Finite Group Databasebeta

← C11×#24012 #14601205

Subgroups — C11×#24012 #14601205

Order 2816.

1340 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#537C211yesmaximal, characteristic
2C2×C11×#481C211yesmaximal, characteristic, complemented
3C2×C11×#483C211yesmaximal, characteristic, complemented
4C11×#2311C211yesmaximal, characteristic, complemented
5C11×#2035C212yesmaximal, complemented
6C11×#2034C212yesmaximal, complemented
7C11×#1875C211yesmaximal, characteristic, complemented
8C11×#1873C211yesmaximal, characteristic, complemented
9C11×#1853C212yesmaximal, complemented
10C11×#1788C212yesmaximal, complemented
11C11×#1780C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×#41C2211yescharacteristic
14C11×#537—24no—
15C11×#537—24no—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121—21no—
20C2×C11×#121—21no—
21C2×C11×#121—21no—
22C2×C11×#121C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C11×#117C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C11×#483—24no—
28C11×#481—24no—
29C2×C11×#106C2212yes—
30C2×C11×#106C2212yes—
31C2×C11×#103C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#102C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2212yes—
38C2×C11×C22⋊C8C2212yes—
39C11×#391—21no—
40C11×#390—21no—
41C11×#386—21no—
42C11×#386—21no—
43C11×#380C2212yes—
44C11×#380C2212yes—
45C11×#340C2212yes—
46C11×#340C2212yes—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41—24no—
52C2×C11×#41—24no—
53C2×C11×#41—42no—
54C2×C11×#41—42no—
55C22×Q8×C11D411yescharacteristic
56C22×Q8×C11C2311yescharacteristic
57C22×D4×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11D411yescharacteristic
61C22×D4×C11D411yescharacteristic
62C22×D4×C11D411yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×C8×C11C2312yes—
71C22×C8×C11C2312yes—
72C11×C22⋊Q8—28no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8D414yes—
77C11×#121—28no—
78C11×#121—28no—
79C11×#121—28no—
80C11×#121—22no—
81C11×#121—22no—
82C11×#121—22no—
83C11×#121D414yes—
84C11×#117—42no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4—22no—
104C2×C42×C11—21no—
105C11×#106—24no—
106C11×#106—24no—
107C11×#103—24no—
108C11×#103—42no—
109C11×#102—24no—
110C11×#102—42no—
111C11×C22⋊C8—22no—
112C11×C22⋊C8—22no—
113C11×C22⋊C8—24no—
114C11×C22⋊C8—42no—
115C11×#95—22no—
116C11×#95—22no—
117#24012C1111yesmaximal, characteristic, direct product factor, Sylow
118C24×C11—21no—
119C24×C11C2×D411yescharacteristic
120C24×C11C2×D411yescharacteristic
121C24×C11C2×D411yescharacteristic
122C11×#41—48no—
123C11×#41—48no—
124C11×#41—48no—
125C11×#41—48no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—41no—
132C2×Q8×C11C2×D412yes—
133C2×D4×C11—24no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—24no—
139C2×D4×C11—24no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—21no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—41no—
146C2×D4×C11—41no—
147C2×D4×C11—41no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11—82no—
151C2×D4×C11—82no—
152C2×D4×C11C2×D412yes—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—24no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—24no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—42no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11—82no—
173C22×C4×C11—82no—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11#4114yes—
180C22×C4×C11C2411yescharacteristic
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C2×C8×C11—22no—
184C2×C8×C11—22no—
185C2×C8×C11—22no—
186C2×C8×C11—22no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—42no—
197C11×C4⋊C4C2×D412yes—
198C11×C4⋊C4C2×D412yes—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—24no—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—24no—
203C11×C22⋊C4—42no—
204C11×C22⋊C4—82no—
205C11×C22⋊C4—82no—
206C42×C11—42no—
207C2×#537C2×C1111yescharacteristic
208C2×#481C2×C1111yescharacteristic, complemented
209C2×#483C2×C1111yescharacteristic, complemented
210#2311C2×C1111yescharacteristic, complemented
211#2035C2×C1112yescomplemented
212#2034C2×C1112yescomplemented
213#1875C2×C1111yescharacteristic, complemented
214#1873C2×C1111yescharacteristic, complemented
215#1853C2×C1112yescomplemented
216#1788C2×C1112yescomplemented
217#1780C2×C1111yescharacteristic, complemented
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—21no—
227C23×C11—22no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11#12012yes—
237C23×C11#12312yes—
238C23×C11C22×D411yescharacteristic
239Q8×C11—24no—
240Q8×C11—44no—
241Q8×C11—42no—
242D4×C11—24no—
243D4×C11—44no—
244D4×C11—44no—
245D4×C11—44no—
246D4×C11—48no—
247D4×C11—42no—
248D4×C11—84no—
249D4×C11—84no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—48no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—84no—
278C2×C4×C11—84no—
279C2×C4×C11#12012yes—
280C2×C4×C11#12312yes—
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C2×#4112yes—
284C2×C4×C11H(5,𝔽2)12yes—
285C8×C11—42no—
286C8×C11—42no—
287C22×#41C22×C1111yescharacteristic
288C22×#41C22×C1111yescharacteristic
289#537—24no—
290#537—24no—
291C2×C22⋊Q8—21no—
292C2×C22⋊Q8C22×C1111yescharacteristic
293C2×C22⋊Q8C22×C1111yescharacteristic
294C2×#121—21no—
295C2×#121—21no—
296C2×#121—21no—
297C2×#121C22×C1111yescharacteristic
298C2×#121C22×C1111yescharacteristic
299C2×#117C22×C1111yescharacteristic
300C22×C4⋊C4C22×C1111yescharacteristic
301C22×C4⋊C4C22×C1111yescharacteristic
302#483—24no—
303#481—24no—
304C2×#106C22×C1112yes—
305C2×#106C22×C1112yes—
306C2×#103C22×C1112yes—
307C2×#103C22×C1112yes—
308C2×#102C22×C1112yes—
309C2×#102C22×C1112yes—
310C2×C22⋊C8C22×C1111yescharacteristic
311C2×C22⋊C8C22×C1111yescharacteristic
312C2×C22⋊C8C22×C1112yes—
313C2×C22⋊C8C22×C1112yes—
314#391—21no—
315#390—21no—
316#386—21no—
317#386—21no—
318#380C22×C1112yes—
319#380C22×C1112yes—
320#340C22×C1112yes—
321#340C22×C1112yes—
322C22×C11—24no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—41no—
335C22×C11—42no—
336C22×C11—41no—
337C22×C11—42no—
338C22×C11—41no—
339C22×C11—42no—
340C22×C11—82no—
341C22×C11—82no—
342C22×C11C2×#12011yescharacteristic
343C22×C11C2×#12311yescharacteristic
344C22×C11#53411yescharacteristic
345C22×C11#57712yes—
346C22×C11#57712yes—
347C4×C11—22no—
348C4×C11—22no—
349C4×C11—41no—
350C4×C11—42no—
351C4×C11—42no—
352C4×C11—42no—
353C4×C11—82no—
354C4×C11—82no—
355C4×C11#54612yes—
356C4×C11#54612yes—
357C2×#41—22no—
358C2×#41—22no—
359C2×#41—22no—
360C2×#41—22no—
361C2×#41—24no—
362C2×#41—24no—
363C2×#41—42no—
364C2×#41—42no—
365C22×Q8D4×C1111yescharacteristic
366C22×Q8C23×C1111yescharacteristic
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4D4×C1111yescharacteristic
371C22×D4D4×C1111yescharacteristic
372C22×D4D4×C1111yescharacteristic
373C22×D4C23×C1111yescharacteristic
374C23×C4—21no—
375C23×C4—21no—
376C23×C4—21no—
377C23×C4C23×C1111yescharacteristic
378C23×C4C23×C1111yescharacteristic
379C23×C4C23×C1111yescharacteristic
380C22×C8C23×C1112yes—
381C22×C8C23×C1112yes—
382C22⋊Q8—28no—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385C22⋊Q8—22no—
386C22⋊Q8D4×C1114yes—
387#121—28no—
388#121—28no—
389#121—28no—
390#121—22no—
391#121—22no—
392#121—22no—
393#121D4×C1114yes—
394#117—42no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4C23×C1112yes—
404C2×C4⋊C4C23×C1112yes—
405C2×C4⋊C4C23×C1111yescharacteristic
406C2×C4⋊C4C23×C1111yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C42—21no—
415#106—24no—
416#106—24no—
417#103—24no—
418#103—42no—
419#102—24no—
420#102—42no—
421C22⋊C8—22no—
422C22⋊C8—22no—
423C22⋊C8—24no—
424C22⋊C8—42no—
425#95—22no—
426#95—22no—
427C2×C11—42no—
428C2×C11—42no—
429C2×C11—81no—
430C2×C11—82no—
431C2×C11#240511yescharacteristic
432C2×C11#300911yescharacteristic
433C2×C11#301011yescharacteristic
434C2×C11#309912yes—
435C2×C11#320412yes—
436C24—21no—
437C24C2×D4×C1111yescharacteristic
438C24C2×D4×C1111yescharacteristic
439C24C2×D4×C1111yescharacteristic
440#41—48no—
441#41—48no—
442#41—48no—
443#41—48no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—21no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—41no—
450C2×Q8C2×D4×C1112yes—
451C2×D4—24no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—82no—
469C2×D4—82no—
470C2×D4C2×D4×C1112yes—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—24no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—82no—
491C22×C4—82no—
492C22×C4C2×D4×C1111yescharacteristic
493C22×C4C2×D4×C1111yescharacteristic
494C22×C4C2×D4×C1112yes—
495C22×C4C2×D4×C1112yes—
496C22×C4C2×D4×C1111yescharacteristic
497C22×C4C11×#4114yes—
498C22×C4C24×C1111yescharacteristic
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C4⋊C4—24no—
506C4⋊C4—24no—
507C4⋊C4—24no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—42no—
515C4⋊C4C2×D4×C1112yes—
516C4⋊C4C2×D4×C1112yes—
517C22⋊C4—24no—
518C22⋊C4—24no—
519C22⋊C4—24no—
520C22⋊C4—24no—
521C22⋊C4—42no—
522C22⋊C4—82no—
523C22⋊C4—82no—
524C42—42no—
525C11#2401211yescharacteristic, direct product factor, Sylow
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—22no—
531C23—22no—
532C23—22no—
533C23—22no—
534C23—21no—
535C23—22no—
536C23—21no—
537C23—21no—
538C23—22no—
539C23—22no—
540C23—41no—
541C23—41no—
542C23—42no—
543C23—42no—
544C23C11×#12012yes—
545C23C11×#12312yes—
546C23C22×D4×C1111yescharacteristic
547Q8—24no—
548Q8—44no—
549Q8—42no—
550D4—24no—
551D4—44no—
552D4—44no—
553D4—44no—
554D4—48no—
555D4—42no—
556D4—84no—
557D4—84no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—48no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—84no—
586C2×C4—84no—
587C2×C4C11×#12012yes—
588C2×C4C11×#12312yes—
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—22no—
598C22—22no—
599C22—24no—
600C22—42no—
601C22—42no—
602C22—41no—
603C22—41no—
604C22—42no—
605C22—42no—
606C22—41no—
607C22—42no—
608C22—41no—
609C22—42no—
610C22—41no—
611C22—42no—
612C22—42no—
613C22—82no—
614C22—82no—
615C22C2×C11×#12011yescharacteristic
616C22C2×C11×#12311yescharacteristic
617C22C11×#53411yescharacteristic
618C22C11×#57712yes—
619C22C11×#57712yes—
620C4—22no—
621C4—22no—
622C4—41no—
623C4—42no—
624C4—42no—
625C4—42no—
626C4—82no—
627C4—82no—
628C4C11×#54612yes—
629C4C11×#54612yes—
630C2—42no—
631C2—42no—
632C2—81no—
633C2—82no—
634C2C11×#240511yescharacteristic
635C2C11×#300911yescharacteristic
636C2C11×#301011yescharacteristic
637C2C11×#309912yes—
638C2C11×#320412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#481C2semidirect
3. C2×C11×#483C2semidirect
4. C11×#2311C2semidirect
5. C11×#2035C2semidirect
6. C11×#2034C2semidirect
7. C11×#1875C2semidirect
8. C11×#1873C2semidirect
9. C11×#1853C2semidirect
10. C11×#1788C2semidirect
11. C11×#1780C2semidirect
117. #24012C11direct (N × H)
208. C2×#481C2×C11semidirect
209. C2×#483C2×C11semidirect
210. #2311C2×C11semidirect
211. #2035C2×C11semidirect
212. #2034C2×C11semidirect
213. #1875C2×C11semidirect
214. #1873C2×C11semidirect
215. #1853C2×C11semidirect
216. #1788C2×C11semidirect
217. #1780C2×C11semidirect
525. C11#24012direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5372
C2×C11×#4812
C2×C11×#4832
C11×#23112
C11×#20352
C11×#20342
C11×#18752
C11×#18732
C11×#18532
C11×#17882
C11×#17802
#2401211