Finite Group Databasebeta

← #14810276

Subgroups — #14810276

Order 2816.

1744 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D44C211yesmaximal, characteristic
2C2×#10622680C211yesmaximal, characteristic, complemented
3C2×#10622679C211yesmaximal, characteristic, complemented
4#13069805C212yesmaximal, complemented
5#13069798C212yesmaximal, complemented
6#13069543C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic, complemented
8#13068546C212yesmaximal, complemented
9#13068546C212yesmaximal, complemented
10#13068444C211yesmaximal, characteristic, complemented
11C11×#2562C211yesmaximal, characteristic, complemented
12C22×D4×D11—21no—
13C23×D44C2212yes—
14C2×C11×#125C2211yescharacteristic, complemented
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66983C2212yes—
17D4×D44—24no—
18D4×D44—24no—
19C2×#66948—21no—
20C2×#66935—22no—
21C2×#66927C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C11×#400—21no—
24C11×#394—21no—
25C11×#388—22no—
26C11×#380C2212yescomplemented
27C11×#380C2212yescomplemented
28C4×C11×C4⋊C4C2211yescharacteristic, complemented
29C2×C22⋊(C11⋊C8)C2212yescomplemented
30C2×C22⋊(C11⋊C8)C2212yescomplemented
31#10622680—24no—
32#10622679—24no—
33C2×#66873C2211yescharacteristic
34C2×#66873C2211yescharacteristic
35C2×#66873C2212yes—
36C2×#66873C2212yescomplemented
37C2×#66873C2212yescomplemented
38C2×#66873C2212yescomplemented
39C2×#66873C2212yescomplemented
40C2×#66872C2211yescharacteristic, complemented
41C2×#66871C2211yescharacteristic, complemented
42C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
43C2×#66867C2211yescharacteristic, complemented
44#10622167C2212yescomplemented
45C24×D11—22no—
46C22×D4×C11D411yescharacteristic
47C23×C4×C11C2312yes—
48C22×C22⋊D11—22no—
49C2×D4×D11—28no—
50C2×D4×D11—48no—
51C22×D44—21no—
52C22×D44—22no—
53C22×D44—21no—
54C22×D44—24no—
55C22×D44—24no—
56C22×D44—24no—
57C22×D44—24no—
58C22×D44—42no—
59C22×D44—42no—
60C22×D44C2312yes—
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C11×#125—22no—
64C11×#125—22no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4D412yes—
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78#66983—24no—
79#66983—24no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—22no—
82C2×C4⋊Dic11C2311yescharacteristic
83C22×C11⋊C8C2312yes—
84C22×C11⋊C8C2311yescharacteristic
85C22×C11⋊C8C2311yescharacteristic
86#66948—28no—
87#66935—216no—
88#66927—22no—
89#66927D414yes—
90C4×D44—22no—
91C4×D44D414yes—
92C11×#95—21no—
93C11×#95—22no—
94C11×#95—22no—
95C22⋊(C11⋊C8)—42no—
96C22⋊(C11⋊C8)—42no—
97#66873—22no—
98#66873—22no—
99#66873—24no—
100#66873—24no—
101#66873—24no—
102#66873—42no—
103#66873—42no—
104#66872—22no—
105#66871—22no—
106C4⋊(C11⋊C8)—22no—
107#66867—22no—
108#25891—111nomaximal, Sylow
109C24×C11C2×D412yes—
110C23×D11—21no—
111C23×D11—22no—
112C23×D11—28no—
113C23×D11—44no—
114C23×D11—44no—
115C23×D11—44no—
116C23×D11—44no—
117C23×D11—82no—
118C23×D11—82no—
119C2×D4×C11—24no—
120C2×D4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C2×C22⋊D11—28no—
135C2×C22⋊D11—44no—
136C2×C22⋊D11—44no—
137C22×Dic11—21no—
138D4×D11—432no—
139C2×D44—28no—
140C2×D44—24no—
141C2×D44—24no—
142C2×D44—21no—
143C2×D44—22no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—44no—
150C2×D44—44no—
151C2×D44—44no—
152C2×D44—48no—
153C2×D44—48no—
154C2×D44—48no—
155C2×D44—48no—
156C2×D44—81no—
157C2×D44—81no—
158C2×D44C2×D414yes—
159C2×D44C2×D412yes—
160C2×D44#4114yes—
161C2×C4×D11—24no—
162C2×C4×D11—44no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—42no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—44no—
174C11×C22⋊C4—82no—
175C42×C11—81no—
176C42×C11C2×D412yes—
177C42×C11C2×D412yes—
178(C2×D11)⋊C4—28no—
179(C2×D11)⋊C4—24no—
180C4⋊Dic11—21no—
181C4⋊Dic11C2×D412yes—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×D42—111no—
190C2×#490—111no—
191C2×#478—111no—
192#2562D1111yescharacteristic, complemented
193#2034—112no—
194#2033—112no—
195#1982—111no—
196#1955—111no—
197#1786—112no—
198#1786—112no—
199#1762—111no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11AGL(1,ℤ/8)14yes—
207C23×C11C22×D411yescharacteristic
208C22×D11—22no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—416no—
212C22×D11—42no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—416no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—88no—
223C22×D11—88no—
224C22×D11—88no—
225C22×D11—88no—
226C22×D11—88no—
227D4×C11—28no—
228C2×C4×C11—22no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11#12012yes—
247C2×C4×C11#12012yes—
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4112yes—
251C2×C4×C11H(5,𝔽2)12yes—
252C22⋊D11—416no—
253C2×Dic11—22no—
254C2×Dic11—42no—
255D44—22no—
256D44—24no—
257D44—24no—
258D44—24no—
259D44—48no—
260D44—416no—
261D44—42no—
262D44—42no—
263D44—84no—
264D44#12414yes—
265C4×D11—48no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—42no—
269C23×D4—112no—
270C23×D4—221no—
271D42—224no—
272D42—224no—
273C2×#127—111no—
274C2×#125C2×D1111yescharacteristic, complemented
275C2×#121—112no—
276C2×#121—221no—
277C2×#120—222no—
278C2×C4×D4—111no—
279C2×C4×D4C2×D1111yescharacteristic
280#490—224no—
281#478—224no—
282C2×#107—111no—
283C2×#106—111no—
284C2×C4⋊C8—111no—
285C2×#102—111no—
286C2×#102—111no—
287C2×#102—112no—
288C2×#102—112no—
289C2×#102—112no—
290C2×#102—112no—
291C2×#102—112no—
292C2×C22⋊C8—112no—
293C2×C22⋊C8—112no—
294C2×#97—111no—
295#400—21no—
296#394—21no—
297#388—22no—
298#380C2×D1112yescomplemented
299#380C2×D1112yescomplemented
300C4×C4⋊C4C2×D1111yescharacteristic, complemented
301#340—112no—
302C22×C11—24no—
303C22×C11—24no—
304C22×C11—24no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11C2×#12011yescharacteristic
310C22×C11#54612yes—
311C22×C11C2×AGL(1,ℤ/8)12yes—
312C22×C11#57611yescharacteristic
313C22×C11#57711yescharacteristic
314C2×D11—24no—
315C2×D11—42no—
316C2×D11—42no—
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—44no—
320C2×D11—44no—
321C2×D11—44no—
322C2×D11—832no—
323C2×D11—82no—
324C2×D11—82no—
325C2×D11—82no—
326C2×D11—82no—
327C4×C11—22no—
328C4×C11—22no—
329C4×C11—42no—
330C4×C11—81no—
331C4×C11—81no—
332C4×C11—82no—
333C4×C11C2×#12411yescharacteristic
334C4×C11#53511yescharacteristic
335C4×C11#54612yes—
336Dic11—42no—
337C25—222no—
338C22×D4—111no—
339C22×D4—112no—
340C22×D4—224no—
341C22×D4—224no—
342C22×D4—224no—
343C22×D4—224no—
344C22×D4—228no—
345C22×D4—222no—
346C22×D4—222no—
347C22×D4—221no—
348C22×D4—221no—
349C22×D4—442no—
350C22×D4—442no—
351C22×D4—448no—
352C22×D4C22⋊D1111yescharacteristic
353C23×C4—221no—
354C23×C4C22×D1112yes—
355C22×C8—112no—
356C22×C8—111no—
357C22×C8—111no—
358#127—114no—
359#127—222no—
360#125—22no—
361#125—22no—
362#121—228no—
363#121—224no—
364#121—224no—
365#120—2216no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—114no—
369C4×D4—222no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4C22⋊D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1112yes—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—222no—
381C2×C22⋊C4C22⋊D1112yes—
382C2×C42—21no—
383C2×C42C22×D1111yescharacteristic
384#107—222no—
385#106—222no—
386C4⋊C8—222no—
387#102—224no—
388#102—222no—
389#102—222no—
390#102—224no—
391#102—224no—
392#102—442no—
393#102—442no—
394C22⋊C8—442no—
395C22⋊C8—442no—
396#97—222no—
397#95—21no—
398#95—22no—
399#95—22no—
400C2×C11—44no—
401C2×C11#243511yescharacteristic
402C2×C11#300311yescharacteristic
403C2×C11#301211yescharacteristic
404C2×C11#331012yes—
405C2×C11#331812yes—
406D11—44no—
407D11—84no—
408C24—228no—
409C24—221no—
410C24—222no—
411C24—444no—
412C24—444no—
413C24—444no—
414C24—444no—
415C24—882no—
416C24—882no—
417C24C2×C22⋊D1112yes—
418C2×D4—24no—
419C2×D4—22no—
420C2×D4—112no—
421C2×D4—114no—
422C2×D4—114no—
423C2×D4—228no—
424C2×D4—228no—
425C2×D4—224no—
426C2×D4—224no—
427C2×D4—221no—
428C2×D4—222no—
429C2×D4—222no—
430C2×D4—222no—
431C2×D4—222no—
432C2×D4—222no—
433C2×D4—222no—
434C2×D4—444no—
435C2×D4—444no—
436C2×D4—444no—
437C2×D4—448no—
438C2×D4—448no—
439C2×D4—448no—
440C2×D4—448no—
441C2×D4—4432no—
442C2×D4—444no—
443C2×D4—444no—
444C2×D4—881no—
445C2×D4—881no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—221no—
456C22×C4—224no—
457C22×C4—444no—
458C22×C4C2×C22⋊D1112yes—
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C23×D1111yescharacteristic
462C2×C8—222no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—222no—
466C2×C8—222no—
467C2×C8—222no—
468C2×C8—222no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4—112no—
479C4⋊C4—221no—
480C22⋊C4—24no—
481C22⋊C4—44no—
482C22⋊C4—82no—
483C22⋊C4—228no—
484C22⋊C4—224no—
485C42—81no—
486C42D4×D1112yes—
487C42D4×D1112yes—
488C11#2589111yescharacteristic, complemented, Sylow
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—222no—
496C23—224no—
497C23—224no—
498C23—4416no—
499C23—4416no—
500C23—442no—
501C23—441no—
502C23—441no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23—442no—
507C23—442no—
508C23—442no—
509C23—888no—
510C23—888no—
511C23—888no—
512C23—888no—
513C23—888no—
514C23#6700214yes—
515C23C22×C22⋊D1111yescharacteristic
516D4—28no—
517D4—114no—
518D4—222no—
519D4—224no—
520D4—224no—
521D4—224no—
522D4—448no—
523D4—4416no—
524D4—4416no—
525D4—442no—
526D4—442no—
527D4—884no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—222no—
547C2×C4—448no—
548C2×C4—442no—
549C2×C4#6699012yes—
550C2×C4#6699012yes—
551C2×C4C2×D4×D1111yescharacteristic
552C2×C4C2×D4×D1111yescharacteristic
553C2×C4#41×D1112yes—
554C2×C4#6704212yes—
555C8—441no—
556C8—441no—
557C8—442no—
558C22—24no—
559C22—24no—
560C22—24no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—224no—
566C22—444no—
567C22—442no—
568C22—442no—
569C22—444no—
570C22—444no—
571C22—444no—
572C22—444no—
573C22—8832no—
574C22—882no—
575C22—882no—
576C22—882no—
577C22—882no—
578C22C2×#6699011yescharacteristic
579C22C2×#6700212yes—
580C22#1062336012yes—
581C22#1062336611yescharacteristic
582C22#1062336811yescharacteristic
583C4—22no—
584C4—22no—
585C4—42no—
586C4—81no—
587C4—81no—
588C4—82no—
589C4—442no—
590C4D11×#12411yescharacteristic
591C4#1062320511yescharacteristic
592C4#1062320712yes—
593C2—44no—
594C2—444no—
595C2—884no—
596C2#1307226411yescharacteristic
597C2#1307784211yescharacteristic
598C2#1307791711yescharacteristic
599C2#1308063112yes—
600C2#1308075112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2562C2
socleC23×C11C22×D4
prime radicalC2×D4×D44C2
hypercenter#2562D11
hypocenterC11#25891
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2562

Complements

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

NH ≅ G/Ntype
2. C2×#10622680C2semidirect
3. C2×#10622679C2semidirect
4. #13069805C2semidirect
5. #13069798C2semidirect
6. #13069543C2semidirect
7. #13069415C2semidirect
8. #13068546C2semidirect
9. #13068546C2semidirect
10. #13068444C2semidirect
11. C11×#2562C2semidirect
14. C2×C11×#125C22semidirect
26. C11×#380C22semidirect
27. C11×#380C22semidirect
28. C4×C11×C4⋊C4C22semidirect
29. C2×C22⋊(C11⋊C8)C22semidirect
30. C2×C22⋊(C11⋊C8)C22semidirect
36. C2×#66873C22semidirect
37. C2×#66873C22semidirect
38. C2×#66873C22semidirect
39. C2×#66873C22semidirect
40. C2×#66872C22semidirect
41. C2×#66871C22semidirect
42. C2×C4⋊(C11⋊C8)C22semidirect
43. C2×#66867C22semidirect
44. #10622167C22semidirect
192. #2562D11semidirect
274. C2×#125C2×D11semidirect
298. #380C2×D11semidirect
299. #380C2×D11semidirect
300. C4×C4⋊C4C2×D11semidirect
488. C11#25891semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D442
C2×#106226802
C2×#106226792
#130698052
#130697982
#130695432
#130694152
#130685462
#130684442
C11×#25622
#2589111