Finite Group Databasebeta

← #15620294

Subgroups — #15620294

Order 2816.

4810 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C212yesmaximal, complemented
2C2×#10623364C211yesmaximal, characteristic, complemented
3#13077931C218yesmaximal, complemented
4#13077920C218yesmaximal, complemented
5#13077876C214yesmaximal, complemented
6#13077868C214yesmaximal, complemented
7C2×#10622845C212yesmaximal, complemented
8#13077061C211yesmaximal, characteristic, complemented
9C2×C11×#585C211yesmaximal, characteristic, complemented
10C11×#585—216no—
11C2×C11×2−1+4—21no—
12C2×C11×2−1+4C2214yescomplemented
13C2×C11×H(5,𝔽2)—21no—
14C2×C11×H(5,𝔽2)—22no—
15C2×C11×H(5,𝔽2)C2214yescomplemented
16C22×C11×#41—24no—
17C22×C11×#41C2214yes—
18C22×C11×#41C2212yes—
19C22×C11×#41C2211yescharacteristic
20C22×#4339C2211yescharacteristic, complemented
21#10623364—24no—
22#10623364C2218yescomplemented
23C2×#67004C2214yescomplemented
24#10623353—216no—
25C2×#67003C2218yescomplemented
26C2×#67002C2214yescomplemented
27C2×#66999—21no—
28C2×#66995C2214yescomplemented
29C2×#66992—22no—
30C2×#66991—21no—
31C2×#66985C2214yescomplemented
32C2×#66983C2212yescomplemented
33C22×C4⋊Dic11C2211yescharacteristic, complemented
34C2×#66977C2212yescomplemented
35C22×#4318C2212yescomplemented
36#10622852C22116yescomplemented
37#10622851C22116yescomplemented
38#10622847C2218yescomplemented
39#10622845C2218yescomplemented
40#10622845C2218yescomplemented
41#10622841C2218yescomplemented
42#10622840C2218yescomplemented
43C2×#66899C2214yescomplemented
44#10622831C2218yescomplemented
45#10622830C2218yescomplemented
46C2×#66896C2214yescomplemented
47#10622820C2214yescomplemented
48C11×2−1+4—216no—
49C11×2−1+4—216no—
50C11×2−1+4—216no—
51C11×H(5,𝔽2)—216no—
52C11×H(5,𝔽2)—232no—
53C11×H(5,𝔽2)—216no—
54C11×H(5,𝔽2)—216no—
55C2×C11×#41—264no—
56C2×C11×#41—232no—
57C2×C11×#41—24no—
58C2×C11×#41—24no—
59C2×C11×#41—28no—
60C2×C11×#41—24no—
61C2×C11×#41—22no—
62C2×C11×#41—24no—
63C2×C11×#41—22no—
64C2×C11×#41—28no—
65C2×C11×#41—28no—
66C2×C11×#41D414yes—
67C2×C11×#41D4116yescomplemented
68C2×C11×#41C2318yes—
69C2×C11×#41C2314yes—
70C2×C11×#41C2314yes—
71C2×C11×#41C2314yes—
72C22×Q8×C11—24no—
73C22×Q8×C11D411yescharacteristic
74C22×Q8×C11C2314yes—
75C22×Q8×C11C2312yes—
76C22×D4×C11—24no—
77C22×D4×C11—22no—
78C22×D4×C11—24no—
79C22×D4×C11—28no—
80C22×D4×C11D411yescharacteristic
81C22×D4×C11D412yes—
82C22×D4×C11C2314yes—
83C22×D4×C11C2312yes—
84C23×C4×C11—24no—
85C23×C4×C11—22no—
86C23×C4×C11C2312yes—
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—21no—
89C22×C22⋊D11—22no—
90C23×Dic11—21no—
91C2×#4339—22no—
92C2×#4339—28no—
93C2×#4339C2314yes—
94C22×D44C2311yescharacteristic
95C22×C4×D11—21no—
96C22×Dic22C2311yescharacteristic
97C2×C22⋊Dic11—22no—
98#67004—216no—
99#67003—232no—
100#67002—216no—
101#66999—28no—
102C2×#4326C2318yes—
103#66995—216no—
104C2×#4325C2318yes—
105#66992—216no—
106#66991—28no—
107C2×#4324C2318yes—
108#66985—216no—
109C2×#4323C2318yes—
110#66983—24no—
111#66983C2318yes—
112C2×(C2×D11)⋊C4—22no—
113C2×C4⋊Dic11—21no—
114C2×C4⋊Dic11—22no—
115C2×C4⋊Dic11C2312yes—
116C2×C4⋊Dic11C2314yes—
117#66977—24no—
118#66977C2318yes—
119C2×Dic11⋊C4—22no—
120C2×#4318—28no—
121C2×#4318C2314yes—
122C2×#4318C2314yes—
123C22×C11⋊C8C2314yes—
124#66899C23116yes—
125#66896C23116yes—
126C22⋊(C11⋊C8)C2318yes—
127C22⋊(C11⋊C8)C2318yes—
128#60371—111nomaximal, Sylow
129C24×C11—24no—
130C24×C11—22no—
131C24×C11C2×D412yes—
132C24×C11C2×D411yescharacteristic
133C23×D11—21no—
134C11×#41—232no—
135C11×#41—264no—
136C11×#41—232no—
137C11×#41—232no—
138C11×#41—232no—
139C11×#41—216no—
140C11×#41—216no—
141C11×#41—216no—
142C11×#41—216no—
143C11×#41—216no—
144C11×#41—28no—
145C11×#41—28no—
146C11×#41—28no—
147C11×#41—28no—
148C11×#41C2×D4116yes—
149C11×#41C2×D4116yescomplemented
150C2×Q8×C11—232no—
151C2×Q8×C11—216no—
152C2×Q8×C11—24no—
153C2×Q8×C11—24no—
154C2×Q8×C11—22no—
155C2×Q8×C11—24no—
156C2×Q8×C11C2×D414yes—
157C2×Q8×C11C2×D418yescomplemented
158C2×Q8×C11C2414yes—
159C2×D4×C11—232no—
160C2×D4×C11—264no—
161C2×D4×C11—232no—
162C2×D4×C11—216no—
163C2×D4×C11—28no—
164C2×D4×C11—28no—
165C2×D4×C11—24no—
166C2×D4×C11—24no—
167C2×D4×C11—216no—
168C2×D4×C11—24no—
169C2×D4×C11—24no—
170C2×D4×C11—22no—
171C2×D4×C11—24no—
172C2×D4×C11C2×D414yes—
173C2×D4×C11C2×D418yes—
174C2×D4×C11C2×D418yescomplemented
175C2×D4×C11C2414yes—
176C22×C4×C11—232no—
177C22×C4×C11—24no—
178C22×C4×C11—22no—
179C22×C4×C11—216no—
180C22×C4×C11—24no—
181C22×C4×C11—28no—
182C22×C4×C11—24no—
183C22×C4×C11—28no—
184C22×C4×C11C2×D412yes—
185C22×C4×C11C2×D414yes—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D412yes—
188C22×C4×C11C2×D418yes—
189C22×C4×C11C2414yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2411yescharacteristic
192C2×C22⋊D11—24no—
193C2×C22⋊D11—28no—
194C2×C22⋊D11—44no—
195C2×C22⋊D11—84no—
196C22×Dic11—21no—
197C22×Dic11—22no—
198C22×Dic11—24no—
199C22×Dic11—82no—
200#4339—28no—
201#4339—28no—
202#4339—48no—
203C2×D44—21no—
204C2×D44—24no—
205C2×D44C2412yes—
206C2×C4×D11—24no—
207C2×C4×D11—44no—
208C2×Dic22—24no—
209C2×Dic22—21no—
210C2×Dic22C2412yes—
211C22⋊Dic11—28no—
212#4326—216no—
213#4325—216no—
214#4324—216no—
215#4323—216no—
216(C2×D11)⋊C4—28no—
217C4⋊Dic11—22no—
218C4⋊Dic11—24no—
219C4⋊Dic11C2414yes—
220Dic11⋊C4—28no—
221#4318—28no—
222#4318—28no—
223C2×C11⋊C8—28no—
224C2×C11⋊C8C2418yes—
225C2×#585D1111yescharacteristic, complemented
226C2×#575—112no—
227C2×#537—111no—
228#3013—118no—
229#3012—118no—
230#3007—114no—
231#3006—114no—
232C2×#417—112no—
233#2879—111no—
234C23×C11—216no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—28no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—82no—
243C23×C11—82no—
244C23×C11—84no—
245C23×C11—84no—
246C23×C11#12014yes—
247C23×C11C22×D414yes—
248C23×C11C22×D411yescharacteristic
249C23×C11C22×D412yes—
250C22×D11—22no—
251C22×D11—42no—
252C22×D11—42no—
253C22×D11—42no—
254Q8×C11—216no—
255Q8×C11—28no—
256Q8×C11—28no—
257Q8×C11—24no—
258Q8×C11C22×D418yes—
259D4×C11—232no—
260D4×C11—216no—
261D4×C11—216no—
262D4×C11—216no—
263D4×C11—216no—
264D4×C11—28no—
265D4×C11—28no—
266D4×C11—24no—
267D4×C11C22×D418yes—
268C2×C4×C11—216no—
269C2×C4×C11—232no—
270C2×C4×C11—28no—
271C2×C4×C11—24no—
272C2×C4×C11—24no—
273C2×C4×C11—216no—
274C2×C4×C11—28no—
275C2×C4×C11—216no—
276C2×C4×C11—28no—
277C2×C4×C11#12014yes—
278C2×C4×C11#12018yes—
279C2×C4×C11C22×D414yes—
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C22×D412yes—
282C2×C4×C11C22×D414yes—
283C2×C4×C11C22×D414yes—
284C2×C4×C11C22×D414yes—
285C2×C4×C11C2511yescharacteristic
286C22⋊D11—48no—
287C22⋊D11—88no—
288C2×Dic11—22no—
289C2×Dic11—24no—
290C2×Dic11—44no—
291C2×Dic11—42no—
292C2×Dic11—84no—
293D44—24no—
294D44—42no—
295C4×D11—48no—
296Dic22—24no—
297Dic22—42no—
298C11⋊C8—28no—
299#585—216no—
300C2×2−1+4—21no—
301C2×2−1+4C2×D1114yescomplemented
302C2×H(5,𝔽2)—21no—
303C2×H(5,𝔽2)—22no—
304C2×H(5,𝔽2)C2×D1114yescomplemented
305C22×#41—24no—
306C22×#41—111no—
307C22×#41C2×D1114yes—
308C22×#41C2×D1112yes—
309C22×#41C2×D1111yescharacteristic
310#575—2216no—
311C2×#137—114no—
312C2×#137—114no—
313C2×AGL(1,ℤ/8)—114no—
314C2×AGL(1,ℤ/8)—114no—
315C2×#135—118no—
316C22×M16—112no—
317#537—118no—
318#537—224no—
319C2×C22⋊Q8—112no—
320C2×C22⋊Q8—221no—
321C2×#121—112no—
322C2×#121—221no—
323C2×#121—222no—
324C22×C4⋊C4—111no—
325#452—1116no—
326#451—118no—
327#450—118no—
328#449—1116no—
329#448—118no—
330#447—118no—
331#417—118no—
332#417—118no—
333C2×#103—114no—
334C2×#102—114no—
335#408—118no—
336#407—114no—
337C22×C11—21no—
338C22×C11—22no—
339C22×C11—21no—
340C22×C11—22no—
341C22×C11—24no—
342C22×C11—24no—
343C22×C11—24no—
344C22×C11—28no—
345C22×C11—44no—
346C22×C11—44no—
347C22×C11—44no—
348C22×C11—84no—
349C22×C11—88no—
350C22×C11—816no—
351C22×C11C2×#12012yes—
352C22×C11C2×#12014yes—
353C22×C11C23×D411yescharacteristic
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—42no—
357C2×D11—84no—
358C4×C11—28no—
359C4×C11—24no—
360C4×C11C2×#12012yes—
361C4×C11C2×#12014yes—
362C4×C11C23×D412yes—
363Dic11—44no—
364Dic11—42no—
3652−1+4—216no—
3662−1+4—216no—
3672−1+4—216no—
368H(5,𝔽2)—216no—
369H(5,𝔽2)—232no—
370H(5,𝔽2)—216no—
371H(5,𝔽2)—216no—
372C2×#41—264no—
373C2×#41—232no—
374C2×#41—24no—
375C2×#41—24no—
376C2×#41—28no—
377C2×#41—24no—
378C2×#41—22no—
379C2×#41—24no—
380C2×#41—22no—
381C2×#41—28no—
382C2×#41—28no—
383C2×#41—114no—
384C2×#41—222no—
385C2×#41—228no—
386C2×#41C22⋊D1114yes—
387C2×#41C22⋊D11116yescomplemented
388C2×#41C22×D1118yes—
389C2×#41C22×D1114yes—
390C2×#41C22×D1114yes—
391C2×#41C22×D1114yes—
392C22×Q8—24no—
393C22×Q8—111no—
394C22×Q8C22⋊D1111yescharacteristic
395C22×Q8C22×D1114yes—
396C22×Q8C22×D1112yes—
397C22×D4—24no—
398C22×D4—22no—
399C22×D4—28no—
400C22×D4—24no—
401C22×D4—111no—
402C22×D4—221no—
403C22×D4—222no—
404C22×D4C22⋊D1112yes—
405C22×D4C22⋊D1111yescharacteristic
406C22×D4C22×D1114yes—
407C22×D4C22×D1112yes—
408C23×C4—24no—
409C23×C4—22no—
410C23×C4—221no—
411C23×C4—221no—
412C23×C4C22×D1112yes—
413C23×C4C22×D1111yescharacteristic
414#137—2216no—
415#137—2216no—
416AGL(1,ℤ/8)—2216no—
417AGL(1,ℤ/8)—2216no—
418#135—2232no—
419C2×Q16—118no—
420C2×SD16—118no—
421C2×SD16—118no—
422C2×D8—118no—
423C2×M16—114no—
424C2×M16—114no—
425C2×M16—228no—
426C22×C8—114no—
427C22⋊Q8—118no—
428C22⋊Q8—228no—
429C22⋊Q8—224no—
430#121—118no—
431#121—228no—
432#121—2216no—
433#121—224no—
434C2×C4⋊C4—112no—
435C2×C4⋊C4—114no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—222no—
438C2×C4⋊C4—222no—
439C2×C22⋊C4—222no—
440C2×C22⋊C4—222no—
441#103—1116no—
442#102—1116no—
443C22⋊C8—118no—
444C22⋊C8—118no—
445C2×C11—22no—
446C2×C11—24no—
447C2×C11—44no—
448C2×C11—48no—
449C2×C11C22×#12011yescharacteristic
450C2×C11#358511yescharacteristic
451C2×C11#358611yescharacteristic
452D11—82no—
453C24—24no—
454C24—22no—
455C24—221no—
456C24C2×C22⋊D1112yes—
457C24C2×C22⋊D1111yescharacteristic
458#41—232no—
459#41—264no—
460#41—232no—
461#41—232no—
462#41—232no—
463#41—216no—
464#41—216no—
465#41—216no—
466#41—216no—
467#41—216no—
468#41—28no—
469#41—28no—
470#41—28no—
471#41—28no—
472#41—228no—
473#41—228no—
474#41—448no—
475#41C2×C22⋊D11116yes—
476#41C2×C22⋊D11116yescomplemented
477C2×Q8—232no—
478C2×Q8—216no—
479C2×Q8—24no—
480C2×Q8—24no—
481C2×Q8—22no—
482C2×Q8—24no—
483C2×Q8—112no—
484C2×Q8—221no—
485C2×Q8—224no—
486C2×Q8C2×C22⋊D1114yes—
487C2×Q8C2×C22⋊D1118yescomplemented
488C2×Q8C23×D1114yes—
489C2×D4—232no—
490C2×D4—264no—
491C2×D4—232no—
492C2×D4—216no—
493C2×D4—28no—
494C2×D4—28no—
495C2×D4—24no—
496C2×D4—24no—
497C2×D4—216no—
498C2×D4—24no—
499C2×D4—24no—
500C2×D4—22no—
501C2×D4—24no—
502C2×D4—112no—
503C2×D4—224no—
504C2×D4—228no—
505C2×D4—224no—
506C2×D4—221no—
507C2×D4—444no—
508C2×D4—884no—
509C2×D4C2×C22⋊D1118yes—
510C2×D4C2×C22⋊D1114yes—
511C2×D4C2×C22⋊D1118yescomplemented
512C2×D4C23×D1114yes—
513C22×C4—232no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—216no—
517C22×C4—24no—
518C22×C4—28no—
519C22×C4—24no—
520C22×C4—28no—
521C22×C4—222no—
522C22×C4—221no—
523C22×C4—224no—
524C22×C4—224no—
525C22×C4—444no—
526C22×C4—882no—
527C22×C4C2×C22⋊D1112yes—
528C22×C4C2×C22⋊D1114yes—
529C22×C4C2×C22⋊D1112yes—
530C22×C4C2×C22⋊D1111yescharacteristic
531C22×C4C2×C22⋊D1118yes—
532C22×C4C23×D1114yes—
533C22×C4C23×D1112yes—
534C22×C4C23×D1111yescharacteristic
535Q16—2216no—
536SD16—2216no—
537SD16—2216no—
538D8—2216no—
539M16—228no—
540M16—228no—
541C2×C8—118no—
542C2×C8—228no—
543C4⋊C4—114no—
544C4⋊C4—222no—
545C4⋊C4—224no—
546C4⋊C4—228no—
547C22⋊C4—228no—
548C22⋊C4—228no—
549C11#6037111yescharacteristic, complemented, Sylow
550C23—216no—
551C23—24no—
552C23—24no—
553C23—28no—
554C23—41no—
555C23—41no—
556C23—42no—
557C23—42no—
558C23—82no—
559C23—82no—
560C23—84no—
561C23—84no—
562C23—222no—
563C23—442no—
564C23—442no—
565C23—442no—
566C23#6700614yes—
567C23C22×C22⋊D1114yes—
568C23C22×C22⋊D1112yes—
569C23C22×C22⋊D1111yescharacteristic
570Q8—216no—
571Q8—28no—
572Q8—28no—
573Q8—24no—
574Q8—224no—
575Q8—442no—
576Q8C22×C22⋊D1118yes—
577D4—232no—
578D4—216no—
579D4—216no—
580D4—216no—
581D4—216no—
582D4—28no—
583D4—28no—
584D4—24no—
585D4—224no—
586D4—448no—
587D4—442no—
588D4—888no—
589D4C22×C22⋊D1118yes—
590C2×C4—216no—
591C2×C4—232no—
592C2×C4—28no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—216no—
596C2×C4—28no—
597C2×C4—216no—
598C2×C4—28no—
599C2×C4—224no—
600C2×C4—222no—
601C2×C4—444no—
602C2×C4—442no—
603C2×C4—448no—
604C2×C4—884no—
605C2×C4#6700618yes—
606C2×C4#6700614yes—
607C2×C4C22×C22⋊D1114yes—
608C2×C4C22×C22⋊D1111yescharacteristic
609C2×C4C22×C22⋊D1112yes—
610C2×C4C22×C22⋊D1114yes—
611C2×C4C22×C22⋊D1114yes—
612C2×C4C22×C22⋊D1114yes—
613C2×C4C24×D1111yescharacteristic
614C8—228no—
615C22—21no—
616C22—22no—
617C22—21no—
618C22—22no—
619C22—24no—
620C22—24no—
621C22—24no—
622C22—28no—
623C22—44no—
624C22—44no—
625C22—44no—
626C22—84no—
627C22—88no—
628C22—816no—
629C22—442no—
630C22—442no—
631C22—442no—
632C22—884no—
633C22C2×#6700612yes—
634C22C2×#6700614yes—
635C22C23×C22⋊D1111yescharacteristic
636C4—28no—
637C4—24no—
638C4—444no—
639C4—442no—
640C4C2×#6700612yes—
641C4C2×#6700614yes—
642C4C23×C22⋊D1112yes—
643C2—22no—
644C2—24no—
645C2—44no—
646C2—48no—
647C2—882no—
648C2C22×#6700611yescharacteristic
649C2#1308339511yescharacteristic
650C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#585C2
socleC22×C11C23×D4
hypercenterC2×#585D11
hypocenterC11#60371
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ C2×#585

Complements

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

NH ≅ G/Ntype
1. C2×#10623353C2semidirect
2. C2×#10623364C2semidirect
3. #13077931C2semidirect
4. #13077920C2semidirect
5. #13077876C2semidirect
6. #13077868C2semidirect
7. C2×#10622845C2semidirect
8. #13077061C2semidirect
9. C2×C11×#585C2semidirect
12. C2×C11×2−1+4C22semidirect
15. C2×C11×H(5,𝔽2)C22semidirect
20. C22×#4339C22semidirect
22. #10623364C22semidirect
23. C2×#67004C22semidirect
25. C2×#67003C22semidirect
26. C2×#67002C22semidirect
28. C2×#66995C22semidirect
31. C2×#66985C22semidirect
32. C2×#66983C22semidirect
33. C22×C4⋊Dic11C22semidirect
34. C2×#66977C22semidirect
35. C22×#4318C22semidirect
36. #10622852C22semidirect
37. #10622851C22semidirect
38. #10622847C22semidirect
39. #10622845C22semidirect
40. #10622845C22semidirect
41. #10622841C22semidirect
42. #10622840C22semidirect
43. C2×#66899C22semidirect
44. #10622831C22semidirect
45. #10622830C22semidirect
46. C2×#66896C22semidirect
47. #10622820C22semidirect
67. C2×C11×#41D4semidirect
149. C11×#41C2×D4semidirect
157. C2×Q8×C11C2×D4semidirect
174. C2×D4×C11C2×D4semidirect
225. C2×#585D11semidirect
301. C2×2−1+4C2×D11semidirect
304. C2×H(5,𝔽2)C2×D11semidirect
387. C2×#41C22⋊D11semidirect
476. #41C2×C22⋊D11semidirect
487. C2×Q8C2×C22⋊D11semidirect
511. C2×D4C2×C22⋊D11semidirect
549. C11#60371semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
C2×#106233642
#130779312
#130779202
#130778762
#130778682
C2×#106228452
#130770612
C2×C11×#5852
#6037111