Finite Group Databasebeta

← C11×#23642 #14600835

Subgroups — C11×#23642 #14600835

Order 2816.

1166 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#428C211yesmaximal, characteristic, complemented
2C2×C11×#407C211yesmaximal, characteristic
3C11×#2280C211yesmaximal, characteristic
4C2×C11×#380C211yesmaximal, characteristic
5C11×#2077C212yesmaximal, complemented
6C11×#2077C212yesmaximal, complemented
7C11×#2076C212yesmaximal, complemented
8C11×#2075C212yesmaximal, complemented
9C11×#1736C211yesmaximal, characteristic, complemented
10C11×#1736C211yesmaximal, characteristic, complemented
11C11×#1736C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4—21no—
20C11×#428—24no—
21C2×C11×#107C2212yescomplemented
22C2×C11×#106C2212yescomplemented
23C11×#407—24no—
24C2×C11×C22⋊C8C2212yes—
25C2×C11×C22⋊C8C2212yes—
26C11×#381—21no—
27C11×#380—21no—
28C11×#380—21no—
29C11×#380C2212yes—
30C11×#380C2212yes—
31C11×#380C2211yescharacteristic
32C11×#380C2211yescharacteristic
33C11×#380C2211yescharacteristic
34C11×#380C2211yescharacteristic
35C11×#379—21no—
36C4×C11×C22⋊C4—21no—
37C4×C11×C22⋊C4—21no—
38C2×C11×#95—21no—
39C11×#340C2212yescomplemented
40C11×#340C2212yescomplemented
41C11×#340C2212yescomplemented
42C11×#340C2212yescomplemented
43C11×#340C2212yescomplemented
44C11×#340C2212yescomplemented
45C25×C11D411yescharacteristic
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—22no—
49C23×C4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11—22no—
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11D411yescharacteristic
55C23×C4×C11D411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C2×C11×M16—22no—
61C2×C11×M16—22no—
62C2×C11×M16—22no—
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16D414yes—
66C22×C8×C11C2312yes—
67C22×C8×C11C2312yes—
68C11×#117—22no—
69C11×#117—22no—
70C11×#117—22no—
71C11×#117—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—44no—
93C2×C42×C11—21no—
94C2×C42×C11—21no—
95C11×#107—24no—
96C11×#106—24no—
97C11×C22⋊C8—24no—
98C11×C22⋊C8—24no—
99C11×#95—22no—
100C11×#95—22no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105#23642C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—41no—
112C24×C11—41no—
113C24×C11C2×D411yescharacteristic
114C24×C11C2×D411yescharacteristic
115C24×C11C2×D411yescharacteristic
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—44no—
144C22×C4×C11—44no—
145C22×C4×C11—44no—
146C22×C4×C11—44no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11#4112yes—
158C22×C4×C11#4112yes—
159C22×C4×C11#4112yes—
160C22×C4×C11#4112yes—
161C22×C4×C11#4112yes—
162C22×C4×C11C2411yescharacteristic
163C11×M16—28no—
164C11×M16—44no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11C2×D414yes—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4—42no—
185C11×C22⋊C4—42no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—44no—
188C11×C22⋊C4—42no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—42no—
191C11×C22⋊C4—44no—
192C11×C22⋊C4—42no—
193C42×C11—42no—
194C42×C11—42no—
195C2×#428C2×C1111yescharacteristic, complemented
196C2×#407C2×C1111yescharacteristic
197#2280C2×C1111yescharacteristic
198C2×#380C2×C1111yescharacteristic
199#2077C2×C1112yescomplemented
200#2077C2×C1112yescomplemented
201#2076C2×C1112yescomplemented
202#2075C2×C1112yescomplemented
203#1736C2×C1111yescharacteristic, complemented
204#1736C2×C1111yescharacteristic, complemented
205#1736C2×C1111yescharacteristic, complemented
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—28no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—44no—
224C23×C11—44no—
225C23×C11—44no—
226C23×C11—44no—
227C23×C11—44no—
228C23×C11—44no—
229C23×C11#12112yes—
230C23×C11#12312yes—
231C23×C11#12312yes—
232C23×C11AGL(1,ℤ/8)12yes—
233C23×C11#13712yes—
234C23×C11C22×D411yescharacteristic
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—44no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—44no—
251C2×C4×C11—44no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—84no—
271C2×C4×C11—84no—
272C2×C4×C11#12112yes—
273C2×C4×C11#12314yes—
274C2×C4×C11#12312yes—
275C2×C4×C11#12312yes—
276C2×C4×C11#12414yes—
277C2×C4×C11#12614yes—
278C2×C4×C11#12614yes—
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C8×C11—24no—
286C8×C11—42no—
287C24×C4C22×C1111yescharacteristic
288C22×M16C22×C1111yescharacteristic
289C22×M16C22×C1111yescharacteristic
290C2×#117C22×C1111yescharacteristic
291C2×#117C22×C1111yescharacteristic
292C22×C4⋊C4C22×C1111yescharacteristic
293C22×C4⋊C4C22×C1111yescharacteristic
294C22×C22⋊C4—21no—
295#428—24no—
296C2×#107C22×C1112yescomplemented
297C2×#106C22×C1112yescomplemented
298#407—24no—
299C2×C22⋊C8C22×C1112yes—
300C2×C22⋊C8C22×C1112yes—
301#381—21no—
302#380—21no—
303#380—21no—
304#380C22×C1111yescharacteristic
305#380C22×C1112yes—
306#380C22×C1111yescharacteristic
307#380C22×C1112yes—
308#380C22×C1111yescharacteristic
309#380C22×C1111yescharacteristic
310#379—21no—
311C4×C22⋊C4—21no—
312C4×C22⋊C4—21no—
313C2×#95—21no—
314#340C22×C1112yescomplemented
315#340C22×C1112yescomplemented
316#340C22×C1112yescomplemented
317#340C22×C1112yescomplemented
318#340C22×C1112yescomplemented
319#340C22×C1112yescomplemented
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—22no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—22no—
332C22×C11—416no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11#39714yes—
342C22×C11C2×#12111yescharacteristic
343C22×C11C2×#12311yescharacteristic
344C22×C11C2×#12311yescharacteristic
345C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C11C2×#13711yescharacteristic
347C22×C11#57511yescharacteristic
348C22×C11#57511yescharacteristic
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—81no—
352C4×C11—81no—
353C4×C11—82no—
354C4×C11—81no—
355C4×C11—82no—
356C4×C11—81no—
357C4×C11#39714yes—
358C4×C11C2×#12311yescharacteristic
359C4×C11C2×#12411yescharacteristic
360C4×C11C2×#12611yescharacteristic
361C4×C11C2×#12611yescharacteristic
362C25D4×C1111yescharacteristic
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—21no—
370C23×C4—21no—
371C23×C4D4×C1111yescharacteristic
372C23×C4D4×C1111yescharacteristic
373C23×C4D4×C1111yescharacteristic
374C23×C4C23×C1111yescharacteristic
375C23×C4C23×C1111yescharacteristic
376C23×C4C23×C1111yescharacteristic
377C2×M16—22no—
378C2×M16—22no—
379C2×M16—22no—
380C2×M16—22no—
381C2×M16—22no—
382C2×M16D4×C1114yes—
383C22×C8C23×C1112yes—
384C22×C8C23×C1112yes—
385#117—22no—
386#117—22no—
387#117—22no—
388#117—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4C23×C1112yes—
396C2×C4⋊C4C23×C1112yes—
397C2×C4⋊C4C23×C1111yescharacteristic
398C2×C4⋊C4C23×C1111yescharacteristic
399C2×C4⋊C4C23×C1111yescharacteristic
400C2×C4⋊C4C23×C1111yescharacteristic
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—44no—
410C2×C42—21no—
411C2×C42—21no—
412#107—24no—
413#106—24no—
414C22⋊C8—24no—
415C22⋊C8—24no—
416#95—22no—
417#95—22no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422C2×C11—24no—
423C2×C11—42no—
424C2×C11—42no—
425C2×C11C2×#39711yescharacteristic
426C2×C11#305511yescharacteristic
427C2×C11#305611yescharacteristic
428C2×C11#309211yescharacteristic
429C2×C11#309311yescharacteristic
430C2×C11#309411yescharacteristic
431C2×C11#309511yescharacteristic
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—41no—
438C24—41no—
439C24C2×D4×C1111yescharacteristic
440C24C2×D4×C1111yescharacteristic
441C24C2×D4×C1111yescharacteristic
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—44no—
470C22×C4—44no—
471C22×C4—44no—
472C22×C4—44no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4C2×D4×C1111yescharacteristic
480C22×C4C2×D4×C1111yescharacteristic
481C22×C4C2×D4×C1111yescharacteristic
482C22×C4C2×D4×C1112yes—
483C22×C4C11×#4112yes—
484C22×C4C11×#4112yes—
485C22×C4C11×#4112yes—
486C22×C4C11×#4112yes—
487C22×C4C11×#4112yes—
488C22×C4C24×C1111yescharacteristic
489M16—28no—
490M16—44no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8C2×D4×C1114yes—
497C4⋊C4—21no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C22⋊C4—44no—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—44no—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C42—42no—
520C42—42no—
521C11#2364211yescharacteristic, direct product factor, Sylow
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—28no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—44no—
540C23—44no—
541C23—44no—
542C23—44no—
543C23—44no—
544C23—44no—
545C23C11×#12112yes—
546C23C11×#12312yes—
547C23C11×#12312yes—
548C23C11×AGL(1,ℤ/8)12yes—
549C23C11×#13712yes—
550C23C22×D4×C1111yescharacteristic
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—44no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—44no—
567C2×C4—44no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—84no—
587C2×C4—84no—
588C2×C4C11×#12112yes—
589C2×C4C11×#12314yes—
590C2×C4C11×#12312yes—
591C2×C4C11×#12312yes—
592C2×C4C11×#12414yes—
593C2×C4C11×#12614yes—
594C2×C4C11×#12614yes—
595C2×C4C22×D4×C1111yescharacteristic
596C2×C4C2×C11×#4111yescharacteristic
597C2×C4C2×C11×#4111yescharacteristic
598C2×C4C2×C11×#4111yescharacteristic
599C2×C4C2×C11×#4111yescharacteristic
600C2×C4C2×C11×#4111yescharacteristic
601C8—24no—
602C8—42no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—416no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22C11×#39714yes—
625C22C2×C11×#12111yescharacteristic
626C22C2×C11×#12311yescharacteristic
627C22C2×C11×#12311yescharacteristic
628C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
629C22C2×C11×#13711yescharacteristic
630C22C11×#57511yescharacteristic
631C22C11×#57511yescharacteristic
632C4—41no—
633C4—41no—
634C4—82no—
635C4—81no—
636C4—81no—
637C4—81no—
638C4—81no—
639C4—82no—
640C4C11×#39714yes—
641C4C2×C11×#12311yescharacteristic
642C4C2×C11×#12411yescharacteristic
643C4C2×C11×#12611yescharacteristic
644C4C2×C11×#12611yescharacteristic
645C2—24no—
646C2—42no—
647C2—42no—
648C2C2×C11×#39711yescharacteristic
649C2C11×#305511yescharacteristic
650C2C11×#305611yescharacteristic
651C2C11×#309211yescharacteristic
652C2C11×#309311yescharacteristic
653C2C11×#309411yescharacteristic
654C2C11×#309511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC25×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#428C2semidirect
5. C11×#2077C2semidirect
6. C11×#2077C2semidirect
7. C11×#2076C2semidirect
8. C11×#2075C2semidirect
9. C11×#1736C2semidirect
10. C11×#1736C2semidirect
11. C11×#1736C2semidirect
21. C2×C11×#107C22semidirect
22. C2×C11×#106C22semidirect
39. C11×#340C22semidirect
40. C11×#340C22semidirect
41. C11×#340C22semidirect
42. C11×#340C22semidirect
43. C11×#340C22semidirect
44. C11×#340C22semidirect
105. #23642C11direct (N × H)
195. C2×#428C2×C11semidirect
199. #2077C2×C11semidirect
200. #2077C2×C11semidirect
201. #2076C2×C11semidirect
202. #2075C2×C11semidirect
203. #1736C2×C11semidirect
204. #1736C2×C11semidirect
205. #1736C2×C11semidirect
296. C2×#107C22×C11semidirect
297. C2×#106C22×C11semidirect
314. #340C22×C11semidirect
315. #340C22×C11semidirect
316. #340C22×C11semidirect
317. #340C22×C11semidirect
318. #340C22×C11semidirect
319. #340C22×C11semidirect
521. C11#23642direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4282
C2×C11×#4072
C11×#22802
C2×C11×#3802
C11×#20772
C11×#20762
C11×#20752
C11×#17362
#2364211