Finite Group Databasebeta

← C11×#23961 #14601154

Subgroups — C11×#23961 #14601154

Order 2816.

1494 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#547C211yesmaximal, characteristic
2C2×C11×#448C211yesmaximal, characteristic, complemented
3C22×C11×#103C211yesmaximal, characteristic, complemented
4C11×#2409C211yesmaximal, characteristic, complemented
5C11×#2024C212yesmaximal, complemented
6C11×#2000C212yesmaximal, complemented
7C11×#1893C211yesmaximal, characteristic, complemented
8C11×#1877C212yesmaximal, complemented
9C11×#1872C212yesmaximal, complemented
10C11×#1869C211yesmaximal, characteristic, complemented
11C11×#1823C211yesmaximal, characteristic, complemented
12C22×C11×#41—21no—
13C23×Q8×C11C2211yescharacteristic
14C22×C11×SD16C2212yes—
15C23×C8×C11C2211yescharacteristic
16C11×#547—24no—
17C11×#547—24no—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×#123—21no—
20C2×C11×#123—21no—
21C2×C11×C22⋊Q8—21no—
22C2×C11×C22⋊Q8C2212yes—
23C2×C11×#121C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C11×#448—24no—
30C2×C11×#103—24no—
31C2×C11×#103C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2212yes—
37C11×#395—21no—
38C11×#393—21no—
39C11×#391C2212yes—
40C11×#386—21no—
41C11×#385—21no—
42C11×#380C2211yescharacteristic
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×Q8×C11—21no—
52C22×Q8×C11—24no—
53C22×Q8×C11—22no—
54C22×Q8×C11—22no—
55C22×Q8×C11—42no—
56C22×Q8×C11C2312yes—
57C22×D4×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11D411yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11—21no—
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C2×C11×SD16—24no—
68C2×C11×SD16—24no—
69C2×C11×SD16—42no—
70C22×C8×C11—22no—
71C22×C8×C11—42no—
72C22×C8×C11C2312yes—
73C22×C8×C11C2312yes—
74C11×C4⋊Q8—22no—
75C11×C4⋊Q8—22no—
76C11×#123—28no—
77C11×#123—28no—
78C11×C22⋊Q8—28no—
79C11×C22⋊Q8—24no—
80C11×C22⋊Q8—42no—
81C11×#121—22no—
82C11×#121—22no—
83C11×#121—22no—
84C11×#121D414yes—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4D414yes—
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4D411yescharacteristic
108C2×C11×C22⋊C4D411yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C11×#103—24no—
111C11×#103—24no—
112C11×#103—24no—
113C11×#102—42no—
114C11×C22⋊C8—22no—
115C11×C22⋊C8—42no—
116C11×#95—21no—
117C11×#95—22no—
118C11×#95—22no—
119#23961C1111yesmaximal, characteristic, direct product factor, Sylow
120C24×C11—21no—
121C24×C11C2×D411yescharacteristic
122C24×C11C2×D411yescharacteristic
123C11×#41—432no—
124C2×Q8×C11—24no—
125C2×Q8×C11—22no—
126C2×Q8×C11—28no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—44no—
132C2×Q8×C11—48no—
133C2×Q8×C11—44no—
134C2×Q8×C11—42no—
135C2×Q8×C11—42no—
136C2×Q8×C11—42no—
137C2×Q8×C11#4114yescomplemented
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—24no—
141C2×D4×C11—24no—
142C2×D4×C11—21no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—42no—
146C2×D4×C11—42no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11SD1614yescomplemented
150C2×D4×C11C2×D412yes—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—24no—
154C22×C4×C11—24no—
155C22×C4×C11—24no—
156C22×C4×C11—22no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—44no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11—42no—
169C22×C4×C11—42no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11—42no—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2411yescharacteristic
180C11×SD16—48no—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C2×C8×C11—22no—
184C2×C8×C11—22no—
185C2×C8×C11—22no—
186C2×C8×C11—22no—
187C2×C8×C11—44no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—44no—
198C11×C4⋊C4C2×D412yes—
199C11×C4⋊C4C2×D412yes—
200C11×C4⋊C4C2×D412yes—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—24no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—24no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—44no—
207C11×C22⋊C4—42no—
208C42×C11—21no—
209C42×C11—21no—
210C2×#547C2×C1111yescharacteristic
211C2×#448C2×C1111yescharacteristic, complemented
212C22×#103C2×C1111yescharacteristic, complemented
213#2409C2×C1111yescharacteristic, complemented
214#2024C2×C1112yescomplemented
215#2000C2×C1112yescomplemented
216#1893C2×C1111yescharacteristic, complemented
217#1877C2×C1112yescomplemented
218#1872C2×C1112yescomplemented
219#1869C2×C1111yescharacteristic, complemented
220#1823C2×C1111yescharacteristic, complemented
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—21no—
224C23×C11—22no—
225C23×C11—21no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—42no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—42no—
232C23×C11#12012yes—
233C23×C11C2×SD1612yes—
234C23×C11C2×SD1612yes—
235C23×C11AGL(1,ℤ/8)12yes—
236C23×C11C22×D411yescharacteristic
237Q8×C11—24no—
238Q8×C11—24no—
239Q8×C11—48no—
240Q8×C11—48no—
241Q8×C11—42no—
242Q8×C11—42no—
243D4×C11—28no—
244D4×C11—24no—
245D4×C11—48no—
246D4×C11—48no—
247D4×C11—41no—
248D4×C11—41no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—24no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—48no—
264C2×C4×C11—48no—
265C2×C4×C11—48no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—48no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11#12012yes—
282C2×C4×C11C2×SD1612yes—
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C2×#4112yes—
286C2×C4×C11H(5,𝔽2)12yes—
287C8×C11—42no—
288C8×C11—42no—
289C22×#41—21no—
290C23×Q8C22×C1111yescharacteristic
291C22×SD16C22×C1112yes—
292C23×C8C22×C1111yescharacteristic
293#547—24no—
294#547—24no—
295C2×C4⋊Q8C22×C1111yescharacteristic
296C2×#123—21no—
297C2×#123—21no—
298C2×C22⋊Q8—21no—
299C2×C22⋊Q8C22×C1112yes—
300C2×#121C22×C1111yescharacteristic
301C2×#121C22×C1111yescharacteristic
302C2×C4×D4C22×C1111yescharacteristic
303C2×C4×D4C22×C1111yescharacteristic
304C22×C4⋊C4C22×C1111yescharacteristic
305C22×C4⋊C4C22×C1111yescharacteristic
306#448—24no—
307C2×#103—24no—
308C2×#103C22×C1112yes—
309C2×#103C22×C1112yes—
310C2×#103C22×C1112yes—
311C2×#102C22×C1112yes—
312C2×C22⋊C8C22×C1111yescharacteristic
313C2×C22⋊C8C22×C1112yes—
314#395—21no—
315#393—21no—
316#391C22×C1112yes—
317#386—21no—
318#385—21no—
319#380C22×C1111yescharacteristic
320#340C22×C1112yes—
321#340C22×C1112yes—
322#340C22×C1112yes—
323#336C22×C1112yes—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—24no—
327C22×C11—24no—
328C22×C11—22no—
329C22×C11—24no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—82no—
337C22×C11—82no—
338C22×C11#45014yes—
339C22×C11C2×#12011yescharacteristic
340C22×C11#54612yes—
341C22×C11C22×SD1611yescharacteristic
342C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C11#57812yes—
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—41no—
347C4×C11—44no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11—42no—
351C4×C11—41no—
352C4×C11—82no—
353C4×C11#52511yescharacteristic
354C4×C11#53511yescharacteristic
355C4×C11#54612yes—
356C2×#41—28no—
357C2×#41—44no—
358C2×#41—44no—
359C22×Q8—21no—
360C22×Q8—21no—
361C22×Q8—24no—
362C22×Q8—22no—
363C22×Q8—22no—
364C22×Q8—42no—
365C22×Q8C23×C1112yes—
366C22×D4—21no—
367C22×D4—21no—
368C22×D4D4×C1111yescharacteristic
369C22×D4C23×C1111yescharacteristic
370C23×C4—21no—
371C23×C4—21no—
372C23×C4—21no—
373C23×C4—21no—
374C23×C4C23×C1111yescharacteristic
375C23×C4C23×C1111yescharacteristic
376C2×SD16—24no—
377C2×SD16—24no—
378C2×SD16—42no—
379C22×C8—22no—
380C22×C8—42no—
381C22×C8C23×C1112yes—
382C22×C8C23×C1112yes—
383C4⋊Q8—22no—
384C4⋊Q8—22no—
385#123—28no—
386#123—28no—
387C22⋊Q8—28no—
388C22⋊Q8—24no—
389C22⋊Q8—42no—
390#121—22no—
391#121—22no—
392#121—22no—
393#121D4×C1114yes—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4D4×C1111yescharacteristic
406C2×C4⋊C4D4×C1114yes—
407C2×C4⋊C4C23×C1112yes—
408C2×C4⋊C4C23×C1111yescharacteristic
409C2×C4⋊C4C23×C1111yescharacteristic
410C2×C4⋊C4C23×C1111yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4D4×C1111yescharacteristic
417C2×C22⋊C4D4×C1111yescharacteristic
418C2×C42C23×C1111yescharacteristic
419#103—24no—
420#103—24no—
421#103—24no—
422#102—42no—
423C22⋊C8—22no—
424C22⋊C8—42no—
425#95—21no—
426#95—22no—
427#95—22no—
428C2×C11—24no—
429C2×C11—42no—
430C2×C11—82no—
431C2×C11#240411yescharacteristic
432C2×C11C2×#45011yescharacteristic
433C2×C11#301111yescharacteristic
434C2×C11#329812yes—
435C2×C11#330812yes—
436C24—21no—
437C24C2×D4×C1111yescharacteristic
438C24C2×D4×C1111yescharacteristic
439#41—432no—
440C2×Q8—24no—
441C2×Q8—22no—
442C2×Q8—28no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—44no—
448C2×Q8—48no—
449C2×Q8—44no—
450C2×Q8—42no—
451C2×Q8—42no—
452C2×Q8—42no—
453C2×Q8C11×#4114yescomplemented
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—21no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4C11×SD1614yescomplemented
466C2×D4C2×D4×C1112yes—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—44no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4C2×D4×C1111yescharacteristic
490C22×C4C2×D4×C1111yescharacteristic
491C22×C4C2×D4×C1111yescharacteristic
492C22×C4C2×D4×C1112yes—
493C22×C4C2×D4×C1112yes—
494C22×C4C2×D4×C1111yescharacteristic
495C22×C4C24×C1111yescharacteristic
496SD16—48no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—44no—
504C4⋊C4—24no—
505C4⋊C4—24no—
506C4⋊C4—24no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—44no—
514C4⋊C4C2×D4×C1112yes—
515C4⋊C4C2×D4×C1112yes—
516C4⋊C4C2×D4×C1112yes—
517C22⋊C4—24no—
518C22⋊C4—24no—
519C22⋊C4—22no—
520C22⋊C4—24no—
521C22⋊C4—22no—
522C22⋊C4—44no—
523C22⋊C4—42no—
524C42—21no—
525C42—21no—
526C11#2396111yescharacteristic, direct product factor, Sylow
527C23—22no—
528C23—22no—
529C23—21no—
530C23—22no—
531C23—21no—
532C23—22no—
533C23—22no—
534C23—42no—
535C23—41no—
536C23—41no—
537C23—42no—
538C23C11×#12012yes—
539C23C2×C11×SD1612yes—
540C23C2×C11×SD1612yes—
541C23C11×AGL(1,ℤ/8)12yes—
542C23C22×D4×C1111yescharacteristic
543Q8—24no—
544Q8—24no—
545Q8—48no—
546Q8—48no—
547Q8—42no—
548Q8—42no—
549D4—28no—
550D4—24no—
551D4—48no—
552D4—48no—
553D4—41no—
554D4—41no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—48no—
570C2×C4—48no—
571C2×C4—48no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—48no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4C11×#12012yes—
588C2×C4C2×C11×SD1612yes—
589C2×C4C22×D4×C1111yescharacteristic
590C2×C4C22×D4×C1111yescharacteristic
591C2×C4C2×C11×#4112yes—
592C2×C4C11×H(5,𝔽2)12yes—
593C8—42no—
594C8—42no—
595C22—22no—
596C22—22no—
597C22—24no—
598C22—24no—
599C22—22no—
600C22—24no—
601C22—41no—
602C22—41no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—82no—
608C22—82no—
609C22C11×#45014yes—
610C22C2×C11×#12011yescharacteristic
611C22C11×#54612yes—
612C22C22×C11×SD1611yescharacteristic
613C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
614C22C11×#57812yes—
615C4—22no—
616C4—22no—
617C4—41no—
618C4—44no—
619C4—42no—
620C4—42no—
621C4—42no—
622C4—41no—
623C4—82no—
624C4C11×#52511yescharacteristic
625C4C11×#53511yescharacteristic
626C4C11×#54612yes—
627C2—24no—
628C2—42no—
629C2—82no—
630C2C11×#240411yescharacteristic
631C2C2×C11×#45011yescharacteristic
632C2C11×#301111yescharacteristic
633C2C11×#329812yes—
634C2C11×#330812yes—
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×#448C2semidirect
3. C22×C11×#103C2semidirect
4. C11×#2409C2semidirect
5. C11×#2024C2semidirect
6. C11×#2000C2semidirect
7. C11×#1893C2semidirect
8. C11×#1877C2semidirect
9. C11×#1872C2semidirect
10. C11×#1869C2semidirect
11. C11×#1823C2semidirect
119. #23961C11direct (N × H)
137. C2×Q8×C11#41semidirect
149. C2×D4×C11SD16semidirect
211. C2×#448C2×C11semidirect
212. C22×#103C2×C11semidirect
213. #2409C2×C11semidirect
214. #2024C2×C11semidirect
215. #2000C2×C11semidirect
216. #1893C2×C11semidirect
217. #1877C2×C11semidirect
218. #1872C2×C11semidirect
219. #1869C2×C11semidirect
220. #1823C2×C11semidirect
453. C2×Q8C11×#41semidirect
465. C2×D4C11×SD16semidirect
526. C11#23961direct (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×#4482
C22×C11×#1032
C11×#24092
C11×#20242
C11×#20002
C11×#18932
C11×#18772
C11×#18722
C11×#18692
C11×#18232
#2396111