Finite Group Databasebeta

← C11×#24094 #14601287

Subgroups — C11×#24094 #14601287

Order 2816.

1100 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#552C211yesmaximal, characteristic
2C2×C11×#483C211yesmaximal, characteristic, complemented
3C22×C11×#107C211yesmaximal, characteristic, complemented
4C11×#2486C211yesmaximal, characteristic
5C11×#2059C212yesmaximal, complemented
6C11×#2036C212yesmaximal, complemented
7C11×#1892C211yesmaximal, characteristic, complemented
8C11×#1869C211yesmaximal, characteristic
9C11×#1863C212yesmaximal, complemented
10C11×#1854C212yesmaximal, complemented
11C11×#1823C211yesmaximal, characteristic, complemented
12C23×C8×C11C2211yescharacteristic
13C11×#552—24no—
14C11×#552—24no—
15C2×C11×#126—21no—
16C2×C11×#125—21no—
17C2×C11×#125C2211yescharacteristic
18C2×C11×#123—21no—
19C2×C11×#123—21no—
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117—21no—
25C2×C11×#117C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C11×#483—24no—
29C2×C11×#107—24no—
30C2×C11×#107C2212yes—
31C2×C11×#107C2212yes—
32C2×C11×#106C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#103C2212yes—
35C2×C11×C22⋊C8C2212yes—
36C2×C11×C22⋊C8C2211yescharacteristic
37C11×#398—21no—
38C11×#397—21no—
39C11×#389C2212yes—
40C11×#381—21no—
41C11×#380C2211yescharacteristic
42C11×#380C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C11×#340C2212yes—
46C11×#336C2212yes—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11D411yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11—21no—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C22×C8×C11—22no—
54C22×C8×C11—24no—
55C22×C8×C11C2312yes—
56C22×C8×C11C2312yes—
57C11×#126—28no—
58C11×#125—28no—
59C11×#125—22no—
60C11×#125—22no—
61C11×#123—28no—
62C11×#123—44no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8D414yes—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C11×#117—28no—
72C11×#117—22no—
73C11×#117—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C4⋊C4D414yes—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C11×C22⋊C4D411yescharacteristic
99C2×C42×C11—21no—
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102C11×#107—24no—
103C11×#107—24no—
104C11×#106—24no—
105C11×#103—24no—
106C11×#103—24no—
107C11×C22⋊C8—22no—
108C11×C22⋊C8—24no—
109C11×#95—22no—
110C11×#95—21no—
111C11×#95—22no—
112#24094C1111yesmaximal, characteristic, direct product factor, Sylow
113C24×C11C2×D411yescharacteristic
114C24×C11C2×D411yescharacteristic
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11C2×D412yes—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—24no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2411yescharacteristic
147C2×C8×C11—28no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11#4114yes—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—44no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4C2×D412yes—
171C11×C4⋊C4C2×D412yes—
172C11×C4⋊C4C2×D412yes—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—44no—
179C11×C22⋊C4—42no—
180C42×C11—24no—
181C42×C11—24no—
182C42×C11—21no—
183C42×C11—21no—
184C2×#552C2×C1111yescharacteristic
185C2×#483C2×C1111yescharacteristic, complemented
186C22×#107C2×C1111yescharacteristic, complemented
187#2486C2×C1111yescharacteristic
188#2059C2×C1112yescomplemented
189#2036C2×C1112yescomplemented
190#1892C2×C1111yescharacteristic, complemented
191#1869C2×C1111yescharacteristic
192#1863C2×C1112yescomplemented
193#1854C2×C1112yescomplemented
194#1823C2×C1111yescharacteristic, complemented
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—21no—
198C23×C11—22no—
199C23×C11—21no—
200C23×C11—21no—
201C23×C11—22no—
202C23×C11#12012yes—
203C23×C11#13512yes—
204C23×C11AGL(1,ℤ/8)12yes—
205C23×C11C22×D411yescharacteristic
206Q8×C11—24no—
207Q8×C11—41no—
208Q8×C11—41no—
209D4×C11—44no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—22no—
225C2×C4×C11—42no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—48no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—84no—
242C2×C4×C11#12012yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4112yes—
246C2×C4×C112−1+412yes—
247C8×C11—24no—
248C8×C11—42no—
249C23×C8C22×C1111yescharacteristic
250#552—24no—
251#552—24no—
252C2×#126—21no—
253C2×#125—21no—
254C2×#125C22×C1111yescharacteristic
255C2×#123—21no—
256C2×#123—21no—
257C2×C22⋊Q8C22×C1111yescharacteristic
258C2×C22⋊Q8C22×C1111yescharacteristic
259C2×C4×Q8C22×C1111yescharacteristic
260C2×C4×D4C22×C1111yescharacteristic
261C2×#117—21no—
262C2×#117C22×C1111yescharacteristic
263C22×C4⋊C4C22×C1111yescharacteristic
264C22×C4⋊C4C22×C1111yescharacteristic
265#483—24no—
266C2×#107—24no—
267C2×#107C22×C1112yes—
268C2×#107C22×C1112yes—
269C2×#106C22×C1112yes—
270C2×#103C22×C1112yes—
271C2×#103C22×C1112yes—
272C2×C22⋊C8C22×C1111yescharacteristic
273C2×C22⋊C8C22×C1112yes—
274#398—21no—
275#397—21no—
276#389C22×C1112yes—
277#381—21no—
278#380C22×C1111yescharacteristic
279#380C22×C1112yes—
280#340C22×C1112yes—
281#340C22×C1112yes—
282#340C22×C1112yes—
283#336C22×C1112yes—
284C22×C11—24no—
285C22×C11—24no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—41no—
291C22×C11—41no—
292C22×C11—41no—
293C22×C11#44914yes—
294C22×C11C2×#12011yescharacteristic
295C22×C11#54712yes—
296C22×C11C2×#13511yescharacteristic
297C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
298C22×C11#57812yes—
299C4×C11—22no—
300C4×C11—41no—
301C4×C11—42no—
302C4×C11—41no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11—41no—
306C4×C11—42no—
307C4×C11—82no—
308C4×C11—82no—
309C4×C11#52511yescharacteristic
310C4×C11#53611yescharacteristic
311C4×C11#54712yes—
312C22×Q8C23×C1111yescharacteristic
313C22×D4D4×C1111yescharacteristic
314C23×C4—21no—
315C23×C4—21no—
316C23×C4C23×C1111yescharacteristic
317C23×C4C23×C1111yescharacteristic
318C22×C8—22no—
319C22×C8—24no—
320C22×C8C23×C1112yes—
321C22×C8C23×C1112yes—
322#126—28no—
323#125—28no—
324#125—22no—
325#125—22no—
326#123—28no—
327#123—44no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8D4×C1114yes—
332C4×Q8—22no—
333C4×Q8—22no—
334C4×D4—22no—
335C4×D4—22no—
336#117—28no—
337#117—22no—
338#117—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4D4×C1111yescharacteristic
351C2×C4⋊C4D4×C1114yes—
352C2×C4⋊C4C23×C1112yes—
353C2×C4⋊C4C23×C1112yes—
354C2×C4⋊C4C23×C1111yescharacteristic
355C2×C4⋊C4C23×C1111yescharacteristic
356C2×C4⋊C4C23×C1111yescharacteristic
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4D4×C1111yescharacteristic
363C2×C22⋊C4D4×C1111yescharacteristic
364C2×C42—21no—
365C2×C42—21no—
366C2×C42C23×C1111yescharacteristic
367#107—24no—
368#107—24no—
369#106—24no—
370#103—24no—
371#103—24no—
372C22⋊C8—22no—
373C22⋊C8—24no—
374#95—22no—
375#95—21no—
376#95—22no—
377C2×C11—24no—
378C2×C11—81no—
379C2×C11#240611yescharacteristic
380C2×C11C2×#44911yescharacteristic
381C2×C11#301111yescharacteristic
382C2×C11#333612yes—
383C2×C11#334312yes—
384C24C2×D4×C1111yescharacteristic
385C24C2×D4×C1111yescharacteristic
386C2×Q8—21no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8C2×D4×C1112yes—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4C2×D4×C1111yescharacteristic
412C22×C4C2×D4×C1111yescharacteristic
413C22×C4C2×D4×C1111yescharacteristic
414C22×C4C2×D4×C1111yescharacteristic
415C22×C4C2×D4×C1112yes—
416C22×C4C2×D4×C1112yes—
417C22×C4C24×C1111yescharacteristic
418C2×C8—28no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8C11×#4114yes—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—44no—
440C4⋊C4—42no—
441C4⋊C4C2×D4×C1112yes—
442C4⋊C4C2×D4×C1112yes—
443C4⋊C4C2×D4×C1112yes—
444C22⋊C4—24no—
445C22⋊C4—24no—
446C22⋊C4—24no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—44no—
450C22⋊C4—42no—
451C42—24no—
452C42—24no—
453C42—21no—
454C42—21no—
455C11#2409411yescharacteristic, direct product factor, Sylow
456C23—22no—
457C23—22no—
458C23—21no—
459C23—22no—
460C23—21no—
461C23—21no—
462C23—22no—
463C23C11×#12012yes—
464C23C11×#13512yes—
465C23C11×AGL(1,ℤ/8)12yes—
466C23C22×D4×C1111yescharacteristic
467Q8—24no—
468Q8—41no—
469Q8—41no—
470D4—44no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—48no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—84no—
503C2×C4C11×#12012yes—
504C2×C4C22×D4×C1111yescharacteristic
505C2×C4C22×D4×C1111yescharacteristic
506C2×C4C2×C11×#4112yes—
507C2×C4C11×2−1+412yes—
508C8—24no—
509C8—42no—
510C22—22no—
511C22—22no—
512C22—24no—
513C22—24no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—42no—
518C22—42no—
519C22C11×#44914yes—
520C22C2×C11×#12011yescharacteristic
521C22C11×#54712yes—
522C22C2×C11×#13511yescharacteristic
523C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
524C22C11×#57812yes—
525C4—22no—
526C4—41no—
527C4—42no—
528C4—41no—
529C4—42no—
530C4—42no—
531C4—41no—
532C4—42no—
533C4—82no—
534C4—82no—
535C4C11×#52511yescharacteristic
536C4C11×#53611yescharacteristic
537C4C11×#54712yes—
538C2—24no—
539C2—81no—
540C2C11×#240611yescharacteristic
541C2C2×C11×#44911yescharacteristic
542C2C11×#301111yescharacteristic
543C2C11×#333612yes—
544C2C11×#334312yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#483C2semidirect
3. C22×C11×#107C2semidirect
5. C11×#2059C2semidirect
6. C11×#2036C2semidirect
7. C11×#1892C2semidirect
9. C11×#1863C2semidirect
10. C11×#1854C2semidirect
11. C11×#1823C2semidirect
112. #24094C11direct (N × H)
185. C2×#483C2×C11semidirect
186. C22×#107C2×C11semidirect
188. #2059C2×C11semidirect
189. #2036C2×C11semidirect
190. #1892C2×C11semidirect
192. #1863C2×C11semidirect
193. #1854C2×C11semidirect
194. #1823C2×C11semidirect
455. C11#24094direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5522
C2×C11×#4832
C22×C11×#1072
C11×#24862
C11×#20592
C11×#20362
C11×#18922
C11×#18692
C11×#18632
C11×#18542
C11×#18232
#2409411