341C2×SD16—24no—
342C2×SD16—24no—
343C2×SD16—42no—
344C22×C8C23×C1112yes—
345C22×C8C23×C1112yes—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4C23×C1112yes—
354C2×C4⋊C4C23×C1111yescharacteristic
355C2×C4⋊C4C23×C1111yescharacteristic
356C2×C4⋊C4C23×C1111yescharacteristic
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42D4×C1111yescharacteristic
368C2×C42D4×C1111yescharacteristic
369C2×C42C23×C1111yescharacteristic
370C2×C42C23×C1111yescharacteristic
371#106—42no—
372C4⋊C8—24no—
373#103—42no—
374#102—24no—
375#102—24no—
376#102—42no—
377C22⋊C8—22no—
378C22⋊C8D4×C1114yes—
379C4×C8—24no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387C2×C11—24no—
388C2×C11—84no—
389C2×C11#241111yescharacteristic
390C2×C11C2×#46511yescharacteristic
391C2×C11#305511yescharacteristic
392C2×C11#310111yescharacteristic
393C2×C11#310511yescharacteristic
394C2×C11#320811yescharacteristic
395C2×C11#321111yescharacteristic
396C24—24no—
397C24—22no—
398C24—42no—
399C24—42no—
400C24—42no—
401C24—42no—
402C24—42no—
403C24—42no—
404C24C2×D4×C1111yescharacteristic
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×D4—24no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—48no—
416C2×D4—48no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4C11×#4114yes—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—41no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4C11×SD1614yescomplemented
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C2×D4×C1112yes—
439C22×C4C2×D4×C1111yescharacteristic
440C22×C4C2×D4×C1111yescharacteristic
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C11×#4112yes—
443C22×C4C24×C1111yescharacteristic
444SD16—48no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8C2×D4×C1114yes—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—42no—
461C22⋊C4—44no—
462C22⋊C4—42no—
463C22⋊C4—42no—
464C22⋊C4—44no—
465C22⋊C4—44no—
466C22⋊C4—44no—
467C42—22no—
468C42—22no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C11#2450111yescharacteristic, direct product factor, Sylow
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—24no—
479C23—48no—
480C23—48no—
481C23—48no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—84no—
489C23—84no—
490C23—84no—
491C23—84no—
492C23C11×#12112yes—
493C23C2×C11×SD1612yes—
494C23C11×#13512yes—
495C23C22×D4×C1111yescharacteristic
496Q8—42no—
497Q8—42no—
498D4—24no—
499D4—24no—
500D4—48no—
501D4—42no—
502D4—42no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—28no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—44no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—84no—
534C2×C4C11×#12112yes—
535C2×C4C2×C11×SD1612yes—
536C2×C4C2×C11×SD1612yes—
537C2×C4C11×AGL(1,ℤ/8)12yes—
538C2×C4C22×D4×C1111yescharacteristic
539C2×C4C2×C11×#4112yes—
540C2×C4C2×C11×#4111yescharacteristic
541C2×C4C11×H(5,𝔽2)12yes—
542C8—24no—
543C8—42no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—44no—
551C22—44no—
552C22—44no—
553C22—816no—
554C22—82no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22C11×#46514yes—
559C22C2×C11×#12111yescharacteristic
560C22C11×#52511yescharacteristic
561C22C11×#53511yescharacteristic
562C22C22×C11×SD1611yescharacteristic
563C22C2×C11×#13511yescharacteristic
564C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
565C22C11×#57511yescharacteristic
566C4—22no—
567C4—22no—
568C4—22no—
569C4—22no—
570C4—41no—
571C4—81no—
572C4—82no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4C11×#54612yes—
577C4C11×#55112yes—
578C2—24no—
579C2—84no—
580C2C11×#241111yescharacteristic
581C2C2×C11×#46511yescharacteristic
582C2C11×#305511yescharacteristic
583C2C11×#310111yescharacteristic
584C2C11×#310511yescharacteristic
585C2C11×#320811yescharacteristic
586C2C11×#321111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#431C2semidirect
3. C11×#2855C2semidirect
5. C11×#2065C2semidirect
6. C11×#2055C2semidirect
7. C11×#1968C2semidirect
8. C11×#1934C2semidirect
9. C11×#1872C2semidirect
10. C11×#1853C2semidirect
21. C2×C11×#106C22semidirect
22. C2×C11×C4⋊C8C22semidirect
23. C2×C11×#103C22semidirect
29. C2×C4×C8×C11C22semidirect
30. C11×#391C22semidirect
31. C11×#391C22semidirect
36. C11×#389C22semidirect
37. C11×#389C22semidirect
43. C11×#340C22semidirect
44. C11×#340C22semidirect
103. #24501C11direct (N × H)
143. C22×C4×C11SD16semidirect
182. C2×#431C2×C11semidirect
183. #2855C2×C11semidirect
185. #2065C2×C11semidirect
186. #2055C2×C11semidirect
187. #1968C2×C11semidirect
188. #1934C2×C11semidirect
189. #1872C2×C11semidirect
190. #1853C2×C11semidirect
271. C2×#106C22×C11semidirect
272. C2×C4⋊C8C22×C11semidirect
273. C2×#103C22×C11semidirect
279. C2×C4×C8C22×C11semidirect
280. #391C22×C11semidirect
281. #391C22×C11semidirect
286. #389C22×C11semidirect
287. #389C22×C11semidirect
293. #340C22×C11semidirect
294. #340C22×C11semidirect
435. C22×C4C11×SD16semidirect
473. C11#24501direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4502
C2×C11×#4312
C11×#28552
C2×C11×#3902
C11×#20652
C11×#20552
C11×#19682
C11×#19342
C11×#18722
C11×#18532
C11×#17862
#2450111