Finite Group Databasebeta

← C11×#32941 #14610134

Subgroups — C11×#32941 #14610134

Order 2816.

1342 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#131C211yesmaximal, characteristic, complemented
2C2×C11×#471C212yesmaximal, complemented
3C2×C11×#465C211yesmaximal, characteristic, complemented
4C11×#3007C211yesmaximal, characteristic, complemented
5C11×#3006C211yesmaximal, characteristic
6C11×#1908C212yesmaximal, complemented
7C11×#1907C212yesmaximal, complemented
8C11×#1901C211yesmaximal, characteristic, complemented
9C11×#1900C211yesmaximal, characteristic, complemented
10C11×#1815C212yesmaximal, complemented
11C11×#1810C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C2×C11×#137C2212yes—
14C2×C11×AGL(1,ℤ/8)C2212yes—
15C22×C11×SD16C2211yescharacteristic, complemented
16C2×C11×#131—28no—
17C2×C11×#131—21no—
18C2×C11×#131—21no—
19C2×C11×#131C2212yes—
20C2×C11×#131C2212yes—
21C22×C11×M16—21no—
22C22×C11×M16C2211yescharacteristic
23C23×C8×C11—21no—
24C23×C8×C11C2211yescharacteristic
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C11×#471—28no—
28C11×#465—21no—
29C11×#465—21no—
30C11×#465—21no—
31C11×#465—21no—
32C11×#452—22no—
33C11×#451—21no—
34C11×#450—21no—
35C11×#449—22no—
36C11×#448—21no—
37C11×#447—21no—
38C2×C11×#108C2212yescomplemented
39C2×C11×#106C2211yescharacteristic, complemented
40C11×#417C2212yes—
41C11×#417C2212yes—
42C2×C11×#103C2211yescharacteristic, complemented
43C2×C11×#102C2211yescharacteristic, complemented
44C2×C11×#101C2212yescomplemented
45C2×C11×#100C2212yescomplemented
46C11×#407C2211yescharacteristic
47C11×#407C2211yescharacteristic
48C11×#343C2212yescomplemented
49C11×#343C2212yescomplemented
50C11×#341C2212yescomplemented
51C2×C11×#41—24no—
52C2×C11×#41—24no—
53C2×C11×#41—21no—
54C2×C11×#41—21no—
55C2×C11×#41D412yes—
56C2×C11×#41C2312yes—
57C22×Q8×C11D411yescharacteristic
58C22×Q8×C11C2311yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11D411yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C11×#137—24no—
66C11×#137—24no—
67C11×AGL(1,ℤ/8)—24no—
68C11×AGL(1,ℤ/8)—24no—
69C2×C11×Q16—22no—
70C2×C11×SD16—22no—
71C2×C11×SD16—22no—
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—24no—
75C2×C11×D8—22no—
76C11×#131—28no—
77C11×#131—28no—
78C11×#131—24no—
79C11×#131—24no—
80C11×#131—24no—
81C11×#131D418yescomplemented
82C2×C11×M16—28no—
83C2×C11×M16—21no—
84C2×C11×M16—24no—
85C2×C11×M16—22no—
86C2×C11×M16—22no—
87C2×C11×M16C2312yes—
88C2×C11×M16C2312yes—
89C2×C11×M16C2312yes—
90C22×C8×C11—28no—
91C22×C8×C11—21no—
92C22×C8×C11—22no—
93C22×C8×C11—22no—
94C22×C8×C11—24no—
95C22×C8×C11D411yescharacteristic
96C22×C8×C11D411yescharacteristic
97C22×C8×C11D411yescharacteristic
98C22×C8×C11D411yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C11×C22⋊Q8—21no—
102C11×C22⋊Q8—21no—
103C11×C22⋊Q8—21no—
104C11×C22⋊Q8—21no—
105C11×#121—21no—
106C11×#121—21no—
107C11×#121—21no—
108C11×#121—21no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C11×#108—24no—
115C11×#106—21no—
116C11×#106—21no—
117C11×#103—22no—
118C11×#103—22no—
119C11×#103—21no—
120C11×#103—21no—
121C11×#102—22no—
122C11×#102—22no—
123C11×#102—21no—
124C11×#102—21no—
125C11×#101—24no—
126C11×#100—24no—
127C11×C22⋊C8—21no—
128C11×C22⋊C8—21no—
129C11×C22⋊C8—21no—
130C11×C22⋊C8—21no—
131#32941C1111yesmaximal, characteristic, direct product factor, Sylow
132C24×C11—21no—
133C24×C11—21no—
134C24×C11#4111yescharacteristic
135C11×#41—24no—
136C11×#41—28no—
137C11×#41—24no—
138C11×#41—24no—
139C11×#41—24no—
140C11×#41—22no—
141C11×#41—22no—
142C11×#41C2×D414yes—
143C11×#41#4114yes—
144C2×Q8×C11—24no—
145C2×Q8×C11—21no—
146C2×Q8×C11—22no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—22no—
150C2×Q8×C11C2×D412yes—
151C2×D4×C11—28no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—24no—
155C2×D4×C11—21no—
156C2×D4×C11—22no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—22no—
160C2×D4×C11—41no—
161C2×D4×C11—41no—
162C2×D4×C11—82no—
163C2×D4×C11C2×D412yes—
164C22×C4×C11—24no—
165C22×C4×C11—24no—
166C22×C4×C11—21no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11#4111yescharacteristic
179C22×C4×C11C2411yescharacteristic
180C11×Q16—44no—
181C11×SD16—42no—
182C11×SD16—42no—
183C11×SD16—44no—
184C11×SD16—44no—
185C11×D8—44no—
186C11×M16—28no—
187C11×M16—24no—
188C11×M16—28no—
189C11×M16—22no—
190C11×M16—22no—
191C11×M16—22no—
192C11×M16—22no—
193C11×M16—22no—
194C11×M16C2×D414yes—
195C2×C8×C11—24no—
196C2×C8×C11—28no—
197C2×C8×C11—22no—
198C2×C8×C11—28no—
199C2×C8×C11—22no—
200C2×C8×C11—22no—
201C2×C8×C11—22no—
202C2×C8×C11—22no—
203C2×C8×C11—22no—
204C2×C8×C11—22no—
205C2×C8×C11—22no—
206C2×C8×C11C2×D411yescharacteristic
207C2×C8×C11C2×D411yescharacteristic
208C2×C8×C11C2×D411yescharacteristic
209C2×C8×C11C2×D411yescharacteristic
210C2×C8×C11C2×D414yes—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—41no—
216C11×C4⋊C4—41no—
217C11×C22⋊C4—41no—
218C11×C22⋊C4—41no—
219C11×C22⋊C4—41no—
220C11×C22⋊C4—41no—
221C22×#131C2×C1111yescharacteristic, complemented
222C2×#471C2×C1112yescomplemented
223C2×#465C2×C1111yescharacteristic, complemented
224#3007C2×C1111yescharacteristic, complemented
225#3006C2×C1111yescharacteristic
226#1908C2×C1112yescomplemented
227#1907C2×C1112yescomplemented
228#1901C2×C1111yescharacteristic, complemented
229#1900C2×C1111yescharacteristic, complemented
230#1815C2×C1112yescomplemented
231#1810C2×C1111yescharacteristic, complemented
232C23×C11—24no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—41no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—41no—
240C23×C11—42no—
241C23×C11—81no—
242C23×C11—81no—
243C23×C11#12111yescharacteristic
244C23×C11#12111yescharacteristic
245C23×C11C2×#4111yescharacteristic
246Q8×C11—24no—
247Q8×C11—22no—
248Q8×C11—41no—
249Q8×C11—42no—
250Q8×C11—41no—
251Q8×C11#12114yes—
252D4×C11—28no—
253D4×C11—24no—
254D4×C11—24no—
255D4×C11—24no—
256D4×C11—22no—
257D4×C11—41no—
258D4×C11—42no—
259D4×C11—41no—
260D4×C11—82no—
261D4×C11—82no—
262D4×C11#12114yes—
263C2×C4×C11—24no—
264C2×C4×C11—28no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—24no—
269C2×C4×C11—21no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—21no—
273C2×C4×C11—24no—
274C2×C4×C11—21no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—42no—
279C2×C4×C11—81no—
280C2×C4×C11—81no—
281C2×C4×C11#12111yescharacteristic
282C2×C4×C11#12111yescharacteristic
283C2×C4×C11C22×D412yes—
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C2×#4112yes—
287C8×C11—21no—
288C8×C11—24no—
289C8×C11—21no—
290C8×C11—42no—
291C8×C11—42no—
292C8×C11#12012yes—
293C8×C11#12012yes—
294C22×#41C22×C1111yescharacteristic
295C2×#137C22×C1112yes—
296C2×AGL(1,ℤ/8)C22×C1112yes—
297C22×SD16C22×C1111yescharacteristic, complemented
298C2×#131—28no—
299C2×#131—21no—
300C2×#131—21no—
301C2×#131C22×C1112yes—
302C2×#131C22×C1112yes—
303C22×M16—21no—
304C22×M16C22×C1111yescharacteristic
305C23×C8—21no—
306C23×C8C22×C1111yescharacteristic
307C2×C22⋊Q8C22×C1111yescharacteristic
308C2×#121C22×C1111yescharacteristic
309#471—28no—
310#465—21no—
311#465—21no—
312#465—21no—
313#465—21no—
314#452—22no—
315#451—21no—
316#450—21no—
317#449—22no—
318#448—21no—
319#447—21no—
320C2×#108C22×C1112yescomplemented
321C2×#106C22×C1111yescharacteristic, complemented
322#417C22×C1112yes—
323#417C22×C1112yes—
324C2×#103C22×C1111yescharacteristic, complemented
325C2×#102C22×C1111yescharacteristic, complemented
326C2×#101C22×C1112yescomplemented
327C2×#100C22×C1112yescomplemented
328#407C22×C1111yescharacteristic
329#407C22×C1111yescharacteristic
330#343C22×C1112yescomplemented
331#343C22×C1112yescomplemented
332#341C22×C1112yescomplemented
333C22×C11—21no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—24no—
339C22×C11—21no—
340C22×C11—21no—
341C22×C11—44no—
342C22×C11—48no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—162no—
349C22×C11#47112yescomplemented
350C22×C11C2×#12111yescharacteristic
351C22×C11#52512yes—
352C4×C11—21no—
353C4×C11—24no—
354C4×C11—21no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11C2×#12011yescharacteristic
359C4×C11C2×#12112yes—
360C4×C11#52511yescharacteristic
361C2×#41—24no—
362C2×#41—24no—
363C2×#41—21no—
364C2×#41—21no—
365C2×#41D4×C1112yes—
366C2×#41C23×C1112yes—
367C22×Q8D4×C1111yescharacteristic
368C22×Q8C23×C1111yescharacteristic
369C22×D4—21no—
370C22×D4—21no—
371C22×D4D4×C1111yescharacteristic
372C22×D4C23×C1111yescharacteristic
373C23×C4—21no—
374C23×C4C23×C1111yescharacteristic
375#137—24no—
376#137—24no—
377AGL(1,ℤ/8)—24no—
378AGL(1,ℤ/8)—24no—
379C2×Q16—22no—
380C2×SD16—22no—
381C2×SD16—22no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—24no—
385C2×D8—22no—
386#131—28no—
387#131—28no—
388#131—24no—
389#131—24no—
390#131—24no—
391#131D4×C1118yescomplemented
392C2×M16—28no—
393C2×M16—21no—
394C2×M16—24no—
395C2×M16—22no—
396C2×M16—22no—
397C2×M16C23×C1112yes—
398C2×M16C23×C1112yes—
399C2×M16C23×C1112yes—
400C22×C8—28no—
401C22×C8—21no—
402C22×C8—22no—
403C22×C8—22no—
404C22×C8—24no—
405C22×C8D4×C1111yescharacteristic
406C22×C8D4×C1111yescharacteristic
407C22×C8D4×C1111yescharacteristic
408C22×C8D4×C1111yescharacteristic
409C22×C8C23×C1111yescharacteristic
410C22×C8C23×C1111yescharacteristic
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8—21no—
414C22⋊Q8—21no—
415#121—21no—
416#121—21no—
417#121—21no—
418#121—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4C23×C1111yescharacteristic
421C2×C4⋊C4C23×C1111yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424#108—24no—
425#106—21no—
426#106—21no—
427#103—22no—
428#103—22no—
429#103—21no—
430#103—21no—
431#102—22no—
432#102—22no—
433#102—21no—
434#102—21no—
435#101—24no—
436#100—24no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—21no—
440C22⋊C8—21no—
441C2×C11—22no—
442C2×C11—22no—
443C2×C11—41no—
444C2×C11—44no—
445C2×C11—161no—
446C2×C11#284711yescharacteristic
447C2×C11C2×#47111yescharacteristic
448C2×C11#306711yescharacteristic
449C24—21no—
450C24—21no—
451C24C11×#4111yescharacteristic
452#41—24no—
453#41—28no—
454#41—24no—
455#41—24no—
456#41—24no—
457#41—22no—
458#41—22no—
459#41C2×D4×C1114yes—
460#41C11×#4114yes—
461C2×Q8—24no—
462C2×Q8—21no—
463C2×Q8—22no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—22no—
467C2×Q8C2×D4×C1112yes—
468C2×D4—28no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—24no—
472C2×D4—21no—
473C2×D4—22no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—22no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—82no—
480C2×D4C2×D4×C1112yes—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4C2×D4×C1111yescharacteristic
492C22×C4C2×D4×C1111yescharacteristic
493C22×C4C2×D4×C1111yescharacteristic
494C22×C4C2×D4×C1111yescharacteristic
495C22×C4C11×#4111yescharacteristic
496C22×C4C24×C1111yescharacteristic
497Q16—44no—
498SD16—44no—
499SD16—44no—
500SD16—42no—
501SD16—42no—
502D8—44no—
503M16—24no—
504M16—28no—
505M16—22no—
506M16—28no—
507M16—22no—
508M16—22no—
509M16—22no—
510M16—22no—
511M16C2×D4×C1114yes—
512C2×C8—24no—
513C2×C8—28no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—28no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8C2×D4×C1111yescharacteristic
524C2×C8C2×D4×C1111yescharacteristic
525C2×C8C2×D4×C1111yescharacteristic
526C2×C8C2×D4×C1111yescharacteristic
527C2×C8C2×D4×C1114yes—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C22⋊C4—41no—
538C11#3294111yescharacteristic, direct product factor, Sylow
539C23—24no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—41no—
544C23—42no—
545C23—42no—
546C23—41no—
547C23—42no—
548C23—81no—
549C23—81no—
550C23C11×#12111yescharacteristic
551C23C11×#12111yescharacteristic
552C23C2×C11×#4111yescharacteristic
553Q8—24no—
554Q8—22no—
555Q8—41no—
556Q8—42no—
557Q8—41no—
558Q8C11×#12114yes—
559D4—28no—
560D4—24no—
561D4—24no—
562D4—24no—
563D4—22no—
564D4—41no—
565D4—42no—
566D4—41no—
567D4—82no—
568D4—82no—
569D4C11×#12114yes—
570C2×C4—24no—
571C2×C4—28no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—24no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—24no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—81no—
587C2×C4—81no—
588C2×C4C11×#12111yescharacteristic
589C2×C4C11×#12111yescharacteristic
590C2×C4C22×D4×C1112yes—
591C2×C4C22×D4×C1111yescharacteristic
592C2×C4C22×D4×C1111yescharacteristic
593C2×C4C2×C11×#4112yes—
594C8—21no—
595C8—24no—
596C8—21no—
597C8—42no—
598C8—42no—
599C8C11×#12012yes—
600C8C11×#12012yes—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—24no—
609C22—44no—
610C22—48no—
611C22—42no—
612C22—42no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—162no—
617C22C11×#47112yescomplemented
618C22C2×C11×#12111yescharacteristic
619C22C11×#52512yes—
620C4—21no—
621C4—24no—
622C4—21no—
623C4—81no—
624C4—81no—
625C4—81no—
626C4C2×C11×#12011yescharacteristic
627C4C2×C11×#12112yes—
628C4C11×#52511yescharacteristic
629C2—22no—
630C2—22no—
631C2—41no—
632C2—44no—
633C2—161no—
634C2C11×#284711yescharacteristic
635C2C2×C11×#47111yescharacteristic
636C2C11×#306711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3006C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#131C2semidirect
2. C2×C11×#471C2semidirect
3. C2×C11×#465C2semidirect
4. C11×#3007C2semidirect
6. C11×#1908C2semidirect
7. C11×#1907C2semidirect
8. C11×#1901C2semidirect
9. C11×#1900C2semidirect
10. C11×#1815C2semidirect
11. C11×#1810C2semidirect
15. C22×C11×SD16C22semidirect
38. C2×C11×#108C22semidirect
39. C2×C11×#106C22semidirect
42. C2×C11×#103C22semidirect
43. C2×C11×#102C22semidirect
44. C2×C11×#101C22semidirect
45. C2×C11×#100C22semidirect
48. C11×#343C22semidirect
49. C11×#343C22semidirect
50. C11×#341C22semidirect
81. C11×#131D4semidirect
131. #32941C11direct (N × H)
221. C22×#131C2×C11semidirect
222. C2×#471C2×C11semidirect
223. C2×#465C2×C11semidirect
224. #3007C2×C11semidirect
226. #1908C2×C11semidirect
227. #1907C2×C11semidirect
228. #1901C2×C11semidirect
229. #1900C2×C11semidirect
230. #1815C2×C11semidirect
231. #1810C2×C11semidirect
297. C22×SD16C22×C11semidirect
320. C2×#108C22×C11semidirect
321. C2×#106C22×C11semidirect
324. C2×#103C22×C11semidirect
325. C2×#102C22×C11semidirect
326. C2×#101C22×C11semidirect
327. C2×#100C22×C11semidirect
330. #343C22×C11semidirect
331. #343C22×C11semidirect
332. #341C22×C11semidirect
349. C22×C11#471semidirect
391. #131D4×C11semidirect
538. C11#32941direct (N × H)
617. C22C11×#471semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1312
C2×C11×#4712
C2×C11×#4652
C11×#30072
C11×#30062
C11×#19082
C11×#19072
C11×#19012
C11×#19002
C11×#18152
C11×#18102
#3294111