Finite Group Databasebeta

← C11×#23973 #14601166

Subgroups — C11×#23973 #14601166

Order 2816.

1488 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#553C211yesmaximal, characteristic, complemented
2C2×C11×#447C211yesmaximal, characteristic, complemented
3C2×C11×#418C211yesmaximal, characteristic, complemented
4C11×#2408C211yesmaximal, characteristic, complemented
5C11×#2025C212yesmaximal, complemented
6C11×#1999C212yesmaximal, complemented
7C11×#1895C211yesmaximal, characteristic, complemented
8C11×#1879C212yesmaximal, complemented
9C11×#1874C212yesmaximal, complemented
10C11×#1870C211yesmaximal, characteristic, complemented
11C11×#1825C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C22×C11×D8C2212yes—
14C22×C11×M16C2211yescharacteristic
15C11×#553—24no—
16C11×#553—24no—
17C2×C11×#126—21no—
18C2×C11×#125C2211yescharacteristic, complemented
19C2×C11×#123—21no—
20C2×C11×#121—21no—
21C2×C11×#121C2212yes—
22C2×C11×#121C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic, complemented
24C2×C11×#120—21no—
25C2×C4×D4×C11—21no—
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic, complemented
28C2×C11×#117C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic, complemented
30C11×#447—24no—
31C11×#418—24no—
32C2×C11×#102C2212yes—
33C2×C11×#102C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×#102C2212yescomplemented
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2212yescomplemented
38C11×#394—21no—
39C11×#392—21no—
40C11×#390C2212yes—
41C11×#380C2211yescharacteristic
42C11×#379—21no—
43C11×#340C2212yescomplemented
44C11×#340C2212yescomplemented
45C11×#340C2212yescomplemented
46C11×#336C2212yescomplemented
47C25×C11—21no—
48C22×D4×C11—24no—
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11—21no—
55C22×D4×C11—42no—
56C22×D4×C11D411yescharacteristic
57C22×D4×C11C2311yescharacteristic
58C22×D4×C11C2312yes—
59C23×C4×C11—21no—
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C2×C11×D8—24no—
64C2×C11×D8—24no—
65C2×C11×D8—42no—
66C2×C11×M16—22no—
67C2×C11×M16—42no—
68C22×C8×C11C2312yes—
69C22×C8×C11C2312yes—
70C11×#126—28no—
71C11×#125—22no—
72C11×#125—22no—
73C11×#123—28no—
74C11×#121—28no—
75C11×#121—22no—
76C11×#121—22no—
77C11×#121—22no—
78C11×#121—24no—
79C11×#121—42no—
80C11×#121D414yescomplemented
81C11×#120—44no—
82C4×D4×C11—28no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C11×#117—22no—
88C11×#117D414yescomplemented
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4D411yescharacteristic
108C2×C11×C22⋊C4D411yescharacteristic
109C2×C42×C11—21no—
110C2×C42×C11C2311yescharacteristic
111C11×#102—24no—
112C11×#102—24no—
113C11×#102—24no—
114C11×#102—42no—
115C11×C22⋊C8—22no—
116C11×C22⋊C8—42no—
117C11×#95—21no—
118#23973C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11—21no—
120C24×C11—22no—
121C24×C11—44no—
122C24×C11—42no—
123C24×C11—42no—
124C24×C11—42no—
125C24×C11—82no—
126C24×C11C2×D411yescharacteristic
127C24×C11C2×D411yescharacteristic
128C2×D4×C11—28no—
129C2×D4×C11—24no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—24no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—48no—
142C2×D4×C11—41no—
143C2×D4×C11—44no—
144C2×D4×C11—44no—
145C2×D4×C11—42no—
146C2×D4×C11—42no—
147C2×D4×C11—44no—
148C2×D4×C11—44no—
149C2×D4×C11—42no—
150C2×D4×C11—82no—
151C2×D4×C11—82no—
152C2×D4×C11C2×D412yes—
153C2×D4×C11#4114yes—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—24no—
160C22×C4×C11—24no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—82no—
167C22×C4×C11—82no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D412yes—
174C22×C4×C11C2411yescharacteristic
175C11×D8—48no—
176C11×M16—44no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4C2×D412yes—
193C11×C4⋊C4C2×D412yes—
194C11×C4⋊C4C2×D412yes—
195C11×C22⋊C4—24no—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—44no—
202C11×C22⋊C4—44no—
203C11×C22⋊C4—42no—
204C11×C22⋊C4—82no—
205C42×C11—24no—
206C42×C11—21no—
207C42×C11—21no—
208C2×#553C2×C1111yescharacteristic, complemented
209C2×#447C2×C1111yescharacteristic, complemented
210C2×#418C2×C1111yescharacteristic, complemented
211#2408C2×C1111yescharacteristic, complemented
212#2025C2×C1112yescomplemented
213#1999C2×C1112yescomplemented
214#1895C2×C1111yescharacteristic, complemented
215#1879C2×C1112yescomplemented
216#1874C2×C1112yescomplemented
217#1870C2×C1111yescharacteristic, complemented
218#1825C2×C1111yescharacteristic, complemented
219C23×C11—21no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—24no—
229C23×C11—48no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—84no—
241C23×C11—84no—
242C23×C11—88no—
243C23×C11—88no—
244C23×C11#12012yes—
245C23×C11AGL(1,ℤ/8)12yes—
246C23×C11C22×D411yescharacteristic
247D4×C11—24no—
248D4×C11—24no—
249D4×C11—24no—
250D4×C11—48no—
251D4×C11—44no—
252D4×C11—48no—
253D4×C11—41no—
254D4×C11—41no—
255D4×C11—42no—
256D4×C11—42no—
257D4×C11—84no—
258D4×C11—88no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—24no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—22no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—42no—
283C2×C4×C11—84no—
284C2×C4×C11—84no—
285C2×C4×C11#12012yes—
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C2×#4112yes—
289C2×C4×C11H(5,𝔽2)12yes—
290C8×C11—42no—
291C8×C11—42no—
292C23×D4C22×C1111yescharacteristic
293C22×D8C22×C1112yes—
294C22×M16C22×C1111yescharacteristic
295#553—24no—
296#553—24no—
297C2×#126—21no—
298C2×#125C22×C1111yescharacteristic, complemented
299C2×#123—21no—
300C2×#121—21no—
301C2×#121C22×C1112yes—
302C2×#121C22×C1111yescharacteristic
303C2×#121C22×C1111yescharacteristic, complemented
304C2×#120—21no—
305C2×C4×D4—21no—
306C2×C4×D4C22×C1111yescharacteristic
307C2×C4×D4C22×C1111yescharacteristic, complemented
308C2×#117C22×C1111yescharacteristic
309C22×C4⋊C4C22×C1111yescharacteristic, complemented
310#447—24no—
311#418—24no—
312C2×#102C22×C1112yes—
313C2×#102C22×C1112yes—
314C2×#102C22×C1112yes—
315C2×#102C22×C1112yescomplemented
316C2×C22⋊C8C22×C1111yescharacteristic
317C2×C22⋊C8C22×C1112yescomplemented
318#394—21no—
319#392—21no—
320#390C22×C1112yes—
321#380C22×C1111yescharacteristic
322#379—21no—
323#340C22×C1112yescomplemented
324#340C22×C1112yescomplemented
325#340C22×C1112yescomplemented
326#336C22×C1112yescomplemented
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—24no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—44no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—44no—
342C22×C11—44no—
343C22×C11—816no—
344C22×C11—82no—
345C22×C11—82no—
346C22×C11—82no—
347C22×C11—82no—
348C22×C11—82no—
349C22×C11—82no—
350C22×C11C2×#12011yescharacteristic
351C22×C11#54612yes—
352C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C11#57511yescharacteristic
354C22×C11#57612yes—
355C4×C11—22no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—42no—
359C4×C11—41no—
360C4×C11—42no—
361C4×C11—42no—
362C4×C11—82no—
363C4×C11#52511yescharacteristic
364C4×C11#53511yescharacteristic
365C4×C11#54612yes—
366C25—21no—
367C22×D4—24no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—22no—
371C22×D4—22no—
372C22×D4—22no—
373C22×D4—21no—
374C22×D4—42no—
375C22×D4D4×C1111yescharacteristic
376C22×D4C23×C1111yescharacteristic
377C22×D4C23×C1112yes—
378C23×C4—21no—
379C23×C4—21no—
380C23×C4C23×C1111yescharacteristic
381C23×C4C23×C1111yescharacteristic
382C2×D8—24no—
383C2×D8—24no—
384C2×D8—42no—
385C2×M16—22no—
386C2×M16—42no—
387C22×C8C23×C1112yes—
388C22×C8C23×C1112yes—
389#126—28no—
390#125—22no—
391#125—22no—
392#123—28no—
393#121—28no—
394#121—22no—
395#121—22no—
396#121—22no—
397#121—24no—
398#121—42no—
399#121D4×C1114yescomplemented
400#120—44no—
401C4×D4—28no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4—22no—
406#117—22no—
407#117D4×C1114yescomplemented
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4D4×C1111yescharacteristic
414C2×C4⋊C4C23×C1112yes—
415C2×C4⋊C4C23×C1111yescharacteristic
416C2×C4⋊C4C23×C1111yescharacteristic
417C2×C4⋊C4C23×C1111yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4D4×C1111yescharacteristic
427C2×C22⋊C4D4×C1111yescharacteristic
428C2×C42—21no—
429C2×C42C23×C1111yescharacteristic
430#102—24no—
431#102—24no—
432#102—24no—
433#102—42no—
434C22⋊C8—22no—
435C22⋊C8—42no—
436#95—21no—
437C2×C11—42no—
438C2×C11—42no—
439C2×C11—82no—
440C2×C11—84no—
441C2×C11#240411yescharacteristic
442C2×C11#300611yescharacteristic
443C2×C11#300811yescharacteristic
444C2×C11#331812yes—
445C2×C11#332212yes—
446C24—21no—
447C24—22no—
448C24—44no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—82no—
453C24C2×D4×C1111yescharacteristic
454C24C2×D4×C1111yescharacteristic
455C2×D4—28no—
456C2×D4—24no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—24no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—48no—
469C2×D4—41no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—42no—
477C2×D4—82no—
478C2×D4—82no—
479C2×D4C2×D4×C1112yes—
480C2×D4C11×#4114yes—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—82no—
494C22×C4—82no—
495C22×C4C2×D4×C1111yescharacteristic
496C22×C4C2×D4×C1111yescharacteristic
497C22×C4C2×D4×C1111yescharacteristic
498C22×C4C2×D4×C1111yescharacteristic
499C22×C4C2×D4×C1112yes—
500C22×C4C2×D4×C1112yes—
501C22×C4C24×C1111yescharacteristic
502D8—48no—
503M16—44no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C4⋊C4—24no—
511C4⋊C4—24no—
512C4⋊C4—24no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4C2×D4×C1112yes—
520C4⋊C4C2×D4×C1112yes—
521C4⋊C4C2×D4×C1112yes—
522C22⋊C4—24no—
523C22⋊C4—24no—
524C22⋊C4—24no—
525C22⋊C4—22no—
526C22⋊C4—24no—
527C22⋊C4—22no—
528C22⋊C4—44no—
529C22⋊C4—44no—
530C22⋊C4—42no—
531C22⋊C4—82no—
532C42—24no—
533C42—21no—
534C42—21no—
535C11#2397311yescharacteristic, direct product factor, Sylow
536C23—21no—
537C23—22no—
538C23—22no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—24no—
546C23—48no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—41no—
552C23—41no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—84no—
558C23—84no—
559C23—88no—
560C23—88no—
561C23C11×#12012yes—
562C23C11×AGL(1,ℤ/8)12yes—
563C23C22×D4×C1111yescharacteristic
564D4—24no—
565D4—24no—
566D4—24no—
567D4—48no—
568D4—44no—
569D4—48no—
570D4—41no—
571D4—41no—
572D4—42no—
573D4—42no—
574D4—84no—
575D4—88no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—84no—
601C2×C4—84no—
602C2×C4C11×#12012yes—
603C2×C4C22×D4×C1111yescharacteristic
604C2×C4C22×D4×C1111yescharacteristic
605C2×C4C2×C11×#4112yes—
606C2×C4C11×H(5,𝔽2)12yes—
607C8—42no—
608C8—42no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—24no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—44no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—44no—
624C22—44no—
625C22—816no—
626C22—82no—
627C22—82no—
628C22—82no—
629C22—82no—
630C22—82no—
631C22—82no—
632C22C2×C11×#12011yescharacteristic
633C22C11×#54612yes—
634C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
635C22C11×#57511yescharacteristic
636C22C11×#57612yes—
637C4—22no—
638C4—41no—
639C4—41no—
640C4—42no—
641C4—41no—
642C4—42no—
643C4—42no—
644C4—82no—
645C4C11×#52511yescharacteristic
646C4C11×#53511yescharacteristic
647C4C11×#54612yes—
648C2—42no—
649C2—42no—
650C2—84no—
651C2—82no—
652C2C11×#240411yescharacteristic
653C2C11×#300611yescharacteristic
654C2C11×#300811yescharacteristic
655C2C11×#331812yes—
656C2C11×#332212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C2×C11×#553C2semidirect
2. C2×C11×#447C2semidirect
3. C2×C11×#418C2semidirect
4. C11×#2408C2semidirect
5. C11×#2025C2semidirect
6. C11×#1999C2semidirect
7. C11×#1895C2semidirect
8. C11×#1879C2semidirect
9. C11×#1874C2semidirect
10. C11×#1870C2semidirect
11. C11×#1825C2semidirect
18. C2×C11×#125C22semidirect
23. C2×C11×#121C22semidirect
27. C2×C4×D4×C11C22semidirect
29. C22×C11×C4⋊C4C22semidirect
35. C2×C11×#102C22semidirect
37. C2×C11×C22⋊C8C22semidirect
43. C11×#340C22semidirect
44. C11×#340C22semidirect
45. C11×#340C22semidirect
46. C11×#336C22semidirect
80. C11×#121D4semidirect
88. C11×#117D4semidirect
118. #23973C11direct (N × H)
208. C2×#553C2×C11semidirect
209. C2×#447C2×C11semidirect
210. C2×#418C2×C11semidirect
211. #2408C2×C11semidirect
212. #2025C2×C11semidirect
213. #1999C2×C11semidirect
214. #1895C2×C11semidirect
215. #1879C2×C11semidirect
216. #1874C2×C11semidirect
217. #1870C2×C11semidirect
218. #1825C2×C11semidirect
298. C2×#125C22×C11semidirect
303. C2×#121C22×C11semidirect
307. C2×C4×D4C22×C11semidirect
309. C22×C4⋊C4C22×C11semidirect
315. C2×#102C22×C11semidirect
317. C2×C22⋊C8C22×C11semidirect
323. #340C22×C11semidirect
324. #340C22×C11semidirect
325. #340C22×C11semidirect
326. #336C22×C11semidirect
399. #121D4×C11semidirect
407. #117D4×C11semidirect
535. C11#23973direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5532
C2×C11×#4472
C2×C11×#4182
C11×#24082
C11×#20252
C11×#19992
C11×#18952
C11×#18792
C11×#18742
C11×#18702
C11×#18252
#2397311