Finite Group Databasebeta

← C11×#23990 #14601183

Subgroups — C11×#23990 #14601183

Order 2816.

1260 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3508C211yesmaximal, characteristic, complemented
2C11×#3027C211yesmaximal, characteristic, complemented
3C11×#3021C211yesmaximal, characteristic, complemented
4C11×#2901C211yesmaximal, characteristic, complemented
5C11×#2031C212yesmaximal, complemented
6C11×#2002C212yesmaximal, complemented
7C11×#1914C211yesmaximal, characteristic, complemented
8C11×#1911C212yesmaximal, complemented
9C11×#1910C211yesmaximal, characteristic, complemented
10C11×#1904C212yesmaximal, complemented
11C11×#1827C211yesmaximal, characteristic, complemented
12C11×#585C2211yescharacteristic
13C2×C11×AGL(1,ℤ/8)C2212yes—
14C11×#568C2211yescharacteristic
15C11×#559—22no—
16C11×#550—22no—
17C11×#546—24no—
18C11×#540—22no—
19C11×#535C2211yescharacteristic
20C11×#535C2212yes—
21C11×#535C2211yescharacteristic
22C11×#533C2211yescharacteristic, complemented
23C11×#532—22no—
24C2×C11×#127C2211yescharacteristic, complemented
25C11×#518C2211yescharacteristic, complemented
26C11×#518C2211yescharacteristic, complemented
27C4×C11×#41C2211yescharacteristic
28C11×B(4,𝔽2)—24no—
29C11×#454—22no—
30C11×#453—22no—
31C11×#421—22no—
32C11×#421C2212yes—
33C11×#421C2212yes—
34C2×C11×#104—22no—
35C2×C11×#104C2212yes—
36C11×#418C2212yescomplemented
37C11×#413C2211yescharacteristic
38C2×C11×#100C2212yescomplemented
39C11×#410C2212yes—
40C11×#410C2211yescharacteristic
41C11×#344C2212yescomplemented
42C11×#339C2212yescomplemented
43C11×H(3,ℤ/4)C2212yescomplemented
44C11×H(3,ℤ/4)C2212yescomplemented
45C11×2−1+4—22no—
46C11×2−1+4—21no—
47C11×H(5,𝔽2)—22no—
48C11×H(5,𝔽2)—22no—
49C11×H(5,𝔽2)—21no—
50C2×C11×#41—24no—
51C2×C11×#41—22no—
52C2×C11×#41—42no—
53C2×C11×#41C2312yes—
54C2×C11×#41C2311yescharacteristic
55C22×D4×C11—22no—
56C22×D4×C11C2311yescharacteristic
57C22×D4×C11C2311yescharacteristic
58C11×AGL(1,ℤ/8)—24no—
59C11×AGL(1,ℤ/8)—42no—
60C2×C11×SD16—22no—
61C2×C11×D8—22no—
62C11×#131—42no—
63C2×C11×M16—22no—
64C2×C11×M16C2312yes—
65C2×C11×M16C2312yes—
66C11×C4⋊Q8—21no—
67C11×#127—22no—
68C11×#127—21no—
69C11×#127—22no—
70C11×#127—21no—
71C11×#127—21no—
72C11×#127D412yescomplemented
73C11×#125—21no—
74C11×#124—24no—
75C11×#124—21no—
76C11×#124—22no—
77C11×#124D412yescomplemented
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×#121—42no—
87C11×#120—22no—
88C11×#120—24no—
89C11×#120D414yes—
90C4×Q8×C11—21no—
91C4×Q8×C11—22no—
92C4×D4×C11—24no—
93C4×D4×C11—22no—
94C4×D4×C11—21no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C11×#117D412yescomplemented
100C11×#117C2312yes—
101C11×#117C2311yescharacteristic
102C11×#117C2311yescharacteristic
103C11×#117C2311yescharacteristic
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C42×C11D412yescomplemented
107C2×C42×C11C2311yescharacteristic
108C11×#104—22no—
109C11×#104—24no—
110C11×#104—22no—
111C11×#104—24no—
112C11×#102—42no—
113C11×#101—21no—
114C11×#100—21no—
115C11×#100—42no—
116C11×#99—22no—
117C11×#99—24no—
118#23990C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11—21no—
120C24×C11C2×D412yes—
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—24no—
124C11×#41—22no—
125C11×#41—22no—
126C11×#41—22no—
127C11×#41—22no—
128C11×#41—44no—
129C11×#41—42no—
130C11×#41—42no—
131C11×#41—42no—
132C11×#41—42no—
133C11×#41—88no—
134C2×Q8×C11—22no—
135C2×Q8×C11—22no—
136C2×Q8×C11—42no—
137C2×Q8×C11C2×D411yescharacteristic
138C2×Q8×C11#4112yescomplemented
139C2×D4×C11—22no—
140C2×D4×C11—24no—
141C2×D4×C11—22no—
142C2×D4×C11—24no—
143C2×D4×C11—24no—
144C2×D4×C11—24no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—42no—
153C2×D4×C11—44no—
154C2×D4×C11—42no—
155C2×D4×C11—44no—
156C2×D4×C11—84no—
157C2×D4×C11C2×D412yes—
158C2×D4×C11C2×D412yes—
159C2×D4×C11C2×D411yescharacteristic
160C2×D4×C11#4112yescomplemented
161C22×C4×C11—22no—
162C22×C4×C11—21no—
163C22×C4×C11—24no—
164C22×C4×C11—24no—
165C22×C4×C11—22no—
166C22×C4×C11—42no—
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2411yescharacteristic
169C11×SD16—44no—
170C11×D8—44no—
171C11×M16—22no—
172C11×M16—22no—
173C11×M16—22no—
174C11×M16—22no—
175C11×M16—42no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—42no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—22no—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—24no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—21no—
191C11×C22⋊C4—21no—
192C11×C22⋊C4—24no—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—44no—
196C11×C22⋊C4C2×D412yes—
197C42×C11—22no—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11—22no—
201C42×C11C2×D411yescharacteristic
202C42×C11C2×D412yes—
203C42×C11C2×D411yescharacteristic
204C42×C11C2×D412yes—
205#3508C2×C1111yescharacteristic, complemented
206#3027C2×C1111yescharacteristic, complemented
207#3021C2×C1111yescharacteristic, complemented
208#2901C2×C1111yescharacteristic, complemented
209#2031C2×C1112yescomplemented
210#2002C2×C1112yescomplemented
211#1914C2×C1111yescharacteristic, complemented
212#1911C2×C1112yescomplemented
213#1910C2×C1111yescharacteristic, complemented
214#1904C2×C1112yescomplemented
215#1827C2×C1111yescharacteristic, complemented
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—24no—
219C23×C11—22no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—82no—
223C23×C11—82no—
224C23×C11#12012yes—
225C23×C11C22×D411yescharacteristic
226Q8×C11—22no—
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—42no—
230Q8×C11—44no—
231D4×C11—24no—
232D4×C11—22no—
233D4×C11—22no—
234D4×C11—22no—
235D4×C11—24no—
236D4×C11—42no—
237D4×C11—48no—
238D4×C11—44no—
239D4×C11—42no—
240D4×C11—42no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—42no—
246D4×C11—84no—
247D4×C11—84no—
248D4×C11—84no—
249D4×C11—164no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—42no—
259C2×C4×C11—44no—
260C2×C4×C11—44no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—84no—
266C2×C4×C11—84no—
267C2×C4×C11#12012yes—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C2×#4112yes—
271C2×C4×C11H(5,𝔽2)12yes—
272C8×C11—42no—
273C8×C11—42no—
274#585C22×C1111yescharacteristic
275C2×AGL(1,ℤ/8)C22×C1112yes—
276#568C22×C1111yescharacteristic
277#559—22no—
278#550—22no—
279#546—24no—
280#540—22no—
281#535C22×C1111yescharacteristic
282#535C22×C1112yes—
283#535C22×C1111yescharacteristic
284#533C22×C1111yescharacteristic, complemented
285#532—22no—
286C2×#127C22×C1111yescharacteristic, complemented
287#518C22×C1111yescharacteristic, complemented
288#518C22×C1111yescharacteristic, complemented
289C4×#41C22×C1111yescharacteristic
290B(4,𝔽2)—24no—
291#454—22no—
292#453—22no—
293#421—22no—
294#421C22×C1112yes—
295#421C22×C1112yes—
296C2×#104—22no—
297C2×#104C22×C1112yes—
298#418C22×C1112yescomplemented
299#413C22×C1111yescharacteristic
300C2×#100C22×C1112yescomplemented
301#410C22×C1111yescharacteristic
302#410C22×C1112yes—
303#344C22×C1112yescomplemented
304#339C22×C1112yescomplemented
305H(3,ℤ/4)C22×C1112yescomplemented
306H(3,ℤ/4)C22×C1112yescomplemented
307C22×C11—22no—
308C22×C11—41no—
309C22×C11—42no—
310C22×C11—44no—
311C22×C11—44no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—82no—
316C22×C11—84no—
317C22×C11—162no—
318C22×C11—162no—
319C22×C11C2×#12011yescharacteristic
320C22×C11#54612yes—
321C4×C11—22no—
322C4×C11—22no—
323C4×C11—42no—
324C4×C11—41no—
325C4×C11—42no—
326C4×C11—42no—
327C4×C11—42no—
328C4×C11—82no—
329C4×C11#52511yescharacteristic
330C4×C11#53511yescharacteristic
331C4×C11#54612yes—
3322−1+4—22no—
3332−1+4—21no—
334H(5,𝔽2)—22no—
335H(5,𝔽2)—22no—
336H(5,𝔽2)—21no—
337C2×#41—24no—
338C2×#41—22no—
339C2×#41—42no—
340C2×#41C23×C1112yes—
341C2×#41C23×C1111yescharacteristic
342C22×D4—22no—
343C22×D4C23×C1111yescharacteristic
344C22×D4C23×C1111yescharacteristic
345AGL(1,ℤ/8)—24no—
346AGL(1,ℤ/8)—42no—
347C2×SD16—22no—
348C2×D8—22no—
349#131—42no—
350C2×M16—22no—
351C2×M16C23×C1112yes—
352C2×M16C23×C1112yes—
353C4⋊Q8—21no—
354#127—22no—
355#127—21no—
356#127—22no—
357#127—21no—
358#127—21no—
359#127D4×C1112yescomplemented
360#125—21no—
361#124—24no—
362#124—21no—
363#124—22no—
364#124D4×C1112yescomplemented
365#123—24no—
366#123—24no—
367C22⋊Q8—22no—
368#121—24no—
369#121—24no—
370#121—24no—
371#121—22no—
372#121—22no—
373#121—42no—
374#120—22no—
375#120—24no—
376#120D4×C1114yes—
377C4×Q8—21no—
378C4×Q8—22no—
379C4×D4—24no—
380C4×D4—22no—
381C4×D4—21no—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—22no—
385C4×D4—22no—
386#117D4×C1112yescomplemented
387#117C23×C1112yes—
388#117C23×C1111yescharacteristic
389#117C23×C1111yescharacteristic
390#117C23×C1111yescharacteristic
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C42D4×C1112yescomplemented
394C2×C42C23×C1111yescharacteristic
395#104—22no—
396#104—24no—
397#104—22no—
398#104—24no—
399#102—42no—
400#101—21no—
401#100—21no—
402#100—42no—
403#99—22no—
404#99—24no—
405C2×C11—21no—
406C2×C11—22no—
407C2×C11—42no—
408C2×C11—82no—
409C2×C11—82no—
410C2×C11—82no—
411C2×C11#240411yescharacteristic
412C24—21no—
413C24C2×D4×C1112yes—
414#41—22no—
415#41—22no—
416#41—24no—
417#41—22no—
418#41—22no—
419#41—22no—
420#41—22no—
421#41—44no—
422#41—42no—
423#41—42no—
424#41—42no—
425#41—42no—
426#41—88no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—42no—
430C2×Q8C2×D4×C1111yescharacteristic
431C2×Q8C11×#4112yescomplemented
432C2×D4—22no—
433C2×D4—24no—
434C2×D4—22no—
435C2×D4—24no—
436C2×D4—24no—
437C2×D4—24no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—42no—
446C2×D4—44no—
447C2×D4—42no—
448C2×D4—44no—
449C2×D4—84no—
450C2×D4C2×D4×C1112yes—
451C2×D4C2×D4×C1112yes—
452C2×D4C2×D4×C1111yescharacteristic
453C2×D4C11×#4112yescomplemented
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—42no—
460C22×C4C2×D4×C1112yes—
461C22×C4C24×C1111yescharacteristic
462SD16—44no—
463D8—44no—
464M16—22no—
465M16—22no—
466M16—22no—
467M16—22no—
468M16—42no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—42no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—22no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—22no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—24no—
486C22⋊C4—24no—
487C22⋊C4—22no—
488C22⋊C4—44no—
489C22⋊C4C2×D4×C1112yes—
490C42—22no—
491C42—21no—
492C42—21no—
493C42—22no—
494C42C2×D4×C1111yescharacteristic
495C42C2×D4×C1112yes—
496C42C2×D4×C1111yescharacteristic
497C42C2×D4×C1112yes—
498C11#2399011yescharacteristic, direct product factor, Sylow
499C23—22no—
500C23—22no—
501C23—24no—
502C23—22no—
503C23—42no—
504C23—42no—
505C23—82no—
506C23—82no—
507C23C11×#12012yes—
508C23C22×D4×C1111yescharacteristic
509Q8—22no—
510Q8—22no—
511Q8—22no—
512Q8—42no—
513Q8—44no—
514D4—24no—
515D4—22no—
516D4—22no—
517D4—22no—
518D4—24no—
519D4—42no—
520D4—48no—
521D4—44no—
522D4—42no—
523D4—42no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—42no—
529D4—84no—
530D4—84no—
531D4—84no—
532D4—164no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—42no—
542C2×C4—44no—
543C2×C4—44no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—84no—
549C2×C4—84no—
550C2×C4C11×#12012yes—
551C2×C4C22×D4×C1111yescharacteristic
552C2×C4C22×D4×C1111yescharacteristic
553C2×C4C2×C11×#4112yes—
554C2×C4C11×H(5,𝔽2)12yes—
555C8—42no—
556C8—42no—
557C22—22no—
558C22—41no—
559C22—42no—
560C22—44no—
561C22—44no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—82no—
566C22—84no—
567C22—162no—
568C22—162no—
569C22C2×C11×#12011yescharacteristic
570C22C11×#54612yes—
571C4—22no—
572C4—22no—
573C4—42no—
574C4—41no—
575C4—42no—
576C4—42no—
577C4—42no—
578C4—82no—
579C4C11×#52511yescharacteristic
580C4C11×#53511yescharacteristic
581C4C11×#54612yes—
582C2—21no—
583C2—22no—
584C2—42no—
585C2—82no—
586C2—82no—
587C2—82no—
588C2C11×#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×#3027C2semidirect
3. C11×#3021C2semidirect
4. C11×#2901C2semidirect
5. C11×#2031C2semidirect
6. C11×#2002C2semidirect
7. C11×#1914C2semidirect
8. C11×#1911C2semidirect
9. C11×#1910C2semidirect
10. C11×#1904C2semidirect
11. C11×#1827C2semidirect
22. C11×#533C22semidirect
24. C2×C11×#127C22semidirect
25. C11×#518C22semidirect
26. C11×#518C22semidirect
36. C11×#418C22semidirect
38. C2×C11×#100C22semidirect
41. C11×#344C22semidirect
42. C11×#339C22semidirect
43. C11×H(3,ℤ/4)C22semidirect
44. C11×H(3,ℤ/4)C22semidirect
72. C11×#127D4semidirect
77. C11×#124D4semidirect
99. C11×#117D4semidirect
106. C2×C42×C11D4semidirect
118. #23990C11direct (N × H)
138. C2×Q8×C11#41semidirect
160. C2×D4×C11#41semidirect
205. #3508C2×C11semidirect
206. #3027C2×C11semidirect
207. #3021C2×C11semidirect
208. #2901C2×C11semidirect
209. #2031C2×C11semidirect
210. #2002C2×C11semidirect
211. #1914C2×C11semidirect
212. #1911C2×C11semidirect
213. #1910C2×C11semidirect
214. #1904C2×C11semidirect
215. #1827C2×C11semidirect
284. #533C22×C11semidirect
286. C2×#127C22×C11semidirect
287. #518C22×C11semidirect
288. #518C22×C11semidirect
298. #418C22×C11semidirect
300. C2×#100C22×C11semidirect
303. #344C22×C11semidirect
304. #339C22×C11semidirect
305. H(3,ℤ/4)C22×C11semidirect
306. H(3,ℤ/4)C22×C11semidirect
359. #127D4×C11semidirect
364. #124D4×C11semidirect
386. #117D4×C11semidirect
393. C2×C42D4×C11semidirect
431. C2×Q8C11×#41semidirect
453. C2×D4C11×#41semidirect
498. C11#23990direct (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×#30272
C11×#30212
C11×#29012
C11×#20312
C11×#20022
C11×#19142
C11×#19112
C11×#19102
C11×#19042
C11×#18272
#2399011