Finite Group Databasebeta

← C11×#24836 #14602029

Subgroups — C11×#24836 #14602029

Order 2816.

988 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×#476C211yesmaximal, characteristic, complemented
2C22×C11×C4⋊C8C211yesmaximal, characteristic, complemented
3C11×#2857C211yesmaximal, characteristic, complemented
4C4×C11×#121C211yesmaximal, characteristic
5C11×#2088C212yesmaximal, complemented
6C11×#2065C212yesmaximal, complemented
7C11×#1987C211yesmaximal, characteristic, complemented
8C11×#1948C211yesmaximal, characteristic, complemented
9C11×#1893C212yesmaximal
10C11×#1807C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C23×C8×C11C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C22⋊Q8—21no—
15C2×C11×#121C2211yescharacteristic
16C2×C4×D4×C11—21no—
17C2×C4×D4×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C11×#476—24no—
20C2×C11×#106C2212yes—
21C2×C11×#106C2212yes—
22C2×C11×C4⋊C8—24no—
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2212yes—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yes—
28C11×#391—21no—
29C11×#390C2211yescharacteristic
30C11×#389—21no—
31C11×#389C2211yescharacteristic
32C11×#389C2212yes—
33C11×#388—21no—
34C11×#386—21no—
35C11×#384C2211yescharacteristic
36C11×#380—21no—
37C11×#380C2212yes—
38C11×#380C2211yescharacteristic
39C4×C11×C4⋊C4C2211yescharacteristic
40C4×C11×C22⋊C4—21no—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×Q8×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×C8×C11—24no—
53C22×C8×C11—24no—
54C22×C8×C11—42no—
55C22×C8×C11C2312yes—
56C22×C8×C11C2312yes—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×C22⋊Q8—44no—
60C11×#121—22no—
61C11×#121Q814yescomplemented
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C4×D4×C11—44no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—22no—
82C2×C42×C11—22no—
83C2×C42×C11—21no—
84C2×C42×C11D411yescharacteristic
85C2×C42×C11D411yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C11×#106—24no—
89C11×#106—42no—
90C11×C4⋊C8—24no—
91C11×C4⋊C8—22no—
92C11×C4⋊C8D414yescomplemented
93C11×#102—24no—
94C11×#102—42no—
95C11×#95—21no—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95—22no—
99C11×#95—22no—
100#24836C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11—21no—
102C24×C11C2×D411yescharacteristic
103C2×Q8×C11—42no—
104C2×Q8×C11—42no—
105C2×Q8×C11—42no—
106C2×D4×C11—24no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—42no—
113C2×D4×C11—42no—
114C2×D4×C11C2×Q812yes—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—41no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11SD1614yes—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×Q812yes—
139C22×C4×C11#4112yes—
140C22×C4×C11C2411yescharacteristic
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—48no—
147C2×C8×C11C2×D414yes—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—44no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4C2×Q812yes—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—42no—
165C11×C22⋊C4—42no—
166C11×C22⋊C4—44no—
167C11×C22⋊C4—42no—
168C11×C22⋊C4—42no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—42no—
174C42×C11C2×D412yes—
175C42×C11#4112yes—
176C2×#476C2×C1111yescharacteristic, complemented
177C22×C4⋊C8C2×C1111yescharacteristic, complemented
178#2857C2×C1111yescharacteristic, complemented
179C4×#121C2×C1111yescharacteristic
180#2088C2×C1112yescomplemented
181#2065C2×C1112yescomplemented
182#1987C2×C1111yescharacteristic, complemented
183#1948C2×C1111yescharacteristic, complemented
184#1893C2×C1112yes—
185#1807C2×C1112yescomplemented
186#1802C2×C1111yescharacteristic, complemented
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—22no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11C22⋊Q812yes—
199C23×C11C2×SD1612yes—
200C23×C11AGL(1,ℤ/8)12yes—
201C23×C11C22×D411yescharacteristic
202Q8×C11—84no—
203D4×C11—22no—
204D4×C11—22no—
205D4×C11—48no—
206D4×C11—41no—
207D4×C11—41no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—28no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—44no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—84no—
239C2×C4×C11#12112yes—
240C2×C4×C11#12112yes—
241C2×C4×C11C22⋊Q812yes—
242C2×C4×C11C2×SD1612yes—
243C2×C4×C11C2×SD1612yes—
244C2×C4×C11#13512yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×Q811yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11H(5,𝔽2)11yescharacteristic
250C2×C4×C112−1+411yescharacteristic
251C8×C11—24no—
252C8×C11—42no—
253C23×C8C22×C1112yes—
254C2×C4⋊Q8C22×C1111yescharacteristic
255C2×C22⋊Q8—21no—
256C2×#121C22×C1111yescharacteristic
257C2×C4×D4—21no—
258C2×C4×D4C22×C1111yescharacteristic
259C22×C42C22×C1111yescharacteristic
260#476—24no—
261C2×#106C22×C1112yes—
262C2×#106C22×C1112yes—
263C2×C4⋊C8—24no—
264C2×C4⋊C8C22×C1111yescharacteristic
265C2×C4⋊C8C22×C1112yes—
266C2×C4⋊C8C22×C1111yescharacteristic
267C2×#102C22×C1112yes—
268C2×#102C22×C1112yes—
269#391—21no—
270#390C22×C1111yescharacteristic
271#389—21no—
272#389C22×C1112yes—
273#389C22×C1111yescharacteristic
274#388—21no—
275#386—21no—
276#384C22×C1111yescharacteristic
277#380—21no—
278#380C22×C1111yescharacteristic
279#380C22×C1112yes—
280C4×C4⋊C4C22×C1111yescharacteristic
281C4×C22⋊C4—21no—
282#340C22×C1112yes—
283#340C22×C1112yes—
284#340C22×C1112yes—
285#340C22×C1112yes—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11#47614yescomplemented
300C22×C11C2×#12111yescharacteristic
301C22×C11C2×C22⋊Q811yescharacteristic
302C22×C11#53711yescharacteristic
303C22×C11C22×SD1611yescharacteristic
304C22×C11C2×#13511yescharacteristic
305C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
306C22×C11#57511yescharacteristic
307C4×C11—22no—
308C4×C11—22no—
309C4×C11—22no—
310C4×C11—41no—
311C4×C11—42no—
312C4×C11—81no—
313C4×C11—82no—
314C4×C11—81no—
315C4×C11—82no—
316C4×C11#46514yes—
317C4×C11#54611yescharacteristic
318C4×C11D4×Q811yescharacteristic
319C4×C11#55211yescharacteristic
320C4×C11#55411yescharacteristic
321C22×Q8—21no—
322C22×D4—21no—
323C22×D4C23×C1111yescharacteristic
324C23×C4—21no—
325C23×C4D4×C1111yescharacteristic
326C23×C4D4×C1111yescharacteristic
327C23×C4C23×C1111yescharacteristic
328C22×C8—24no—
329C22×C8—24no—
330C22×C8—42no—
331C22×C8C23×C1112yes—
332C22×C8C23×C1112yes—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C22⋊Q8—44no—
336#121—22no—
337#121Q8×C1114yescomplemented
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—44no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4C23×C1111yescharacteristic
347C2×C4⋊C4C23×C1112yes—
348C2×C4⋊C4C23×C1111yescharacteristic
349C2×C4⋊C4C23×C1112yes—
350C2×C4⋊C4C23×C1111yescharacteristic
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—21no—
360C2×C42D4×C1111yescharacteristic
361C2×C42D4×C1111yescharacteristic
362C2×C42C23×C1111yescharacteristic
363C2×C42C23×C1111yescharacteristic
364#106—24no—
365#106—42no—
366C4⋊C8—24no—
367C4⋊C8—22no—
368C4⋊C8D4×C1114yescomplemented
369#102—24no—
370#102—42no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—22no—
375#95—22no—
376C2×C11—24no—
377C2×C11—82no—
378C2×C11#241711yescharacteristic
379C2×C11C2×#46511yescharacteristic
380C2×C11#305511yescharacteristic
381C2×C11C2×#47611yescharacteristic
382C2×C11#307611yescharacteristic
383C2×C11#324611yescharacteristic
384C2×C11#324711yescharacteristic
385C24—21no—
386C24C2×D4×C1111yescharacteristic
387C2×Q8—42no—
388C2×Q8—42no—
389C2×Q8—42no—
390C2×D4—24no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4C2×Q8×C1112yes—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—41no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4C11×SD1614yes—
417C22×C4C2×D4×C1111yescharacteristic
418C22×C4C2×D4×C1111yescharacteristic
419C22×C4C2×D4×C1111yescharacteristic
420C22×C4C2×D4×C1111yescharacteristic
421C22×C4C2×D4×C1111yescharacteristic
422C22×C4C2×Q8×C1112yes—
423C22×C4C11×#4112yes—
424C22×C4C24×C1111yescharacteristic
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—22no—
430C2×C8—48no—
431C2×C8C2×D4×C1114yes—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—42no—
442C4⋊C4—44no—
443C4⋊C4—42no—
444C4⋊C4—42no—
445C4⋊C4—42no—
446C4⋊C4C2×Q8×C1112yes—
447C22⋊C4—24no—
448C22⋊C4—42no—
449C22⋊C4—42no—
450C22⋊C4—44no—
451C22⋊C4—42no—
452C22⋊C4—42no—
453C42—22no—
454C42—22no—
455C42—21no—
456C42—21no—
457C42—42no—
458C42C2×D4×C1112yes—
459C42C11×#4112yes—
460C11#2483611yescharacteristic, direct product factor, Sylow
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—22no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23C11×C22⋊Q812yes—
473C23C2×C11×SD1612yes—
474C23C11×AGL(1,ℤ/8)12yes—
475C23C22×D4×C1111yescharacteristic
476Q8—84no—
477D4—22no—
478D4—22no—
479D4—48no—
480D4—41no—
481D4—41no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—28no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—44no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—84no—
513C2×C4C11×#12112yes—
514C2×C4C11×#12112yes—
515C2×C4C11×C22⋊Q812yes—
516C2×C4C2×C11×SD1612yes—
517C2×C4C2×C11×SD1612yes—
518C2×C4C11×#13512yes—
519C2×C4C22×D4×C1111yescharacteristic
520C2×C4C22×Q8×C1111yescharacteristic
521C2×C4C2×C11×#4111yescharacteristic
522C2×C4C2×C11×#4111yescharacteristic
523C2×C4C11×H(5,𝔽2)11yescharacteristic
524C2×C4C11×2−1+411yescharacteristic
525C8—24no—
526C8—42no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22C11×#47614yescomplemented
541C22C2×C11×#12111yescharacteristic
542C22C2×C11×C22⋊Q811yescharacteristic
543C22C11×#53711yescharacteristic
544C22C22×C11×SD1611yescharacteristic
545C22C2×C11×#13511yescharacteristic
546C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
547C22C11×#57511yescharacteristic
548C4—22no—
549C4—22no—
550C4—22no—
551C4—41no—
552C4—42no—
553C4—81no—
554C4—82no—
555C4—81no—
556C4—82no—
557C4C11×#46514yes—
558C4C11×#54611yescharacteristic
559C4D4×Q8×C1111yescharacteristic
560C4C11×#55211yescharacteristic
561C4C11×#55411yescharacteristic
562C2—24no—
563C2—82no—
564C2C11×#241711yescharacteristic
565C2C2×C11×#46511yescharacteristic
566C2C11×#305511yescharacteristic
567C2C2×C11×#47611yescharacteristic
568C2C11×#307611yescharacteristic
569C2C11×#324611yescharacteristic
570C2C11×#324711yescharacteristic
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
1. C2×C11×#476C2semidirect
2. C22×C11×C4⋊C8C2semidirect
3. C11×#2857C2semidirect
5. C11×#2088C2semidirect
6. C11×#2065C2semidirect
7. C11×#1987C2semidirect
8. C11×#1948C2semidirect
10. C11×#1807C2semidirect
11. C11×#1802C2semidirect
61. C11×#121Q8semidirect
92. C11×C4⋊C8D4semidirect
100. #24836C11direct (N × H)
176. C2×#476C2×C11semidirect
177. C22×C4⋊C8C2×C11semidirect
178. #2857C2×C11semidirect
180. #2088C2×C11semidirect
181. #2065C2×C11semidirect
182. #1987C2×C11semidirect
183. #1948C2×C11semidirect
185. #1807C2×C11semidirect
186. #1802C2×C11semidirect
299. C22×C11#476semidirect
337. #121Q8×C11semidirect
368. C4⋊C8D4×C11semidirect
460. C11#24836direct (N × H)
540. C22C11×#476semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4762
C22×C11×C4⋊C82
C11×#28572
C4×C11×#1212
C11×#20882
C11×#20652
C11×#19872
C11×#19482
C11×#18932
C11×#18072
C11×#18022
#2483611