Finite Group Databasebeta

← C11×#24271 #14601464

Subgroups — C11×#24271 #14601464

Order 2816.

1452 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#135C211yesmaximal, characteristic, complemented
2C2×C11×#470C211yesmaximal, characteristic, complemented
3C2×C11×#469C211yesmaximal, characteristic, complemented
4C2×C11×#435C211yesmaximal, characteristic, complemented
5C11×#2407C212yesmaximal, complemented
6C11×#2055C212yesmaximal, complemented
7C11×#2000C212yesmaximal, complemented
8C11×#1972C211yesmaximal, characteristic, complemented
9C11×#1971C211yesmaximal, characteristic, complemented
10C11×#1807C211yesmaximal, characteristic, complemented
11C11×#1788C212yesmaximal, complemented
12C22×C11×#41C2212yes—
13C2×C11×#135—24no—
14C2×C11×#135—24no—
15C2×C11×#135—24no—
16C22×C11×Q16C2211yescharacteristic
17C22×C11×SD16C2212yes—
18C22×C11×D8C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C2×C11×C22⋊Q8C2212yes—
22C2×C11×#121C2212yes—
23C2×C4×D4×C11C2211yescharacteristic
24C11×#470—24no—
25C11×#469—24no—
26C11×#435—24no—
27C2×C11×#106C2211yescharacteristic
28C2×C11×#106C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2212yes—
31C2×C11×#103C2212yes—
32C2×C11×#102C2212yes—
33C2×C11×#102C2212yes—
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×#97C2211yescharacteristic
37C11×#394—22no—
38C11×#392—22no—
39C11×#391C2212yes—
40C11×#390C2212yes—
41C11×#386—22no—
42C11×#385—22no—
43C11×#380C2212yes—
44C11×#340C2212yes—
45C2×C11×#41—24no—
46C2×C11×#41—24no—
47C2×C11×#41—24no—
48C2×C11×#41—24no—
49C2×C11×#41—42no—
50C2×C11×#41—42no—
51C22×Q8×C11C2312yes—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11D411yescharacteristic
55C22×D4×C11C2312yes—
56C23×C4×C11—22no—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C11×#135—232no—
60C2×C11×Q16—22no—
61C2×C11×Q16—22no—
62C2×C11×Q16D414yescomplemented
63C2×C11×SD16—24no—
64C2×C11×SD16—24no—
65C2×C11×SD16—24no—
66C2×C11×D8—22no—
67C2×C11×D8—22no—
68C2×C11×D8D414yescomplemented
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C22×C8×C11—22no—
73C22×C8×C11—22no—
74C22×C8×C11D414yescomplemented
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C11×C22⋊Q8—24no—
80C11×C22⋊Q8—42no—
81C11×#121—24no—
82C11×#121—42no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C11×C22⋊C4D411yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C11×#106—22no—
98C11×#106—22no—
99C11×C4⋊C8—22no—
100C11×#103—24no—
101C11×#103—42no—
102C11×#102—24no—
103C11×#102—42no—
104C11×C22⋊C8—22no—
105C11×C22⋊C8—22no—
106C11×#97—22no—
107C11×#95—22no—
108C11×#95—22no—
109C11×#95—22no—
110#24271C1111yesmaximal, characteristic, direct product factor, Sylow
111C24×C11—22no—
112C24×C11C2×D411yescharacteristic
113C24×C11C2×D411yescharacteristic
114C11×#41—216no—
115C11×#41—48no—
116C11×#41—48no—
117C11×#41—48no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11C2×D414yes—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—42no—
131C2×D4×C11—44no—
132C2×D4×C11—44no—
133C2×D4×C11—44no—
134C2×D4×C11—44no—
135C2×D4×C11—44no—
136C2×D4×C11—82no—
137C2×D4×C11C2×D414yes—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—44no—
152C22×C4×C11—44no—
153C22×C4×C11—44no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11#4112yes—
160C22×C4×C11C2411yescharacteristic
161C11×Q16—28no—
162C11×SD16—216no—
163C11×D8—28no—
164C11×M16—44no—
165C2×C8×C11—28no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11C2×D412yes—
175C2×C8×C11C2×D412yes—
176C2×C8×C11C2×D412yes—
177C2×C8×C11C2×D412yes—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—44no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—44no—
187C11×C22⋊C4—44no—
188C11×C22⋊C4—44no—
189C11×C22⋊C4—82no—
190C11×C22⋊C4—82no—
191C42×C11—21no—
192C42×C11—21no—
193C22×#135C2×C1111yescharacteristic, complemented
194C2×#470C2×C1111yescharacteristic, complemented
195C2×#469C2×C1111yescharacteristic, complemented
196C2×#435C2×C1111yescharacteristic, complemented
197#2407C2×C1112yescomplemented
198#2055C2×C1112yescomplemented
199#2000C2×C1112yescomplemented
200#1972C2×C1111yescharacteristic, complemented
201#1971C2×C1111yescharacteristic, complemented
202#1807C2×C1111yescharacteristic, complemented
203#1788C2×C1112yescomplemented
204C23×C11—21no—
205C23×C11—21no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—24no—
211C23×C11—21no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11#12112yes—
221C23×C11C22×D411yescharacteristic
222Q8×C11—24no—
223Q8×C11—24no—
224Q8×C11—42no—
225Q8×C11—42no—
226D4×C11—24no—
227D4×C11—24no—
228D4×C11—44no—
229D4×C11—416no—
230D4×C11—42no—
231D4×C11—42no—
232D4×C11—88no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—24no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—416no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
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—42no—
260C2×C4×C11#12112yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C8×C11—22no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11#12014yes—
271C22×#41C22×C1112yes—
272C2×#135—24no—
273C2×#135—24no—
274C2×#135—24no—
275C22×Q16C22×C1111yescharacteristic
276C22×SD16C22×C1112yes—
277C22×D8C22×C1111yescharacteristic
278C22×M16C22×C1111yescharacteristic
279C23×C8C22×C1111yescharacteristic
280C2×C22⋊Q8C22×C1112yes—
281C2×#121C22×C1112yes—
282C2×C4×D4C22×C1111yescharacteristic
283#470—24no—
284#469—24no—
285#435—24no—
286C2×#106C22×C1111yescharacteristic
287C2×#106C22×C1111yescharacteristic
288C2×C4⋊C8C22×C1111yescharacteristic
289C2×#103C22×C1112yes—
290C2×#103C22×C1112yes—
291C2×#102C22×C1112yes—
292C2×#102C22×C1112yes—
293C2×C22⋊C8C22×C1111yescharacteristic
294C2×C22⋊C8C22×C1111yescharacteristic
295C2×#97C22×C1111yescharacteristic
296#394—22no—
297#392—22no—
298#391C22×C1112yes—
299#390C22×C1112yes—
300#386—22no—
301#385—22no—
302#380C22×C1112yes—
303#340C22×C1112yes—
304C22×C11—22no—
305C22×C11—22no—
306C22×C11—22no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—44no—
310C22×C11—41no—
311C22×C11—42no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—42no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11—82no—
318C22×C11—82no—
319C22×C11—82no—
320C22×C11—82no—
321C22×C11C2×#12111yescharacteristic
322C22×C11D4211yescharacteristic
323C22×C11D4211yescharacteristic
324C22×C11#57512yes—
325C22×C11#57712yes—
326C4×C11—22no—
327C4×C11—41no—
328C4×C11—44no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—82no—
332C4×C11—82no—
333C4×C11C2×#12011yescharacteristic
334C4×C11#53511yescharacteristic
335C4×C11#54611yescharacteristic
336C4×C11#54611yescharacteristic
337C2×#41—24no—
338C2×#41—24no—
339C2×#41—24no—
340C2×#41—24no—
341C2×#41—42no—
342C2×#41—42no—
343C22×Q8C23×C1112yes—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4D4×C1111yescharacteristic
347C22×D4C23×C1112yes—
348C23×C4—22no—
349C23×C4C23×C1111yescharacteristic
350C23×C4C23×C1111yescharacteristic
351#135—232no—
352C2×Q16—22no—
353C2×Q16—22no—
354C2×Q16D4×C1114yescomplemented
355C2×SD16—24no—
356C2×SD16—24no—
357C2×SD16—24no—
358C2×D8—22no—
359C2×D8—22no—
360C2×D8D4×C1114yescomplemented
361C2×M16—22no—
362C2×M16—22no—
363C2×M16—22no—
364C22×C8—22no—
365C22×C8—22no—
366C22×C8D4×C1114yescomplemented
367C22×C8C23×C1111yescharacteristic
368C22×C8C23×C1111yescharacteristic
369C22×C8C23×C1111yescharacteristic
370C22×C8C23×C1111yescharacteristic
371C22⋊Q8—24no—
372C22⋊Q8—42no—
373#121—24no—
374#121—42no—
375C4×D4—22no—
376C4×D4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4D4×C1111yescharacteristic
379C2×C4⋊C4C23×C1112yes—
380C2×C4⋊C4C23×C1112yes—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4D4×C1111yescharacteristic
387C2×C22⋊C4D4×C1111yescharacteristic
388C2×C42C23×C1111yescharacteristic
389#106—22no—
390#106—22no—
391C4⋊C8—22no—
392#103—24no—
393#103—42no—
394#102—24no—
395#102—42no—
396C22⋊C8—22no—
397C22⋊C8—22no—
398#97—22no—
399#95—22no—
400#95—22no—
401#95—22no—
402C2×C11—42no—
403C2×C11—81no—
404C2×C11—84no—
405C2×C11#240811yescharacteristic
406C2×C11#305411yescharacteristic
407C2×C11#306011yescharacteristic
408C2×C11#326712yes—
409C2×C11#327112yes—
410C24—22no—
411C24C2×D4×C1111yescharacteristic
412C24C2×D4×C1111yescharacteristic
413#41—216no—
414#41—48no—
415#41—48no—
416#41—48no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8C2×D4×C1114yes—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—42no—
430C2×D4—44no—
431C2×D4—44no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—82no—
436C2×D4C2×D4×C1114yes—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—44no—
451C22×C4—44no—
452C22×C4—44no—
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C2×D4×C1111yescharacteristic
455C22×C4C2×D4×C1111yescharacteristic
456C22×C4C2×D4×C1111yescharacteristic
457C22×C4C2×D4×C1112yes—
458C22×C4C11×#4112yes—
459C22×C4C24×C1111yescharacteristic
460Q16—28no—
461SD16—216no—
462D8—28no—
463M16—44no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—28no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8C2×D4×C1112yes—
474C2×C8C2×D4×C1112yes—
475C2×C8C2×D4×C1112yes—
476C2×C8C2×D4×C1112yes—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—44no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—44no—
486C22⋊C4—44no—
487C22⋊C4—44no—
488C22⋊C4—82no—
489C22⋊C4—82no—
490C42—21no—
491C42—21no—
492C11#2427111yescharacteristic, direct product factor, Sylow
493C23—21no—
494C23—21no—
495C23—22no—
496C23—22no—
497C23—21no—
498C23—21no—
499C23—24no—
500C23—21no—
501C23—22no—
502C23—22no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23C11×#12112yes—
510C23C22×D4×C1111yescharacteristic
511Q8—24no—
512Q8—24no—
513Q8—42no—
514Q8—42no—
515D4—24no—
516D4—24no—
517D4—44no—
518D4—416no—
519D4—42no—
520D4—42no—
521D4—88no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—24no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—416no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4C11×#12112yes—
550C2×C4C22×D4×C1111yescharacteristic
551C2×C4C22×D4×C1111yescharacteristic
552C2×C4C22×D4×C1111yescharacteristic
553C2×C4C2×C11×#4111yescharacteristic
554C2×C4C11×H(5,𝔽2)11yescharacteristic
555C2×C4C11×H(5,𝔽2)11yescharacteristic
556C8—22no—
557C8—41no—
558C8—41no—
559C8C11×#12014yes—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—42no—
564C22—42no—
565C22—44no—
566C22—41no—
567C22—42no—
568C22—44no—
569C22—44no—
570C22—42no—
571C22—41no—
572C22—41no—
573C22—82no—
574C22—82no—
575C22—82no—
576C22—82no—
577C22C2×C11×#12111yescharacteristic
578C22D42×C1111yescharacteristic
579C22D42×C1111yescharacteristic
580C22C11×#57512yes—
581C22C11×#57712yes—
582C4—22no—
583C4—41no—
584C4—44no—
585C4—41no—
586C4—41no—
587C4—82no—
588C4—82no—
589C4C2×C11×#12011yescharacteristic
590C4C11×#53511yescharacteristic
591C4C11×#54611yescharacteristic
592C4C11×#54611yescharacteristic
593C2—42no—
594C2—81no—
595C2—84no—
596C2C11×#240811yescharacteristic
597C2C11×#305411yescharacteristic
598C2C11×#306011yescharacteristic
599C2C11×#326712yes—
600C2C11×#327112yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C22×C11×#135C2semidirect
2. C2×C11×#470C2semidirect
3. C2×C11×#469C2semidirect
4. C2×C11×#435C2semidirect
5. C11×#2407C2semidirect
6. C11×#2055C2semidirect
7. C11×#2000C2semidirect
8. C11×#1972C2semidirect
9. C11×#1971C2semidirect
10. C11×#1807C2semidirect
11. C11×#1788C2semidirect
62. C2×C11×Q16D4semidirect
68. C2×C11×D8D4semidirect
74. C22×C8×C11D4semidirect
110. #24271C11direct (N × H)
193. C22×#135C2×C11semidirect
194. C2×#470C2×C11semidirect
195. C2×#469C2×C11semidirect
196. C2×#435C2×C11semidirect
197. #2407C2×C11semidirect
198. #2055C2×C11semidirect
199. #2000C2×C11semidirect
200. #1972C2×C11semidirect
201. #1971C2×C11semidirect
202. #1807C2×C11semidirect
203. #1788C2×C11semidirect
354. C2×Q16D4×C11semidirect
360. C2×D8D4×C11semidirect
366. C22×C8D4×C11semidirect
492. C11#24271direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1352
C2×C11×#4702
C2×C11×#4692
C2×C11×#4352
C11×#24072
C11×#20552
C11×#20002
C11×#19722
C11×#19712
C11×#18072
C11×#17882
#2427111