Finite Group Databasebeta

← C11×#24088 #14601281

Subgroups — C11×#24088 #14601281

Order 2816.

1354 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#547C211yesmaximal, characteristic
2C2×C11×#480C211yesmaximal, characteristic, complemented
3C22×C11×#107C211yesmaximal, characteristic, complemented
4C11×#2486C211yesmaximal, characteristic, complemented
5C11×#2057C212yesmaximal, complemented
6C11×#2033C212yesmaximal, complemented
7C11×#1893C211yesmaximal, characteristic, complemented
8C11×#1869C211yesmaximal, characteristic, complemented
9C11×#1862C212yesmaximal, complemented
10C11×#1852C212yesmaximal, complemented
11C11×#1823C211yesmaximal, characteristic, complemented
12C22×C11×#41—21no—
13C23×C8×C11C2211yescharacteristic
14C11×#547—24no—
15C11×#547—24no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#123—21no—
18C2×C11×#123—21no—
19C2×C11×#123—21no—
20C2×C11×C22⋊Q8—21no—
21C2×C11×#121C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C11×#480—24no—
29C2×C11×#107—24no—
30C2×C11×#107C2212yes—
31C2×C11×#107C2212yes—
32C2×C11×#107C2212yes—
33C2×C11×#102C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×C22⋊C8C2212yes—
36C2×C11×C22⋊C8C2211yescharacteristic
37C11×#398—21no—
38C11×#397—21no—
39C11×#389C2212yes—
40C11×#381—21no—
41C11×#380C2211yescharacteristic
42C11×#380C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C11×#340C2212yes—
46C11×#336C2212yes—
47C2×C11×#41—28no—
48C2×C11×#41—44no—
49C2×C11×#41—44no—
50C22×Q8×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11D411yescharacteristic
54C22×D4×C11C2311yescharacteristic
55C23×C4×C11—21no—
56C23×C4×C11—21no—
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C8×C11—22no—
62C22×C8×C11—24no—
63C22×C8×C11C2312yes—
64C22×C8×C11C2312yes—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—22no—
67C11×#123—28no—
68C11×#123—28no—
69C11×#123—44no—
70C11×C22⋊Q8—28no—
71C11×#121—22no—
72C11×#121—22no—
73C11×#121—22no—
74C11×#121D414yes—
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4D414yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C11×#107—24no—
105C11×#107—24no—
106C11×#107—24no—
107C11×#102—24no—
108C11×#102—24no—
109C11×C22⋊C8—22no—
110C11×C22⋊C8—24no—
111C11×#95—22no—
112C11×#95—21no—
113C11×#95—22no—
114#24088C1111yesmaximal, characteristic, direct product factor, Sylow
115C24×C11—21no—
116C24×C11C2×D411yescharacteristic
117C24×C11C2×D411yescharacteristic
118C11×#41—432no—
119C2×Q8×C11—24no—
120C2×Q8×C11—42no—
121C2×Q8×C11—42no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—24no—
125C2×D4×C11—24no—
126C2×D4×C11—21no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—42no—
130C2×D4×C11—42no—
131C2×D4×C11—42no—
132C2×D4×C11—42no—
133C2×D4×C11D814yes—
134C2×D4×C11C2×D412yes—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2411yescharacteristic
165C2×C8×C11—28no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11#4114yescomplemented
172C11×C4⋊C4—24no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4—44no—
185C11×C4⋊C4C2×D412yes—
186C11×C4⋊C4C2×D412yes—
187C11×C4⋊C4C2×D412yes—
188C11×C22⋊C4—24no—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—24no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—42no—
194C11×C22⋊C4—44no—
195C42×C11—21no—
196C42×C11—21no—
197C2×#547C2×C1111yescharacteristic
198C2×#480C2×C1111yescharacteristic, complemented
199C22×#107C2×C1111yescharacteristic, complemented
200#2486C2×C1111yescharacteristic, complemented
201#2057C2×C1112yescomplemented
202#2033C2×C1112yescomplemented
203#1893C2×C1111yescharacteristic, complemented
204#1869C2×C1111yescharacteristic, complemented
205#1862C2×C1112yescomplemented
206#1852C2×C1112yescomplemented
207#1823C2×C1111yescharacteristic, complemented
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—21no—
211C23×C11—22no—
212C23×C11—21no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—42no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—42no—
219C23×C11#12012yes—
220C23×C11C2×D812yes—
221C23×C11C2×D812yes—
222C23×C11AGL(1,ℤ/8)12yes—
223C23×C11C22×D411yescharacteristic
224Q8×C11—48no—
225D4×C11—28no—
226D4×C11—24no—
227D4×C11—48no—
228D4×C11—48no—
229D4×C11—41no—
230D4×C11—41no—
231C2×C4×C11—21no—
232C2×C4×C11—22no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—48no—
245C2×C4×C11—48no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—48no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—84no—
263C2×C4×C11#12012yes—
264C2×C4×C11C2×D812yes—
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C2×#4112yes—
268C2×C4×C112−1+412yes—
269C8×C11—24no—
270C8×C11—42no—
271C22×#41—21no—
272C23×C8C22×C1111yescharacteristic
273#547—24no—
274#547—24no—
275C2×C4⋊Q8C22×C1111yescharacteristic
276C2×#123—21no—
277C2×#123—21no—
278C2×#123—21no—
279C2×C22⋊Q8—21no—
280C2×#121C22×C1111yescharacteristic
281C2×#121C22×C1111yescharacteristic
282C2×C4×D4C22×C1111yescharacteristic
283C2×C4×D4C22×C1111yescharacteristic
284C22×C4⋊C4C22×C1111yescharacteristic
285C22×C4⋊C4C22×C1111yescharacteristic
286C22×C4⋊C4C22×C1111yescharacteristic
287#480—24no—
288C2×#107—24no—
289C2×#107C22×C1112yes—
290C2×#107C22×C1112yes—
291C2×#107C22×C1112yes—
292C2×#102C22×C1112yes—
293C2×#102C22×C1112yes—
294C2×C22⋊C8C22×C1111yescharacteristic
295C2×C22⋊C8C22×C1112yes—
296#398—21no—
297#397—21no—
298#389C22×C1112yes—
299#381—21no—
300#380C22×C1111yescharacteristic
301#380C22×C1112yes—
302#340C22×C1112yes—
303#340C22×C1112yes—
304#340C22×C1112yes—
305#336C22×C1112yes—
306C22×C11—24no—
307C22×C11—24no—
308C22×C11—22no—
309C22×C11—22no—
310C22×C11—24no—
311C22×C11—22no—
312C22×C11—42no—
313C22×C11—41no—
314C22×C11—41no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—82no—
319C22×C11—82no—
320C22×C11#44714yes—
321C22×C11C2×#12011yescharacteristic
322C22×C11#54712yes—
323C22×C11C22×D811yescharacteristic
324C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C11#57812yes—
326C4×C11—22no—
327C4×C11—22no—
328C4×C11—41no—
329C4×C11—42no—
330C4×C11—42no—
331C4×C11—42no—
332C4×C11—41no—
333C4×C11—82no—
334C4×C11—82no—
335C4×C11#52511yescharacteristic
336C4×C11#53611yescharacteristic
337C4×C11#54712yes—
338C2×#41—28no—
339C2×#41—44no—
340C2×#41—44no—
341C22×Q8—21no—
342C22×D4—21no—
343C22×D4—21no—
344C22×D4D4×C1111yescharacteristic
345C22×D4C23×C1111yescharacteristic
346C23×C4—21no—
347C23×C4—21no—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4C23×C1111yescharacteristic
351C23×C4C23×C1111yescharacteristic
352C22×C8—22no—
353C22×C8—24no—
354C22×C8C23×C1112yes—
355C22×C8C23×C1112yes—
356C4⋊Q8—22no—
357C4⋊Q8—22no—
358#123—28no—
359#123—28no—
360#123—44no—
361C22⋊Q8—28no—
362#121—22no—
363#121—22no—
364#121—22no—
365#121D4×C1114yes—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4D4×C1111yescharacteristic
381C2×C4⋊C4D4×C1114yes—
382C2×C4⋊C4C23×C1112yes—
383C2×C4⋊C4C23×C1112yes—
384C2×C4⋊C4C23×C1111yescharacteristic
385C2×C4⋊C4C23×C1111yescharacteristic
386C2×C4⋊C4C23×C1111yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4D4×C1111yescharacteristic
393C2×C22⋊C4D4×C1111yescharacteristic
394C2×C42C23×C1111yescharacteristic
395#107—24no—
396#107—24no—
397#107—24no—
398#102—24no—
399#102—24no—
400C22⋊C8—22no—
401C22⋊C8—24no—
402#95—22no—
403#95—21no—
404#95—22no—
405C2×C11—24no—
406C2×C11—42no—
407C2×C11—82no—
408C2×C11#240611yescharacteristic
409C2×C11C2×#44711yescharacteristic
410C2×C11#301111yescharacteristic
411C2×C11#333412yes—
412C2×C11#334312yes—
413C24—21no—
414C24C2×D4×C1111yescharacteristic
415C24C2×D4×C1111yescharacteristic
416#41—432no—
417C2×Q8—24no—
418C2×Q8—42no—
419C2×Q8—42no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—24no—
423C2×D4—24no—
424C2×D4—21no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—42no—
428C2×D4—42no—
429C2×D4—42no—
430C2×D4—42no—
431C2×D4C11×D814yes—
432C2×D4C2×D4×C1112yes—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4C2×D4×C1111yescharacteristic
457C22×C4C2×D4×C1111yescharacteristic
458C22×C4C2×D4×C1111yescharacteristic
459C22×C4C2×D4×C1112yes—
460C22×C4C2×D4×C1112yes—
461C22×C4C2×D4×C1111yescharacteristic
462C22×C4C24×C1111yescharacteristic
463C2×C8—28no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8C11×#4114yescomplemented
470C4⋊C4—24no—
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—22no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—42no—
482C4⋊C4—44no—
483C4⋊C4C2×D4×C1112yes—
484C4⋊C4C2×D4×C1112yes—
485C4⋊C4C2×D4×C1112yes—
486C22⋊C4—24no—
487C22⋊C4—24no—
488C22⋊C4—22no—
489C22⋊C4—24no—
490C22⋊C4—22no—
491C22⋊C4—42no—
492C22⋊C4—44no—
493C42—21no—
494C42—21no—
495C11#2408811yescharacteristic, direct product factor, Sylow
496C23—22no—
497C23—22no—
498C23—21no—
499C23—22no—
500C23—21no—
501C23—22no—
502C23—22no—
503C23—42no—
504C23—41no—
505C23—41no—
506C23—42no—
507C23C11×#12012yes—
508C23C2×C11×D812yes—
509C23C2×C11×D812yes—
510C23C11×AGL(1,ℤ/8)12yes—
511C23C22×D4×C1111yescharacteristic
512Q8—48no—
513D4—28no—
514D4—24no—
515D4—48no—
516D4—48no—
517D4—41no—
518D4—41no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—48no—
533C2×C4—48no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—48no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—84no—
551C2×C4C11×#12012yes—
552C2×C4C2×C11×D812yes—
553C2×C4C22×D4×C1111yescharacteristic
554C2×C4C22×D4×C1111yescharacteristic
555C2×C4C2×C11×#4112yes—
556C2×C4C11×2−1+412yes—
557C8—24no—
558C8—42no—
559C22—22no—
560C22—22no—
561C22—24no—
562C22—24no—
563C22—22no—
564C22—24no—
565C22—41no—
566C22—41no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—82no—
572C22—82no—
573C22C11×#44714yes—
574C22C2×C11×#12011yescharacteristic
575C22C11×#54712yes—
576C22C22×C11×D811yescharacteristic
577C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
578C22C11×#57812yes—
579C4—22no—
580C4—22no—
581C4—41no—
582C4—42no—
583C4—42no—
584C4—42no—
585C4—41no—
586C4—82no—
587C4—82no—
588C4C11×#52511yescharacteristic
589C4C11×#53611yescharacteristic
590C4C11×#54712yes—
591C2—24no—
592C2—42no—
593C2—82no—
594C2C11×#240611yescharacteristic
595C2C2×C11×#44711yescharacteristic
596C2C11×#301111yescharacteristic
597C2C11×#333412yes—
598C2C11×#334312yes—
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×#480C2semidirect
3. C22×C11×#107C2semidirect
4. C11×#2486C2semidirect
5. C11×#2057C2semidirect
6. C11×#2033C2semidirect
7. C11×#1893C2semidirect
8. C11×#1869C2semidirect
9. C11×#1862C2semidirect
10. C11×#1852C2semidirect
11. C11×#1823C2semidirect
114. #24088C11direct (N × H)
171. C2×C8×C11#41semidirect
198. C2×#480C2×C11semidirect
199. C22×#107C2×C11semidirect
200. #2486C2×C11semidirect
201. #2057C2×C11semidirect
202. #2033C2×C11semidirect
203. #1893C2×C11semidirect
204. #1869C2×C11semidirect
205. #1862C2×C11semidirect
206. #1852C2×C11semidirect
207. #1823C2×C11semidirect
469. C2×C8C11×#41semidirect
495. C11#24088direct (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×#4802
C22×C11×#1072
C11×#24862
C11×#20572
C11×#20332
C11×#18932
C11×#18692
C11×#18622
C11×#18522
C11×#18232
#2408811