Finite Group Databasebeta

← C11×#24254 #14601447

Subgroups — C11×#24254 #14601447

Order 2816.

1476 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#550C211yesmaximal, characteristic
2C2×C11×#460C211yesmaximal, characteristic, complemented
3C2×C11×#452C212yesmaximal, complemented
4C2×C11×#441C211yesmaximal, characteristic, complemented
5C11×#2536C211yesmaximal, characteristic, complemented
6C11×#2034C212yesmaximal, complemented
7C11×#2000C212yesmaximal, complemented
8C11×#1961C211yesmaximal, characteristic, complemented
9C11×#1955C211yesmaximal, characteristic, complemented
10C11×#1805C211yesmaximal, characteristic, complemented
11C11×#1788C212yesmaximal, complemented
12C22×C11×#41C2212yes—
13C22×C11×Q16C2211yescharacteristic
14C22×C11×SD16C2212yes—
15C11×#550—24no—
16C11×#550—24no—
17C2×C11×#127—21no—
18C2×C11×#127C2211yescharacteristic
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×#121—22no—
21C2×C11×#121C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×D4×C11—21no—
25C2×C4×D4×C11C2211yescharacteristic
26C11×#460—24no—
27C11×#452—28no—
28C11×#441—24no—
29C2×C11×#106C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×#102C2212yes—
36C2×C11×#102C2212yes—
37C2×C11×C22⋊C8C2212yes—
38C2×C11×C22⋊C8C2212yes—
39C2×C11×#97C2211yescharacteristic
40C11×#398—21no—
41C11×#394—21no—
42C11×#388—22no—
43C11×#382C2211yescharacteristic
44C11×#380C2212yes—
45C11×#340C2212yes—
46C2×C11×#41—24no—
47C2×C11×#41—24no—
48C2×C11×#41—24no—
49C2×C11×#41—24no—
50C2×C11×#41—42no—
51C2×C11×#41—42no—
52C22×Q8×C11C2311yescharacteristic
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11—22no—
55C22×D4×C11—22no—
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11D411yescharacteristic
59C22×D4×C11C2312yes—
60C23×C4×C11—22no—
61C23×C4×C11C2312yes—
62C2×C11×Q16—22no—
63C2×C11×Q16—22no—
64C2×C11×Q16D414yescomplemented
65C2×C11×SD16—24no—
66C2×C11×SD16—24no—
67C2×C11×SD16—42no—
68C22×C8×C11C2312yes—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×#127—28no—
72C11×#127—22no—
73C11×#127D414yes—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—42no—
76C11×#121—216no—
77C11×#121—24no—
78C11×#121—24no—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×Q8×C11D414yes—
83C4×D4×C11—28no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4D412yes—
97C2×C42×C11—21no—
98C2×C42×C11—21no—
99C2×C42×C11C2311yescharacteristic
100C11×#106—22no—
101C11×C4⋊C8—22no—
102C11×#103—22no—
103C11×#103—24no—
104C11×#103—22no—
105C11×#102—24no—
106C11×#102—24no—
107C11×#102—42no—
108C11×C22⋊C8—24no—
109C11×C22⋊C8—42no—
110C11×#97—22no—
111C11×#95—22no—
112C11×#95—21no—
113C11×#95—21no—
114#24254C1111yesmaximal, characteristic, direct product factor, Sylow
115C24×C11—22no—
116C24×C11C2×D412yes—
117C11×#41—48no—
118C11×#41—48no—
119C11×#41—48no—
120C11×#41—48no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11C2×D412yes—
130C2×Q8×C11C2×D412yes—
131C2×Q8×C11C2×D412yes—
132C2×Q8×C11#4112yes—
133C2×D4×C11—28no—
134C2×D4×C11—28no—
135C2×D4×C11—22no—
136C2×D4×C11—24no—
137C2×D4×C11—24no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—42no—
144C2×D4×C11—44no—
145C2×D4×C11—44no—
146C2×D4×C11—44no—
147C2×D4×C11—82no—
148C2×D4×C11—82no—
149C2×D4×C11—82no—
150C2×D4×C11C2×D414yes—
151C22×C4×C11—21no—
152C22×C4×C11—28no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—21no—
163C22×C4×C11—44no—
164C22×C4×C11—44no—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2411yescharacteristic
169C11×Q16—28no—
170C11×SD16—48no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—22no—
178C2×C8×C11—21no—
179C2×C8×C11C2×D412yes—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—44no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4C2×D412yes—
190C11×C22⋊C4—28no—
191C11×C22⋊C4—24no—
192C11×C22⋊C4—44no—
193C11×C22⋊C4—44no—
194C42×C11—24no—
195C42×C11—42no—
196C42×C11C2×D412yes—
197C42×C11C2×D412yes—
198C2×#550C2×C1111yescharacteristic
199C2×#460C2×C1111yescharacteristic, complemented
200C2×#452C2×C1112yescomplemented
201C2×#441C2×C1111yescharacteristic, complemented
202#2536C2×C1111yescharacteristic, complemented
203#2034C2×C1112yescomplemented
204#2000C2×C1112yescomplemented
205#1961C2×C1111yescharacteristic, complemented
206#1955C2×C1111yescharacteristic, complemented
207#1805C2×C1111yescharacteristic, complemented
208#1788C2×C1112yescomplemented
209C23×C11—22no—
210C23×C11—24no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11C22×D411yescharacteristic
224Q8×C11—22no—
225Q8×C11—22no—
226Q8×C11—22no—
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11#12114yes—
232D4×C11—24no—
233D4×C11—24no—
234D4×C11—44no—
235D4×C11—48no—
236D4×C11—416no—
237D4×C11—42no—
238D4×C11—42no—
239D4×C11—84no—
240D4×C11—88no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—416no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11#12012yes—
265C2×C4×C11#12012yes—
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C8×C11—22no—
273C8×C11—41no—
274C8×C11—42no—
275C22×#41C22×C1112yes—
276C22×Q16C22×C1111yescharacteristic
277C22×SD16C22×C1112yes—
278#550—24no—
279#550—24no—
280C2×#127—21no—
281C2×#127C22×C1111yescharacteristic
282C2×C22⋊Q8C22×C1112yes—
283C2×#121—22no—
284C2×#121C22×C1112yes—
285C2×C4×Q8C22×C1111yescharacteristic
286C2×C4×Q8C22×C1111yescharacteristic
287C2×C4×D4—21no—
288C2×C4×D4C22×C1111yescharacteristic
289#460—24no—
290#452—28no—
291#441—24no—
292C2×#106C22×C1111yescharacteristic
293C2×C4⋊C8C22×C1111yescharacteristic
294C2×#103C22×C1112yes—
295C2×#103C22×C1111yescharacteristic
296C2×#103C22×C1111yescharacteristic
297C2×#102C22×C1112yes—
298C2×#102C22×C1112yes—
299C2×#102C22×C1112yes—
300C2×C22⋊C8C22×C1112yes—
301C2×C22⋊C8C22×C1112yes—
302C2×#97C22×C1111yescharacteristic
303#398—21no—
304#394—21no—
305#388—22no—
306#382C22×C1111yescharacteristic
307#380C22×C1112yes—
308#340C22×C1112yes—
309C22×C11—44no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—44no—
313C22×C11—42no—
314C22×C11—44no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—82no—
320C22×C11—82no—
321C22×C11—82no—
322C22×C11—82no—
323C22×C11C2×#12011yescharacteristic
324C22×C11D4211yescharacteristic
325C22×C11#54611yescharacteristic
326C22×C11#57512yes—
327C22×C11#57712yes—
328C4×C11—24no—
329C4×C11—22no—
330C4×C11—22no—
331C4×C11—42no—
332C4×C11—42no—
333C4×C11—42no—
334C4×C11—81no—
335C4×C11—82no—
336C4×C11C2×#12111yescharacteristic
337C4×C11#53511yescharacteristic
338C4×C11D4211yescharacteristic
339C4×C11#54611yescharacteristic
340C2×#41—24no—
341C2×#41—24no—
342C2×#41—24no—
343C2×#41—24no—
344C2×#41—42no—
345C2×#41—42no—
346C22×Q8C23×C1111yescharacteristic
347C22×Q8C23×C1111yescharacteristic
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—21no—
351C22×D4—21no—
352C22×D4D4×C1111yescharacteristic
353C22×D4C23×C1112yes—
354C23×C4—22no—
355C23×C4C23×C1112yes—
356C2×Q16—22no—
357C2×Q16—22no—
358C2×Q16D4×C1114yescomplemented
359C2×SD16—24no—
360C2×SD16—24no—
361C2×SD16—42no—
362C22×C8C23×C1112yes—
363C22×C8C23×C1111yescharacteristic
364C22×C8C23×C1111yescharacteristic
365#127—28no—
366#127—22no—
367#127D4×C1114yes—
368C22⋊Q8—24no—
369C22⋊Q8—42no—
370#121—216no—
371#121—24no—
372#121—24no—
373C4×Q8—22no—
374C4×Q8—22no—
375C4×Q8—22no—
376C4×Q8D4×C1114yes—
377C4×D4—28no—
378C4×D4—22no—
379C4×D4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4D4×C1111yescharacteristic
384C2×C4⋊C4C23×C1111yescharacteristic
385C2×C4⋊C4C23×C1112yes—
386C2×C4⋊C4C23×C1111yescharacteristic
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4D4×C1112yes—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42C23×C1111yescharacteristic
394#106—22no—
395C4⋊C8—22no—
396#103—22no—
397#103—24no—
398#103—22no—
399#102—24no—
400#102—24no—
401#102—42no—
402C22⋊C8—24no—
403C22⋊C8—42no—
404#97—22no—
405#95—22no—
406#95—21no—
407#95—21no—
408C2×C11—82no—
409C2×C11—84no—
410C2×C11#240811yescharacteristic
411C2×C11#300511yescharacteristic
412C2×C11#300911yescharacteristic
413C2×C11#327112yes—
414C2×C11#331712yes—
415C24—22no—
416C24C2×D4×C1112yes—
417#41—48no—
418#41—48no—
419#41—48no—
420#41—48no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8C2×D4×C1112yes—
430C2×Q8C2×D4×C1112yes—
431C2×Q8C2×D4×C1112yes—
432C2×Q8C11×#4112yes—
433C2×D4—28no—
434C2×D4—28no—
435C2×D4—22no—
436C2×D4—24no—
437C2×D4—24no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—42no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—44no—
447C2×D4—82no—
448C2×D4—82no—
449C2×D4—82no—
450C2×D4C2×D4×C1114yes—
451C22×C4—21no—
452C22×C4—28no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—44no—
464C22×C4—44no—
465C22×C4C2×D4×C1112yes—
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C24×C1111yescharacteristic
469Q16—28no—
470SD16—48no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—21no—
477C2×C8—22no—
478C2×C8—21no—
479C2×C8C2×D4×C1112yes—
480C4⋊C4—24no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—44no—
488C4⋊C4—42no—
489C4⋊C4C2×D4×C1112yes—
490C22⋊C4—28no—
491C22⋊C4—24no—
492C22⋊C4—44no—
493C22⋊C4—44no—
494C42—24no—
495C42—42no—
496C42C2×D4×C1112yes—
497C42C2×D4×C1112yes—
498C11#2425411yescharacteristic, direct product factor, Sylow
499C23—22no—
500C23—24no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23C22×D4×C1111yescharacteristic
514Q8—22no—
515Q8—22no—
516Q8—22no—
517Q8—22no—
518Q8—22no—
519Q8—41no—
520Q8—41no—
521Q8C11×#12114yes—
522D4—24no—
523D4—24no—
524D4—44no—
525D4—48no—
526D4—416no—
527D4—42no—
528D4—42no—
529D4—84no—
530D4—88no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—416no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4C11×#12012yes—
555C2×C4C11×#12012yes—
556C2×C4C22×D4×C1111yescharacteristic
557C2×C4C22×D4×C1111yescharacteristic
558C2×C4C22×D4×C1111yescharacteristic
559C2×C4C2×C11×#4111yescharacteristic
560C2×C4C11×H(5,𝔽2)11yescharacteristic
561C2×C4C11×H(5,𝔽2)11yescharacteristic
562C8—22no—
563C8—41no—
564C8—42no—
565C22—44no—
566C22—42no—
567C22—42no—
568C22—44no—
569C22—42no—
570C22—44no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—82no—
576C22—82no—
577C22—82no—
578C22—82no—
579C22C2×C11×#12011yescharacteristic
580C22D42×C1111yescharacteristic
581C22C11×#54611yescharacteristic
582C22C11×#57512yes—
583C22C11×#57712yes—
584C4—24no—
585C4—22no—
586C4—22no—
587C4—42no—
588C4—42no—
589C4—42no—
590C4—81no—
591C4—82no—
592C4C2×C11×#12111yescharacteristic
593C4C11×#53511yescharacteristic
594C4D42×C1111yescharacteristic
595C4C11×#54611yescharacteristic
596C2—82no—
597C2—84no—
598C2C11×#240811yescharacteristic
599C2C11×#300511yescharacteristic
600C2C11×#300911yescharacteristic
601C2C11×#327112yes—
602C2C11×#331712yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#550C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#460C2semidirect
3. C2×C11×#452C2semidirect
4. C2×C11×#441C2semidirect
5. C11×#2536C2semidirect
6. C11×#2034C2semidirect
7. C11×#2000C2semidirect
8. C11×#1961C2semidirect
9. C11×#1955C2semidirect
10. C11×#1805C2semidirect
11. C11×#1788C2semidirect
64. C2×C11×Q16D4semidirect
114. #24254C11direct (N × H)
199. C2×#460C2×C11semidirect
200. C2×#452C2×C11semidirect
201. C2×#441C2×C11semidirect
202. #2536C2×C11semidirect
203. #2034C2×C11semidirect
204. #2000C2×C11semidirect
205. #1961C2×C11semidirect
206. #1955C2×C11semidirect
207. #1805C2×C11semidirect
208. #1788C2×C11semidirect
358. C2×Q16D4×C11semidirect
498. C11#24254direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5502
C2×C11×#4602
C2×C11×#4522
C2×C11×#4412
C11×#25362
C11×#20342
C11×#20002
C11×#19612
C11×#19552
C11×#18052
C11×#17882
#2425411