Finite Group Databasebeta

← C11×#24120 #14601313

Subgroups — C11×#24120 #14601313

Order 2816.

1350 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#547C211yesmaximal, characteristic
2C2×C11×#475C211yesmaximal, characteristic, complemented
3C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
4C11×#2538C211yesmaximal, characteristic, complemented
5C11×#2034C212yesmaximal, complemented
6C11×#2000C212yesmaximal, complemented
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1954C211yesmaximal, characteristic, complemented
9C11×#1872C212yesmaximal, complemented
10C11×#1853C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C22×C11×#41—21no—
13C22×C11×SD16C2211yescharacteristic
14C11×#547—24no—
15C11×#547—24no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#123—22no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×#121C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C22×C11×C4⋊C4C2212yes—
25C11×#475—24no—
26C4×C11×SD16—24no—
27C2×C11×#106C2211yescharacteristic
28C2×C11×#106C2212yes—
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2212yes—
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2212yes—
34C2×C11×C22⋊C8C2212yes—
35C2×C11×C22⋊C8C2212yes—
36C2×C4×C8×C11C2211yescharacteristic
37C11×#396—22no—
38C11×#390—21no—
39C11×#389—21no—
40C11×#384C2211yescharacteristic
41C11×#380C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C2×C11×#41—28no—
46C2×C11×#41—44no—
47C2×C11×#41—44no—
48C22×Q8×C11—21no—
49C22×Q8×C11C2311yescharacteristic
50C22×D4×C11—22no—
51C22×D4×C11D411yescharacteristic
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11—22no—
54C23×C4×C11—21no—
55C23×C4×C11C2312yes—
56C2×C11×SD16—22no—
57C2×C11×SD16—22no—
58C2×C11×SD16—22no—
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2312yes—
61C22×C8×C11C2311yescharacteristic
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8D414yes—
64C11×#123—216no—
65C11×C22⋊Q8—28no—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8—42no—
68C11×#121—24no—
69C11×#121—24no—
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C4×D4×C11D414yes—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4D412yes—
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96C11×#106—22no—
97C11×#106—24no—
98C11×C4⋊C8—22no—
99C11×#103—22no—
100C11×#103—24no—
101C11×#102—22no—
102C11×#102—42no—
103C11×C22⋊C8—24no—
104C11×C22⋊C8—42no—
105C4×C8×C11—22no—
106C11×#95—22no—
107#24120C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11—21no—
109C24×C11C2×D412yes—
110C11×#41—432no—
111C2×Q8×C11—24no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—42no—
118C2×Q8×C11—42no—
119C2×Q8×C11#4112yescomplemented
120C2×D4×C11—28no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—44no—
129C2×D4×C11—44no—
130C2×D4×C11SD1614yescomplemented
131C2×D4×C11C2×D412yes—
132C22×C4×C11—28no—
133C22×C4×C11—21no—
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—44no—
146C22×C4×C11—44no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C11×SD16—28no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—22no—
157C2×C8×C11—21no—
158C2×C8×C11—22no—
159C2×C8×C11—21no—
160C2×C8×C11—22no—
161C2×C8×C11—21no—
162C2×C8×C11#4112yescomplemented
163C11×C4⋊C4—28no—
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—44no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4—81no—
176C11×C4⋊C4C2×D412yes—
177C11×C4⋊C4C2×D414yes—
178C11×C22⋊C4—28no—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—44no—
182C11×C22⋊C4—82no—
183C42×C11—42no—
184C42×C11C2×D412yes—
185C42×C11C2×D412yes—
186C2×#547C2×C1111yescharacteristic
187C2×#475C2×C1111yescharacteristic, complemented
188C2×C4×SD16C2×C1111yescharacteristic, complemented
189#2538C2×C1111yescharacteristic, complemented
190#2034C2×C1112yescomplemented
191#2000C2×C1112yescomplemented
192#1990C2×C1111yescharacteristic, complemented
193#1954C2×C1111yescharacteristic, complemented
194#1872C2×C1112yescomplemented
195#1853C2×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—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11C2×SD1614yes—
211C23×C11C22×D411yescharacteristic
212Q8×C11—22no—
213Q8×C11—22no—
214Q8×C11—41no—
215Q8×C11—41no—
216Q8×C11—48no—
217D4×C11—22no—
218D4×C11—22no—
219D4×C11—28no—
220D4×C11—416no—
221D4×C11—41no—
222D4×C11—41no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—416no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—48no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11#12012yes—
250C2×C4×C11#12012yes—
251C2×C4×C11C2×SD1612yes—
252C2×C4×C11AGL(1,ℤ/8)12yes—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11H(5,𝔽2)11yescharacteristic
258C2×C4×C112−1+411yescharacteristic
259C8×C11—22no—
260C8×C11—41no—
261C8×C11—42no—
262C22×#41—21no—
263C22×SD16C22×C1111yescharacteristic
264#547—24no—
265#547—24no—
266C2×C4⋊Q8C22×C1111yescharacteristic
267C2×#123—22no—
268C2×C22⋊Q8—21no—
269C2×C22⋊Q8C22×C1112yes—
270C2×#121C22×C1112yes—
271C2×C4×Q8C22×C1111yescharacteristic
272C2×C4×D4C22×C1111yescharacteristic
273C2×C4×D4C22×C1111yescharacteristic
274C22×C4⋊C4C22×C1112yes—
275#475—24no—
276C4×SD16—24no—
277C2×#106C22×C1112yes—
278C2×#106C22×C1111yescharacteristic
279C2×C4⋊C8C22×C1111yescharacteristic
280C2×#103C22×C1112yes—
281C2×#103C22×C1111yescharacteristic
282C2×#102C22×C1111yescharacteristic
283C2×#102C22×C1112yes—
284C2×C22⋊C8C22×C1112yes—
285C2×C22⋊C8C22×C1112yes—
286C2×C4×C8C22×C1111yescharacteristic
287#396—22no—
288#390—21no—
289#389—21no—
290#384C22×C1111yescharacteristic
291#380C22×C1112yes—
292#340C22×C1112yes—
293#340C22×C1112yes—
294#340C22×C1112yes—
295C22×C11—24no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—81no—
306C22×C11—81no—
307C22×C11—81no—
308C22×C11—81no—
309C22×C11C2×#12011yescharacteristic
310C22×C11#54611yescharacteristic
311C22×C11#54711yescharacteristic
312C22×C11C22×SD1611yescharacteristic
313C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C11#57711yescharacteristic
315C22×C11#57811yescharacteristic
316C4×C11—22no—
317C4×C11—42no—
318C4×C11—42no—
319C4×C11—42no—
320C4×C11—44no—
321C4×C11—82no—
322C4×C11—81no—
323C4×C11#45014yes—
324C4×C11#52511yescharacteristic
325C4×C11#53711yescharacteristic
326C4×C11#54811yescharacteristic
327C4×C11#55011yescharacteristic
328C2×#41—28no—
329C2×#41—44no—
330C2×#41—44no—
331C22×Q8—21no—
332C22×Q8C23×C1111yescharacteristic
333C22×D4—22no—
334C22×D4D4×C1111yescharacteristic
335C22×D4C23×C1111yescharacteristic
336C23×C4—22no—
337C23×C4—21no—
338C23×C4C23×C1112yes—
339C2×SD16—22no—
340C2×SD16—22no—
341C2×SD16—22no—
342C22×C8C23×C1111yescharacteristic
343C22×C8C23×C1112yes—
344C22×C8C23×C1111yescharacteristic
345C4⋊Q8—22no—
346C4⋊Q8D4×C1114yes—
347#123—216no—
348C22⋊Q8—28no—
349C22⋊Q8—24no—
350C22⋊Q8—42no—
351#121—24no—
352#121—24no—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4D4×C1114yes—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4D4×C1111yescharacteristic
368C2×C4⋊C4C23×C1111yescharacteristic
369C2×C4⋊C4C23×C1112yes—
370C2×C4⋊C4C23×C1111yescharacteristic
371C2×C4⋊C4C23×C1112yes—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4D4×C1112yes—
377C2×C42—21no—
378C2×C42C23×C1111yescharacteristic
379#106—22no—
380#106—24no—
381C4⋊C8—22no—
382#103—22no—
383#103—24no—
384#102—22no—
385#102—42no—
386C22⋊C8—24no—
387C22⋊C8—42no—
388C4×C8—22no—
389#95—22no—
390C2×C11—44no—
391C2×C11—82no—
392C2×C11#240711yescharacteristic
393C2×C11C2×#45011yescharacteristic
394C2×C11#301311yescharacteristic
395C2×C11#329811yescharacteristic
396C2×C11#333211yescharacteristic
397C2×C11#333511yescharacteristic
398C2×C11#335311yescharacteristic
399C24—21no—
400C24C2×D4×C1112yes—
401#41—432no—
402C2×Q8—24no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—42no—
409C2×Q8—42no—
410C2×Q8C11×#4112yescomplemented
411C2×D4—28no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4C11×SD1614yescomplemented
422C2×D4C2×D4×C1112yes—
423C22×C4—28no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—44no—
437C22×C4—44no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4C2×D4×C1112yes—
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C2×D4×C1111yescharacteristic
443C22×C4C24×C1111yescharacteristic
444SD16—28no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—21no—
451C2×C8—22no—
452C2×C8—21no—
453C2×C8C11×#4112yescomplemented
454C4⋊C4—28no—
455C4⋊C4—24no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—22no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—44no—
464C4⋊C4—42no—
465C4⋊C4—42no—
466C4⋊C4—81no—
467C4⋊C4C2×D4×C1112yes—
468C4⋊C4C2×D4×C1114yes—
469C22⋊C4—28no—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—44no—
473C22⋊C4—82no—
474C42—42no—
475C42C2×D4×C1112yes—
476C42C2×D4×C1112yes—
477C11#2412011yescharacteristic, direct product factor, Sylow
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23C2×C11×SD1614yes—
492C23C22×D4×C1111yescharacteristic
493Q8—22no—
494Q8—22no—
495Q8—41no—
496Q8—41no—
497Q8—48no—
498D4—22no—
499D4—22no—
500D4—28no—
501D4—416no—
502D4—41no—
503D4—41no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—416no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—48no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4C11×#12012yes—
531C2×C4C11×#12012yes—
532C2×C4C2×C11×SD1612yes—
533C2×C4C11×AGL(1,ℤ/8)12yes—
534C2×C4C22×D4×C1111yescharacteristic
535C2×C4C22×D4×C1111yescharacteristic
536C2×C4C2×C11×#4111yescharacteristic
537C2×C4C2×C11×#4111yescharacteristic
538C2×C4C11×H(5,𝔽2)11yescharacteristic
539C2×C4C11×2−1+411yescharacteristic
540C8—22no—
541C8—41no—
542C8—42no—
543C22—24no—
544C22—24no—
545C22—24no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×C11×#12011yescharacteristic
558C22C11×#54611yescharacteristic
559C22C11×#54711yescharacteristic
560C22C22×C11×SD1611yescharacteristic
561C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
562C22C11×#57711yescharacteristic
563C22C11×#57811yescharacteristic
564C4—22no—
565C4—42no—
566C4—42no—
567C4—42no—
568C4—44no—
569C4—81no—
570C4—82no—
571C4C11×#45014yes—
572C4C11×#52511yescharacteristic
573C4C11×#53711yescharacteristic
574C4C11×#54811yescharacteristic
575C4C11×#55011yescharacteristic
576C2—44no—
577C2—82no—
578C2C11×#240711yescharacteristic
579C2C2×C11×#45011yescharacteristic
580C2C11×#301311yescharacteristic
581C2C11×#329811yescharacteristic
582C2C11×#333211yescharacteristic
583C2C11×#333511yescharacteristic
584C2C11×#335311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#547C2
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
2. C2×C11×#475C2semidirect
3. C2×C4×C11×SD16C2semidirect
4. C11×#2538C2semidirect
5. C11×#2034C2semidirect
6. C11×#2000C2semidirect
7. C11×#1990C2semidirect
8. C11×#1954C2semidirect
9. C11×#1872C2semidirect
10. C11×#1853C2semidirect
11. C11×#1802C2semidirect
107. #24120C11direct (N × H)
119. C2×Q8×C11#41semidirect
130. C2×D4×C11SD16semidirect
162. C2×C8×C11#41semidirect
187. C2×#475C2×C11semidirect
188. C2×C4×SD16C2×C11semidirect
189. #2538C2×C11semidirect
190. #2034C2×C11semidirect
191. #2000C2×C11semidirect
192. #1990C2×C11semidirect
193. #1954C2×C11semidirect
194. #1872C2×C11semidirect
195. #1853C2×C11semidirect
196. #1802C2×C11semidirect
410. C2×Q8C11×#41semidirect
421. C2×D4C11×SD16semidirect
453. C2×C8C11×#41semidirect
477. C11#24120direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5472
C2×C11×#4752
C2×C4×C11×SD162
C11×#25382
C11×#20342
C11×#20002
C11×#19902
C11×#19542
C11×#18722
C11×#18532
C11×#18022
#2412011