Finite Group Databasebeta

← C11×#23901 #14601094

Subgroups — C11×#23901 #14601094

Order 2816.

2056 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3484C211yesmaximal, characteristic
2C22×C11×#123C211yesmaximal, characteristic, complemented
3C2×C11×#458C212yesmaximal, complemented
4C11×#2849C212yesmaximal, complemented
5C11×#2022C214yesmaximal, complemented
6C11×#1898C212yesmaximal, complemented
7C11×#1890C212yesmaximal, complemented
8C11×#1781C211yesmaximal, characteristic, complemented
9C2×C11×H(5,𝔽2)C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic, complemented
12C11×#546—24no—
13D42×C11—24no—
14C11×#535—21no—
15C11×#534—21no—
16C11×#534C2212yes—
17C11×#525—21no—
18C2×C11×#123—21no—
19C2×C11×#123—21no—
20C2×C11×#123—28no—
21C2×C11×#123C2212yes—
22C2×C11×#123C2212yescomplemented
23C2×C11×#123C2214yescomplemented
24C2×C11×#120—21no—
25C2×C11×#120C2212yes—
26C11×#518C2211yescharacteristic
27C22×C11×C4⋊C4—21no—
28C22×C11×C22⋊C4—21no—
29C22×C11×C22⋊C4C2211yescharacteristic, complemented
30C11×#458—28no—
31C2×C11×#99C2212yes—
32C2×C11×#99C2214yescomplemented
33C2×C11×#99C2212yescomplemented
34C11×#386—24no—
35C11×#385—24no—
36C11×#381C2214yescomplemented
37C11×#379C2212yescomplemented
38C11×#342C2214yescomplemented
39C25×C11D411yescharacteristic
40C25×C11C2311yescharacteristic
41C11×H(5,𝔽2)—24no—
42C11×H(5,𝔽2)—42no—
43C2×C11×#41—21no—
44C2×C11×#41—22no—
45C22×D4×C11—21no—
46C22×D4×C11—22no—
47C22×D4×C11—24no—
48C22×D4×C11—22no—
49C22×D4×C11—24no—
50C22×D4×C11—42no—
51C22×D4×C11D411yescharacteristic
52C22×D4×C11D411yescharacteristic
53C22×D4×C11D414yes—
54C22×D4×C11C2312yes—
55C22×D4×C11C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C23×C4×C11—21no—
60C23×C4×C11—24no—
61C23×C4×C11—24no—
62C23×C4×C11—42no—
63C23×C4×C11D411yescharacteristic
64C23×C4×C11C2312yes—
65C11×#127—22no—
66C11×#124—22no—
67C11×#123—28no—
68C11×#123—28no—
69C11×#123—22no—
70C11×#123—24no—
71C11×#123—22no—
72C11×#123—22no—
73C11×#123—24no—
74C11×#123—24no—
75C11×#123—28no—
76C11×#123—44no—
77C11×#123D418yescomplemented
78C11×C22⋊Q8—22no—
79C11×#121—22no—
80C11×#121—24no—
81C11×#121—24no—
82C11×#121—24no—
83C11×#120—24no—
84C11×#120—22no—
85C11×#120—22no—
86C11×#120—22no—
87C11×#120—22no—
88C11×#120—24no—
89C11×#120—22no—
90C4×D4×C11—24no—
91C4×D4×C11—24no—
92C11×#117—21no—
93C2×C11×C4⋊C4—28no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—24no—
97C2×C11×C22⋊C4—28no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—24no—
104C2×C11×C22⋊C4—24no—
105C2×C11×C22⋊C4—24no—
106C2×C11×C22⋊C4D414yes—
107C2×C11×C22⋊C4C2314yes—
108C2×C11×C22⋊C4C2312yes—
109C2×C11×C22⋊C4C2312yes—
110C11×#99—24no—
111C11×#99—28no—
112C11×#99—42no—
113C11×#95—28no—
114#23901C1111yesmaximal, characteristic, direct product factor, Sylow
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—21no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—44no—
121C24×C11—41no—
122C24×C11—44no—
123C24×C11C2×D411yescharacteristic
124C24×C11C2×D414yes—
125C24×C11C2×D411yescharacteristic
126C24×C11C2×D412yes—
127C24×C11C2×D411yescharacteristic
128C24×C11C2×D411yescharacteristic
129C24×C11C2411yescharacteristic
130C11×#41—48no—
131C11×#41—42no—
132C11×#41—42no—
133C2×Q8×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—24no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—24no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—24no—
149C2×D4×C11—24no—
150C2×D4×C11—24no—
151C2×D4×C11—22no—
152C2×D4×C11—41no—
153C2×D4×C11—41no—
154C2×D4×C11—416no—
155C2×D4×C11—48no—
156C2×D4×C11—42no—
157C2×D4×C11—42no—
158C2×D4×C11—48no—
159C2×D4×C11—84no—
160C2×D4×C11C2×D414yes—
161C22×C4×C11—24no—
162C22×C4×C11—24no—
163C22×C4×C11—21no—
164C22×C4×C11—22no—
165C22×C4×C11—24no—
166C22×C4×C11—22no—
167C22×C4×C11—24no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—24no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—24no—
175C22×C4×C11—41no—
176C22×C4×C11—416no—
177C22×C4×C11—44no—
178C22×C4×C11—42no—
179C22×C4×C11—42no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11C2×D412yes—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D414yes—
186C22×C4×C11C2×D414yescomplemented
187C11×C4⋊C4—28no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—28no—
191C11×C4⋊C4—48no—
192C11×C22⋊C4—24no—
193C11×C22⋊C4—28no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—24no—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—28no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—24no—
204C11×C22⋊C4—24no—
205C11×C22⋊C4—48no—
206C11×C22⋊C4—48no—
207C11×C22⋊C4C2×D414yescomplemented
208C42×C11—22no—
209#3484C2×C1111yescharacteristic
210C22×#123C2×C1111yescharacteristic, complemented
211C2×#458C2×C1112yescomplemented
212#2849C2×C1112yescomplemented
213#2022C2×C1114yescomplemented
214#1898C2×C1112yescomplemented
215#1890C2×C1112yescomplemented
216#1781C2×C1111yescharacteristic, complemented
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—24no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—28no—
224C23×C11—28no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—22no—
229C23×C11—21no—
230C23×C11—24no—
231C23×C11—44no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—44no—
235C23×C11—48no—
236C23×C11—48no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—48no—
240C23×C11—42no—
241C23×C11—44no—
242C23×C11—44no—
243C23×C11—82no—
244C23×C11—84no—
245C23×C11—82no—
246C23×C11#12012yes—
247C23×C11#12012yes—
248C23×C11#12012yes—
249C23×C11C22×D411yescharacteristic
250C23×C11C22×D412yes—
251C23×C11C22×D412yes—
252C23×C11H(5,𝔽2)12yes—
253Q8×C11—42no—
254D4×C11—28no—
255D4×C11—44no—
256D4×C11—42no—
257D4×C11—44no—
258D4×C11—44no—
259D4×C11—42no—
260D4×C11—42no—
261D4×C11—44no—
262D4×C11—44no—
263D4×C11—48no—
264D4×C11—84no—
265D4×C11—84no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—21no—
271C2×C4×C11—24no—
272C2×C4×C11—22no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—28no—
276C2×C4×C11—24no—
277C2×C4×C11—44no—
278C2×C4×C11—44no—
279C2×C4×C11—48no—
280C2×C4×C11—44no—
281C2×C4×C11—48no—
282C2×C4×C11—48no—
283C2×C4×C11—42no—
284C2×C4×C11—42no—
285C2×C4×C11—42no—
286C2×C4×C11—44no—
287C2×C4×C11—44no—
288C2×C4×C11—48no—
289C2×C4×C11—44no—
290C2×C4×C11—82no—
291C2×C4×C11#12012yes—
292C2×H(5,𝔽2)C22×C1111yescharacteristic
293C23×D4C22×C1111yescharacteristic
294C24×C4C22×C1111yescharacteristic, complemented
295#546—24no—
296D42—24no—
297#535—21no—
298#534—21no—
299#534C22×C1112yes—
300#525—21no—
301C2×#123—21no—
302C2×#123—21no—
303C2×#123—28no—
304C2×#123C22×C1112yes—
305C2×#123C22×C1112yescomplemented
306C2×#123C22×C1114yescomplemented
307C2×#120—21no—
308C2×#120C22×C1112yes—
309#518C22×C1111yescharacteristic
310C22×C4⋊C4—21no—
311C22×C22⋊C4—21no—
312C22×C22⋊C4C22×C1111yescharacteristic, complemented
313#458—28no—
314C2×#99C22×C1112yes—
315C2×#99C22×C1114yescomplemented
316C2×#99C22×C1112yescomplemented
317#386—24no—
318#385—24no—
319#381C22×C1114yescomplemented
320#379C22×C1112yescomplemented
321#342C22×C1114yescomplemented
322C22×C11—24no—
323C22×C11—24no—
324C22×C11—22no—
325C22×C11—24no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—22no—
330C22×C11—24no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—416no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—41no—
341C22×C11—44no—
342C22×C11—42no—
343C22×C11—81no—
344C22×C11—88no—
345C22×C11—84no—
346C22×C11—81no—
347C22×C11—162no—
348C22×C11#45814yescomplemented
349C22×C11C2×#12011yescharacteristic
350C22×C11C2×#12011yescharacteristic
351C22×C11#53411yescharacteristic
352C22×C11D4214yes—
353C4×C11—22no—
354C4×C11—44no—
355C4×C11—44no—
356C4×C11—41no—
357C4×C11—42no—
358C4×C11—44no—
359C4×C11—84no—
360C25D4×C1111yescharacteristic
361C25C23×C1111yescharacteristic
362H(5,𝔽2)—24no—
363H(5,𝔽2)—42no—
364C2×#41—21no—
365C2×#41—22no—
366C22×D4—21no—
367C22×D4—22no—
368C22×D4—24no—
369C22×D4—22no—
370C22×D4—24no—
371C22×D4—42no—
372C22×D4D4×C1111yescharacteristic
373C22×D4D4×C1111yescharacteristic
374C22×D4D4×C1114yes—
375C22×D4C23×C1112yes—
376C22×D4C23×C1111yescharacteristic
377C22×D4C23×C1111yescharacteristic
378C23×C4—21no—
379C23×C4—21no—
380C23×C4—21no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—42no—
384C23×C4D4×C1111yescharacteristic
385C23×C4C23×C1112yes—
386#127—22no—
387#124—22no—
388#123—28no—
389#123—28no—
390#123—22no—
391#123—24no—
392#123—22no—
393#123—22no—
394#123—24no—
395#123—24no—
396#123—28no—
397#123—44no—
398#123D4×C1118yescomplemented
399C22⋊Q8—22no—
400#121—22no—
401#121—24no—
402#121—24no—
403#121—24no—
404#120—24no—
405#120—22no—
406#120—22no—
407#120—22no—
408#120—22no—
409#120—24no—
410#120—22no—
411C4×D4—24no—
412C4×D4—24no—
413#117—21no—
414C2×C4⋊C4—28no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—24no—
418C2×C22⋊C4—28no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—24no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4D4×C1114yes—
428C2×C22⋊C4C23×C1114yes—
429C2×C22⋊C4C23×C1112yes—
430C2×C22⋊C4C23×C1112yes—
431#99—24no—
432#99—28no—
433#99—42no—
434#95—28no—
435C2×C11—21no—
436C2×C11—24no—
437C2×C11—21no—
438C2×C11—24no—
439C2×C11—42no—
440C2×C11—42no—
441C2×C11—81no—
442C2×C11—82no—
443C2×C11#240311yescharacteristic
444C2×C11C2×#45812yes—
445C24—22no—
446C24—22no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24—44no—
451C24—41no—
452C24—44no—
453C24C2×D4×C1111yescharacteristic
454C24C2×D4×C1114yes—
455C24C2×D4×C1111yescharacteristic
456C24C2×D4×C1112yes—
457C24C2×D4×C1111yescharacteristic
458C24C2×D4×C1111yescharacteristic
459C24C24×C1111yescharacteristic
460#41—48no—
461#41—42no—
462#41—42no—
463C2×Q8—21no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—24no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—24no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—24no—
479C2×D4—24no—
480C2×D4—24no—
481C2×D4—22no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—416no—
485C2×D4—48no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—48no—
489C2×D4—84no—
490C2×D4C2×D4×C1114yes—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—41no—
506C22×C4—416no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—44no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4C2×D4×C1112yes—
513C22×C4C2×D4×C1111yescharacteristic
514C22×C4C2×D4×C1111yescharacteristic
515C22×C4C2×D4×C1114yes—
516C22×C4C2×D4×C1114yescomplemented
517C4⋊C4—28no—
518C4⋊C4—22no—
519C4⋊C4—24no—
520C4⋊C4—28no—
521C4⋊C4—48no—
522C22⋊C4—24no—
523C22⋊C4—28no—
524C22⋊C4—22no—
525C22⋊C4—24no—
526C22⋊C4—24no—
527C22⋊C4—28no—
528C22⋊C4—24no—
529C22⋊C4—24no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—24no—
534C22⋊C4—24no—
535C22⋊C4—48no—
536C22⋊C4—48no—
537C22⋊C4C2×D4×C1114yescomplemented
538C42—22no—
539C11#2390111yescharacteristic, direct product factor, Sylow
540C23—21no—
541C23—21no—
542C23—24no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—28no—
547C23—28no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—22no—
552C23—21no—
553C23—24no—
554C23—44no—
555C23—42no—
556C23—42no—
557C23—44no—
558C23—48no—
559C23—48no—
560C23—42no—
561C23—42no—
562C23—48no—
563C23—42no—
564C23—44no—
565C23—44no—
566C23—82no—
567C23—84no—
568C23—82no—
569C23C11×#12012yes—
570C23C11×#12012yes—
571C23C11×#12012yes—
572C23C22×D4×C1111yescharacteristic
573C23C22×D4×C1112yes—
574C23C22×D4×C1112yes—
575C23C11×H(5,𝔽2)12yes—
576Q8—42no—
577D4—28no—
578D4—44no—
579D4—42no—
580D4—44no—
581D4—44no—
582D4—42no—
583D4—42no—
584D4—44no—
585D4—44no—
586D4—48no—
587D4—84no—
588D4—84no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—28no—
599C2×C4—24no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—48no—
603C2×C4—44no—
604C2×C4—48no—
605C2×C4—48no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—48no—
612C2×C4—44no—
613C2×C4—82no—
614C2×C4C11×#12012yes—
615C22—24no—
616C22—24no—
617C22—22no—
618C22—24no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—24no—
624C22—42no—
625C22—42no—
626C22—416no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—41no—
634C22—44no—
635C22—42no—
636C22—81no—
637C22—88no—
638C22—81no—
639C22—84no—
640C22—162no—
641C22C11×#45814yescomplemented
642C22C2×C11×#12011yescharacteristic
643C22C2×C11×#12011yescharacteristic
644C22C11×#53411yescharacteristic
645C22D42×C1114yes—
646C4—22no—
647C4—44no—
648C4—44no—
649C4—41no—
650C4—42no—
651C4—44no—
652C4—84no—
653C2—21no—
654C2—24no—
655C2—21no—
656C2—24no—
657C2—42no—
658C2—42no—
659C2—81no—
660C2—82no—
661C2C11×#240311yescharacteristic
662C2C2×C11×#45812yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC24C24×C11
prime radicalC11×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#123C2semidirect
3. C2×C11×#458C2semidirect
4. C11×#2849C2semidirect
5. C11×#2022C2semidirect
6. C11×#1898C2semidirect
7. C11×#1890C2semidirect
8. C11×#1781C2semidirect
11. C24×C4×C11C22semidirect
22. C2×C11×#123C22semidirect
23. C2×C11×#123C22semidirect
29. C22×C11×C22⋊C4C22semidirect
32. C2×C11×#99C22semidirect
33. C2×C11×#99C22semidirect
36. C11×#381C22semidirect
37. C11×#379C22semidirect
38. C11×#342C22semidirect
77. C11×#123D4semidirect
114. #23901C11direct (N × H)
186. C22×C4×C11C2×D4semidirect
207. C11×C22⋊C4C2×D4semidirect
210. C22×#123C2×C11semidirect
211. C2×#458C2×C11semidirect
212. #2849C2×C11semidirect
213. #2022C2×C11semidirect
214. #1898C2×C11semidirect
215. #1890C2×C11semidirect
216. #1781C2×C11semidirect
294. C24×C4C22×C11semidirect
305. C2×#123C22×C11semidirect
306. C2×#123C22×C11semidirect
312. C22×C22⋊C4C22×C11semidirect
315. C2×#99C22×C11semidirect
316. C2×#99C22×C11semidirect
319. #381C22×C11semidirect
320. #379C22×C11semidirect
321. #342C22×C11semidirect
348. C22×C11#458semidirect
398. #123D4×C11semidirect
516. C22×C4C2×D4×C11semidirect
537. C22⋊C4C2×D4×C11semidirect
539. C11#23901direct (N × H)
641. C22C11×#458semidirect

Maximal subgroups

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

subgroupindex
C11×#34842
C22×C11×#1232
C2×C11×#4582
C11×#28492
C11×#20222
C11×#18982
C11×#18902
C11×#17812
#2390111