Finite Group Databasebeta

← #25098290

Subgroups — #25098290

Order 11008.

1914 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D43C211yesmaximal, characteristic, complemented
2C2×#14583409C211yesmaximal, characteristic
3C2×#14582892C212yesmaximal, complemented
4#19136977C211yesmaximal, characteristic, complemented
5#19135034C211yesmaximal, characteristic, complemented
6#19135030C212yesmaximal, complemented
7#19135028C211yesmaximal, characteristic, complemented
8#19135027C212yesmaximal, complemented
9#19135026C211yesmaximal, characteristic, complemented
10#19134310C212yesmaximal, complemented
11C43×#1895C211yesmaximal, characteristic, complemented
12C22×#10621900C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C22×#10621877C2211yescharacteristic
15C22×#10621872C2212yes—
16C2×M16×D43—24no—
17C2×M16×D43—28no—
18C22×C8×D43C2212yes—
19#14583409—24no—
20#14583409C418yescomplemented
21C2×#13063307—21no—
22C2×#13063305C2211yescharacteristic
23C2×#13063304C2211yescharacteristic
24C2×#13063296C2211yescharacteristic
25C2×#13063293—21no—
26C2×D4×Dic43—21no—
27C2×(C22⋊D43)⋊C4—21no—
28C2×#13063283C2212yes—
29C2×#13063283C2211yescharacteristic
30#14582892—28no—
31C2×#13063250C2212yescomplemented
32C2×#13063248C2212yescomplemented
33C2×#13063246C2212yescomplemented
34#14582761—21no—
35#14582759C2211yescharacteristic
36#14582756C2212yes—
37#14582754—21no—
38C22⋊C4×Dic43—21no—
39#14582746—21no—
40#14582662C2212yescomplemented
41#14582661C2212yescomplemented
42#14582661C2212yescomplemented
43C22×M16×C43C2211yescharacteristic
44C2×#121×C43C2211yescharacteristic
45C2×#102×C43C2212yescomplemented
46C43×#380C2211yescharacteristic
47C43×#340C2212yescomplemented
48C24×D43D411yescharacteristic
49C2×#10621900—24no—
50C2×#10621900—22no—
51C2×#10621900—24no—
52C2×#10621900C2×C414yes—
53C22×Dic86C2311yescharacteristic
54C22×C22⋊D43—21no—
55C22×C22⋊D43—21no—
56C23×Dic43—21no—
57C23×Dic43D411yescharacteristic
58C22×C4×D43—24no—
59C22×C4×D43—24no—
60C22×C4×D43C2×C414yes—
61C22×C4×D43D411yescharacteristic
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D414yes—
64C22×C4×D43C2311yescharacteristic
65C22×C4×D43C2311yescharacteristic
66C2×#10621877—22no—
67C2×#10621877—24no—
68C2×#10621872—24no—
69C2×#10621872—24no—
70C2×#10621872—24no—
71M16×D43—232no—
72C22×C43⋊C8C2312yes—
73C2×C8×D43—24no—
74C2×C8×D43—24no—
75C2×C8×D43D418yescomplemented
76#13063307—28no—
77#13063305—22no—
78#13063305C2×C414yes—
79#13063304—22no—
80#13063304C2×C414yes—
81#13063296—22no—
82#13063296C2×C414yes—
83#13063293—28no—
84D4×Dic43—28no—
85(C22⋊D43)⋊C4—28no—
86#13063283—22no—
87#13063283—24no—
88#13063283—24no—
89#13063283C2×C414yes—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43C2312yes—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—22no—
100C2×(C2×D43)⋊C4—22no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—22no—
103#13063250—24no—
104#13063248—24no—
105#13063246—24no—
106C43⋊#95—21no—
107C43⋊#95—22no—
108C22×D4×C43—21no—
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43C2311yescharacteristic
111C2×M16×C43—22no—
112C2×M16×C43—24no—
113C22×C8×C43C2312yes—
114#121×C43—22no—
115#121×C43C2×C414yes—
116C2×C4⋊C4×C43C2312yes—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120#102×C43—24no—
121#95×C43—21no—
122C24×C43—21no—
123C24×C43C2×D411yescharacteristic
124C23×D43—24no—
125C23×D43—42no—
126C23×D43—41no—
127C23×D43—41no—
128C23×D43C22⋊C414yes—
129C23×D43C2×D411yescharacteristic
130C23×D43C2×D411yescharacteristic
131C2×D4×C43—21no—
132C2×D4×C43—24no—
133C2×D4×C43—22no—
134C2×D4×C43—22no—
135C2×D4×C43—44no—
136C2×D4×C43C22×C412yes—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—21no—
140C22×C4×C43—22no—
141C22×C4×C43C22×C412yes—
142C22×C4×C43C2×D412yes—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C2×C22⋊D43—24no—
146C2×C22⋊D43—24no—
147C2×C22⋊D43—42no—
148C2×C22⋊D43—42no—
149C2×C22⋊D43—44no—
150C22×Dic43—24no—
151C22×Dic43—24no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—22no—
155C22×Dic43—44no—
156C22×Dic43C22⋊C414yes—
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159#10621900—216no—
160#10621900—44no—
161#10621900—44no—
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—24no—
165C2×C4×D43—216no—
166C2×C4×D43—28no—
167C2×C4×D43—28no—
168C2×C4×D43—24no—
169C2×C4×D43C22⋊C414yes—
170C2×C4×D43C22⋊C414yes—
171C2×C4×D43C22×C412yes—
172C2×C4×D43C22×C412yes—
173C2×C4×D43C2×D412yes—
174C2×C4×D43C2×D412yes—
175C2×C4×D43C2×D414yes—
176C2×C4×D43#4114yes—
177C2×Dic86—22no—
178C2×Dic86—22no—
179C2×Dic86—21no—
180C2×Dic86C22×C412yes—
181M16×C43—28no—
182C2×C8×C43—22no—
183C2×C8×C43—22no—
184C2×C8×C43C2×D414yes—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—22no—
187C4⋊C4×C43—22no—
188C4⋊C4×C43C22×C412yes—
189C22⋊C4×C43—24no—
190C22⋊C4×C43—42no—
191C22⋊Dic43—24no—
192C22⋊Dic43—24no—
193C22⋊Dic43—42no—
194(C2×D43)⋊C4—24no—
195(C2×D43)⋊C4—24no—
196(C2×D43)⋊C4—44no—
197(C2×D43)⋊C4—44no—
198C4⋊Dic43—21no—
199C4⋊Dic43—24no—
200C4⋊Dic43—22no—
201C4⋊Dic43—22no—
202C4⋊Dic43C22×C412yes—
203Dic43⋊C4—24no—
204C4×Dic43—24no—
205C4×Dic43—44no—
206#10621877—28no—
207C2×C43⋊C8—22no—
208C2×C43⋊C8—22no—
209C2×C43⋊C8C2×D414yes—
210#10621872—216no—
211C8×D43—216no—
212C23×C43—22no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—22no—
216C23×C43—22no—
217C23×C43—42no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—42no—
221C23×C43C2×C22⋊C412yes—
222C23×C43C22×D411yescharacteristic
223C22×D43—22no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—22no—
227C22×D43—22no—
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—28no—
231C22×D43—44no—
232C22×D43—44no—
233C22×D43—48no—
234C22×D43—48no—
235C22×D43C2×C22⋊C412yes—
236C22×D43C2×C22⋊C412yes—
237C22×D43#12114yes—
238D4×C43—24no—
239D4×C43—48no—
240D4×C43—41no—
241D4×C43—41no—
242C2×C4×C43—22no—
243C2×C4×C43—24no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43C2×C22⋊C412yes—
252C2×C4×C43C23×C411yescharacteristic
253C2×C4×C43C22×D412yes—
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C2×#4112yes—
256C22⋊D43—48no—
257C22⋊D43—48no—
258C2×Dic43—22no—
259C2×Dic43—28no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—42no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—48no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43C2×C22⋊C412yes—
270C2×Dic43C2×C22⋊C412yes—
271C2×Dic43#12114yes—
272C4×D43—28no—
273C4×D43—24no—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—28no—
277C4×D43C4×D418yes—
278C4×D43#12014yes—
279C4×D43#12314yes—
280Dic86—24no—
281Dic86—41no—
282Dic86—41no—
283C8×C43—24no—
284C43⋊C8—24no—
285#20970—431nomaximal, Sylow
286C22×C43—22no—
287C22×C43—22no—
288C22×C43—22no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—82no—
295C22×C43—82no—
296C22×C43C22×C22⋊C411yescharacteristic
297C22×C43C2×#12112yes—
298C22×C43#57512yes—
299C22×C43#57511yescharacteristic
300C22×C43#57511yescharacteristic
301C2×D43—22no—
302C2×D43—22no—
303C2×D43—24no—
304C2×D43—24no—
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—22no—
308C2×D43—416no—
309C2×D43—42no—
310C2×D43—42no—
311C2×D43#38614yes—
312C4×C43—22no—
313C4×C43—42no—
314C4×C43—82no—
315C4×C43C2×C4×D412yes—
316C4×C43C2×#12011yescharacteristic
317C4×C43C2×#12311yescharacteristic
318Dic43—22no—
319Dic43—42no—
320Dic43—42no—
321Dic43—82no—
322Dic43#38614yes—
323C23×M16—431no—
324C2×#525—431no—
325C2×#416—432no—
326#2280—431no—
327#1895—432no—
328#1895—431no—
329#1895D4311yescharacteristic, complemented
330#1894—431no—
331#1894—432no—
332#1894—431no—
333#1735—432no—
334C2×C43—42no—
335C2×C43—82no—
336C2×C43C2×#38611yescharacteristic
337C2×C43#289611yescharacteristic
338C2×C43#289611yescharacteristic
339C2×C43#305412yes—
340C2×C43#305412yes—
341D43—24no—
342D43—42no—
343C22×#41—431no—
344C24×C4—431no—
345C22×M16—431no—
346C22×M16—432no—
347C22×M16—868no—
348C22×M16—864no—
349C22×M16C2×D4311yescharacteristic
350C23×C8—432no—
351#525—438no—
352#525—864no—
353C2×#123—861no—
354C2×C22⋊Q8—431no—
355C2×C22⋊Q8—431no—
356C2×#121—431no—
357C2×#121C2×D4311yescharacteristic
358C2×#120—861no—
359C2×C4×D4—861no—
360C2×C4×D4—861no—
361C2×#117—431no—
362C2×#117—432no—
363#416—868no—
364C2×#103—432no—
365C2×#103—432no—
366C2×#102—432no—
367C2×#102C2×D4312yescomplemented
368#381—861no—
369#380—431no—
370#380—432no—
371#380C2×D4311yescharacteristic
372#379—861no—
373C4×C22⋊C4—861no—
374C4×C22⋊C4—861no—
375#340—432no—
376#340—432no—
377#340—432no—
378#340C2×D4312yescomplemented
379C43#2097011yescharacteristic, complemented, Sylow
380C25—431no—
381C2×#41—434no—
382C2×#41—862no—
383C2×#41—864no—
384C2×#41—864no—
385C22×Q8—431no—
386C22×D4—21no—
387C22×D4—861no—
388C22×D4—861no—
389C22×D4C22×D4311yescharacteristic
390C23×C4—431no—
391C23×C4—431no—
392C23×C4—434no—
393C23×C4—431no—
394C23×C4—431no—
395C23×C4—434no—
396C23×C4—431no—
397C23×C4—864no—
398C23×C4—864no—
399C23×C4—861no—
400C23×C4C22×D4311yescharacteristic
401C2×M16—22no—
402C2×M16—24no—
403C2×M16—864no—
404C2×M16—864no—
405C2×M16—864no—
406C2×M16—8632no—
407C2×M16—862no—
408C2×M16—864no—
409C22×C8—432no—
410C22×C8—438no—
411C22×C8—864no—
412C22×C8—864no—
413C22×C8C22×D4312yes—
414#123—868no—
415C22⋊Q8—434no—
416C22⋊Q8—434no—
417C22⋊Q8—862no—
418C22⋊Q8—862no—
419#121—22no—
420#121—434no—
421#121—862no—
422#121C4×D4314yes—
423#120—868no—
424C4×D4—868no—
425C4×D4—868no—
426#117—434no—
427#117—862no—
428#117—864no—
429#117—864no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—432no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4C22×D4312yes—
435C2×C4⋊C4C22×D4311yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—862no—
443C2×C22⋊C4—862no—
444C2×C22⋊C4—861no—
445C2×C42—861no—
446C2×C42—862no—
447#103—864no—
448#103—864no—
449#102—24no—
450#102—864no—
451#95—21no—
452#95—862no—
453#95—861no—
454C24—21no—
455C24—431no—
456C24—431no—
457C24—434no—
458C24—864no—
459C24—1721no—
460C24—1722no—
461C24—1721no—
462C24D4×D4311yescharacteristic
463#41—8616no—
464#41—1724no—
465#41—1724no—
466C2×Q8—432no—
467C2×Q8—861no—
468C2×Q8—862no—
469C2×Q8—862no—
470C2×D4—24no—
471C2×D4—22no—
472C2×D4—21no—
473C2×D4—22no—
474C2×D4—44no—
475C2×D4—864no—
476C2×D4—864no—
477C2×D4—1724no—
478C2×D4—1722no—
479C2×D4—1722no—
480C2×D4C2×C4×D4312yes—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—431no—
486C22×C4—432no—
487C22×C4—434no—
488C22×C4—432no—
489C22×C4—434no—
490C22×C4—434no—
491C22×C4—431no—
492C22×C4—434no—
493C22×C4—434no—
494C22×C4—432no—
495C22×C4—432no—
496C22×C4—868no—
497C22×C4—864no—
498C22×C4—8616no—
499C22×C4—868no—
500C22×C4—864no—
501C22×C4—864no—
502C22×C4—864no—
503C22×C4—862no—
504C22×C4—862no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—862no—
508C22×C4—1724no—
509C22×C4C2×C4×D4312yes—
510C22×C4D4×D4311yescharacteristic
511C22×C4D4×D4312yes—
512C22×C4C23×D4311yescharacteristic
513M16—28no—
514M16—8616no—
515M16—868no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—434no—
519C2×C8—8616no—
520C2×C8—862no—
521C2×C8—862no—
522C2×C8D4×D4314yes—
523C4⋊C4—21no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—432no—
527C4⋊C4—864no—
528C4⋊C4—864no—
529C4⋊C4—861no—
530C4⋊C4—862no—
531C4⋊C4—862no—
532C4⋊C4C2×C4×D4312yes—
533C22⋊C4—24no—
534C22⋊C4—42no—
535C22⋊C4—864no—
536C22⋊C4—864no—
537C22⋊C4—864no—
538C22⋊C4—864no—
539C22⋊C4—1724no—
540C22⋊C4—1724no—
541C22⋊C4—1722no—
542C42—864no—
543C42—1724no—
544C23—22no—
545C23—21no—
546C23—22no—
547C23—21no—
548C23—22no—
549C23—42no—
550C23—42no—
551C23—41no—
552C23—41no—
553C23—432no—
554C23—434no—
555C23—432no—
556C23—868no—
557C23—862no—
558C23—861no—
559C23—861no—
560C23—862no—
561C23—862no—
562C23—861no—
563C23—861no—
564C23—1724no—
565C23—1724no—
566C23—1728no—
567C23—1728no—
568C23C22⋊C4×D4312yes—
569C23C2×D4×D4311yescharacteristic
570Q8—864no—
571Q8—1721no—
572Q8—1721no—
573D4—24no—
574D4—48no—
575D4—41no—
576D4—41no—
577D4—1728no—
578D4—1728no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—432no—
589C2×C4—434no—
590C2×C4—438no—
591C2×C4—434no—
592C2×C4—434no—
593C2×C4—432no—
594C2×C4—868no—
595C2×C4—868no—
596C2×C4—868no—
597C2×C4—862no—
598C2×C4—864no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—1728no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4—1722no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4C22⋊C4×D4312yes—
611C2×C4C22×C4×D4311yescharacteristic
612C2×C4C2×D4×D4312yes—
613C2×C4C2×D4×D4311yescharacteristic
614C2×C4#41×D4312yes—
615C8—24no—
616C8—864no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—82no—
626C22—82no—
627C22—434no—
628C22—864no—
629C22—864no—
630C22—862no—
631C22—862no—
632C22—862no—
633C22—862no—
634C22—862no—
635C22—17216no—
636C22—1722no—
637C22—1722no—
638C22C2×C22⋊C4×D4311yescharacteristic
639C22#121×D4312yes—
640C22#1458369512yes—
641C22#1458369511yescharacteristic
642C22#1458369811yescharacteristic
643C4—22no—
644C4—42no—
645C4—82no—
646C4—434no—
647C4—862no—
648C4—3442no—
649C4—1722no—
650C4—1722no—
651C4C4×D4×D4312yes—
652C4#120×D4311yescharacteristic
653C4#123×D4311yescharacteristic
654C2—42no—
655C2—82no—
656C2—864no—
657C2—1722no—
658C2#386×D4311yescharacteristic
659C2#1914310911yescharacteristic
660C2#1914311111yescharacteristic
661C2#1914419912yes—
662C2#1914420212yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1895C2
socleC23×C43C22×D4
prime radicalC2×#14583409C2
cosocleC22×C4×C43C24
hypercenter#1895D43
hypocenterC43#20970
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
1. C22×M16×D43C2semidirect
3. C2×#14582892C2semidirect
4. #19136977C2semidirect
5. #19135034C2semidirect
6. #19135030C2semidirect
7. #19135028C2semidirect
8. #19135027C2semidirect
9. #19135026C2semidirect
10. #19134310C2semidirect
11. C43×#1895C2semidirect
20. #14583409C4semidirect
31. C2×#13063250C22semidirect
32. C2×#13063248C22semidirect
33. C2×#13063246C22semidirect
40. #14582662C22semidirect
41. #14582661C22semidirect
42. #14582661C22semidirect
45. C2×#102×C43C22semidirect
47. C43×#340C22semidirect
75. C2×C8×D43D4semidirect
329. #1895D43semidirect
367. C2×#102C2×D43semidirect
378. #340C2×D43semidirect
379. C43#20970semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D432
C2×#145834092
C2×#145828922
#191369772
#191350342
#191350302
#191350282
#191350272
#191350262
#191343102
C43×#18952
#2097043