Finite Group Databasebeta

← C11×#32888 #14610081

Subgroups — C11×#32888 #14610081

Order 2816.

4070 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2C2×C11×#453C214yesmaximal, complemented
3C11×#3006C212yesmaximal, complemented
4C11×#2433C211yesmaximal, characteristic, complemented
5C11×#1792C214yesmaximal, complemented
6C11×#1789C212yesmaximal, complemented
7C11×#1783C211yesmaximal, characteristic, complemented
8C2×C11×H(5,𝔽2)—216no—
9C2×C11×H(5,𝔽2)—24no—
10C2×C11×H(5,𝔽2)—22no—
11C2×C11×H(5,𝔽2)C2214yes—
12C22×C11×#41—22no—
13C22×C11×#41C2212yes—
14C23×D4×C11—22no—
15C23×D4×C11—22no—
16C23×D4×C11C2211yescharacteristic
17C2×C11×AGL(1,ℤ/8)C2214yescomplemented
18C2×C11×#127C2212yescomplemented
19C2×C11×#121C2211yescharacteristic, complemented
20C2×C11×#120—22no—
21C11×#453—216no—
22C11×#449—24no—
23C11×#448—22no—
24C11×#447—22no—
25C2×C11×#104C2218yescomplemented
26C11×#417C2214yescomplemented
27C2×C11×#100C2214yescomplemented
28C11×#407C2212yescomplemented
29C11×#392—22no—
30C11×#390C2212yescomplemented
31C4×C11×C22⋊C4C2211yescharacteristic, complemented
32C25×C11—22no—
33C25×C11D412yes—
34C11×H(5,𝔽2)—232no—
35C11×H(5,𝔽2)—232no—
36C11×H(5,𝔽2)—232no—
37C11×H(5,𝔽2)—216no—
38C11×H(5,𝔽2)—28no—
39C11×H(5,𝔽2)D4116yescomplemented
40C2×C11×#41—232no—
41C2×C11×#41—28no—
42C2×C11×#41—216no—
43C2×C11×#41—28no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41D414yescomplemented
47C2×C11×#41C2314yes—
48C22×Q8×C11D412yescomplemented
49C22×D4×C11—24no—
50C22×D4×C11—232no—
51C22×D4×C11—232no—
52C22×D4×C11—28no—
53C22×D4×C11—28no—
54C22×D4×C11—22no—
55C22×D4×C11—28no—
56C22×D4×C11—28no—
57C22×D4×C11—28no—
58C22×D4×C11—21no—
59C22×D4×C11—24no—
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11D412yes—
63C22×D4×C11D412yescomplemented
64C22×D4×C11C2312yes—
65C22×D4×C11C2311yescharacteristic, complemented
66C23×C4×C11—22no—
67C23×C4×C11—22no—
68C23×C4×C11C2311yescharacteristic
69C11×AGL(1,ℤ/8)—216no—
70C2×C11×SD16—24no—
71C2×C11×D8—24no—
72C2×C11×M16C2314yescomplemented
73C11×#127—28no—
74C11×#121—22no—
75C11×#121—22no—
76C11×#120—48no—
77C2×C11×C4⋊C4C2311yescharacteristic, complemented
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11C2312yescomplemented
82C11×#104—216no—
83C11×#103—24no—
84C11×#102—24no—
85C11×#100—28no—
86C11×C22⋊C8—22no—
87C11×C22⋊C8—22no—
88C11×#95—21no—
89#32888C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11—216no—
91C24×C11—28no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—28no—
95C24×C11—22no—
96C24×C11—21no—
97C24×C11—44no—
98C24×C11—82no—
99C24×C11—84no—
100C24×C11—84no—
101C24×C11C2×D411yescharacteristic
102C24×C11C2×D414yes—
103C11×#41—264no—
104C11×#41—216no—
105C11×#41—232no—
106C11×#41—216no—
107C11×#41—232no—
108C11×#41—28no—
109C11×#41—28no—
110C11×#41—28no—
111C11×#41C2×D4116yes—
112C2×Q8×C11—28no—
113C2×Q8×C11—22no—
114C2×Q8×C11C2×D414yes—
115C2×D4×C11—232no—
116C2×D4×C11—216no—
117C2×D4×C11—216no—
118C2×D4×C11—216no—
119C2×D4×C11—264no—
120C2×D4×C11—264no—
121C2×D4×C11—232no—
122C2×D4×C11—232no—
123C2×D4×C11—216no—
124C2×D4×C11—24no—
125C2×D4×C11—232no—
126C2×D4×C11—28no—
127C2×D4×C11—24no—
128C2×D4×C11—28no—
129C2×D4×C11—232no—
130C2×D4×C11—24no—
131C2×D4×C11—22no—
132C2×D4×C11—24no—
133C2×D4×C11—24no—
134C2×D4×C11—22no—
135C2×D4×C11—24no—
136C2×D4×C11—48no—
137C2×D4×C11—44no—
138C2×D4×C11—41no—
139C2×D4×C11—41no—
140C2×D4×C11—48no—
141C2×D4×C11—84no—
142C2×D4×C11C2×D418yes—
143C2×D4×C11C2×D414yes—
144C22×C4×C11—216no—
145C22×C4×C11—216no—
146C22×C4×C11—28no—
147C22×C4×C11—22no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2411yescharacteristic
157C11×SD16—48no—
158C11×D8—48no—
159C11×M16—28no—
160C2×C8×C11—24no—
161C11×C4⋊C4—22no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—48no—
164C11×C22⋊C4—42no—
165C42×C11—24no—
166C22×H(5,𝔽2)C2×C1111yescharacteristic, complemented
167C2×#453C2×C1114yescomplemented
168#3006C2×C1112yescomplemented
169#2433C2×C1111yescharacteristic, complemented
170#1792C2×C1114yescomplemented
171#1789C2×C1112yescomplemented
172#1783C2×C1111yescharacteristic, complemented
173C23×C11—28no—
174C23×C11—28no—
175C23×C11—28no—
176C23×C11—232no—
177C23×C11—22no—
178C23×C11—24no—
179C23×C11—24no—
180C23×C11—22no—
181C23×C11—24no—
182C23×C11—41no—
183C23×C11—44no—
184C23×C11—44no—
185C23×C11—44no—
186C23×C11—44no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—44no—
190C23×C11—44no—
191C23×C11—42no—
192C23×C11—41no—
193C23×C11—82no—
194C23×C11—82no—
195C23×C11—816no—
196C23×C11—832no—
197C23×C11—88no—
198C23×C11—88no—
199C23×C11#12011yescharacteristic
200C23×C11#12011yescharacteristic
201C23×C11#12018yes—
202C23×C11C22×D411yescharacteristic
203Q8×C11—28no—
204Q8×C11—24no—
205Q8×C11#12018yescomplemented
206D4×C11—264no—
207D4×C11—216no—
208D4×C11—216no—
209D4×C11—28no—
210D4×C11—216no—
211D4×C11—216no—
212D4×C11—24no—
213D4×C11—44no—
214D4×C11—816no—
215D4×C11—82no—
216D4×C11—82no—
217D4×C11#12018yescomplemented
218C2×C4×C11—28no—
219C2×C4×C11—232no—
220C2×C4×C11—216no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—216no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11#12012yes—
232C2×C4×C11C22×D414yes—
233C2×C4×C11C22×D412yes—
234C8×C11—44no—
235C2×H(5,𝔽2)—216no—
236C2×H(5,𝔽2)—24no—
237C2×H(5,𝔽2)—22no—
238C2×H(5,𝔽2)C22×C1114yes—
239C22×#41—22no—
240C22×#41C22×C1112yes—
241C23×D4—22no—
242C23×D4—22no—
243C23×D4C22×C1111yescharacteristic
244C2×AGL(1,ℤ/8)C22×C1114yescomplemented
245C2×#127C22×C1112yescomplemented
246C2×#121C22×C1111yescharacteristic, complemented
247C2×#120—22no—
248#453—216no—
249#449—24no—
250#448—22no—
251#447—22no—
252C2×#104C22×C1118yescomplemented
253#417C22×C1114yescomplemented
254C2×#100C22×C1114yescomplemented
255#407C22×C1112yescomplemented
256#392—22no—
257#390C22×C1112yescomplemented
258C4×C22⋊C4C22×C1111yescharacteristic, complemented
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—28no—
265C22×C11—28no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—44no—
269C22×C11—48no—
270C22×C11—416no—
271C22×C11—416no—
272C22×C11—44no—
273C22×C11—44no—
274C22×C11—44no—
275C22×C11—44no—
276C22×C11—84no—
277C22×C11—84no—
278C22×C11—88no—
279C22×C11—832no—
280C22×C11—81no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11#45312yescomplemented
284C22×C11C2×#12012yes—
285C22×C11C2×#12011yescharacteristic
286C4×C11—28no—
287C4×C11—22no—
288C4×C11—44no—
289C4×C11—81no—
290C4×C11C2×#12014yes—
291C25—22no—
292C25D4×C1112yes—
293H(5,𝔽2)—232no—
294H(5,𝔽2)—232no—
295H(5,𝔽2)—232no—
296H(5,𝔽2)—216no—
297H(5,𝔽2)—28no—
298H(5,𝔽2)D4×C11116yescomplemented
299C2×#41—232no—
300C2×#41—28no—
301C2×#41—216no—
302C2×#41—28no—
303C2×#41—22no—
304C2×#41—22no—
305C2×#41D4×C1114yescomplemented
306C2×#41C23×C1114yes—
307C22×Q8D4×C1112yescomplemented
308C22×D4—24no—
309C22×D4—232no—
310C22×D4—232no—
311C22×D4—28no—
312C22×D4—28no—
313C22×D4—22no—
314C22×D4—28no—
315C22×D4—28no—
316C22×D4—28no—
317C22×D4—21no—
318C22×D4—24no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4D4×C1112yes—
322C22×D4D4×C1112yescomplemented
323C22×D4C23×C1112yes—
324C22×D4C23×C1111yescharacteristic, complemented
325C23×C4—22no—
326C23×C4—22no—
327C23×C4C23×C1111yescharacteristic
328AGL(1,ℤ/8)—216no—
329C2×SD16—24no—
330C2×D8—24no—
331C2×M16C23×C1114yescomplemented
332#127—28no—
333#121—22no—
334#121—22no—
335#120—48no—
336C2×C4⋊C4C23×C1111yescharacteristic, complemented
337C2×C22⋊C4—21no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—21no—
340C2×C42C23×C1112yescomplemented
341#104—216no—
342#103—24no—
343#102—24no—
344#100—28no—
345C22⋊C8—22no—
346C22⋊C8—22no—
347#95—21no—
348C2×C11—22no—
349C2×C11—22no—
350C2×C11—41no—
351C2×C11—48no—
352C2×C11—48no—
353C2×C11—161no—
354C2×C11#284611yescharacteristic
355C2×C11C2×#45311yescharacteristic
356C2×C11#301911yescharacteristic
357C24—216no—
358C24—28no—
359C24—22no—
360C24—22no—
361C24—28no—
362C24—22no—
363C24—21no—
364C24—44no—
365C24—82no—
366C24—84no—
367C24—84no—
368C24C2×D4×C1111yescharacteristic
369C24C2×D4×C1114yes—
370#41—264no—
371#41—216no—
372#41—232no—
373#41—216no—
374#41—232no—
375#41—28no—
376#41—28no—
377#41—28no—
378#41C2×D4×C11116yes—
379C2×Q8—28no—
380C2×Q8—22no—
381C2×Q8C2×D4×C1114yes—
382C2×D4—232no—
383C2×D4—216no—
384C2×D4—216no—
385C2×D4—216no—
386C2×D4—264no—
387C2×D4—264no—
388C2×D4—232no—
389C2×D4—232no—
390C2×D4—216no—
391C2×D4—24no—
392C2×D4—232no—
393C2×D4—28no—
394C2×D4—24no—
395C2×D4—28no—
396C2×D4—232no—
397C2×D4—24no—
398C2×D4—22no—
399C2×D4—24no—
400C2×D4—24no—
401C2×D4—22no—
402C2×D4—24no—
403C2×D4—48no—
404C2×D4—44no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—48no—
408C2×D4—84no—
409C2×D4C2×D4×C1118yes—
410C2×D4C2×D4×C1114yes—
411C22×C4—216no—
412C22×C4—216no—
413C22×C4—28no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4C2×D4×C1111yescharacteristic
421C22×C4C2×D4×C1112yes—
422C22×C4C2×D4×C1112yes—
423C22×C4C24×C1111yescharacteristic
424SD16—48no—
425D8—48no—
426M16—28no—
427C2×C8—24no—
428C4⋊C4—22no—
429C22⋊C4—24no—
430C22⋊C4—48no—
431C22⋊C4—42no—
432C42—24no—
433C11#3288811yescharacteristic, direct product factor, Sylow
434C23—28no—
435C23—28no—
436C23—28no—
437C23—232no—
438C23—22no—
439C23—24no—
440C23—24no—
441C23—22no—
442C23—24no—
443C23—41no—
444C23—44no—
445C23—44no—
446C23—44no—
447C23—44no—
448C23—42no—
449C23—42no—
450C23—44no—
451C23—44no—
452C23—41no—
453C23—42no—
454C23—82no—
455C23—82no—
456C23—816no—
457C23—832no—
458C23—88no—
459C23—88no—
460C23C11×#12011yescharacteristic
461C23C11×#12011yescharacteristic
462C23C11×#12018yes—
463C23C22×D4×C1111yescharacteristic
464Q8—28no—
465Q8—24no—
466Q8C11×#12018yescomplemented
467D4—264no—
468D4—216no—
469D4—216no—
470D4—28no—
471D4—216no—
472D4—216no—
473D4—24no—
474D4—44no—
475D4—816no—
476D4—82no—
477D4—82no—
478D4C11×#12018yescomplemented
479C2×C4—28no—
480C2×C4—232no—
481C2×C4—216no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—216no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4C11×#12012yes—
493C2×C4C22×D4×C1114yes—
494C2×C4C22×D4×C1112yes—
495C8—44no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—28no—
504C22—28no—
505C22—44no—
506C22—48no—
507C22—416no—
508C22—416no—
509C22—44no—
510C22—44no—
511C22—44no—
512C22—44no—
513C22—84no—
514C22—84no—
515C22—88no—
516C22—832no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22C11×#45312yescomplemented
521C22C2×C11×#12012yes—
522C22C2×C11×#12011yescharacteristic
523C4—28no—
524C4—22no—
525C4—44no—
526C4—81no—
527C4C2×C11×#12014yes—
528C2—22no—
529C2—22no—
530C2—41no—
531C2—48no—
532C2—48no—
533C2—161no—
534C2C11×#284611yescharacteristic
535C2C2×C11×#45311yescharacteristic
536C2C11×#301911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
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×H(5,𝔽2)C2semidirect
2. C2×C11×#453C2semidirect
3. C11×#3006C2semidirect
4. C11×#2433C2semidirect
5. C11×#1792C2semidirect
6. C11×#1789C2semidirect
7. C11×#1783C2semidirect
17. C2×C11×AGL(1,ℤ/8)C22semidirect
18. C2×C11×#127C22semidirect
19. C2×C11×#121C22semidirect
25. C2×C11×#104C22semidirect
26. C11×#417C22semidirect
27. C2×C11×#100C22semidirect
28. C11×#407C22semidirect
30. C11×#390C22semidirect
31. C4×C11×C22⋊C4C22semidirect
39. C11×H(5,𝔽2)D4semidirect
46. C2×C11×#41D4semidirect
48. C22×Q8×C11D4semidirect
63. C22×D4×C11D4semidirect
65. C22×D4×C11C23semidirect
72. C2×C11×M16C23semidirect
77. C2×C11×C4⋊C4C23semidirect
81. C2×C42×C11C23semidirect
89. #32888C11direct (N × H)
166. C22×H(5,𝔽2)C2×C11semidirect
167. C2×#453C2×C11semidirect
168. #3006C2×C11semidirect
169. #2433C2×C11semidirect
170. #1792C2×C11semidirect
171. #1789C2×C11semidirect
172. #1783C2×C11semidirect
205. Q8×C11#120semidirect
217. D4×C11#120semidirect
244. C2×AGL(1,ℤ/8)C22×C11semidirect
245. C2×#127C22×C11semidirect
246. C2×#121C22×C11semidirect
252. C2×#104C22×C11semidirect
253. #417C22×C11semidirect
254. C2×#100C22×C11semidirect
255. #407C22×C11semidirect
257. #390C22×C11semidirect
258. C4×C22⋊C4C22×C11semidirect
283. C22×C11#453semidirect
298. H(5,𝔽2)D4×C11semidirect
305. C2×#41D4×C11semidirect
307. C22×Q8D4×C11semidirect
322. C22×D4D4×C11semidirect
324. C22×D4C23×C11semidirect
331. C2×M16C23×C11semidirect
336. C2×C4⋊C4C23×C11semidirect
340. C2×C42C23×C11semidirect
433. C11#32888direct (N × H)
466. Q8C11×#120semidirect
478. D4C11×#120semidirect
520. C22C11×#453semidirect

Maximal subgroups

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

subgroupindex
C22×C11×H(5,𝔽2)2
C2×C11×#4532
C11×#30062
C11×#24332
C11×#17922
C11×#17892
C11×#17832
#3288811