Finite Group Databasebeta

← C11×#24014 #14601207

Subgroups — C11×#24014 #14601207

Order 2816.

1276 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#536C211yesmaximal, characteristic
2C2×C11×#484C211yesmaximal, characteristic, complemented
3C2×C11×#483C211yesmaximal, characteristic, complemented
4C11×#2311C211yesmaximal, characteristic
5C11×#2036C212yesmaximal, complemented
6C11×#2035C212yesmaximal, complemented
7C11×#1873C211yesmaximal, characteristic, complemented
8C11×#1873C211yesmaximal, characteristic, complemented
9C11×#1854C212yesmaximal, complemented
10C11×#1787C212yesmaximal, complemented
11C11×#1780C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C23×Q8×C11C2211yescharacteristic
14C11×#536—24no—
15C11×#536—24no—
16C2×C11×C4⋊Q8—21no—
17C2×C11×#124—21no—
18C2×C11×#123—21no—
19C2×C11×#123—21no—
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#117C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C11×#484—24no—
28C11×#483—24no—
29C2×C11×#107C2212yes—
30C2×C11×#106C2212yes—
31C2×C11×#103C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#103C2212yes—
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2212yes—
38C2×C11×C22⋊C8C2212yes—
39C11×#391—21no—
40C11×#390—21no—
41C11×#386—21no—
42C11×#386—21no—
43C11×#380C2212yes—
44C11×#380C2212yes—
45C11×#340C2212yes—
46C11×#340C2212yes—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—24no—
50C2×C11×#41—42no—
51C22×Q8×C11—22no—
52C22×Q8×C11—22no—
53C22×Q8×C11—21no—
54C22×Q8×C11—24no—
55C22×Q8×C11—42no—
56C22×Q8×C11D411yescharacteristic
57C22×Q8×C11C2311yescharacteristic
58C22×Q8×C11C2311yescharacteristic
59C22×D4×C11D411yescharacteristic
60C22×D4×C11D411yescharacteristic
61C22×D4×C11D411yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C8×C11C2312yes—
68C22×C8×C11C2312yes—
69C11×C4⋊Q8—28no—
70C11×#124—28no—
71C11×#123—28no—
72C11×#123—28no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8D414yes—
80C11×C22⋊Q8D414yes—
81C11×#117—22no—
82C11×#117—22no—
83C11×#117—42no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
103C2×C42×C11—21no—
104C2×C42×C11—21no—
105C11×#107—24no—
106C11×#106—24no—
107C11×#103—24no—
108C11×#103—24no—
109C11×#103—42no—
110C11×#103—42no—
111C11×C22⋊C8—22no—
112C11×C22⋊C8—22no—
113C11×C22⋊C8—24no—
114C11×C22⋊C8—42no—
115C11×#95—22no—
116C11×#95—22no—
117#24014C1111yesmaximal, characteristic, direct product factor, Sylow
118C24×C11C2×D411yescharacteristic
119C24×C11C2×D411yescharacteristic
120C24×C11C2×D411yescharacteristic
121C11×#41—48no—
122C11×#41—48no—
123C2×Q8×C11—24no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—41no—
133C2×Q8×C11—48no—
134C2×Q8×C11—48no—
135C2×Q8×C11—42no—
136C2×Q8×C11—42no—
137C2×Q8×C11C2×D412yes—
138C2×Q8×C11C2×D412yes—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—41no—
146C2×D4×C11—41no—
147C2×D4×C11—41no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—24no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—42no—
165C22×C4×C11—42no—
166C22×C4×C11—42no—
167C22×C4×C11—82no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11#4114yes—
174C22×C4×C11C2411yescharacteristic
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—42no—
192C11×C4⋊C4C2×D412yes—
193C11×C4⋊C4C2×D412yes—
194C11×C22⋊C4—24no—
195C11×C22⋊C4—24no—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—42no—
200C11×C22⋊C4—82no—
201C11×C22⋊C4—82no—
202C42×C11—24no—
203C42×C11—42no—
204C2×#536C2×C1111yescharacteristic
205C2×#484C2×C1111yescharacteristic, complemented
206C2×#483C2×C1111yescharacteristic, complemented
207#2311C2×C1111yescharacteristic
208#2036C2×C1112yescomplemented
209#2035C2×C1112yescomplemented
210#1873C2×C1111yescharacteristic, complemented
211#1873C2×C1111yescharacteristic, complemented
212#1854C2×C1112yescomplemented
213#1787C2×C1112yescomplemented
214#1780C2×C1111yescharacteristic
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11#12012yes—
229C23×C11#12312yes—
230C23×C11C22×D411yescharacteristic
231Q8×C11—24no—
232Q8×C11—24no—
233Q8×C11—44no—
234Q8×C11—48no—
235Q8×C11—42no—
236Q8×C11—42no—
237D4×C11—44no—
238D4×C11—44no—
239D4×C11—44no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—48no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—84no—
271C2×C4×C11#12012yes—
272C2×C4×C11#12312yes—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C2×#4112yes—
276C2×C4×C11H(5,𝔽2)12yes—
277C8×C11—42no—
278C8×C11—42no—
279C22×#41C22×C1111yescharacteristic
280C23×Q8C22×C1111yescharacteristic
281#536—24no—
282#536—24no—
283C2×C4⋊Q8—21no—
284C2×#124—21no—
285C2×#123—21no—
286C2×#123—21no—
287C2×C22⋊Q8C22×C1111yescharacteristic
288C2×C22⋊Q8C22×C1111yescharacteristic
289C2×C22⋊Q8C22×C1111yescharacteristic
290C2×C22⋊Q8C22×C1111yescharacteristic
291C2×#117C22×C1111yescharacteristic
292C2×#117C22×C1111yescharacteristic
293C22×C4⋊C4C22×C1111yescharacteristic
294#484—24no—
295#483—24no—
296C2×#107C22×C1112yes—
297C2×#106C22×C1112yes—
298C2×#103C22×C1112yes—
299C2×#103C22×C1112yes—
300C2×#103C22×C1112yes—
301C2×#103C22×C1112yes—
302C2×C22⋊C8C22×C1111yescharacteristic
303C2×C22⋊C8C22×C1111yescharacteristic
304C2×C22⋊C8C22×C1112yes—
305C2×C22⋊C8C22×C1112yes—
306#391—21no—
307#390—21no—
308#386—21no—
309#386—21no—
310#380C22×C1112yes—
311#380C22×C1112yes—
312#340C22×C1112yes—
313#340C22×C1112yes—
314C22×C11—24no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—42no—
325C22×C11—41no—
326C22×C11—42no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11C2×#12011yescharacteristic
330C22×C11C2×#12311yescharacteristic
331C22×C11#53411yescharacteristic
332C22×C11#57712yes—
333C22×C11#57812yes—
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—41no—
337C4×C11—42no—
338C4×C11—42no—
339C4×C11—42no—
340C4×C11—42no—
341C4×C11—82no—
342C4×C11—82no—
343C4×C11#54612yes—
344C4×C11#54612yes—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41—24no—
348C2×#41—42no—
349C22×Q8—22no—
350C22×Q8—22no—
351C22×Q8—21no—
352C22×Q8—24no—
353C22×Q8—42no—
354C22×Q8D4×C1111yescharacteristic
355C22×Q8C23×C1111yescharacteristic
356C22×Q8C23×C1111yescharacteristic
357C22×D4D4×C1111yescharacteristic
358C22×D4D4×C1111yescharacteristic
359C22×D4D4×C1111yescharacteristic
360C23×C4—21no—
361C23×C4—21no—
362C23×C4C23×C1111yescharacteristic
363C23×C4C23×C1111yescharacteristic
364C23×C4C23×C1111yescharacteristic
365C22×C8C23×C1112yes—
366C22×C8C23×C1112yes—
367C4⋊Q8—28no—
368#124—28no—
369#123—28no—
370#123—28no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377C22⋊Q8D4×C1114yes—
378C22⋊Q8D4×C1114yes—
379#117—22no—
380#117—22no—
381#117—42no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4C23×C1112yes—
390C2×C4⋊C4C23×C1112yes—
391C2×C4⋊C4C23×C1111yescharacteristic
392C2×C4⋊C4C23×C1111yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C42—21no—
402C2×C42—21no—
403#107—24no—
404#106—24no—
405#103—24no—
406#103—24no—
407#103—42no—
408#103—42no—
409C22⋊C8—22no—
410C22⋊C8—22no—
411C22⋊C8—24no—
412C22⋊C8—42no—
413#95—22no—
414#95—22no—
415C2×C11—42no—
416C2×C11—42no—
417C2×C11—81no—
418C2×C11#240511yescharacteristic
419C2×C11#301011yescharacteristic
420C2×C11#301111yescharacteristic
421C2×C11#309712yes—
422C2×C11#320112yes—
423C24C2×D4×C1111yescharacteristic
424C24C2×D4×C1111yescharacteristic
425C24C2×D4×C1111yescharacteristic
426#41—48no—
427#41—48no—
428C2×Q8—24no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—41no—
438C2×Q8—48no—
439C2×Q8—48no—
440C2×Q8—42no—
441C2×Q8—42no—
442C2×Q8C2×D4×C1112yes—
443C2×Q8C2×D4×C1112yes—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—82no—
473C22×C4C2×D4×C1111yescharacteristic
474C22×C4C2×D4×C1111yescharacteristic
475C22×C4C2×D4×C1112yes—
476C22×C4C2×D4×C1112yes—
477C22×C4C2×D4×C1111yescharacteristic
478C22×C4C11×#4114yes—
479C22×C4C24×C1111yescharacteristic
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C4⋊C4—24no—
487C4⋊C4—24no—
488C4⋊C4—24no—
489C4⋊C4—24no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—42no—
497C4⋊C4C2×D4×C1112yes—
498C4⋊C4C2×D4×C1112yes—
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—24no—
504C22⋊C4—42no—
505C22⋊C4—82no—
506C22⋊C4—82no—
507C42—24no—
508C42—42no—
509C11#2401411yescharacteristic, direct product factor, Sylow
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—22no—
522C23—22no—
523C23C11×#12012yes—
524C23C11×#12312yes—
525C23C22×D4×C1111yescharacteristic
526Q8—24no—
527Q8—24no—
528Q8—44no—
529Q8—48no—
530Q8—42no—
531Q8—42no—
532D4—44no—
533D4—44no—
534D4—44no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—48no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—84no—
566C2×C4C11×#12012yes—
567C2×C4C11×#12312yes—
568C2×C4C22×D4×C1111yescharacteristic
569C2×C4C22×D4×C1111yescharacteristic
570C2×C4C2×C11×#4112yes—
571C2×C4C11×H(5,𝔽2)12yes—
572C8—42no—
573C8—42no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—24no—
579C22—42no—
580C22—42no—
581C22—41no—
582C22—41no—
583C22—42no—
584C22—41no—
585C22—42no—
586C22—41no—
587C22—41no—
588C22—42no—
589C22C2×C11×#12011yescharacteristic
590C22C2×C11×#12311yescharacteristic
591C22C11×#53411yescharacteristic
592C22C11×#57712yes—
593C22C11×#57812yes—
594C4—22no—
595C4—22no—
596C4—41no—
597C4—42no—
598C4—42no—
599C4—42no—
600C4—42no—
601C4—82no—
602C4—82no—
603C4C11×#54612yes—
604C4C11×#54612yes—
605C2—42no—
606C2—42no—
607C2—81no—
608C2C11×#240511yescharacteristic
609C2C11×#301011yescharacteristic
610C2C11×#301111yescharacteristic
611C2C11×#309712yes—
612C2C11×#320112yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#484C2semidirect
3. C2×C11×#483C2semidirect
5. C11×#2036C2semidirect
6. C11×#2035C2semidirect
7. C11×#1873C2semidirect
8. C11×#1873C2semidirect
9. C11×#1854C2semidirect
10. C11×#1787C2semidirect
117. #24014C11direct (N × H)
205. C2×#484C2×C11semidirect
206. C2×#483C2×C11semidirect
208. #2036C2×C11semidirect
209. #2035C2×C11semidirect
210. #1873C2×C11semidirect
211. #1873C2×C11semidirect
212. #1854C2×C11semidirect
213. #1787C2×C11semidirect
509. C11#24014direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5362
C2×C11×#4842
C2×C11×#4832
C11×#23112
C11×#20362
C11×#20352
C11×#18732
C11×#18542
C11×#17872
C11×#17802
#2401411