Finite Group Databasebeta

← #25128762

Subgroups — #25128762

Order 11008.

1494 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583553C211yesmaximal, characteristic
2C2×#14583038C211yesmaximal, characteristic, complemented
3C22×#13063249C211yesmaximal, characteristic, complemented
4#19135736C212yesmaximal, complemented
5#19135596C212yesmaximal, complemented
6#19135021C211yesmaximal, characteristic, complemented
7#19134932C212yesmaximal, complemented
8#19134903C212yesmaximal, complemented
9#19134888C211yesmaximal, characteristic, complemented
10#19134679C211yesmaximal, characteristic, complemented
11C43×#2409C211yesmaximal, characteristic, complemented
12C22×#10621900—21no—
13C22×#10621884C2212yes—
14C23×C43⋊C8C2211yescharacteristic
15#14583553—24no—
16#14583553—24no—
17C2×#13063325C2211yescharacteristic
18C2×#13063309—21no—
19C2×#13063309—21no—
20C2×#13063305—21no—
21C2×#13063299C2211yescharacteristic
22C2×#13063299C2211yescharacteristic
23C2×C4×D172C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C22×C4⋊Dic43C2211yescharacteristic
26#14583038—24no—
27C2×#13063249—24no—
28C2×#13063249C2212yes—
29C2×#13063249C2212yes—
30C2×#13063249C2212yes—
31C2×#13063245C2212yes—
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2212yes—
34#14582661C2212yes—
35#14582661C2212yes—
36#14582661C2212yes—
37#14582654C2212yes—
38C23×Q8×C43C2211yescharacteristic
39C2×C22⋊Q8×C43C2212yes—
40C2×C4×D4×C43C2211yescharacteristic
41C43×#395—21no—
42C43×#393—21no—
43C43×#391C2212yes—
44C43×#386—21no—
45C43×#385—21no—
46C43×#380C2211yescharacteristic
47C2×#10621900—28no—
48C2×#10621900—44no—
49C2×#10621900—44no—
50C22×Dic86—21no—
51C22×D172C2311yescharacteristic
52C22×C22⋊D43—21no—
53C22×C22⋊D43—21no—
54C23×Dic43—21no—
55C23×Dic43—21no—
56C22×C4×D43—21no—
57C2×#10621884—24no—
58C2×#10621884—24no—
59C2×#10621884—42no—
60C22×C43⋊C8—22no—
61C22×C43⋊C8—42no—
62C22×C43⋊C8C2312yes—
63C22×C43⋊C8C2312yes—
64#13063325—22no—
65#13063325—22no—
66#13063309—28no—
67#13063309—28no—
68#13063305—28no—
69#13063299—22no—
70#13063299—22no—
71#13063299—22no—
72#13063299D414yes—
73C4×D172—22no—
74C4×D172—22no—
75C2×C4⋊Dic43—22no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—22no—
80C2×C4⋊Dic43—22no—
81C2×C4⋊Dic43D414yes—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88#13063249—24no—
89#13063249—24no—
90#13063249—24no—
91#13063245—42no—
92C22⋊(C43⋊C8)—22no—
93C22⋊(C43⋊C8)—42no—
94C22×Q8×C43—21no—
95C22×Q8×C43—24no—
96C22×Q8×C43—22no—
97C22×Q8×C43—22no—
98C22×Q8×C43—42no—
99C22×Q8×C43C2312yes—
100C22×D4×C43D411yescharacteristic
101C23×C4×C43—21no—
102C23×C4×C43C2311yescharacteristic
103C23×C4×C43C2311yescharacteristic
104C22⋊Q8×C43—24no—
105C22⋊Q8×C43—42no—
106C4×D4×C43—22no—
107C4×D4×C43—22no—
108C2×C4⋊C4×C43—22no—
109C2×C4⋊C4×C43D411yescharacteristic
110C2×C4⋊C4×C43C2312yes—
111C2×C22⋊C4×C43—22no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43D411yescharacteristic
114C2×C22⋊C4×C43D411yescharacteristic
115C2×C42×C43C2311yescharacteristic
116#95×C43—21no—
117#95×C43—22no—
118#95×C43—22no—
119C24×C43C2×D411yescharacteristic
120C24×C43C2×D411yescharacteristic
121C23×D43—21no—
122C2×Q8×C43—22no—
123C2×Q8×C43—28no—
124C2×Q8×C43—22no—
125C2×Q8×C43—22no—
126C2×Q8×C43—22no—
127C2×Q8×C43—22no—
128C2×Q8×C43—44no—
129C2×Q8×C43—48no—
130C2×Q8×C43—44no—
131C2×Q8×C43—42no—
132C2×Q8×C43#4114yescomplemented
133C2×D4×C43—22no—
134C2×D4×C43—22no—
135C2×D4×C43SD1614yescomplemented
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—44no—
145C22×C4×C43—42no—
146C22×C4×C43C2×D412yes—
147C22×C4×C43C2×D412yes—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2411yescharacteristic
153C2×C22⋊D43—24no—
154C2×C22⋊D43—24no—
155C2×C22⋊D43—42no—
156C2×C22⋊D43—42no—
157C2×C22⋊D43—42no—
158C2×C22⋊D43—42no—
159C22×Dic43—24no—
160C22×Dic43—24no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—42no—
165C22×Dic43—42no—
166C22×Dic43—42no—
167C22×Dic43—42no—
168#10621900—432no—
169C2×D172—21no—
170C2×D172—22no—
171C2×D172—22no—
172C2×D172C2×D412yes—
173C2×C4×D43—24no—
174C2×C4×D43—42no—
175C2×C4×D43—42no—
176C2×Dic86—24no—
177C2×Dic86—42no—
178C2×Dic86—42no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—44no—
183C22⋊C4×C43—22no—
184C22⋊C4×C43—22no—
185C22⋊C4×C43—44no—
186C22⋊C4×C43—42no—
187C42×C43—21no—
188C42×C43—21no—
189#10621884—48no—
190(C2×D43)⋊C4—24no—
191(C2×D43)⋊C4—24no—
192(C2×D43)⋊C4—24no—
193C4⋊Dic43—24no—
194C4⋊Dic43—24no—
195C4⋊Dic43—24no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43C2×D412yes—
200C4⋊Dic43C2×D412yes—
201C4⋊Dic43C2×D412yes—
202C2×C43⋊C8—22no—
203C2×C43⋊C8—22no—
204C2×C43⋊C8—22no—
205C2×C43⋊C8—22no—
206C2×C43⋊C8—22no—
207C2×C43⋊C8—22no—
208C2×C43⋊C8—44no—
209C23×C43—22no—
210C23×C43—22no—
211C23×C43—21no—
212C23×C43—22no—
213C23×C43—21no—
214C23×C43—22no—
215C23×C43#12012yes—
216C23×C43C2×SD1612yes—
217C23×C43C2×SD1612yes—
218C23×C43AGL(1,ℤ/8)12yes—
219C23×C43C22×D411yescharacteristic
220C22×D43—22no—
221C22×D43—42no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—42no—
225Q8×C43—24no—
226Q8×C43—24no—
227Q8×C43—48no—
228Q8×C43—42no—
229Q8×C43—42no—
230D4×C43—28no—
231C2×C4×C43—21no—
232C2×C4×C43—22no—
233C2×C4×C43—21no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—24no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—24no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—48no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43#12012yes—
252C2×C4×C43C2×SD1612yes—
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C2×#4112yes—
256C2×C4×C43H(5,𝔽2)12yes—
257C22⋊D43—48no—
258C22⋊D43—48no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—48no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—48no—
270D172—24no—
271D172—41no—
272D172—41no—
273C4×D43—48no—
274Dic86—48no—
275C43⋊C8—42no—
276C43⋊C8—42no—
277#23961—431nomaximal, Sylow
278C22×C43—22no—
279C22×C43—22no—
280C22×C43—24no—
281C22×C43—24no—
282C22×C43—22no—
283C22×C43—24no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—42no—
287C22×C43#45014yes—
288C22×C43C2×#12011yescharacteristic
289C22×C43#54612yes—
290C22×C43C22×SD1611yescharacteristic
291C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
292C22×C43#57812yes—
293C2×D43—42no—
294C2×D43—42no—
295C2×D43—42no—
296C2×D43—82no—
297C2×D43—82no—
298C4×C43—22no—
299C4×C43—22no—
300C4×C43—41no—
301C4×C43—44no—
302C4×C43—41no—
303C4×C43—82no—
304C4×C43#52511yescharacteristic
305C4×C43#53511yescharacteristic
306C4×C43#54612yes—
307Dic43—42no—
308Dic43—42no—
309Dic43—42no—
310C2×#547—431no—
311C2×#448—431no—
312C22×#103—431no—
313#2409D4311yescharacteristic, complemented
314#2024—432no—
315#2000—432no—
316#1893—431no—
317#1877—432no—
318#1872—432no—
319#1869—431no—
320#1823—431no—
321C2×C43—24no—
322C2×C43—42no—
323C2×C43#240411yescharacteristic
324C2×C43C2×#45011yescharacteristic
325C2×C43#301111yescharacteristic
326C2×C43#329812yes—
327C2×C43#330812yes—
328D43—82no—
329C22×#41—861no—
330C23×Q8C2×D4311yescharacteristic
331C22×SD16—432no—
332C23×C8—431no—
333#547—864no—
334#547—864no—
335C2×C4⋊Q8—431no—
336C2×#123—861no—
337C2×#123—861no—
338C2×C22⋊Q8—861no—
339C2×C22⋊Q8C2×D4312yes—
340C2×#121—431no—
341C2×#121—431no—
342C2×C4×D4—431no—
343C2×C4×D4C2×D4311yescharacteristic
344C22×C4⋊C4—431no—
345C22×C4⋊C4—431no—
346#448—864no—
347C2×#103—432no—
348C2×#103—432no—
349C2×#103—432no—
350C2×#103—864no—
351C2×#102—432no—
352C2×C22⋊C8—431no—
353C2×C22⋊C8—432no—
354#395—21no—
355#393—21no—
356#391C2×D4312yes—
357#386—21no—
358#385—21no—
359#380C2×D4311yescharacteristic
360#340—432no—
361#340—432no—
362#340—432no—
363#336—432no—
364C43#2396111yescharacteristic, complemented, Sylow
365C2×#41—868no—
366C2×#41—1724no—
367C2×#41—1724no—
368C22×Q8—21no—
369C22×Q8—24no—
370C22×Q8—22no—
371C22×Q8—22no—
372C22×Q8—42no—
373C22×Q8—861no—
374C22×Q8C22×D4312yes—
375C22×D4—431no—
376C22×D4—861no—
377C22×D4—861no—
378C22×D4C22⋊D4311yescharacteristic
379C23×C4—21no—
380C23×C4—861no—
381C23×C4—861no—
382C23×C4—861no—
383C23×C4C22×D4311yescharacteristic
384C23×C4C22×D4311yescharacteristic
385C2×SD16—864no—
386C2×SD16—864no—
387C2×SD16—1722no—
388C22×C8—432no—
389C22×C8—432no—
390C22×C8—862no—
391C22×C8—1722no—
392C4⋊Q8—862no—
393C4⋊Q8—862no—
394#123—868no—
395#123—868no—
396C22⋊Q8—24no—
397C22⋊Q8—42no—
398C22⋊Q8—868no—
399#121—434no—
400#121—862no—
401#121—862no—
402#121—862no—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4—862no—
406C4×D4—862no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—434no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—862no—
413C2×C4⋊C4—862no—
414C2×C4⋊C4—862no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4C22⋊D4311yescharacteristic
419C2×C4⋊C4C22×D4312yes—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4C22⋊D4311yescharacteristic
426C2×C22⋊C4C22⋊D4311yescharacteristic
427C2×C42C22×D4311yescharacteristic
428#103—864no—
429#103—864no—
430#103—864no—
431#102—1722no—
432C22⋊C8—862no—
433C22⋊C8—1722no—
434#95—21no—
435#95—22no—
436#95—22no—
437C24—861no—
438C24C2×C22⋊D4311yescharacteristic
439C24C2×C22⋊D4311yescharacteristic
440#41—17232no—
441C2×Q8—22no—
442C2×Q8—28no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—44no—
448C2×Q8—48no—
449C2×Q8—44no—
450C2×Q8—42no—
451C2×Q8—864no—
452C2×Q8—1722no—
453C2×Q8—1722no—
454C2×Q8#1062190014yescomplemented
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—432no—
458C2×D4—864no—
459C2×D4—864no—
460C2×D4—861no—
461C2×D4—862no—
462C2×D4—862no—
463C2×D4—1722no—
464C2×D4—1722no—
465C2×D4—1722no—
466C2×D4—1722no—
467C2×D4#1062188414yescomplemented
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—44no—
477C22×C4—42no—
478C22×C4—864no—
479C22×C4—864no—
480C22×C4—864no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—1722no—
485C22×C4—1722no—
486C22×C4—1722no—
487C22×C4—1722no—
488C22×C4—1722no—
489C22×C4—1722no—
490C22×C4D4×D4312yes—
491C22×C4D4×D4312yes—
492C22×C4C2×C22⋊D4311yescharacteristic
493C22×C4C2×C22⋊D4311yescharacteristic
494C22×C4C2×C22⋊D4311yescharacteristic
495C22×C4C2×C22⋊D4311yescharacteristic
496C22×C4C23×D4311yescharacteristic
497SD16—1728no—
498C2×C8—862no—
499C2×C8—862no—
500C2×C8—862no—
501C2×C8—862no—
502C2×C8—862no—
503C2×C8—862no—
504C2×C8—1724no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—44no—
509C4⋊C4—432no—
510C4⋊C4—432no—
511C4⋊C4—432no—
512C4⋊C4—864no—
513C4⋊C4—864no—
514C4⋊C4—864no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—44no—
521C22⋊C4—42no—
522C22⋊C4—864no—
523C22⋊C4—864no—
524C22⋊C4—864no—
525C42—21no—
526C42—21no—
527C23—22no—
528C23—22no—
529C23—21no—
530C23—21no—
531C23—22no—
532C23—22no—
533C23—862no—
534C23—1721no—
535C23—1721no—
536C23—1722no—
537C23—1722no—
538C23#1306329312yes—
539C23C2×#1062188412yes—
540C23C2×#1062188412yes—
541C23#1306335012yes—
542C23C22×C22⋊D4311yescharacteristic
543Q8—24no—
544Q8—24no—
545Q8—48no—
546Q8—42no—
547Q8—42no—
548Q8—1728no—
549D4—28no—
550D4—864no—
551D4—1728no—
552D4—1728no—
553D4—1721no—
554D4—1721no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—48no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—1728no—
579C2×C4—1728no—
580C2×C4—1728no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4#1306329312yes—
588C2×C4C2×#1062188412yes—
589C2×C4C2×D4×D4311yescharacteristic
590C2×C4C2×D4×D4311yescharacteristic
591C2×C4C2×#1062190012yes—
592C2×C4#1306337012yes—
593C8—1722no—
594C8—1722no—
595C22—24no—
596C22—22no—
597C22—22no—
598C22—24no—
599C22—22no—
600C22—24no—
601C22—42no—
602C22—41no—
603C22—41no—
604C22—3442no—
605C22—3442no—
606C22—1722no—
607C22—1722no—
608C22—1722no—
609C22#1458304914yes—
610C22C2×#1306329311yescharacteristic
611C22#1458354312yes—
612C22C22×#1062188411yescharacteristic
613C22C2×#1306335011yescharacteristic
614C22#1458371412yes—
615C4—22no—
616C4—22no—
617C4—41no—
618C4—44no—
619C4—41no—
620C4—82no—
621C4—1722no—
622C4—1722no—
623C4—1722no—
624C4#1458340511yescharacteristic
625C4#1458346411yescharacteristic
626C4#1458353612yes—
627C2—24no—
628C2—42no—
629C2—3442no—
630C2#1913791111yescharacteristic
631C2C2×#1458304911yescharacteristic
632C2#1914388811yescharacteristic
633C2#1914646012yes—
634C2#1914658612yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2409C2
socleC23×C43C22×D4
prime radicalC2×#14583553C2
hypercenter#2409D43
hypocenterC43#23961
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2409

Complements

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

NH ≅ G/Ntype
2. C2×#14583038C2semidirect
3. C22×#13063249C2semidirect
4. #19135736C2semidirect
5. #19135596C2semidirect
6. #19135021C2semidirect
7. #19134932C2semidirect
8. #19134903C2semidirect
9. #19134888C2semidirect
10. #19134679C2semidirect
11. C43×#2409C2semidirect
132. C2×Q8×C43#41semidirect
135. C2×D4×C43SD16semidirect
313. #2409D43semidirect
364. C43#23961semidirect
454. C2×Q8#10621900semidirect
467. C2×D4#10621884semidirect

Maximal subgroups

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

subgroupindex
C2×#145835532
C2×#145830382
C22×#130632492
#191357362
#191355962
#191350212
#191349322
#191349032
#191348882
#191346792
C43×#24092
#2396143