Finite Group Databasebeta

← C11×#19072 #14596265

Subgroups — C11×#19072 #14596265

Order 2816.

992 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3545C211yesmaximal, characteristic, complemented
2C11×#3180C212yesmaximal, complemented
3C11×#3153C211yesmaximal, characteristic, complemented
4C11×#1661C212yesmaximal, complemented
5C11×#1660C211yesmaximal, characteristic, complemented
6C11×#1659C211yesmaximal, characteristic, complemented
7C11×#1657C211yesmaximal, characteristic, complemented
8C11×#1656C212yesmaximal, complemented
9C11×#1655C211yesmaximal, characteristic, complemented
10C11×#1524C212yesmaximal, complemented
11C2×C11×#329C211yesmaximal, characteristic, complemented
12C2×C11×#137—21no—
13C2×C11×AGL(1,ℤ/8)—21no—
14C11×#563C2211yescharacteristic
15C11×#562C2212yes—
16C11×H(3,𝔽4)C2211yescharacteristic
17C11×#555—21no—
18C11×#551—21no—
19C11×#551—22no—
20C11×#546—22no—
21C11×#542—22no—
22C11×#538—22no—
23C11×#536—21no—
24C11×#534—21no—
25C11×#532C2211yescharacteristic, complemented
26C11×#529C2212yes—
27C2×C11×#124C2211yescharacteristic
28C11×#501C2212yescomplemented
29C11×#497C2211yescharacteristic
30C11×#497C2211yescharacteristic, complemented
31C11×#496C2211yescharacteristic
32C11×#496C2211yescharacteristic, complemented
33C11×#496C2212yescomplemented
34C11×#495—21no—
35C11×#495—21no—
36C11×#490C2212yescomplemented
37C11×#489C2212yescomplemented
38C11×#466—22no—
39C11×#465—22no—
40C11×#442—22no—
41C11×#440—22no—
42C4×C11×M16C2211yescharacteristic, complemented
43C2×C11×#97C2212yescomplemented
44C11×#330C2212yescomplemented
45C11×#330C2212yescomplemented
46C11×#329C2211yescharacteristic
47C11×#329C2211yescharacteristic
48C11×#329C2212yescomplemented
49C11×#329C2212yescomplemented
50C11×#329C2212yescomplemented
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C22×Q8×C11D411yescharacteristic
54C22×D4×C11—21no—
55C22×D4×C11D411yescharacteristic
56C11×#137—44no—
57C11×AGL(1,ℤ/8)—44no—
58C2×C11×Q16—21no—
59C2×C11×Q16—21no—
60C2×C11×SD16—21no—
61C2×C11×SD16—21no—
62C2×C11×SD16—22no—
63C2×C11×SD16—21no—
64C2×C11×SD16—21no—
65C2×C11×D8—21no—
66C2×C11×D8—21no—
67C2×C11×D8—22no—
68C2×C11×M16—21no—
69C22×C8×C11—22no—
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8C2311yescharacteristic
73C11×#127C2311yescharacteristic
74C11×#126—22no—
75C11×#126—22no—
76C11×#126—22no—
77C11×#125C2312yes—
78C11×#124—21no—
79C11×#124—22no—
80C11×#124—21no—
81C11×#124—22no—
82C11×#124—22no—
83C11×#124—21no—
84C11×#124D411yescharacteristic
85C11×#124D411yescharacteristic
86C11×#124C2312yes—
87C11×#124C2311yescharacteristic
88C11×#124C2311yescharacteristic
89C11×#123—21no—
90C11×#123—22no—
91C11×#123—22no—
92C11×#123—21no—
93C11×#123—22no—
94C11×#123—22no—
95C11×#123—22no—
96C11×C22⋊Q8—22no—
97C11×C22⋊Q8—22no—
98C11×C22⋊Q8—22no—
99C11×C22⋊Q8—22no—
100C11×C22⋊Q8D412yes—
101C11×#121—22no—
102C11×#121—22no—
103C11×#121—22no—
104C11×#121—22no—
105C11×#121—22no—
106C11×#121D412yes—
107C11×#120—21no—
108C11×#120—22no—
109C11×#120—21no—
110C11×#120—22no—
111C4×Q8×C11D412yes—
112C4×D4×C11—22no—
113C4×D4×C11—22no—
114C4×D4×C11—22no—
115C4×D4×C11—22no—
116C4×D4×C11D412yes—
117C11×#117—21no—
118C11×#117—22no—
119C11×#117—22no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—22no—
122C2×C11×C22⋊C4—22no—
123C2×C42×C11C2311yescharacteristic
124C11×#107—22no—
125C11×#106—22no—
126C11×#103—22no—
127C11×#102—22no—
128C11×#102—22no—
129C11×#102—22no—
130C11×#97—22no—
131C11×#97C2312yes—
132C11×#97C2312yes—
133C11×#97C2311yescharacteristic
134C11×#97C2311yescharacteristic
135C4×C8×C11—21no—
136#19072C1111yesmaximal, characteristic, direct product factor, Sylow
137C24×C11—21no—
138C24×C11—21no—
139C11×#41—42no—
140C11×#41—42no—
141C11×#41—82no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—42no—
146C2×Q8×C11C2×D412yes—
147C2×Q8×C11C2×D411yescharacteristic
148C2×Q8×C11C2×D411yescharacteristic
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—21no—
153C2×D4×C11—22no—
154C2×D4×C11—21no—
155C2×D4×C11—22no—
156C2×D4×C11—21no—
157C2×D4×C11—42no—
158C2×D4×C11—41no—
159C2×D4×C11—82no—
160C2×D4×C11C2×D412yes—
161C2×D4×C11C2×D411yescharacteristic
162C2×D4×C11C2×D411yescharacteristic
163C22×C4×C11—21no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—21no—
167C22×C4×C11—22no—
168C22×C4×C11—41no—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D412yes—
171C11×Q16—42no—
172C11×Q16—42no—
173C11×SD16—44no—
174C11×SD16—42no—
175C11×SD16—42no—
176C11×SD16—42no—
177C11×SD16—42no—
178C11×D8—44no—
179C11×D8—42no—
180C11×D8—42no—
181C11×M16—24no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—22no—
185C2×C8×C11—22no—
186C2×C8×C11—44no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4C2×D412yes—
196C11×C4⋊C4C2×D412yes—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—21no—
199C11×C22⋊C4—21no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—42no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—22no—
216C42×C11C2×D411yescharacteristic
217C42×C11C2×D412yes—
218C42×C11C2411yescharacteristic
219#3545C2×C1111yescharacteristic, complemented
220#3180C2×C1112yescomplemented
221#3153C2×C1111yescharacteristic, complemented
222#1661C2×C1112yescomplemented
223#1660C2×C1111yescharacteristic, complemented
224#1659C2×C1111yescharacteristic, complemented
225#1657C2×C1111yescharacteristic, complemented
226#1656C2×C1112yescomplemented
227#1655C2×C1111yescharacteristic, complemented
228#1524C2×C1112yescomplemented
229C2×#329C2×C1111yescharacteristic, complemented
230C23×C11—21no—
231C23×C11—22no—
232C23×C11—21no—
233C23×C11—42no—
234C23×C11—41no—
235C23×C11—82no—
236C23×C11—81no—
237C23×C11—82no—
238C23×C11#12011yescharacteristic
239Q8×C11—41no—
240Q8×C11—41no—
241Q8×C11—42no—
242Q8×C11—41no—
243Q8×C11—41no—
244Q8×C11—81no—
245Q8×C11—81no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—42no—
249D4×C11—41no—
250D4×C11—42no—
251D4×C11—41no—
252D4×C11—42no—
253D4×C11—44no—
254D4×C11—81no—
255D4×C11—82no—
256D4×C11—82no—
257D4×C11—82no—
258D4×C11—81no—
259D4×C11—82no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—41no—
269C2×C4×C11—82no—
270C2×C4×C11—82no—
271C2×C4×C11—82no—
272C2×C4×C11—81no—
273C2×C4×C11—82no—
274C2×C4×C11#12012yes—
275C2×C4×C11#12011yescharacteristic
276C2×C4×C11C22×D412yes—
277C2×C4×C11C22×D411yescharacteristic
278C8×C11—24no—
279C8×C11—22no—
280C8×C11—22no—
281C8×C11—42no—
282C2×#137—21no—
283C2×AGL(1,ℤ/8)—21no—
284#563C22×C1111yescharacteristic
285#562C22×C1112yes—
286H(3,𝔽4)C22×C1111yescharacteristic
287#555—21no—
288#551—21no—
289#551—22no—
290#546—22no—
291#542—22no—
292#538—22no—
293#536—21no—
294#534—21no—
295#532C22×C1111yescharacteristic, complemented
296#529C22×C1112yes—
297C2×#124C22×C1111yescharacteristic
298#501C22×C1112yescomplemented
299#497C22×C1111yescharacteristic
300#497C22×C1111yescharacteristic, complemented
301#496C22×C1111yescharacteristic
302#496C22×C1111yescharacteristic, complemented
303#496C22×C1112yescomplemented
304#495—21no—
305#495—21no—
306#490C22×C1112yescomplemented
307#489C22×C1112yescomplemented
308#466—22no—
309#465—22no—
310#442—22no—
311#440—22no—
312C4×M16C22×C1111yescharacteristic, complemented
313C2×#97C22×C1112yescomplemented
314#330C22×C1112yescomplemented
315#330C22×C1112yescomplemented
316#329C22×C1111yescharacteristic
317#329C22×C1111yescharacteristic
318#329C22×C1112yescomplemented
319#329C22×C1112yescomplemented
320#329C22×C1112yescomplemented
321C22×C11—22no—
322C22×C11—42no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—81no—
330C22×C11—82no—
331C22×C11—162no—
332C22×C11—162no—
333C22×C11#45312yes—
334C22×C11C2×#12011yescharacteristic
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—22no—
338C4×C11—22no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—42no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11—81no—
345C2×#41—21no—
346C2×#41—21no—
347C22×Q8D4×C1111yescharacteristic
348C22×D4—21no—
349C22×D4D4×C1111yescharacteristic
350#137—44no—
351AGL(1,ℤ/8)—44no—
352C2×Q16—21no—
353C2×Q16—21no—
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16—22no—
357C2×SD16—21no—
358C2×SD16—21no—
359C2×D8—21no—
360C2×D8—21no—
361C2×D8—22no—
362C2×M16—21no—
363C22×C8—22no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8C23×C1111yescharacteristic
367#127C23×C1111yescharacteristic
368#126—22no—
369#126—22no—
370#126—22no—
371#125C23×C1112yes—
372#124—21no—
373#124—22no—
374#124—21no—
375#124—22no—
376#124—22no—
377#124—21no—
378#124D4×C1111yescharacteristic
379#124D4×C1111yescharacteristic
380#124C23×C1111yescharacteristic
381#124C23×C1111yescharacteristic
382#124C23×C1112yes—
383#123—21no—
384#123—22no—
385#123—22no—
386#123—21no—
387#123—22no—
388#123—22no—
389#123—22no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8D4×C1112yes—
395#121—22no—
396#121—22no—
397#121—22no—
398#121—22no—
399#121—22no—
400#121D4×C1112yes—
401#120—21no—
402#120—22no—
403#120—21no—
404#120—22no—
405C4×Q8D4×C1112yes—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4D4×C1112yes—
411#117—21no—
412#117—22no—
413#117—22no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C42C23×C1111yescharacteristic
418#107—22no—
419#106—22no—
420#103—22no—
421#102—22no—
422#102—22no—
423#102—22no—
424#97—22no—
425#97C23×C1112yes—
426#97C23×C1112yes—
427#97C23×C1111yescharacteristic
428#97C23×C1111yescharacteristic
429C4×C8—21no—
430C2×C11—22no—
431C2×C11—82no—
432C2×C11—81no—
433C2×C11—81no—
434C2×C11—161no—
435C2×C11C2×#45311yescharacteristic
436C2×C11#301812yes—
437C24—21no—
438C24—21no—
439#41—42no—
440#41—42no—
441#41—82no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—42no—
446C2×Q8C2×D4×C1112yes—
447C2×Q8C2×D4×C1111yescharacteristic
448C2×Q8C2×D4×C1111yescharacteristic
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—21no—
453C2×D4—22no—
454C2×D4—21no—
455C2×D4—22no—
456C2×D4—21no—
457C2×D4—42no—
458C2×D4—41no—
459C2×D4—82no—
460C2×D4C2×D4×C1112yes—
461C2×D4C2×D4×C1111yescharacteristic
462C2×D4C2×D4×C1111yescharacteristic
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—41no—
469C22×C4C2×D4×C1111yescharacteristic
470C22×C4C2×D4×C1112yes—
471Q16—42no—
472Q16—42no—
473SD16—42no—
474SD16—42no—
475SD16—42no—
476SD16—42no—
477SD16—44no—
478D8—42no—
479D8—42no—
480D8—44no—
481M16—24no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—44no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4C2×D4×C1112yes—
496C4⋊C4C2×D4×C1112yes—
497C22⋊C4—22no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—42no—
513C42—21no—
514C42—21no—
515C42—22no—
516C42C2×D4×C1111yescharacteristic
517C42C2×D4×C1112yes—
518C42C24×C1111yescharacteristic
519C11#1907211yescharacteristic, direct product factor, Sylow
520C23—21no—
521C23—22no—
522C23—21no—
523C23—42no—
524C23—41no—
525C23—82no—
526C23—81no—
527C23—82no—
528C23C11×#12011yescharacteristic
529Q8—41no—
530Q8—41no—
531Q8—42no—
532Q8—41no—
533Q8—41no—
534Q8—81no—
535Q8—81no—
536D4—41no—
537D4—41no—
538D4—42no—
539D4—41no—
540D4—42no—
541D4—41no—
542D4—42no—
543D4—44no—
544D4—81no—
545D4—82no—
546D4—82no—
547D4—82no—
548D4—81no—
549D4—82no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4—81no—
563C2×C4—82no—
564C2×C4C11×#12012yes—
565C2×C4C11×#12011yescharacteristic
566C2×C4C22×D4×C1112yes—
567C2×C4C22×D4×C1111yescharacteristic
568C8—24no—
569C8—22no—
570C8—22no—
571C8—42no—
572C22—22no—
573C22—42no—
574C22—41no—
575C22—41no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—81no—
581C22—82no—
582C22—162no—
583C22—162no—
584C22C11×#45312yes—
585C22C2×C11×#12011yescharacteristic
586C4—21no—
587C4—21no—
588C4—22no—
589C4—22no—
590C4—41no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—42no—
595C4—81no—
596C2—22no—
597C2—81no—
598C2—82no—
599C2—81no—
600C2—161no—
601C2C2×C11×#45311yescharacteristic
602C2C11×#301812yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3545C2semidirect
2. C11×#3180C2semidirect
3. C11×#3153C2semidirect
4. C11×#1661C2semidirect
5. C11×#1660C2semidirect
6. C11×#1659C2semidirect
7. C11×#1657C2semidirect
8. C11×#1656C2semidirect
9. C11×#1655C2semidirect
10. C11×#1524C2semidirect
11. C2×C11×#329C2semidirect
25. C11×#532C22semidirect
28. C11×#501C22semidirect
30. C11×#497C22semidirect
32. C11×#496C22semidirect
33. C11×#496C22semidirect
36. C11×#490C22semidirect
37. C11×#489C22semidirect
42. C4×C11×M16C22semidirect
43. C2×C11×#97C22semidirect
44. C11×#330C22semidirect
45. C11×#330C22semidirect
48. C11×#329C22semidirect
49. C11×#329C22semidirect
50. C11×#329C22semidirect
136. #19072C11direct (N × H)
219. #3545C2×C11semidirect
220. #3180C2×C11semidirect
221. #3153C2×C11semidirect
222. #1661C2×C11semidirect
223. #1660C2×C11semidirect
224. #1659C2×C11semidirect
225. #1657C2×C11semidirect
226. #1656C2×C11semidirect
227. #1655C2×C11semidirect
228. #1524C2×C11semidirect
229. C2×#329C2×C11semidirect
295. #532C22×C11semidirect
298. #501C22×C11semidirect
300. #497C22×C11semidirect
302. #496C22×C11semidirect
303. #496C22×C11semidirect
306. #490C22×C11semidirect
307. #489C22×C11semidirect
312. C4×M16C22×C11semidirect
313. C2×#97C22×C11semidirect
314. #330C22×C11semidirect
315. #330C22×C11semidirect
318. #329C22×C11semidirect
319. #329C22×C11semidirect
320. #329C22×C11semidirect
519. C11#19072direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35452
C11×#31802
C11×#31532
C11×#16612
C11×#16602
C11×#16592
C11×#16572
C11×#16562
C11×#16552
C11×#15242
C2×C11×#3292
#1907211