Finite Group Databasebeta

← C11×#24222 #14601415

Subgroups — C11×#24222 #14601415

Order 2816.

1586 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3496C211yesmaximal, characteristic, complemented
2C11×#3036C212yesmaximal, complemented
3C2×C11×#453C212yesmaximal, complemented
4C4×C11×#127C211yesmaximal, characteristic, complemented
5C11×#2039C212yesmaximal, complemented
6C11×#2006C212yesmaximal, complemented
7C11×#1962C212yesmaximal, complemented
8C11×#1800C211yesmaximal, characteristic, complemented
9C11×#1792C212yesmaximal, complemented
10C2×C11×H(5,𝔽2)C2212yes—
11C2×C11×AGL(1,ℤ/8)C2214yescomplemented
12C11×#547—22no—
13C11×#546—24no—
14D42×C11—22no—
15C11×#537C2212yes—
16C11×#534—22no—
17C11×#532C2212yes—
18C2×C11×#127C2211yescharacteristic
19C2×C11×#121—22no—
20C2×C4×D4×C11—22no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic, complemented
23C11×#463—24no—
24C11×#461—22no—
25C11×#459—22no—
26C11×#453—28no—
27C11×#423C2212yescomplemented
28C2×C11×#104C2214yescomplemented
29C2×C11×#104C2214yescomplemented
30C11×#417C2214yescomplemented
31C2×C11×#100C2212yes—
32C11×#390—22no—
33C11×#390C2211yescharacteristic
34C11×#390C2211yescharacteristic, complemented
35C11×#384C2211yescharacteristic, complemented
36C43×C11C2211yescharacteristic, complemented
37C11×#343C2212yescomplemented
38C11×H(5,𝔽2)—24no—
39C11×H(5,𝔽2)—24no—
40C11×H(5,𝔽2)—44no—
41C2×C11×#41—24no—
42C2×C11×#41C2314yes—
43C22×D4×C11—22no—
44C22×D4×C11—24no—
45C22×D4×C11—22no—
46C22×D4×C11—24no—
47C22×D4×C11C2311yescharacteristic
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11D412yes—
51C11×AGL(1,ℤ/8)—28no—
52C11×AGL(1,ℤ/8)—44no—
53C2×C11×SD16—24no—
54C2×C11×D8—24no—
55C2×C11×M16C2314yes—
56C11×C4⋊Q8D412yescomplemented
57C11×#127—22no—
58C11×#127D412yescomplemented
59C11×#127D414yescomplemented
60C11×#124D414yescomplemented
61C11×#123—28no—
62C11×C22⋊Q8—24no—
63C11×#121—24no—
64C11×#121—24no—
65C11×#121—24no—
66C11×#121—22no—
67C11×#121—24no—
68C11×#121—22no—
69C11×#120—28no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C4×D4×C11—22no—
76C4×D4×C11—48no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4D412yes—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C11×C4⋊C8—22no—
92C11×C4⋊C8—22no—
93C11×#104—28no—
94C11×#104—44no—
95C11×#103—24no—
96C11×#102—24no—
97C11×#100—24no—
98#24222C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11—24no—
100C24×C11—21no—
101C24×C11C2×D412yes—
102C11×#41—24no—
103C11×#41—24no—
104C11×#41—24no—
105C11×#41—24no—
106C11×#41—48no—
107C11×#41—48no—
108C2×Q8×C11C2×D414yes—
109C2×D4×C11—28no—
110C2×D4×C11—28no—
111C2×D4×C11—24no—
112C2×D4×C11—24no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—44no—
121C2×D4×C11—44no—
122C2×D4×C11—48no—
123C2×D4×C11—48no—
124C2×D4×C11—48no—
125C2×D4×C11—48no—
126C2×D4×C11—84no—
127C2×D4×C11C2×D414yes—
128C2×D4×C11C2×D412yes—
129C2×D4×C11C2×D412yescomplemented
130C2×D4×C11#4112yes—
131C22×C4×C11—21no—
132C22×C4×C11—24no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—44no—
139C22×C4×C11—44no—
140C22×C4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C11×SD16—48no—
147C11×D8—48no—
148C11×M16—24no—
149C11×M16—24no—
150C2×C8×C11—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—44no—
157C11×C22⋊C4—28no—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—44no—
162C11×C22⋊C4—44no—
163C11×C22⋊C4—42no—
164C42×C11—24no—
165C42×C11—21no—
166C42×C11—22no—
167C42×C11—42no—
168C42×C11C2×D412yes—
169C42×C11C2×D412yes—
170C42×C11C2×D412yescomplemented
171#3496C2×C1111yescharacteristic, complemented
172#3036C2×C1112yescomplemented
173C2×#453C2×C1112yescomplemented
174C4×#127C2×C1111yescharacteristic, complemented
175#2039C2×C1112yescomplemented
176#2006C2×C1112yescomplemented
177#1962C2×C1112yescomplemented
178#1800C2×C1111yescharacteristic, complemented
179#1792C2×C1112yescomplemented
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—24no—
183C23×C11—22no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—48no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—84no—
192C23×C11—84no—
193C23×C11#12114yes—
194C23×C11C22×D411yescharacteristic
195Q8×C11—24no—
196Q8×C11—24no—
197D4×C11—24no—
198D4×C11—24no—
199D4×C11—24no—
200D4×C11—24no—
201D4×C11—24no—
202D4×C11—416no—
203D4×C11—416no—
204D4×C11—44no—
205D4×C11—44no—
206D4×C11—42no—
207D4×C11—44no—
208D4×C11—82no—
209D4×C11—84no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—48no—
220C2×C4×C11—41no—
221C2×C4×C11—44no—
222C2×C4×C11—44no—
223C2×C4×C11—44no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—41no—
227C2×C4×C11—82no—
228C2×C4×C11—82no—
229C2×C4×C11—82no—
230C2×C4×C11#12012yes—
231C2×C4×C11#12011yescharacteristic
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D412yes—
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11H(5,𝔽2)12yes—
237C8×C11—44no—
238C2×H(5,𝔽2)C22×C1112yes—
239C2×AGL(1,ℤ/8)C22×C1114yescomplemented
240#547—22no—
241#546—24no—
242D42—22no—
243#537C22×C1112yes—
244#534—22no—
245#532C22×C1112yes—
246C2×#127C22×C1111yescharacteristic
247C2×#121—22no—
248C2×C4×D4—22no—
249C2×C4×D4C22×C1111yescharacteristic
250C2×C4×D4C22×C1111yescharacteristic, complemented
251#463—24no—
252#461—22no—
253#459—22no—
254#453—28no—
255#423C22×C1112yescomplemented
256C2×#104C22×C1114yescomplemented
257C2×#104C22×C1114yescomplemented
258#417C22×C1114yescomplemented
259C2×#100C22×C1112yes—
260#390—22no—
261#390C22×C1111yescharacteristic
262#390C22×C1111yescharacteristic, complemented
263#384C22×C1111yescharacteristic, complemented
264C43C22×C1111yescharacteristic, complemented
265#343C22×C1112yescomplemented
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—24no—
269C22×C11—44no—
270C22×C11—44no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—44no—
274C22×C11—42no—
275C22×C11—44no—
276C22×C11—44no—
277C22×C11—82no—
278C22×C11—82no—
279C22×C11—81no—
280C22×C11—81no—
281C22×C11—168no—
282C22×C11C2×#12011yescharacteristic
283C22×C11C2×#12111yescharacteristic
284C22×C11#53511yescharacteristic
285C4×C11—24no—
286C4×C11—21no—
287C4×C11—22no—
288C4×C11—42no—
289C4×C11—44no—
290C4×C11—42no—
291C4×C11—81no—
292C4×C11#45312yescomplemented
293C4×C11D4212yes—
294C4×C11#54612yes—
295H(5,𝔽2)—24no—
296H(5,𝔽2)—24no—
297H(5,𝔽2)—44no—
298C2×#41—24no—
299C2×#41C23×C1114yes—
300C22×D4—22no—
301C22×D4—24no—
302C22×D4—22no—
303C22×D4—24no—
304C22×D4C23×C1111yescharacteristic
305C22×D4C23×C1111yescharacteristic
306C23×C4—21no—
307C23×C4D4×C1112yes—
308AGL(1,ℤ/8)—28no—
309AGL(1,ℤ/8)—44no—
310C2×SD16—24no—
311C2×D8—24no—
312C2×M16C23×C1114yes—
313C4⋊Q8D4×C1112yescomplemented
314#127—22no—
315#127D4×C1112yescomplemented
316#127D4×C1114yescomplemented
317#124D4×C1114yescomplemented
318#123—28no—
319C22⋊Q8—24no—
320#121—24no—
321#121—24no—
322#121—24no—
323#121—22no—
324#121—24no—
325#121—22no—
326#120—28no—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—22no—
332C4×D4—22no—
333C4×D4—48no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4C23×C1111yescharacteristic
337C2×C4⋊C4C23×C1111yescharacteristic
338C2×C22⋊C4—24no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4D4×C1112yes—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42C23×C1111yescharacteristic
346C2×C42C23×C1111yescharacteristic
347C2×C42C23×C1111yescharacteristic
348C4⋊C8—22no—
349C4⋊C8—22no—
350#104—28no—
351#104—44no—
352#103—24no—
353#102—24no—
354#100—24no—
355C2×C11—21no—
356C2×C11—21no—
357C2×C11—44no—
358C2×C11—82no—
359C2×C11—84no—
360C2×C11#240811yescharacteristic
361C2×C11C2×#45311yescharacteristic
362C2×C11#301811yescharacteristic
363C24—24no—
364C24—21no—
365C24C2×D4×C1112yes—
366#41—24no—
367#41—24no—
368#41—24no—
369#41—24no—
370#41—48no—
371#41—48no—
372C2×Q8C2×D4×C1114yes—
373C2×D4—28no—
374C2×D4—28no—
375C2×D4—24no—
376C2×D4—24no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—48no—
387C2×D4—48no—
388C2×D4—48no—
389C2×D4—48no—
390C2×D4—84no—
391C2×D4C2×D4×C1114yes—
392C2×D4C2×D4×C1112yes—
393C2×D4C2×D4×C1112yescomplemented
394C2×D4C11×#4112yes—
395C22×C4—21no—
396C22×C4—24no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—44no—
403C22×C4—44no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4C2×D4×C1111yescharacteristic
407C22×C4C2×D4×C1112yes—
408C22×C4C2×D4×C1111yescharacteristic
409C22×C4C24×C1111yescharacteristic
410SD16—48no—
411D8—48no—
412M16—24no—
413M16—24no—
414C2×C8—24no—
415C4⋊C4—24no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—44no—
421C22⋊C4—28no—
422C22⋊C4—24no—
423C22⋊C4—24no—
424C22⋊C4—24no—
425C22⋊C4—44no—
426C22⋊C4—44no—
427C22⋊C4—42no—
428C42—24no—
429C42—21no—
430C42—22no—
431C42—42no—
432C42C2×D4×C1112yes—
433C42C2×D4×C1112yes—
434C42C2×D4×C1112yescomplemented
435C11#2422211yescharacteristic, direct product factor, Sylow
436C23—22no—
437C23—22no—
438C23—24no—
439C23—22no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—48no—
445C23—41no—
446C23—41no—
447C23—84no—
448C23—84no—
449C23C11×#12114yes—
450C23C22×D4×C1111yescharacteristic
451Q8—24no—
452Q8—24no—
453D4—24no—
454D4—24no—
455D4—24no—
456D4—24no—
457D4—24no—
458D4—416no—
459D4—416no—
460D4—44no—
461D4—44no—
462D4—42no—
463D4—44no—
464D4—82no—
465D4—84no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—48no—
476C2×C4—41no—
477C2×C4—44no—
478C2×C4—44no—
479C2×C4—44no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4—82no—
486C2×C4C11×#12012yes—
487C2×C4C11×#12011yescharacteristic
488C2×C4C11×#12011yescharacteristic
489C2×C4C22×D4×C1111yescharacteristic
490C2×C4C22×D4×C1112yes—
491C2×C4C2×C11×#4111yescharacteristic
492C2×C4C11×H(5,𝔽2)12yes—
493C8—44no—
494C22—21no—
495C22—21no—
496C22—24no—
497C22—44no—
498C22—44no—
499C22—42no—
500C22—42no—
501C22—44no—
502C22—42no—
503C22—44no—
504C22—44no—
505C22—82no—
506C22—82no—
507C22—81no—
508C22—81no—
509C22—168no—
510C22C2×C11×#12011yescharacteristic
511C22C2×C11×#12111yescharacteristic
512C22C11×#53511yescharacteristic
513C4—24no—
514C4—21no—
515C4—22no—
516C4—42no—
517C4—44no—
518C4—42no—
519C4—81no—
520C4C11×#45312yescomplemented
521C4D42×C1112yes—
522C4C11×#54612yes—
523C2—21no—
524C2—21no—
525C2—44no—
526C2—82no—
527C2—84no—
528C2C11×#240811yescharacteristic
529C2C2×C11×#45311yescharacteristic
530C2C11×#301811yescharacteristic
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. C11×#3496C2semidirect
2. C11×#3036C2semidirect
3. C2×C11×#453C2semidirect
4. C4×C11×#127C2semidirect
5. C11×#2039C2semidirect
6. C11×#2006C2semidirect
7. C11×#1962C2semidirect
8. C11×#1800C2semidirect
9. C11×#1792C2semidirect
11. C2×C11×AGL(1,ℤ/8)C22semidirect
22. C2×C4×D4×C11C22semidirect
27. C11×#423C22semidirect
28. C2×C11×#104C22semidirect
29. C2×C11×#104C22semidirect
30. C11×#417C22semidirect
34. C11×#390C22semidirect
35. C11×#384C22semidirect
36. C43×C11C22semidirect
37. C11×#343C22semidirect
56. C11×C4⋊Q8D4semidirect
58. C11×#127D4semidirect
59. C11×#127D4semidirect
60. C11×#124D4semidirect
98. #24222C11direct (N × H)
129. C2×D4×C11C2×D4semidirect
170. C42×C11C2×D4semidirect
171. #3496C2×C11semidirect
172. #3036C2×C11semidirect
173. C2×#453C2×C11semidirect
174. C4×#127C2×C11semidirect
175. #2039C2×C11semidirect
176. #2006C2×C11semidirect
177. #1962C2×C11semidirect
178. #1800C2×C11semidirect
179. #1792C2×C11semidirect
239. C2×AGL(1,ℤ/8)C22×C11semidirect
250. C2×C4×D4C22×C11semidirect
255. #423C22×C11semidirect
256. C2×#104C22×C11semidirect
257. C2×#104C22×C11semidirect
258. #417C22×C11semidirect
262. #390C22×C11semidirect
263. #384C22×C11semidirect
264. C43C22×C11semidirect
265. #343C22×C11semidirect
292. C4×C11#453semidirect
313. C4⋊Q8D4×C11semidirect
315. #127D4×C11semidirect
316. #127D4×C11semidirect
317. #124D4×C11semidirect
393. C2×D4C2×D4×C11semidirect
434. C42C2×D4×C11semidirect
435. C11#24222direct (N × H)
520. C4C11×#453semidirect

Maximal subgroups

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

subgroupindex
C11×#34962
C11×#30362
C2×C11×#4532
C4×C11×#1272
C11×#20392
C11×#20062
C11×#19622
C11×#18002
C11×#17922
#2422211