Finite Group Databasebeta

← #25245442

Subgroups — #25245442

Order 11008.

1894 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic43C211yesmaximal, characteristic, complemented
2C2×#14583112C212yesmaximal, complemented
3C2×#14583050C211yesmaximal, characteristic, complemented
4#19142894C211yesmaximal, characteristic, complemented
5#19134945C212yesmaximal, complemented
6#19134927C212yesmaximal, complemented
7#19134913C211yesmaximal, characteristic, complemented
8#19134900C211yesmaximal, characteristic, complemented
9#19134603C212yesmaximal, complemented
10#19134573C211yesmaximal, characteristic, complemented
11C2×C43×#447C211yesmaximal, characteristic
12C24×Dic43—21no—
13C22×#10621883C2212yes—
14C2×#13063312C2211yescharacteristic, 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#14583112—28no—
25#14583050—24no—
26C2×Dic43⋊C8C2212yescomplemented
27C2×#13063250C2212yescomplemented
28C2×#13063246C2212yes—
29C2×#13063246C2212yescomplemented
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31#14582804C2211yescharacteristic, complemented
32#14582802C2211yescharacteristic, complemented
33#14582793—21no—
34#14582793—21no—
35#14582779—21no—
36#14582779—21no—
37#14582764C2211yescharacteristic, complemented
38#14582662C2212yescomplemented
39#14582661C2212yescomplemented
40#14582653C2212yescomplemented
41C23×D4×C43C2211yescharacteristic
42C22×D8×C43C2212yes—
43C2×#121×C43C2211yescharacteristic
44C43×#447—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#13063312—24no—
61#13063304—22no—
62#13063304—22no—
63D4×Dic43—28no—
64D4×Dic43—28no—
65D4×Dic43—24no—
66D4×Dic43—24no—
67D4×Dic43—24no—
68D4×Dic43D418yescomplemented
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—24no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2312yes—
73C2×Dic43⋊C4—21no—
74C2×C22⋊Dic43—28no—
75C2×C22⋊Dic43—22no—
76C2×C22⋊Dic43—22no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
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#13063246—24no—
90#13063246—24no—
91C22⋊(C43⋊C8)—22no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C25×C43—21no—
97C22×D4×C43—24no—
98C22×D4×C43—24no—
99C22×D4×C43—21no—
100C22×D4×C43—21no—
101C22×D4×C43—22no—
102C22×D4×C43D414yes—
103C22×D4×C43C2311yescharacteristic
104C22×D4×C43C2312yes—
105C23×C4×C43C2311yescharacteristic
106C2×D8×C43—24no—
107C2×D8×C43—24no—
108C2×D8×C43—24no—
109C22×C8×C43C2312yes—
110#121×C43—22no—
111#121×C43—22no—
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—21no—
121C24×C43—42no—
122C24×C43—42no—
123C24×C43—42no—
124C24×C43—42no—
125C24×C43C2×D411yescharacteristic
126C2×D4×C43—216no—
127C2×D4×C43—24no—
128C2×D4×C43—24no—
129C2×D4×C43—216no—
130C2×D4×C43—24no—
131C2×D4×C43—22no—
132C2×D4×C43—22no—
133C2×D4×C43—22no—
134C2×D4×C43—21no—
135C2×D4×C43—22no—
136C2×D4×C43—21no—
137C2×D4×C43—22no—
138C2×D4×C43—42no—
139C2×D4×C43—42no—
140C2×D4×C43—42no—
141C2×D4×C43C2×D414yes—
142C2×D4×C43C2×D414yes—
143C2×D4×C43#4114yes—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—21no—
147C22×C4×C43C2×D412yes—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43#4112yes—
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—24no—
154C22×Dic43—28no—
155C22×Dic43—22no—
156C22×Dic43—28no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—41no—
163C22×Dic43—42no—
164C22×Dic43—432no—
165C22×Dic43—44no—
166C22×Dic43—44no—
167C22×Dic43—44no—
168C22×Dic43—44no—
169C22×Dic43—42no—
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C2×Dic86—22no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—22no—
178D8×C43—48no—
179C2×C8×C43—22no—
180C2×C8×C43—22no—
181C2×C8×C43—22no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C22⋊C4×C43—42no—
185C22⋊Dic43—28no—
186C22⋊Dic43—28no—
187C22⋊Dic43—42no—
188C22⋊Dic43—42no—
189C22⋊Dic43—42no—
190C22⋊Dic43—42no—
191C22⋊Dic43—42no—
192#10621883—48no—
193C4⋊Dic43—24no—
194C4⋊Dic43—22no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43C2×D414yes—
198Dic43⋊C4—42no—
199C4×Dic43—22no—
200C4×Dic43—22no—
201C4×Dic43—22no—
202C4×Dic43C2×D414yes—
203C2×C43⋊C8—22no—
204C2×C43⋊C8—22no—
205C2×C43⋊C8—22no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—216no—
211C23×C43—24no—
212C23×C43—24no—
213C23×C43—24no—
214C23×C43—48no—
215C23×C43—48no—
216C23×C43—48no—
217C23×C43—48no—
218C23×C43—48no—
219C23×C43—42no—
220C23×C43—42no—
221C23×C43—42no—
222C23×C43—42no—
223C23×C43—48no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43#12112yes—
232C23×C43#13512yes—
233C23×C43AGL(1,ℤ/8)12yes—
234C23×C43C22×D411yescharacteristic
235D4×C43—216no—
236D4×C43—24no—
237D4×C43—24no—
238D4×C43—24no—
239D4×C43—42no—
240D4×C43—42no—
241D4×C43—84no—
242D4×C43#12118yes—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—24no—
246C2×C4×C43—24no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43#12112yes—
251C2×C4×C43C22×D412yes—
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C2×#4112yes—
254C2×C4×C43C2×#4111yescharacteristic
255C2×Dic43—28no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—24no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—44no—
267C2×Dic43—416no—
268C2×Dic43—416no—
269C2×Dic43—48no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43#12012yes—
279C2×Dic43#12012yes—
280C2×Dic43AGL(1,ℤ/8)12yes—
281Dic86—42no—
282Dic86—42no—
283C8×C43—42no—
284C43⋊C8—42no—
285#32908—431nomaximal, Sylow
286C22×C43—22no—
287C22×C43—22no—
288C22×C43—22no—
289C22×C43—22no—
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—28no—
293C22×C43—432no—
294C22×C43—44no—
295C22×C43—44no—
296C22×C43—44no—
297C22×C43—44no—
298C22×C43—44no—
299C22×C43—44no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43#46314yescomplemented
308C22×C43C2×#12011yescharacteristic
309C22×C43C2×#12111yescharacteristic
310C22×C43#52511yescharacteristic
311C22×C43C2×#13511yescharacteristic
312C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C43#57511yescharacteristic
315C4×C43—22no—
316C4×C43—81no—
317C4×C43C2×#12112yes—
318C4×C43#52512yes—
319Dic43—22no—
320Dic43—22no—
321Dic43—22no—
322Dic43—41no—
323Dic43—44no—
324Dic43—81no—
325Dic43—81no—
326C22×C4×D4—431no—
327C2×#463—432no—
328C2×#450—431no—
329C2×#447D4311yescharacteristic
330#2850—431no—
331#1879—432no—
332#1877—432no—
333#1874—431no—
334#1872—431no—
335#1804—432no—
336#1797—431no—
337C2×C43—24no—
338C2×C43—48no—
339C2×C43—161no—
340C2×C43#284711yescharacteristic
341C2×C43#300211yescharacteristic
342C2×C43#300311yescharacteristic
343C2×C43C2×#46311yescharacteristic
344C2×C43#303611yescharacteristic
345C2×C43#310511yescharacteristic
346C2×C43#311411yescharacteristic
347C23×D4C2×D4311yescharacteristic
348C24×C4—861no—
349C22×SD16—432no—
350C22×D8C2×D4312yes—
351C2×#124—431no—
352C2×C22⋊Q8—431no—
353C2×#121C2×D4311yescharacteristic
354C2×C4×D4—432no—
355C2×C4×D4—432no—
356C2×C4×D4—861no—
357C2×C4×D4—861no—
358C2×C4×D4—868no—
359C22×C4⋊C4—431no—
360C22×C22⋊C4—861no—
361C22×C42—431no—
362#463—868no—
363#450—864no—
364#447—24no—
365C2×C4⋊C8—432no—
366C2×#103—432no—
367C2×#102—432no—
368C2×#102—432no—
369C2×#102C2×D4312yes—
370C2×C22⋊C8—431no—
371C2×C22⋊C8C2×D4311yescharacteristic
372#391—431no—
373#390—431no—
374#388—861no—
375#388—861no—
376#386—861no—
377#386—861no—
378#382—431no—
379#340—432no—
380#340—432no—
381#336—432no—
382C43#3290811yescharacteristic, complemented, Sylow
383C25—21no—
384C22×Q8—431no—
385C22×D4—24no—
386C22×D4—24no—
387C22×D4—21no—
388C22×D4—21no—
389C22×D4—22no—
390C22×D4C22⋊D4314yes—
391C22×D4C22×D4311yescharacteristic
392C22×D4C22×D4312yes—
393C23×C4—431no—
394C23×C4—431no—
395C23×C4—862no—
396C23×C4—862no—
397C23×C4—868no—
398C23×C4—861no—
399C23×C4—1724no—
400C23×C4—1724no—
401C23×C4C22×D4311yescharacteristic
402C2×SD16—864no—
403C2×SD16—864no—
404C2×SD16—864no—
405C2×D8—24no—
406C2×D8—24no—
407C2×D8—24no—
408C22×C8—432no—
409C22×C8C22×D4312yes—
410#124—864no—
411C22⋊Q8—862no—
412C22⋊Q8—862no—
413#121—22no—
414#121—22no—
415C4×D4—438no—
416C4×D4—864no—
417C4×D4—864no—
418C4×D4—868no—
419C4×D4—868no—
420C4×D4—864no—
421C2×C4⋊C4—432no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—864no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—862no—
429C2×C22⋊C4—862no—
430C2×C22⋊C4—868no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—864no—
441C4⋊C8—864no—
442#103—864no—
443#102—24no—
444#102—864no—
445#102—864no—
446C22⋊C8—22no—
447C22⋊C8—862no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452C24—24no—
453C24—24no—
454C24—24no—
455C24—22no—
456C24—21no—
457C24—42no—
458C24—42no—
459C24—42no—
460C24—42no—
461C24D4×D4311yescharacteristic
462C2×Q8—862no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—862no—
466C2×D4—24no—
467C2×D4—24no—
468C2×D4—216no—
469C2×D4—216no—
470C2×D4—24no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—21no—
477C2×D4—22no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4D4×D4314yes—
482C2×D4#1062190014yes—
483C2×D4C2×C22⋊D4314yes—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—868no—
495C22×C4—862no—
496C22×C4—864no—
497C22×C4—868no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—1724no—
503C22×C4—1721no—
504C22×C4—17232no—
505C22×C4—1724no—
506C22×C4—1724no—
507C22×C4—1724no—
508C22×C4—1722no—
509C22×C4—1722no—
510C22×C4D4×D4311yescharacteristic
511C22×C4#1062190012yes—
512C22×C4C2×C22⋊D4312yes—
513C22×C4C23×D4311yescharacteristic
514SD16—1728no—
515D8—48no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—862no—
520C2×C8—862no—
521C2×C8—862no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—434no—
525C4⋊C4—864no—
526C4⋊C4—862no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—1722no—
530C22⋊C4—42no—
531C22⋊C4—868no—
532C22⋊C4—868no—
533C22⋊C4—1722no—
534C22⋊C4—1722no—
535C22⋊C4—1722no—
536C22⋊C4—1722no—
537C22⋊C4—1722no—
538C42—434no—
539C42—862no—
540C42—862no—
541C42—862no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—216no—
547C23—24no—
548C23—24no—
549C23—24no—
550C23—48no—
551C23—48no—
552C23—48no—
553C23—48no—
554C23—48no—
555C23—48no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23#1306329712yes—
568C23#1306334412yes—
569C23#1306334912yes—
570C23C2×D4×D4311yescharacteristic
571Q8—1722no—
572Q8—1722no—
573D4—216no—
574D4—24no—
575D4—24no—
576D4—24no—
577D4—42no—
578D4—42no—
579D4—84no—
580D4#1306329718yes—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—432no—
589C2×C4—432no—
590C2×C4—432no—
591C2×C4—868no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—864no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—1724no—
603C2×C4—17216no—
604C2×C4—17216no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1728no—
612C2×C4—1722no—
613C2×C4—1722no—
614C2×C4#1306329712yes—
615C2×C4C2×D4×D4312yes—
616C2×C4C22×C22⋊D4311yescharacteristic
617C2×C4C2×#1062190012yes—
618C2×C4C2×#1062190011yescharacteristic
619C8—42no—
620C8—1722no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—22no—
627C22—28no—
628C22—432no—
629C22—44no—
630C22—44no—
631C22—44no—
632C22—44no—
633C22—44no—
634C22—44no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22#1458311214yescomplemented
643C22#120×D4311yescharacteristic
644C22C2×#1306329711yescharacteristic
645C22#1458340511yescharacteristic
646C22C2×#1306334411yescharacteristic
647C22AGL(1,ℤ/8)×D4311yescharacteristic
648C22C2×#1306334911yescharacteristic
649C22#1458369511yescharacteristic
650C4—22no—
651C4—81no—
652C4—862no—
653C4—862no—
654C4—862no—
655C4—3441no—
656C4—3441no—
657C4—1721no—
658C4—1724no—
659C4C2×#1306329712yes—
660C4#1458340512yes—
661C2—24no—
662C2—48no—
663C2—161no—
664C2#1914287511yescharacteristic
665C2#1914380811yescharacteristic
666C2#1914381911yescharacteristic
667C2C2×#1458311211yescharacteristic
668C2#1914405611yescharacteristic
669C2#1914463711yescharacteristic
670C2#1914472811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#447C2
socleC23×C43C22×D4
hypercenterC2×#447D43
hypocenterC43#32908
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic43C2semidirect
2. C2×#14583112C2semidirect
3. C2×#14583050C2semidirect
4. #19142894C2semidirect
5. #19134945C2semidirect
6. #19134927C2semidirect
7. #19134913C2semidirect
8. #19134900C2semidirect
9. #19134603C2semidirect
10. #19134573C2semidirect
14. C2×#13063312C22semidirect
26. C2×Dic43⋊C8C22semidirect
27. C2×#13063250C22semidirect
29. C2×#13063246C22semidirect
31. #14582804C22semidirect
32. #14582802C22semidirect
37. #14582764C22semidirect
38. #14582662C22semidirect
39. #14582661C22semidirect
40. #14582653C22semidirect
68. D4×Dic43D4semidirect
307. C22×C43#463semidirect
382. C43#32908semidirect
642. C22#14583112semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic432
C2×#145831122
C2×#145830502
#191428942
#191349452
#191349272
#191349132
#191349002
#191346032
#191345732
C2×C43×#4472
#3290843