Finite Group Databasebeta

← C11×#24188 #14601381

Subgroups — C11×#24188 #14601381

Order 2816.

1394 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#550C211yesmaximal, characteristic
2C2×C11×#460C211yesmaximal, characteristic, complemented
3C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
4C11×#2582C211yesmaximal, characteristic, complemented
5C11×#2041C212yesmaximal, complemented
6C11×#2014C212yesmaximal, complemented
7C11×#1984C211yesmaximal, characteristic, complemented
8C11×#1957C211yesmaximal, characteristic, complemented
9C11×#1877C212yesmaximal, complemented
10C11×#1864C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C22×C11×#41—21no—
13C22×C11×SD16C2211yescharacteristic
14C22×C11×SD16C2212yes—
15C11×#550—24no—
16C11×#550—24no—
17C2×C11×#127C2212yes—
18C2×C11×#127C2211yescharacteristic
19C2×C11×#121—21no—
20C2×C11×#121—22no—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2212yes—
24C2×C4×D4×C11C2211yescharacteristic
25C11×#460—24no—
26C4×C11×SD16—24no—
27C2×C11×#106C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2212yes—
32C2×C11×#102C2212yes—
33C2×C11×#102C2212yes—
34C2×C11×#102C2212yes—
35C2×C4×C8×C11C2211yescharacteristic
36C11×#398—22no—
37C11×#391—21no—
38C11×#391C2212yes—
39C11×#389—21no—
40C11×#389C2212yes—
41C11×#384C2211yescharacteristic
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C2×C11×#41—28no—
46C2×C11×#41—44no—
47C2×C11×#41—44no—
48C22×Q8×C11D411yescharacteristic
49C22×Q8×C11C2311yescharacteristic
50C22×D4×C11—22no—
51C22×D4×C11—21no—
52C22×D4×C11—22no—
53C22×D4×C11—21no—
54C22×D4×C11C2312yes—
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11—22no—
57C23×C4×C11—21no—
58C2×C11×SD16—22no—
59C2×C11×SD16—22no—
60C2×C11×SD16—24no—
61C2×C11×SD16—24no—
62C2×C11×SD16—22no—
63C2×C11×SD16—42no—
64C22×C8×C11C2312yes—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#127—24no—
68C11×#127—24no—
69C11×#127—22no—
70C11×#127D414yes—
71C11×#121—28no—
72C11×#121—216no—
73C4×Q8×C11—22no—
74C4×Q8×C11—22no—
75C4×Q8×C11—22no—
76C4×Q8×C11—22no—
77C4×D4×C11—24no—
78C4×D4×C11—24no—
79C4×D4×C11—22no—
80C4×D4×C11D414yes—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C4⋊C4D412yes—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—21no—
92C2×C42×C11—21no—
93C2×C42×C11C2312yes—
94C2×C42×C11C2311yescharacteristic
95C11×#106—22no—
96C11×C4⋊C8—22no—
97C11×#103—22no—
98C11×#102—22no—
99C11×#102—24no—
100C11×#102—24no—
101C11×#102—42no—
102C11×#102—42no—
103C4×C8×C11—22no—
104C11×#95—22no—
105C11×#95—22no—
106C11×#95—22no—
107#24188C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11—22no—
109C24×C11—21no—
110C11×#41—432no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11SD1614yescomplemented
119C2×Q8×C11#4112yescomplemented
120C2×D4×C11—28no—
121C2×D4×C11—28no—
122C2×D4×C11—24no—
123C2×D4×C11—24no—
124C2×D4×C11—22no—
125C2×D4×C11—21no—
126C2×D4×C11—22no—
127C2×D4×C11—21no—
128C2×D4×C11—22no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—22no—
132C2×D4×C11—21no—
133C2×D4×C11—22no—
134C2×D4×C11—44no—
135C2×D4×C11—44no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11—81no—
139C2×D4×C11—81no—
140C2×D4×C11—82no—
141C2×D4×C11—82no—
142C2×D4×C11C2×D414yes—
143C2×D4×C11C2×D412yes—
144C22×C4×C11—28no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—44no—
151C22×C4×C11—44no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C11×SD16—28no—
160C11×SD16—48no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—22no—
164C2×C8×C11—21no—
165C2×C8×C11—22no—
166C2×C8×C11—21no—
167C2×C8×C11—22no—
168C2×C8×C11—21no—
169C2×C8×C11#4112yescomplemented
170C11×C4⋊C4—24no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4—81no—
180C11×C4⋊C4—82no—
181C11×C4⋊C4C2×D412yes—
182C11×C22⋊C4—28no—
183C11×C22⋊C4—24no—
184C42×C11—22no—
185C42×C11—22no—
186C42×C11—42no—
187C42×C11C2×D412yes—
188C42×C11C2×D412yes—
189C2×#550C2×C1111yescharacteristic
190C2×#460C2×C1111yescharacteristic, complemented
191C2×C4×SD16C2×C1111yescharacteristic, complemented
192#2582C2×C1111yescharacteristic, complemented
193#2041C2×C1112yescomplemented
194#2014C2×C1112yescomplemented
195#1984C2×C1111yescharacteristic, complemented
196#1957C2×C1111yescharacteristic, complemented
197#1877C2×C1112yescomplemented
198#1864C2×C1112yescomplemented
199#1802C2×C1111yescharacteristic, complemented
200C23×C11—24no—
201C23×C11—22no—
202C23×C11—41no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—41no—
206C23×C11—42no—
207C23×C11—41no—
208C23×C11—42no—
209C23×C11—41no—
210C23×C11—42no—
211C23×C11—41no—
212C23×C11—42no—
213C23×C11—41no—
214C23×C11C22×D411yescharacteristic
215Q8×C11—28no—
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—41no—
219Q8×C11—41no—
220D4×C11—22no—
221D4×C11—22no—
222D4×C11—24no—
223D4×C11—24no—
224D4×C11—416no—
225D4×C11—42no—
226D4×C11—42no—
227D4×C11—41no—
228D4×C11—41no—
229D4×C11—48no—
230D4×C11—84no—
231D4×C11—88no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—416no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—48no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11#12012yes—
254C2×C4×C11#12012yes—
255C2×C4×C11C2×SD1614yes—
256C2×C4×C11C2×SD1612yes—
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×#41—21no—
268C22×SD16C22×C1111yescharacteristic
269C22×SD16C22×C1112yes—
270#550—24no—
271#550—24no—
272C2×#127C22×C1112yes—
273C2×#127C22×C1111yescharacteristic
274C2×#121—21no—
275C2×#121—22no—
276C2×C4×Q8C22×C1111yescharacteristic
277C2×C4×Q8C22×C1111yescharacteristic
278C2×C4×D4C22×C1112yes—
279C2×C4×D4C22×C1111yescharacteristic
280#460—24no—
281C4×SD16—24no—
282C2×#106C22×C1111yescharacteristic
283C2×C4⋊C8C22×C1111yescharacteristic
284C2×#103C22×C1111yescharacteristic
285C2×#102C22×C1112yes—
286C2×#102C22×C1112yes—
287C2×#102C22×C1111yescharacteristic
288C2×#102C22×C1112yes—
289C2×#102C22×C1112yes—
290C2×C4×C8C22×C1111yescharacteristic
291#398—22no—
292#391—21no—
293#391C22×C1112yes—
294#389—21no—
295#389C22×C1112yes—
296#384C22×C1111yescharacteristic
297#340C22×C1112yes—
298#336C22×C1112yes—
299#336C22×C1112yes—
300C22×C11—42no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—42no—
304C22×C11—44no—
305C22×C11—42no—
306C22×C11—81no—
307C22×C11—82no—
308C22×C11—82no—
309C22×C11—81no—
310C22×C11—82no—
311C22×C11—81no—
312C22×C11—82no—
313C22×C11—81no—
314C22×C11C2×#12011yescharacteristic
315C22×C11#54811yescharacteristic
316C22×C11#55011yescharacteristic
317C22×C11C22×SD1611yescharacteristic
318C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
319C22×C11#57611yescharacteristic
320C22×C11#57711yescharacteristic
321C4×C11—24no—
322C4×C11—22no—
323C4×C11—42no—
324C4×C11—42no—
325C4×C11—42no—
326C4×C11—82no—
327C4×C11—81no—
328C4×C11#45014yes—
329C4×C11#52511yescharacteristic
330C4×C11#53711yescharacteristic
331C4×C11#54611yescharacteristic
332C4×C11#54711yescharacteristic
333C2×#41—28no—
334C2×#41—44no—
335C2×#41—44no—
336C22×Q8D4×C1111yescharacteristic
337C22×Q8C23×C1111yescharacteristic
338C22×D4—22no—
339C22×D4—21no—
340C22×D4—22no—
341C22×D4—21no—
342C22×D4C23×C1112yes—
343C22×D4C23×C1111yescharacteristic
344C23×C4—22no—
345C23×C4—21no—
346C2×SD16—22no—
347C2×SD16—22no—
348C2×SD16—24no—
349C2×SD16—24no—
350C2×SD16—22no—
351C2×SD16—42no—
352C22×C8C23×C1112yes—
353C22×C8C23×C1111yescharacteristic
354C22×C8C23×C1111yescharacteristic
355#127—24no—
356#127—24no—
357#127—22no—
358#127D4×C1114yes—
359#121—28no—
360#121—216no—
361C4×Q8—22no—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×Q8—22no—
365C4×D4—24no—
366C4×D4—24no—
367C4×D4—22no—
368C4×D4D4×C1114yes—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4D4×C1111yescharacteristic
374C2×C4⋊C4D4×C1112yes—
375C2×C4⋊C4C23×C1111yescharacteristic
376C2×C4⋊C4C23×C1112yes—
377C2×C4⋊C4C23×C1111yescharacteristic
378C2×C22⋊C4—22no—
379C2×C22⋊C4—21no—
380C2×C42—21no—
381C2×C42C23×C1112yes—
382C2×C42C23×C1111yescharacteristic
383#106—22no—
384C4⋊C8—22no—
385#103—22no—
386#102—22no—
387#102—24no—
388#102—24no—
389#102—42no—
390#102—42no—
391C4×C8—22no—
392#95—22no—
393#95—22no—
394#95—22no—
395C2×C11—82no—
396C2×C11—84no—
397C2×C11#240711yescharacteristic
398C2×C11C2×#45011yescharacteristic
399C2×C11#301211yescharacteristic
400C2×C11#336211yescharacteristic
401C2×C11#336811yescharacteristic
402C2×C11#339211yescharacteristic
403C2×C11#339911yescharacteristic
404C24—22no—
405C24—21no—
406#41—432no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8C11×SD1614yescomplemented
415C2×Q8C11×#4112yescomplemented
416C2×D4—28no—
417C2×D4—28no—
418C2×D4—24no—
419C2×D4—24no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—22no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—22no—
428C2×D4—21no—
429C2×D4—22no—
430C2×D4—44no—
431C2×D4—44no—
432C2×D4—42no—
433C2×D4—42no—
434C2×D4—81no—
435C2×D4—81no—
436C2×D4—82no—
437C2×D4—82no—
438C2×D4C2×D4×C1114yes—
439C2×D4C2×D4×C1112yes—
440C22×C4—28no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—44no—
447C22×C4—44no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4C2×D4×C1112yes—
451C22×C4C2×D4×C1111yescharacteristic
452C22×C4C2×D4×C1112yes—
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C24×C1111yescharacteristic
455SD16—28no—
456SD16—48no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—21no—
463C2×C8—22no—
464C2×C8—21no—
465C2×C8C11×#4112yescomplemented
466C4⋊C4—24no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—81no—
476C4⋊C4—82no—
477C4⋊C4C2×D4×C1112yes—
478C22⋊C4—28no—
479C22⋊C4—24no—
480C42—22no—
481C42—22no—
482C42—42no—
483C42C2×D4×C1112yes—
484C42C2×D4×C1112yes—
485C11#2418811yescharacteristic, direct product factor, Sylow
486C23—24no—
487C23—22no—
488C23—41no—
489C23—42no—
490C23—42no—
491C23—41no—
492C23—42no—
493C23—41no—
494C23—42no—
495C23—41no—
496C23—42no—
497C23—41no—
498C23—42no—
499C23—41no—
500C23C22×D4×C1111yescharacteristic
501Q8—28no—
502Q8—22no—
503Q8—22no—
504Q8—41no—
505Q8—41no—
506D4—22no—
507D4—22no—
508D4—24no—
509D4—24no—
510D4—416no—
511D4—42no—
512D4—42no—
513D4—41no—
514D4—41no—
515D4—48no—
516D4—84no—
517D4—88no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—416no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—48no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4C11×#12012yes—
540C2×C4C11×#12012yes—
541C2×C4C2×C11×SD1614yes—
542C2×C4C2×C11×SD1612yes—
543C2×C4C11×AGL(1,ℤ/8)12yes—
544C2×C4C22×D4×C1111yescharacteristic
545C2×C4C22×D4×C1111yescharacteristic
546C2×C4C2×C11×#4111yescharacteristic
547C2×C4C2×C11×#4111yescharacteristic
548C2×C4C11×H(5,𝔽2)11yescharacteristic
549C2×C4C11×2−1+411yescharacteristic
550C8—22no—
551C8—41no—
552C8—42no—
553C22—42no—
554C22—44no—
555C22—44no—
556C22—42no—
557C22—44no—
558C22—42no—
559C22—81no—
560C22—82no—
561C22—82no—
562C22—81no—
563C22—82no—
564C22—81no—
565C22—82no—
566C22—81no—
567C22C2×C11×#12011yescharacteristic
568C22C11×#54811yescharacteristic
569C22C11×#55011yescharacteristic
570C22C22×C11×SD1611yescharacteristic
571C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
572C22C11×#57611yescharacteristic
573C22C11×#57711yescharacteristic
574C4—24no—
575C4—22no—
576C4—42no—
577C4—42no—
578C4—42no—
579C4—81no—
580C4—82no—
581C4C11×#45014yes—
582C4C11×#52511yescharacteristic
583C4C11×#53711yescharacteristic
584C4C11×#54611yescharacteristic
585C4C11×#54711yescharacteristic
586C2—82no—
587C2—84no—
588C2C11×#240711yescharacteristic
589C2C2×C11×#45011yescharacteristic
590C2C11×#301211yescharacteristic
591C2C11×#336211yescharacteristic
592C2C11×#336811yescharacteristic
593C2C11×#339211yescharacteristic
594C2C11×#339911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#550C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#460C2semidirect
3. C2×C4×C11×SD16C2semidirect
4. C11×#2582C2semidirect
5. C11×#2041C2semidirect
6. C11×#2014C2semidirect
7. C11×#1984C2semidirect
8. C11×#1957C2semidirect
9. C11×#1877C2semidirect
10. C11×#1864C2semidirect
11. C11×#1802C2semidirect
107. #24188C11direct (N × H)
118. C2×Q8×C11SD16semidirect
119. C2×Q8×C11#41semidirect
169. C2×C8×C11#41semidirect
190. C2×#460C2×C11semidirect
191. C2×C4×SD16C2×C11semidirect
192. #2582C2×C11semidirect
193. #2041C2×C11semidirect
194. #2014C2×C11semidirect
195. #1984C2×C11semidirect
196. #1957C2×C11semidirect
197. #1877C2×C11semidirect
198. #1864C2×C11semidirect
199. #1802C2×C11semidirect
414. C2×Q8C11×SD16semidirect
415. C2×Q8C11×#41semidirect
465. C2×C8C11×#41semidirect
485. C11#24188direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5502
C2×C11×#4602
C2×C4×C11×SD162
C11×#25822
C11×#20412
C11×#20142
C11×#19842
C11×#19572
C11×#18772
C11×#18642
C11×#18022
#2418811