Finite Group Databasebeta

← C11×#24117 #14601310

Subgroups — C11×#24117 #14601310

Order 2816.

1238 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#555C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic, complemented
3C2×C4×C11×D8C211yesmaximal, characteristic, complemented
4C11×#2537C211yesmaximal, characteristic, complemented
5C11×#2034C212yesmaximal, complemented
6C11×#1999C212yesmaximal, complemented
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1954C211yesmaximal, characteristic, complemented
9C11×#1875C212yesmaximal, complemented
10C11×#1854C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C11×#555—24no—
14C11×#555—24no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#124—22no—
17C2×C11×#121—21no—
18C2×C11×#121—21no—
19C2×C11×#121C2212yes—
20C2×C11×#121C2212yes—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117—21no—
25C2×C11×#117C2212yes—
26C11×#476—24no—
27C4×C11×D8—24no—
28C2×C11×#107C2211yescharacteristic
29C2×C11×#106C2212yes—
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2212yes—
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2212yes—
35C2×C11×C22⋊C8C2212yes—
36C2×C11×C22⋊C8C2212yes—
37C2×C4×C8×C11C2211yescharacteristic
38C11×#394—22no—
39C11×#384C2211yescharacteristic
40C11×#380—21no—
41C11×#380C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×Q8×C11—21no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11D411yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C23×C4×C11C2312yes—
54C2×C11×D8—22no—
55C2×C11×D8—22no—
56C2×C11×D8—22no—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2312yes—
59C22×C8×C11C2311yescharacteristic
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8D414yescomplemented
62C11×#124—216no—
63C11×#121—28no—
64C11×#121—24no—
65C11×#121—24no—
66C11×#121—24no—
67C11×#121—42no—
68C11×#121—44no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11D414yescomplemented
75C11×#117—28no—
76C11×#117—24no—
77C11×#117—24no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4D412yes—
93C2×C42×C11—22no—
94C2×C42×C11C2311yescharacteristic
95C11×#107—22no—
96C11×#106—24no—
97C11×C4⋊C8—22no—
98C11×#102—22no—
99C11×#102—22no—
100C11×#102—24no—
101C11×#102—42no—
102C11×C22⋊C8—24no—
103C11×C22⋊C8—42no—
104C4×C8×C11—22no—
105C11×#95—22no—
106#24117C1111yesmaximal, characteristic, direct product factor, Sylow
107C24×C11—21no—
108C24×C11—21no—
109C24×C11C2×D412yes—
110C2×Q8×C11—24no—
111C2×Q8×C11—81no—
112C2×Q8×C11—81no—
113C2×D4×C11—28no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—44no—
128C2×D4×C11—44no—
129C2×D4×C11—82no—
130C2×D4×C11—82no—
131C2×D4×C11—82no—
132C2×D4×C11C2×D412yes—
133C2×D4×C11#4112yes—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C11×D8—28no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—22no—
158C2×C8×C11—21no—
159C2×C8×C11—22no—
160C2×C8×C11—21no—
161C2×C8×C11—22no—
162C2×C8×C11—21no—
163C2×C8×C11#4112yes—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4—81no—
174C11×C4⋊C4C2×D414yes—
175C11×C4⋊C4C2×D412yes—
176C11×C22⋊C4—28no—
177C11×C22⋊C4—28no—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—44no—
181C11×C22⋊C4—44no—
182C11×C22⋊C4—42no—
183C42×C11—28no—
184C42×C11C2×D412yes—
185C42×C11C2×D412yes—
186C2×#555C2×C1111yescharacteristic, complemented
187C2×#476C2×C1111yescharacteristic, complemented
188C2×C4×D8C2×C1111yescharacteristic, complemented
189#2537C2×C1111yescharacteristic, complemented
190#2034C2×C1112yescomplemented
191#1999C2×C1112yescomplemented
192#1990C2×C1111yescharacteristic, complemented
193#1954C2×C1111yescharacteristic, complemented
194#1875C2×C1112yescomplemented
195#1854C2×C1112yescomplemented
196#1802C2×C1111yescharacteristic, complemented
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11C22×D411yescharacteristic
219Q8×C11—84no—
220D4×C11—22no—
221D4×C11—22no—
222D4×C11—22no—
223D4×C11—22no—
224D4×C11—41no—
225D4×C11—41no—
226D4×C11—41no—
227D4×C11—41no—
228D4×C11—44no—
229D4×C11—88no—
230D4×C11—88no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—48no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—84no—
254C2×C4×C11#12012yes—
255C2×C4×C11#12012yes—
256C2×C4×C11#13512yes—
257C2×C4×C11AGL(1,ℤ/8)12yes—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C8×C11—22no—
265C8×C11—41no—
266C8×C11—42no—
267C22×D8C22×C1111yescharacteristic
268#555—24no—
269#555—24no—
270C2×C4⋊Q8C22×C1111yescharacteristic
271C2×#124—22no—
272C2×#121—21no—
273C2×#121—21no—
274C2×#121C22×C1112yes—
275C2×#121C22×C1112yes—
276C2×C4×D4C22×C1111yescharacteristic
277C2×C4×D4C22×C1111yescharacteristic
278C2×C4×D4C22×C1111yescharacteristic
279C2×#117—21no—
280C2×#117C22×C1112yes—
281#476—24no—
282C4×D8—24no—
283C2×#107C22×C1111yescharacteristic
284C2×#106C22×C1112yes—
285C2×C4⋊C8C22×C1111yescharacteristic
286C2×#102C22×C1111yescharacteristic
287C2×#102C22×C1112yes—
288C2×#102C22×C1111yescharacteristic
289C2×#102C22×C1112yes—
290C2×C22⋊C8C22×C1112yes—
291C2×C22⋊C8C22×C1112yes—
292C2×C4×C8C22×C1111yescharacteristic
293#394—22no—
294#384C22×C1111yescharacteristic
295#380—21no—
296#380C22×C1112yes—
297#340C22×C1112yes—
298#340C22×C1112yes—
299#340C22×C1112yes—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—81no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11—81no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11C2×#12011yescharacteristic
322C22×C11#54611yescharacteristic
323C22×C11#54711yescharacteristic
324C22×C11C2×#13511yescharacteristic
325C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C11#57611yescharacteristic
327C22×C11#57711yescharacteristic
328C4×C11—22no—
329C4×C11—42no—
330C4×C11—42no—
331C4×C11—44no—
332C4×C11—81no—
333C4×C11—82no—
334C4×C11#44914yes—
335C4×C11#52511yescharacteristic
336C4×C11#53711yescharacteristic
337C4×C11#54811yescharacteristic
338C4×C11#55011yescharacteristic
339C22×Q8—21no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4D4×C1111yescharacteristic
343C22×D4C23×C1111yescharacteristic
344C22×D4C23×C1111yescharacteristic
345C23×C4—21no—
346C23×C4—21no—
347C23×C4C23×C1112yes—
348C2×D8—22no—
349C2×D8—22no—
350C2×D8—22no—
351C22×C8C23×C1111yescharacteristic
352C22×C8C23×C1112yes—
353C22×C8C23×C1111yescharacteristic
354C4⋊Q8—22no—
355C4⋊Q8D4×C1114yescomplemented
356#124—216no—
357#121—28no—
358#121—24no—
359#121—24no—
360#121—24no—
361#121—42no—
362#121—44no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4D4×C1114yescomplemented
369#117—28no—
370#117—24no—
371#117—24no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4D4×C1111yescharacteristic
376C2×C4⋊C4C23×C1111yescharacteristic
377C2×C4⋊C4C23×C1112yes—
378C2×C4⋊C4C23×C1111yescharacteristic
379C2×C4⋊C4C23×C1112yes—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4D4×C1112yes—
387C2×C42—22no—
388C2×C42C23×C1111yescharacteristic
389#107—22no—
390#106—24no—
391C4⋊C8—22no—
392#102—22no—
393#102—22no—
394#102—24no—
395#102—42no—
396C22⋊C8—24no—
397C22⋊C8—42no—
398C4×C8—22no—
399#95—22no—
400C2×C11—82no—
401C2×C11—82no—
402C2×C11—82no—
403C2×C11#240711yescharacteristic
404C2×C11C2×#44911yescharacteristic
405C2×C11#301211yescharacteristic
406C2×C11#330311yescharacteristic
407C2×C11#332511yescharacteristic
408C2×C11#334111yescharacteristic
409C2×C11#335411yescharacteristic
410C24—21no—
411C24—21no—
412C24C2×D4×C1112yes—
413C2×Q8—24no—
414C2×Q8—81no—
415C2×Q8—81no—
416C2×D4—28no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—44no—
431C2×D4—44no—
432C2×D4—82no—
433C2×D4—82no—
434C2×D4—82no—
435C2×D4C2×D4×C1112yes—
436C2×D4C11×#4112yes—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4C2×D4×C1112yes—
454C22×C4C2×D4×C1111yescharacteristic
455C22×C4C2×D4×C1111yescharacteristic
456C22×C4C24×C1111yescharacteristic
457D8—28no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—21no—
464C2×C8—22no—
465C2×C8—21no—
466C2×C8C11×#4112yes—
467C4⋊C4—24no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—42no—
476C4⋊C4—81no—
477C4⋊C4C2×D4×C1114yes—
478C4⋊C4C2×D4×C1112yes—
479C22⋊C4—28no—
480C22⋊C4—28no—
481C22⋊C4—24no—
482C22⋊C4—24no—
483C22⋊C4—44no—
484C22⋊C4—44no—
485C22⋊C4—42no—
486C42—28no—
487C42C2×D4×C1112yes—
488C42C2×D4×C1112yes—
489C11#2411711yescharacteristic, direct product factor, Sylow
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C22×D4×C1111yescharacteristic
512Q8—84no—
513D4—22no—
514D4—22no—
515D4—22no—
516D4—22no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—44no—
522D4—88no—
523D4—88no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—48no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—84no—
547C2×C4C11×#12012yes—
548C2×C4C11×#12012yes—
549C2×C4C11×#13512yes—
550C2×C4C11×AGL(1,ℤ/8)12yes—
551C2×C4C22×D4×C1111yescharacteristic
552C2×C4C22×D4×C1111yescharacteristic
553C2×C4C2×C11×#4111yescharacteristic
554C2×C4C2×C11×#4111yescharacteristic
555C2×C4C11×H(5,𝔽2)11yescharacteristic
556C2×C4C11×2−1+411yescharacteristic
557C8—22no—
558C8—41no—
559C8—42no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22C2×C11×#12011yescharacteristic
582C22C11×#54611yescharacteristic
583C22C11×#54711yescharacteristic
584C22C2×C11×#13511yescharacteristic
585C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
586C22C11×#57611yescharacteristic
587C22C11×#57711yescharacteristic
588C4—22no—
589C4—42no—
590C4—42no—
591C4—44no—
592C4—81no—
593C4—82no—
594C4C11×#44914yes—
595C4C11×#52511yescharacteristic
596C4C11×#53711yescharacteristic
597C4C11×#54811yescharacteristic
598C4C11×#55011yescharacteristic
599C2—82no—
600C2—82no—
601C2—82no—
602C2C11×#240711yescharacteristic
603C2C2×C11×#44911yescharacteristic
604C2C11×#301211yescharacteristic
605C2C11×#330311yescharacteristic
606C2C11×#332511yescharacteristic
607C2C11×#334111yescharacteristic
608C2C11×#335411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#555C2semidirect
2. C2×C11×#476C2semidirect
3. C2×C4×C11×D8C2semidirect
4. C11×#2537C2semidirect
5. C11×#2034C2semidirect
6. C11×#1999C2semidirect
7. C11×#1990C2semidirect
8. C11×#1954C2semidirect
9. C11×#1875C2semidirect
10. C11×#1854C2semidirect
11. C11×#1802C2semidirect
61. C11×C4⋊Q8D4semidirect
74. C4×D4×C11D4semidirect
106. #24117C11direct (N × H)
186. C2×#555C2×C11semidirect
187. C2×#476C2×C11semidirect
188. C2×C4×D8C2×C11semidirect
189. #2537C2×C11semidirect
190. #2034C2×C11semidirect
191. #1999C2×C11semidirect
192. #1990C2×C11semidirect
193. #1954C2×C11semidirect
194. #1875C2×C11semidirect
195. #1854C2×C11semidirect
196. #1802C2×C11semidirect
355. C4⋊Q8D4×C11semidirect
368. C4×D4D4×C11semidirect
489. C11#24117direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5552
C2×C11×#4762
C2×C4×C11×D82
C11×#25372
C11×#20342
C11×#19992
C11×#19902
C11×#19542
C11×#18752
C11×#18542
C11×#18022
#2411711