Finite Group Databasebeta

← C11×#24503 #14601696

Subgroups — C11×#24503 #14601696

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#448C211yesmaximal, characteristic
2C2×C11×#431C211yesmaximal, characteristic, complemented
3C11×#2854C211yesmaximal, characteristic
4C2×C11×#391C211yesmaximal, characteristic, complemented
5C11×#2066C212yesmaximal, complemented
6C11×#2055C212yesmaximal, complemented
7C11×#1968C212yesmaximal, complemented
8C11×#1933C212yesmaximal, complemented
9C11×#1874C211yesmaximal, characteristic
10C11×#1853C211yesmaximal, characteristic, complemented
11C11×#1787C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C2×C11×#123—21no—
15C2×C11×#121C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C11×#448—24no—
19C11×#431—24no—
20C2×C11×#106C2212yes—
21C2×C11×C4⋊C8C2212yes—
22C2×C11×#103C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#103C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C4×C8×C11C2212yes—
29C11×#391—21no—
30C11×#391—21no—
31C11×#391C2212yes—
32C11×#391C2212yes—
33C11×#390C2211yescharacteristic
34C11×#390C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#389C2211yescharacteristic
37C11×#388—21no—
38C11×#388—21no—
39C11×#386—21no—
40C11×#380C2211yescharacteristic
41C2×C11×#95—21no—
42C2×C11×#95—21no—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×Q8×C11—24no—
46C22×Q8×C11—21no—
47C22×Q8×C11—22no—
48C22×Q8×C11—22no—
49C22×Q8×C11—42no—
50C22×Q8×C11C2312yes—
51C22×D4×C11—21no—
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11—21no—
54C23×C4×C11—21no—
55C23×C4×C11D411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C2×C11×SD16—24no—
59C2×C11×SD16—24no—
60C2×C11×SD16—42no—
61C22×C8×C11C2312yes—
62C22×C8×C11C2312yes—
63C11×#123—44no—
64C11×#121—22no—
65C11×#121—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—42no—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—22no—
81C2×C42×C11—22no—
82C2×C42×C11D411yescharacteristic
83C2×C42×C11D411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C11×#106—42no—
87C11×C4⋊C8—24no—
88C11×#103—24no—
89C11×#103—24no—
90C11×#103—42no—
91C11×#102—42no—
92C11×C22⋊C8—22no—
93C11×C22⋊C8D414yes—
94C4×C8×C11—24no—
95C11×#95—22no—
96C11×#95—22no—
97C11×#95—22no—
98C11×#95—22no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102#24503C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—21no—
104C24×C11C2×D411yescharacteristic
105C2×Q8×C11—24no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—48no—
112C2×Q8×C11—48no—
113C2×Q8×C11—42no—
114C2×Q8×C11—42no—
115C2×Q8×C11#4114yes—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11—42no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—41no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11SD1614yescomplemented
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4112yes—
149C22×C4×C11C2411yescharacteristic
150C11×SD16—48no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11C2×D414yes—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4—42no—
166C11×C22⋊C4—42no—
167C11×C22⋊C4—42no—
168C11×C22⋊C4—42no—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—42no—
172C42×C11—22no—
173C42×C11—22no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C2×#448C2×C1111yescharacteristic
179C2×#431C2×C1111yescharacteristic, complemented
180#2854C2×C1111yescharacteristic
181C2×#391C2×C1111yescharacteristic, complemented
182#2066C2×C1112yescomplemented
183#2055C2×C1112yescomplemented
184#1968C2×C1112yescomplemented
185#1933C2×C1112yescomplemented
186#1874C2×C1111yescharacteristic
187#1853C2×C1111yescharacteristic, complemented
188#1787C2×C1111yescharacteristic, complemented
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11#12112yes—
201C23×C11C2×SD1612yes—
202C23×C11#13512yes—
203C23×C11C22×D411yescharacteristic
204Q8×C11—24no—
205Q8×C11—24no—
206Q8×C11—48no—
207Q8×C11—42no—
208Q8×C11—42no—
209D4×C11—42no—
210D4×C11—42no—
211D4×C11—84no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—28no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—21no—
224C2×C4×C11—24no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—44no—
228C2×C4×C11—48no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—84no—
244C2×C4×C11#12112yes—
245C2×C4×C11C2×SD1612yes—
246C2×C4×C11C2×SD1612yes—
247C2×C4×C11#13712yes—
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4112yes—
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11H(5,𝔽2)12yes—
252C8×C11—24no—
253C8×C11—42no—
254C23×Q8C22×C1111yescharacteristic
255C22×SD16C22×C1112yes—
256C2×#123—21no—
257C2×#121C22×C1111yescharacteristic
258C22×C4⋊C4C22×C1111yescharacteristic
259C22×C42C22×C1111yescharacteristic
260#448—24no—
261#431—24no—
262C2×#106C22×C1112yes—
263C2×C4⋊C8C22×C1112yes—
264C2×#103C22×C1112yes—
265C2×#103C22×C1112yes—
266C2×#103C22×C1112yes—
267C2×#102C22×C1112yes—
268C2×C22⋊C8C22×C1111yescharacteristic
269C2×C22⋊C8C22×C1111yescharacteristic
270C2×C4×C8C22×C1112yes—
271#391—21no—
272#391—21no—
273#391C22×C1112yes—
274#391C22×C1112yes—
275#390C22×C1111yescharacteristic
276#390C22×C1111yescharacteristic
277#389C22×C1111yescharacteristic
278#389C22×C1111yescharacteristic
279#388—21no—
280#388—21no—
281#386—21no—
282#380C22×C1111yescharacteristic
283C2×#95—21no—
284C2×#95—21no—
285#340C22×C1112yes—
286#340C22×C1112yes—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11#46514yes—
301C22×C11C2×#12111yescharacteristic
302C22×C11#52511yescharacteristic
303C22×C11#53511yescharacteristic
304C22×C11C22×SD1611yescharacteristic
305C22×C11C2×#13511yescharacteristic
306C22×C11C2×#13711yescharacteristic
307C22×C11#57511yescharacteristic
308C4×C11—22no—
309C4×C11—22no—
310C4×C11—22no—
311C4×C11—22no—
312C4×C11—44no—
313C4×C11—41no—
314C4×C11—81no—
315C4×C11—81no—
316C4×C11—82no—
317C4×C11—81no—
318C4×C11#54612yes—
319C4×C11#55112yes—
320C22×Q8—24no—
321C22×Q8—21no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—42no—
325C22×Q8C23×C1112yes—
326C22×D4—21no—
327C22×D4C23×C1111yescharacteristic
328C23×C4—21no—
329C23×C4—21no—
330C23×C4D4×C1111yescharacteristic
331C23×C4D4×C1111yescharacteristic
332C23×C4C23×C1111yescharacteristic
333C2×SD16—24no—
334C2×SD16—24no—
335C2×SD16—42no—
336C22×C8C23×C1112yes—
337C22×C8C23×C1112yes—
338#123—44no—
339#121—22no—
340#121—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4C23×C1112yes—
346C2×C4⋊C4C23×C1111yescharacteristic
347C2×C4⋊C4C23×C1111yescharacteristic
348C2×C4⋊C4C23×C1111yescharacteristic
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42D4×C1111yescharacteristic
358C2×C42D4×C1111yescharacteristic
359C2×C42C23×C1111yescharacteristic
360C2×C42C23×C1111yescharacteristic
361#106—42no—
362C4⋊C8—24no—
363#103—24no—
364#103—24no—
365#103—42no—
366#102—42no—
367C22⋊C8—22no—
368C22⋊C8D4×C1114yes—
369C4×C8—24no—
370#95—22no—
371#95—22no—
372#95—22no—
373#95—22no—
374#95—21no—
375#95—21no—
376#95—21no—
377C2×C11—24no—
378C2×C11—161no—
379C2×C11#241111yescharacteristic
380C2×C11C2×#46511yescharacteristic
381C2×C11#305611yescharacteristic
382C2×C11#310311yescharacteristic
383C2×C11#310811yescharacteristic
384C2×C11#320611yescharacteristic
385C2×C11#321111yescharacteristic
386C24—21no—
387C24C2×D4×C1111yescharacteristic
388C2×Q8—24no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—48no—
395C2×Q8—48no—
396C2×Q8—42no—
397C2×Q8—42no—
398C2×Q8C11×#4114yes—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—42no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—41no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4C11×SD1614yescomplemented
425C22×C4C2×D4×C1111yescharacteristic
426C22×C4C2×D4×C1111yescharacteristic
427C22×C4C2×D4×C1112yes—
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C2×D4×C1111yescharacteristic
430C22×C4C2×D4×C1111yescharacteristic
431C22×C4C11×#4112yes—
432C22×C4C24×C1111yescharacteristic
433SD16—48no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8C2×D4×C1114yes—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—42no—
447C4⋊C4—42no—
448C4⋊C4—42no—
449C22⋊C4—42no—
450C22⋊C4—42no—
451C22⋊C4—42no—
452C22⋊C4—42no—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C42—22no—
456C42—22no—
457C42—21no—
458C42—21no—
459C42—21no—
460C42—21no—
461C11#2450311yescharacteristic, direct product factor, Sylow
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23C11×#12112yes—
474C23C2×C11×SD1612yes—
475C23C11×#13512yes—
476C23C22×D4×C1111yescharacteristic
477Q8—24no—
478Q8—24no—
479Q8—48no—
480Q8—42no—
481Q8—42no—
482D4—42no—
483D4—42no—
484D4—84no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—28no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—21no—
497C2×C4—24no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—44no—
501C2×C4—48no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—84no—
517C2×C4C11×#12112yes—
518C2×C4C2×C11×SD1612yes—
519C2×C4C2×C11×SD1612yes—
520C2×C4C11×#13712yes—
521C2×C4C22×D4×C1111yescharacteristic
522C2×C4C2×C11×#4112yes—
523C2×C4C2×C11×#4111yescharacteristic
524C2×C4C11×H(5,𝔽2)12yes—
525C8—24no—
526C8—42no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22C11×#46514yes—
541C22C2×C11×#12111yescharacteristic
542C22C11×#52511yescharacteristic
543C22C11×#53511yescharacteristic
544C22C22×C11×SD1611yescharacteristic
545C22C2×C11×#13511yescharacteristic
546C22C2×C11×#13711yescharacteristic
547C22C11×#57511yescharacteristic
548C4—22no—
549C4—22no—
550C4—22no—
551C4—22no—
552C4—44no—
553C4—41no—
554C4—81no—
555C4—82no—
556C4—81no—
557C4—81no—
558C4C11×#54612yes—
559C4C11×#55112yes—
560C2—24no—
561C2—161no—
562C2C11×#241111yescharacteristic
563C2C2×C11×#46511yescharacteristic
564C2C11×#305611yescharacteristic
565C2C11×#310311yescharacteristic
566C2C11×#310811yescharacteristic
567C2C11×#320611yescharacteristic
568C2C11×#321111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#431C2semidirect
4. C2×C11×#391C2semidirect
5. C11×#2066C2semidirect
6. C11×#2055C2semidirect
7. C11×#1968C2semidirect
8. C11×#1933C2semidirect
10. C11×#1853C2semidirect
11. C11×#1787C2semidirect
102. #24503C11direct (N × H)
141. C22×C4×C11SD16semidirect
179. C2×#431C2×C11semidirect
181. C2×#391C2×C11semidirect
182. #2066C2×C11semidirect
183. #2055C2×C11semidirect
184. #1968C2×C11semidirect
185. #1933C2×C11semidirect
187. #1853C2×C11semidirect
188. #1787C2×C11semidirect
424. C22×C4C11×SD16semidirect
461. C11#24503direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4482
C2×C11×#4312
C11×#28542
C2×C11×#3912
C11×#20662
C11×#20552
C11×#19682
C11×#19332
C11×#18742
C11×#18532
C11×#17872
#2450311