Finite Group Databasebeta

← C11×#24079 #14601272

Subgroups — C11×#24079 #14601272

Order 2816.

1030 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
1C11×#3492C211yesmaximal, characteristic
2C11×#3093C212yesmaximal, complemented
3C11×#2317C211yesmaximal, characteristic, complemented
4C11×#2061C211yesmaximal, characteristic, complemented
5C11×#2060C211yesmaximal, characteristic, complemented
6C11×#2040C211yesmaximal, characteristic, complemented
7C11×#2039C211yesmaximal, characteristic, complemented
8C11×#1897C212yesmaximal, complemented
9C11×#1860C212yesmaximal, complemented
10C11×#1859C212yesmaximal, complemented
11C11×#1821C211yesmaximal, characteristic, complemented
12C11×#554—22no—
13C11×#553—22no—
14C11×#552—22no—
15C11×#547—22no—
16C11×#544C2211yescharacteristic
17C11×#539—22no—
18C11×#537C2211yescharacteristic
19C11×#525—22no—
20C11×#525C2212yes—
21C11×#520C2212yes—
22C2×C11×#117C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C11×#485—22no—
26C11×#485—22no—
27C11×#482—22no—
28C11×#482—22no—
29C11×#428C2212yes—
30C11×#428C2212yes—
31C2×C11×#104C2212yes—
32C2×C11×#104C2212yes—
33C11×#417C2212yes—
34C11×#417C2212yes—
35C11×#407C2212yes—
36C11×#389—22no—
37C11×#385—22no—
38C11×#384C2211yescharacteristic
39C11×#384C2211yescharacteristic
40C11×#382C2211yescharacteristic
41C11×#382C2211yescharacteristic
42C11×#343C2211yescharacteristic
43C11×#343C2211yescharacteristic
44C11×#343C2212yes—
45C11×#339C2212yes—
46C11×#339C2212yes—
47C2×C11×#41—22no—
48C2×C11×#41C2312yes—
49C23×C4×C11D412yes—
50C23×C4×C11C2311yescharacteristic
51C2×C11×M16C2312yes—
52C2×C11×M16C2312yes—
53C11×C4⋊Q8—22no—
54C11×#126—24no—
55C11×#125—24no—
56C11×#125—22no—
57C11×#123—24no—
58C11×#123—24no—
59C11×#123—22no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8D412yes—
65C11×C22⋊Q8D412yes—
66C11×#121—22no—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121D412yes—
70C11×#121D412yes—
71C11×#120—22no—
72C4×Q8×C11—22no—
73C4×D4×C11—24no—
74C4×D4×C11—22no—
75C4×D4×C11—24no—
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C11×#117—22no—
79C11×#117—22no—
80C11×#117—22no—
81C11×#117—22no—
82C11×#117—22no—
83C11×#117—22no—
84C11×#117C2312yes—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4D412yes—
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C42×C11—21no—
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C11×#107—22no—
102C11×#107—22no—
103C11×#106—22no—
104C11×#106—22no—
105C11×#104—24no—
106C11×#104—24no—
107C11×#103—22no—
108C11×#103—22no—
109C11×#102—22no—
110C11×#102—22no—
111C11×C22⋊C8—22no—
112C11×C22⋊C8—22no—
113C11×#95—22no—
114C11×#95—22no—
115#24079C1111yesmaximal, characteristic, direct product factor, Sylow
116C24×C11C2×D411yescharacteristic
117C11×#41—22no—
118C11×#41—22no—
119C11×#41—22no—
120C11×#41—22no—
121C11×#41—84no—
122C2×Q8×C11—22no—
123C2×Q8×C11C2×D412yes—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11C2×D412yes—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—82no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2411yescharacteristic
147C11×M16—22no—
148C11×M16—22no—
149C11×M16—22no—
150C11×M16—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—82no—
166C11×C4⋊C4—82no—
167C11×C4⋊C4C2×D412yes—
168C11×C4⋊C4C2×D412yes—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—41no—
178C11×C22⋊C4—41no—
179C42×C11—24no—
180C42×C11—22no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—42no—
184C42×C11#4112yescomplemented
185C42×C11#4112yescomplemented
186#3492C2×C1111yescharacteristic
187#3093C2×C1112yescomplemented
188#2317C2×C1111yescharacteristic, complemented
189#2061C2×C1111yescharacteristic, complemented
190#2060C2×C1111yescharacteristic, complemented
191#2040C2×C1111yescharacteristic, complemented
192#2039C2×C1111yescharacteristic, complemented
193#1897C2×C1112yescomplemented
194#1860C2×C1112yescomplemented
195#1859C2×C1112yescomplemented
196#1821C2×C1111yescharacteristic, complemented
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—22no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11#12011yescharacteristic
203C23×C11#12011yescharacteristic
204C23×C11C22×D411yescharacteristic
205Q8×C11—22no—
206Q8×C11—22no—
207Q8×C11—82no—
208D4×C11—22no—
209D4×C11—22no—
210D4×C11—44no—
211D4×C11—44no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—82no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—44no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—82no—
242C2×C4×C11—84no—
243C2×C4×C11#12012yes—
244C2×C4×C11C22×D412yes—
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C112−1+412yes—
248C8×C11—42no—
249C8×C11—42no—
250#554—22no—
251#553—22no—
252#552—22no—
253#547—22no—
254#544C22×C1111yescharacteristic
255#539—22no—
256#537C22×C1111yescharacteristic
257#525—22no—
258#525C22×C1112yes—
259#520C22×C1112yes—
260C2×#117C22×C1111yescharacteristic
261C2×#117C22×C1111yescharacteristic
262C22×C4⋊C4C22×C1111yescharacteristic
263#485—22no—
264#485—22no—
265#482—22no—
266#482—22no—
267#428C22×C1112yes—
268#428C22×C1112yes—
269C2×#104C22×C1112yes—
270C2×#104C22×C1112yes—
271#417C22×C1112yes—
272#417C22×C1112yes—
273#407C22×C1112yes—
274#389—22no—
275#385—22no—
276#384C22×C1111yescharacteristic
277#384C22×C1111yescharacteristic
278#382C22×C1111yescharacteristic
279#382C22×C1111yescharacteristic
280#343C22×C1111yescharacteristic
281#343C22×C1111yescharacteristic
282#343C22×C1112yes—
283#339C22×C1112yes—
284#339C22×C1112yes—
285C22×C11—21no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11C2×#12011yescharacteristic
299C22×C11#52511yescharacteristic
300C22×C11#53611yescharacteristic
301C4×C11—22no—
302C4×C11—42no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—81no—
310C4×C11—81no—
311C4×C11#54712yes—
312C4×C11#54712yes—
313C2×#41—22no—
314C2×#41C23×C1112yes—
315C23×C4D4×C1112yes—
316C23×C4C23×C1111yescharacteristic
317C2×M16C23×C1112yes—
318C2×M16C23×C1112yes—
319C4⋊Q8—22no—
320#126—24no—
321#125—24no—
322#125—22no—
323#123—24no—
324#123—24no—
325#123—22no—
326C22⋊Q8—22no—
327C22⋊Q8—24no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8D4×C1112yes—
331C22⋊Q8D4×C1112yes—
332#121—22no—
333#121—22no—
334#121—22no—
335#121D4×C1112yes—
336#121D4×C1112yes—
337#120—22no—
338C4×Q8—22no—
339C4×D4—24no—
340C4×D4—22no—
341C4×D4—24no—
342C4×D4—22no—
343C4×D4—22no—
344#117—22no—
345#117—22no—
346#117—22no—
347#117—22no—
348#117—22no—
349#117—22no—
350#117C23×C1112yes—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4D4×C1112yes—
358C2×C4⋊C4C23×C1111yescharacteristic
359C2×C4⋊C4C23×C1111yescharacteristic
360C2×C4⋊C4C23×C1111yescharacteristic
361C2×C4⋊C4C23×C1111yescharacteristic
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C42—21no—
365C2×C42C23×C1111yescharacteristic
366C2×C42C23×C1111yescharacteristic
367#107—22no—
368#107—22no—
369#106—22no—
370#106—22no—
371#104—24no—
372#104—24no—
373#103—22no—
374#103—22no—
375#102—22no—
376#102—22no—
377C22⋊C8—22no—
378C22⋊C8—22no—
379#95—22no—
380#95—22no—
381C2×C11—21no—
382C2×C11—21no—
383C2×C11—41no—
384C2×C11—41no—
385C2×C11—82no—
386C2×C11#240611yescharacteristic
387C2×C11#301911yescharacteristic
388C2×C11#302011yescharacteristic
389C24C2×D4×C1111yescharacteristic
390#41—22no—
391#41—22no—
392#41—22no—
393#41—22no—
394#41—84no—
395C2×Q8—22no—
396C2×Q8C2×D4×C1112yes—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4C2×D4×C1112yes—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—82no—
414C22×C4C2×D4×C1111yescharacteristic
415C22×C4C2×D4×C1112yes—
416C22×C4C2×D4×C1112yes—
417C22×C4C2×D4×C1112yes—
418C22×C4C2×D4×C1112yes—
419C22×C4C24×C1111yescharacteristic
420M16—22no—
421M16—22no—
422M16—22no—
423M16—22no—
424C2×C8—22no—
425C2×C8—22no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—82no—
439C4⋊C4—82no—
440C4⋊C4C2×D4×C1112yes—
441C4⋊C4C2×D4×C1112yes—
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C42—24no—
453C42—22no—
454C42—21no—
455C42—21no—
456C42—42no—
457C42C11×#4112yescomplemented
458C42C11×#4112yescomplemented
459C11#2407911yescharacteristic, direct product factor, Sylow
460C23—21no—
461C23—21no—
462C23—22no—
463C23—41no—
464C23—41no—
465C23C11×#12011yescharacteristic
466C23C11×#12011yescharacteristic
467C23C22×D4×C1111yescharacteristic
468Q8—22no—
469Q8—22no—
470Q8—82no—
471D4—22no—
472D4—22no—
473D4—44no—
474D4—44no—
475D4—42no—
476D4—42no—
477D4—82no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—44no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—82no—
505C2×C4—84no—
506C2×C4C11×#12012yes—
507C2×C4C22×D4×C1112yes—
508C2×C4C2×C11×#4111yescharacteristic
509C2×C4C2×C11×#4111yescharacteristic
510C2×C4C11×2−1+412yes—
511C8—42no—
512C8—42no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22C2×C11×#12011yescharacteristic
527C22C11×#52511yescharacteristic
528C22C11×#53611yescharacteristic
529C4—22no—
530C4—42no—
531C4—42no—
532C4—42no—
533C4—42no—
534C4—42no—
535C4—42no—
536C4—42no—
537C4—81no—
538C4—81no—
539C4C11×#54712yes—
540C4C11×#54712yes—
541C2—21no—
542C2—21no—
543C2—41no—
544C2—41no—
545C2—82no—
546C2C11×#240611yescharacteristic
547C2C11×#301911yescharacteristic
548C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3492C2
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
2. C11×#3093C2semidirect
3. C11×#2317C2semidirect
4. C11×#2061C2semidirect
5. C11×#2060C2semidirect
6. C11×#2040C2semidirect
7. C11×#2039C2semidirect
8. C11×#1897C2semidirect
9. C11×#1860C2semidirect
10. C11×#1859C2semidirect
11. C11×#1821C2semidirect
115. #24079C11direct (N × H)
184. C42×C11#41semidirect
185. C42×C11#41semidirect
187. #3093C2×C11semidirect
188. #2317C2×C11semidirect
189. #2061C2×C11semidirect
190. #2060C2×C11semidirect
191. #2040C2×C11semidirect
192. #2039C2×C11semidirect
193. #1897C2×C11semidirect
194. #1860C2×C11semidirect
195. #1859C2×C11semidirect
196. #1821C2×C11semidirect
457. C42C11×#41semidirect
458. C42C11×#41semidirect
459. C11#24079direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34922
C11×#30932
C11×#23172
C11×#20612
C11×#20602
C11×#20402
C11×#20392
C11×#18972
C11×#18602
C11×#18592
C11×#18212
#2407911