Finite Group Databasebeta

← C11×#32920 #14610113

Subgroups — C11×#32920 #14610113

Order 2816.

1590 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2C11×#3038C212yesmaximal, complemented
3C2×C11×#453C212yesmaximal, complemented
4C11×#2541C211yesmaximal, characteristic, complemented
5C11×#1887C212yesmaximal, complemented
6C11×#1883C214yesmaximal, complemented
7C11×#1806C212yesmaximal, complemented
8C11×#1800C211yesmaximal, characteristic, complemented
9C2×C11×H(5,𝔽2)C2211yescharacteristic
10C2×C11×AGL(1,ℤ/8)C2214yes—
11C2×C11×#127C2212yes—
12C2×C11×#127C2211yescharacteristic, complemented
13C2×C11×#121—22no—
14C11×#520—22no—
15C11×#520C2212yes—
16C11×#518—22no—
17C11×#518—22no—
18C11×#518C2211yescharacteristic
19C4×C11×#41—22no—
20C4×C11×#41C2212yes—
21C2×C4×D4×C11—22no—
22C2×C4×D4×C11—22no—
23C2×C4×D4×C11C2211yescharacteristic
24C11×#460—22no—
25C11×#460—22no—
26C11×#459—22no—
27C11×#459—22no—
28C11×#453—28no—
29C11×#423C2212yescomplemented
30C2×C11×#104C2214yes—
31C11×#418C2214yescomplemented
32C2×C11×#100C2212yes—
33C11×#392—22no—
34C11×#390C2212yescomplemented
35C4×C11×C4⋊C4C2211yescharacteristic, complemented
36C11×#343C2212yescomplemented
37C11×#339C2214yescomplemented
38C11×H(5,𝔽2)—24no—
39C11×H(5,𝔽2)—22no—
40C11×H(5,𝔽2)D414yescomplemented
41C2×C11×#41—22no—
42C2×C11×#41C2312yes—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—24no—
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11C2312yes—
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—22no—
51C23×C4×C11D412yes—
52C11×AGL(1,ℤ/8)—28no—
53C11×AGL(1,ℤ/8)—28no—
54C2×C11×SD16—24no—
55C2×C11×D8—24no—
56C2×C11×M16C2314yes—
57C11×#127—24no—
58C11×#127—24no—
59C11×#127—22no—
60C11×#127—22no—
61C11×#121—48no—
62C4×Q8×C11—22no—
63C4×Q8×C11D412yescomplemented
64C4×Q8×C11D412yescomplemented
65C4×D4×C11—24no—
66C4×D4×C11—24no—
67C4×D4×C11—24no—
68C4×D4×C11—24no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—24no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C4×D4×C11D412yescomplemented
78C4×D4×C11D412yescomplemented
79C11×#117—24no—
80C11×#117—22no—
81C11×#117—22no—
82C11×#117C2312yes—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—24no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—24no—
91C2×C11×C22⋊C4D412yes—
92C2×C42×C11—22no—
93C2×C42×C11—22no—
94C2×C42×C11C2312yes—
95C2×C42×C11C2311yescharacteristic
96C11×C4⋊C8—22no—
97C11×C4⋊C8—22no—
98C11×#104—28no—
99C11×#102—24no—
100C11×#102—24no—
101C11×#100—24no—
102C11×#95—21no—
103#32920C1111yesmaximal, characteristic, direct product factor, Sylow
104C24×C11—22no—
105C24×C11—22no—
106C24×C11C2×D412yes—
107C11×#41—28no—
108C11×#41—28no—
109C11×#41—22no—
110C11×#41—22no—
111C11×#41C2×D414yes—
112C11×#41#4114yes—
113C2×Q8×C11C2×D412yes—
114C2×D4×C11—24no—
115C2×D4×C11—28no—
116C2×D4×C11—28no—
117C2×D4×C11—28no—
118C2×D4×C11—22no—
119C2×D4×C11—28no—
120C2×D4×C11—22no—
121C2×D4×C11—24no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—24no—
126C2×D4×C11—44no—
127C2×D4×C11—48no—
128C2×D4×C11—48no—
129C2×D4×C11—42no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C2×D4×C11—82no—
133C2×D4×C11—84no—
134C2×D4×C11C2×D412yes—
135C2×D4×C11C2×D412yes—
136C2×D4×C11#4112yes—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—44no—
148C22×C4×C11—84no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C11×SD16—48no—
154C11×D8—48no—
155C11×M16—24no—
156C11×M16—24no—
157C2×C8×C11—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4C2×D412yes—
164C11×C4⋊C4C2×D412yes—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—48no—
172C42×C11—24no—
173C42×C11—22no—
174C42×C11—22no—
175C42×C11—22no—
176C42×C11—22no—
177C42×C11—22no—
178C42×C11C2×D412yes—
179C42×C11C2×D412yes—
180C4×H(5,𝔽2)C2×C1111yescharacteristic, complemented
181#3038C2×C1112yescomplemented
182C2×#453C2×C1112yescomplemented
183#2541C2×C1111yescharacteristic, complemented
184#1887C2×C1112yescomplemented
185#1883C2×C1114yescomplemented
186#1806C2×C1112yescomplemented
187#1800C2×C1111yescharacteristic, complemented
188C23×C11—28no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—44no—
195C23×C11—44no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—82no—
200C23×C11—82no—
201C23×C11#12114yes—
202C23×C11C22×D411yescharacteristic
203Q8×C11—22no—
204Q8×C11#12114yescomplemented
205D4×C11—216no—
206D4×C11—24no—
207D4×C11—24no—
208D4×C11—24no—
209D4×C11—22no—
210D4×C11—24no—
211D4×C11—44no—
212D4×C11—44no—
213D4×C11—82no—
214D4×C11—84no—
215D4×C11—816no—
216D4×C11—82no—
217D4×C11#12114yescomplemented
218C2×C4×C11—28no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—44no—
231C2×C4×C11—44no—
232C2×C4×C11—42no—
233C2×C4×C11—82no—
234C2×C4×C11—82no—
235C2×C4×C11—82no—
236C2×C4×C11—84no—
237C2×C4×C11—82no—
238C2×C4×C11#12012yes—
239C2×C4×C11#12011yescharacteristic
240C2×C4×C11#12011yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D412yes—
243C2×C4×C11C2×#4112yes—
244C2×C4×C11C2×#4111yescharacteristic
245C8×C11—44no—
246C2×H(5,𝔽2)C22×C1111yescharacteristic
247C2×AGL(1,ℤ/8)C22×C1114yes—
248C2×#127C22×C1112yes—
249C2×#127C22×C1111yescharacteristic, complemented
250C2×#121—22no—
251#520—22no—
252#520C22×C1112yes—
253#518—22no—
254#518—22no—
255#518C22×C1111yescharacteristic
256C4×#41—22no—
257C4×#41C22×C1112yes—
258C2×C4×D4—22no—
259C2×C4×D4—22no—
260C2×C4×D4C22×C1111yescharacteristic
261#460—22no—
262#460—22no—
263#459—22no—
264#459—22no—
265#453—28no—
266#423C22×C1112yescomplemented
267C2×#104C22×C1114yes—
268#418C22×C1114yescomplemented
269C2×#100C22×C1112yes—
270#392—22no—
271#390C22×C1112yescomplemented
272C4×C4⋊C4C22×C1111yescharacteristic, complemented
273#343C22×C1112yescomplemented
274#339C22×C1114yescomplemented
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—24no—
278C22×C11—24no—
279C22×C11—44no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—82no—
285C22×C11—84no—
286C22×C11—84no—
287C22×C11—88no—
288C22×C11—82no—
289C22×C11—82no—
290C22×C11—82no—
291C22×C11C2×#12011yescharacteristic
292C22×C11C2×#12111yescharacteristic
293C22×C11#52511yescharacteristic
294C4×C11—24no—
295C4×C11—21no—
296C4×C11—22no—
297C4×C11—44no—
298C4×C11—42no—
299C4×C11—42no—
300C4×C11—42no—
301C4×C11#45312yescomplemented
302C4×C11C2×#12112yes—
303C4×C11#52512yes—
304H(5,𝔽2)—24no—
305H(5,𝔽2)—22no—
306H(5,𝔽2)D4×C1114yescomplemented
307C2×#41—22no—
308C2×#41C23×C1112yes—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—24no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4C23×C1112yes—
315C22×D4C23×C1111yescharacteristic
316C23×C4—22no—
317C23×C4D4×C1112yes—
318AGL(1,ℤ/8)—28no—
319AGL(1,ℤ/8)—28no—
320C2×SD16—24no—
321C2×D8—24no—
322C2×M16C23×C1114yes—
323#127—24no—
324#127—24no—
325#127—22no—
326#127—22no—
327#121—48no—
328C4×Q8—22no—
329C4×Q8D4×C1112yescomplemented
330C4×Q8D4×C1112yescomplemented
331C4×D4—24no—
332C4×D4—24no—
333C4×D4—24no—
334C4×D4—24no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4—24no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4D4×C1112yescomplemented
344C4×D4D4×C1112yescomplemented
345#117—24no—
346#117—22no—
347#117—22no—
348#117C23×C1112yes—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4C23×C1111yescharacteristic
353C2×C22⋊C4—22no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4D4×C1112yes—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42C23×C1112yes—
361C2×C42C23×C1111yescharacteristic
362C4⋊C8—22no—
363C4⋊C8—22no—
364#104—28no—
365#102—24no—
366#102—24no—
367#100—24no—
368#95—21no—
369C2×C11—21no—
370C2×C11—21no—
371C2×C11—44no—
372C2×C11—44no—
373C2×C11—162no—
374C2×C11#284711yescharacteristic
375C2×C11C2×#45311yescharacteristic
376C2×C11#302111yescharacteristic
377C24—22no—
378C24—22no—
379C24C2×D4×C1112yes—
380#41—28no—
381#41—28no—
382#41—22no—
383#41—22no—
384#41C2×D4×C1114yes—
385#41C11×#4114yes—
386C2×Q8C2×D4×C1112yes—
387C2×D4—24no—
388C2×D4—28no—
389C2×D4—28no—
390C2×D4—28no—
391C2×D4—22no—
392C2×D4—28no—
393C2×D4—22no—
394C2×D4—24no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—24no—
399C2×D4—44no—
400C2×D4—48no—
401C2×D4—48no—
402C2×D4—42no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—82no—
406C2×D4—84no—
407C2×D4C2×D4×C1112yes—
408C2×D4C2×D4×C1112yes—
409C2×D4C11×#4112yes—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—44no—
421C22×C4—84no—
422C22×C4C2×D4×C1111yescharacteristic
423C22×C4C2×D4×C1112yes—
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C24×C1111yescharacteristic
426SD16—48no—
427D8—48no—
428M16—24no—
429M16—24no—
430C2×C8—24no—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4C2×D4×C1112yes—
437C4⋊C4C2×D4×C1112yes—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—24no—
444C22⋊C4—48no—
445C42—24no—
446C42—22no—
447C42—22no—
448C42—22no—
449C42—22no—
450C42—22no—
451C42C2×D4×C1112yes—
452C42C2×D4×C1112yes—
453C11#3292011yescharacteristic, direct product factor, Sylow
454C23—28no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—42no—
459C23—42no—
460C23—44no—
461C23—44no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—82no—
466C23—82no—
467C23C11×#12114yes—
468C23C22×D4×C1111yescharacteristic
469Q8—22no—
470Q8C11×#12114yescomplemented
471D4—216no—
472D4—24no—
473D4—24no—
474D4—24no—
475D4—22no—
476D4—24no—
477D4—44no—
478D4—44no—
479D4—82no—
480D4—84no—
481D4—816no—
482D4—82no—
483D4C11×#12114yescomplemented
484C2×C4—28no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—44no—
497C2×C4—44no—
498C2×C4—42no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—84no—
503C2×C4—82no—
504C2×C4C11×#12012yes—
505C2×C4C11×#12011yescharacteristic
506C2×C4C11×#12011yescharacteristic
507C2×C4C22×D4×C1111yescharacteristic
508C2×C4C22×D4×C1112yes—
509C2×C4C2×C11×#4112yes—
510C2×C4C2×C11×#4111yescharacteristic
511C8—44no—
512C22—21no—
513C22—21no—
514C22—24no—
515C22—24no—
516C22—44no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—82no—
522C22—84no—
523C22—84no—
524C22—88no—
525C22—82no—
526C22—82no—
527C22—82no—
528C22C2×C11×#12011yescharacteristic
529C22C2×C11×#12111yescharacteristic
530C22C11×#52511yescharacteristic
531C4—21no—
532C4—22no—
533C4—24no—
534C4—44no—
535C4—42no—
536C4—42no—
537C4—42no—
538C4C11×#45312yescomplemented
539C4C2×C11×#12112yes—
540C4C11×#52512yes—
541C2—21no—
542C2—21no—
543C2—44no—
544C2—44no—
545C2—162no—
546C2C11×#284711yescharacteristic
547C2C2×C11×#45311yescharacteristic
548C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C4×C11×H(5,𝔽2)C2semidirect
2. C11×#3038C2semidirect
3. C2×C11×#453C2semidirect
4. C11×#2541C2semidirect
5. C11×#1887C2semidirect
6. C11×#1883C2semidirect
7. C11×#1806C2semidirect
8. C11×#1800C2semidirect
12. C2×C11×#127C22semidirect
29. C11×#423C22semidirect
31. C11×#418C22semidirect
34. C11×#390C22semidirect
35. C4×C11×C4⋊C4C22semidirect
36. C11×#343C22semidirect
37. C11×#339C22semidirect
40. C11×H(5,𝔽2)D4semidirect
63. C4×Q8×C11D4semidirect
64. C4×Q8×C11D4semidirect
77. C4×D4×C11D4semidirect
78. C4×D4×C11D4semidirect
103. #32920C11direct (N × H)
180. C4×H(5,𝔽2)C2×C11semidirect
181. #3038C2×C11semidirect
182. C2×#453C2×C11semidirect
183. #2541C2×C11semidirect
184. #1887C2×C11semidirect
185. #1883C2×C11semidirect
186. #1806C2×C11semidirect
187. #1800C2×C11semidirect
204. Q8×C11#121semidirect
217. D4×C11#121semidirect
249. C2×#127C22×C11semidirect
266. #423C22×C11semidirect
268. #418C22×C11semidirect
271. #390C22×C11semidirect
272. C4×C4⋊C4C22×C11semidirect
273. #343C22×C11semidirect
274. #339C22×C11semidirect
301. C4×C11#453semidirect
306. H(5,𝔽2)D4×C11semidirect
329. C4×Q8D4×C11semidirect
330. C4×Q8D4×C11semidirect
343. C4×D4D4×C11semidirect
344. C4×D4D4×C11semidirect
453. C11#32920direct (N × H)
470. Q8C11×#121semidirect
483. D4C11×#121semidirect
538. C4C11×#453semidirect

Maximal subgroups

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

subgroupindex
C4×C11×H(5,𝔽2)2
C11×#30382
C2×C11×#4532
C11×#25412
C11×#18872
C11×#18832
C11×#18062
C11×#18002
#3292011