Finite Group Databasebeta

← C11×#32935 #14610128

Subgroups — C11×#32935 #14610128

Order 2816.

1580 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×M16C211yesmaximal, characteristic, complemented
2C2×C11×#468C212yesmaximal, complemented
3C2×C11×#465C211yesmaximal, characteristic, complemented
4C11×#2848C211yesmaximal, characteristic, complemented
5C11×#2847C211yesmaximal, characteristic
6C11×#1895C212yesmaximal, complemented
7C11×#1894C212yesmaximal, complemented
8C11×#1893C211yesmaximal, characteristic, complemented
9C11×#1892C211yesmaximal, characteristic, complemented
10C11×#1809C212yesmaximal, complemented
11C11×#1808C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C22×C11×SD16C2211yescharacteristic, complemented
14C22×C11×M16—28no—
15C22×C11×M16—24no—
16C22×C11×M16C2212yes—
17C22×C11×M16C2212yes—
18C23×C8×C11C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×C22⋊Q8C2212yes—
22C2×C11×#121C2211yescharacteristic
23C2×C11×#121C2212yes—
24C2×C11×#120—21no—
25C11×#468—28no—
26C11×#465—24no—
27C2×C11×#107C2212yescomplemented
28C2×C11×#106C2211yescharacteristic, complemented
29C2×C11×#103C2212yescomplemented
30C2×C11×#103C2211yescharacteristic, complemented
31C2×C11×#102C2212yescomplemented
32C2×C11×#102C2211yescharacteristic, complemented
33C11×#386—22no—
34C11×#386—21no—
35C11×#385—22no—
36C11×#385—21no—
37C11×#380C2211yescharacteristic
38C11×#380C2211yescharacteristic
39C11×#380C2212yes—
40C11×#380C2212yes—
41C11×#379—21no—
42C11×#340C2212yescomplemented
43C11×#340C2212yescomplemented
44C11×#340C2212yescomplemented
45C25×C11D411yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—22no—
48C22×D4×C11—21no—
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—24no—
51C23×C4×C11—22no—
52C23×C4×C11—24no—
53C23×C4×C11—22no—
54C23×C4×C11D412yes—
55C23×C4×C11D411yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2312yes—
58C2×C11×SD16—22no—
59C2×C11×SD16—24no—
60C2×C11×M16—232no—
61C2×C11×M16—24no—
62C2×C11×M16—24no—
63C2×C11×M16—24no—
64C2×C11×M16—24no—
65C2×C11×M16—24no—
66C2×C11×M16D418yescomplemented
67C22×C8×C11—22no—
68C22×C8×C11—24no—
69C22×C8×C11—24no—
70C22×C8×C11D414yescomplemented
71C22×C8×C11C2312yes—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—24no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—24no—
78C11×#121—22no—
79C11×#121—24no—
80C11×#121—22no—
81C11×#121—24no—
82C11×#120—44no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—22no—
97C11×#107—24no—
98C11×#106—22no—
99C11×#103—22no—
100C11×#103—24no—
101C11×#102—22no—
102C11×#102—24no—
103C11×#95—21no—
104C11×#95—22no—
105C11×#95—21no—
106C11×#95—22no—
107#32935C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11—24no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—21no—
113C24×C11—42no—
114C24×C11C2×D412yes—
115C24×C11C2×D411yescharacteristic
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—21no—
119C2×Q8×C11—22no—
120C2×D4×C11—21no—
121C2×D4×C11—22no—
122C2×D4×C11—21no—
123C2×D4×C11—22no—
124C2×D4×C11—44no—
125C2×D4×C11—44no—
126C2×D4×C11—44no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C22×C4×C11—28no—
131C22×C4×C11—28no—
132C22×C4×C11—216no—
133C22×C4×C11—24no—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D414yes—
153C22×C4×C11#4114yes—
154C22×C4×C11#4112yes—
155C22×C4×C11C2411yescharacteristic
156C11×SD16—44no—
157C11×M16—216no—
158C11×M16—216no—
159C2×C8×C11—28no—
160C2×C8×C11—28no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11C2×D414yes—
165C2×C8×C11C2×D412yes—
166C2×C8×C11C2×D412yes—
167C2×C8×C11C2×D414yes—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4—44no—
178C11×C22⋊C4—44no—
179C11×C22⋊C4—44no—
180C11×C22⋊C4—44no—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—42no—
185C11×C22⋊C4—44no—
186C23×M16C2×C1111yescharacteristic, complemented
187C2×#468C2×C1112yescomplemented
188C2×#465C2×C1111yescharacteristic, complemented
189#2848C2×C1111yescharacteristic, complemented
190#2847C2×C1111yescharacteristic
191#1895C2×C1112yescomplemented
192#1894C2×C1112yescomplemented
193#1893C2×C1111yescharacteristic, complemented
194#1892C2×C1111yescharacteristic, complemented
195#1809C2×C1112yescomplemented
196#1808C2×C1111yescharacteristic, complemented
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—28no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—48no—
207C23×C11—48no—
208C23×C11—44no—
209C23×C11—44no—
210C23×C11—41no—
211C23×C11—42no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—42no—
215C23×C11#12114yes—
216C23×C11#12112yes—
217C23×C11AGL(1,ℤ/8)12yes—
218C23×C11#13712yes—
219C23×C11C22×D411yescharacteristic
220Q8×C11—41no—
221Q8×C11—41no—
222Q8×C11—42no—
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—42no—
226D4×C11—88no—
227D4×C11—84no—
228C2×C4×C11—28no—
229C2×C4×C11—216no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—41no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11#12112yes—
254C2×C4×C11#12114yes—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D412yes—
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4112yes—
259C8×C11—24no—
260C8×C11—22no—
261C8×C11#12014yescomplemented
262C24×C4C22×C1111yescharacteristic
263C22×SD16C22×C1111yescharacteristic, complemented
264C22×M16—28no—
265C22×M16—24no—
266C22×M16C22×C1112yes—
267C22×M16C22×C1112yes—
268C23×C8C22×C1111yescharacteristic
269C23×C8C22×C1111yescharacteristic
270C2×C22⋊Q8C22×C1111yescharacteristic
271C2×C22⋊Q8C22×C1112yes—
272C2×#121C22×C1111yescharacteristic
273C2×#121C22×C1112yes—
274C2×#120—21no—
275#468—28no—
276#465—24no—
277C2×#107C22×C1112yescomplemented
278C2×#106C22×C1111yescharacteristic, complemented
279C2×#103C22×C1112yescomplemented
280C2×#103C22×C1111yescharacteristic, complemented
281C2×#102C22×C1112yescomplemented
282C2×#102C22×C1111yescharacteristic, complemented
283#386—22no—
284#386—21no—
285#385—22no—
286#385—21no—
287#380C22×C1111yescharacteristic
288#380C22×C1111yescharacteristic
289#380C22×C1112yes—
290#380C22×C1112yes—
291#379—21no—
292#340C22×C1112yescomplemented
293#340C22×C1112yescomplemented
294#340C22×C1112yescomplemented
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—24no—
298C22×C11—24no—
299C22×C11—24no—
300C22×C11—24no—
301C22×C11—24no—
302C22×C11—416no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—81no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11#46814yescomplemented
313C22×C11C2×#12111yescharacteristic
314C22×C11C2×#12112yes—
315C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
316C22×C11C2×#13711yescharacteristic
317C22×C11#57512yes—
318C4×C11—22no—
319C4×C11—24no—
320C4×C11—81no—
321C4×C11—81no—
322C4×C11—81no—
323C4×C11—82no—
324C4×C11—82no—
325C4×C11C2×#12011yescharacteristic
326C4×C11#52511yescharacteristic
327C4×C11#52512yes—
328C25D4×C1111yescharacteristic
329C22×Q8C23×C1111yescharacteristic
330C22×D4—22no—
331C22×D4—21no—
332C22×D4C23×C1111yescharacteristic
333C23×C4—24no—
334C23×C4—22no—
335C23×C4—24no—
336C23×C4—22no—
337C23×C4D4×C1112yes—
338C23×C4D4×C1111yescharacteristic
339C23×C4C23×C1111yescharacteristic
340C23×C4C23×C1112yes—
341C2×SD16—22no—
342C2×SD16—24no—
343C2×M16—232no—
344C2×M16—24no—
345C2×M16—24no—
346C2×M16—24no—
347C2×M16—24no—
348C2×M16—24no—
349C2×M16D4×C1118yescomplemented
350C22×C8—22no—
351C22×C8—24no—
352C22×C8—24no—
353C22×C8D4×C1114yescomplemented
354C22×C8C23×C1112yes—
355C22×C8C23×C1111yescharacteristic
356C22×C8C23×C1111yescharacteristic
357C22⋊Q8—22no—
358C22⋊Q8—24no—
359C22⋊Q8—22no—
360C22⋊Q8—24no—
361#121—22no—
362#121—24no—
363#121—22no—
364#121—24no—
365#120—44no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4C23×C1111yescharacteristic
369C2×C4⋊C4C23×C1112yes—
370C2×C4⋊C4C23×C1111yescharacteristic
371C2×C4⋊C4C23×C1112yes—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—22no—
380#107—24no—
381#106—22no—
382#103—22no—
383#103—24no—
384#102—22no—
385#102—24no—
386#95—21no—
387#95—22no—
388#95—21no—
389#95—22no—
390C2×C11—24no—
391C2×C11—44no—
392C2×C11—161no—
393C2×C11#284711yescharacteristic
394C2×C11C2×#46811yescharacteristic
395C2×C11#305411yescharacteristic
396C2×C11#305512yes—
397C2×C11#305612yes—
398C24—24no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—21no—
403C24—42no—
404C24C2×D4×C1112yes—
405C24C2×D4×C1111yescharacteristic
406C2×Q8—21no—
407C2×Q8—22no—
408C2×Q8—21no—
409C2×Q8—22no—
410C2×D4—21no—
411C2×D4—22no—
412C2×D4—21no—
413C2×D4—22no—
414C2×D4—44no—
415C2×D4—44no—
416C2×D4—44no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—42no—
420C22×C4—28no—
421C22×C4—28no—
422C22×C4—216no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4C2×D4×C1111yescharacteristic
440C22×C4C2×D4×C1112yes—
441C22×C4C2×D4×C1112yes—
442C22×C4C2×D4×C1114yes—
443C22×C4C11×#4114yes—
444C22×C4C11×#4112yes—
445C22×C4C24×C1111yescharacteristic
446SD16—44no—
447M16—216no—
448M16—216no—
449C2×C8—28no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—28no—
454C2×C8C2×D4×C1114yes—
455C2×C8C2×D4×C1112yes—
456C2×C8C2×D4×C1112yes—
457C2×C8C2×D4×C1114yes—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—42no—
467C4⋊C4—44no—
468C22⋊C4—44no—
469C22⋊C4—44no—
470C22⋊C4—44no—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—44no—
476C11#3293511yescharacteristic, direct product factor, Sylow
477C23—22no—
478C23—22no—
479C23—28no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—48no—
487C23—48no—
488C23—44no—
489C23—44no—
490C23—41no—
491C23—42no—
492C23—41no—
493C23—41no—
494C23—42no—
495C23C11×#12114yes—
496C23C11×#12112yes—
497C23C11×AGL(1,ℤ/8)12yes—
498C23C11×#13712yes—
499C23C22×D4×C1111yescharacteristic
500Q8—41no—
501Q8—41no—
502Q8—42no—
503D4—41no—
504D4—41no—
505D4—42no—
506D4—88no—
507D4—84no—
508C2×C4—28no—
509C2×C4—216no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4C11×#12112yes—
534C2×C4C11×#12114yes—
535C2×C4C22×D4×C1111yescharacteristic
536C2×C4C22×D4×C1112yes—
537C2×C4C2×C11×#4111yescharacteristic
538C2×C4C2×C11×#4112yes—
539C8—24no—
540C8—22no—
541C8C11×#12014yescomplemented
542C22—22no—
543C22—24no—
544C22—24no—
545C22—22no—
546C22—24no—
547C22—24no—
548C22—24no—
549C22—416no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—81no—
555C22—81no—
556C22—82no—
557C22—82no—
558C22—81no—
559C22C11×#46814yescomplemented
560C22C2×C11×#12111yescharacteristic
561C22C2×C11×#12112yes—
562C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
563C22C2×C11×#13711yescharacteristic
564C22C11×#57512yes—
565C4—22no—
566C4—24no—
567C4—81no—
568C4—81no—
569C4—82no—
570C4—82no—
571C4—81no—
572C4C2×C11×#12011yescharacteristic
573C4C11×#52511yescharacteristic
574C4C11×#52512yes—
575C2—24no—
576C2—44no—
577C2—161no—
578C2C11×#284711yescharacteristic
579C2C2×C11×#46811yescharacteristic
580C2C11×#305411yescharacteristic
581C2C11×#305512yes—
582C2C11×#305612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2847C2
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. C23×C11×M16C2semidirect
2. C2×C11×#468C2semidirect
3. C2×C11×#465C2semidirect
4. C11×#2848C2semidirect
6. C11×#1895C2semidirect
7. C11×#1894C2semidirect
8. C11×#1893C2semidirect
9. C11×#1892C2semidirect
10. C11×#1809C2semidirect
11. C11×#1808C2semidirect
13. C22×C11×SD16C22semidirect
27. C2×C11×#107C22semidirect
28. C2×C11×#106C22semidirect
29. C2×C11×#103C22semidirect
30. C2×C11×#103C22semidirect
31. C2×C11×#102C22semidirect
32. C2×C11×#102C22semidirect
42. C11×#340C22semidirect
43. C11×#340C22semidirect
44. C11×#340C22semidirect
66. C2×C11×M16D4semidirect
70. C22×C8×C11D4semidirect
107. #32935C11direct (N × H)
186. C23×M16C2×C11semidirect
187. C2×#468C2×C11semidirect
188. C2×#465C2×C11semidirect
189. #2848C2×C11semidirect
191. #1895C2×C11semidirect
192. #1894C2×C11semidirect
193. #1893C2×C11semidirect
194. #1892C2×C11semidirect
195. #1809C2×C11semidirect
196. #1808C2×C11semidirect
261. C8×C11#120semidirect
263. C22×SD16C22×C11semidirect
277. C2×#107C22×C11semidirect
278. C2×#106C22×C11semidirect
279. C2×#103C22×C11semidirect
280. C2×#103C22×C11semidirect
281. C2×#102C22×C11semidirect
282. C2×#102C22×C11semidirect
292. #340C22×C11semidirect
293. #340C22×C11semidirect
294. #340C22×C11semidirect
312. C22×C11#468semidirect
349. C2×M16D4×C11semidirect
353. C22×C8D4×C11semidirect
476. C11#32935direct (N × H)
541. C8C11×#120semidirect
559. C22C11×#468semidirect

Maximal subgroups

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

subgroupindex
C23×C11×M162
C2×C11×#4682
C2×C11×#4652
C11×#28482
C11×#28472
C11×#18952
C11×#18942
C11×#18932
C11×#18922
C11×#18092
C11×#18082
#3293511