Finite Group Databasebeta

← C11×#23480 #14600673

Subgroups — C11×#23480 #14600673

Order 2816.

1902 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#121C211yesmaximal, characteristic
2C2×C11×#428C211yesmaximal, characteristic, complemented
3C2×C11×#418C211yesmaximal, characteristic, complemented
4C2×C11×#418C211yesmaximal, characteristic, complemented
5C2×C11×#407C211yesmaximal, characteristic, complemented
6C11×#2280C211yesmaximal, characteristic, complemented
7C11×#2034C214yesmaximal, complemented
8C11×#2033C214yesmaximal, complemented
9C11×#1736C211yesmaximal, characteristic, complemented
10C23×D4×C11—21no—
11C23×D4×C11C2211yescharacteristic
12C24×C4×C11C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C2×C11×#121—24no—
16C2×C11×#121—22no—
17C2×C11×#121—24no—
18C2×C11×#121C2214yes—
19C2×C11×#117C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4—21no—
23C11×#428—24no—
24C2×C11×#107C2212yescomplemented
25C2×C11×#106C2212yescomplemented
26C11×#418—24no—
27C11×#418—24no—
28C2×C11×#102C2212yescomplemented
29C2×C11×#102C2214yescomplemented
30C2×C11×#102C2212yescomplemented
31C11×#407—24no—
32C2×C11×C22⋊C8C2214yescomplemented
33C11×#381—21no—
34C11×#380C2212yescomplemented
35C11×#380C2212yescomplemented
36C11×#379—21no—
37C4×C11×C22⋊C4—22no—
38C11×#340C2214yescomplemented
39C25×C11—21no—
40C25×C11D411yescharacteristic
41C22×D4×C11—28no—
42C22×D4×C11—24no—
43C22×D4×C11—22no—
44C22×D4×C11—21no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—48no—
50C22×D4×C11D414yes—
51C22×D4×C11C2312yes—
52C23×C4×C11—21no—
53C23×C4×C11—22no—
54C23×C4×C11—22no—
55C23×C4×C11—22no—
56C23×C4×C11—22no—
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11D411yescharacteristic
60C23×C4×C11D412yes—
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16—22no—
66C2×C11×M16—22no—
67C2×C11×M16—22no—
68C2×C11×M16D414yescomplemented
69C22×C8×C11C2312yes—
70C22×C8×C11C2312yes—
71C11×#121—216no—
72C11×#121—28no—
73C11×#121—28no—
74C11×#117—22no—
75C11×#117—22no—
76C11×#117—22no—
77C11×#117—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4D414yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C22⋊C4—28no—
86C2×C11×C22⋊C4—24no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C42×C11—21no—
92C2×C42×C11—21no—
93C11×#107—24no—
94C11×#106—24no—
95C11×#102—24no—
96C11×#102—24no—
97C11×#102—28no—
98C11×C22⋊C8—28no—
99C11×#95—22no—
100C11×#95—22no—
101#23480C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—22no—
103C24×C11—24no—
104C24×C11—24no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—42no—
109C24×C11—44no—
110C24×C11—44no—
111C24×C11—42no—
112C24×C11—42no—
113C24×C11C2×D412yes—
114C24×C11C2×D411yescharacteristic
115C2×D4×C11—216no—
116C2×D4×C11—24no—
117C2×D4×C11—28no—
118C2×D4×C11—28no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—432no—
125C2×D4×C11—48no—
126C2×D4×C11—48no—
127C2×D4×C11—44no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11—44no—
131C2×D4×C11C2×D414yes—
132C22×C4×C11—22no—
133C22×C4×C11—24no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—44no—
150C22×C4×C11—44no—
151C22×C4×C11—44no—
152C22×C4×C11—44no—
153C22×C4×C11—44no—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11#4112yes—
160C22×C4×C11#4112yes—
161C22×C4×C11#4112yes—
162C22×C4×C11C2411yescharacteristic
163C11×M16—28no—
164C11×M16—44no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11C2×D414yescomplemented
171C11×C4⋊C4—24no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4C2×D414yes—
180C11×C22⋊C4—216no—
181C11×C22⋊C4—44no—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—44no—
185C42×C11—42no—
186C42×C11—42no—
187C22×#121C2×C1111yescharacteristic
188C2×#428C2×C1111yescharacteristic, complemented
189C2×#418C2×C1111yescharacteristic, complemented
190C2×#418C2×C1111yescharacteristic, complemented
191C2×#407C2×C1111yescharacteristic, complemented
192#2280C2×C1111yescharacteristic, complemented
193#2034C2×C1114yescomplemented
194#2033C2×C1114yescomplemented
195#1736C2×C1111yescharacteristic, complemented
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—28no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—24no—
206C23×C11—48no—
207C23×C11—48no—
208C23×C11—44no—
209C23×C11—48no—
210C23×C11—48no—
211C23×C11—44no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—44no—
215C23×C11—44no—
216C23×C11—48no—
217C23×C11—88no—
218C23×C11—88no—
219C23×C11#12012yes—
220C23×C11#12112yes—
221C23×C11#12312yes—
222C23×C11AGL(1,ℤ/8)14yes—
223C23×C11C22×D411yescharacteristic
224D4×C11—24no—
225D4×C11—24no—
226D4×C11—432no—
227D4×C11—42no—
228D4×C11—42no—
229D4×C11—48no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—48no—
235C2×C4×C11—44no—
236C2×C4×C11—44no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—48no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11#12012yes—
250C2×C4×C11#12114yes—
251C2×C4×C11#12114yes—
252C2×C4×C11#12112yes—
253C2×C4×C11#12314yes—
254C2×C4×C11#12312yes—
255C2×C4×C11#12414yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C8×C11—24no—
263C8×C11—42no—
264C23×D4—21no—
265C23×D4C22×C1111yescharacteristic
266C24×C4C22×C1111yescharacteristic
267C22×M16C22×C1111yescharacteristic
268C22×M16C22×C1111yescharacteristic
269C2×#121—24no—
270C2×#121—22no—
271C2×#121—24no—
272C2×#121C22×C1114yes—
273C2×#117C22×C1111yescharacteristic
274C2×#117C22×C1111yescharacteristic
275C22×C4⋊C4C22×C1111yescharacteristic
276C22×C22⋊C4—21no—
277#428—24no—
278C2×#107C22×C1112yescomplemented
279C2×#106C22×C1112yescomplemented
280#418—24no—
281#418—24no—
282C2×#102C22×C1112yescomplemented
283C2×#102C22×C1114yescomplemented
284C2×#102C22×C1112yescomplemented
285#407—24no—
286C2×C22⋊C8C22×C1114yescomplemented
287#381—21no—
288#380C22×C1112yescomplemented
289#380C22×C1112yescomplemented
290#379—21no—
291C4×C22⋊C4—22no—
292#340C22×C1114yescomplemented
293C22×C11—24no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—24no—
299C22×C11—24no—
300C22×C11—416no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—816no—
309C22×C11—84no—
310C22×C11—84no—
311C22×C11#39414yes—
312C22×C11C2×#12011yescharacteristic
313C22×C11C2×#12111yescharacteristic
314C22×C11C2×#12311yescharacteristic
315C22×C11C2×AGL(1,ℤ/8)12yes—
316C22×C11#57512yes—
317C4×C11—42no—
318C4×C11—44no—
319C4×C11—81no—
320C4×C11—81no—
321C4×C11—82no—
322C4×C11#39414yes—
323C4×C11C2×#12111yescharacteristic
324C4×C11C2×#12111yescharacteristic
325C4×C11C2×#12311yescharacteristic
326C4×C11C2×#12411yescharacteristic
327C25—21no—
328C25D4×C1111yescharacteristic
329C22×D4—28no—
330C22×D4—24no—
331C22×D4—22no—
332C22×D4—21no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—48no—
338C22×D4D4×C1114yes—
339C22×D4C23×C1112yes—
340C23×C4—21no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4D4×C1111yescharacteristic
348C23×C4D4×C1112yes—
349C23×C4C23×C1112yes—
350C23×C4C23×C1111yescharacteristic
351C2×M16—22no—
352C2×M16—22no—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—22no—
356C2×M16D4×C1114yescomplemented
357C22×C8C23×C1112yes—
358C22×C8C23×C1112yes—
359#121—216no—
360#121—28no—
361#121—28no—
362#117—22no—
363#117—22no—
364#117—22no—
365#117—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4D4×C1114yes—
369C2×C4⋊C4C23×C1112yes—
370C2×C4⋊C4C23×C1111yescharacteristic
371C2×C4⋊C4C23×C1111yescharacteristic
372C2×C4⋊C4C23×C1112yes—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C42—21no—
380C2×C42—21no—
381#107—24no—
382#106—24no—
383#102—24no—
384#102—24no—
385#102—28no—
386C22⋊C8—28no—
387#95—22no—
388#95—22no—
389C2×C11—24no—
390C2×C11—44no—
391C2×C11—84no—
392C2×C11C2×#39411yescharacteristic
393C2×C11#300311yescharacteristic
394C2×C11#300511yescharacteristic
395C2×C11#305512yes—
396C2×C11#309412yes—
397C24—22no—
398C24—24no—
399C24—24no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—42no—
404C24—44no—
405C24—44no—
406C24—42no—
407C24—42no—
408C24C2×D4×C1112yes—
409C24C2×D4×C1111yescharacteristic
410C2×D4—216no—
411C2×D4—24no—
412C2×D4—28no—
413C2×D4—28no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—432no—
420C2×D4—48no—
421C2×D4—48no—
422C2×D4—44no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—44no—
426C2×D4C2×D4×C1114yes—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—44no—
445C22×C4—44no—
446C22×C4—44no—
447C22×C4—44no—
448C22×C4—44no—
449C22×C4C2×D4×C1112yes—
450C22×C4C2×D4×C1111yescharacteristic
451C22×C4C2×D4×C1112yes—
452C22×C4C2×D4×C1112yes—
453C22×C4C2×D4×C1112yes—
454C22×C4C11×#4112yes—
455C22×C4C11×#4112yes—
456C22×C4C11×#4112yes—
457C22×C4C24×C1111yescharacteristic
458M16—28no—
459M16—44no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8C2×D4×C1114yescomplemented
466C4⋊C4—24no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—22no—
474C4⋊C4C2×D4×C1114yes—
475C22⋊C4—216no—
476C22⋊C4—44no—
477C22⋊C4—42no—
478C22⋊C4—42no—
479C22⋊C4—44no—
480C42—42no—
481C42—42no—
482C11#2348011yescharacteristic, direct product factor, Sylow
483C23—22no—
484C23—22no—
485C23—28no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—48no—
494C23—48no—
495C23—44no—
496C23—48no—
497C23—48no—
498C23—44no—
499C23—42no—
500C23—42no—
501C23—48no—
502C23—44no—
503C23—44no—
504C23—88no—
505C23—88no—
506C23C11×#12012yes—
507C23C11×#12112yes—
508C23C11×#12312yes—
509C23C11×AGL(1,ℤ/8)14yes—
510C23C22×D4×C1111yescharacteristic
511D4—24no—
512D4—24no—
513D4—432no—
514D4—42no—
515D4—42no—
516D4—48no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—48no—
522C2×C4—44no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—48no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4C11×#12012yes—
537C2×C4C11×#12114yes—
538C2×C4C11×#12114yes—
539C2×C4C11×#12112yes—
540C2×C4C11×#12314yes—
541C2×C4C11×#12312yes—
542C2×C4C11×#12414yes—
543C2×C4C22×D4×C1111yescharacteristic
544C2×C4C22×D4×C1111yescharacteristic
545C2×C4C22×D4×C1111yescharacteristic
546C2×C4C2×C11×#4111yescharacteristic
547C2×C4C2×C11×#4111yescharacteristic
548C2×C4C2×C11×#4111yescharacteristic
549C8—24no—
550C8—42no—
551C22—22no—
552C22—22no—
553C22—24no—
554C22—24no—
555C22—24no—
556C22—24no—
557C22—24no—
558C22—416no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—44no—
564C22—44no—
565C22—44no—
566C22—816no—
567C22—84no—
568C22—84no—
569C22C11×#39414yes—
570C22C2×C11×#12011yescharacteristic
571C22C2×C11×#12111yescharacteristic
572C22C2×C11×#12311yescharacteristic
573C22C2×C11×AGL(1,ℤ/8)12yes—
574C22C11×#57512yes—
575C4—42no—
576C4—44no—
577C4—81no—
578C4—81no—
579C4—82no—
580C4C11×#39414yes—
581C4C2×C11×#12111yescharacteristic
582C4C2×C11×#12111yescharacteristic
583C4C2×C11×#12311yescharacteristic
584C4C2×C11×#12411yescharacteristic
585C2—24no—
586C2—44no—
587C2—84no—
588C2C2×C11×#39411yescharacteristic
589C2C11×#300311yescharacteristic
590C2C11×#300511yescharacteristic
591C2C11×#305512yes—
592C2C11×#309412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#121C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#428C2semidirect
3. C2×C11×#418C2semidirect
4. C2×C11×#418C2semidirect
5. C2×C11×#407C2semidirect
6. C11×#2280C2semidirect
7. C11×#2034C2semidirect
8. C11×#2033C2semidirect
9. C11×#1736C2semidirect
24. C2×C11×#107C22semidirect
25. C2×C11×#106C22semidirect
28. C2×C11×#102C22semidirect
29. C2×C11×#102C22semidirect
30. C2×C11×#102C22semidirect
32. C2×C11×C22⋊C8C22semidirect
34. C11×#380C22semidirect
35. C11×#380C22semidirect
38. C11×#340C22semidirect
68. C2×C11×M16D4semidirect
101. #23480C11direct (N × H)
170. C2×C8×C11C2×D4semidirect
188. C2×#428C2×C11semidirect
189. C2×#418C2×C11semidirect
190. C2×#418C2×C11semidirect
191. C2×#407C2×C11semidirect
192. #2280C2×C11semidirect
193. #2034C2×C11semidirect
194. #2033C2×C11semidirect
195. #1736C2×C11semidirect
278. C2×#107C22×C11semidirect
279. C2×#106C22×C11semidirect
282. C2×#102C22×C11semidirect
283. C2×#102C22×C11semidirect
284. C2×#102C22×C11semidirect
286. C2×C22⋊C8C22×C11semidirect
288. #380C22×C11semidirect
289. #380C22×C11semidirect
292. #340C22×C11semidirect
356. C2×M16D4×C11semidirect
465. C2×C8C2×D4×C11semidirect
482. C11#23480direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1212
C2×C11×#4282
C2×C11×#4182
C2×C11×#4072
C11×#22802
C11×#20342
C11×#20332
C11×#17362
#2348011