Finite Group Databasebeta

← C11×#23431 #14600624

Subgroups — C11×#23431 #14600624

Order 2816.

2146 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#137C211yesmaximal, characteristic, complemented
2C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
3C22×C11×#124C211yesmaximal, characteristic, complemented
4C2×C11×#419C211yesmaximal, characteristic, complemented
5C2×C11×#418C211yesmaximal, characteristic, complemented
6C11×#2297C211yesmaximal, characteristic, complemented
7C11×#2015C214yesmaximal, complemented
8C11×#2012C214yesmaximal, complemented
9C11×#1728C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C23×D4×C11C2211yescharacteristic
13C2×C11×#137—24no—
14C2×C11×#137—24no—
15C2×C11×#137—24no—
16C2×C11×AGL(1,ℤ/8)—24no—
17C2×C11×AGL(1,ℤ/8)—24no—
18C2×C11×AGL(1,ℤ/8)—24no—
19C22×C11×Q16C2212yescomplemented
20C22×C11×SD16C2212yes—
21C22×C11×SD16C2212yescomplemented
22C22×C11×D8C2212yes—
23C22×C11×M16C2211yescharacteristic
24C22×C11×M16C2211yescharacteristic
25C2×C11×#124—24no—
26C2×C11×#124—24no—
27C2×C11×#124—22no—
28C2×C11×#124C2214yes—
29C2×C11×#117C2211yescharacteristic
30C22×C11×C22⋊C4—22no—
31C22×C42×C11C2211yescharacteristic
32C11×#419—24no—
33C11×#418—24no—
34C2×C11×#103C2214yescomplemented
35C2×C11×#102C2214yes—
36C11×#391C2212yescomplemented
37C11×#390C2212yescomplemented
38C11×#386—22no—
39C4×C11×C22⋊C4—22no—
40C11×#336C2214yescomplemented
41C25×C11—21no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41D414yes—
48C22×Q8×C11—22no—
49C22×Q8×C11—21no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11—22no—
53C22×Q8×C11—22no—
54C22×Q8×C11D414yes—
55C22×Q8×C11C2312yes—
56C22×Q8×C11C2311yescharacteristic
57C22×D4×C11—21no—
58C22×D4×C11—22no—
59C22×D4×C11—22no—
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11—21no—
63C22×D4×C11—22no—
64C22×D4×C11D414yes—
65C22×D4×C11C2312yes—
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11—21no—
69C23×C4×C11D412yes—
70C23×C4×C11C2311yescharacteristic
71C11×#137—232no—
72C11×AGL(1,ℤ/8)—232no—
73C2×C11×Q16—24no—
74C2×C11×Q16—24no—
75C2×C11×Q16—24no—
76C2×C11×SD16—24no—
77C2×C11×SD16—24no—
78C2×C11×SD16—24no—
79C2×C11×SD16—24no—
80C2×C11×SD16—24no—
81C2×C11×SD16—24no—
82C2×C11×D8—24no—
83C2×C11×D8—24no—
84C2×C11×D8—24no—
85C2×C11×M16—22no—
86C2×C11×M16—22no—
87C2×C11×M16—22no—
88C2×C11×M16—22no—
89C2×C11×M16D414yes—
90C2×C11×M16D414yes—
91C22×C8×C11C2312yes—
92C22×C8×C11C2312yes—
93C11×#124—216no—
94C11×#124—28no—
95C11×#124—28no—
96C11×#117—22no—
97C11×#117—22no—
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C22⋊C4—216no—
100C2×C11×C22⋊C4—28no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—24no—
103C2×C42×C11—22no—
104C2×C42×C11—22no—
105C2×C42×C11—21no—
106C2×C42×C11D412yes—
107C2×C42×C11C2312yes—
108C11×#103—28no—
109C11×#102—28no—
110C11×#95—24no—
111#23431C1111yesmaximal, characteristic, direct product factor, Sylow
112C24×C11—24no—
113C24×C11—21no—
114C24×C11—22no—
115C24×C11—48no—
116C24×C11—42no—
117C24×C11—42no—
118C24×C11C2×D411yescharacteristic
119C11×#41—28no—
120C11×#41—28no—
121C11×#41—44no—
122C11×#41—44no—
123C2×Q8×C11—24no—
124C2×Q8×C11—22no—
125C2×Q8×C11—21no—
126C2×Q8×C11—28no—
127C2×Q8×C11—28no—
128C2×Q8×C11—22no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—22no—
136C2×Q8×C11—44no—
137C2×Q8×C11—42no—
138C2×Q8×C11—44no—
139C2×Q8×C11—42no—
140C2×Q8×C11C2×D414yes—
141C2×Q8×C11C2×D412yes—
142C2×D4×C11—24no—
143C2×D4×C11—28no—
144C2×D4×C11—24no—
145C2×D4×C11—28no—
146C2×D4×C11—22no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—21no—
156C2×D4×C11—42no—
157C2×D4×C11—42no—
158C2×D4×C11—44no—
159C2×D4×C11—44no—
160C2×D4×C11—42no—
161C2×D4×C11—42no—
162C2×D4×C11C2×D414yes—
163C2×D4×C11C2×D412yes—
164C22×C4×C11—24no—
165C22×C4×C11—24no—
166C22×C4×C11—21no—
167C22×C4×C11—22no—
168C22×C4×C11—24no—
169C22×C4×C11—22no—
170C22×C4×C11—44no—
171C22×C4×C11—42no—
172C22×C4×C11—42no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11C2×D414yes—
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D412yes—
181C22×C4×C11C2×D412yes—
182C22×C4×C11#4112yes—
183C22×C4×C11C2411yescharacteristic
184C11×Q16—216no—
185C11×SD16—216no—
186C11×SD16—216no—
187C11×D8—216no—
188C11×M16—28no—
189C11×M16—28no—
190C2×C8×C11—22no—
191C2×C8×C11—22no—
192C2×C8×C11—22no—
193C2×C8×C11—22no—
194C2×C8×C11C2×D414yes—
195C2×C8×C11C2×D414yes—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
198C11×C22⋊C4—232no—
199C11×C22⋊C4—48no—
200C11×C22⋊C4—42no—
201C42×C11—24no—
202C42×C11—22no—
203C42×C11—22no—
204C42×C11—42no—
205C22×#137C2×C1111yescharacteristic, complemented
206C22×AGL(1,ℤ/8)C2×C1111yescharacteristic
207C22×#124C2×C1111yescharacteristic, complemented
208C2×#419C2×C1111yescharacteristic, complemented
209C2×#418C2×C1111yescharacteristic, complemented
210#2297C2×C1111yescharacteristic, complemented
211#2015C2×C1114yescomplemented
212#2012C2×C1114yescomplemented
213#1728C2×C1111yescharacteristic, complemented
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—22no—
217C23×C11—416no—
218C23×C11—41no—
219C23×C11—42no—
220C23×C11—41no—
221C23×C11—42no—
222C23×C11—44no—
223C23×C11—48no—
224C23×C11—48no—
225C23×C11—88no—
226C23×C11—88no—
227C23×C11#12012yes—
228C23×C11#12112yes—
229C23×C11#12712yes—
230C23×C11C22×D411yescharacteristic
231Q8×C11—22no—
232Q8×C11—24no—
233Q8×C11—22no—
234Q8×C11—24no—
235Q8×C11—42no—
236Q8×C11—42no—
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11—48no—
240D4×C11—22no—
241D4×C11—24no—
242D4×C11—22no—
243D4×C11—24no—
244D4×C11—48no—
245D4×C11—42no—
246D4×C11—42no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—48no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—48no—
256C2×C4×C11—41no—
257C2×C4×C11—42no—
258C2×C4×C11—41no—
259C2×C4×C11—42no—
260C2×C4×C11—48no—
261C2×C4×C11—48no—
262C2×C4×C11—42no—
263C2×C4×C11—44no—
264C2×C4×C11#12014yes—
265C2×C4×C11#12014yes—
266C2×C4×C11#12012yes—
267C2×C4×C11#12114yes—
268C2×C4×C11#12114yes—
269C2×C4×C11#12112yes—
270C2×C4×C11#12712yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C8×C11—24no—
278C8×C11—24no—
279C22×#41C22×C1111yescharacteristic
280C23×Q8C22×C1111yescharacteristic
281C23×D4C22×C1111yescharacteristic
282C2×#137—24no—
283C2×#137—24no—
284C2×#137—24no—
285C2×AGL(1,ℤ/8)—24no—
286C2×AGL(1,ℤ/8)—24no—
287C2×AGL(1,ℤ/8)—24no—
288C22×Q16C22×C1112yescomplemented
289C22×SD16C22×C1112yes—
290C22×SD16C22×C1112yescomplemented
291C22×D8C22×C1112yes—
292C22×M16C22×C1111yescharacteristic
293C22×M16C22×C1111yescharacteristic
294C2×#124—24no—
295C2×#124—24no—
296C2×#124—22no—
297C2×#124C22×C1114yes—
298C2×#117C22×C1111yescharacteristic
299C22×C22⋊C4—22no—
300C22×C42C22×C1111yescharacteristic
301#419—24no—
302#418—24no—
303C2×#103C22×C1114yescomplemented
304C2×#102C22×C1114yes—
305#391C22×C1112yescomplemented
306#390C22×C1112yescomplemented
307#386—22no—
308C4×C22⋊C4—22no—
309#336C22×C1114yescomplemented
310C22×C11—24no—
311C22×C11—24no—
312C22×C11—24no—
313C22×C11—42no—
314C22×C11—44no—
315C22×C11—48no—
316C22×C11—44no—
317C22×C11—816no—
318C22×C11—82no—
319C22×C11—84no—
320C22×C11—82no—
321C22×C11—84no—
322C22×C11#39214yes—
323C22×C11C2×#12011yescharacteristic
324C22×C11C2×#12111yescharacteristic
325C22×C11C2×#12711yescharacteristic
326C22×C11#57514yes—
327C4×C11—42no—
328C4×C11—44no—
329C4×C11—44no—
330C4×C11—82no—
331C4×C11#39214yes—
332C4×C11C2×#12011yescharacteristic
333C4×C11C2×#12011yescharacteristic
334C4×C11C2×#12111yescharacteristic
335C4×C11C2×#12111yescharacteristic
336C25—21no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41—22no—
342C2×#41D4×C1114yes—
343C22×Q8—22no—
344C22×Q8—21no—
345C22×Q8—22no—
346C22×Q8—22no—
347C22×Q8—22no—
348C22×Q8—22no—
349C22×Q8D4×C1114yes—
350C22×Q8C23×C1112yes—
351C22×Q8C23×C1111yescharacteristic
352C22×D4—21no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—21no—
358C22×D4—22no—
359C22×D4D4×C1114yes—
360C22×D4C23×C1112yes—
361C22×D4C23×C1111yescharacteristic
362C23×C4—21no—
363C23×C4—21no—
364C23×C4D4×C1112yes—
365C23×C4C23×C1111yescharacteristic
366#137—232no—
367AGL(1,ℤ/8)—232no—
368C2×Q16—24no—
369C2×Q16—24no—
370C2×Q16—24no—
371C2×SD16—24no—
372C2×SD16—24no—
373C2×SD16—24no—
374C2×SD16—24no—
375C2×SD16—24no—
376C2×SD16—24no—
377C2×D8—24no—
378C2×D8—24no—
379C2×D8—24no—
380C2×M16—22no—
381C2×M16—22no—
382C2×M16—22no—
383C2×M16—22no—
384C2×M16D4×C1114yes—
385C2×M16D4×C1114yes—
386C22×C8C23×C1112yes—
387C22×C8C23×C1112yes—
388#124—216no—
389#124—28no—
390#124—28no—
391#117—22no—
392#117—22no—
393C2×C4⋊C4C23×C1112yes—
394C2×C22⋊C4—216no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—24no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—21no—
401C2×C42D4×C1112yes—
402C2×C42C23×C1112yes—
403#103—28no—
404#102—28no—
405#95—24no—
406C2×C11—24no—
407C2×C11—82no—
408C2×C11—84no—
409C2×C11C2×#39211yescharacteristic
410C2×C11#300512yes—
411C2×C11#304012yes—
412C2×C11#315312yes—
413C24—24no—
414C24—21no—
415C24—22no—
416C24—48no—
417C24—42no—
418C24—42no—
419C24C2×D4×C1111yescharacteristic
420#41—28no—
421#41—28no—
422#41—44no—
423#41—44no—
424C2×Q8—24no—
425C2×Q8—22no—
426C2×Q8—21no—
427C2×Q8—28no—
428C2×Q8—28no—
429C2×Q8—22no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—22no—
437C2×Q8—44no—
438C2×Q8—42no—
439C2×Q8—44no—
440C2×Q8—42no—
441C2×Q8C2×D4×C1114yes—
442C2×Q8C2×D4×C1112yes—
443C2×D4—24no—
444C2×D4—28no—
445C2×D4—24no—
446C2×D4—28no—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—21no—
457C2×D4—42no—
458C2×D4—42no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4C2×D4×C1114yes—
464C2×D4C2×D4×C1112yes—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—44no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4C2×D4×C1114yes—
477C22×C4C2×D4×C1112yes—
478C22×C4C2×D4×C1112yes—
479C22×C4C2×D4×C1112yes—
480C22×C4C2×D4×C1111yescharacteristic
481C22×C4C2×D4×C1112yes—
482C22×C4C2×D4×C1112yes—
483C22×C4C11×#4112yes—
484C22×C4C24×C1111yescharacteristic
485Q16—216no—
486SD16—216no—
487SD16—216no—
488D8—216no—
489M16—28no—
490M16—28no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8C2×D4×C1114yes—
496C2×C8C2×D4×C1114yes—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C22⋊C4—232no—
500C22⋊C4—48no—
501C22⋊C4—42no—
502C42—24no—
503C42—22no—
504C42—22no—
505C42—42no—
506C11#2343111yescharacteristic, direct product factor, Sylow
507C23—24no—
508C23—24no—
509C23—22no—
510C23—416no—
511C23—41no—
512C23—42no—
513C23—48no—
514C23—41no—
515C23—42no—
516C23—44no—
517C23—48no—
518C23—88no—
519C23—88no—
520C23C11×#12012yes—
521C23C11×#12112yes—
522C23C11×#12712yes—
523C23C22×D4×C1111yescharacteristic
524Q8—22no—
525Q8—24no—
526Q8—22no—
527Q8—24no—
528Q8—42no—
529Q8—42no—
530Q8—41no—
531Q8—41no—
532Q8—48no—
533D4—22no—
534D4—24no—
535D4—22no—
536D4—24no—
537D4—48no—
538D4—42no—
539D4—42no—
540D4—41no—
541D4—41no—
542D4—48no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—48no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—48no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—48no—
555C2×C4—42no—
556C2×C4—44no—
557C2×C4C11×#12014yes—
558C2×C4C11×#12014yes—
559C2×C4C11×#12012yes—
560C2×C4C11×#12114yes—
561C2×C4C11×#12114yes—
562C2×C4C11×#12112yes—
563C2×C4C11×#12712yes—
564C2×C4C22×D4×C1111yescharacteristic
565C2×C4C22×D4×C1111yescharacteristic
566C2×C4C22×D4×C1111yescharacteristic
567C2×C4C22×D4×C1111yescharacteristic
568C2×C4C22×D4×C1111yescharacteristic
569C2×C4C2×C11×#4111yescharacteristic
570C8—24no—
571C8—24no—
572C22—24no—
573C22—24no—
574C22—24no—
575C22—42no—
576C22—44no—
577C22—48no—
578C22—44no—
579C22—816no—
580C22—84no—
581C22—82no—
582C22—82no—
583C22—84no—
584C22C11×#39214yes—
585C22C2×C11×#12011yescharacteristic
586C22C2×C11×#12111yescharacteristic
587C22C2×C11×#12711yescharacteristic
588C22C11×#57514yes—
589C4—42no—
590C4—44no—
591C4—44no—
592C4—82no—
593C4C11×#39214yes—
594C4C2×C11×#12011yescharacteristic
595C4C2×C11×#12011yescharacteristic
596C4C2×C11×#12111yescharacteristic
597C4C2×C11×#12111yescharacteristic
598C2—24no—
599C2—84no—
600C2—82no—
601C2C2×C11×#39211yescharacteristic
602C2C11×#300512yes—
603C2C11×#304012yes—
604C2C11×#315312yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×AGL(1,ℤ/8)C2
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. C22×C11×#137C2semidirect
3. C22×C11×#124C2semidirect
4. C2×C11×#419C2semidirect
5. C2×C11×#418C2semidirect
6. C11×#2297C2semidirect
7. C11×#2015C2semidirect
8. C11×#2012C2semidirect
9. C11×#1728C2semidirect
19. C22×C11×Q16C22semidirect
21. C22×C11×SD16C22semidirect
34. C2×C11×#103C22semidirect
36. C11×#391C22semidirect
37. C11×#390C22semidirect
40. C11×#336C22semidirect
111. #23431C11direct (N × H)
205. C22×#137C2×C11semidirect
207. C22×#124C2×C11semidirect
208. C2×#419C2×C11semidirect
209. C2×#418C2×C11semidirect
210. #2297C2×C11semidirect
211. #2015C2×C11semidirect
212. #2012C2×C11semidirect
213. #1728C2×C11semidirect
288. C22×Q16C22×C11semidirect
290. C22×SD16C22×C11semidirect
303. C2×#103C22×C11semidirect
305. #391C22×C11semidirect
306. #390C22×C11semidirect
309. #336C22×C11semidirect
506. C11#23431direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1372
C22×C11×AGL(1,ℤ/8)2
C22×C11×#1242
C2×C11×#4192
C2×C11×#4182
C11×#22972
C11×#20152
C11×#20122
C11×#17282
#2343111