Finite Group Databasebeta

← C11×#23573 #14600766

Subgroups — C11×#23573 #14600766

Order 2816.

1508 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#532C211yesmaximal, characteristic, complemented
2C2×C11×#442C212yesmaximal, complemented
3C4×C11×#121C211yesmaximal, characteristic, complemented
4C11×#2058C211yesmaximal, characteristic, complemented
5C11×#2041C211yesmaximal, characteristic, complemented
6C11×#2034C212yesmaximal, complemented
7C11×#2023C211yesmaximal, characteristic, complemented
8C11×#2011C211yesmaximal, characteristic, complemented
9C11×#1999C212yesmaximal, complemented
10C11×#1762C212yesmaximal, complemented
11C11×#1749C211yesmaximal, characteristic, complemented
12C22×C11×#41—21no—
13C22×C11×D8C2212yes—
14C11×#532—28no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#127C2211yescharacteristic
17C2×C11×#124—21no—
18C2×C11×#121—21no—
19C2×C11×#121C2212yes—
20C2×C11×#121C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2212yes—
25C22×C42×C11C2211yescharacteristic
26C11×#442—28no—
27C2×C11×#106C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×#102C2212yes—
32C2×C11×C22⋊C8C2212yes—
33C2×C11×#97C2212yes—
34C11×#390C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#388—21no—
37C11×#386—21no—
38C11×#380C2211yescharacteristic
39C4×C11×C4⋊C4C2211yescharacteristic
40C4×C11×C22⋊C4—21no—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2211yescharacteristic
44C11×#336C2211yescharacteristic
45C2×C11×#41—28no—
46C2×C11×#41—44no—
47C2×C11×#41—44no—
48C22×Q8×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11—22no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11C2312yes—
54C22×D4×C11C2311yescharacteristic
55C23×C4×C11—22no—
56C23×C4×C11—21no—
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D411yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C2×C11×D8—24no—
61C2×C11×D8—24no—
62C2×C11×D8—24no—
63C22×C8×C11C2312yes—
64C22×C8×C11C2312yes—
65C11×C4⋊Q8—24no—
66C11×#127—24no—
67C11×#124—28no—
68C11×#121—28no—
69C11×#121—24no—
70C11×#121—22no—
71C11×#121—24no—
72C11×#121—22no—
73C4×D4×C11—28no—
74C4×D4×C11—24no—
75C4×D4×C11—24no—
76C4×D4×C11—44no—
77C4×D4×C11D418yescomplemented
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C42×C11—24no—
92C2×C42×C11—21no—
93C2×C42×C11D411yescharacteristic
94C2×C42×C11D411yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C11×#106—24no—
98C11×#102—24no—
99C11×#102—24no—
100C11×#102—24no—
101C11×#102—24no—
102C11×C22⋊C8—24no—
103C11×#97—24no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107#23573C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11—21no—
109C24×C11—22no—
110C24×C11C2×D411yescharacteristic
111C11×#41—432no—
112C2×Q8×C11—24no—
113C2×Q8×C11—42no—
114C2×Q8×C11—42no—
115C2×D4×C11—24no—
116C2×D4×C11—28no—
117C2×D4×C11—24no—
118C2×D4×C11—24no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—21no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11—44no—
131C2×D4×C11—42no—
132C2×D4×C11—44no—
133C2×D4×C11—42no—
134C2×D4×C11—42no—
135C2×D4×C11C2×D414yes—
136C2×D4×C11#4112yescomplemented
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—28no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—41no—
152C22×C4×C11—44no—
153C22×C4×C11—44no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2411yescharacteristic
163C11×D8—216no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11#4114yescomplemented
170C11×C4⋊C4—24no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4C2×D414yes—
177C11×C4⋊C4#4112yescomplemented
178C11×C22⋊C4—28no—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—28no—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—42no—
185C42×C11—22no—
186C42×C11—22no—
187C42×C11—22no—
188C42×C11—42no—
189C42×C11C2×D414yes—
190C2×#532C2×C1111yescharacteristic, complemented
191C2×#442C2×C1112yescomplemented
192C4×#121C2×C1111yescharacteristic, complemented
193#2058C2×C1111yescharacteristic, complemented
194#2041C2×C1111yescharacteristic, complemented
195#2034C2×C1112yescomplemented
196#2023C2×C1111yescharacteristic, complemented
197#2011C2×C1111yescharacteristic, complemented
198#1999C2×C1112yescomplemented
199#1762C2×C1112yescomplemented
200#1749C2×C1111yescharacteristic, complemented
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—21no—
204C23×C11—21no—
205C23×C11—21no—
206C23×C11—21no—
207C23×C11—24no—
208C23×C11—22no—
209C23×C11—41no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—41no—
218C23×C11—42no—
219C23×C11—41no—
220C23×C11—42no—
221C23×C11AGL(1,ℤ/8)12yes—
222C23×C11C22×D411yescharacteristic
223Q8×C11—48no—
224D4×C11—24no—
225D4×C11—24no—
226D4×C11—24no—
227D4×C11—48no—
228D4×C11—48no—
229D4×C11—48no—
230D4×C11—416no—
231D4×C11—42no—
232D4×C11—42no—
233D4×C11—42no—
234C2×C4×C11—28no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—24no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—44no—
249C2×C4×C11—416no—
250C2×C4×C11—41no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—84no—
263C2×C4×C11#12012yes—
264C2×C4×C11#12012yes—
265C2×C4×C11AGL(1,ℤ/8)12yes—
266C2×C4×C11AGL(1,ℤ/8)12yes—
267C2×C4×C11C22×D412yes—
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4112yes—
270C2×C4×C11C2×#4111yescharacteristic
271C8×C11—24no—
272C8×C11—42no—
273C22×#41—21no—
274C22×D8C22×C1112yes—
275#532—28no—
276C2×C4⋊Q8C22×C1111yescharacteristic
277C2×#127C22×C1111yescharacteristic
278C2×#124—21no—
279C2×#121—21no—
280C2×#121C22×C1112yes—
281C2×#121C22×C1111yescharacteristic
282C2×C4×D4—21no—
283C2×C4×D4—21no—
284C2×C4×D4C22×C1111yescharacteristic
285C2×C4×D4C22×C1112yes—
286C22×C42C22×C1111yescharacteristic
287#442—28no—
288C2×#106C22×C1112yes—
289C2×#102C22×C1112yes—
290C2×#102C22×C1112yes—
291C2×#102C22×C1112yes—
292C2×#102C22×C1112yes—
293C2×C22⋊C8C22×C1112yes—
294C2×#97C22×C1112yes—
295#390C22×C1111yescharacteristic
296#389C22×C1111yescharacteristic
297#388—21no—
298#386—21no—
299#380C22×C1111yescharacteristic
300C4×C4⋊C4C22×C1111yescharacteristic
301C4×C22⋊C4—21no—
302#340C22×C1112yes—
303#340C22×C1112yes—
304#336C22×C1111yescharacteristic
305#336C22×C1111yescharacteristic
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—22no—
309C22×C11—41no—
310C22×C11—41no—
311C22×C11—41no—
312C22×C11—41no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—44no—
316C22×C11—42no—
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—82no—
320C22×C11—82no—
321C22×C11—82no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11—82no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11C2×#12011yescharacteristic
328C22×C11#52511yescharacteristic
329C22×C11#53211yescharacteristic
330C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
331C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C11#57511yescharacteristic
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—22no—
337C4×C11—22no—
338C4×C11—42no—
339C4×C11—41no—
340C4×C11—44no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11#52512yes—
344C4×C11#53212yes—
345C2×#41—28no—
346C2×#41—44no—
347C2×#41—44no—
348C22×Q8—21no—
349C22×D4—21no—
350C22×D4—22no—
351C22×D4—21no—
352C22×D4—21no—
353C22×D4C23×C1112yes—
354C22×D4C23×C1111yescharacteristic
355C23×C4—22no—
356C23×C4—21no—
357C23×C4D4×C1111yescharacteristic
358C23×C4D4×C1111yescharacteristic
359C23×C4C23×C1111yescharacteristic
360C2×D8—24no—
361C2×D8—24no—
362C2×D8—24no—
363C22×C8C23×C1112yes—
364C22×C8C23×C1112yes—
365C4⋊Q8—24no—
366#127—24no—
367#124—28no—
368#121—28no—
369#121—24no—
370#121—22no—
371#121—24no—
372#121—22no—
373C4×D4—28no—
374C4×D4—24no—
375C4×D4—24no—
376C4×D4—44no—
377C4×D4D4×C1118yescomplemented
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4C23×C1111yescharacteristic
381C2×C4⋊C4C23×C1111yescharacteristic
382C2×C4⋊C4C23×C1112yes—
383C2×C4⋊C4C23×C1111yescharacteristic
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C42—24no—
392C2×C42—21no—
393C2×C42D4×C1111yescharacteristic
394C2×C42D4×C1111yescharacteristic
395C2×C42C23×C1111yescharacteristic
396C2×C42C23×C1111yescharacteristic
397#106—24no—
398#102—24no—
399#102—24no—
400#102—24no—
401#102—24no—
402C22⋊C8—24no—
403#97—24no—
404#95—21no—
405#95—21no—
406#95—21no—
407C2×C11—42no—
408C2×C11—82no—
409C2×C11—84no—
410C2×C11#238811yescharacteristic
411C2×C11#300311yescharacteristic
412C2×C11#300611yescharacteristic
413C2×C11#310911yescharacteristic
414C2×C11#311511yescharacteristic
415C2×C11#318011yescharacteristic
416C2×C11#318411yescharacteristic
417C24—21no—
418C24—22no—
419C24C2×D4×C1111yescharacteristic
420#41—432no—
421C2×Q8—24no—
422C2×Q8—42no—
423C2×Q8—42no—
424C2×D4—24no—
425C2×D4—28no—
426C2×D4—24no—
427C2×D4—24no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—21no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—44no—
440C2×D4—44no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4C2×D4×C1114yes—
445C2×D4C11×#4112yescomplemented
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—41no—
461C22×C4—44no—
462C22×C4—44no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C2×D4×C1111yescharacteristic
469C22×C4C2×D4×C1111yescharacteristic
470C22×C4C2×D4×C1111yescharacteristic
471C22×C4C24×C1111yescharacteristic
472D8—216no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8C11×#4114yescomplemented
479C4⋊C4—24no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—42no—
485C4⋊C4C2×D4×C1114yes—
486C4⋊C4C11×#4112yescomplemented
487C22⋊C4—28no—
488C22⋊C4—24no—
489C22⋊C4—28no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C22⋊C4—42no—
494C42—22no—
495C42—22no—
496C42—22no—
497C42—42no—
498C42C2×D4×C1114yes—
499C11#2357311yescharacteristic, direct product factor, Sylow
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—24no—
507C23—22no—
508C23—41no—
509C23—42no—
510C23—42no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—41no—
518C23—41no—
519C23—42no—
520C23C11×AGL(1,ℤ/8)12yes—
521C23C22×D4×C1111yescharacteristic
522Q8—48no—
523D4—24no—
524D4—24no—
525D4—24no—
526D4—48no—
527D4—48no—
528D4—48no—
529D4—416no—
530D4—42no—
531D4—42no—
532D4—42no—
533C2×C4—28no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—24no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—44no—
548C2×C4—416no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—84no—
562C2×C4C11×#12012yes—
563C2×C4C11×#12012yes—
564C2×C4C11×AGL(1,ℤ/8)12yes—
565C2×C4C11×AGL(1,ℤ/8)12yes—
566C2×C4C22×D4×C1112yes—
567C2×C4C2×C11×#4111yescharacteristic
568C2×C4C2×C11×#4112yes—
569C2×C4C2×C11×#4111yescharacteristic
570C8—24no—
571C8—42no—
572C22—22no—
573C22—22no—
574C22—22no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—44no—
580C22—42no—
581C22—44no—
582C22—44no—
583C22—42no—
584C22—42no—
585C22—82no—
586C22—81no—
587C22—81no—
588C22—82no—
589C22—81no—
590C22—81no—
591C22—82no—
592C22—82no—
593C22C2×C11×#12011yescharacteristic
594C22C11×#52511yescharacteristic
595C22C11×#53211yescharacteristic
596C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
597C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
598C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
599C22C11×#57511yescharacteristic
600C4—22no—
601C4—22no—
602C4—22no—
603C4—22no—
604C4—41no—
605C4—44no—
606C4—42no—
607C4—81no—
608C4—81no—
609C4C11×#52512yes—
610C4C11×#53212yes—
611C2—42no—
612C2—84no—
613C2—82no—
614C2C11×#238811yescharacteristic
615C2C11×#300311yescharacteristic
616C2C11×#300611yescharacteristic
617C2C11×#310911yescharacteristic
618C2C11×#311511yescharacteristic
619C2C11×#318011yescharacteristic
620C2C11×#318411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#532C2semidirect
2. C2×C11×#442C2semidirect
3. C4×C11×#121C2semidirect
4. C11×#2058C2semidirect
5. C11×#2041C2semidirect
6. C11×#2034C2semidirect
7. C11×#2023C2semidirect
8. C11×#2011C2semidirect
9. C11×#1999C2semidirect
10. C11×#1762C2semidirect
11. C11×#1749C2semidirect
77. C4×D4×C11D4semidirect
107. #23573C11direct (N × H)
136. C2×D4×C11#41semidirect
169. C2×C8×C11#41semidirect
177. C11×C4⋊C4#41semidirect
190. C2×#532C2×C11semidirect
191. C2×#442C2×C11semidirect
192. C4×#121C2×C11semidirect
193. #2058C2×C11semidirect
194. #2041C2×C11semidirect
195. #2034C2×C11semidirect
196. #2023C2×C11semidirect
197. #2011C2×C11semidirect
198. #1999C2×C11semidirect
199. #1762C2×C11semidirect
200. #1749C2×C11semidirect
377. C4×D4D4×C11semidirect
445. C2×D4C11×#41semidirect
478. C2×C8C11×#41semidirect
486. C4⋊C4C11×#41semidirect
499. C11#23573direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5322
C2×C11×#4422
C4×C11×#1212
C11×#20582
C11×#20412
C11×#20342
C11×#20232
C11×#20112
C11×#19992
C11×#17622
C11×#17492
#2357311