Finite Group Databasebeta

← C11×#24731 #14601924

Subgroups — C11×#24731 #14601924

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#463C212yesmaximal, complemented
2C2×C11×#459C211yesmaximal, characteristic
3C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
4C11×#2548C211yesmaximal, characteristic, complemented
5D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
6C11×#2065C212yesmaximal, complemented
7C11×#2042C212yesmaximal, complemented
8C11×#1957C211yesmaximal, characteristic, complemented
9C11×#1939C211yesmaximal, characteristic, complemented
10C11×#1879C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C22×C11×D8C2212yes—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C4⋊C4—21no—
20C11×#463—28no—
21C11×#459—24no—
22C4×C11×SD16—24no—
23C2×C11×#106C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2212yes—
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2212yes—
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×#102C2212yes—
32C2×C4×C8×C11C2211yescharacteristic
33C11×#394—22no—
34C11×#390—21no—
35C11×#390—21no—
36C11×#390C2212yes—
37C11×#389C2212yes—
38C11×#385—22no—
39C11×#384C2211yescharacteristic
40C11×#380—21no—
41C4×C11×C4⋊C4C2211yescharacteristic
42C11×#340C2212yes—
43C11×#336C2212yes—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11C2312yes—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11—22no—
51C2×C11×SD16—22no—
52C2×C11×SD16—22no—
53C2×C11×SD16D414yescomplemented
54C2×C11×D8—24no—
55C2×C11×D8—24no—
56C2×C11×D8—24no—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2312yes—
59C22×C8×C11C2311yescharacteristic
60C11×#127—22no—
61C11×#127—22no—
62C11×#124—24no—
63C11×#124—42no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×D4×C11—24no—
67C4×D4×C11—22no—
68C4×D4×C11—42no—
69C4×D4×C11D414yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—44no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C42×C11—21no—
87C2×C42×C11C2312yes—
88C2×C42×C11C2311yescharacteristic
89C11×#106—22no—
90C11×C4⋊C8—24no—
91C11×C4⋊C8—22no—
92C11×#103—24no—
93C11×#103—22no—
94C11×#102—22no—
95C11×#102—24no—
96C11×#102—24no—
97C11×#102—42no—
98C4×C8×C11—22no—
99C11×#95—22no—
100C11×#95D412yes—
101#24731C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—21no—
103C24×C11—22no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11C2×D412yes—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11—42no—
123C2×D4×C11—81no—
124C2×D4×C11—81no—
125C2×D4×C11C2×D412yes—
126C2×D4×C11C2×D412yes—
127C2×D4×C11#4112yes—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—44no—
134C22×C4×C11—44no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11—82no—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C11×SD16—28no—
144C11×D8—48no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—21no—
150C2×C8×C11—22no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11C2×D412yes—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—44no—
162C11×C4⋊C4—42no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—81no—
165C11×C4⋊C4C2×D412yes—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—44no—
168C11×C22⋊C4—44no—
169C11×C22⋊C4—44no—
170C11×C22⋊C4—82no—
171C11×C22⋊C4—82no—
172C42×C11—22no—
173C42×C11—22no—
174C42×C11—42no—
175C42×C11C2×D412yes—
176C42×C11#4112yes—
177C2×#463C2×C1112yescomplemented
178C2×#459C2×C1111yescharacteristic
179C2×C4×SD16C2×C1111yescharacteristic, complemented
180#2548C2×C1111yescharacteristic, complemented
181D4×C4⋊C4C2×C1111yescharacteristic, complemented
182#2065C2×C1112yescomplemented
183#2042C2×C1112yescomplemented
184#1957C2×C1111yescharacteristic, complemented
185#1939C2×C1111yescharacteristic, complemented
186#1879C2×C1112yescomplemented
187#1803C2×C1111yescharacteristic, complemented
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11C22×D411yescharacteristic
203Q8×C11—22no—
204Q8×C11—22no—
205Q8×C11—41no—
206Q8×C11—41no—
207D4×C11—22no—
208D4×C11—22no—
209D4×C11—22no—
210D4×C11—42no—
211D4×C11—42no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—84no—
215D4×C11—84no—
216D4×C11#12114yes—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
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—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—48no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
237C2×C4×C11—41no—
238C2×C4×C11—88no—
239C2×C4×C11#12112yes—
240C2×C4×C11#12112yes—
241C2×C4×C11#13512yes—
242C2×C4×C11AGL(1,ℤ/8)12yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11H(5,𝔽2)11yescharacteristic
248C2×C4×C112−1+411yescharacteristic
249C8×C11—22no—
250C8×C11—42no—
251C8×C11—41no—
252C22×SD16C22×C1111yescharacteristic
253C22×D8C22×C1112yes—
254C2×#127C22×C1111yescharacteristic
255C2×#124C22×C1112yes—
256C2×C4×Q8C22×C1111yescharacteristic
257C2×C4×D4C22×C1112yes—
258C2×C4×D4C22×C1111yescharacteristic
259C22×C4⋊C4—21no—
260#463—28no—
261#459—24no—
262C4×SD16—24no—
263C2×#106C22×C1111yescharacteristic
264C2×C4⋊C8C22×C1111yescharacteristic
265C2×C4⋊C8C22×C1112yes—
266C2×#103C22×C1112yes—
267C2×#103C22×C1111yescharacteristic
268C2×#102C22×C1112yes—
269C2×#102C22×C1112yes—
270C2×#102C22×C1111yescharacteristic
271C2×#102C22×C1112yes—
272C2×C4×C8C22×C1111yescharacteristic
273#394—22no—
274#390—21no—
275#390—21no—
276#390C22×C1112yes—
277#389C22×C1112yes—
278#385—22no—
279#384C22×C1111yescharacteristic
280#380—21no—
281C4×C4⋊C4C22×C1111yescharacteristic
282#340C22×C1112yes—
283#336C22×C1112yes—
284C22×C11—24no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—82no—
292C22×C11—82no—
293C22×C11—82no—
294C22×C11—82no—
295C22×C11—82no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11C2×#12111yescharacteristic
299C22×C11D4211yescharacteristic
300C22×C11#54811yescharacteristic
301C22×C11C2×#13511yescharacteristic
302C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
303C22×C11#57611yescharacteristic
304C22×C11#57711yescharacteristic
305C4×C11—22no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11—82no—
311C4×C11—81no—
312C4×C11#46314yescomplemented
313C4×C11C2×#12111yescharacteristic
314C4×C11#53711yescharacteristic
315C4×C11#54711yescharacteristic
316C4×C11#55311yescharacteristic
317C22×Q8C23×C1111yescharacteristic
318C22×D4—21no—
319C22×D4—21no—
320C22×D4C23×C1112yes—
321C22×D4C23×C1111yescharacteristic
322C23×C4—21no—
323C23×C4—22no—
324C2×SD16—22no—
325C2×SD16—22no—
326C2×SD16D4×C1114yescomplemented
327C2×D8—24no—
328C2×D8—24no—
329C2×D8—24no—
330C22×C8C23×C1112yes—
331C22×C8C23×C1111yescharacteristic
332C22×C8C23×C1111yescharacteristic
333#127—22no—
334#127—22no—
335#124—24no—
336#124—42no—
337C4×Q8—22no—
338C4×Q8—22no—
339C4×D4—24no—
340C4×D4—22no—
341C4×D4—42no—
342C4×D4D4×C1114yes—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4D4×C1111yescharacteristic
349C2×C4⋊C4D4×C1111yescharacteristic
350C2×C4⋊C4C23×C1112yes—
351C2×C4⋊C4C23×C1111yescharacteristic
352C2×C4⋊C4C23×C1111yescharacteristic
353C2×C22⋊C4—21no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C42—21no—
360C2×C42C23×C1112yes—
361C2×C42C23×C1111yescharacteristic
362#106—22no—
363C4⋊C8—24no—
364C4⋊C8—22no—
365#103—24no—
366#103—22no—
367#102—22no—
368#102—24no—
369#102—24no—
370#102—42no—
371C4×C8—22no—
372#95—22no—
373#95D4×C1112yes—
374C2×C11—44no—
375C2×C11—162no—
376C2×C11#241611yescharacteristic
377C2×C11C2×#46311yescharacteristic
378C2×C11#304511yescharacteristic
379C2×C11#327411yescharacteristic
380C2×C11#328411yescharacteristic
381C2×C11#336111yescharacteristic
382C2×C11#337311yescharacteristic
383C24—21no—
384C24—22no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8C2×D4×C1112yes—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—21no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—21no—
397C2×D4—22no—
398C2×D4—21no—
399C2×D4—22no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—81no—
405C2×D4—81no—
406C2×D4C2×D4×C1112yes—
407C2×D4C2×D4×C1112yes—
408C2×D4C11×#4112yes—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—44no—
415C22×C4—44no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—82no—
419C22×C4C2×D4×C1112yes—
420C22×C4C2×D4×C1112yes—
421C22×C4C2×D4×C1111yescharacteristic
422C22×C4C2×D4×C1111yescharacteristic
423C22×C4C24×C1111yescharacteristic
424SD16—28no—
425D8—48no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8C2×D4×C1112yes—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—44no—
443C4⋊C4—42no—
444C4⋊C4—42no—
445C4⋊C4—81no—
446C4⋊C4C2×D4×C1112yes—
447C22⋊C4—24no—
448C22⋊C4—44no—
449C22⋊C4—44no—
450C22⋊C4—44no—
451C22⋊C4—82no—
452C22⋊C4—82no—
453C42—22no—
454C42—22no—
455C42—42no—
456C42C2×D4×C1112yes—
457C42C11×#4112yes—
458C11#2473111yescharacteristic, direct product factor, Sylow
459C23—22no—
460C23—22no—
461C23—22no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23C22×D4×C1111yescharacteristic
474Q8—22no—
475Q8—22no—
476Q8—41no—
477Q8—41no—
478D4—22no—
479D4—22no—
480D4—22no—
481D4—42no—
482D4—42no—
483D4—42no—
484D4—42no—
485D4—84no—
486D4—84no—
487D4C11×#12114yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—48no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—88no—
510C2×C4C11×#12112yes—
511C2×C4C11×#12112yes—
512C2×C4C11×#13512yes—
513C2×C4C11×AGL(1,ℤ/8)12yes—
514C2×C4C22×D4×C1111yescharacteristic
515C2×C4C22×D4×C1111yescharacteristic
516C2×C4C2×C11×#4111yescharacteristic
517C2×C4C2×C11×#4111yescharacteristic
518C2×C4C11×H(5,𝔽2)11yescharacteristic
519C2×C4C11×2−1+411yescharacteristic
520C8—22no—
521C8—42no—
522C8—41no—
523C22—24no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22—82no—
535C22—82no—
536C22—82no—
537C22C2×C11×#12111yescharacteristic
538C22D42×C1111yescharacteristic
539C22C11×#54811yescharacteristic
540C22C2×C11×#13511yescharacteristic
541C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
542C22C11×#57611yescharacteristic
543C22C11×#57711yescharacteristic
544C4—22no—
545C4—42no—
546C4—42no—
547C4—42no—
548C4—42no—
549C4—82no—
550C4—81no—
551C4C11×#46314yescomplemented
552C4C2×C11×#12111yescharacteristic
553C4C11×#53711yescharacteristic
554C4C11×#54711yescharacteristic
555C4C11×#55311yescharacteristic
556C2—44no—
557C2—162no—
558C2C11×#241611yescharacteristic
559C2C2×C11×#46311yescharacteristic
560C2C11×#304511yescharacteristic
561C2C11×#327411yescharacteristic
562C2C11×#328411yescharacteristic
563C2C11×#336111yescharacteristic
564C2C11×#337311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#459C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#463C2semidirect
3. C2×C4×C11×SD16C2semidirect
4. C11×#2548C2semidirect
5. D4×C11×C4⋊C4C2semidirect
6. C11×#2065C2semidirect
7. C11×#2042C2semidirect
8. C11×#1957C2semidirect
9. C11×#1939C2semidirect
10. C11×#1879C2semidirect
11. C11×#1803C2semidirect
53. C2×C11×SD16D4semidirect
101. #24731C11direct (N × H)
177. C2×#463C2×C11semidirect
179. C2×C4×SD16C2×C11semidirect
180. #2548C2×C11semidirect
181. D4×C4⋊C4C2×C11semidirect
182. #2065C2×C11semidirect
183. #2042C2×C11semidirect
184. #1957C2×C11semidirect
185. #1939C2×C11semidirect
186. #1879C2×C11semidirect
187. #1803C2×C11semidirect
312. C4×C11#463semidirect
326. C2×SD16D4×C11semidirect
458. C11#24731direct (N × H)
551. C4C11×#463semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4632
C2×C11×#4592
C2×C4×C11×SD162
C11×#25482
D4×C11×C4⋊C42
C11×#20652
C11×#20422
C11×#19572
C11×#19392
C11×#18792
C11×#18032
#2473111