Finite Group Databasebeta

← #14810267

Subgroups — #14810267

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×#10622684C211yesmaximal, characteristic, complemented
2C2×#10622622C211yesmaximal, characteristic, complemented
3#13073782C211yesmaximal, characteristic, complemented
4#13069802C212yesmaximal, complemented
5#13069795C212yesmaximal, complemented
6#13069544C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic, complemented
8#13068547C212yesmaximal, complemented
9#13068547C212yesmaximal, complemented
10#13068441C211yesmaximal, characteristic, complemented
11C2×D42×C11C211yesmaximal, characteristic
12C23×D4×C11—21no—
13C23×D4×C11C2212yes—
14D42×C11—24no—
15D42×C11—24no—
16C2×C11×#127C2211yescharacteristic
17C2×C11×#121—21no—
18C2×C11×#121C2212yes—
19C2×C11×#120—22no—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66923C2211yescharacteristic, complemented
23#10622835—21no—
24C2×#66896C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C2×#66896C2212yes—
27C2×#66896C2212yescomplemented
28C2×#66896C2212yescomplemented
29C2×#66896C2212yescomplemented
30C2×#66896C2212yescomplemented
31#10622825C2212yescomplemented
32#10622825C2212yescomplemented
33C2×C22⋊(C11⋊C8)C2212yescomplemented
34C2×C22⋊(C11⋊C8)C2212yescomplemented
35#10622684—24no—
36#10622622—24no—
37#10622595—21no—
38C2×#66872C2211yescharacteristic, complemented
39C2×#66871C2211yescharacteristic, complemented
40#10622558—22no—
41C4×C4⋊Dic11C2211yescharacteristic, complemented
42C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
43C2×#66867C2211yescharacteristic, complemented
44#10622167C2212yescomplemented
45C25×C11—22no—
46C22×D4×C11—28no—
47C22×D4×C11—22no—
48C22×D4×C11—24no—
49C22×D4×C11—24no—
50C22×D4×C11—24no—
51C22×D4×C11—24no—
52C22×D4×C11—22no—
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11—42no—
56C22×D4×C11—42no—
57C22×D4×C11—48no—
58C22×D4×C11D411yescharacteristic
59C22×D4×C11C2312yes—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2312yes—
63C11×#127—22no—
64C11×#127D414yes—
65C11×#121—28no—
66C11×#121—24no—
67C11×#121—24no—
68C11×#120—216no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11D414yes—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4D412yes—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—22no—
80C2×C22⋊Dic11—22no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2312yes—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C22×C11⋊C8C2312yes—
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90#66923—22no—
91#66923—22no—
92#66896—22no—
93#66896—22no—
94#66896—24no—
95#66896—24no—
96#66896—24no—
97#66896—42no—
98#66896—42no—
99C11⋊#95—21no—
100C11⋊#95—22no—
101C11⋊#95—22no—
102C22⋊(C11⋊C8)—42no—
103C22⋊(C11⋊C8)—42no—
104#66872—22no—
105#66871—22no—
106C4⋊(C11⋊C8)—22no—
107#66867—22no—
108#25891—111nomaximal, Sylow
109C24×C11—21no—
110C24×C11—28no—
111C24×C11—22no—
112C24×C11—44no—
113C24×C11—44no—
114C24×C11—44no—
115C24×C11—44no—
116C24×C11—82no—
117C24×C11—82no—
118C24×C11C2×D412yes—
119C2×D4×C11—24no—
120C2×D4×C11—28no—
121C2×D4×C11—28no—
122C2×D4×C11—22no—
123C2×D4×C11—24no—
124C2×D4×C11—24no—
125C2×D4×C11—21no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—44no—
133C2×D4×C11—44no—
134C2×D4×C11—44no—
135C2×D4×C11—48no—
136C2×D4×C11—48no—
137C2×D4×C11—432no—
138C2×D4×C11—48no—
139C2×D4×C11—44no—
140C2×D4×C11—44no—
141C2×D4×C11—48no—
142C2×D4×C11—81no—
143C2×D4×C11—81no—
144C2×D4×C11C2×D414yes—
145C2×D4×C11C2×D412yes—
146C2×D4×C11#4114yes—
147C22×C4×C11—21no—
148C22×C4×C11—24no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—44no—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—22no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4C2×D412yes—
166C11×C22⋊C4—28no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—24no—
169C42×C11C2×D412yes—
170C42×C11C2×D412yes—
171C22⋊Dic11—44no—
172C22⋊Dic11—82no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179Dic11⋊C4—42no—
180Dic11⋊C4—42no—
181C4×Dic11—81no—
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×D42D1111yescharacteristic
190C2×#490—111no—
191C2×#478—111no—
192#2562—111no—
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—24no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—24no—
209C23×C11—416no—
210C23×C11—416no—
211C23×C11—42no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—88no—
221C23×C11—88no—
222C23×C11—88no—
223C23×C11—88no—
224C23×C11—88no—
225C23×C11AGL(1,ℤ/8)14yes—
226C23×C11C22×D411yescharacteristic
227D4×C11—28no—
228D4×C11—22no—
229D4×C11—24no—
230D4×C11—24no—
231D4×C11—24no—
232D4×C11—48no—
233D4×C11—416no—
234D4×C11—416no—
235D4×C11—42no—
236D4×C11—42no—
237D4×C11—84no—
238D4×C11#12414yes—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—48no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11#12012yes—
253C2×C4×C11#12012yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4112yes—
257C2×C4×C11H(5,𝔽2)12yes—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—42no—
269C23×D4—21no—
270C23×D4C2×D1112yes—
271D42—24no—
272D42—24no—
273C2×#127C2×D1111yescharacteristic
274C2×#125—111no—
275C2×#121—21no—
276C2×#121C2×D1112yes—
277C2×#120—22no—
278C2×C4×D4C2×D1111yescharacteristic
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—221no—
296#394—221no—
297#388—222no—
298#380—112no—
299#380—112no—
300C4×C4⋊C4—111no—
301#340—112no—
302C22×C11—24no—
303C22×C11—24no—
304C22×C11—24no—
305C22×C11—24no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—44no—
312C22×C11—42no—
313C22×C11—44no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—832no—
318C22×C11—82no—
319C22×C11—82no—
320C22×C11—82no—
321C22×C11—82no—
322C22×C11C2×#12011yescharacteristic
323C22×C11#54612yes—
324C22×C11C2×AGL(1,ℤ/8)12yes—
325C22×C11#57611yescharacteristic
326C22×C11#57711yescharacteristic
327C4×C11—22no—
328C4×C11—22no—
329C4×C11—42no—
330C4×C11—42no—
331C4×C11C2×#12411yescharacteristic
332C4×C11#53511yescharacteristic
333C4×C11#54612yes—
334Dic11—81no—
335Dic11—81no—
336Dic11—82no—
337C25—22no—
338C22×D4—28no—
339C22×D4—22no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—22no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4—42no—
348C22×D4—42no—
349C22×D4—48no—
350C22×D4C22⋊D1111yescharacteristic
351C22×D4C22×D1112yes—
352C22×D4C22×D1111yescharacteristic
353C23×C4—21no—
354C23×C4C22×D1112yes—
355C22×C8—112no—
356C22×C8—111no—
357C22×C8—111no—
358#127—22no—
359#127C22⋊D1114yes—
360#125—222no—
361#125—222no—
362#121—28no—
363#121—24no—
364#121—24no—
365#120—216no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4C22⋊D1114yes—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—112no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4C22⋊D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C22⋊C4—21no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—222no—
380C2×C22⋊C4—222no—
381C2×C22⋊C4C22⋊D1112yes—
382C2×C42—221no—
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—221no—
398#95—222no—
399#95—222no—
400C2×C11—44no—
401C2×C11—44no—
402C2×C11—84no—
403C2×C11#243511yescharacteristic
404C2×C11#300311yescharacteristic
405C2×C11#301211yescharacteristic
406C2×C11#331012yes—
407C2×C11#331812yes—
408C24—21no—
409C24—28no—
410C24—22no—
411C24—44no—
412C24—44no—
413C24—44no—
414C24—44no—
415C24—82no—
416C24—82no—
417C24C2×C22⋊D1112yes—
418C2×D4—24no—
419C2×D4—28no—
420C2×D4—28no—
421C2×D4—22no—
422C2×D4—24no—
423C2×D4—24no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—44no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—48no—
435C2×D4—48no—
436C2×D4—432no—
437C2×D4—48no—
438C2×D4—44no—
439C2×D4—44no—
440C2×D4—48no—
441C2×D4—81no—
442C2×D4—81no—
443C2×D4#434114yes—
444C2×D4C2×C22⋊D1114yes—
445C2×D4C2×C22⋊D1112yes—
446C22×C4—21no—
447C22×C4—24no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—44no—
455C22×C4—222no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4C2×C22⋊D1112yes—
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C23×D1111yescharacteristic
462C2×C8—222no—
463C2×C8—222no—
464C2×C8—222no—
465C2×C8—222no—
466C2×C8—222no—
467C2×C8—221no—
468C2×C8—221no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—222no—
472C4⋊C4—222no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—442no—
478C4⋊C4—442no—
479C4⋊C4C2×C22⋊D1112yes—
480C22⋊C4—28no—
481C22⋊C4—24no—
482C22⋊C4—24no—
483C22⋊C4—444no—
484C22⋊C4—882no—
485C42—881no—
486C42C2×C22⋊D1112yes—
487C42C2×C22⋊D1112yes—
488C11#2589111yescharacteristic, complemented, Sylow
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—24no—
498C23—416no—
499C23—416no—
500C23—42no—
501C23—41no—
502C23—41no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—88no—
510C23—88no—
511C23—88no—
512C23—88no—
513C23—88no—
514C23#6698514yes—
515C23C22×C22⋊D1111yescharacteristic
516D4—28no—
517D4—22no—
518D4—24no—
519D4—24no—
520D4—24no—
521D4—48no—
522D4—416no—
523D4—416no—
524D4—42no—
525D4—42no—
526D4—84no—
527D4#6698914yes—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—48no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4#6700612yes—
550C2×C4#6700612yes—
551C2×C4C2×#434112yes—
552C2×C4#6703712yes—
553C2×C4C22×C22⋊D1111yescharacteristic
554C2×C4C22×C22⋊D1111yescharacteristic
555C8—441no—
556C8—441no—
557C8—442no—
558C22—24no—
559C22—24no—
560C22—24no—
561C22—24no—
562C22—42no—
563C22—44no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—44no—
570C22—44no—
571C22—44no—
572C22—44no—
573C22—832no—
574C22—82no—
575C22—82no—
576C22—82no—
577C22—82no—
578C22C2×#6698512yes—
579C22#1062333712yes—
580C22#1062336611yescharacteristic
581C22#1062336711yescharacteristic
582C22C2×#6700611yescharacteristic
583C4—22no—
584C4—22no—
585C4—42no—
586C4—42no—
587C4—881no—
588C4—881no—
589C4—882no—
590C4C2×#6698911yescharacteristic
591C4#1062333611yescharacteristic
592C4#1062333712yes—
593C2—44no—
594C2—44no—
595C2—84no—
596C2#1307226311yescharacteristic
597C2#1307784311yescharacteristic
598C2#1307792011yescharacteristic
599C2#1308063712yes—
600C2#1308075712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×D42×C11C2
socleC23×C11C22×D4
hypercenterC2×D42D11
hypocenterC11#25891
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C2×#10622684C2semidirect
2. C2×#10622622C2semidirect
3. #13073782C2semidirect
4. #13069802C2semidirect
5. #13069795C2semidirect
6. #13069544C2semidirect
7. #13069415C2semidirect
8. #13068547C2semidirect
9. #13068547C2semidirect
10. #13068441C2semidirect
22. C2×#66923C22semidirect
27. C2×#66896C22semidirect
28. C2×#66896C22semidirect
29. C2×#66896C22semidirect
30. C2×#66896C22semidirect
31. #10622825C22semidirect
32. #10622825C22semidirect
33. C2×C22⋊(C11⋊C8)C22semidirect
34. C2×C22⋊(C11⋊C8)C22semidirect
38. C2×#66872C22semidirect
39. C2×#66871C22semidirect
41. C4×C4⋊Dic11C22semidirect
42. C2×C4⋊(C11⋊C8)C22semidirect
43. C2×#66867C22semidirect
44. #10622167C22semidirect
488. C11#25891semidirect

Maximal subgroups

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

subgroupindex
C2×#106226842
C2×#106226222
#130737822
#130698022
#130697952
#130695442
#130694152
#130685472
#130684412
C2×D42×C112
#2589111