Finite Group Databasebeta

← C11×#33559 #14610752

Subgroups — C11×#33559 #14610752

Order 2816.

1248 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3549C211yesmaximal, characteristic, complemented
2C11×#3027C212yesmaximal, complemented
3C11×#3018C211yesmaximal, characteristic, complemented
4C11×#2199C214yesmaximal, complemented
5C11×#2196C214yesmaximal, complemented
6C11×#2126C211yesmaximal, characteristic, complemented
7C11×#2122C212yesmaximal, complemented
8C11×#585C2211yescharacteristic, complemented
9C11×#575—21no—
10C11×H(3,𝔽4)—21no—
11C11×H(3,𝔽4)C2212yescomplemented
12C11×#555—21no—
13C11×#555—22no—
14D42×C11—22no—
15D42×C11C2212yescomplemented
16C11×#535—21no—
17C11×#535—22no—
18C11×#535—24no—
19C11×#535C2212yes—
20C11×#532—21no—
21C11×#532C2211yescharacteristic
22C11×B(4,𝔽2)—24no—
23C11×B(4,𝔽2)C2218yescomplemented
24C11×#456—21no—
25C11×#455C2212yescomplemented
26C11×#454—21no—
27C11×#453C2212yes—
28C2×C11×#104—21no—
29C11×#413C2211yescharacteristic, complemented
30C11×#410—22no—
31C11×#410C2212yescomplemented
32C11×#354C2212yescomplemented
33C11×#353C2212yescomplemented
34C11×AΣL(1,𝔽16)C2218yescomplemented
35C11×2−1+4—21no—
36C11×2−1+4—41no—
37C11×H(5,𝔽2)—22no—
38C11×H(5,𝔽2)—41no—
39C11×H(5,𝔽2)C2312yes—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—21no—
43C2×C11×#41—42no—
44C2×C11×#41D411yescharacteristic, complemented
45C2×C11×#41C2311yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11—24no—
48C22×D4×C11D412yescomplemented
49C11×#137—22no—
50C11×#137—41no—
51C11×AGL(1,ℤ/8)—22no—
52C11×AGL(1,ℤ/8)—41no—
53C11×#135—42no—
54C2×C11×M16—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8D411yescharacteristic, complemented
57C11×#127—21no—
58C11×#127—22no—
59C11×#127—22no—
60C11×#127—42no—
61C11×#127C2311yescharacteristic
62C11×#124—24no—
63C11×#124—22no—
64C11×#124—22no—
65C11×#124—24no—
66C11×#124—22no—
67C11×#124—42no—
68C11×#124D411yescharacteristic, complemented
69C11×#124C2311yescharacteristic
70C11×#121—22no—
71C11×#121—22no—
72C11×#121—24no—
73C11×#121—22no—
74C11×#121—22no—
75C11×#121—22no—
76C11×#121—24no—
77C11×#121—44no—
78C11×#120—22no—
79C11×#120—24no—
80C11×#120—24no—
81C11×#120—22no—
82C11×#120—28no—
83C11×#120D414yescomplemented
84C11×#120C2314yes—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C11×#117—21no—
89C11×#117—24no—
90C11×#117—22no—
91C11×#117D412yescomplemented
92C2×C42×C11D411yescharacteristic, complemented
93C11×#104—22no—
94C11×#104—22no—
95C11×#101—21no—
96C11×#100C2312yes—
97C11×#99—22no—
98C11×#99—28no—
99C11×#99C2314yes—
100#33559C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11—22no—
102C24×C11C2×D414yes—
103C11×#41—22no—
104C11×#41—22no—
105C11×#41—41no—
106C11×#41—41no—
107C11×#41—42no—
108C11×#41—42no—
109C11×#41—42no—
110C11×#41—41no—
111C11×#41—44no—
112C11×#41—41no—
113C11×#41—41no—
114C11×#41—42no—
115C11×#41—42no—
116C11×#41—41no—
117C11×#41—84no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—21no—
121C2×Q8×C11—42no—
122C2×Q8×C11C2×D411yescharacteristic
123C2×Q8×C11C2×D411yescharacteristic
124C2×D4×C11—21no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—24no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—24no—
132C2×D4×C11—21no—
133C2×D4×C11—24no—
134C2×D4×C11—24no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—42no—
138C2×D4×C11—42no—
139C2×D4×C11—42no—
140C2×D4×C11—44no—
141C2×D4×C11—41no—
142C2×D4×C11—48no—
143C2×D4×C11—88no—
144C2×D4×C11—81no—
145C2×D4×C11—81no—
146C2×D4×C11C2×D412yes—
147C2×D4×C11C2×D411yescharacteristic
148C2×D4×C11C2411yescharacteristic
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—41no—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D411yescharacteristic
156C11×Q16—42no—
157C11×SD16—42no—
158C11×SD16—42no—
159C11×D8—42no—
160C11×M16—22no—
161C11×M16—41no—
162C2×C8×C11—41no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—42no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—48no—
176C11×C22⋊C4C2×D414yes—
177C42×C11—22no—
178C42×C11—22no—
179C42×C11—21no—
180C42×C11—42no—
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183#3549C2×C1111yescharacteristic, complemented
184#3027C2×C1112yescomplemented
185#3018C2×C1111yescharacteristic, complemented
186#2199C2×C1114yescomplemented
187#2196C2×C1114yescomplemented
188#2126C2×C1111yescharacteristic, complemented
189#2122C2×C1112yescomplemented
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—21no—
193C23×C11—41no—
194C23×C11—44no—
195C23×C11—84no—
196C23×C11—84no—
197C23×C11—82no—
198C23×C11#12011yescharacteristic
199C23×C11C22×D412yes—
200Q8×C11—22no—
201Q8×C11—41no—
202Q8×C11—41no—
203Q8×C11—42no—
204Q8×C11—41no—
205Q8×C11—82no—
206D4×C11—22no—
207D4×C11—42no—
208D4×C11—41no—
209D4×C11—41no—
210D4×C11—42no—
211D4×C11—44no—
212D4×C11—44no—
213D4×C11—44no—
214D4×C11—42no—
215D4×C11—42no—
216D4×C11—41no—
217D4×C11—42no—
218D4×C11—42no—
219D4×C11—82no—
220D4×C11—81no—
221D4×C11—84no—
222D4×C11—84no—
223D4×C11—82no—
224D4×C11—84no—
225D4×C11—82no—
226D4×C11—168no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—24no—
233C2×C4×C11—21no—
234C2×C4×C11—24no—
235C2×C4×C11—21no—
236C2×C4×C11—44no—
237C2×C4×C11—48no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—41no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—44no—
245C2×C4×C11#12012yes—
246C2×C4×C11#12011yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C8×C11—42no—
249#585C22×C1111yescharacteristic, complemented
250#575—21no—
251H(3,𝔽4)—21no—
252H(3,𝔽4)C22×C1112yescomplemented
253#555—21no—
254#555—22no—
255D42—22no—
256D42C22×C1112yescomplemented
257#535—21no—
258#535—22no—
259#535—24no—
260#535C22×C1112yes—
261#532—21no—
262#532C22×C1111yescharacteristic
263B(4,𝔽2)—24no—
264B(4,𝔽2)C22×C1118yescomplemented
265#456—21no—
266#455C22×C1112yescomplemented
267#454—21no—
268#453C22×C1112yes—
269C2×#104—21no—
270#413C22×C1111yescharacteristic, complemented
271#410—22no—
272#410C22×C1112yescomplemented
273#354C22×C1112yescomplemented
274#353C22×C1112yescomplemented
275AΣL(1,𝔽16)C22×C1118yescomplemented
276C22×C11—22no—
277C22×C11—21no—
278C22×C11—41no—
279C22×C11—42no—
280C22×C11—44no—
281C22×C11—44no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—41no—
285C22×C11—44no—
286C22×C11—84no—
287C22×C11—88no—
288C22×C11—161no—
289C22×C11—164no—
290C22×C11C2×#12011yescharacteristic
291C4×C11—22no—
292C4×C11—22no—
293C4×C11—21no—
294C4×C11—44no—
295C4×C11—41no—
296C4×C11—42no—
297C4×C11—41no—
298C4×C11—84no—
299C4×C11B(4,𝔽2)11yescharacteristic
300C4×C11B(4,𝔽2)11yescharacteristic
3012−1+4—21no—
3022−1+4—41no—
303H(5,𝔽2)—22no—
304H(5,𝔽2)—41no—
305H(5,𝔽2)C23×C1112yes—
306C2×#41—22no—
307C2×#41—22no—
308C2×#41—21no—
309C2×#41—42no—
310C2×#41D4×C1111yescharacteristic, complemented
311C2×#41C23×C1111yescharacteristic
312C22×D4—21no—
313C22×D4—24no—
314C22×D4D4×C1112yescomplemented
315#137—22no—
316#137—41no—
317AGL(1,ℤ/8)—22no—
318AGL(1,ℤ/8)—41no—
319#135—42no—
320C2×M16—21no—
321C4⋊Q8—21no—
322C4⋊Q8D4×C1111yescharacteristic, complemented
323#127—21no—
324#127—22no—
325#127—22no—
326#127—42no—
327#127C23×C1111yescharacteristic
328#124—24no—
329#124—22no—
330#124—22no—
331#124—24no—
332#124—22no—
333#124—42no—
334#124D4×C1111yescharacteristic, complemented
335#124C23×C1111yescharacteristic
336#121—22no—
337#121—22no—
338#121—24no—
339#121—22no—
340#121—22no—
341#121—22no—
342#121—24no—
343#121—44no—
344#120—22no—
345#120—24no—
346#120—24no—
347#120—22no—
348#120—28no—
349#120D4×C1114yescomplemented
350#120C23×C1114yes—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—22no—
354#117—21no—
355#117—24no—
356#117—22no—
357#117D4×C1112yescomplemented
358C2×C42D4×C1111yescharacteristic, complemented
359#104—22no—
360#104—22no—
361#101—21no—
362#100C23×C1112yes—
363#99—22no—
364#99—28no—
365#99C23×C1114yes—
366C2×C11—21no—
367C2×C11—42no—
368C2×C11—41no—
369C2×C11—84no—
370C2×C11—81no—
371C2×C11—82no—
372C2×C11C2×B(4,𝔽2)11yescharacteristic
373C24—22no—
374C24C2×D4×C1114yes—
375#41—22no—
376#41—22no—
377#41—41no—
378#41—41no—
379#41—42no—
380#41—42no—
381#41—42no—
382#41—41no—
383#41—44no—
384#41—41no—
385#41—41no—
386#41—42no—
387#41—41no—
388#41—42no—
389#41—84no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—21no—
393C2×Q8—42no—
394C2×Q8C2×D4×C1111yescharacteristic
395C2×Q8C2×D4×C1111yescharacteristic
396C2×D4—21no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—24no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—24no—
404C2×D4—21no—
405C2×D4—24no—
406C2×D4—24no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—42no—
412C2×D4—44no—
413C2×D4—41no—
414C2×D4—48no—
415C2×D4—88no—
416C2×D4—81no—
417C2×D4—81no—
418C2×D4C2×D4×C1112yes—
419C2×D4C2×D4×C1111yescharacteristic
420C2×D4C24×C1111yescharacteristic
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—41no—
426C22×C4C2×D4×C1112yes—
427C22×C4C2×D4×C1111yescharacteristic
428Q16—42no—
429SD16—42no—
430SD16—42no—
431D8—42no—
432M16—22no—
433M16—41no—
434C2×C8—41no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—42no—
439C22⋊C4—24no—
440C22⋊C4—22no—
441C22⋊C4—24no—
442C22⋊C4—22no—
443C22⋊C4—24no—
444C22⋊C4—22no—
445C22⋊C4—24no—
446C22⋊C4—24no—
447C22⋊C4—48no—
448C22⋊C4C2×D4×C1114yes—
449C42—22no—
450C42—21no—
451C42—22no—
452C42—42no—
453C42C2×D4×C1111yescharacteristic
454C42C2×D4×C1111yescharacteristic
455C11#3355911yescharacteristic, direct product factor, Sylow
456C23—24no—
457C23—24no—
458C23—21no—
459C23—41no—
460C23—44no—
461C23—84no—
462C23—84no—
463C23—82no—
464C23C11×#12011yescharacteristic
465C23C22×D4×C1112yes—
466Q8—22no—
467Q8—41no—
468Q8—41no—
469Q8—42no—
470Q8—41no—
471Q8—82no—
472D4—22no—
473D4—42no—
474D4—41no—
475D4—41no—
476D4—42no—
477D4—44no—
478D4—44no—
479D4—44no—
480D4—42no—
481D4—42no—
482D4—41no—
483D4—42no—
484D4—42no—
485D4—82no—
486D4—81no—
487D4—84no—
488D4—84no—
489D4—82no—
490D4—84no—
491D4—82no—
492D4—168no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—24no—
499C2×C4—21no—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—44no—
503C2×C4—48no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—44no—
511C2×C4C11×#12012yes—
512C2×C4C11×#12011yescharacteristic
513C2×C4C22×D4×C1111yescharacteristic
514C8—42no—
515C22—22no—
516C22—21no—
517C22—41no—
518C22—42no—
519C22—44no—
520C22—44no—
521C22—42no—
522C22—42no—
523C22—41no—
524C22—44no—
525C22—84no—
526C22—88no—
527C22—161no—
528C22—164no—
529C22C2×C11×#12011yescharacteristic
530C4—22no—
531C4—21no—
532C4—22no—
533C4—44no—
534C4—41no—
535C4—42no—
536C4—41no—
537C4—84no—
538C4C11×B(4,𝔽2)11yescharacteristic
539C4C11×B(4,𝔽2)11yescharacteristic
540C2—21no—
541C2—42no—
542C2—41no—
543C2—84no—
544C2—81no—
545C2—82no—
546C2C2×C11×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C11C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C11
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C2×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3549C2semidirect
2. C11×#3027C2semidirect
3. C11×#3018C2semidirect
4. C11×#2199C2semidirect
5. C11×#2196C2semidirect
6. C11×#2126C2semidirect
7. C11×#2122C2semidirect
8. C11×#585C22semidirect
11. C11×H(3,𝔽4)C22semidirect
15. D42×C11C22semidirect
23. C11×B(4,𝔽2)C22semidirect
25. C11×#455C22semidirect
29. C11×#413C22semidirect
31. C11×#410C22semidirect
32. C11×#354C22semidirect
33. C11×#353C22semidirect
34. C11×AΣL(1,𝔽16)C22semidirect
44. C2×C11×#41D4semidirect
48. C22×D4×C11D4semidirect
56. C11×C4⋊Q8D4semidirect
68. C11×#124D4semidirect
83. C11×#120D4semidirect
91. C11×#117D4semidirect
92. C2×C42×C11D4semidirect
100. #33559C11direct (N × H)
183. #3549C2×C11semidirect
184. #3027C2×C11semidirect
185. #3018C2×C11semidirect
186. #2199C2×C11semidirect
187. #2196C2×C11semidirect
188. #2126C2×C11semidirect
189. #2122C2×C11semidirect
249. #585C22×C11semidirect
252. H(3,𝔽4)C22×C11semidirect
256. D42C22×C11semidirect
264. B(4,𝔽2)C22×C11semidirect
266. #455C22×C11semidirect
270. #413C22×C11semidirect
272. #410C22×C11semidirect
273. #354C22×C11semidirect
274. #353C22×C11semidirect
275. AΣL(1,𝔽16)C22×C11semidirect
310. C2×#41D4×C11semidirect
314. C22×D4D4×C11semidirect
322. C4⋊Q8D4×C11semidirect
334. #124D4×C11semidirect
349. #120D4×C11semidirect
357. #117D4×C11semidirect
358. C2×C42D4×C11semidirect
455. C11#33559direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35492
C11×#30272
C11×#30182
C11×#21992
C11×#21962
C11×#21262
C11×#21222
#3355911