Finite Group Databasebeta

← #25128756

Subgroups — #25128756

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×#14583549C211yesmaximal, characteristic
2C22×#13063249C211yesmaximal, characteristic, complemented
3#19137954C211yesmaximal, characteristic, complemented
4#19135734C212yesmaximal, complemented
5#19135595C212yesmaximal, complemented
6#19135024C211yesmaximal, characteristic, complemented
7#19134931C212yesmaximal, complemented
8#19134899C212yesmaximal, complemented
9#19134885C211yesmaximal, characteristic, complemented
10#19134682C211yesmaximal, characteristic, complemented
11C2×C43×#448C211yesmaximal, characteristic, complemented
12C22×#10621900—21no—
13C23×C43⋊C8C2211yescharacteristic
14#14583549—24no—
15#14583549—24no—
16C2×#13063324C2211yescharacteristic
17C2×#13063307—21no—
18C2×#13063306—21no—
19C2×#13063302—21no—
20C2×#13063301C2212yes—
21C2×#13063296C2211yescharacteristic
22C2×D4×Dic43C2211yescharacteristic
23C2×C4×C22⋊D43C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C2×C4⋊C4×D43C2211yescharacteristic
26C2×#13063249—24no—
27C2×#13063249C2212yes—
28C2×#13063249C2212yes—
29C2×#13063246C2212yes—
30C2×(C2×D43)⋊C8C2212yes—
31#14582818—21no—
32#14582810—21no—
33#14582806C2212yes—
34#14582778—21no—
35#14582772—21no—
36#14582759C2211yescharacteristic
37#14582662C2212yes—
38#14582662C2212yes—
39#14582661C2212yes—
40#14582653C2212yes—
41C23×Q8×C43C2211yescharacteristic
42C22×SD16×C43C2212yes—
43C2×#121×C43C2211yescharacteristic
44C43×#448—24no—
45C2×#103×C43C2212yes—
46C2×C22⋊C8×C43C2211yescharacteristic
47C2×#10621900—28no—
48C2×#10621900—44no—
49C2×#10621900—44no—
50C22×Dic86—21no—
51C22×C22⋊D43—21no—
52C22×C22⋊D43D411yescharacteristic
53C23×Dic43—21no—
54C23×Dic43—21no—
55C22×C4×D43—21no—
56C22×C4×D43C2311yescharacteristic
57C22×C43⋊C8—22no—
58C22×C43⋊C8—42no—
59C22×C43⋊C8C2312yes—
60#13063324—22no—
61#13063324—22no—
62#13063307—28no—
63#13063306—28no—
64#13063302—28no—
65#13063301—24no—
66#13063301—42no—
67#13063296—22no—
68#13063296—22no—
69D4×Dic43—22no—
70D4×Dic43—22no—
71C4×C22⋊D43—22no—
72C4×C22⋊D43—22no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—22no—
75C2×C4⋊Dic43D414yes—
76C2×C4⋊Dic43C2312yes—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—22no—
82C2×Dic43⋊C4D411yescharacteristic
83C4⋊C4×D43—22no—
84C4⋊C4×D43—22no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43D411yescharacteristic
89C2×(C2×D43)⋊C4—22no—
90C2×(C2×D43)⋊C4D411yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92#13063249—24no—
93#13063249—24no—
94#13063246—42no—
95(C2×D43)⋊C8—42no—
96C43⋊#95—21no—
97C43⋊#95—22no—
98C43⋊#95—22no—
99C22×Q8×C43—21no—
100C22×Q8×C43—24no—
101C22×Q8×C43—22no—
102C22×Q8×C43—22no—
103C22×Q8×C43—42no—
104C22×Q8×C43C2312yes—
105C22×D4×C43—21no—
106C22×D4×C43C2311yescharacteristic
107C23×C4×C43—21no—
108C23×C4×C43C2311yescharacteristic
109C2×SD16×C43—24no—
110C2×SD16×C43—24no—
111C2×SD16×C43—42no—
112C22×C8×C43C2312yes—
113#121×C43—22no—
114#121×C43D414yes—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117#103×C43—24no—
118C22⋊C8×C43—22no—
119C24×C43—21no—
120C24×C43C2×D411yescharacteristic
121C23×D43C2×D411yescharacteristic
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—21no—
134C2×D4×C43—24no—
135C2×D4×C43—22no—
136C2×D4×C43—22no—
137C2×D4×C43—42no—
138C2×D4×C43—42no—
139C2×D4×C43C2×D412yes—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—21no—
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×C43C2411yescharacteristic
150C2×C22⋊D43—24no—
151C2×C22⋊D43—22no—
152C2×C22⋊D43—22no—
153C2×C22⋊D43—42no—
154C2×C22⋊D43—42no—
155C2×C22⋊D43SD1614yescomplemented
156C22×Dic43—24no—
157C22×Dic43—24no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—22no—
161C22×Dic43—42no—
162C22×Dic43—42no—
163C22×Dic43—42no—
164C22×Dic43—42no—
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168#10621900—432no—
169C2×C4×D43—24no—
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—22no—
173C2×C4×D43—22no—
174C2×C4×D43—42no—
175C2×C4×D43—42no—
176C2×Dic86—24no—
177C2×Dic86—42no—
178C2×Dic86—42no—
179SD16×C43—48no—
180C2×C8×C43—22no—
181C2×C8×C43—22no—
182C2×C8×C43—22no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43C2×D412yes—
185C22⋊C4×C43—24no—
186C22⋊Dic43—24no—
187C22⋊Dic43—24no—
188C22⋊Dic43—22no—
189C22⋊Dic43—42no—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—44no—
192C4⋊Dic43—24no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—22no—
196C4⋊Dic43—22no—
197C4⋊Dic43C2×D412yes—
198C4⋊Dic43C2×D412yes—
199Dic43⋊C4—24no—
200Dic43⋊C4—24no—
201Dic43⋊C4—22no—
202Dic43⋊C4—44no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C2×C43⋊C8—22no—
206C2×C43⋊C8—22no—
207C2×C43⋊C8—22no—
208C2×C43⋊C8—44no—
209C23×C43—22no—
210C23×C43—22no—
211C23×C43—22no—
212C23×C43—42no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—42no—
216C23×C43#12012yes—
217C23×C43C2×SD1612yes—
218C23×C43AGL(1,ℤ/8)12yes—
219C23×C43C22×D411yescharacteristic
220C22×D43—21no—
221C22×D43—22no—
222C22×D43—21no—
223C22×D43—22no—
224C22×D43C2×SD1612yes—
225Q8×C43—24no—
226Q8×C43—24no—
227Q8×C43—48no—
228Q8×C43—42no—
229Q8×C43—42no—
230D4×C43—24no—
231D4×C43—48no—
232D4×C43—41no—
233D4×C43—41no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—24no—
238C2×C4×C43—22no—
239C2×C4×C43—24no—
240C2×C4×C43—48no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43#12012yes—
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C2×#4112yes—
249C2×C4×C43H(5,𝔽2)12yes—
250C22⋊D43—28no—
251C22⋊D43—48no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—48no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—48no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43C2×SD1612yes—
270C4×D43—48no—
271C4×D43—41no—
272C4×D43—41no—
273C4×D43—42no—
274Dic86—48no—
275C8×C43—42no—
276C43⋊C8—42no—
277#23961—431nomaximal, Sylow
278C22×C43—22no—
279C22×C43—22no—
280C22×C43—24no—
281C22×C43—24no—
282C22×C43—42no—
283C22×C43—42no—
284C22×C43—42no—
285C22×C43—82no—
286C22×C43—82no—
287C22×C43#45014yes—
288C22×C43C2×#12011yescharacteristic
289C22×C43#54612yes—
290C22×C43C22×SD1611yescharacteristic
291C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
292C22×C43#57812yes—
293C2×D43—22no—
294C2×D43—24no—
295C2×D43—41no—
296C2×D43—41no—
297C2×D43—42no—
298C4×C43—22no—
299C4×C43—44no—
300C4×C43—42no—
301C4×C43#52511yescharacteristic
302C4×C43#53511yescharacteristic
303C4×C43#54612yes—
304Dic43—22no—
305Dic43—41no—
306Dic43—42no—
307Dic43—42no—
308Dic43—41no—
309Dic43—82no—
310C2×#547—431no—
311C2×#448D4311yescharacteristic, complemented
312C22×#103—431no—
313#2409—431no—
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—82no—
323C2×C43#240411yescharacteristic
324C2×C43C2×#45011yescharacteristic
325C2×C43#301111yescharacteristic
326C2×C43#329812yes—
327C2×C43#330812yes—
328D43—42no—
329C22×#41—861no—
330C23×Q8C2×D4311yescharacteristic
331C22×SD16C2×D4312yes—
332C23×C8—431no—
333#547—864no—
334#547—864no—
335C2×C4⋊Q8—431no—
336C2×#123—861no—
337C2×#123—861no—
338C2×C22⋊Q8—432no—
339C2×C22⋊Q8—861no—
340C2×#121—431no—
341C2×#121C2×D4311yescharacteristic
342C2×C4×D4—431no—
343C2×C4×D4—431no—
344C22×C4⋊C4—431no—
345C22×C4⋊C4—431no—
346#448—24no—
347C2×#103—432no—
348C2×#103—432no—
349C2×#103—864no—
350C2×#103C2×D4312yes—
351C2×#102—432no—
352C2×C22⋊C8—432no—
353C2×C22⋊C8C2×D4311yescharacteristic
354#395—861no—
355#393—861no—
356#391—432no—
357#386—861no—
358#385—861no—
359#380—431no—
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—21no—
376C22×D4—431no—
377C22×D4—861no—
378C22×D4C22×D4311yescharacteristic
379C23×C4—21no—
380C23×C4—431no—
381C23×C4—861no—
382C23×C4—861no—
383C23×C4—861no—
384C23×C4C22×D4311yescharacteristic
385C2×SD16—24no—
386C2×SD16—24no—
387C2×SD16—42no—
388C22×C8—432no—
389C22×C8—862no—
390C22×C8—1722no—
391C22×C8C22×D4312yes—
392C4⋊Q8—862no—
393C4⋊Q8—862no—
394#123—868no—
395#123—868no—
396C22⋊Q8—868no—
397C22⋊Q8—864no—
398C22⋊Q8—1722no—
399#121—22no—
400#121—862no—
401#121—862no—
402#121C22⋊D4314yes—
403C4×D4—862no—
404C4×D4—862no—
405C4×D4—862no—
406C4×D4—862no—
407C2×C4⋊C4—434no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—432no—
412C2×C4⋊C4—862no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—862no—
417C2×C4⋊C4—862no—
418C2×C4⋊C4—862no—
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—431no—
422C2×C22⋊C4—431no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—862no—
426C2×C22⋊C4—861no—
427C2×C42—431no—
428#103—24no—
429#103—864no—
430#103—864no—
431#102—1722no—
432C22⋊C8—22no—
433C22⋊C8—1722no—
434#95—862no—
435#95—862no—
436#95—861no—
437C24—21no—
438C24—431no—
439C24D4×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—24no—
456C2×D4—21no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—42no—
460C2×D4—42no—
461C2×D4—434no—
462C2×D4—862no—
463C2×D4—862no—
464C2×D4—864no—
465C2×D4—1722no—
466C2×D4—1722no—
467C2×D4C2×C22⋊D4312yes—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—44no—
473C22×C4—42no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—864no—
478C22×C4—864no—
479C22×C4—864no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—1722no—
488C22×C4—1722no—
489C22×C4—1722no—
490C22×C4—1722no—
491C22×C4—1722no—
492C22×C4—1722no—
493C22×C4D4×D4311yescharacteristic
494C22×C4D4×D4312yes—
495C22×C4C2×C22⋊D4312yes—
496C22×C4C23×D4311yescharacteristic
497SD16—48no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—862no—
502C2×C8—862no—
503C2×C8—862no—
504C2×C8—1724no—
505C4⋊C4—21no—
506C4⋊C4—432no—
507C4⋊C4—432no—
508C4⋊C4—864no—
509C4⋊C4—864no—
510C4⋊C4—864no—
511C4⋊C4—862no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—862no—
515C4⋊C4—862no—
516C4⋊C4—1724no—
517C4⋊C4C2×C22⋊D4312yes—
518C22⋊C4—24no—
519C22⋊C4—864no—
520C22⋊C4—864no—
521C22⋊C4—862no—
522C22⋊C4—862no—
523C22⋊C4—1724no—
524C22⋊C4—1722no—
525C42—861no—
526C42—861no—
527C23—22no—
528C23—22no—
529C23—22no—
530C23—41no—
531C23—41no—
532C23—42no—
533C23—42no—
534C23—432no—
535C23—861no—
536C23—861no—
537C23—862no—
538C23—862no—
539C23#1306329312yes—
540C23SD16×D4312yes—
541C23#1306335212yes—
542C23C2×D4×D4311yescharacteristic
543Q8—24no—
544Q8—24no—
545Q8—48no—
546Q8—42no—
547Q8—42no—
548Q8—1728no—
549D4—24no—
550D4—48no—
551D4—41no—
552D4—41no—
553D4—868no—
554D4—1728no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—48no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—432no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—1728no—
576C2×C4—1728no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4—1728no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1722no—
588C2×C4#1306329312yes—
589C2×C4C2×D4×D4311yescharacteristic
590C2×C4C22×C22⋊D4311yescharacteristic
591C2×C4C2×#1062190012yes—
592C2×C4#1306337012yes—
593C8—42no—
594C8—1722no—
595C22—24no—
596C22—22no—
597C22—22no—
598C22—24no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—82no—
603C22—82no—
604C22—862no—
605C22—864no—
606C22—1722no—
607C22—1721no—
608C22—1721no—
609C22#1458304814yes—
610C22C2×#1306329311yescharacteristic
611C22#1458353612yes—
612C22C2×SD16×D4311yescharacteristic
613C22C2×#1306335211yescharacteristic
614C22#1458371512yes—
615C4—22no—
616C4—42no—
617C4—44no—
618C4—862no—
619C4—3442no—
620C4—1722no—
621C4—1722no—
622C4—1721no—
623C4—1721no—
624C4#1458340511yescharacteristic
625C4#1458346411yescharacteristic
626C4#1458354312yes—
627C2—24no—
628C2—82no—
629C2—1722no—
630C2#1913791111yescharacteristic
631C2C2×#1458304811yescharacteristic
632C2#1914388911yescharacteristic
633C2#1914645312yes—
634C2#1914659012yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#448C2
socleC23×C43C22×D4
prime radicalC2×#14583549C2
hypercenterC2×#448D43
hypocenterC43#23961
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
2. C22×#13063249C2semidirect
3. #19137954C2semidirect
4. #19135734C2semidirect
5. #19135595C2semidirect
6. #19135024C2semidirect
7. #19134931C2semidirect
8. #19134899C2semidirect
9. #19134885C2semidirect
10. #19134682C2semidirect
11. C2×C43×#448C2semidirect
132. C2×Q8×C43#41semidirect
155. C2×C22⋊D43SD16semidirect
311. C2×#448D43semidirect
364. C43#23961semidirect
454. C2×Q8#10621900semidirect

Maximal subgroups

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

subgroupindex
C2×#145835492
C22×#130632492
#191379542
#191357342
#191355952
#191350242
#191349312
#191348992
#191348852
#191346822
C2×C43×#4482
#2396143