Finite Group Databasebeta

← #14788869

Subgroups — #14788869

Order 2816.

1642 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622670C212yesmaximal, complemented
2C2×#10622840C211yesmaximal, characteristic, complemented
3C2×#10622830C211yesmaximal, characteristic
4C4×#66983C211yesmaximal, characteristic, complemented
5#13069852C212yesmaximal, complemented
6#13069693C212yesmaximal, complemented
7#13069549C212yesmaximal, complemented
8#13068596C211yesmaximal, characteristic, complemented
9#13068551C211yesmaximal, characteristic, complemented
10#13068547C211yesmaximal, characteristic, complemented
11C22×C11×#124C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C2×C11×#124—28no—
15C2×C11×#124—21no—
16C2×C11×#124—21no—
17C2×C11×#124C2212yes—
18C2×C11×#124C2212yes—
19C22×C11×C22⋊C4—21no—
20C22×C11×C22⋊C4—21no—
21C22×C42×C11C2211yescharacteristic
22C22×#4325C2212yescomplemented
23C22×#4323C2212yes—
24C2×#66983C2211yescharacteristic
25C2×C4×C22⋊D11—21no—
26C2×C4×D44C2211yescharacteristic, complemented
27#10622840—24no—
28C2×#66899C2212yescomplemented
29C2×#66899C2212yescomplemented
30C2×#66899C2212yescomplemented
31#10622830—24no—
32C2×#66896C2212yes—
33C2×#66896C2212yes—
34C2×#66896C2212yes—
35#10622826—21no—
36#10622825C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39#10622670—28no—
40#10622553—21no—
41#10622552C2211yescharacteristic, complemented
42C4×(C2×D11)⋊C4—21no—
43C4×C4⋊Dic11C2211yescharacteristic, complemented
44#10622541C2211yescharacteristic, complemented
45C2×C4⋊(C11⋊C8)C2212yescomplemented
46#10622162C2212yescomplemented
47C25×C11—21no—
48C22×Q8×C11—24no—
49C22×Q8×C11—21no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11—42no—
53C22×Q8×C11C2312yes—
54C22×D4×C11—24no—
55C22×D4×C11—21no—
56C22×D4×C11—22no—
57C22×D4×C11—22no—
58C22×D4×C11—42no—
59C22×D4×C11C2312yes—
60C23×C4×C11—21no—
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D411yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C11×#124—28no—
68C11×#124—28no—
69C11×#124—24no—
70C11×#124—24no—
71C11×#124—24no—
72C11×#124D418yescomplemented
73C2×C11×C22⋊C4—28no—
74C2×C11×C22⋊C4—28no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C42×C11—24no—
80C2×C42×C11D411yescharacteristic
81C2×C42×C11D411yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85C2×#4325—24no—
86C2×#4325—24no—
87C2×#4325—42no—
88C2×#4323—24no—
89C2×#4323—24no—
90C2×#4323—42no—
91#66983—22no—
92#66983D414yes—
93C4×C22⋊D11—44no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C22×C11⋊C8C2312yes—
104C22×C11⋊C8C2312yes—
105C4×D44—24no—
106#66899—24no—
107#66899—24no—
108#66899—42no—
109#66896—24no—
110#66896—24no—
111#66896—42no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C22⋊(C11⋊C8)—22no—
116C22⋊(C11⋊C8)—22no—
117C4⋊(C11⋊C8)—24no—
118#24215—111nomaximal, Sylow
119C24×C11—24no—
120C24×C11—22no—
121C24×C11—42no—
122C24×C11—42no—
123C24×C11—42no—
124C24×C11—42no—
125C24×C11—42no—
126C24×C11—42no—
127C24×C11C2×D411yescharacteristic
128C23×D11—21no—
129C2×Q8×C11—24no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11—48no—
136C2×Q8×C11—48no—
137C2×Q8×C11—42no—
138C2×Q8×C11—42no—
139C2×Q8×C11C2×D414yes—
140C2×D4×C11—24no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—48no—
147C2×D4×C11—48no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11C2×D414yes—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—24no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—41no—
160C22×C4×C11—41no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D412yes—
169C22×C4×C11#4112yes—
170C22×C4×C11C2411yescharacteristic
171C2×C22⋊D11—24no—
172C2×C22⋊D11—42no—
173C2×C22⋊D11—42no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C2×D44—22no—
178C2×D44—21no—
179C2×D44—22no—
180C2×D44C2×D412yes—
181C2×C4×D11—42no—
182C2×C4×D11—42no—
183C2×C4×D11—42no—
184C11×C22⋊C4—28no—
185C11×C22⋊C4—28no—
186C11×C22⋊C4—28no—
187C11×C22⋊C4—28no—
188C42×C11—22no—
189C42×C11—22no—
190C42×C11—22no—
191C42×C11C2×D414yes—
192C22⋊Dic11—42no—
193#4325—48no—
194#4323—48no—
195(C2×D11)⋊C4—24no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199C4⋊Dic11—22no—
200C4⋊Dic11—21no—
201C4⋊Dic11—22no—
202C4⋊Dic11C2×D412yes—
203Dic11⋊C4—42no—
204C4×Dic11—42no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—22no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8—22no—
210C2×C11⋊C8—22no—
211C22×#124D1111yescharacteristic, complemented
212C2×#463—112no—
213C2×#448—111no—
214C2×#447—111no—
215C4×#121—111no—
216#2042—112no—
217#2012—112no—
218#1983—112no—
219#1797—111no—
220#1787—111no—
221#1786—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#12112yes—
241C23×C11#13512yes—
242C23×C11AGL(1,ℤ/8)12yes—
243C23×C11C22×D411yescharacteristic
244C22×D11—22no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251Q8×C11—24no—
252Q8×C11—24no—
253Q8×C11—48no—
254Q8×C11—42no—
255Q8×C11—42no—
256D4×C11—24no—
257D4×C11—24no—
258D4×C11—48no—
259D4×C11—42no—
260D4×C11—42no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—24no—
268C2×C4×C11—24no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—24no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—44no—
277C2×C4×C11—44no—
278C2×C4×C11—48no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11#12012yes—
282C2×C4×C11#12012yes—
283C2×C4×C11#12112yes—
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C22×D412yes—
286C2×C4×C11C2×#4111yescharacteristic
287C2×C4×C11H(5,𝔽2)12yes—
288C22⋊D11—48no—
289C2×Dic11—22no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298D44—24no—
299D44—42no—
300C4×D11—84no—
301C11⋊C8—42no—
302C11⋊C8—42no—
303C23×Q8C2×D1111yescharacteristic
304C23×D4C2×D1111yescharacteristic
305C22×SD16—112no—
306C22×D8—112no—
307C2×#124—28no—
308C2×#124—21no—
309C2×#124—21no—
310C2×#124C2×D1112yes—
311C2×#124C2×D1112yes—
312C2×#121—111no—
313C2×C4×D4—111no—
314C2×C4×D4—221no—
315C22×C22⋊C4—21no—
316C22×C22⋊C4—21no—
317C22×C42C2×D1111yescharacteristic
318#463—228no—
319#448—224no—
320#447—224no—
321C2×C4⋊C8—112no—
322C2×#103—112no—
323C2×#103—112no—
324C2×#103—112no—
325C2×#102—112no—
326C2×#102—112no—
327C2×#102—112no—
328C2×C22⋊C8—111no—
329C2×C22⋊C8—111no—
330#390—111no—
331#389—111no—
332#388—221no—
333#386—221no—
334#380—111no—
335C4×C4⋊C4—111no—
336C4×C22⋊C4—221no—
337#336—112no—
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—44no—
345C22×C11—44no—
346C22×C11—44no—
347C22×C11—816no—
348C22×C11—82no—
349C22×C11—82no—
350C22×C11—82no—
351C22×C11—82no—
352C22×C11#46314yescomplemented
353C22×C11C2×#12011yescharacteristic
354C22×C11C2×#12111yescharacteristic
355C22×C11#53511yescharacteristic
356C22×C11C2×#13511yescharacteristic
357C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
358C22×C11#57511yescharacteristic
359C22×C11#57511yescharacteristic
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—42no—
363C2×D11—81no—
364C2×D11—81no—
365C2×D11—81no—
366C2×D11—81no—
367C4×C11—22no—
368C4×C11—22no—
369C4×C11—22no—
370C4×C11—44no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11D4212yes—
374C4×C11#54612yes—
375Dic11—42no—
376Dic11—81no—
377Dic11—81no—
378C25—21no—
379C22×Q8—24no—
380C22×Q8—21no—
381C22×Q8—22no—
382C22×Q8—22no—
383C22×Q8—42no—
384C22×Q8C22×D1112yes—
385C22×D4—24no—
386C22×D4—22no—
387C22×D4—22no—
388C22×D4—21no—
389C22×D4—42no—
390C22×D4—111no—
391C22×D4—221no—
392C22×D4C22×D1112yes—
393C23×C4—21no—
394C23×C4—221no—
395C23×C4C22⋊D1111yescharacteristic
396C23×C4C22⋊D1111yescharacteristic
397C23×C4C22×D1111yescharacteristic
398C2×SD16—224no—
399C2×SD16—224no—
400C2×SD16—442no—
401C2×D8—224no—
402C2×D8—224no—
403C2×D8—442no—
404C22×C8—112no—
405C22×C8—112no—
406#124—28no—
407#124—28no—
408#124—24no—
409#124—24no—
410#124—24no—
411#124C22⋊D1118yescomplemented
412#121—114no—
413#121—222no—
414C4×D4—224no—
415C4×D4—444no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—221no—
420C2×C22⋊C4—28no—
421C2×C22⋊C4—28no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C42—24no—
432C2×C42—221no—
433C2×C42C22⋊D1111yescharacteristic
434C2×C42C22⋊D1111yescharacteristic
435C2×C42C22×D1111yescharacteristic
436C2×C42C22×D1111yescharacteristic
437C4⋊C8—224no—
438#103—224no—
439#103—224no—
440#103—442no—
441#102—224no—
442#102—224no—
443#102—442no—
444C22⋊C8—222no—
445C22⋊C8—222no—
446#95—221no—
447#95—221no—
448#95—221no—
449C2×C11—24no—
450C2×C11—84no—
451C2×C11#240811yescharacteristic
452C2×C11#300211yescharacteristic
453C2×C11#300611yescharacteristic
454C2×C11C2×#46311yescharacteristic
455C2×C11#304011yescharacteristic
456C2×C11#321111yescharacteristic
457C2×C11#321311yescharacteristic
458D11—82no—
459C24—24no—
460C24—22no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—221no—
468C24C2×C22⋊D1111yescharacteristic
469C2×Q8—24no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—48no—
476C2×Q8—48no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8C2×C22⋊D1114yes—
480C2×D4—24no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—112no—
491C2×D4—224no—
492C2×D4—221no—
493C2×D4—222no—
494C2×D4—222no—
495C2×D4—442no—
496C2×D4—442no—
497C2×D4C2×C22⋊D1114yes—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—442no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4D4×D1112yes—
517C22×C4#434112yes—
518C22×C4C2×C22⋊D1111yescharacteristic
519C22×C4C2×C22⋊D1111yescharacteristic
520C22×C4C2×C22⋊D1111yescharacteristic
521C22×C4C2×C22⋊D1111yescharacteristic
522C22×C4C2×C22⋊D1111yescharacteristic
523C22×C4C23×D1111yescharacteristic
524SD16—448no—
525D8—448no—
526C2×C8—222no—
527C2×C8—222no—
528C2×C8—222no—
529C2×C8—222no—
530C2×C8—222no—
531C2×C8—222no—
532C4⋊C4—112no—
533C4⋊C4—221no—
534C4⋊C4—222no—
535C4⋊C4—222no—
536C4⋊C4—442no—
537C22⋊C4—28no—
538C22⋊C4—28no—
539C22⋊C4—28no—
540C22⋊C4—28no—
541C22⋊C4—224no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C22⋊C4—442no—
545C22⋊C4—442no—
546C42—22no—
547C42—22no—
548C42—22no—
549C42—442no—
550C42C2×C22⋊D1114yes—
551C11#2421511yescharacteristic, complemented, Sylow
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—24no—
557C23—48no—
558C23—48no—
559C23—48no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—84no—
567C23—84no—
568C23—84no—
569C23—84no—
570C23—222no—
571C23—441no—
572C23—441no—
573C23—441no—
574C23—441no—
575C23—441no—
576C23—441no—
577C23#6699112yes—
578C23#6700212yes—
579C23#6700312yes—
580C23C22×C22⋊D1111yescharacteristic
581Q8—24no—
582Q8—24no—
583Q8—48no—
584Q8—42no—
585Q8—42no—
586D4—24no—
587D4—24no—
588D4—48no—
589D4—42no—
590D4—42no—
591D4—224no—
592D4—448no—
593D4—442no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—24no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—48no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—222no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—884no—
624C2×C4#6699112yes—
625C2×C4#6700612yes—
626C2×C4#6700612yes—
627C2×C4C2×D4×D1111yescharacteristic
628C2×C4C2×#434111yescharacteristic
629C2×C4#6703712yes—
630C2×C4C22×C22⋊D1112yes—
631C8—442no—
632C8—442no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—22no—
639C22—44no—
640C22—44no—
641C22—44no—
642C22—816no—
643C22—82no—
644C22—82no—
645C22—82no—
646C22—82no—
647C22—442no—
648C22—442no—
649C22—442no—
650C22—881no—
651C22—881no—
652C22—881no—
653C22—881no—
654C22#1062267014yescomplemented
655C22C2×#6699111yescharacteristic
656C22#1062333611yescharacteristic
657C22C2×#6700211yescharacteristic
658C22C2×#6700311yescharacteristic
659C22#1062335311yescharacteristic
660C22#1062335311yescharacteristic
661C22C2×#6700611yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—41no—
666C4—44no—
667C4—41no—
668C4—442no—
669C4—881no—
670C4—881no—
671C4D4×C22⋊D1112yes—
672C4#1062333712yes—
673C2—24no—
674C2—84no—
675C2—882no—
676C2#1307196611yescharacteristic
677C2#1307783411yescharacteristic
678C2#1307786811yescharacteristic
679C2C2×#1062267011yescharacteristic
680C2#1307810611yescharacteristic
681C2#1307958111yescharacteristic
682C2#1307960311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#124C2
socleC23×C11C22×D4
prime radicalC2×#10622830C2
hypercenterC22×#124D11
hypocenterC11#24215
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C2×#10622670C2semidirect
2. C2×#10622840C2semidirect
4. C4×#66983C2semidirect
5. #13069852C2semidirect
6. #13069693C2semidirect
7. #13069549C2semidirect
8. #13068596C2semidirect
9. #13068551C2semidirect
10. #13068547C2semidirect
11. C22×C11×#124C2semidirect
22. C22×#4325C22semidirect
26. C2×C4×D44C22semidirect
28. C2×#66899C22semidirect
29. C2×#66899C22semidirect
30. C2×#66899C22semidirect
41. #10622552C22semidirect
43. C4×C4⋊Dic11C22semidirect
44. #10622541C22semidirect
45. C2×C4⋊(C11⋊C8)C22semidirect
46. #10622162C22semidirect
72. C11×#124D4semidirect
211. C22×#124D11semidirect
352. C22×C11#463semidirect
411. #124C22⋊D11semidirect
551. C11#24215semidirect
654. C22#10622670semidirect

Maximal subgroups

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

subgroupindex
C2×#106226702
C2×#106228402
C2×#106228302
C4×#669832
#130698522
#130696932
#130695492
#130685962
#130685512
#130685472
C22×C11×#1242
#2421511