Finite Group Databasebeta

← C11×#23998 #14601191

Subgroups — C11×#23998 #14601191

Order 2816.

1266 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3508C211yesmaximal, characteristic, complemented
2C11×#3019C211yesmaximal, characteristic, complemented
3C2×C11×#453C211yesmaximal, characteristic, complemented
4C11×#2883C211yesmaximal, characteristic, complemented
5C11×#2031C212yesmaximal, complemented
6C11×#2008C212yesmaximal, complemented
7C11×#1911C211yesmaximal, characteristic, complemented
8C11×#1906C212yesmaximal, complemented
9C11×#1904C212yesmaximal, complemented
10C11×#1887C211yesmaximal, characteristic, complemented
11C11×#1829C211yesmaximal, characteristic, complemented
12C2×C11×H(5,𝔽2)C2211yescharacteristic
13C11×#575C2212yes—
14C2×C11×AGL(1,ℤ/8)C2212yes—
15C11×#559—22no—
16C11×#550—22no—
17C11×#546—24no—
18C11×#540—22no—
19C11×#535C2211yescharacteristic
20C11×#535C2211yescharacteristic, complemented
21C11×#533C2211yescharacteristic, complemented
22C11×#532—22no—
23C2×C11×#127C2211yescharacteristic
24C11×#518C2211yescharacteristic
25C11×#518C2211yescharacteristic
26C11×#518C2211yescharacteristic, complemented
27C4×C11×#41C2211yescharacteristic, complemented
28C11×#455—22no—
29C11×#453—22no—
30C11×#453—22no—
31C11×#453—22no—
32C11×#421C2212yes—
33C11×#421C2212yescomplemented
34C2×C11×#104C2212yes—
35C11×#418C2212yescomplemented
36C2×C11×#100C2211yescharacteristic
37C2×C11×#100C2211yescharacteristic
38C11×#410C2212yes—
39C11×#410C2212yes—
40C2×C11×#99—24no—
41C11×#344C2212yescomplemented
42C11×#344C2212yescomplemented
43C11×#339C2212yescomplemented
44C11×H(3,ℤ/4)C2212yescomplemented
45C11×H(5,𝔽2)—22no—
46C11×H(5,𝔽2)—22no—
47C11×H(5,𝔽2)—42no—
48C2×C11×#41—24no—
49C2×C11×#41—22no—
50C2×C11×#41C2311yescharacteristic
51C2×C11×#41C2312yes—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C11×#137—22no—
58C11×#137—22no—
59C11×AGL(1,ℤ/8)—24no—
60C11×AGL(1,ℤ/8)—22no—
61C11×AGL(1,ℤ/8)—22no—
62C11×AGL(1,ℤ/8)—42no—
63C11×#135—42no—
64C2×C11×SD16—22no—
65C2×C11×D8—22no—
66C2×C11×M16C2312yes—
67C2×C11×M16C2312yes—
68C11×C4⋊Q8—21no—
69C11×#127—22no—
70C11×#127—21no—
71C11×#127D412yes—
72C11×#127D412yes—
73C11×#127D412yes—
74C11×#125—21no—
75C11×#124—24no—
76C11×#124—21no—
77C11×#124D412yes—
78C11×#123—24no—
79C11×#123—24no—
80C11×C22⋊Q8—22no—
81C11×#121—24no—
82C11×#121—24no—
83C11×#121—24no—
84C11×#121—22no—
85C11×#121—22no—
86C11×#120—22no—
87C11×#120—22no—
88C4×Q8×C11—21no—
89C4×Q8×C11—22no—
90C4×D4×C11—24no—
91C4×D4×C11—21no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—42no—
98C11×#117—21no—
99C11×#117C2312yes—
100C11×#117C2311yescharacteristic
101C11×#117C2311yescharacteristic
102C11×#117C2311yescharacteristic
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4D414yes—
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108C11×#104—22no—
109C11×#104—22no—
110C11×#104—24no—
111C11×#104—42no—
112C11×#102—42no—
113C11×#100—22no—
114C11×#100—22no—
115C11×#99—24no—
116C11×#99—24no—
117#23998C1111yesmaximal, characteristic, direct product factor, Sylow
118C24×C11—22no—
119C24×C11—21no—
120C24×C11C2×D412yes—
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—22no—
124C11×#41—22no—
125C11×#41—22no—
126C11×#41—22no—
127C11×#41—44no—
128C11×#41—44no—
129C11×#41—88no—
130C2×Q8×C11—22no—
131C2×Q8×C11C2×D411yescharacteristic
132C2×Q8×C11#4112yescomplemented
133C2×D4×C11—24no—
134C2×D4×C11—24no—
135C2×D4×C11—22no—
136C2×D4×C11—21no—
137C2×D4×C11—24no—
138C2×D4×C11—24no—
139C2×D4×C11—24no—
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—44no—
146C2×D4×C11—44no—
147C2×D4×C11—44no—
148C2×D4×C11—44no—
149C2×D4×C11—84no—
150C2×D4×C11C2×D412yes—
151C2×D4×C11C2×D411yescharacteristic
152C2×D4×C11C2×D412yes—
153C2×D4×C11C2×D412yes—
154C2×D4×C11#4112yescomplemented
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—21no—
158C22×C4×C11—24no—
159C22×C4×C11—24no—
160C22×C4×C11—21no—
161C22×C4×C11—22no—
162C22×C4×C11—42no—
163C22×C4×C11C2411yescharacteristic
164C11×Q16—42no—
165C11×SD16—44no—
166C11×SD16—42no—
167C11×SD16—42no—
168C11×D8—44no—
169C11×D8—42no—
170C11×M16—22no—
171C11×M16—22no—
172C11×M16—22no—
173C11×M16—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—22no—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—24no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—42no—
192C11×C22⋊C4C2×D412yes—
193C11×C22⋊C4C2×D412yes—
194C42×C11—22no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—22no—
199C42×C11C2×D411yescharacteristic
200C42×C11C2×D411yescharacteristic
201C42×C11C2×D412yes—
202#3508C2×C1111yescharacteristic, complemented
203#3019C2×C1111yescharacteristic, complemented
204C2×#453C2×C1111yescharacteristic, complemented
205#2883C2×C1111yescharacteristic, complemented
206#2031C2×C1112yescomplemented
207#2008C2×C1112yescomplemented
208#1911C2×C1111yescharacteristic, complemented
209#1906C2×C1112yescomplemented
210#1904C2×C1112yescomplemented
211#1887C2×C1111yescharacteristic, complemented
212#1829C2×C1111yescharacteristic, complemented
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—21no—
217C23×C11—22no—
218C23×C11—44no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—82no—
222C23×C11—82no—
223C23×C11—162no—
224C23×C11#12014yes—
225C23×C11C22×D411yescharacteristic
226Q8×C11—22no—
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—44no—
230D4×C11—24no—
231D4×C11—24no—
232D4×C11—22no—
233D4×C11—24no—
234D4×C11—22no—
235D4×C11—22no—
236D4×C11—48no—
237D4×C11—48no—
238D4×C11—42no—
239D4×C11—41no—
240D4×C11—42no—
241D4×C11—41no—
242D4×C11—42no—
243D4×C11—84no—
244D4×C11—84no—
245D4×C11—84no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—42no—
254C2×C4×C11—44no—
255C2×C4×C11—44no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—84no—
261C2×C4×C11—84no—
262C2×C4×C11—162no—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C2×#4112yes—
266C2×C4×C11H(5,𝔽2)12yes—
267C8×C11—42no—
268C8×C11—42no—
269C2×H(5,𝔽2)C22×C1111yescharacteristic
270#575C22×C1112yes—
271C2×AGL(1,ℤ/8)C22×C1112yes—
272#559—22no—
273#550—22no—
274#546—24no—
275#540—22no—
276#535C22×C1111yescharacteristic
277#535C22×C1111yescharacteristic, complemented
278#533C22×C1111yescharacteristic, complemented
279#532—22no—
280C2×#127C22×C1111yescharacteristic
281#518C22×C1111yescharacteristic
282#518C22×C1111yescharacteristic
283#518C22×C1111yescharacteristic, complemented
284C4×#41C22×C1111yescharacteristic, complemented
285#455—22no—
286#453—22no—
287#453—22no—
288#453—22no—
289#421C22×C1112yes—
290#421C22×C1112yescomplemented
291C2×#104C22×C1112yes—
292#418C22×C1112yescomplemented
293C2×#100C22×C1111yescharacteristic
294C2×#100C22×C1111yescharacteristic
295#410C22×C1112yes—
296#410C22×C1112yes—
297C2×#99—24no—
298#344C22×C1112yescomplemented
299#344C22×C1112yescomplemented
300#339C22×C1112yescomplemented
301H(3,ℤ/4)C22×C1112yescomplemented
302C22×C11—24no—
303C22×C11—41no—
304C22×C11—44no—
305C22×C11—42no—
306C22×C11—44no—
307C22×C11—42no—
308C22×C11—41no—
309C22×C11—42no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11—82no—
313C22×C11—161no—
314C22×C11—161no—
315C22×C11—164no—
316C22×C11C2×#12011yescharacteristic
317C22×C11#52511yescharacteristic
318C22×C11#53511yescharacteristic
319C4×C11—22no—
320C4×C11—42no—
321C4×C11—41no—
322C4×C11—42no—
323C4×C11—42no—
324C4×C11—42no—
325C4×C11—41no—
326C4×C11—82no—
327C4×C11#54612yes—
328C4×C11#54612yes—
329H(5,𝔽2)—22no—
330H(5,𝔽2)—22no—
331H(5,𝔽2)—42no—
332C2×#41—24no—
333C2×#41—22no—
334C2×#41C23×C1111yescharacteristic
335C2×#41C23×C1112yes—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4C23×C1111yescharacteristic
340C22×D4C23×C1111yescharacteristic
341#137—22no—
342#137—22no—
343AGL(1,ℤ/8)—24no—
344AGL(1,ℤ/8)—22no—
345AGL(1,ℤ/8)—22no—
346AGL(1,ℤ/8)—42no—
347#135—42no—
348C2×SD16—22no—
349C2×D8—22no—
350C2×M16C23×C1112yes—
351C2×M16C23×C1112yes—
352C4⋊Q8—21no—
353#127—22no—
354#127—21no—
355#127D4×C1112yes—
356#127D4×C1112yes—
357#127D4×C1112yes—
358#125—21no—
359#124—24no—
360#124—21no—
361#124D4×C1112yes—
362#123—24no—
363#123—24no—
364C22⋊Q8—22no—
365#121—24no—
366#121—24no—
367#121—24no—
368#121—22no—
369#121—22no—
370#120—22no—
371#120—22no—
372C4×Q8—21no—
373C4×Q8—22no—
374C4×D4—24no—
375C4×D4—21no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—42no—
382#117—21no—
383#117C23×C1112yes—
384#117C23×C1111yescharacteristic
385#117C23×C1111yescharacteristic
386#117C23×C1111yescharacteristic
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4D4×C1114yes—
390C2×C42—21no—
391C2×C42C23×C1111yescharacteristic
392#104—22no—
393#104—22no—
394#104—24no—
395#104—42no—
396#102—42no—
397#100—22no—
398#100—22no—
399#99—24no—
400#99—24no—
401C2×C11—21no—
402C2×C11—21no—
403C2×C11—21no—
404C2×C11—44no—
405C2×C11—81no—
406C2×C11—82no—
407C2×C11—82no—
408C2×C11#240411yescharacteristic
409C24—22no—
410C24—21no—
411C24C2×D4×C1112yes—
412#41—22no—
413#41—22no—
414#41—22no—
415#41—22no—
416#41—22no—
417#41—22no—
418#41—44no—
419#41—44no—
420#41—88no—
421C2×Q8—22no—
422C2×Q8C2×D4×C1111yescharacteristic
423C2×Q8C11×#4112yescomplemented
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—24no—
431C2×D4—21no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—44no—
437C2×D4—44no—
438C2×D4—44no—
439C2×D4—44no—
440C2×D4—84no—
441C2×D4C2×D4×C1112yes—
442C2×D4C2×D4×C1111yescharacteristic
443C2×D4C2×D4×C1112yes—
444C2×D4C2×D4×C1112yes—
445C2×D4C11×#4112yescomplemented
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—42no—
454C22×C4C24×C1111yescharacteristic
455Q16—42no—
456SD16—44no—
457SD16—42no—
458SD16—42no—
459D8—44no—
460D8—42no—
461M16—22no—
462M16—22no—
463M16—22no—
464M16—22no—
465C2×C8—22no—
466C2×C8—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C22⋊C4—24no—
476C22⋊C4—22no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—21no—
481C22⋊C4—22no—
482C22⋊C4—42no—
483C22⋊C4C2×D4×C1112yes—
484C22⋊C4C2×D4×C1112yes—
485C42—22no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—22no—
490C42C2×D4×C1111yescharacteristic
491C42C2×D4×C1111yescharacteristic
492C42C2×D4×C1112yes—
493C11#2399811yescharacteristic, direct product factor, Sylow
494C23—22no—
495C23—22no—
496C23—22no—
497C23—21no—
498C23—22no—
499C23—44no—
500C23—41no—
501C23—41no—
502C23—82no—
503C23—82no—
504C23—162no—
505C23C11×#12014yes—
506C23C22×D4×C1111yescharacteristic
507Q8—22no—
508Q8—22no—
509Q8—22no—
510Q8—44no—
511D4—24no—
512D4—24no—
513D4—22no—
514D4—24no—
515D4—22no—
516D4—22no—
517D4—48no—
518D4—48no—
519D4—42no—
520D4—41no—
521D4—42no—
522D4—41no—
523D4—42no—
524D4—84no—
525D4—84no—
526D4—84no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—42no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—84no—
542C2×C4—84no—
543C2×C4—162no—
544C2×C4C22×D4×C1111yescharacteristic
545C2×C4C22×D4×C1111yescharacteristic
546C2×C4C2×C11×#4112yes—
547C2×C4C11×H(5,𝔽2)12yes—
548C8—42no—
549C8—42no—
550C22—24no—
551C22—41no—
552C22—44no—
553C22—42no—
554C22—44no—
555C22—42no—
556C22—41no—
557C22—42no—
558C22—82no—
559C22—82no—
560C22—82no—
561C22—161no—
562C22—161no—
563C22—164no—
564C22C2×C11×#12011yescharacteristic
565C22C11×#52511yescharacteristic
566C22C11×#53511yescharacteristic
567C4—22no—
568C4—42no—
569C4—41no—
570C4—42no—
571C4—42no—
572C4—42no—
573C4—41no—
574C4—82no—
575C4C11×#54612yes—
576C4C11×#54612yes—
577C2—21no—
578C2—21no—
579C2—21no—
580C2—44no—
581C2—82no—
582C2—81no—
583C2—82no—
584C2C11×#240411yescharacteristic
subgroupG/H
center, socleC2×C11#2404
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3508C2semidirect
2. C11×#3019C2semidirect
3. C2×C11×#453C2semidirect
4. C11×#2883C2semidirect
5. C11×#2031C2semidirect
6. C11×#2008C2semidirect
7. C11×#1911C2semidirect
8. C11×#1906C2semidirect
9. C11×#1904C2semidirect
10. C11×#1887C2semidirect
11. C11×#1829C2semidirect
20. C11×#535C22semidirect
21. C11×#533C22semidirect
26. C11×#518C22semidirect
27. C4×C11×#41C22semidirect
33. C11×#421C22semidirect
35. C11×#418C22semidirect
41. C11×#344C22semidirect
42. C11×#344C22semidirect
43. C11×#339C22semidirect
44. C11×H(3,ℤ/4)C22semidirect
117. #23998C11direct (N × H)
132. C2×Q8×C11#41semidirect
154. C2×D4×C11#41semidirect
202. #3508C2×C11semidirect
203. #3019C2×C11semidirect
204. C2×#453C2×C11semidirect
205. #2883C2×C11semidirect
206. #2031C2×C11semidirect
207. #2008C2×C11semidirect
208. #1911C2×C11semidirect
209. #1906C2×C11semidirect
210. #1904C2×C11semidirect
211. #1887C2×C11semidirect
212. #1829C2×C11semidirect
277. #535C22×C11semidirect
278. #533C22×C11semidirect
283. #518C22×C11semidirect
284. C4×#41C22×C11semidirect
290. #421C22×C11semidirect
292. #418C22×C11semidirect
298. #344C22×C11semidirect
299. #344C22×C11semidirect
300. #339C22×C11semidirect
301. H(3,ℤ/4)C22×C11semidirect
423. C2×Q8C11×#41semidirect
445. C2×D4C11×#41semidirect
493. C11#23998direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35082
C11×#30192
C2×C11×#4532
C11×#28832
C11×#20312
C11×#20082
C11×#19112
C11×#19062
C11×#19042
C11×#18872
C11×#18292
#2399811