Finite Group Databasebeta

← #25245415

Subgroups — #25245415

Order 11008.

1868 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic43C211yesmaximal, characteristic
2C2×#14583102C212yesmaximal, complemented
3C2×#14583050C211yesmaximal, characteristic
4#19142943C211yesmaximal, characteristic, complemented
5#19134931C212yesmaximal, complemented
6#19134927C212yesmaximal, complemented
7#19134903C211yesmaximal, characteristic, complemented
8#19134900C211yesmaximal, characteristic, complemented
9#19134593C212yesmaximal, complemented
10#19134573C211yesmaximal, characteristic, complemented
11C2×C43×#450C211yesmaximal, characteristic
12C24×Dic43—21no—
13C22×#10621883C2212yes—
14C2×#13063323C2211yescharacteristic, complemented
15C2×#13063304C2211yescharacteristic
16C2×D4×Dic43—28no—
17C2×D4×Dic43—21no—
18C2×D4×Dic43—21no—
19C2×D4×Dic43C2212yes—
20C2×D4×Dic43C2212yes—
21C22×C4⋊Dic43C2211yescharacteristic
22C22×C22⋊Dic43—21no—
23C22×C4×Dic43C2211yescharacteristic
24#14583102—28no—
25#14583050—24no—
26C2×Dic43⋊C8C2212yescomplemented
27C2×#13063250C2212yescomplemented
28C2×#13063249C2212yescomplemented
29C2×#13063246C2212yes—
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31#14582806C2211yescharacteristic, complemented
32#14582804C2211yescharacteristic, complemented
33#14582794—21no—
34#14582794—21no—
35#14582768C2211yescharacteristic, complemented
36#14582757—21no—
37#14582757—21no—
38#14582662C2212yescomplemented
39#14582661C2212yescomplemented
40#14582653C2212yescomplemented
41C23×D4×C43C2211yescharacteristic
42C22×SD16×C43C2212yes—
43C2×C22⋊Q8×C43C2211yescharacteristic
44C43×#450—24no—
45C2×#102×C43C2212yes—
46C2×C22⋊C8×C43C2211yescharacteristic
47C22×Dic86C2311yescharacteristic
48C23×Dic43—28no—
49C23×Dic43—21no—
50C23×Dic43—22no—
51C23×Dic43—22no—
52C23×Dic43—44no—
53C23×Dic43—44no—
54C23×Dic43D411yescharacteristic
55C23×Dic43D411yescharacteristic
56C2×#10621883—24no—
57C2×#10621883—24no—
58C2×#10621883—24no—
59C22×C43⋊C8C2312yes—
60#13063323—24no—
61#13063304—22no—
62#13063304—22no—
63D4×Dic43—28no—
64D4×Dic43—28no—
65D4×Dic43—24no—
66D4×Dic43—24no—
67D4×Dic43—24no—
68D4×Dic43D418yes—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—24no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2312yes—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—28no—
79C2×C22⋊Dic43—22no—
80C2×C22⋊Dic43—22no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—24no—
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43D411yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86C2×C4×Dic43C2311yescharacteristic
87Dic43⋊C8—24no—
88#13063250—24no—
89#13063249—24no—
90#13063246—24no—
91C22⋊(C43⋊C8)—22no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C25×C43—21no—
97C22×Q8×C43C2311yescharacteristic
98C22×D4×C43—24no—
99C22×D4×C43—24no—
100C22×D4×C43—21no—
101C22×D4×C43—22no—
102C22×D4×C43D414yes—
103C22×D4×C43C2312yes—
104C23×C4×C43C2311yescharacteristic
105C2×SD16×C43—24no—
106C2×SD16×C43—24no—
107C2×SD16×C43—24no—
108C22×C8×C43C2312yes—
109C22⋊Q8×C43—22no—
110C22⋊Q8×C43—22no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C22⋊C4×C43—21no—
114#102×C43—24no—
115C22⋊C8×C43—22no—
116C24×C43—24no—
117C24×C43—24no—
118C24×C43—24no—
119C24×C43—22no—
120C24×C43—42no—
121C24×C43—42no—
122C24×C43—42no—
123C24×C43—42no—
124C24×C43C2×D411yescharacteristic
125C2×Q8×C43—21no—
126C2×Q8×C43—22no—
127C2×Q8×C43—21no—
128C2×Q8×C43—22no—
129C2×D4×C43—216no—
130C2×D4×C43—24no—
131C2×D4×C43—24no—
132C2×D4×C43—216no—
133C2×D4×C43—24no—
134C2×D4×C43—22no—
135C2×D4×C43—22no—
136C2×D4×C43—22no—
137C2×D4×C43C2×D414yes—
138C2×D4×C43C2×D414yes—
139C2×D4×C43#4114yes—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43C2×D412yes—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4112yes—
147C22×C4×C43C2411yescharacteristic
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—24no—
151C22×Dic43—28no—
152C22×Dic43—22no—
153C22×Dic43—28no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—41no—
159C22×Dic43—42no—
160C22×Dic43—432no—
161C22×Dic43—44no—
162C22×Dic43—44no—
163C22×Dic43—44no—
164C22×Dic43—44no—
165C22×Dic43—42no—
166C22×Dic43SD1614yescomplemented
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C2×Dic86—22no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—22no—
175SD16×C43—48no—
176C2×C8×C43—22no—
177C2×C8×C43—22no—
178C2×C8×C43—22no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—42no—
182C22⋊C4×C43—42no—
183C22⋊Dic43—28no—
184C22⋊Dic43—28no—
185C22⋊Dic43—42no—
186#10621883—48no—
187C4⋊Dic43—24no—
188C4⋊Dic43—22no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43C2×D414yes—
192Dic43⋊C4—42no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197C4×Dic43—22no—
198C4×Dic43—22no—
199C4×Dic43—22no—
200C4×Dic43C2×D414yes—
201C2×C43⋊C8—22no—
202C2×C43⋊C8—22no—
203C2×C43⋊C8—22no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—216no—
209C23×C43—24no—
210C23×C43—24no—
211C23×C43—24no—
212C23×C43—48no—
213C23×C43—48no—
214C23×C43—48no—
215C23×C43—48no—
216C23×C43—48no—
217C23×C43—42no—
218C23×C43—42no—
219C23×C43—42no—
220C23×C43—42no—
221C23×C43—48no—
222C23×C43#12112yes—
223C23×C43C2×SD1612yes—
224C23×C43#13712yes—
225C23×C43C22×D411yescharacteristic
226Q8×C43—42no—
227Q8×C43—42no—
228D4×C43—216no—
229D4×C43—24no—
230D4×C43—24no—
231D4×C43—24no—
232D4×C43#12118yes—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—24no—
236C2×C4×C43—24no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43#12112yes—
244C2×C4×C43C22×D412yes—
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C2×#4112yes—
247C2×C4×C43C2×#4111yescharacteristic
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—28no—
253C2×Dic43—21no—
254C2×Dic43—24no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—44no—
258C2×Dic43—416no—
259C2×Dic43—48no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—416no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43#12012yes—
270C2×Dic43#12012yes—
271C2×Dic43C2×SD1612yes—
272C2×Dic43C2×SD1612yes—
273C2×Dic43AGL(1,ℤ/8)12yes—
274Dic86—42no—
275Dic86—42no—
276C8×C43—42no—
277C43⋊C8—42no—
278#32905—431nomaximal, Sylow
279C22×C43—22no—
280C22×C43—22no—
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—22no—
284C22×C43—22no—
285C22×C43—28no—
286C22×C43—432no—
287C22×C43—44no—
288C22×C43—44no—
289C22×C43—44no—
290C22×C43—44no—
291C22×C43—44no—
292C22×C43—44no—
293C22×C43#46114yescomplemented
294C22×C43C2×#12011yescharacteristic
295C22×C43C2×#12111yescharacteristic
296C22×C43#52511yescharacteristic
297C22×C43C22×SD1611yescharacteristic
298C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
299C22×C43C2×#13711yescharacteristic
300C22×C43#57511yescharacteristic
301C4×C43—22no—
302C4×C43—81no—
303C4×C43—81no—
304C4×C43C2×#12112yes—
305C4×C43#52512yes—
306Dic43—22no—
307Dic43—22no—
308Dic43—44no—
309Dic43—41no—
310Dic43—81no—
311Dic43—81no—
312Dic43#45014yescomplemented
313C22×C4×D4—431no—
314C2×#461—432no—
315C2×#450—431no—
316C2×#450D4311yescharacteristic
317#2857—431no—
318#1877—432no—
319#1877—432no—
320#1872—431no—
321#1872—431no—
322#1802—432no—
323#1797—431no—
324C2×C43—24no—
325C2×C43—48no—
326C2×C43#284711yescharacteristic
327C2×C43C2×#45011yescharacteristic
328C2×C43#300711yescharacteristic
329C2×C43C2×#46111yescharacteristic
330C2×C43#303611yescharacteristic
331C2×C43#310111yescharacteristic
332C2×C43#311011yescharacteristic
333C23×D4C2×D4311yescharacteristic
334C24×C4—861no—
335C22×SD16—432no—
336C22×SD16C2×D4312yes—
337C2×C4⋊Q8—431no—
338C2×C22⋊Q8—431no—
339C2×C22⋊Q8C2×D4311yescharacteristic
340C2×C4×D4—432no—
341C2×C4×D4—432no—
342C2×C4×D4—861no—
343C2×C4×D4—861no—
344C2×C4×D4—868no—
345C22×C4⋊C4—431no—
346C22×C22⋊C4—861no—
347C22×C42—431no—
348#461—868no—
349#450—24no—
350#450—864no—
351C2×C4⋊C8—432no—
352C2×#103—432no—
353C2×#103—432no—
354C2×#102—432no—
355C2×#102C2×D4312yes—
356C2×C22⋊C8—431no—
357C2×C22⋊C8C2×D4311yescharacteristic
358#391—431no—
359#391—431no—
360#389—861no—
361#389—861no—
362#384—431no—
363#380—861no—
364#380—861no—
365#340—432no—
366#340—432no—
367#336—432no—
368C43#3290511yescharacteristic, complemented, Sylow
369C25—21no—
370C22×Q8—431no—
371C22×Q8C22×D4311yescharacteristic
372C22×D4—24no—
373C22×D4—24no—
374C22×D4—21no—
375C22×D4—22no—
376C22×D4C22⋊D4314yes—
377C22×D4C22×D4312yes—
378C23×C4—431no—
379C23×C4—431no—
380C23×C4—862no—
381C23×C4—862no—
382C23×C4—868no—
383C23×C4—861no—
384C23×C4—1724no—
385C23×C4—1724no—
386C23×C4C22×D4311yescharacteristic
387C2×SD16—24no—
388C2×SD16—24no—
389C2×SD16—24no—
390C2×SD16—864no—
391C2×SD16—864no—
392C2×SD16—864no—
393C22×C8—432no—
394C22×C8C22×D4312yes—
395C4⋊Q8—864no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—862no—
399C22⋊Q8—862no—
400C4×D4—438no—
401C4×D4—864no—
402C4×D4—864no—
403C4×D4—868no—
404C4×D4—868no—
405C4×D4—864no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—432no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—864no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—862no—
419C2×C22⋊C4—862no—
420C2×C22⋊C4—868no—
421C2×C22⋊C4—861no—
422C2×C42—431no—
423C2×C42—431no—
424C2×C42—431no—
425C2×C42—431no—
426C2×C42—864no—
427C4⋊C8—864no—
428#103—864no—
429#103—864no—
430#102—24no—
431#102—864no—
432C22⋊C8—22no—
433C22⋊C8—862no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438C24—24no—
439C24—24no—
440C24—24no—
441C24—22no—
442C24—42no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24D4×D4311yescharacteristic
447C2×Q8—22no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—22no—
451C2×Q8—862no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—862no—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—216no—
458C2×D4—216no—
459C2×D4—24no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4D4×D4314yes—
464C2×D4#1062190014yes—
465C2×D4C2×C22⋊D4314yes—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—431no—
471C22×C4—434no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—868no—
479C22×C4—864no—
480C22×C4—868no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—1724no—
486C22×C4—1724no—
487C22×C4—1724no—
488C22×C4—1721no—
489C22×C4—17232no—
490C22×C4—1724no—
491C22×C4—1722no—
492C22×C4—1722no—
493C22×C4D4×D4311yescharacteristic
494C22×C4#1062190012yes—
495C22×C4C2×C22⋊D4312yes—
496C22×C4C23×D4311yescharacteristic
497SD16—48no—
498SD16—1728no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—862no—
503C2×C8—862no—
504C2×C8—862no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—42no—
508C4⋊C4—434no—
509C4⋊C4—864no—
510C4⋊C4—862no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—1722no—
514C4⋊C4—1722no—
515C4⋊C4—1722no—
516C4⋊C4—1722no—
517C4⋊C4—1722no—
518C22⋊C4—42no—
519C22⋊C4—868no—
520C22⋊C4—868no—
521C22⋊C4—1722no—
522C42—434no—
523C42—862no—
524C42—862no—
525C42—862no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—216no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—48no—
535C23—48no—
536C23—48no—
537C23—48no—
538C23—48no—
539C23—48no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23#1306329712yes—
545C23SD16×D4312yes—
546C23#1306335412yes—
547C23C2×D4×D4311yescharacteristic
548Q8—42no—
549Q8—42no—
550Q8—1722no—
551Q8—1722no—
552D4—216no—
553D4—24no—
554D4—24no—
555D4—24no—
556D4#1306329718yes—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—432no—
568C2×C4—432no—
569C2×C4—432no—
570C2×C4—432no—
571C2×C4—432no—
572C2×C4—868no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—864no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—17216no—
582C2×C4—1724no—
583C2×C4—17216no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1728no—
591C2×C4—1722no—
592C2×C4—1722no—
593C2×C4#1306329712yes—
594C2×C4C2×D4×D4312yes—
595C2×C4C22×C22⋊D4311yescharacteristic
596C2×C4C2×#1062190012yes—
597C2×C4C2×#1062190011yescharacteristic
598C8—42no—
599C8—1722no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—28no—
607C22—432no—
608C22—44no—
609C22—44no—
610C22—44no—
611C22—44no—
612C22—44no—
613C22—44no—
614C22#1458310214yescomplemented
615C22#120×D4311yescharacteristic
616C22C2×#1306329711yescharacteristic
617C22#1458340511yescharacteristic
618C22C2×SD16×D4311yescharacteristic
619C22AGL(1,ℤ/8)×D4311yescharacteristic
620C22C2×#1306335411yescharacteristic
621C22#1458369511yescharacteristic
622C4—22no—
623C4—81no—
624C4—81no—
625C4—434no—
626C4—862no—
627C4—862no—
628C4—3441no—
629C4—3441no—
630C4—1724no—
631C4—1721no—
632C4C2×#1306329712yes—
633C4#1458340512yes—
634C2—24no—
635C2—48no—
636C2#1914287511yescharacteristic
637C2#450×D4311yescharacteristic
638C2#1914385011yescharacteristic
639C2C2×#1458310211yescharacteristic
640C2#1914405611yescharacteristic
641C2#1914459811yescharacteristic
642C2#1914468911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#450C2
socleC23×C43C22×D4
prime radicalC23×D4×C43C22
hypercenterC2×#450D43
hypocenterC43#32905
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
2. C2×#14583102C2semidirect
4. #19142943C2semidirect
5. #19134931C2semidirect
6. #19134927C2semidirect
7. #19134903C2semidirect
8. #19134900C2semidirect
9. #19134593C2semidirect
10. #19134573C2semidirect
14. C2×#13063323C22semidirect
26. C2×Dic43⋊C8C22semidirect
27. C2×#13063250C22semidirect
28. C2×#13063249C22semidirect
31. #14582806C22semidirect
32. #14582804C22semidirect
35. #14582768C22semidirect
38. #14582662C22semidirect
39. #14582661C22semidirect
40. #14582653C22semidirect
166. C22×Dic43SD16semidirect
293. C22×C43#461semidirect
312. Dic43#450semidirect
368. C43#32905semidirect
614. C22#14583102semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic432
C2×#145831022
C2×#145830502
#191429432
#191349312
#191349272
#191349032
#191349002
#191345932
#191345732
C2×C43×#4502
#3290543