Finite Group Databasebeta

← C11×#24185 #14601378

Subgroups — C11×#24185 #14601378

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#556C211yesmaximal, characteristic, complemented
2C2×C11×#461C211yesmaximal, characteristic, complemented
3C2×C4×C11×D8C211yesmaximal, characteristic
4C11×#2538C211yesmaximal, characteristic, complemented
5C11×#2042C212yesmaximal, complemented
6C11×#2012C212yesmaximal
7C11×#1984C211yesmaximal, characteristic, complemented
8C11×#1956C211yesmaximal, characteristic, complemented
9C11×#1880C212yesmaximal, complemented
10C11×#1863C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2212yes—
13C22×C11×D8C2211yescharacteristic
14C11×#556—24no—
15C11×#556—24no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#126—22no—
18C2×C11×#124C2212yes—
19C2×C11×C22⋊Q8—21no—
20C2×C11×C22⋊Q8—21no—
21C2×C4×Q8×C11C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C2×C11×#117—21no—
26C11×#461—24no—
27C4×C11×D8—24no—
28C2×C11×#107C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2212yes—
31C2×C11×#103C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2212yes—
36C2×C4×C8×C11C2211yescharacteristic
37C11×#396—22no—
38C11×#390C2212yes—
39C11×#389C2212yes—
40C11×#384C2211yescharacteristic
41C11×#380—21no—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2312yes—
47C22×D4×C11C2311yescharacteristic
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11—21no—
51C2×C11×SD16—24no—
52C2×C11×SD16—24no—
53C2×C11×SD16—42no—
54C2×C11×D8—22no—
55C2×C11×D8—22no—
56C2×C11×D8—22no—
57C22×C8×C11C2312yes—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8D414yes—
62C11×#126—216no—
63C11×#124—24no—
64C11×#124—24no—
65C11×C22⋊Q8—28no—
66C11×C22⋊Q8—44no—
67C4×Q8×C11—24no—
68C4×Q8×C11—24no—
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11D414yes—
75C11×#117—28no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4D412yes—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C42×C11—22no—
94C2×C42×C11C2312yes—
95C2×C42×C11C2311yescharacteristic
96C11×#107—22no—
97C11×C4⋊C8—22no—
98C11×#103—24no—
99C11×#103—24no—
100C11×#103—42no—
101C11×#102—22no—
102C11×#102—22no—
103C11×#102—42no—
104C4×C8×C11—22no—
105C11×#95—22no—
106#24185C1111yesmaximal, characteristic, direct product factor, Sylow
107C24×C11—21no—
108C24×C11—21no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11C2×D414yes—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11C2×D412yes—
129C2×D4×C11#4112yes—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—24no—
133C22×C4×C11—21no—
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×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C11×SD16—48no—
146C11×D8—28no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—22no—
150C2×C8×C11—21no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11#4112yes—
156C11×C4⋊C4—28no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—44no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4—81no—
169C11×C4⋊C4C2×D412yes—
170C11×C22⋊C4—28no—
171C11×C22⋊C4—28no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—44no—
174C11×C22⋊C4—42no—
175C11×C22⋊C4—82no—
176C42×C11—28no—
177C42×C11—22no—
178C42×C11—22no—
179C42×C11C2×D412yes—
180C42×C11C2×D412yes—
181C2×#556C2×C1111yescharacteristic, complemented
182C2×#461C2×C1111yescharacteristic, complemented
183C2×C4×D8C2×C1111yescharacteristic
184#2538C2×C1111yescharacteristic, complemented
185#2042C2×C1112yescomplemented
186#2012C2×C1112yes—
187#1984C2×C1111yescharacteristic, complemented
188#1956C2×C1111yescharacteristic, complemented
189#1880C2×C1112yescomplemented
190#1863C2×C1112yescomplemented
191#1802C2×C1111yescharacteristic, complemented
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11C22×D411yescharacteristic
207Q8×C11—24no—
208Q8×C11—24no—
209Q8×C11—42no—
210Q8×C11—42no—
211Q8×C11—44no—
212D4×C11—22no—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—22no—
216D4×C11—41no—
217D4×C11—41no—
218D4×C11—41no—
219D4×C11—41no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—48no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—84no—
242C2×C4×C11#12012yes—
243C2×C4×C11#12012yes—
244C2×C4×C11#13512yes—
245C2×C4×C11AGL(1,ℤ/8)12yes—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11H(5,𝔽2)11yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C8×C11—22no—
253C8×C11—41no—
254C8×C11—42no—
255C22×SD16C22×C1112yes—
256C22×D8C22×C1111yescharacteristic
257#556—24no—
258#556—24no—
259C2×C4⋊Q8C22×C1111yescharacteristic
260C2×#126—22no—
261C2×#124C22×C1112yes—
262C2×C22⋊Q8—21no—
263C2×C22⋊Q8—21no—
264C2×C4×Q8C22×C1112yes—
265C2×C4×Q8C22×C1111yescharacteristic
266C2×C4×D4C22×C1111yescharacteristic
267C2×C4×D4C22×C1111yescharacteristic
268C2×#117—21no—
269#461—24no—
270C4×D8—24no—
271C2×#107C22×C1111yescharacteristic
272C2×C4⋊C8C22×C1111yescharacteristic
273C2×#103C22×C1112yes—
274C2×#103C22×C1112yes—
275C2×#103C22×C1112yes—
276C2×#102C22×C1111yescharacteristic
277C2×#102C22×C1111yescharacteristic
278C2×#102C22×C1112yes—
279C2×C4×C8C22×C1111yescharacteristic
280#396—22no—
281#390C22×C1112yes—
282#389C22×C1112yes—
283#384C22×C1111yescharacteristic
284#380—21no—
285#340C22×C1112yes—
286#336C22×C1112yes—
287#336C22×C1112yes—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11C2×#12011yescharacteristic
303C22×C11#54811yescharacteristic
304C22×C11#55011yescharacteristic
305C22×C11C2×#13511yescharacteristic
306C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C11#57711yescharacteristic
308C22×C11#57811yescharacteristic
309C4×C11—22no—
310C4×C11—44no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11—42no—
314C4×C11—82no—
315C4×C11—81no—
316C4×C11#44914yes—
317C4×C11#52511yescharacteristic
318C4×C11#53711yescharacteristic
319C4×C11#54611yescharacteristic
320C4×C11#54711yescharacteristic
321C22×Q8D4×C1111yescharacteristic
322C22×Q8C23×C1112yes—
323C22×D4C23×C1111yescharacteristic
324C22×D4C23×C1111yescharacteristic
325C23×C4—21no—
326C23×C4—21no—
327C2×SD16—24no—
328C2×SD16—24no—
329C2×SD16—42no—
330C2×D8—22no—
331C2×D8—22no—
332C2×D8—22no—
333C22×C8C23×C1112yes—
334C22×C8C23×C1111yescharacteristic
335C22×C8C23×C1111yescharacteristic
336C4⋊Q8—22no—
337C4⋊Q8D4×C1114yes—
338#126—216no—
339#124—24no—
340#124—24no—
341C22⋊Q8—28no—
342C22⋊Q8—44no—
343C4×Q8—24no—
344C4×Q8—24no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4D4×C1114yes—
351#117—28no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4D4×C1111yescharacteristic
359C2×C4⋊C4D4×C1112yes—
360C2×C4⋊C4C23×C1111yescharacteristic
361C2×C4⋊C4C23×C1112yes—
362C2×C4⋊C4C23×C1111yescharacteristic
363C2×C22⋊C4—22no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C42—22no—
370C2×C42C23×C1112yes—
371C2×C42C23×C1111yescharacteristic
372#107—22no—
373C4⋊C8—22no—
374#103—24no—
375#103—24no—
376#103—42no—
377#102—22no—
378#102—22no—
379#102—42no—
380C4×C8—22no—
381#95—22no—
382C2×C11—82no—
383C2×C11—82no—
384C2×C11#240711yescharacteristic
385C2×C11C2×#44911yescharacteristic
386C2×C11#301311yescharacteristic
387C2×C11#336011yescharacteristic
388C2×C11#336711yescharacteristic
389C2×C11#339311yescharacteristic
390C2×C11#339711yescharacteristic
391C24—21no—
392C24—21no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8C2×D4×C1114yes—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4C2×D4×C1112yes—
413C2×D4C11×#4112yes—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4C2×D4×C1112yes—
425C22×C4C2×D4×C1112yes—
426C22×C4C2×D4×C1111yescharacteristic
427C22×C4C2×D4×C1111yescharacteristic
428C22×C4C24×C1111yescharacteristic
429SD16—48no—
430D8—28no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8C11×#4112yes—
440C4⋊C4—28no—
441C4⋊C4—24no—
442C4⋊C4—24no—
443C4⋊C4—22no—
444C4⋊C4—24no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—44no—
451C4⋊C4—42no—
452C4⋊C4—81no—
453C4⋊C4C2×D4×C1112yes—
454C22⋊C4—28no—
455C22⋊C4—28no—
456C22⋊C4—24no—
457C22⋊C4—44no—
458C22⋊C4—42no—
459C22⋊C4—82no—
460C42—28no—
461C42—22no—
462C42—22no—
463C42C2×D4×C1112yes—
464C42C2×D4×C1112yes—
465C11#2418511yescharacteristic, direct product factor, Sylow
466C23—22no—
467C23—22no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23C22×D4×C1111yescharacteristic
481Q8—24no—
482Q8—24no—
483Q8—42no—
484Q8—42no—
485Q8—44no—
486D4—22no—
487D4—22no—
488D4—22no—
489D4—22no—
490D4—41no—
491D4—41no—
492D4—41no—
493D4—41no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—48no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—84no—
516C2×C4C11×#12012yes—
517C2×C4C11×#12012yes—
518C2×C4C11×#13512yes—
519C2×C4C11×AGL(1,ℤ/8)12yes—
520C2×C4C22×D4×C1111yescharacteristic
521C2×C4C22×D4×C1111yescharacteristic
522C2×C4C2×C11×#4111yescharacteristic
523C2×C4C2×C11×#4111yescharacteristic
524C2×C4C11×H(5,𝔽2)11yescharacteristic
525C2×C4C11×2−1+411yescharacteristic
526C8—22no—
527C8—41no—
528C8—42no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22C2×C11×#12011yescharacteristic
544C22C11×#54811yescharacteristic
545C22C11×#55011yescharacteristic
546C22C2×C11×#13511yescharacteristic
547C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
548C22C11×#57711yescharacteristic
549C22C11×#57811yescharacteristic
550C4—22no—
551C4—44no—
552C4—42no—
553C4—42no—
554C4—42no—
555C4—81no—
556C4—82no—
557C4C11×#44914yes—
558C4C11×#52511yescharacteristic
559C4C11×#53711yescharacteristic
560C4C11×#54611yescharacteristic
561C4C11×#54711yescharacteristic
562C2—82no—
563C2—82no—
564C2C11×#240711yescharacteristic
565C2C2×C11×#44911yescharacteristic
566C2C11×#301311yescharacteristic
567C2C11×#336011yescharacteristic
568C2C11×#336711yescharacteristic
569C2C11×#339311yescharacteristic
570C2C11×#339711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#556C2semidirect
2. C2×C11×#461C2semidirect
4. C11×#2538C2semidirect
5. C11×#2042C2semidirect
7. C11×#1984C2semidirect
8. C11×#1956C2semidirect
9. C11×#1880C2semidirect
10. C11×#1863C2semidirect
11. C11×#1802C2semidirect
106. #24185C11direct (N × H)
181. C2×#556C2×C11semidirect
182. C2×#461C2×C11semidirect
184. #2538C2×C11semidirect
185. #2042C2×C11semidirect
187. #1984C2×C11semidirect
188. #1956C2×C11semidirect
189. #1880C2×C11semidirect
190. #1863C2×C11semidirect
191. #1802C2×C11semidirect
465. C11#24185direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5562
C2×C11×#4612
C2×C4×C11×D82
C11×#25382
C11×#20422
C11×#20122
C11×#19842
C11×#19562
C11×#18802
C11×#18632
C11×#18022
#2418511