Finite Group Databasebeta

← #14786404

Subgroups — #14786404

Order 2816.

1844 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66991C211yesmaximal, characteristic
2C2×#10622387C212yesmaximal, complemented
3D11×#380C211yesmaximal, characteristic, complemented
4#13069797C212yesmaximal, complemented
5#13069796C212yesmaximal, complemented
6#13068930C212yesmaximal, complemented
7#13068806C211yesmaximal, characteristic, complemented
8#13068803C211yesmaximal, characteristic, complemented
9#13068547C211yesmaximal, characteristic, complemented
10#13068525C211yesmaximal, characteristic, complemented
11C11×#1786C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C23×C22⋊D11—21no—
14C23×C4×D11C2211yescharacteristic
15C22×C22⋊Dic11—21no—
16C2×#66991—21no—
17C2×#66991—21no—
18C2×#66991—28no—
19C2×#66991C2212yes—
20C2×#66991C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic, complemented
23C2×C4⋊C4×D11C2211yescharacteristic, complemented
24C2×C22⋊C4×D11—21no—
25C2×C11×#102C2212yescomplemented
26C2×C11×#102C2212yescomplemented
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#380C2211yescharacteristic
29C2×#66896C2212yescomplemented
30C2×#66896C2212yescomplemented
31#10622825C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×(C2×D11)⋊C8C2212yescomplemented
34C2×(C2×D11)⋊C8C2212yescomplemented
35C2×#66882C2212yescomplemented
36#10622600C2211yescharacteristic, complemented
37#10622600C2211yescharacteristic, complemented
38C2×#66871C2212yescomplemented
39#10622555—21no—
40#10622387—28no—
41#10622280—21no—
42D11×#95—21no—
43#10622189C2212yescomplemented
44#10622167C2212yescomplemented
45C25×C11—21no—
46C24×D11D411yescharacteristic
47C22×D4×C11—24no—
48C22×D4×C11—21no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—42no—
52C22×D4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11—28no—
55C22×C22⋊D11—22no—
56C22×C22⋊D11—22no—
57C22×C22⋊D11—44no—
58C22×C22⋊D11—44no—
59C23×Dic11—21no—
60C23×Dic11D411yescharacteristic
61C22×C4×D11—22no—
62C22×C4×D11—22no—
63C22×C4×D11—24no—
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C4×D11—42no—
67C22×C4×D11D411yescharacteristic
68C22×C4×D11D411yescharacteristic
69C22×C4×D11C2311yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×C8×C11C2312yes—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C22⋊Dic11—28no—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11—22no—
78C2×C22⋊Dic11—21no—
79#66991—28no—
80#66991—28no—
81#66991—24no—
82#66991—24no—
83#66991—24no—
84#66991D418yes—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—24no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2312yes—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C22×C11⋊C8C2312yes—
95C4⋊C4×D11—24no—
96C4⋊C4×D11—42no—
97C22⋊C4×D11—44no—
98C11×#102—24no—
99C11×#102—42no—
100C11×C22⋊C8—22no—
101C11×#95—21no—
102#66896—24no—
103#66896—42no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C22⋊(C11⋊C8)—22no—
108(C2×D11)⋊C8—24no—
109(C2×D11)⋊C8—42no—
110#66882—24no—
111#66871—24no—
112#24002—111nomaximal, Sylow
113C24×C11—24no—
114C24×C11—22no—
115C24×C11—42no—
116C24×C11—42no—
117C24×C11—42no—
118C24×C11—42no—
119C24×C11—42no—
120C24×C11—42no—
121C24×C11C2×D411yescharacteristic
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11—41no—
127C23×D11—41no—
128C23×D11D814yes—
129C23×D11C2×D411yescharacteristic
130C23×D11C2×D411yescharacteristic
131C2×D4×C11—24no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—48no—
138C2×D4×C11—48no—
139C2×D4×C11—42no—
140C2×D4×C11—42no—
141C2×D4×C11C2×D414yes—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4112yes—
148C22×C4×C11#4112yes—
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11—28no—
151C2×C22⋊D11—28no—
152C2×C22⋊D11—44no—
153C2×C22⋊D11—432no—
154C2×C22⋊D11—44no—
155C2×C22⋊D11—44no—
156C2×C22⋊D11—44no—
157C22×Dic11—24no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—41no—
164C22×Dic11—42no—
165C22×Dic11—42no—
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C2×C4×D11—22no—
169C2×C4×D11—22no—
170C2×C4×D11—22no—
171C2×C4×D11—22no—
172C2×C4×D11—22no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C4×D11—21no—
176C2×C4×D11—21no—
177C2×C4×D11—22no—
178C2×C4×D11—22no—
179C2×C4×D11—41no—
180C2×C4×D11—41no—
181C2×C4×D11—48no—
182C2×C4×D11—48no—
183C2×C4×D11—42no—
184C2×C4×D11—42no—
185C2×C4×D11—42no—
186C2×C4×D11—42no—
187C2×C4×D11—42no—
188C2×C4×D11—42no—
189C2×C4×D11C2×D414yes—
190C2×C8×C11—22no—
191C2×C8×C11—22no—
192C2×C8×C11—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—22no—
195C11×C22⋊C4—42no—
196C22⋊Dic11—28no—
197C22⋊Dic11—28no—
198C22⋊Dic11—42no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—42no—
201C4⋊Dic11—24no—
202C4⋊Dic11—22no—
203C4⋊Dic11—22no—
204C4⋊Dic11—22no—
205C4⋊Dic11C2×D414yes—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8—22no—
210C2×C11⋊C8—22no—
211C22×#121—111no—
212C2×#480—112no—
213C2×#380—111no—
214#2033—112no—
215#2033—112no—
216#1874—112no—
217#1852—111no—
218#1852—111no—
219#1786—111no—
220#1786D1111yescharacteristic, complemented
221#1779—111no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—24no—
227C23×C11—48no—
228C23×C11—48no—
229C23×C11—48no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—84no—
237C23×C11—84no—
238C23×C11—84no—
239C23×C11—84no—
240C23×C11#12312yes—
241C23×C11C2×D812yes—
242C23×C11#13712yes—
243C23×C11C22×D411yescharacteristic
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—21no—
252C22×D11—21no—
253C22×D11—21no—
254C22×D11—28no—
255C22×D11—28no—
256C22×D11—44no—
257C22×D11—44no—
258C22×D11—44no—
259C22×D11—44no—
260C22×D11—44no—
261C22×D11#12012yes—
262C22×D11C2×D812yes—
263C22×D11C2×D812yes—
264C22×D11AGL(1,ℤ/8)12yes—
265D4×C11—24no—
266D4×C11—24no—
267D4×C11—48no—
268D4×C11—42no—
269D4×C11—42no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—24no—
273C2×C4×C11—24no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11#12312yes—
281C2×C4×C11C22×D412yes—
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11H(5,𝔽2)12yes—
285C22⋊D11—416no—
286C22⋊D11—416no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—24no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—44no—
294C2×Dic11—48no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11#12012yes—
304C4×D11—24no—
305C4×D11—24no—
306C4×D11—44no—
307C4×D11—44no—
308C4×D11—42no—
309C4×D11—42no—
310C4×D11—84no—
311C4×D11—84no—
312C8×C11—42no—
313C11⋊C8—42no—
314C23×D4—221no—
315C23×D4C2×D1111yescharacteristic
316C24×C4—111no—
317C2×#121—112no—
318C2×#121—112no—
319C2×#121—228no—
320C2×#121—221no—
321C2×#121—221no—
322C22×C4⋊C4—111no—
323C22×C4⋊C4—111no—
324C22×C4⋊C4—111no—
325C22×C22⋊C4—221no—
326C22×C22⋊C4—221no—
327#480—228no—
328C2×#107—112no—
329C2×#107—112no—
330C2×#102—112no—
331C2×#102—112no—
332C2×#102C2×D1112yescomplemented
333C2×#102C2×D1112yescomplemented
334C2×C22⋊C8—111no—
335C2×C22⋊C8—112no—
336C2×C22⋊C8—112no—
337C2×C22⋊C8C2×D1111yescharacteristic
338#380—111no—
339#380—111no—
340#380—111no—
341#380—221no—
342#380—221no—
343#380C2×D1111yescharacteristic
344C2×#95—221no—
345#340—112no—
346#340—112no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—44no—
354C22×C11—44no—
355C22×C11—44no—
356C22×C11—816no—
357C22×C11—82no—
358C22×C11—82no—
359C22×C11—82no—
360C22×C11—82no—
361C22×C11#48014yescomplemented
362C22×C11C2×#12011yescharacteristic
363C22×C11C2×#12311yescharacteristic
364C22×C11#53411yescharacteristic
365C22×C11C22×D811yescharacteristic
366C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C11C2×#13711yescharacteristic
368C22×C11#57511yescharacteristic
369C2×D11—22no—
370C2×D11—22no—
371C2×D11—22no—
372C2×D11—22no—
373C2×D11—22no—
374C2×D11—22no—
375C2×D11—22no—
376C2×D11—22no—
377C2×D11—22no—
378C2×D11—416no—
379C2×D11—41no—
380C2×D11—41no—
381C2×D11—41no—
382C2×D11—41no—
383C2×D11#44714yes—
384C4×C11—22no—
385C4×C11—81no—
386C4×C11—81no—
387C4×C11#54612yes—
388C4×C11#54612yes—
389Dic11—22no—
390Dic11—41no—
391Dic11—44no—
392Dic11—81no—
393Dic11—81no—
394C25—21no—
395C25—111no—
396C22×D4—24no—
397C22×D4—22no—
398C22×D4—21no—
399C22×D4—22no—
400C22×D4—42no—
401C22×D4—222no—
402C22×D4—222no—
403C22×D4—228no—
404C22×D4—444no—
405C22×D4—444no—
406C22×D4C22×D1112yes—
407C23×C4—111no—
408C23×C4—111no—
409C23×C4—111no—
410C23×C4—111no—
411C23×C4—111no—
412C23×C4—224no—
413C23×C4—221no—
414C23×C4—221no—
415C23×C4—221no—
416C23×C4—222no—
417C23×C4—222no—
418C23×C4—442no—
419C23×C4C22×D1111yescharacteristic
420C22×C8—112no—
421C22×C8C22×D1112yes—
422#121—118no—
423#121—224no—
424#121—224no—
425#121—228no—
426#121—228no—
427#121—224no—
428C2×C4⋊C4—112no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—224no—
432C2×C4⋊C4—224no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—442no—
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—222no—
441C2×C22⋊C4—222no—
442C2×C22⋊C4—228no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—444no—
447#107—224no—
448#107—224no—
449#102—24no—
450#102—42no—
451#102—224no—
452#102—442no—
453C22⋊C8—22no—
454C22⋊C8—224no—
455C22⋊C8—222no—
456C22⋊C8—442no—
457#95—21no—
458#95—221no—
459#95—221no—
460#95—221no—
461C2×C11—24no—
462C2×C11—84no—
463C2×C11#240511yescharacteristic
464C2×C11C2×#44711yescharacteristic
465C2×C11#300711yescharacteristic
466C2×C11C2×#48011yescharacteristic
467C2×C11#309411yescharacteristic
468C2×C11#318611yescharacteristic
469C2×C11#319311yescharacteristic
470D11—24no—
471D11—42no—
472C24—24no—
473C24—22no—
474C24—42no—
475C24—42no—
476C24—42no—
477C24—42no—
478C24—42no—
479C24—42no—
480C24—111no—
481C24—111no—
482C24—114no—
483C24—222no—
484C24—222no—
485C24—222no—
486C24—222no—
487C24—441no—
488C24—441no—
489C24D4×D1111yescharacteristic
490C2×D4—24no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—228no—
501C2×D4—228no—
502C2×D4—444no—
503C2×D4—444no—
504C2×D4—444no—
505C2×D4—4432no—
506C2×D4—444no—
507C2×D4D4×D1114yes—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—111no—
513C22×C4—114no—
514C22×C4—111no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—222no—
521C22×C4—224no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—221no—
527C22×C4—222no—
528C22×C4—221no—
529C22×C4—222no—
530C22×C4—221no—
531C22×C4—221no—
532C22×C4—441no—
533C22×C4—441no—
534C22×C4—448no—
535C22×C4—448no—
536C22×C4—442no—
537C22×C4—442no—
538C22×C4—442no—
539C22×C4—442no—
540C22×C4—442no—
541C22×C4—442no—
542C22×C4—441no—
543C22×C4—442no—
544C22×C4—442no—
545C22×C4#433912yes—
546C22×C4D4×D1111yescharacteristic
547C22×C4#434112yes—
548C22×C4C23×D1111yescharacteristic
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—222no—
553C2×C8—222no—
554C2×C8—222no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—114no—
558C4⋊C4—224no—
559C4⋊C4—222no—
560C4⋊C4—222no—
561C4⋊C4—222no—
562C4⋊C4—442no—
563C4⋊C4—442no—
564C22⋊C4—42no—
565C22⋊C4—228no—
566C22⋊C4—228no—
567C22⋊C4—442no—
568C22⋊C4—442no—
569C22⋊C4—442no—
570C11#2400211yescharacteristic, complemented, Sylow
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—24no—
576C23—48no—
577C23—48no—
578C23—48no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—84no—
586C23—84no—
587C23—84no—
588C23—84no—
589C23—112no—
590C23—112no—
591C23—112no—
592C23—112no—
593C23—228no—
594C23—221no—
595C23—221no—
596C23—221no—
597C23—221no—
598C23—221no—
599C23—221no—
600C23—221no—
601C23—221no—
602C23—221no—
603C23—221no—
604C23—228no—
605C23—444no—
606C23—444no—
607C23—444no—
608C23—444no—
609C23—444no—
610C23#6693612yes—
611C23D8×D1112yes—
612C23#6696812yes—
613C23C2×D4×D1111yescharacteristic
614D4—24no—
615D4—24no—
616D4—48no—
617D4—42no—
618D4—42no—
619D4—4416no—
620D4—4416no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—112no—
632C2×C4—221no—
633C2×C4—221no—
634C2×C4—224no—
635C2×C4—224no—
636C2×C4—221no—
637C2×C4—221no—
638C2×C4—224no—
639C2×C4—221no—
640C2×C4—444no—
641C2×C4—444no—
642C2×C4—444no—
643C2×C4—448no—
644C2×C4—442no—
645C2×C4—442no—
646C2×C4—442no—
647C2×C4—442no—
648C2×C4—441no—
649C2×C4—441no—
650C2×C4—441no—
651C2×C4—441no—
652C2×C4—441no—
653C2×C4—441no—
654C2×C4—884no—
655C2×C4—884no—
656C2×C4#6693612yes—
657C2×C4C2×#433911yescharacteristic
658C2×C4C2×D4×D1112yes—
659C2×C4C2×#434111yescharacteristic
660C2×C4#6703712yes—
661C8—42no—
662C8—442no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—44no—
670C22—44no—
671C22—44no—
672C22—816no—
673C22—82no—
674C22—82no—
675C22—82no—
676C22—82no—
677C22—114no—
678C22—222no—
679C22—222no—
680C22—222no—
681C22—222no—
682C22—222no—
683C22—222no—
684C22—222no—
685C22—222no—
686C22—222no—
687C22—4416no—
688C22—441no—
689C22—441no—
690C22—441no—
691C22—441no—
692C22#1062238714yescomplemented
693C22C2×#6693611yescharacteristic
694C22D11×#12011yescharacteristic
695C22#1062312011yescharacteristic
696C22C2×D8×D1111yescharacteristic
697C22C2×#6696811yescharacteristic
698C22D11×AGL(1,ℤ/8)11yescharacteristic
699C22#1062330411yescharacteristic
700C4—22no—
701C4—81no—
702C4—81no—
703C4—222no—
704C4—444no—
705C4—441no—
706C4—881no—
707C4—881no—
708C4#1062302112yes—
709C4#1062312212yes—
710C2—24no—
711C2—84no—
712C2—224no—
713C2—442no—
714C2#1307194111yescharacteristic
715C2D11×#44711yescharacteristic
716C2#1307787111yescharacteristic
717C2C2×#1062238711yescharacteristic
718C2#1307855411yescharacteristic
719C2#1307936511yescharacteristic
720C2#1307941911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1786C2
socleC23×C11C22×D4
prime radicalC22×#66991C2
hypercenter#1786D11
hypocenterC11#24002
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. C2×#10622387C2semidirect
3. D11×#380C2semidirect
4. #13069797C2semidirect
5. #13069796C2semidirect
6. #13068930C2semidirect
7. #13068806C2semidirect
8. #13068803C2semidirect
9. #13068547C2semidirect
10. #13068525C2semidirect
11. C11×#1786C2semidirect
22. C2×C4⋊C4×D11C22semidirect
23. C2×C4⋊C4×D11C22semidirect
25. C2×C11×#102C22semidirect
26. C2×C11×#102C22semidirect
29. C2×#66896C22semidirect
30. C2×#66896C22semidirect
33. C2×(C2×D11)⋊C8C22semidirect
34. C2×(C2×D11)⋊C8C22semidirect
35. C2×#66882C22semidirect
36. #10622600C22semidirect
37. #10622600C22semidirect
38. C2×#66871C22semidirect
43. #10622189C22semidirect
44. #10622167C22semidirect
220. #1786D11semidirect
332. C2×#102C2×D11semidirect
333. C2×#102C2×D11semidirect
361. C22×C11#480semidirect
570. C11#24002semidirect
692. C22#10622387semidirect

Maximal subgroups

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

subgroupindex
C22×#669912
C2×#106223872
D11×#3802
#130697972
#130697962
#130689302
#130688062
#130688032
#130685472
#130685252
C11×#17862
#2400211