Finite Group Databasebeta

← C11×#23945 #14601138

Subgroups — C11×#23945 #14601138

Order 2816.

1382 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#542C211yesmaximal, characteristic, complemented
2C2×C11×#450C211yesmaximal, characteristic, complemented
3C2×C11×#447C211yesmaximal, characteristic
4C11×#2309C211yesmaximal, characteristic, complemented
5C11×#2023C212yesmaximal, complemented
6C11×#2012C212yesmaximal, complemented
7C11×#1880C212yesmaximal, complemented
8C11×#1879C212yesmaximal, complemented
9C11×#1875C211yesmaximal, characteristic, complemented
10C11×#1873C211yesmaximal, characteristic, complemented
11C11×#1818C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C22×C11×D8C2212yes—
15C11×#542—24no—
16C11×#542—24no—
17C2×C11×C4⋊Q8C2211yescharacteristic, complemented
18C2×C11×#126—21no—
19C2×C11×#124—21no—
20C2×C11×#124C2211yescharacteristic, complemented
21C2×C11×#123—21no—
22C2×C11×C22⋊Q8—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic, complemented
26C2×C4×D4×C11C2211yescharacteristic, complemented
27C2×C11×#117C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C11×#450—24no—
30C11×#447—24no—
31C2×C11×#103C2212yescomplemented
32C2×C11×#102C2212yes—
33C2×C11×#102C2212yes—
34C2×C11×#102C2212yescomplemented
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C11×#390—21no—
38C11×#390—21no—
39C11×#390C2212yes—
40C11×#390C2212yes—
41C11×#379—21no—
42C11×#379—21no—
43C11×#340C2212yescomplemented
44C11×#340C2212yescomplemented
45C11×#336C2212yescomplemented
46C11×#336C2212yescomplemented
47C25×C11—21no—
48C22×Q8×C11—21no—
49C22×Q8×C11C2311yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11—24no—
52C22×D4×C11—21no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11—42no—
56C22×D4×C11C2311yescharacteristic
57C22×D4×C11C2312yes—
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C2×C11×SD16—24no—
61C2×C11×SD16—24no—
62C2×C11×SD16—42no—
63C2×C11×D8—24no—
64C2×C11×D8—24no—
65C2×C11×D8—42no—
66C22×C8×C11C2312yes—
67C22×C8×C11C2312yes—
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8—22no—
70C11×#126—28no—
71C11×#124—28no—
72C11×#124—22no—
73C11×#124—22no—
74C11×#123—28no—
75C11×C22⋊Q8—28no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8D414yes—
78C11×#121—22no—
79C11×#121D414yes—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C11×#117—22no—
85C11×#117—22no—
86C11×#117—42no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4D411yescharacteristic
91C2×C11×C4⋊C4D411yescharacteristic
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×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4D411yescharacteristic
106C2×C11×C22⋊C4D411yescharacteristic
107C2×C42×C11—21no—
108C2×C42×C11—21no—
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C11×#103—42no—
112C11×#102—24no—
113C11×#102—24no—
114C11×#102—42no—
115C11×C22⋊C8—22no—
116C11×C22⋊C8—22no—
117#23945C1111yesmaximal, characteristic, direct product factor, Sylow
118C24×C11—24no—
119C24×C11—21no—
120C24×C11—22no—
121C24×C11—42no—
122C24×C11—42no—
123C24×C11—82no—
124C24×C11—82no—
125C24×C11C2×D411yescharacteristic
126C2×Q8×C11—24no—
127C2×Q8×C11—21no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—82no—
131C2×Q8×C11C2×D412yes—
132C2×D4×C11—24no—
133C2×D4×C11—24no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—48no—
143C2×D4×C11—48no—
144C2×D4×C11—42no—
145C2×D4×C11—42no—
146C2×D4×C11—82no—
147C2×D4×C11C2×D412yes—
148C2×D4×C11#4114yes—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—24no—
155C22×C4×C11—22no—
156C22×C4×C11—82no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2411yescharacteristic
165C11×SD16—48no—
166C11×D8—48no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4C2×D412yes—
183C11×C4⋊C4C2×D412yes—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—24no—
191C11×C22⋊C4—42no—
192C11×C22⋊C4—82no—
193C11×C22⋊C4—82no—
194C11×C22⋊C4—82no—
195C11×C22⋊C4—82no—
196C42×C11—24no—
197C42×C11—21no—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—42no—
202C2×#542C2×C1111yescharacteristic, complemented
203C2×#450C2×C1111yescharacteristic, complemented
204C2×#447C2×C1111yescharacteristic
205#2309C2×C1111yescharacteristic, complemented
206#2023C2×C1112yescomplemented
207#2012C2×C1112yescomplemented
208#1880C2×C1112yescomplemented
209#1879C2×C1112yescomplemented
210#1875C2×C1111yescharacteristic, complemented
211#1873C2×C1111yescharacteristic, complemented
212#1818C2×C1111yescharacteristic, complemented
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—24no—
219C23×C11—48no—
220C23×C11—42no—
221C23×C11—41no—
222C23×C11—42no—
223C23×C11—41no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—84no—
231C23×C11—84no—
232C23×C11—88no—
233C23×C11—88no—
234C23×C11#12012yes—
235C23×C11C22×D411yescharacteristic
236Q8×C11—24no—
237Q8×C11—42no—
238Q8×C11—84no—
239D4×C11—24no—
240D4×C11—24no—
241D4×C11—24no—
242D4×C11—48no—
243D4×C11—42no—
244D4×C11—42no—
245D4×C11—42no—
246D4×C11—84no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—84no—
270C2×C4×C11#12012yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C2×#4112yes—
274C2×C4×C11H(5,𝔽2)12yes—
275C8×C11—42no—
276C8×C11—42no—
277C23×D4C22×C1111yescharacteristic
278C22×SD16C22×C1112yes—
279C22×D8C22×C1112yes—
280#542—24no—
281#542—24no—
282C2×C4⋊Q8C22×C1111yescharacteristic, complemented
283C2×#126—21no—
284C2×#124—21no—
285C2×#124C22×C1111yescharacteristic, complemented
286C2×#123—21no—
287C2×C22⋊Q8—21no—
288C2×C22⋊Q8C22×C1111yescharacteristic
289C2×#121C22×C1111yescharacteristic
290C2×C4×Q8C22×C1111yescharacteristic, complemented
291C2×C4×D4C22×C1111yescharacteristic, complemented
292C2×#117C22×C1111yescharacteristic
293C2×#117C22×C1111yescharacteristic
294#450—24no—
295#447—24no—
296C2×#103C22×C1112yescomplemented
297C2×#102C22×C1112yes—
298C2×#102C22×C1112yes—
299C2×#102C22×C1112yescomplemented
300C2×C22⋊C8C22×C1111yescharacteristic
301C2×C22⋊C8C22×C1111yescharacteristic
302#390—21no—
303#390—21no—
304#390C22×C1112yes—
305#390C22×C1112yes—
306#379—21no—
307#379—21no—
308#340C22×C1112yescomplemented
309#340C22×C1112yescomplemented
310#336C22×C1112yescomplemented
311#336C22×C1112yescomplemented
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—816no—
324C22×C11—82no—
325C22×C11—82no—
326C22×C11—82no—
327C22×C11—82no—
328C22×C11—82no—
329C22×C11—82no—
330C22×C11C2×#12011yescharacteristic
331C22×C11#52511yescharacteristic
332C22×C11#53511yescharacteristic
333C22×C11#57612yes—
334C22×C11#57712yes—
335C4×C11—22no—
336C4×C11—42no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—42no—
340C4×C11—42no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—82no—
344C4×C11#54612yes—
345C4×C11#54612yes—
346C25—21no—
347C22×Q8—21no—
348C22×Q8C23×C1111yescharacteristic
349C22×D4—21no—
350C22×D4—24no—
351C22×D4—21no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—42no—
355C22×D4C23×C1111yescharacteristic
356C22×D4C23×C1112yes—
357C23×C4—21no—
358C23×C4C23×C1111yescharacteristic
359C2×SD16—24no—
360C2×SD16—24no—
361C2×SD16—42no—
362C2×D8—24no—
363C2×D8—24no—
364C2×D8—42no—
365C22×C8C23×C1112yes—
366C22×C8C23×C1112yes—
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369#126—28no—
370#124—28no—
371#124—22no—
372#124—22no—
373#123—28no—
374C22⋊Q8—28no—
375C22⋊Q8—22no—
376C22⋊Q8D4×C1114yes—
377#121—22no—
378#121D4×C1114yes—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×D4—22no—
382C4×D4—22no—
383#117—22no—
384#117—22no—
385#117—42no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4D4×C1111yescharacteristic
390C2×C4⋊C4D4×C1111yescharacteristic
391C2×C4⋊C4C23×C1112yes—
392C2×C4⋊C4C23×C1111yescharacteristic
393C2×C4⋊C4C23×C1111yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4D4×C1111yescharacteristic
405C2×C22⋊C4D4×C1111yescharacteristic
406C2×C42—21no—
407C2×C42—21no—
408C2×C42C23×C1111yescharacteristic
409C2×C42C23×C1111yescharacteristic
410#103—42no—
411#102—24no—
412#102—24no—
413#102—42no—
414C22⋊C8—22no—
415C22⋊C8—22no—
416C2×C11—42no—
417C2×C11—82no—
418C2×C11—84no—
419C2×C11#240411yescharacteristic
420C2×C11#300811yescharacteristic
421C2×C11#301011yescharacteristic
422C2×C11#311812yes—
423C2×C11#322412yes—
424C24—24no—
425C24—21no—
426C24—22no—
427C24—42no—
428C24—42no—
429C24—82no—
430C24—82no—
431C24C2×D4×C1111yescharacteristic
432C2×Q8—24no—
433C2×Q8—21no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—82no—
437C2×Q8C2×D4×C1112yes—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—21no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—48no—
449C2×D4—48no—
450C2×D4—42no—
451C2×D4—42no—
452C2×D4—82no—
453C2×D4C2×D4×C1112yes—
454C2×D4C11×#4114yes—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—82no—
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C2×D4×C1111yescharacteristic
465C22×C4C2×D4×C1111yescharacteristic
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C2×D4×C1112yes—
469C22×C4C2×D4×C1112yes—
470C22×C4C24×C1111yescharacteristic
471SD16—48no—
472D8—48no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C4⋊C4—24no—
480C4⋊C4—24no—
481C4⋊C4—24no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4C2×D4×C1112yes—
489C4⋊C4C2×D4×C1112yes—
490C22⋊C4—24no—
491C22⋊C4—24no—
492C22⋊C4—24no—
493C22⋊C4—24no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—24no—
497C22⋊C4—42no—
498C22⋊C4—82no—
499C22⋊C4—82no—
500C22⋊C4—82no—
501C22⋊C4—82no—
502C42—24no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—42no—
508C11#2394511yescharacteristic, direct product factor, Sylow
509C23—21no—
510C23—21no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—24no—
515C23—48no—
516C23—42no—
517C23—41no—
518C23—42no—
519C23—41no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—84no—
527C23—84no—
528C23—88no—
529C23—88no—
530C23C11×#12012yes—
531C23C22×D4×C1111yescharacteristic
532Q8—24no—
533Q8—42no—
534Q8—84no—
535D4—24no—
536D4—24no—
537D4—24no—
538D4—48no—
539D4—42no—
540D4—42no—
541D4—42no—
542D4—84no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—84no—
566C2×C4C11×#12012yes—
567C2×C4C22×D4×C1111yescharacteristic
568C2×C4C22×D4×C1111yescharacteristic
569C2×C4C2×C11×#4112yes—
570C2×C4C11×H(5,𝔽2)12yes—
571C8—42no—
572C8—42no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—42no—
577C22—42no—
578C22—44no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—44no—
583C22—44no—
584C22—816no—
585C22—82no—
586C22—82no—
587C22—82no—
588C22—82no—
589C22—82no—
590C22—82no—
591C22C2×C11×#12011yescharacteristic
592C22C11×#52511yescharacteristic
593C22C11×#53511yescharacteristic
594C22C11×#57612yes—
595C22C11×#57712yes—
596C4—22no—
597C4—42no—
598C4—41no—
599C4—41no—
600C4—42no—
601C4—42no—
602C4—41no—
603C4—41no—
604C4—82no—
605C4C11×#54612yes—
606C4C11×#54612yes—
607C2—42no—
608C2—84no—
609C2—82no—
610C2C11×#240411yescharacteristic
611C2C11×#300811yescharacteristic
612C2C11×#301011yescharacteristic
613C2C11×#311812yes—
614C2C11×#322412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#542C2semidirect
2. C2×C11×#450C2semidirect
4. C11×#2309C2semidirect
5. C11×#2023C2semidirect
6. C11×#2012C2semidirect
7. C11×#1880C2semidirect
8. C11×#1879C2semidirect
9. C11×#1875C2semidirect
10. C11×#1873C2semidirect
11. C11×#1818C2semidirect
17. C2×C11×C4⋊Q8C22semidirect
20. C2×C11×#124C22semidirect
25. C2×C4×Q8×C11C22semidirect
26. C2×C4×D4×C11C22semidirect
31. C2×C11×#103C22semidirect
34. C2×C11×#102C22semidirect
43. C11×#340C22semidirect
44. C11×#340C22semidirect
45. C11×#336C22semidirect
46. C11×#336C22semidirect
117. #23945C11direct (N × H)
202. C2×#542C2×C11semidirect
203. C2×#450C2×C11semidirect
205. #2309C2×C11semidirect
206. #2023C2×C11semidirect
207. #2012C2×C11semidirect
208. #1880C2×C11semidirect
209. #1879C2×C11semidirect
210. #1875C2×C11semidirect
211. #1873C2×C11semidirect
212. #1818C2×C11semidirect
282. C2×C4⋊Q8C22×C11semidirect
285. C2×#124C22×C11semidirect
290. C2×C4×Q8C22×C11semidirect
291. C2×C4×D4C22×C11semidirect
296. C2×#103C22×C11semidirect
299. C2×#102C22×C11semidirect
308. #340C22×C11semidirect
309. #340C22×C11semidirect
310. #336C22×C11semidirect
311. #336C22×C11semidirect
508. C11#23945direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5422
C2×C11×#4502
C2×C11×#4472
C11×#23092
C11×#20232
C11×#20122
C11×#18802
C11×#18792
C11×#18752
C11×#18732
C11×#18182
#2394511