Finite Group Databasebeta

← C11×#24157 #14601350

Subgroups — C11×#24157 #14601350

Order 2816.

1114 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic
2C2×C11×#475C211yesmaximal, characteristic, complemented
3C2×C11×#462C211yesmaximal, characteristic, complemented
4C4×C11×C22⋊Q8C211yesmaximal, characteristic
5C11×#2035C212yesmaximal
6C11×#2001C212yesmaximal
7C11×#1988C211yesmaximal, characteristic, complemented
8C11×#1981C211yesmaximal, characteristic, complemented
9C11×#1878C212yesmaximal, complemented
10C11×#1865C212yesmaximal, complemented
11C11×#1797C211yesmaximal, characteristic
12C22×C11×Q16C2212yes—
13C11×#533—24no—
14C11×#533—24no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#125—21no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C4×Q8×C11—21no—
22C2×C4×Q8×C11C2212yes—
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C11×#117—21no—
25C22×C42×C11C2211yescharacteristic
26C11×#475—24no—
27C11×#462—24no—
28C2×C11×#106C2212yes—
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#103C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#103C2212yes—
35C2×C11×C22⋊C8C2212yes—
36C11×#391C2211yescharacteristic
37C11×#389C2211yescharacteristic
38C11×#387—21no—
39C11×#385—21no—
40C11×#380C2211yescharacteristic
41C4×C11×C4⋊C4—21no—
42C4×C11×C4⋊C4C2211yescharacteristic
43C4×C11×C22⋊C4—21no—
44C11×#340C2212yes—
45C11×#340C2212yes—
46C11×#336C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11C2312yes—
49C22×Q8×C11C2311yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C2×C11×Q16—24no—
54C2×C11×Q16—24no—
55C2×C11×Q16—42no—
56C22×C8×C11C2312yes—
57C22×C8×C11C2312yes—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8D414yes—
61C11×C4⋊Q8D414yes—
62C11×#125—28no—
63C11×C22⋊Q8—28no—
64C11×C22⋊Q8—24no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8—22no—
68C4×Q8×C11—28no—
69C4×Q8×C11—24no—
70C4×Q8×C11—24no—
71C4×Q8×C11—22no—
72C4×Q8×C11—22no—
73C11×#117—28no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C42×C11—22no—
90C2×C42×C11—22no—
91C2×C42×C11—22no—
92C2×C42×C11—21no—
93C2×C42×C11—21no—
94C2×C42×C11D411yescharacteristic
95C2×C42×C11D411yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C11×#106—24no—
99C11×C4⋊C8—22no—
100C11×C4⋊C8—22no—
101C11×#103—24no—
102C11×#103—24no—
103C11×#103—24no—
104C11×#103—42no—
105C11×C22⋊C8—42no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111#24157C1111yesmaximal, characteristic, direct product factor, Sylow
112C24×C11C2×D411yescharacteristic
113C2×Q8×C11—24no—
114C2×Q8×C11—22no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—21no—
122C2×Q8×C11—22no—
123C2×Q8×C11—21no—
124C2×Q8×C11—42no—
125C2×Q8×C11—42no—
126C2×Q8×C11C2×D414yes—
127C2×Q8×C11#4112yes—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C11×Q16—48no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C11×C4⋊C4—28no—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4C2×D414yes—
174C11×C4⋊C4#4112yes—
175C11×C22⋊C4—28no—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—42no—
178C42×C11—28no—
179C42×C11—22no—
180C42×C11—22no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—42no—
184C42×C11—42no—
185C42×C11C2×D412yes—
186C42×C11C2×D412yes—
187C2×#533C2×C1111yescharacteristic
188C2×#475C2×C1111yescharacteristic, complemented
189C2×#462C2×C1111yescharacteristic, complemented
190C4×C22⋊Q8C2×C1111yescharacteristic
191#2035C2×C1112yes—
192#2001C2×C1112yes—
193#1988C2×C1111yescharacteristic, complemented
194#1981C2×C1111yescharacteristic, complemented
195#1878C2×C1112yescomplemented
196#1865C2×C1112yescomplemented
197#1797C2×C1111yescharacteristic
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—21no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—21no—
204C23×C11#13712yes—
205C23×C11C22×D411yescharacteristic
206Q8×C11—22no—
207Q8×C11—24no—
208Q8×C11—24no—
209Q8×C11—22no—
210Q8×C11—41no—
211Q8×C11—42no—
212Q8×C11—42no—
213Q8×C11—41no—
214Q8×C11—48no—
215C2×C4×C11—28no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—44no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11#12012yes—
250C2×C4×C11#12012yes—
251C2×C4×C11#13512yes—
252C2×C4×C11#13712yes—
253C2×C4×C11#13712yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C112−1+411yescharacteristic
260C8×C11—42no—
261C8×C11—42no—
262C22×Q16C22×C1112yes—
263#533—24no—
264#533—24no—
265C2×C4⋊Q8C22×C1111yescharacteristic
266C2×C4⋊Q8C22×C1111yescharacteristic
267C2×#125—21no—
268C2×C22⋊Q8—21no—
269C2×C22⋊Q8C22×C1112yes—
270C2×C22⋊Q8C22×C1111yescharacteristic
271C2×C4×Q8—21no—
272C2×C4×Q8C22×C1111yescharacteristic
273C2×C4×Q8C22×C1112yes—
274C2×#117—21no—
275C22×C42C22×C1111yescharacteristic
276#475—24no—
277#462—24no—
278C2×#106C22×C1112yes—
279C2×C4⋊C8C22×C1111yescharacteristic
280C2×C4⋊C8C22×C1111yescharacteristic
281C2×#103C22×C1112yes—
282C2×#103C22×C1112yes—
283C2×#103C22×C1112yes—
284C2×#103C22×C1112yes—
285C2×C22⋊C8C22×C1112yes—
286#391C22×C1111yescharacteristic
287#389C22×C1111yescharacteristic
288#387—21no—
289#385—21no—
290#380C22×C1111yescharacteristic
291C4×C4⋊C4—21no—
292C4×C4⋊C4C22×C1111yescharacteristic
293C4×C22⋊C4—21no—
294#340C22×C1112yes—
295#340C22×C1112yes—
296#336C22×C1112yes—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11C2×#12011yescharacteristic
305C22×C11#52511yescharacteristic
306C22×C11#53711yescharacteristic
307C22×C11C2×#13511yescharacteristic
308C22×C11C2×#13711yescharacteristic
309C22×C11C2×#13711yescharacteristic
310C22×C11C2×#13711yescharacteristic
311C4×C11—22no—
312C4×C11—22no—
313C4×C11—42no—
314C4×C11—41no—
315C4×C11—44no—
316C4×C11—42no—
317C4×C11—41no—
318C4×C11—44no—
319C4×C11—81no—
320C4×C11—81no—
321C4×C11#45214yes—
322C4×C11#54611yescharacteristic
323C4×C11#54711yescharacteristic
324C4×C11#54811yescharacteristic
325C4×C11#55011yescharacteristic
326C22×Q8—21no—
327C22×Q8C23×C1112yes—
328C22×Q8C23×C1111yescharacteristic
329C23×C4D4×C1111yescharacteristic
330C23×C4D4×C1111yescharacteristic
331C23×C4C23×C1111yescharacteristic
332C2×Q16—24no—
333C2×Q16—24no—
334C2×Q16—42no—
335C22×C8C23×C1112yes—
336C22×C8C23×C1112yes—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8D4×C1114yes—
340C4⋊Q8D4×C1114yes—
341#125—28no—
342C22⋊Q8—28no—
343C22⋊Q8—24no—
344C22⋊Q8—22no—
345C22⋊Q8—24no—
346C22⋊Q8—22no—
347C4×Q8—28no—
348C4×Q8—24no—
349C4×Q8—24no—
350C4×Q8—22no—
351C4×Q8—22no—
352#117—28no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4C23×C1111yescharacteristic
362C2×C4⋊C4C23×C1111yescharacteristic
363C2×C4⋊C4C23×C1112yes—
364C2×C4⋊C4C23×C1111yescharacteristic
365C2×C22⋊C4—22no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42D4×C1111yescharacteristic
374C2×C42D4×C1111yescharacteristic
375C2×C42C23×C1111yescharacteristic
376C2×C42C23×C1111yescharacteristic
377#106—24no—
378C4⋊C8—22no—
379C4⋊C8—22no—
380#103—24no—
381#103—24no—
382#103—24no—
383#103—42no—
384C22⋊C8—42no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390C2×C11—42no—
391C2×C11#240711yescharacteristic
392C2×C11C2×#45211yescharacteristic
393C2×C11#300411yescharacteristic
394C2×C11#310711yescharacteristic
395C2×C11#311311yescharacteristic
396C2×C11#324811yescharacteristic
397C2×C11#325511yescharacteristic
398C24C2×D4×C1111yescharacteristic
399C2×Q8—24no—
400C2×Q8—22no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—21no—
408C2×Q8—22no—
409C2×Q8—21no—
410C2×Q8—42no—
411C2×Q8—42no—
412C2×Q8C2×D4×C1114yes—
413C2×Q8C11×#4112yes—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4C2×D4×C1111yescharacteristic
433C22×C4C2×D4×C1111yescharacteristic
434C22×C4C2×D4×C1111yescharacteristic
435C22×C4C2×D4×C1111yescharacteristic
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C24×C1111yescharacteristic
438Q16—48no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C4⋊C4—28no—
446C4⋊C4—28no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—24no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4C2×D4×C1114yes—
460C4⋊C4C11×#4112yes—
461C22⋊C4—28no—
462C22⋊C4—24no—
463C22⋊C4—42no—
464C42—28no—
465C42—22no—
466C42—22no—
467C42—21no—
468C42—21no—
469C42—42no—
470C42—42no—
471C42C2×D4×C1112yes—
472C42C2×D4×C1112yes—
473C11#2415711yescharacteristic, direct product factor, Sylow
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23C11×#13712yes—
481C23C22×D4×C1111yescharacteristic
482Q8—22no—
483Q8—24no—
484Q8—24no—
485Q8—22no—
486Q8—41no—
487Q8—42no—
488Q8—42no—
489Q8—41no—
490Q8—48no—
491C2×C4—28no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—44no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4C11×#12012yes—
526C2×C4C11×#12012yes—
527C2×C4C11×#13512yes—
528C2×C4C11×#13712yes—
529C2×C4C11×#13712yes—
530C2×C4C22×D4×C1111yescharacteristic
531C2×C4C22×D4×C1111yescharacteristic
532C2×C4C2×C11×#4111yescharacteristic
533C2×C4C2×C11×#4111yescharacteristic
534C2×C4C11×H(5,𝔽2)11yescharacteristic
535C2×C4C11×2−1+411yescharacteristic
536C8—42no—
537C8—42no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22C2×C11×#12011yescharacteristic
546C22C11×#52511yescharacteristic
547C22C11×#53711yescharacteristic
548C22C2×C11×#13511yescharacteristic
549C22C2×C11×#13711yescharacteristic
550C22C2×C11×#13711yescharacteristic
551C22C2×C11×#13711yescharacteristic
552C4—22no—
553C4—22no—
554C4—41no—
555C4—44no—
556C4—42no—
557C4—41no—
558C4—44no—
559C4—42no—
560C4—81no—
561C4—81no—
562C4C11×#45214yes—
563C4C11×#54611yescharacteristic
564C4C11×#54711yescharacteristic
565C4C11×#54811yescharacteristic
566C4C11×#55011yescharacteristic
567C2—42no—
568C2C11×#240711yescharacteristic
569C2C2×C11×#45211yescharacteristic
570C2C11×#300411yescharacteristic
571C2C11×#310711yescharacteristic
572C2C11×#311311yescharacteristic
573C2C11×#324811yescharacteristic
574C2C11×#325511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
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×#475C2semidirect
3. C2×C11×#462C2semidirect
7. C11×#1988C2semidirect
8. C11×#1981C2semidirect
9. C11×#1878C2semidirect
10. C11×#1865C2semidirect
111. #24157C11direct (N × H)
188. C2×#475C2×C11semidirect
189. C2×#462C2×C11semidirect
193. #1988C2×C11semidirect
194. #1981C2×C11semidirect
195. #1878C2×C11semidirect
196. #1865C2×C11semidirect
473. C11#24157direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5332
C2×C11×#4752
C2×C11×#4622
C4×C11×C22⋊Q82
C11×#20352
C11×#20012
C11×#19882
C11×#19812
C11×#18782
C11×#18652
C11×#17972
#2415711