Finite Group Databasebeta

← #14732242

Subgroups — #14732242

Order 2816.

1688 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079534C211yesmaximal, characteristic, complemented
2#13078616C211yesmaximal, characteristic, complemented
3#13078080C211yesmaximal, characteristic, complemented
4#13067795C214yesmaximal, complemented
5#13067670C214yesmaximal, complemented
6#13067284C211yesmaximal, characteristic, complemented
7#13067041C211yesmaximal, characteristic, complemented
8#13067007C211yesmaximal, characteristic, complemented
9C2×D42×C11C211yesmaximal, characteristic, complemented
10C23×D4×C11—21no—
11C23×D4×C11—21no—
12D42×C11—22no—
13D42×C11—22no—
14D42×C11—22no—
15D42×C11C2214yes—
16C2×C11×#127C2211yescharacteristic
17C2×C11×#121—21no—
18C2×C11×#121—21no—
19C2×C11×#120—22no—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66985—21no—
23#10623008C2211yescharacteristic, complemented
24#10622830—21no—
25#10622830—22no—
26#10622686C2212yescomplemented
27#10622685—22no—
28#10622683C2212yescomplemented
29#10622632C2212yescomplemented
30#10622629—22no—
31#10622628C2212yescomplemented
32#10622628C2212yescomplemented
33C4×#4323—22no—
34#10622620C2212yescomplemented
35#10622580—21no—
36#10622579—21no—
37#10622538C2211yescharacteristic, complemented
38#10622538C2211yescharacteristic, complemented
39#10622537C2211yescharacteristic, complemented
40#10622182C2214yescomplemented
41D4⋊(C11⋊C8)C2214yescomplemented
42D4⋊(C11⋊C8)C2214yescomplemented
43C25×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—24no—
47C22×D4×C11—24no—
48C22×D4×C11—24no—
49C22×D4×C11—24no—
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11—48no—
53C22×D4×C11—44no—
54C22×D4×C11—44no—
55C22×D4×C11D411yescharacteristic
56C22×D4×C11D411yescharacteristic
57C22×D4×C11D412yes—
58C23×C4×C11—21no—
59C23×C4×C11—21no—
60C2×#4339—21no—
61C11×#127—21no—
62C11×#127—21no—
63C11×#127D412yes—
64C11×#127C2312yes—
65C11×#121—24no—
66C11×#121—24no—
67C11×#121—24no—
68C11×#121—24no—
69C11×#120—28no—
70C11×#120—28no—
71C4×D4×C11—21no—
72C4×D4×C11—21no—
73C4×D4×C11—21no—
74C4×D4×C11—21no—
75C4×D4×C11D412yes—
76C4×D4×C11D412yes—
77C4×D4×C11C2312yes—
78C4×D4×C11C2312yes—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C42×C11C2311yescharacteristic
85C2×#4324—22no—
86#66985—44no—
87C2×#4323—22no—
88C2×#4323—22no—
89C2×#4323—24no—
90#66983—21no—
91#66983—21no—
92C2×#4318—21no—
93#66928—21no—
94#66927C2311yescharacteristic, complemented
95C4×D44—21no—
96C4×D44—21no—
97#66922C2311yescharacteristic, complemented
98#66896—22no—
99#66896—24no—
100C22⋊(C11⋊C8)—21no—
101C22⋊(C11⋊C8)—21no—
102#66874—22no—
103#66873—22no—
104#66873—22no—
105#66871—22no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)—21no—
108C4⋊(C11⋊C8)C2312yescomplemented
109C4⋊(C11⋊C8)C2312yescomplemented
110C4×C11⋊C8—21no—
111C4×C11⋊C8C2312yescomplemented
112#18746—111nomaximal, Sylow
113C24×C11—21no—
114C24×C11—21no—
115C24×C11—28no—
116C24×C11—22no—
117C24×C11—48no—
118C24×C11—48no—
119C24×C11—84no—
120C2×D4×C11—24no—
121C2×D4×C11—28no—
122C2×D4×C11—28no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—44no—
132C2×D4×C11—416no—
133C2×D4×C11—48no—
134C2×D4×C11—48no—
135C2×D4×C11—416no—
136C2×D4×C11—48no—
137C2×D4×C11—48no—
138C2×D4×C11—48no—
139C2×D4×C11—48no—
140C2×D4×C11—42no—
141C2×D4×C11—42no—
142C2×D4×C11—82no—
143C2×D4×C11D814yescomplemented
144C2×D4×C11C2×D412yes—
145C2×D4×C11C2×D412yes—
146C2×D4×C11C2×D414yes—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—44no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C2×C22⋊D11—41no—
160#4339—42no—
161#4339—42no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×C4×D11—41no—
166C2×Dic22—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—28no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C42×C11C2×D411yescharacteristic
177C42×C11C2×D411yescharacteristic
178C42×C11C2×D411yescharacteristic
179C42×C11C2411yescharacteristic
180#4324—44no—
181#4323—44no—
182#4323—44no—
183#4323—84no—
184(C2×D11)⋊C4—41no—
185(C2×D11)⋊C4—41no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188#4318—42no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×D42D1111yescharacteristic, complemented
193#3205—111no—
194#3100—111no—
195#3036—111no—
196#1639—114no—
197#1619—114no—
198#1545—111no—
199#1486—111no—
200#1478—111no—
201C23×C11—24no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—44no—
210C23×C11—416no—
211C23×C11—416no—
212C23×C11—44no—
213C23×C11—42no—
214C23×C11—44no—
215C23×C11—88no—
216C23×C11—832no—
217C23×C11#12011yescharacteristic
218C22×D11—41no—
219D4×C11—24no—
220D4×C11—22no—
221D4×C11—22no—
222D4×C11—24no—
223D4×C11—44no—
224D4×C11—44no—
225D4×C11—416no—
226D4×C11—416no—
227D4×C11—42no—
228D4×C11—42no—
229D4×C11—44no—
230D4×C11—44no—
231D4×C11—82no—
232D4×C11C2×D814yes—
233D4×C11AGL(1,ℤ/8)14yescomplemented
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—41no—
238C2×C4×C11—44no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—44no—
244C2×C4×C11—44no—
245C2×C4×C11#12011yescharacteristic
246C2×C4×C11#12011yescharacteristic
247C2×C4×C11#12011yescharacteristic
248C2×C4×C11C2×D812yes—
249C2×C4×C11AGL(1,ℤ/8)12yes—
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C22⋊D11—82no—
254C2×Dic11—41no—
255D44—42no—
256D44—41no—
257D44—42no—
258D44—41no—
259C4×D11—82no—
260Dic22—41no—
261Dic22—41no—
262C11⋊C8—42no—
263C11⋊C8—42no—
264C11⋊C8—42no—
265C23×D4—21no—
266C23×D4—21no—
267C2×AGL(1,ℤ/8)—221no—
268D42—22no—
269D42—22no—
270D42—22no—
271D42C2×D1114yes—
272#532—111no—
273C2×#127C2×D1111yescharacteristic
274C2×#121—21no—
275C2×#121—21no—
276C2×#120—22no—
277C2×C4×D4C2×D1111yescharacteristic
278C2×C4×D4C2×D1111yescharacteristic
279#493—112no—
280#486—112no—
281#480—221no—
282#474—112no—
283#463—222no—
284#461—112no—
285#459—112no—
286#459—112no—
287#459—222no—
288#447—221no—
289#447—222no—
290C4×D8—222no—
291#431—111no—
292#431—111no—
293#423—111no—
294#417—221no—
295#331—114no—
296D4⋊C8—114no—
297D4⋊C8—114no—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—24no—
301C22×C11—24no—
302C22×C11—48no—
303C22×C11—48no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—44no—
309C22×C11—44no—
310C22×C11—44no—
311C22×C11—88no—
312C22×C11—832no—
313C22×C11#44712yes—
314C22×C11C2×#12011yescharacteristic
315C2×D11—81no—
316C2×D11—81no—
317C2×D11—81no—
318C4×C11—21no—
319C4×C11—21no—
320C4×C11—21no—
321C4×C11—42no—
322C4×C11—42no—
323C4×C11#44712yes—
324C4×C11C22×D811yescharacteristic
325C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
326C4×C11C2×AGL(1,ℤ/8)12yes—
327Dic11—81no—
328C25—22no—
329C2×#41—221no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—21no—
337C22×D4—21no—
338C22×D4—48no—
339C22×D4—44no—
340C22×D4—44no—
341C22×D4C22⋊D1111yescharacteristic
342C22×D4C22⋊D1111yescharacteristic
343C22×D4C22⋊D1112yes—
344C23×C4—21no—
345C23×C4—21no—
346AGL(1,ℤ/8)—444no—
347C2×SD16—222no—
348C2×D8—222no—
349C2×D8—222no—
350C2×D8—224no—
351C2×M16—221no—
352C4⋊Q8—111no—
353#127—21no—
354#127—21no—
355#127—111no—
356#127C22⋊D1112yes—
357#127C22×D1112yes—
358#124—221no—
359#121—24no—
360#121—24no—
361#121—24no—
362#121—24no—
363#121—221no—
364#121—221no—
365#120—28no—
366#120—28no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—221no—
372C4×D4—221no—
373C4×D4C22⋊D1112yes—
374C4×D4C22⋊D1112yes—
375C4×D4C22×D1112yes—
376C4×D4C22×D1112yes—
377C2×C4⋊C4C22⋊D1111yescharacteristic
378C2×C4⋊C4C22⋊D1111yescharacteristic
379C2×C22⋊C4—22no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C42C22×D1111yescharacteristic
383#107—222no—
384C4⋊C8—112no—
385C4⋊C8—112no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388#103—222no—
389#102—222no—
390#102—224no—
391#102—222no—
392#102—222no—
393C22⋊C8—221no—
394C22⋊C8—221no—
395C4×C8—112no—
396C4×C8—221no—
397C2×C11—22no—
398C2×C11—44no—
399C2×C11—44no—
400C2×C11—84no—
401C2×C11C2×#44711yescharacteristic
402C2×C11#300311yescharacteristic
403C2×C11#301911yescharacteristic
404D11—161no—
405C24—21no—
406C24—21no—
407C24—28no—
408C24—22no—
409C24—48no—
410C24—48no—
411C24—84no—
412#41—442no—
413#41—442no—
414C2×Q8—221no—
415C2×D4—24no—
416C2×D4—28no—
417C2×D4—28no—
418C2×D4—22no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—44no—
427C2×D4—416no—
428C2×D4—48no—
429C2×D4—48no—
430C2×D4—416no—
431C2×D4—48no—
432C2×D4—48no—
433C2×D4—48no—
434C2×D4—48no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—82no—
438C2×D4—221no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—441no—
442C2×D4#432314yescomplemented
443C2×D4C2×C22⋊D1112yes—
444C2×D4C2×C22⋊D1112yes—
445C2×D4C2×C22⋊D1114yes—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—44no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—441no—
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C2×C22⋊D1111yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459SD16—444no—
460D8—444no—
461D8—444no—
462D8—884no—
463M16—442no—
464C2×C8—222no—
465C2×C8—222no—
466C2×C8—222no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4C2×C22⋊D1112yes—
472C4⋊C4C2×C22⋊D1112yes—
473C22⋊C4—28no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—441no—
479C22⋊C4—441no—
480C42C2×C22⋊D1111yescharacteristic
481C42C2×C22⋊D1111yescharacteristic
482C42C2×C22⋊D1111yescharacteristic
483C42C23×D1111yescharacteristic
484C11#1874611yescharacteristic, complemented, Sylow
485C23—24no—
486C23—24no—
487C23—22no—
488C23—22no—
489C23—24no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—44no—
494C23—416no—
495C23—416no—
496C23—44no—
497C23—42no—
498C23—44no—
499C23—88no—
500C23—832no—
501C23—441no—
502C23#6700611yescharacteristic
503Q8—441no—
504Q8—441no—
505D4—24no—
506D4—22no—
507D4—22no—
508D4—24no—
509D4—44no—
510D4—44no—
511D4—416no—
512D4—416no—
513D4—42no—
514D4—42no—
515D4—44no—
516D4—44no—
517D4—82no—
518D4—442no—
519D4—441no—
520D4—442no—
521D4—441no—
522D4—882no—
523D4C2×#432314yes—
524D4#6698514yescomplemented
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—41no—
529C2×C4—44no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—441no—
537C2×C4—882no—
538C2×C4C2×#432312yes—
539C2×C4#6698512yes—
540C2×C4#6700611yescharacteristic
541C2×C4#6700611yescharacteristic
542C2×C4#6700611yescharacteristic
543C2×C4C22×C22⋊D1111yescharacteristic
544C2×C4C22×C22⋊D1111yescharacteristic
545C2×C4C22×C22⋊D1111yescharacteristic
546C8—442no—
547C8—442no—
548C8—442no—
549C22—21no—
550C22—21no—
551C22—24no—
552C22—24no—
553C22—48no—
554C22—48no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—44no—
560C22—44no—
561C22—44no—
562C22—88no—
563C22—832no—
564C22—881no—
565C22—881no—
566C22—881no—
567C22#1062283012yes—
568C22C2×#6700611yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—42no—
573C4—42no—
574C4—881no—
575C4#1062283012yes—
576C4C22×#432311yescharacteristic
577C4C2×#6698511yescharacteristic
578C4C2×#6698512yes—
579C2—22no—
580C2—44no—
581C2—44no—
582C2—84no—
583C2—1761no—
584C2C2×#1062283011yescharacteristic
585C2#1307784311yescharacteristic
586C2#1307797311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×D42×C11C2
socleC22×C11C2×#120
hypercenterC2×D42D11
hypocenterC11#18746
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. #13079534C2semidirect
2. #13078616C2semidirect
3. #13078080C2semidirect
4. #13067795C2semidirect
5. #13067670C2semidirect
6. #13067284C2semidirect
7. #13067041C2semidirect
8. #13067007C2semidirect
9. C2×D42×C11C2semidirect
23. #10623008C22semidirect
26. #10622686C22semidirect
28. #10622683C22semidirect
29. #10622632C22semidirect
31. #10622628C22semidirect
32. #10622628C22semidirect
34. #10622620C22semidirect
37. #10622538C22semidirect
38. #10622538C22semidirect
39. #10622537C22semidirect
40. #10622182C22semidirect
41. D4⋊(C11⋊C8)C22semidirect
42. D4⋊(C11⋊C8)C22semidirect
94. #66927C23semidirect
97. #66922C23semidirect
108. C4⋊(C11⋊C8)C23semidirect
109. C4⋊(C11⋊C8)C23semidirect
111. C4×C11⋊C8C23semidirect
143. C2×D4×C11D8semidirect
192. C2×D42D11semidirect
233. D4×C11AGL(1,ℤ/8)semidirect
442. C2×D4#4323semidirect
484. C11#18746semidirect
524. D4#66985semidirect

Maximal subgroups

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

subgroupindex
#130795342
#130786162
#130780802
#130677952
#130676702
#130672842
#130670412
#130670072
C2×D42×C112
#1874611